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Washington, DC - Below are the prepared remarks of Congressman Pete Visclosky from today’s International Trade Commission (ITC) hearing on heavy walled rectangular welded carbon steel pipe and tube products.
I want to thank Chairman Broadbent, Vice Chairman Pinkert, all other members of the Commission, and the dedicated staff for the opportunity to testify today in the case involving heavy walled rectangular welded carbon steel pipes and tubes from Korea, Mexico, and Turkey.
American steel is the backbone of our infrastructure. We construct bridges, skyscrapers, and transportation systems with steel produced by hardworking American steelworkers and steel companies. The product we are discussing today, heavy walled rectangular pipes and tubes, are used to construct building frames, support columns, and protective barriers. They are used to build truck beds, trailers, and agricultural implements. We cannot continue to allow illegal imports of products that are the foundation of the economy and transportation infrastructure of our communities. American steelworkers and steel companies make the best steel in the world, more efficiently than anyone else. We should be using that steel in our infrastructure and transportations systems. We should be using that steel to build our nation.
While the entire steel industry is facing a constant onslaught of illegal imports, the pipe and tube market has been hit particularly hard. In 2015, imports captured 65 percent of the pipe and tube market share, an 11 percent increase from 2014, while domestic shipments decreased by 38 percent. This is absolutely unacceptable. I appreciate that the ITC has previously ruled in favor of the domestic pipe and tube industry, with 42 existing antidumping and countervailing duty orders on steel pipe, tube, and fittings products currently in place, but it is clear that more must be done to ensure that this dangerous trend does not continue.
I also would point out that the countries cited in this case are exporting more pipe and tube products into the American market than almost all of our other foreign competitors. For example, this past June, the U.S. imported 316,882 metric tons of pipe and tube products. Of those imports, 69,285 metric tons came from Korea, 22,008 metric tons came from Turkey, and 53,057 metric tons came from Mexico. This Commission has consistently issued antidumping and countervailing duty orders against these countries for pipe and tube products. In total, Korea, Turkey, and Mexico each have roughly half a dozen standing countervailing and antidumping orders for pipe and tube products, including standing orders for light walled rectangular pipe and tube. It is evident that the countries we are discussing today are repeat offenders who have demonstrated that they have no regard for our trade laws. They have shown that they will continually dump steel into our markets and threaten American steelworkers. We must put a stop to their actions.
I urge the Commission to recognize the material injury caused by these imports and to fully enforce out trade laws in an expedient and effective manner. Our foreign competitors in the pipe and tube industry have demonstrated time and time again that they are unwilling to adhere to our trade laws. American steelworkers and steel companies deserve a fair playing field.
I thank you all for the opportunity to testify here today and appreciate your thorough investigation of the facts of this case.
Source:
New antidumping and countervailing duty petitions on heavy-walled rectangular welded steel pipe
Date: 2015-07-26 Views: 750 Time Label: heavy-walled rectangular pipe, welded carbon steel pipe
New antidumping (AD) petitions were filed regarding heavy-walled rectangular welded carbon steel pipes and tubes from Korea, Mexico, and Turkey, and a countervailing duty (CVD) petition was filed with respect to the same product from Turkey. The petitioners are: Atlas Tube (a division of JMC Steel Group); Bull Moose Tube Company; EXLTUBE (but not a petitioner in the case against Mexico); Hannibal Industries, Inc.; Independence Tube Corporation; Maruichi American Corporation; Searing Industries; Southland Tube; and Vest, Inc.
The petition proposes the following scope of investigation:
Certain welded carbon steel pipes and tubes of rectangular (including square) cross section, having a wall thickness of not less than 4 mm, not threaded and not otherwise advanced.
Included products are those in which: (1) iron predominates, by weight, over each of the other contained elements; (2) the carbon content is 2 percent or less, by weight; and (3) none of the elements listed below exceeds the quantity, by weight, respectively indicated:
The subject merchandise is currently provided for in item 7306.61.1000 of the Harmonized Tariff Schedule of the United States (HTSUS). While the HTSUS subheadings are provided for convenience and customs purposes, the written description of the scope of this investigation is dispositive.
Alleged Dumping Margins:
Petitioners allege a 79.8 percent dumping margin for Korean producers. Petitioners allege a 23.4 percent dumping margin for Mexican producers. Finally, petitioners allege dumping margins for Turkish producers ranging from 96.5 percent to 108.6 percent.
Alleged Subsidy Programs:
Petitioners allege that Turkish producers benefit from the following countervailable subsidies:
Source:
On 21 July 2015, a group of petitioners ("Petitioners ") asked the United States Department of Commerce ("DoC ") to initiate an anti-dumping investigation into import of "heavy-walled rectangular welded carbon steel pipes and tubes", which originate from Turkey, South Korea or Mexico and are classified under the tariff code numbered 7306.61.1000 ("Product "). The Petitioners also requested a subsidy investigation be launched into imports of the Product from Turkey.
The Petitioners were Atlas Tube, a division of JMC Steel Group, Bull Moose Tube Company, EXL TUBE, Hannibal Industries, Inc. Independence Tube Corporation, Maruichi American Corporation, Searing Industries, Southland Tube, and Vest, Inc.
The request against Turkey claimed that producers in the United States were being damaged through establishment of unfair competition conditions. In particular, the Petitioners claimed:
Accordingly, the United States International Trade Commission ("ITC ") will investigate the Petitioners' allegations regarding injury of local producers, while the DoC will investigate whether dumping or subsidies exist.
The Petitioners identified 14 Turkish producers and exporters which will likely be involved in the investigations. The DoC and the ITC will likely have already sent questionnaires to selected Turkish producers and exporters; most likely the largest ones.
Other Turkish producers can voluntarily respond to the questionnaires, if the ITC or the DoC respectively allow. The ITC and the DoC aim to collect as much detailed data as possible in relation to the amount of dumping, subsidy, or injuries. The information includes sale volumes, as well as production or material cost.
It is crucial to respond to the questionnaires and cooperate with the ITC and the DoC. Failure to do so can result in less favorable investigation outcomes for Turkish producers and exporters.
Non-cooperation will essentially result in the investigation determinations being made based exclusively on data provided by the Petitioners. Accordingly, the Turkish producers and exporters could be forced to pay anti-dumping and/or countervailing duties at higher rates. This will naturally decrease the market share of Turkish Products in the United States.
The estimated investigation dates are (subject to change):
Turkish manufacturers have become more familiar with United States trade remedies as a result of recurring investigations over the last decade. However, the latest investigation confirms that Turkish manufacturers should very cautiously and carefully monitor their prices to ensure they do not lose market share established abroad.
The latest investigation is a good illustration that both developing and developed countries are prepared and willing to adopt trade measures as a shield to protect local industries.
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Orçun Çetinkaya, LL.M. and Metin Abut - August 3, 2015
On 21 July 2015, a group of petitioners (“Petitioners ”) asked the United States Department of Commerce (“DoC ”) to initiate an anti-dumping investigation into import of “heavy-walled rectangular welded carbon steel pipes and tubes”, which originate from Turkey, South Korea or Mexico and are classified under the tariff code numbered 7306.61.1000 (“Product ”). The Petitioners also requested a subsidy investigation be launched into imports of the Product from Turkey.
The Petitioners were Atlas Tube, a division of JMC Steel Group, Bull Moose Tube Company, EXL TUBE, Hannibal Industries, Inc. Independence Tube Corporation, Maruichi American Corporation, Searing Industries, Southland Tube, and Vest, Inc.
The request against Turkey claimed that producers in the United States were being damaged through establishment of unfair competition conditions. In particular, the Petitioners claimed:
Accordingly, the United States International Trade Commission (“ITC ”) will investigate the Petitioners’ allegations regarding injury of local producers, while the DoC will investigate whether dumping or subsidies exist.
The Petitioners identified 14 Turkish producers and exporters which will likely be involved in the investigations. The DoC and the ITC will likely have already sent questionnaires to selected Turkish producers and exporters; most likely the largest ones.
Other Turkish producers can voluntarily respond to the questionnaires, if the ITC or the DoC respectively allow. The ITC and the DoC aim to collect as much detailed data as possible in relation to the amount of dumping, subsidy, or injuries. The information includes sale volumes, as well as production or material cost.
It is crucial to respond to the questionnaires and cooperate with the ITC and the DoC. Failure to do so can result in less favorable investigation outcomes for Turkish producers and exporters.
Non-cooperation will essentially result in the investigation determinations being made based exclusively on data provided by the Petitioners. Accordingly, the Turkish producers and exporters could be forced to pay anti-dumping and/or countervailing duties at higher rates. This will naturally decrease the market share of Turkish Products in the United States.
