Semiconductor deposition on a metallic base near a microprobe in a strong electric field

Computer simulation results are reported for the width of a semiconductor strip deposited on a metallic base near a microprobe in a strong electric field. The strip width is a function of the microprobe head radius and the potential difference in the working zone.V. M. Glushkov Institute of Cybernetics of the Ukrainian Academy of Sciences. Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 74, pp. 49–53, 1992;     

Uniform estimation of a segment function by a polynomial strip of fixed width

The best uniform approximation of a segment function on an interval by a polynomial strip of fixed width (in ordinate) with respect to the Hausdorff measure at each point of the interval is considered. Ranges of strip widths are indicated for which this problem gives outer and inner estimates for the graph of the segment function in terms of the polynomial strip, and a range of strip widths is given for which the problem has an independent value. A necessary and sufficient condition for the existence of a solution and uniqueness conditions are obtained in a form comparable to the Chebyshev alternance. A range of strip widths is indicated for which the solution of the problem is always unique. Certain variational properties of the solution are examined.     

Mathematical model of metal deposition on a dielectric base near a microprobe in a strong electric field

A mathematical model is proposed for computing the width of a metal strip deposited on a dielectric surface near a microprobe in a strong electric field. The deposited strip width is a function of the geometrical parameters of the microprobe and the potential difference in the working zone.V. M. Glushkov Institute of Cybernetics of the Ukrainian Academy of Sciences. Institute of Electrodynamics of the Ukrainian Academy of Sciences. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 74, pp. 53–60, 1992;     

An approximation of the thermal field in a continuous casting process of a thin metal layer

We consider the problem of a phase change in a continuous casting process: molten bronze is poured on to a moving steel strip cooled from below, in order to solidify the bronze. An estimate of the width of the solidification zone, depending on the thickness of the strip and on the casting velocity, is obtained, neglecting conduction in the direction of the strip motion.     

Asymptotic Expansions for the Distribution of the Crossing Number of a Strip by Sample Paths of a Random Walk

The complete asymptotic expansions are obtained for the distribution of the crossing number of a strip in n steps by sample paths of an integer-valued random walk with zero mean. We suppose that the Cramer condition holds for the distribution of jumps and the width of strip increases together with n; the results are proven under various conditions on the width growth rate. The method is based on the Wiener–Hopf factorization; it consists in finding representations of the moment generating functions of the distributions under study, the distinguishing of the main terms of the asymptotics of these representations, and the subsequent inversion of the main terms by the modified saddle-point method.     

Diffraction of a sinusoidal impulse by a rigid strip

The diffraction of a sinusoidal impulse by an absolutely rigid strip is considered. Approximate formulas are obtained for the field measured at large distances from the strip in the direction of the incident impulse (the case of location). The results are expressed in terms of Fresnel integrals. The possibility of determining the width of the strip and the angle between it and the direction of the incident impulse or the basis of the envelope of the location field is discussed. Graphs of the envelopes for certain specific cases are presented.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 62, pp. 39–47, 1976.The author is grateful to D. P. Kouzov for his attention to the work.     

功能梯度材料有限宽板的反平面断裂问题研究

研究了功能梯度材料有限宽板中与板边平行的III型裂纹问题．假设材料的剪切模量沿板宽度方向呈指数规律变化,利用Fourier变换将问题描述为奇异积分方程,并进一步将未知的位错密度函数表示为Chebyshev多项式的级数式,从而将奇异积分方程化为线性代数方程组进行配点数值求解．基于数值结果,讨论了材料非均匀性参数、板和裂纹的几何参数等对应力强度因子（SIF）的影响．研究表明,SIF随裂纹长度的增大而增大,随裂纹所在区域材料刚度的增大而减小;板越窄,SIF对非均匀性参数的变化越敏感,且变化规律也越复杂．随着非均匀性参数的增大,SIF既可能增大也可能减小还可能基本保持不变,这主要取决于板的相对宽度和裂纹的相对位置．当裂纹位于板的中央或当板较宽时,SIF对非均匀性参数的变化都不太敏感．     

Asymptotic expansions for the distribution of the crossing number of a strip by a Markov-modulated random walk

We obtain complete asymptotic expansions for the distribution of the crossing number of a strip in n steps by sample paths of a random walk defined on a finite Markov chain. We assume that the Cramér condition holds for the distribution of jumps and the width of the strip grows with n. The method consists in finding factorization representations of the moment generating functions of the distributions under study, isolating the main terms in the asymptotics of the representations, and inverting those main terms by the modified saddle-point method.     

Asymptotics of the Eigenelements of the Laplace Operator when the Boundary-Condition Type Changes on a Narrow Flattened Strip

In this paper, the method of matching asymptotic expansions is used to construct an asymptotics (in a small parameter) of the eigenvalues and eigenfunctions of the Laplace operator in a domain when the boundary-condition type changes on a narrow flattened strip, provided that on the narrow strip of the boundary a Neumann condition is given and on the remaining part of the boundary a Dirichlet condition is given. The width of the strip is taken as the small parameter.     

New Upper Bound on the Transversal Width of T(3)-Families of Discs

A result of Eckhoff implies that to every finite T(3)-family of pairwise disjoint copies of a closed disc of unit diameter there exists a strip of width 1 meeting all members of the family. Our goal is to generalize this result giving a stricter upper bound by proving that the narrowest transversal strip has width < 0.65.     

