Design of manufacturing systems using queueing models

Design issues in various types of manufacturing systems such as flow lines, automatic transfer lines, job shops, flexible machining systems, flexible assembly systems and multiple cell systems are addressed in this paper. Approaches to resolving these design issues of these systems using queueing models are reviewed. In particular, we show how the structural properties that are recently derived for single and multiple stage queueing systems can be used effectively in the solution of certain design optimization problems.Supported in part by the Natural Sciences and Engineering Research Council of Canada via Operating and Strategic Grants on Modeling and Analyses of Production Systems and Modeling and Implementation of Just-in-Time Cells.Supported in part by the NSF Grants ECS-8811234 and DDM-9113008 and by Sloan Foundation Grants for the Consortium for Competitiveness and Cooperation and for the study on Competitive Semiconductor Manufacturing.     

The Cantor-Lebesgue and Denjoy-Luzin properties for double systems of functions

{ _mn ():, =1, 2, ...}, (X, , ). , ( ) , . { _mn }. . — — ( ) .     

Нормаляный поридок аддитявных арифметичыских функций на множестве дсдвинутых” пностых чясел

.      

Stream vectors in three dimensional aerodynamics

Summary This work deals with the decomposition of a vector fieldu intou=×+. Non homogeneous boundary conditions on or are investigated; applications to the computation of inviscid flows are given; finally a conforming finite element implementation is studied and tested.     

Round-off error analysis of iterations for large linear systems

Summary We deal with the rounding error analysis of successive approximation iterations for the solution of large linear systemsA _x =b. We prove that Jacobi, Richardson, Gauss-Seidel and SOR iterations arenumerically stable wheneverA=A ^*>0 andA has PropertyA. This means that the computed resultx _k approximates the exact solution with relative error of order A·A ^–1 where is the relative computer precision. However with the exception of Gauss-Seidel iteration the residual vector Ax _k –b is of order A² A ^–1 and hence the remaining three iterations arenot well-behaved.This work was partly done during the author's visit at Carnegie-Mellon University and it was supported in part by the Office of Naval Research under Contract N00014-76-C-0370; NR 044-422 and by the National Science Foundation under Grant MCS75-222-55     

On the angular derivative and univalence

f . , , — , A f f(). , , f() 0 . , , ,A , f . , f() - f() . , , . (1976) ( ¦f(z)¦<1) . . (1969) ( ).     

Bochner-Riesz means of functions in weak-L p

The Bochner-Riesz means of order 0 for suitable test functions on ^N are defined via the Fourier transform by . We show that the means of the critical index , do not mapL ^p,( ^N ) intoL ^p,( ^N ), but they map radial functions ofL ^p,( ^N ) intoL ^p,( ^N ). Moreover, iff is radial and in theL ^p,( ^N ) closure of test functions,S _R f(x) converges, asR+, tof(x) in norm and for almost everyx in ^N . We also observe that the means of the function|x| ^–N/p, which belongs toL ^p,( ^N ) but not to the closure of test functions, converge for nox.     

An algorithm for constructing an optimal structural schedule

The article is devoted to the problem of finding an optimal schedule for a class of functionals ƒ which allows for the existence of a structural set of activities. The functionalƒ(R), where, is defined in the following way: where {_i(t)} is a structural set of functions, and the function F is defined on any finite set of arguments and satisfies the following conditions: 1)F(x)=(x); 2) F(x₁,x₂)=(x₁,x₂), F(x₁,x₂,...x₃)= (x₁, F(x₂,...,x_s)), S2; 3) and do not decrease in each of their arguments, and moreover, 3a) strictly increases with the increase of both arguments, 3b) if (x₁,x₂)>(x₁, x₂ (x₂, x₃)> (x₂,x₃), then F(x₁,x₂,x₃)>F(x₁,x₂,x₃).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 124, pp. 5–20, 1983.     

On term by term dyadic differentiability of Walsh series

. . . . : {ja _j },j=1,2,... — , f(x) , , f ^[1](x) — f .     