The estimated investigation dates are (subject to change):
Turkish manufacturers have become more familiar with United States trade remedies as a result of recurring investigations over the last decade. However, the latest investigation confirms that Turkish manufacturers should very cautiously and carefully monitor their prices to ensure they do not lose market share established abroad.
The latest investigation is a good illustration that both developing and developed countries are prepared and willing to adopt trade measures as a shield to protect local industries.
By their nature, investigations may be politically driven, regardless of where they are initiated. Accordingly, it can be difficult to obtain positive results by simply filing responses to the authorities unless price determinations and market monitoring have been carried out and recorded during the course of trade.
Source:
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of Five-Year (``Sunset'') Review, 76 FR 38613 (July 1, 2011) and Certain Pipe and Tube From Brazil. Order; Light-Walled Welded Rectangular Carbon Steel Tubing From Taiwan, 54 FR 12467 (March 27, 1989). As. within a reasonably foreseeable time. See Light-Walled Rectangular Pipe and Tube From Taiwan, 77 FR.
Mexico: Preliminary Results and Partial Rescission of Antidumping Duty Administrative Review, 77 FR 55186. the order is certain welded carbon-quality light-walled steel pipe and tube, of rectangular (including. Than Fair Value, 73 FR 45403, 45405 (August 5, 2008). In accordance with 19 CFR 356.8(a).
2006). Thus, we calculated NV by adding together the value of the FOPs, general expenses, profit, and. Rectangular Pipe and Tube from the People's Republic of China, 73 FR 35652 (June 24, 2008). On August 5, 2008. Determination of Sales at Less Than Fair Value, 73 FR 45403 (August 5, 2008). On August 3, 2009, the.
Yang, Shuhong; Jiang, Fayu; Xiang, Yongyuan
With the high tempo-spatial \\emph
Hou, Y. J.; Li, T.; Yang, S. H.; Zhang, J.
Context. The Interface Region Imaging Spectrograph (IRIS) mission provides high-resolution observations of the chromosphere and transition region. Using these data, some authors have reported the new finding of light walls above sunspot light bridges. Aims: We try to determine whether the light walls exist somewhere else in active regions in addition to the light bridges. We also examine how the material of these walls evolves. Methods: Employing six months of (from 2014 December to 2015 June) high tempo-spatial data from the IRIS, we find many light walls either around sunspots or above light bridges. Results: For the first time, we report one light wall near an umbral-penumbral boundary and another along a neutral line between two small sunspots. The former light wall has a multilayer structure and is associated with the emergence of positive magnetic flux in the ambient negative field. The latter light wall is associated with a filament activation, and the wall body consists of the filament material, which flowed to a remote plage region with a negative magnetic field after the light wall disappeared. Conclusions: These new observations reveal that these light walls are multilayer and multithermal structures that occur along magnetic neutral lines in active regions. Movies associated to Figs. 1-4 are available in electronic form at http://www.aanda.org
subject merchandise, SG&A expenses, profit, and U.S. packing costs. However, as explained above, for these. 73 FR 31065 (May 30, 2008). On May 1, 2009, the Department published the notice of opportunity to. Suspended Investigation; Opportunity To Request Administrative Review, 74 FR 20278 (May 1, 2009). On May.
provided in the U.S. market. While both markets had many similar selling functions (i.e. sales promotion. Than Fair Value, 73 FR 45403 (August 5, 2008) (Order). On August 3, 2009, the Department published in. Request Administrative Review, 74 FR 38397 (August 3, 2009), covering, inter alia, LWRPT from Mexico.
In the first section of this paper we prove a theorem for the number of columns of a rectangular area that are identical to the given one. In the next section we apply this theorem to derive several combinatorial identities by counting specified subsets of a finite set.
A solution of the time-transient Heat Transfer Differential Equation in rectangular coordinates is presented, leading to a model which describes the temperature drop with time in rectangular bars. It is similar to an other model for cilindrical bars which has been previously developed in the Laboratory of Mechanical Metallurgy of UFRGS. Following these models, a generalization has been made, which permits cooling time evaluation for all profiles. These results are compared with experimental laboratory data in the 1200 to 8000C range. Some other existing models were also studied which have the purpose of studing the same phenomenon. Their mathematical forms and their evaluated values are analyzed and compared with experimental ones. (Author)
Driscoll, Tobin A.
Boundary conditions in spectral collocation methods are typically imposed by removing some rows of the discretized differential operator and replacing them with others that enforce the required conditions at the boundary. A new approach based upon resampling differentiated polynomials into a lower-degree subspace makes differentiation matrices, and operators built from them, rectangular without any row deletions. Then, boundary and interface conditions can be adjoined to yield a square system. The resulting method is both flexible and robust, and avoids ambiguities that arise when applying the classical row deletion method outside of two-point scalar boundary-value problems. The new method is the basis for ordinary differential equation solutions in Chebfun software, and is demonstrated for a variety of boundary-value, eigenvalue and time-dependent problems.
A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square \\left[0,1\\right]^<2>. The topological properties, such as connectivity, average degree, average path length and clustering, of the random rectangular graphs (RRGs) generated by this model are then studied as a function of the rectangle sides lengths a and b=1/a, and the radius r used to connect the nodes. When a=1 we recover the RGG, and when a\\rightarrow\\infty the very elongated rectangle generated resembles a one-dimensional RGG. We provided computational and analytical evidence that the topological properties of the RRG differ significantly from those of the RGG. The connectivity of the RRG depends not only on the number of nodes as in the case of the RGG, but also on the side length of the rectangle. As the rectangle is more elongated the critical radius for connectivity increases following first a power-law an.
Terrell, George R.
It is well known that the smaller and the larger of a random sample of size two are positively correlated. The coefficient of correlation is at most one-half, and the upper bound is attained only for rectangular distributions.
Olshen, Richard A; 10.1214/09-AOS743
Standard statistical techniques often require transforming data to have mean 0 and standard deviation 1. Typically, this process of "standardization" or "normalization" is applied across subjects when each subject produces a single number. High throughput genomic and financial data often come as rectangular arrays where each coordinate in one direction concerns subjects who might have different status (case or control, say), and each coordinate in the other designates "outcome" for a specific feature, for example, "gene," "polymorphic site" or some aspect of financial profile. It may happen, when analyzing data that arrive as a rectangular array, that one requires BOTH the subjects and the features to be "on the same footing." Thus there may be a need to standardize across rows and columns of the rectangular matrix. There arises the question as to how to achieve this double normalization. We propose and investigate the convergence of what seems to us a natural approach to successive normalization which we lea.
Estrada, Ernesto, E-mail: ernesto.estrada@strath.ac.uk; Chen, Guanrong [Department of Mathematics & Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XQ, United Kingdom and Department of Electronic Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon (Hong Kong)
Random rectangular graphs (RRGs) represent a generalization of the random geometric graphs in which the nodes are embedded into hyperrectangles instead of on hypercubes. The synchronizability of RRG model is studied. Both upper and lower bounds of the eigenratio of the network Laplacian matrix are determined analytically. It is proven that as the rectangular network is more elongated, the network becomes harder to synchronize. The synchronization processing behavior of a RRG network of chaotic Lorenz system nodes is numerically investigated, showing complete consistence with the theoretical results.
Random rectangular graphs (RRGs) represent a generalization of the random geometric graphs in which the nodes are embedded into hyperrectangles instead of on hypercubes. The synchronizability of RRG model is studied. Both upper and lower bounds of the eigenratio of the network Laplacian matrix are determined analytically. It is proven that as the rectangular network is more elongated, the network becomes harder to synchronize. The synchronization processing behavior of a RRG network of chaotic Lorenz system nodes is numerically investigated, showing complete consistence with the theoretical results
Lafrance, Rene; Myers, Robert C.
Several new results on the multicritical behavior of rectangular matrix models are presented. We calculate the free energy in the saddle point approximation, and show that at the triple-scaling point, the result is the same as that derived from the recursion formulae. In the triple-scaling limit, we obtain the string equation and a flow equation for arbitrary multicritical points. Parametric solutions are also examined for the limit of almost-square matrix models. This limit is shown to provi.