The strip of minimum width covering a centrally symmetric set of points

In this paper the following is proved: let be a centrally symmetric set of points, such that the distance between any pair of points is at least 1 and every three of them can be covered by a strip of width 1. Then there is a strip of width √2 covering . Supported by CONACYT, SNI 38848     

A branch-and-price algorithm for the two-dimensional level strip packing problem

The two-dimensional level strip packing problem (2LSPP) consists in packing rectangular items of given size into a strip of given width divided into levels. Items packed into the same level cannot be put on top of one another and their overall width cannot exceed the width of the strip. The objective is to accommodate all the items while minimizing the overall height of the strip. The problem is -hard and arises from applications in logistics and transportation. We present a set covering formulation of the 2LSPP suitable for a column generation approach, where each column corresponds to a feasible combination of items inserted into the same level. For the exact optimization of the 2LSPP we present a branch-and-price algorithm, in which the pricing problem is a penalized knapsack problem. Computational results are reported for benchmark instances with some hundreds items.     

Parallel greedy algorithms for packing unequal circles into a strip or a rectangle

Given a finite set of circles of different sizes we study the strip packing problem (SPP) as well as the Knapsack Problem (KP). The SPP asks for a placement of all circles within a rectangular strip of fixed width so that the variable length of the strip is minimized. The KP requires packing of a subset of the circles in a given rectangle so that the wasted area is minimized. To solve these problems some greedy algorithms were developed which enhance the algorithms proposed by Huang et al. (J Oper Res Soc 56:539–548, 2005). Furthermore, the new greedy algorithms were parallelized using a master slave approach. The resulting parallel methods were tested using the instances introduced by Stoyan and Yaskov (Eur J Oper Res 156:590–600, 2004). Additionally, two sets of 128 instances each for the SPP and for the KP were generated and results for these new instances are also reported.     

Asymptotic formula for an eigenvalue of the dirichlet problem in a cranked waveguide

The asymptotic behavior of an eigenvalue of the Dirichlet problem for a spectral Helmholtz equation in a two-dimensional cranked acoustic waveguide with yielding walls or in a quantum waveguide is obtained. A waveguide is thought of as a cranked strip, but the boundary value problem is posed in a straight strip of unit width with wedge-shaped notches, with appropriate conjugation conditions on the edges of the notches, which provide for a smooth wave field after the initial form of the waveguide is restored. The bend angles are assumed to be small; i.e., the wedge-shaped notches are supposed to be thin, the asymptotic behavior is built from the corresponding small geometric parameter.     

一般随机Dirichlet级数所表示的整函数

该文研究了一般随机Dirichlet级数的所表示整函数增长性和值分布，得出了重要结论：在适当条件下，任何水平带形上或水平线上增长级与全面上相同，对于ρ随机Dirichlet级数(0＜ρ＜∞)a.s.在任何宽为〖SX(〗π[]ρ〖SX)〗的水平带形内，至少有一条ρ级没有有穷例外值的Borel线。     

A bound for the distortion near the boundary in the conformal mapping of infinite strips

A bound is given for the modulus of the derivative of the function effecting the conformal transformation of an infinite strip of constant width into a strip with curvilinear boundaries which are concave in the neighborhood of an infinitely distant point.Translated from Matematicheskie Zametki, Vol.4, No. 6, pp. 723–728, December, 1968.     

A block-based layer building approach for the 2D guillotine strip packing problem

We examine the 2D strip packing problems with guillotine-cut constraint, where the objective is to pack all rectangles into a strip with fixed width and minimize the total height of the strip. We combine three most successful ideas for the orthogonal rectangular packing problems into a single coherent algorithm: (1) packing a block of rectangles instead of a single rectangle in each step; (2) dividing the strip into layers and pack layer by layer; and (3) unrolling and repacking the top portion of the solutions where usually wasted space occurs. Computational experiments on benchmark test sets suggest that our approach rivals existing approaches.     

A heuristic algorithm for the strip packing problem

The two-dimensional strip packing problem is to pack a given set of rectangles into a strip with a given width and infinite height so as to minimize the required height of the packing. From the computational point of view, the strip packing problem is an NP-hard problem. With the B*-tree representation, this paper first presents a heuristic packing strategy which evaluates the positions used by the rectangles. Then an effective local search method is introduced to improve the results and a heuristic algorithm (HA) is further developed to find a desirable solution. Computational results on randomly generated instances and popular test instances show that the proposed method is efficient for the strip packing problem.     

Nonattacking Queens in a Rectangular Strip

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.     

FEM analysis for residual stress prediction in hot rolled steel strip during the run-out table cooling

With the increasing demand of higher quality hot rolled strips, flatness defects occurred on the strips during the cooling process on the run-out table have received significant attention and should be considered in the online shape control model. Non-uniform temperature distribution and cooling across the strip width are the main reasons why the strip becomes unflatten after cooling process although the strip is rolled flat at the finishing mill. A thermal, microstructural and mechanical coupling analysis model for predicting flatness change of steel strip during the run-out table cooling process was established using ABAQUS Finite Element Software. In this model, Esaka phase transformation kinetics model was employed to calculate the phase transformation, and coupled with temperature calculation by means of the user subroutine program HETVAL. An elasto-plasticity constitutive model of the material, in which conventional elastic and plastic strains, thermal strain, phase transformation strain and transformation induced plastic strain were taken into account, was derived and realized using the user subroutine program UMAT. The conclusion that the flatness of the steel strip will develop to edge wave defect under the functions of the different thermal and microstructural behaviors across strip width direction during the run-out table cooling procedure was acquired through the analysis results of this model. The calculation results of this analysis model agree with the actual measurements and observation, therefore this model has a high accuracy. To better control the flatness quality of hot rolled steel strip, the shape compensation control strategy of slight center wave rolling is proposed based on the analysis result. This control strategy has been verified by actual measurements, and applied in actual production.