Multiprocessor systems with reserves and preferences

Two models involving multiprocessor systems with two different groups of processors are examined. In the first model, the processors which are in use break down from time to time; one of the two groups is used only when the other one is entirely inoperative. In the second model, the breakdowns are replaced by a Poisson stream of jobs. Again, one group of processors is used in preference to the other one. In both cases, the analysis is based on finding a polynomial in two variables which satisfies a partial differential-functional equation. Exact solutions are obtained.     

需求受价格影响的三层供应链协调模型

针对由一个制造商、一个批发商和一个零售商构成的三层供应链系统,在随机市场需求且需求受商品零售价格影响的情况下,研究了零售商如何定价和确定订货量.在此基础上给出了一个能使供应链系统达到完美协调的收益分享合约策略,最后给出了数值例子.     

Rearrangements of series in the Walsh system

In the paper one considers the convergence of some rearrangements of series in the Walsh-Paley system. In particular, one shows that the Walsh and Walsh-Kaczmarz systems are convergence systems.     

Class number one problem for normal CM-fields

It is known that if we assume the Generalized Riemann Hypothesis, then any normal CM-field with relative class number one is of degree less than or equal to 96. All normal CM-fields of degree less than 48 with class number one are known. In addition, for normal CM-fields of degree 48 the class number one problem is partially solved. In this paper we will show that under the Generalized Riemann Hypothesis there is no more normal CM-fields with class number one except for the possible fields of degrees 64 or 96.     

Dispersive blow-up for nonlinear Schrödinger equations revisited

The possibility of finite-time, dispersive blow-up for nonlinear equations of Schrödinger type is revisited. This mathematical phenomena is one of the conceivable explanations for oceanic and optical rogue waves. In dimension one, the fact that dispersive blow up does occur for nonlinear Schrödinger equations already appears in [9]. In the present work, the existing results are extended in several ways. In one direction, the theory is broadened to include the Davey–Stewartson and Gross–Pitaevskii equations. In another, dispersive blow up is shown to obtain for nonlinear Schrödinger equations in spatial dimensions larger than one and for more general power-law nonlinearities. As a by-product of our analysis, a sharp global smoothing estimate for the integral term appearing in Duhamel's formula is obtained.     

Multiple SLE and the complex Burgers equation

In this note we ask whether one can take the limit of multiple SLE as the number of slits goes to infinity. In the special case of n slits that connect n points of the boundary to one fixed point, one can take the limit of the Loewner equation that describes the growth of those slits in a simultaneous way. In this case, the limit is a deterministic Loewner equation whose vector field is determined by a complex Burgers equation.     

Stability of Periodic Solutions Generated by Hopf Points Emanating from a Z＿2－symmetry－breaking Takens－Bogdanov Point

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Numerical quenching for the semilinear heat equation with a singular absorption

In this paper we study the numerical approximation for the heat equation with a singular absorption. We prove that the numerical quenching rate coincides with the continuous one. We also see that the quenching time and the quenching set converge to the continuous one. In fact, under some restriction on the initial data, the numerical quenching coincides with the continuous one. Finally, we give some numerical results to illustrate our analysis.     

Optimal control of a one product recovery system with backlogging

In this paper a product recovery system for one product is investigated.The system contains one inventory for returned and recoverableitems and one for serviceable items. Demands are satisfied fromserviceable inventory where backlogging of demands is allowed.In addition, there is the possibility of disposal for the returnedproducts. We assume deterministic but dynamic return and demandrates and a linear cost structure. The Pontryagin maximum principleis used to determine the optimal production, remanufacturingand disposal policy.     

A Remark on a Fourier Bounding Method of Proof for Convergence of Sums of Periodograms

This paper studies sums of periodograms in a random field setting. In a one dimensional or time series setting these can be studied using a method of cumulants, as done by Brillinger. This method does not carry over well to the random field case. Instead one should apply an argument as used by Rosenblatt. In order to have asymptotically correct confidence intervals, one needs to center these sums properly in the random field case.     