In this paper the authors calculate the energy spectrum of vacuum fluctuations for a massless scalar field which satisfies boundary conditions inside a wave guide or a rectangular box. The spectrum is piecewise continuous in the first case and discrete in the second, and exhibits resonances which correspond, as expected, to the energy levels of a particle in a box (with the difference that all these levels are occupied). Since it is known that these fluctuations exhibit a very slow convergence to a Poisson distribution, we conjecture that a realistic detector must find severe quantum vacuum deviations from white noise, except in the non-realistic limit of extremely high frequencies
Villarreal, C.; Jauregui, R.; Hacyan, S.; Cocho, G. (Universidad Nacional Autonoma de Mexico, Mexico City (Mexico). Inst. de Fisica)
In this paper the authors calculate the energy spectrum of vacuum fluctuations for a massless scalar field which satisfies boundary conditions inside a wave guide or a rectangular box. The spectrum is piecewise continuous in the first case and discrete in the second, and exhibits resonances which correspond, as expected, to the energy levels of a particle in a box (with the difference that all these levels are occupied). Since it is known that these fluctuations exhibit a very slow convergence to a Poisson distribution, we conjecture that a realistic detector must find severe quantum vacuum deviations from white noise, except in the non-realistic limit of extremely high frequencies.
Suk, Tomáš; Höschl, Cyril; Flusser, Jan
Berlin. Springer, 2012 - (Blanc-Talon, J.; Popescu, D.; Philips, W.; Scheunders, P.), s. 213-224 ISBN 978-3-642-33139-8. - (Lecture Notes in Computer Science. 7517). [Advanced Concepts for Intelligent Vision Systems (Acivs 2012). Brno (CZ), 04.09.2012-07.09.2012] R&D Projects: GA ČR GAP103/11/1552 Institutional support: RVO:67985556 Keywords. binary image decomposition * generalized delta-method * distance transformation * quadtree * bipartite graph * image compression * fast convolution Subject RIV: IN - Informatics, Computer Science http://library.utia.cas.cz/separaty/2012/ZOI/suk- rectangular decomposition of binary images.pdf
Hai-Bin Zhang; Zhen-Hua Duan
This paper investigates symbolic algorithmic analysis of rectangular hybrid systems. To deal with the symbolic reachability problem, a restricted constraint system called hybrid zone is formalized for the representation and manipulation of rectangular automata state-spaces. Hybrid zones are proved to be closed over symbolic reachability operations of rectangular hybrid systems. They are also applied to model-checking procedures for verifying some important classes of timed computation tree logic formulas. To represent hybrid zones, a data structure called difference constraint matrix is defined.These enable us to deal with the symbolic algorithmic analysis of rectangular hybrid systems in an efficient way.
Campisi, Michele; Accoto, Dino; Dario, Paolo
Motivated by the growing interest in ac electroosmosis as a reliable no moving parts strategy to control fluid motion in microfluidic devices for biomedical applications, such as lab-on-a-chip, we study transient and steady-state electrokinetic phenomena (electroosmosis and streaming currents) in infinitely extended rectangular charged microchannels. With the aid of Fourier series and Laplace transforms we provide a general formal solution of the problem, which is used to study the time-dependent response to sudden ac applied voltage differences in case of finite electric double layer. The Debye-Huckel approximation has been adopted to allow for an algebraic solution of the Poisson-Boltzmann problem in Fourier space. We obtain the expressions of flow velocity profiles, flow rates, streaming currents, as well as expressions of the complex hydraulic and electrokinetic conductances. We analyze in detail the dependence of the electrokinetic conductance on the extension of linear dimensions relative to the Debye length, with an eye on finite electric double layer effects. PMID:16351310
Richard A. Olshen
Full Text Available In this note we illustrate and develop further with mathematics and examples, the work on successive standardization (or normalization that is studied earlier by the same authors in [1] and [2]. Thus, we deal with successive iterations applied to rectangular arrays of numbers, where to avoid technical difficulties an array has at least three rows and at least three columns. Without loss, an iteration begins with operations on columns: first subtract the mean of each column; then divide by its standard deviation. The iteration continues with the same two operations done successively for rows. These four operations applied in sequence completes one iteration. One then iterates again, and again, and again. In [1] it was argued that if arrays are made up of real numbers, then the set for which convergence of these successive iterations fails has Lebesgue measure 0. The limiting array has row and column means 0, row and column standard deviations 1. A basic result on convergence given in [1] is true, though the argument in [1] is faulty. The result is stated in the form of a theorem here, and the argument for the theorem is correct. Moreover, many graphics given in [1] suggest that except for a set of entries of any array with Lebesgue measure 0, convergence is very rapid, eventually exponentially fast in the number of iterations. Because we learned this set of rules from Bradley Efron, we call it “Efron’s algorithm”. More importantly, the rapidity of convergence is illustrated by numerical examples.
A method is presented for calculating the track density distribution of Radon Alpha particles in the plastic track detectors placed along the wall of a rectangular dosimeter. The track density is taken as proportional to the volume of a sphere of radius 'R', where R is comparable to the range of the alpha particles. This volume has been calculated for a rectangular box of dimensions, a x a x b, as a function of the distance η of the centre of the sphere from the edge of the box. The distribution so obtained has been compared with the experimental track density distribution of Radon Alpha particles found in CN85 plastic track detectors placed along the wall of a rectangular box of 6 x 6 x 8 cm3 in an artificial mine in the laboratory. Conclusions regarding the suitability of rectangular geometry as compared to the cylindrical geometry have been drawn. (author)
The rectangular flange is adapted in the heater of TEP deaeration tower(Fig.1).The rectangular flange is no-round type flange,the evaluation of which is worked on equivalent round flange method.Thecalculation is based on no-round type flange evaluation chapter in HGT 20582—2011 Steel chemical vessel strength calculation code.The loads on the flange are inner pressure,nozzle loads and seismic loads.The nozzle loads is
Beltoft, Dan; Boutillier, Cédric; Enriquez, Nathanaël
We exhibit the limit shape of random Young diagrams having a distribution proportional to the exponential of their area, and confined in a rectangular box. The Ornstein-Uhlenbeck bridge arises from the fluctuations around the limit shape. We exhibit the limit shape of random Young diagrams having a distribution proportional to the exponential of their area, and confined in a rectangular box. The Ornstein-Uhlenbeck bridge arises from the fluctuations around the limit shape.
Cussen, L.D. E-mail: leo.cussen@vu.edu.au; Hoeghoj, P.; Anderson, I.S
Several Soller slit-type neutron collimators which give rectangular profiles of transmission as a function of angular divergence have been constructed. The collimators accept a beam of realistic dimensions - greater than 12x22 mm^{ in all cases. The blades of the collimators are 280 m thick wafers of single-crystal silicon each coated with a Ni-Gd-Ni multilayer on one side. Tests at a neutron wavelength of 7.5 A confirm that the transmission profiles are rectangular. Tests at a wavelength of 4.2 A show that two such collimators rocked against each other give dramatically enhanced transmission and resolution by comparison with conventional collimators. This is the first such demonstration of increased counting rates in a scan on an instrument from rectangular profile collimators, an effect expected but not produced for over 40 years.}
Cussen, L D; Anderson, I S
Several Soller slit-type neutron collimators which give rectangular profiles of transmission as a function of angular divergence have been constructed. The collimators accept a beam of realistic dimensions - greater than 12x22 mm sup 2 in all cases. The blades of the collimators are 280 mu m thick wafers of single-crystal silicon each coated with a Ni-Gd-Ni multilayer on one side. Tests at a neutron wavelength of 7.5 A confirm that the transmission profiles are rectangular. Tests at a wavelength of 4.2 A show that two such collimators rocked against each other give dramatically enhanced transmission and resolution by comparison with conventional collimators. This is the first such demonstration of increased counting rates in a scan on an instrument from rectangular profile collimators, an effect expected but not produced for over 40 years.
Several Soller slit-type neutron collimators which give rectangular profiles of transmission as a function of angular divergence have been constructed. The collimators accept a beam of realistic dimensions - greater than 12x22 mm2 in all cases. The blades of the collimators are 280 μm thick wafers of single-crystal silicon each coated with a Ni-Gd-Ni multilayer on one side. Tests at a neutron wavelength of 7.5 A confirm that the transmission profiles are rectangular. Tests at a wavelength of 4.2 A show that two such collimators rocked against each other give dramatically enhanced transmission and resolution by comparison with conventional collimators. This is the first such demonstration of increased counting rates in a scan on an instrument from rectangular profile collimators, an effect expected but not produced for over 40 years
CUI; Licheng; (崔立成); YANG; Hongsheng; (杨鸿生)
Mode matching method is used to analyze the scattering characteristics of the rectangular -to-circular groove waveguide junction. Firstly, the scattering matrix equation is obtained by matching the electromagnetic fields at the boundary of the junction. The scattering coefficients can be obtained from the equation. Secondly the scattering characteristics of the iris with rectangular window positioned in circular groove waveguide are briefly analyzed. Thirdly, the convergent problem is discussed and the numerical results are given. At last experiment is made and good agreement is found between the calculated results and the measured results.