Some extensions of the Hewitt-Savage zero-one law

Summary Let denote the class of infinite product probability measures = ₁× ₂× defined on an infinite product of replications of a given measurable space (X, A), and let denote the subset of for which (A) =0 or 1 for each permutation invariant event A. Previous works by Hewitt and Savage, Horn and Schach, Blum and Pathak, and Sendler (referenced in the paper) discuss very restrictive sufficient conditions under which a given member , of belongs to . In the present paper, the class is shown to possess several closure properties. E.g., if and _{0 n} for some n 1, then ₀× ₁× ₂×.... While the current results do not permit a complete characterization of they demonstrate conclusively that is a much larger subset of than previous results indicated. The interesting special case X={0,1} is discussed in detail.Research supported by the National Science Foundation under grant No. MCS75-07556     

Imbedding problem with non-Abelian kernel of order p4

This paper considers the imbedding problem for numerical fields and p-groups with nonabelian kernel of order p⁴, two generators and , and defining relations =1, ^p=1, [,,]=1, and [,,]= 1. For p=2 and almost always for odd p, the Hasse principle is valid, and the problem is solvable if and only if all related local problems are solvable. Counterexamples in which the Hasse principle is not valid are constructed for some exceptional cases.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 175, pp. 46–62, 1989.     

Sets of uniqueness and closed subgroups in Vilenkin groups

, ( ) . , : , , .

---

---

This research was partially supported by National Science Foundation under grant INT-8400708.     

On the Riemann derivatives ofC sP-integrable functions

[4] , .     

Some inequalities about the covering radius of Reed-Muller codes

Let R(r, m) be the rth order Reed-Muller code of length 2 ^m , and let (r, m) be its covering radius. We prove that if 2 k m - r - 1, then (r + k, m + k) (r, m + 2(k - 1). We also prove that if m - r 4, 2 k m - r - 1, and R(r, m) has a coset with minimal weight (r, m) which does not contain any vector of weight (r, m) + 2, then (r + k, m + k) (r, m) + 2k(. These inequalities improve repeated use of the known result (r + 1, m + 1) (r, m).This work was supported by a grant from the Research Council of Wright State University.     

On Gibbs' phenomenon for Riesz spherical means of multiple Fourier integrals and Fourier series

- - , .     

Phragmén-Lindelöf theorems for second-order quasilinear elliptic equations

Analogues are formulated of the well-known, in the theory of analytic functions, Phragmen-Lindelöf theorem for the gradients of solutions of a broad class of quasilinear equations of elliptic type. Examples are given illustrating the accuracy of the results obtained for the gradients of solutions of the equations of the form div(|U|^–2u)=f(x, u, u), where f(x, u, u) is a function locally bounded in ²ⁿ⁺¹. f(x, 0, u)=0, uf(x, u, u) c¦u¦1+q(1+ ¦u|), > 1, c > 0, q > 0, is an arbitrary real number, and n >- 2. The basic role in the technique employed in the paper is played by the apparatus of capacitary characteristics.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 10, pp. 1376–1381, October, 1992.The author sincerely appreciates E. M. Landis's permanent attention and numerous useful discussions.     

A result from diophantine approximation which has applications in economics

We say that a real number allows poor approximations if we can find 0<=()<1 and a sequence of integers n₁2<... such that for all rationals p/q with qn. we have |–.p/q| > Kn _j ^–l– where K is a constant depending only on .In this note we prove that the set of numbers which allow poor approximations are precisely the very well-approximable numbers.The existence of numbers with poor approximations has been used by Cheng [1] to show the existence of a dense set of economies whose cone converges to the Walras equilibrium as slowly as 0(n^–1/2–) after n replications.     

Sur un mouvement particulier d'un profil muni d'une cavité fermée par un couvercle élastique et remplie de liquide

Resumé L'auteur considère le mouvement d'un profil sans pointe pesant, possédant une cavité fermée par un couvercle élastique et contenant un liquide parfait, dans un fluide parfait incompressible, en mouvement irrotationnel, au repos à l'infini. Dans la première partie, il forme les équations du mouvement du système, démontre l'existence de mouvements de translation horizontale uniforme du profil avec repos relatif du liquide et du couvercle et établit que l'un d'eux, noté mouvement _o est stable.Dans le deuxiéme partie, il étudie les petits mouvements du système voisins du mouvement _o.

---

The motion of a heavy profile without sharp edge, with a cavity closed by an elastic cover and containing an in viscid liquid in an inviscid incompressible fluid in irrotational motion (at rest at infinity) is investigated.In the first part the equations of motion of the system are given. The existence of motions of horizontal uniform translation of the profile with liquid and cover at rest is proved. The stability of one of them, denoted by motion _o, is established. The second part deals with the study of the small oscillations of the system in the vicinity of the motion _o.

     

Investigation of Haar and Franklin series in Hardy spaces

(L ¹,H) (, ) , ; H — . , , L ¹ . [13] , . , , , .     

Morera type theorems on the unit disc

, . . : , , , , .