Countercurrent air-water two phase flow limitation in vertical narrow rectangular ducts was investigated. The scale effect was investigated using three narrow rectangular ducts with different gaps (2 x 100, 5 x 100, 10 x 100 mm). The experimental data showed similar tendency in spite of gap or upper plenum liquid level. The Wallis type correlation with constant C = 0.65 gave a good agreement with the experimental data. A comparison with the prediction by the envelope theory using the Bharathan friction factor correlation was also discussed. (author)
Bambang Setia Nugroho
Full Text Available An analytical model for a frequency reconfigurable rectangular-ring microstrip antenna is proposed. The resonant frequencies and input impedance of the reconfigurable antenna are analyzed using a lossy-transmission-line (LTL model. By making use of Y-admittance matrices, a formulation for the input impedance is analytically derived. The structure of the frequency reconfigurable antenna consists of a rectangular-ring shaped microstrip antenna which is loaded with a rectangular patch in the middle of the rectangular-ring antenna and fed by a microstrip line. RF switches are applied to connect the load to the antenna in order to reconfigure the operating frequencies. By modeling the antenna into a multiport equivalent circuit, the total input impedance is analytically derived to predict the resonant frequencies. To verify the analysis, the model input impedance and reflection coefficient calculation have been compared with the full-wave simulation and measurement results. The proposed model shows good agreement with full-wave simulated and measured results in the range of 1–3 GHz.
Assuah, Charles K.; Wiest, Lynda R.
Can middle-grades students determine which of two rectangular prisms has a larger volume? Can they do so without using a formula? Geometry, and particularly the concept of volume, is important in many subjects, such as physics and chemistry. Students greatly enhance their mathematics knowledge when they make generalizations and construct arguments…
A numerical, magnetostatic model of the internal magnetic field of a rectangular prism is extended to the case of a stack of rectangular prisms. The model enables the calculation of the spatially resolved, three-dimensional internal field in such a stack given any magnetic state function, stack configuration, temperature distribution and applied magnetic field. In this paper the model is applied to the case of a stack of parallel, ferromagnetic rectangular prisms and the resulting internal field is found as a function of the orientation of the applied field, the number of prisms in the stack, the spacing between the prisms and the packing density of the stack. The results show that the resulting internal field is far from being equal to the applied field and that the various stack configurations investigated affect the resulting internal field significantly and non-linearly. The results have a direct impact on the design of, e.g. active magnetic regenerators made of stacked rectangular prisms in terms of optimizing the internal field.
Full Text Available We introduce the notion of cone rectangular metric space and prove
Babloyan A.H.; Baghdasaryan A.V.
The solution of a problem of elasticity theory for rectangular weakened by a centrally located vertical crack is brought. On the horizontal sides of the rectangular and on the crack faces the stresses are given. On the vertical sides of the rectangular three types of boundary conditions are given.
Full Text Available We prove some common fixed-point theorems for the ordered g-weak contractions in cone rectangular metric spaces without assuming the normality of cone. Our results generalize some recent results from cone metric and cone rectangular metric spaces into ordered cone rectangular metric spaces. Examples are provided which illustrate the results.
In order to optimize frequency response and determine the tolerances required to meet RF specifications, accurate computer modeling of passive rectangular waveguide components is often required. Many rectangular waveguide components may be represented either exactly or approximately as a number of different size rectangular waveguides which are connected in series. RWGSCAT, Rectangular WaveGuide junction SCATtering program, solves for the scattering properties of a waveguide device. This device must consist of a number of rectangular waveguide sections of different cross sectional area which are connected in series. Devices which fall into this category include step transformers, filters, and smooth or corrugated rectangular horns. RWGSCAT will model such devices and accurately predict the reflection and transmission characteristics, taking into account higher order (other than dominant TE 10) mode excitation if it occurs, as well as multiple reflections and stored energy at each discontinuity. For devices which are large with respect to the wavelength of operation, the characteristics of the device may be required for computing a higher order mode or a number of higher order modes exciting the device. Such interactions can be represented by defining a scattering matrix for each discontinuity in the device, and then cascading the individual scattering matrices in order to determine the scattering matrix for the overall device. The individual matrices are obtained using the mode matching method. RWGSCAT is written in FORTRAN 77 for IBM PC series and compatible computers running MS-DOS. It has been successfully compiled and implemented using Lahey FORTRAN 77 under MS-DOS. A sample MS-DOS executable is provided on the distribution medium. It requires 377K of RAM for execution. Sample input data is also provided on the distribution medium. The standard distribution medium for this program is one 5.25 inch 360K MS-DOS format diskette. The contents of the diskette are
We propose a new method for anisotropic polygonal surface remeshing. Our algorithm takes as input a surface triangle mesh. An anisotropic rectangular metric, defined at each triangle facet of the input mesh, is derived from both a user-specified normal-based tolerance error and the requirement to favor rectangle-shaped polygons. Our algorithm uses a greedy optimization procedure that adds, deletes and relocates generators so as to match two criteria related to partitioning and conformity.
Experimental investigation of impulse-bit and propellant consumption rate, or mass shot, per single pulse discharge was conducted to characterize the thrust performance of the rectangular laser-electromagnetic hybrid acceleration thruster with various propellant materials. From the result, alumina propellant showed significantly superior performance. The largest values of the measured impulse-bit, specific impulse and thrust efficiency were 49 μNsec, 6,200 sec and 22%, respectively.
A Lakshmi Narayana; Krishnamohana Rao; R Vijaya Kumar
A numerical study is carried out using finite element method, to examine the effects of square and rectangular cutout on the buckling behavior of a sixteen ply quasi-isotropic graphite/epoxy symmetrically laminated rectangular composite plate $[0^\\circ /+45^\\circ /-45^\\circ /90^\\circ ]_<2s>$, subjected to various linearly varying in-plane compressive loads. Further, this paper addresses the effects of size of square/ rectangular cutout, orientation of square/ rectangular cutout, plate aspect ratio(a/b), plate length/thickness ratio(a/t), boundary conditions on the buckling bahaviour of symmetrically laminated rectangular composite plates subjected to various linearly varying in-plane compressive loading. It is observed that the various linearly varying in-plane loads and boundary conditions have a substantial influence on buckling strength of rectangular composite plate with square/ rectangular cutout.
Christensen, Dennis; Nielsen, Kaspar Kirstein; Bahl, Christian Robert Haffenden;
configuration, temperature distribution and applied magnetic field. In this paper the model is applied to the case of a stack of parallel, ferromagnetic rectangular prisms and the resulting internal field is found as a function of the orientation of the applied field, the number of prisms in the stack, the. spacing between the prisms and the packing density of the stack. The results show that the resulting internal field is far from being equal to the applied field and that the various stack configurations investigated affect the resulting internal field significantly and non-linearly. The results have a.
Hydraulic performance of an airlift pump having a rectangular cross-section 20 mm × 80 mm was investigated through an experimental program. The pump was operated at six different submergence ratios and the liquid flow rate was measured at various flowrates of air injected. The effectiveness of the pump, defined as the ratio of the mass of liquid pumped to the mass of air injected, was determined as a function of the mass of air injected for different submergence ratios. Results obtained were.
We discuss conformal field theories (CFTs) in rectangular geometries, and develop a formalism that involves a conformal boundary state for the 1+1d open system. We focus on the case of homogeneous boundary conditions (no insertion of a boundary condition changing operator), for which we derive an explicit expression of the associated boundary state, valid for any arbitrary CFT. We check the validity of our solution, comparing it with known results for partition functions, numerical simulations of lattice discretizations, and coherent state expressions for free theories.
Hinds, Kirsten; Jensen, David
The IsoBeam is a rectangular. unidirectional, composite lattice structure designed for beam applications. Three carbon fiber specimens each 2 ft (0.61 m) long, 6 in. (152.4 mm) tall and 3 in. (76.2 mm) wide with four 6 in. (152.4 mm) bays were hand-woven and tested in bending. The beams each weighed between 1.82-1.86 lbs (8.09-8.27 N). A low maximum strength was achieved, primarily due to insufficient consolidation and inadequate manufacturing quality but the structure is seen to be very duct.
Rao, N. H.; Sarma, P. B. S.
A generalized analytical solution is derived for the growth of groundwater mound in finite aquifers bounded by open water bodies, in response to recharge from rectangular areas. Finite Fourier transforms are used to solve the linearized differential equation of groundwater flow. Unlike earlier solutions, the method presented here does not require the use of tables for evaluation of complicated functions. The solution is evaluated by comparison with existing numerical and analytical results. In stream-aquifer systems similar to those described above, application of the proposed solution is more realistic than using solutions available for infinite aquifers.
Chaiken, Seth; Zaslavsky, Thomas; 10.1007/s00026-011-0068-7
The function that counts the number of ways to place nonattacking identical chess or fairy chess pieces in a rectangular strip of fixed height and variable width, as a function of the width, is a piecewise polynomial which is eventually a polynomial and whose behavior can be described in some detail. We deduce this by converting the problem to one of counting lattice points outside an affinographic hyperplane arrangement, which Forge and Zaslavsky solved by means of weighted integral gain graphs. We extend their work by developing both generating functions and a detailed analysis of deletion and contraction for weighted integral gain graphs. For chess pieces we find the asymptotic probability that a random configuration is nonattacking, and we obtain exact counts of nonattacking configurations of small numbers of queens, bishops, knights, and nightriders.
In this paper, we present a mathematical model for the angular projection of a rectangular arrangement of points in a grid. This simple, yet interesting problem, has both a scholarly value and applications for data extraction techniques to study the physics of various systems. Our work can interest undergraduate students to understand subtle points in the angular projection of a grid and describes various quantities of interest in the projection with completeness and sufficient rigour. We show that for certain angular ranges, the projection has non-distinctness, and calculate the details of such angles, and correspondingly, the number of distinct points and the total projected length. We focus on interesting trends obtained for the projected length of the grid elements and present a simple application of the model to determine the geometry of an unknown grid whose spatial extensions are known, using measurement of the grid projection at two angles only. Towards the end, our model is shown to have potential ap.
Full Text Available The Venturi scrubber is a device which uses liquid in the form of droplets to efficiently remove fine particulate matter from gaseous streams. Droplet size is of fundamental importance for the scrubber performance. In the present experimental study, a laser diffraction technique was used in order to measure droplet size in situ in a Venturi scrubber with a rectangular cross section. Droplet size distribution was measured as a function of gas velocity (58.3 to 74.9 m/s, liquid-to-gas ratio (0.07 to 0.27 l/m³, and distance from liquid injection point (64 to 173 mm. It was found that all these variables significantly affect droplet size. The results were compared with the predictions from correlations found in the literature.
An investigation of rectangular resonators with a view to the compensation of astigmatism has been performed. In order to have beam waists placed at the same positions in the tangential and sagittal planes, pairs of equal mirrors were considered. It was found that at least two concave mirrors are. necessary to obtain compensation. Four-concave-mirror systems are most stable close to the quadratic geometry, although the symmetric quadratic resonator itself cannot be compensated for astigmatism. Using four equal concave mirrors, compensation of astigmatism can be obtained in two arms at the same time. Usually several stability ranges are found for four-mirror resonators with pair-wise equal mirrors, and it is possible with these systems to obtain small compensated beam waist radii suitable for frequency conversion. Relevant formulae are given and several relevant examples are shown using simulation.
A method is described for obtaining S values between a tumor and its host organ for use with the MIRD formalism. It applies the point-source specific absorbed fractions for an infinite water medium, tabulated by Berger, to a rectangular solid of arbitrary dimensions which contains a rectangular tumor of arbitrary dimensions. Contributions from pairs of source and target volume elements are summed for the S values between the tumor and itself, between the remaining healthy host organ and itself, and between the tumor and the remaining healthy host organ, with the reciprocity theorem assumed for the last. This method labeled MTUMOR, is interfaced with the widely used MIRDOSE program which incorporates the MIRD formalism. An example is calculated
Least square method is used to fit power and astigmatism of rectangular pupil wavefront data, which avoids data interpolation of the blank area in circular domain. In the experiments, the maximal difference of power and astigmatism of circular domain data between commercial software and our method is less than 0.005 wavelength, which proves the proposed method's feasibility. For rectangular pupil wavefront data, the differences of astigmatism increase as the rectangle element's length-width ratio increases, Therefore the proposed method is more applicable for rectangular pupil wavefront calculation. (authors)
C Erdem İmrak; Ismail Gerdemeli
The examination of the exact solution of the governing equation of the rectangular plate is important for many reasons. This report discusses in exact solution of the governing equation of an isotropic rectangular plate with four clamped edges. A numerical method for clamped isotropic rectangular plate under distributed loads and an exact solution of the governing equation in terms of trigonometric and hyperbolic function are given. Finally, an illustrative example is given and the results are compared with those reported earlier. This method is found to be easier and effective. The results show reasonable agreement with other available results, but with a simpler and practical approach.
Full Text Available A multi-band microstrip patch antenna is developed and presented in this paper. The radiating elements in this antenna are composed of rectangular and triangular slots. These slots are engraved in the rectangular and triangular patch, joined together in one structure, and by single probe feed. The rectangular and triangular slots make the antenna to operate at multiband with relatively high gain. Therefore, this antenna can be used for wireless communication applications like WLAN, WiMax and radar system applications.
Full Text Available Deep drawing is a process for shaping flat sheets into cup shaped articles without fracture or excessive localized thinning. The complex deep drawing of thin metallic sheets is widely used during industrial material forming applications. It allows production of thin walled parts with complicated shapes such as automotive panels or structural parts. The process consists of the plastic deformation of an initial at blank subjected to the action of a rigid punch and die while constrained on the periphery by a blank holder. Conventional design processes for sheet metal forming are usually based on a empirical approach. However, due to the requirement of high precision and reliability in shaped parts, these methods are far away from a final and reliable solution. Nowadays, Finite Element Method (FEM is being gradually adopted by industry to envisage the formability properties of sheet metals. The design and control of a deep drawing process depends not only on the work piece material, but also on the condition at the tool work piece interface, the mechanics of plastic deformation and the equipment used. In this paper, rectangular cup component of EDDQ Steel and Mild Steel is simulated using HYPERMESH 11 by varying various process parameters.
Lee, Gwo-Bin; Chang, Chih-Chang; Huang, Sung-Bin; Yang, Ruey-Jen
This paper presents a theoretical and experimental investigation into the hydrodynamic focusing effect in rectangular microchannels. Two theoretical models for two-dimensional hydrodynamic focusing are proposed. The first model predicts the width of the focused stream in symmetric hydrodynamic focusing in microchannels of various aspect ratios. The second model predicts the location and the width of the focused stream in asymmetric hydrodynamic focusing in microchannels with a low or high aspect ratio. In both models, the theoretical results are shown to be in good agreement with the experimental data. Hence, the models provide a useful means of performing a theoretical analysis of flow control in microfluidic devices using hydrodynamic focusing effects. The ability of the proposed models to control the focused stream within a micro flow cytometer is verified in a series of experimental trials performed using polystyrene microparticles with a diameter of 20 µm. The experimental data show that the width of the focused stream can be reduced to the same order of magnitude as that of the particle size. Furthermore, it is shown that the microparticles can be successfully hydrodynamically focused and switched to the desired outlet port of the cytometer. Hence, the models presented in this study provide sufficient control to support cell/particle counting and sorting applications.
Minoru YAGA; Yoshio KINJO; Masumi TAMASHIRO; Kenyu OYAKAWA
In this paper, the flow fields of underexpanded impinging jet issued from rectangular nozzles of aspect ratio 1,3 and 5 are numerically and experimentally studied. Two dimensional temperature and pressure distributions are measured by using infrared camera and the combination of a pressure scanning device and a stepping motor, respectively. The variation of the stagnation pressure on the impinging plate reveals that a hystcretic phenomenon exists during the increasing and decreasing of the pressure ratio for the aspect ratio of 3.0 and 5.0. It is also found that the nozzle of aspect ratio 1.0 caused the largest total pressure loss pc/p0 = 0.27 at the pressure ratio of p0/pb, = 6.5, where pc is the stagnation center pressure on the wall, p0 the upstream stagnation pressure, pb the ambient pressure. The other two nozzles showed that the pressure loss pc / p0=0.52 and 0.55 were achieved by the nozzles of the aspect ratio 3,0 and 5.0, respectively. The comparison between the calculations and experiments is fairly good, showing the three dimensional streamlines and structures of the shock waves in the jets. However, the hysteresis of the pressure variations observed in the experiments between the pressure ratio of 3.5 and 4.5 cannot be confirmed in the calculations.
Kong, Nicholas; Heer, Jeffrey; Agrawala, Maneesh
Treemaps are space-filling visualizations that make efficient use of limited display space to depict large amounts of hierarchical data. Creating perceptually effective treemaps requires carefully managing a number of design parameters including the aspect ratio and luminance of rectangles. Moreover, treemaps encode values using area, which has been found to be less accurate than judgments of other visual encodings, such as length. We conduct a series of controlled experiments aimed at producing a set of design guidelines for creating effective rectangular treemaps. We find no evidence that luminance affects area judgments, but observe that aspect ratio does have an effect. Specifically, we find that the accuracy of area comparisons suffers when the compared rectangles have extreme aspect ratios or when both are squares. Contrary to common assumptions, the optimal distribution of rectangle aspect ratios within a treemap should include non-squares, but should avoid extremes. We then compare treemaps with hierarchical bar chart displays to identify the data densities at which length-encoded bar charts become less effective than area-encoded treemaps. We report the transition points at which treemaps exhibit judgment accuracy on par with bar charts for both leaf and non-leaf tree nodes. We also find that even at relatively low data densities treemaps result in faster comparisons than bar charts. Based on these results, we present a set of guidelines for the effective use of treemaps and suggest alternate approaches for treemap layout. PMID:20975136
Wang, Changbiao; Yakovlev, Vyacheslav P
For high frequency accelerators with normal-conducting structures studied by the NLC/GLC collaboration and the CLIC group, rf breakdown is the main gradient limitation. In this paper, a Ka-band rectangular dielectric-lined structure is described as an attempt to increase accelerating gradient beyond the limits suitable for metallic structures. The structure is based on amorphous dielectrics that are known to exhibit high breakdown limits (
GV/m). An example is artificial diamond that has already been successfully used on an industrial basis for large-diameter output windows of high power gyrotrons, and is produced industrially in increasing quantities. Artificial diamond has low loss tangent, moderate dielectric constant and high breakdown limit of
2 GV/m. In the proposed structure diamond-slabs are employed to support high-gradient acceleration fields. Interposition of vacuum gaps between the dielectric slabs and the side walls is shown to reduce Ohmic losses substantially, leading to an increase in shunt.
Estrada, Ernesto; Moreno, Yamir
Recently, Estrada and Sheerin (Phys. Rev. E 91, 042805 (2015)) developed the random rectangular graph (RRG) model to account for the spatial distribution of nodes in a network allowing the variation of the shape of the unit square commonly used in random geometric graphs (RGGs). Here, we consider an epidemics dynamics taking place on the nodes and edges of an RRG and we derive analytically a lower bound for the epidemic threshold for a Susceptible-Infected-Susceptible (SIS) or Susceptible-Infected-Recovered (SIR) model on these networks. Using extensive numerical simulations of the SIS dynamics we show that the lower bound found is very tight. We conclude that the elongation of the area in which the nodes are distributed makes the network more resilient to the propagation of an epidemics due to the fact that the epidemic threshold increases with the elongation of the rectangle. On the other hand, using the "classical" RGG for modeling epidemics on non-squared cities generates a larger error due to the effects.
Xiaoxing Zhang; Yefei Han; Wei Li; Xuetao Duan
A rectangular planar spiral antenna sensor was designed for detecting the partial discharge in gas insulation substations (GIS). It can expediently receive electromagnetic waves leaked from basin-type insulators and can effectively suppress low frequency electromagnetic interference from the surrounding environment. Certain effective techniques such as rectangular spiral structure, bow-tie loading, and back cavity structure optimization during the antenna design process can miniaturize antenn.
Anshul Shrivastava1 Abhinav Bhargava2 Samrat Ghosh3
Full Text Available In this paper we present a proposed design for Rectangular micro-strip patch antenna by cutting five U shaped slots in the Rectangular patch. Using proposed antenna design and probe feeding at proper position we find the resultant return loss, VSWR and bandwidth. We are using IE3D simulation software for designing and analysis. We have observed that using slotted patch antenna and using probe feed at proper location we can get better return loss, VSWR and bandwidth.
B R Koushik; B Ajeya
In this paper a Rectangular Patch Antenna is specifically designed and analysed using metamaterial concepts. Based on an ordinary patch antenna, it has a double C shaped resonant structure embedded in the centre of the substrate of the Rectangular Patch Antenna. The resonant structure has a strong electric response in a certain frequency of interest, and can be used to construct metamaterials with negative permittivity. It is found the great impact on the antenna performance to modify the dim.
We developed a new model for calculating diffraction radiation (DR) from an electron moving through a rectangular hole in a rectangular screen. The calculations show that short wavelength DR is very sensitive to the beam size. For example, optical DR (ODR) could be used to measure the beam size as small as 10 μm. Moreover, splitting two polarization components it becomes possible to measure vertical and horizontal beam sizes independently. We have calculated the DR spectra and compared them with TR ones for a finite size target. It is shown that when the DR wavelength is comparable with or longer than the hole size, the photon yield is mostly determined by the outer target dimensions. It means that in case transversal beam dimensions smaller than the observation wavelength the coherent DR could be used for non-invasive bunch length measurements with the same accuracy as the coherent TR techniques. However, the outer target dimensions must be taken into account because the finite target size causes a significant intensity suppression in the long wavelength spectral range as well as distortion of the coherent spectrum
From the molecular current viewpoint,an analytic expression exactly describing magnetic field distribution of rectangular permanent magnets magnetized sufficiently in one direction was derived from the Biot-Savart's law. This expression is useful not only for the case of one rectangular permanent magnet bulk, but also for that of several rectangular permanent magnet bulks. By using this expression,the relations between magnetic field distribution and the size of rectangular permanent magnets as well as the magnitude of magnetic field and the distance from the point in the space to the top (or bottom) surface of rectangular permanent magnets were discussed in detail. All the calculating results are consistent with experimental ones. For transverse magnetic field which is a main magnetic field of rectangular permanent magnets,in order to describe its distribution,two quantities,one is the uniformity in magnitude and the other is the uniformity in distribution of magnetic field,were defined. Furthermore, the relations between them and the geometric size of the magnet as well as the distance from the surface of permanent magnets were investigated by these formulas. The numerical results show that the geometric size and the distance have a visible influence on the uniformity in magnitude and the uniformity in distribution of the magnetic field.
Han, Sang Yeop; Taghavi, Ray R.; Farokhi, Saeed
Mixing characteristics of under-expanded supersonic jets emerging from plane and notched rectangular nozzles are computationally studied using nozzle exit boundary layer swirl as a mean of passive flow control. The coupling of the rectangular jet instability modes, such as flapping, and the swirl is investigated. A three-dimensional unsteady Reynolds-Averaged Navier-Stokes (RANS) code with shock adaptive grids is utilized. For plane rectangular nozzle with boundary layer swirl, the flapping and spanwise oscillations are captured in the jet's small and large dimensions at twice the frequencies of the nozzles without swirl. A symmetrical oscillatory mode is also observed in the jet with double the frequency of spanwise oscillation mode. For the notched rectangular nozzle with boundary layer swirl, the flapping oscillation in the small jet dimension and the spanwise oscillation in the large jet dimension are observed at the same frequency as those without boundary layer swirl. The mass flow rates in jets at 11 and 8 nozzle heights downstream of the nozzles increased by nearly 25% and 41% for the plane and notched rectangular nozzles respectively, due to swirl. The axial gross thrust penalty due to induced swirl was 5.1% for the plane and 4.9% for the notched rectangular nozzle.
Full Text Available The classic puzzle of finding a closed knight’s tour on a chessboard consists of moving a knight from square to square in such a way that it lands on every square once and returns to its starting point. The 8 × 8 chessboard can easily be extended to rectangular boards, and in 1991, A. Schwenk characterized all rectangular boards that have a closed knight’s tour. More recently, Demaio and Hippchen investigated the impossible boards and determined the fewest number of squares that must be removed from a rectangular board so that the remaining board has a closed knight’s tour. In this paper we define an extended closed knight’s tour for a rectangular chessboard as a closed knight’s tour that includes all squares of the board and possibly additional squares beyond the boundaries of the board and answer the following question: how many squares must be added to a rectangular chessboard so that the new board has a closed knight’s tour?
The phenomenon of counter-current flow limitation (CCFL) in thin rectangular channels is important in determining the heat removal capability of research reactors which use plate-type fuel elements similar to the MTR design. An analytical expression for predicting CCFL in narrow rectangular channels was derived from the momentum equations for the liquid and gas phase. The model assumes that the liquid downflow is in the form of a film along the narrower side walls of the channel, while the gas flow occupies the wide span of the rectangular channel. The average thickness of liquid film is related to the rate of gas flow through a stability criterion for the liquid film. The CCFL correlation agrees with air/water data taken at relatively high gas velocities. Depending on the magnitude of the dimensionless channel width W*, the new CCFL correlation approaches zero liquid penetration either in the form of a Wallis correlation or in terms of a Kutateladze number. The new correlation indicates that for a thin rectangular channel, the constant C in the Wallis flooding correlation depends on the aspect ratio of the channel. The approach to the appropriate asymptotic solutions also justifies the use of twice the wide span as the correct length scale for thin rectangular channels. 14 refs. 6 figs
Klosak, Andrzej K.; Gade, Anders Christian
Extensive acoustics computer simulations have been made using Odeon computer simulation software. In 24 rectangular rooms representing "shoe-box" type concert halls with volumes of 8 000 m3, 12 000 m3 and 16 000 m3 from 300 to 850 measurements positions have been analysed. Only room averaged. objective measures are considered here, in particular Clarity (C80), Strength (G) and Early Lateral Energy Fraction (LF80). Results from simulations have been compared with regression models created based on real hall measurements. In general, simulated results of C80 and G are found to be in good agreement. with regression models. Divergences are found in LF80 behaviour; these have been associated with influence of proportions of rectangular halls. Updated formula for predicting of LF80 in rectangular halls has been proposed, which takes into the account both width and length of hall.
We rewrite the recently proposed differential expansion formula for HOMFLY polynomials of the knot $4_1$ in arbitrary rectangular representation $R=[r^s]$ as a sum over all Young sub-diagrams $\\lambda$ of $R$ with extraordinary simple coefficients $D_<\\lambda^>(r)\\cdot D_\\lambda(s)$ in front of the $Z$-factors. Somewhat miraculously, these coefficients are made from quantum dimensions of symmetric representations of the groups $SL(r)$ and $SL(s)$ and restrict summation to diagrams with no more than $s$ rows and $r$ columns. They possess a natural $\\beta$-deformation to Macdonald dimensions and produces positive Laurent polynomials, which can be considered as plausible candidates for the role of the rectangular superpolynomials. Both polynomiality and positivity are non-evident properties of arising expressions, still they are true. This extends the previous suggestions for symmetric and antisymmetric representations (when $s=1$ or $r=1$ respectively) to arbitrary rectangular representations. As usual for.
Basirovich, Sabitov Kamil
In recent years, developed an interest in the study of boundary value problems for equations of mixed type in rectangular areas. This method proved theorems on the unique solubility and stability of the Dirichlet problem [1 - 3] under certain restrictions on the aspect ratio of the rectangular region of the hyperbolic. In this paper, for the mixed type equation with the Lavrent'ev-Bitsadze Dirichlet problem in a rectangular area. The criterion of uniqueness of the solution of the Dirichlet problem. The solution is built as the sum of the Fourier series. In justifying the convergence of a problem of small denominators regarding the relationship of the parties of the hyperbolic part of the rectangle. In connection with this evaluation are set to secede from scratch small denominator corresponding to the asymptotic behavior of rational and irrational values of the ratio, which allowed to substantiate the convergence of the series constructed in the class of regular solutions.
This study examined critical submergence for isolated and dual rectangular intakes. It is shown that the critical submergence for an isolated intake can be predicted by disregarding whole boundary blockages on the complete imaginary critical sink surface that is the combination of imaginary complete critical cylindrical and hemi-spherical sink surfaces. It is proposed that this theory can be applied to the rectangular intakes located in general geometrical and flow conditions (i.e. intake in still water, circulation imposed flow, non-developedcross-flow, multiple intakes, etc.) and that it does not require computation of blockages caused from flow boundaries. The concept of complete sink surface (disregarding whole boundary blockages) developed for an isolated intake was also applied to dual rectangular intakes. The agreement between available test data and theoretical results was found to be satisfactory.
Cai, Libing; Wang, Jianguo, E-mail: wanguiuc@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of Ministry of Education, Xi' an Jiaotong University, Xi' an 710049 (China); Northwest Institute of Nuclear Technology, Xi' an, Shaanxi 710024 (China); Cheng, Guoxin; Zhu, Xiangqin; Xia, Hongfu [Northwest Institute of Nuclear Technology, Xi' an, Shaanxi 710024 (China)
Multipactor discharge on the rectangular grooved dielectric surface is simulated self-consistently by using a two-and-a-half dimensional (2.5 D) electrostatic particle-in-cell (PIC) code. Compared with the electromagnetic PIC code, the former can give much more accurate solution for the space charge field caused by the multipactor electrons and the deposited surface charge. According to the rectangular groove width and height, the multipactor can be divided into four models, the spatial distributions of the multipactor electrons and the space charge fields are presented for these models. It shows that the rectangular groove in different models gives very different suppression effect on the multipactor, effective and efficient suppression on the multipactor can only be reached with a proper groove size.
Full Text Available The microstrip patch is one of the most preferred antenna structures for low cost and compact design for wireless system. Dual and triple band antennas are of a relative interest since they can support multiple communication systems. In this paper we present designs of compact small size microstrip antennas suitable for dual and triple band operations. By loading properly arranged slots on a rectangular microstrip patch, dual and triple frequencies and broadband operations of a single feed rectangular patch is achieved. Dual and triple frequency operation is achieved by loading U and H slots in rectangular patch. The impedance bandwidth of 150MHz, 1.26GHz band for U slot and 154MHz, 484MHz, 396MHz for H slot is obtained in the proposed designs
This paper presents a semi-analytical approach for the dynamic analysis of rectangular plates. The mathematical model is developed using a hybrid combination of the finite element method and Sanders' shell theory. The in-plane, membrane displacement components are modelled by bilinear polynomials and the out-of-plane, normal to mid-surface displacement component is modelled by an exponential function that represents a general form of the exact solution of the equations of motion. The displacement functions are obtained by exact solution of the equilibrium equations of the rectangular plates. The mass and stiffness matrices are then determined by exact analytical integration to establish the plate's dynamic equations. The effect of various geometrical parameters and boundary conditions on the dynamic responses of the rectangular plates has been explored in this work. The results are in satisfactory agreement with those of experiments and other theories
Biao Li; Yang Ding; Ying-Zeng Yin
A coplanar waveguide fed dual-band circularly polarized rectangular slot antenna is presented. The proposed antenna consists of a rectangular metal frame acting as a ground and an S-shaped monopole as a radiator. The spatial distribution of the surface current density is employed to demonstrate that the circular polarization is generated by the S-shaped monopole which controls the path of the surface currents. An antenna prototype, having overall dimension 37 × 37 × 1 mm3, has been fabricated.
Full Text Available A rigorous full-wave analysis of high Tc superconducting rectangular microstrip patch over ground plane with rectangular aperture in the case where the patch is printed on a uniaxially anisotropic substrate material is presented. The dyadic Green’s functions of the considered structure are efficiently determined in the vector Fourier transform domain. The effect of the superconductivity of the patch is taken into account using the concept of the complex resistive boundary condition. The accuracy of the analysis is tested by comparing the computed results with measurements and previously published data for several anisotropic substrate materials. Numerical results showing variation of the resonant frequency and the quality factor of the superconducting antenna with regard to operating temperature are given. Finally, the effects of uniaxial anisotropy in the substrate on the resonant frequencies of different TM modes of the superconducting microstrip antenna with rectangular aperture in the ground plane are presented.
I consider a Josephson junction crossing the middle of a thin rectangular superconducting strip of length L and width W subjected to a perpendicular magnetic induction B. I calculate the spatial dependence of the gauge-invariant phase difference across the junction and the resulting B dependence of the critical current Ic(B).
We present applications of rectangular matrix models to various combinatorial problems, among which the enumeration of face-bicolored graphs with prescribed vertex degrees, and vertex-tricolored triangulations. We also mention possible applications to interaction-round-a-face and hard-particle statistical models defined on random lattices
Mayer, Stefan; Nielsen, Kristian Bendix; Hansen, E.A.
Wave impact on one and two structural beams with rectangular cross section is simulated with a two-dimensional finite volume method, solving the unsteady Euler equations and employing a VOF-type method for the description of the free surface. Four different test series are carried out, each.
I consider a Josephson junction crossing the middle of a thin rectangular superconducting strip of length L and width W subjected to a perpendicular magnetic induction B. I calculate the spatial dependence of the gauge-invariant phase difference across the junction and the resulting B dependence of the critical current Ic(B).
Full Text Available Calculated and analyzed the basic parameters of electromagnetic wave in a circular waveguide with a rectangular metal plate in the following cases: when the circular waveguide without metal plate for a H11 wave of subcritical, critical and supercritical. For calculations was used a finite element method and Ansoft HFSS program.
Zhao Hui; Yu Liang; Ning Tao; Xi Ping
Optimal layout of rectangular stock cutting is still in great demand from industry for diversified applications. This paper introduces four basic solution methods to the problem: linear programming, dynamic programming, tree search and heuristic approach. A prototype of application software is developed to verify the pros and cons of various approaches.
The experiment of dryout heat transfer in rectangular channel has been carried out on the basic experimental loop of flow and heat transfer at NPIC. The results of the experimental study of thermal-hydraulic parameters on characteristics of dryout heat transfer in rectangular channel show that: (1) The dryout heat flux, wall temperature and heat transfer coefficient decrease, while the dryout quality increases with the increase of inlet quality; (2) The dryout heat flux, wall temperature and heat transfer coefficient increase, while the dryout quality decreases with the increase of mass flow velocity; (3) The dryout heat flux, quality, wall temperature and heat transfer coefficient increase with the increase of system pressure. Comparing the experimental data with empirical correlations, it finds out that these correlations are appropriate for the situations of middle-high pressure and low-middle mass flow velocity, and deviate seriously in low pressure and high mass flow velocity cases. Based on the Gutajellade correlation, and considering the effects of the dimension of rectangular channel and inlet enthalpy on heat transfer, a new correlation for dryout in rectangular channel is developed, which correlates the experimental data quite well. (authors)
Smith, Anders; Nielsen, Kaspar Kirstein; Christensen, Dennis;
The effect of demagnetization on the magnetic properties of a rectangular ferromagnetic prism under non-uniform conditions is investigated. A numerical model for solving the spatially varying internal magnetic field is developed, validated and applied to relevant cases. The demagnetizing field is. -uniformity of the internal field, especially for non-constant temperature distributions and composite magnetic materials.
Moerel, J.-L.; Veraar, R.G.; Halswijk, W.H.C.; Pimentel, R.; Corriveau, D.; Hamel, N.; Lesage, F.; Vos, J.B.
Two research institutes TNO Defence, Security and Safety and DRDC-Valcartier have worked together on the improvement of modeling and simulation tools for the functioning of supersonic air intakes for realistic ramjet engines of tactical missiles. The emphasis laid on complex rectangular intake desig
Recent developments in the analysis of various waveguide components and feedhorns using Modal Analysis (Mode Matching Method) are summarized. A brief description of the theory is presented, and the important features of the method are pointed out. Specific examples in circular, rectangular. and coaxial waveguides are included, with comparisons between the theory and experimental measurements. Extensions to the methods are described.
The welding temperature field and deformation of parallel arrangement small-section rectangular tubes is calculated by using a non-contact model. After comparing the computed results with the experimentally measured results, it shows that there exist big errors when applying this model to the numerical simulation of small-section rectangular tube's welding temperature field and deformation. Based on a simple analysis of the errors, a contact model is presented. The heat transfer and stress analysis between small-section rectangular tubes and clamping fixture are simulated by using direct constraints method, and then the laws of the temperature distribution, which coincide with experiment, are obtained. A further numerical analysis of the stress and deformation are made, it shows that a "T" shaped stress-field is formed in the vicinity of the weld. As the stress-field departs from the centroid of tubes', this leads to the small rectangular tubes not only have a longitudinal deflection, but also have a transverse bending and deformation.
Noelia Ortiz; Francisco Falcone; Mario Sorolla
A simple and successful dual band patch linear polarized rectangular antenna design is presented. The dual band antenna is designed etching a complementary rectangular split-ring resonator in the patch of a conventional rectangular patch antenna. Furthermore, a parametric study shows the influence of the location of the CSRR particle on the radiation characteristics of the dual band antenna. Going further, a miniaturization of the conventional rectangular patch antenna and an enhancement of t.
Sangjin Jo; Hyunjin Choi; Beomsoo Shin; Sangyeol Oh; Jaehoon Lee
We present a simple coplanar waveguide- (CPW-) fed rectangular ring monopole antenna designed for dual-band wireless local area network (WLAN) applications. The antenna is based on a simple structure composed of a CPW feed line and a rectangular ring. Dual-band WLAN operation can be achieved by controlling the distance between the rectangular ring and the ground plane of the CPW feed line, as well as the horizontal vertical lengths of the rectangular ring. Simulated and measured data show tha.
Differential expansion (DE) for a Wilson loop average in representation $R$ is built to respect degenerations of representations for small groups. At the same time it behaves nicely under some changes of the loop, e.g. of some knots in the case of $3d$ Chern-Simons theory. Especially simple is the relation between the DE for the trefoil $3_1$ and for the figure eight knot $4_1$. Since arbitrary colored HOMFLY for the trefoil are known from the Rosso-Jones formula, it is therefore enough to find their DE in order to make a conjecture for the figure eight. We fulfil this program for all rectangular representation $R=[r^s]$, i.e. make a plausible conjecture for the rectangularly colored HOMFLY of the figure eight knot, which generalizes the old result for totally symmetric and antisymmetric representations.
A graphical method for determining the size of a resonant rectangular microstrip patch for a specified frequency is given. Using an expression obtained from the reflection coefficient of a transverse electromagnetic (TEM) wave in a semi-infinite microstrip patch, the resonance condition of a given mode for a patch of finite size is derived in a manner analogous to that of a rectangular. waveguide cavity. Radiation is shown to be in the form of both surface waves and space waves and is dependent on the angles of incidence for waves impinging onto the edges of the patch. By varying the aspect ratio, it is also possible to modify the Q factor of a resonant path. Analytical expressions for the resonant frequency and the Q factor are then derived under the assumption of a very thin substrate slab, encountered frequently in the application. Design curves in the form of the 'Argand diagram' are then presented for microstrip patches with fixed aspect ratios.
Resheidat, M.; Ghanma, M.; Sutton, C.; Chen, Wai-Fah
An exact analysis is carried out utilizing the parabola-rectangle stress-strain curve for concrete and a typical idealized stress-strain curve for steel to develop the moment-curvature relationship for biaxially loaded reinforced concrete rectangular column sections. Based on that, the flexural rigidity EI of the section is determined at the yield curvature. A computer program is written by FORTRAN 77 to handle the required computations. The influence of material properties, the effect of steel ratios, and the impact of axial loads on the EI estimation were investigated. This study leads to the development of a new equation to estimate the flexural rigidity EI of reinforced concrete biaxially loaded rectangular columns in which these factors were considered. It is shown that the new equation stems from the actual behavior of the column. Therefore, it is recommended for general use in the design of slender columns.
Full Text Available A coplanar waveguide fed dual-band circularly polarized rectangular slot antenna is presented. The proposed antenna consists of a rectangular metal frame acting as a ground and an S-shaped monopole as a radiator. The spatial distribution of the surface current density is employed to demonstrate that the circular polarization is generated by the S-shaped monopole which controls the path of the surface currents. An antenna prototype, having overall dimension 37 × 37 × 1 mm3, has been fabricated on FR4 substrate with dielectric constant 4.4. The proposed antenna achieves 10 dB return loss bandwidths and 3 dB axial ratio (AR in the frequency bands 2.39–2.81 GHz and 5.42–5.92 GHz, respectively. Both these characteristics are suitable for WLAN and WiMAX applications.
The paper presents a theoretical model to compute the end depth of a free overfall in steeply sloping rough rectangular channels. A momentum equation based on the Boussinesq approximation is applied to obtain the equation of the end depth. The effect ofstreamline curvature at the free surface is utilized to develop the differential equation for the flow profile upstream of the free overfall of a wide rectangular channel. As direct solutions for the end depth and flow profile cannot be obtained owing to implicit forms of the developed equations, an auto-recursive search scheme is evolved to solve these equations simultaneously. A method for estimation of discharge from the known end depth and Nikuradse equivalent sand roughness is also presented. Results from the present model correspond satisfactorily with experimental observations except for some higher roughnesses.
Full Text Available A nine-node isoparametric plate element in conjunction with first-order shear deformation theory is used for free vibration analysis of rectangular plates with central cutouts. Both thick and thin plate problems are solved for various aspect ratios and boundary conditions. In this article, primary focus is given to the effect of rotary inertia on natural frequencies of perforated rectangular plates. It is found that rotary inertia has significant effect on thick plates, while for thin plates the rotary inertia term can be ignored. It is seen that the numerical convergence is very rapid and based on comparison with experimental and analytical data from literature, it is proposed that the present formulation is capable of yielding highly accurate results. Finally, some new numerical solutions are provided here, which may serve as benchmark for future research on similar problems.
Sutherland, Adam P; Miller, Katrina R; Seifahrt, Andreas; Bean, Jacob L
We report on the scrambling performance and focal-ratio-degradation (FRD) of various octagonal and rectangular fibers considered for MAROON-X. Our measurements demonstrate the detrimental effect of thin claddings on the FRD of octagonal and rectangular fibers and that stress induced at the connectors can further increase the FRD. We find that fibers with a thick, round cladding show low FRD. We further demonstrate that the scrambling behavior of non-circular fibers is often complex and introduce a new metric to fully capture non-linear scrambling performance, leading to much lower scrambling gain values than are typically reported in the literature (
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