Schur rings and non-symmetric association schemes on 64 vertices

In this paper we enumerate essentially all non-symmetric association schemes with three classes, less than 96 vertices and with a regular group of automorphisms. The enumeration is based on a computer search in Schur rings. The most interesting cases have 64 vertices.In one primitive case and in one imprimitive case where no association scheme was previously known we find several new association schemes. In one other imprimitive case with 64 vertices we find association schemes with an automorphism group of rank 4, which was previously assumed not to be possible.     

The enumeration of several classes of hexagonal systems

Ahexagonalsystemisafiniteconnectedplanegraphwithnocutvertexinwhicheveryinteriorfaceisboundedbyaregularhexagonofsidelengthone.AhexagonalsystemHissaidtobeacata-condensedhexagonalsystemifeaChvertexofHisontheboundaryofH;otherwise,apert-condensedhexagonalsystem.Chemistsusuallycallthembenzenoidsystems,andsomemathematicianscallthempolyhexgraphs.Chemistsareillterestedinthistakeofgraphsandtheenumerationofthemsincetheyrepreselltthecarbonatomskeletongraphsofbenzenoidhydrocarbons[2--31.Ontheotherhand,th…     

On unequal powers of primes and powers of 2

We consider Linnik’s type of the Waring–Goldbach problem with unequal powers of primes. In particular, it is proved that every sufficiently large even integer can be represented as a sum of one prime, one square of prime, one cube of prime, one fourth power of prime and 18 powers of 2.     

Lower bounds on the number of scattering poles under lines parallel to the axis

We provide lower bounds in slab domains on the number of scattering poles, generated by two different types of periodic non-hyperbolic rays. For the first one all eigenvalues of the corresponding Poincaré map are equal to one and for the second one two of the eigenvalues are equal to one and two are different from one. In the second case we find also the closest to the real axis “line of poles”     

Nonlinear equations of a variable type

In the paper one gives a survey of the investigations regarding, basically one-dimensional, model equations of the Navier-Stokes type with a variable nonlinear viscosity, including sign-changing viscosity. For concrete dependences of the viscosity on the velocity gradient, one establishes a priori estimates, one carries out a numerical investigation and one formulates results regarding the uniqueness of the solution.     

微积分学中中值定理的统一证明

由一个定理的结论,给出Lagrange中值定理,Cauchy中值定理,积分中值定理和Taylor中值定理的统一证明及一个计算待定型极限的方法.     

Mittag-Leffler vector random fields with Mittag-Leffler direct and cross covariance functions

In terms of the two-parameter Mittag-Leffler function with specified parameters, this paper introduces the Mittag-Leffler vector random field through its finite-dimensional characteristic functions, which is essentially an elliptically contoured one and reduces to a Gaussian one when the two parameters of the Mittag-Leffler function equal 1. Having second-order moments, a Mittag-Leffler vector random field is characterized by its mean function and its covariance matrix function, just like a Gaussian one. In particular, we construct direct and cross covariances of Mittag-Leffler type for such vector random fields.     

Bifurcation of rough heteroclinic loop with orbit and inclination flips

In this paper, we are concerned with the heteroclinic loop bifurcations accompanied by one orbit flip and one inclination flip under some roughness conditions. The existence of one 1-periodic orbit, one 1-homoclinic orbit, two 1-periodic orbits, one double 1-periodic orbit is obtained, respectively, approximate expressions of the corresponding bifurcation curves (or surfaces) and the corresponding bifurcation graphs under nontwisted or twisted conditions are also given.     

Minimax systems

The variational approach to solving nonlinear problems eventually leads to the search for critical points of related functionals. In case of semibounded functionals, one can look for extrema. Otherwise, one is forced to use minimax methods. There are several approaches to such methods. In this paper we unify these approaches providing one theory that works for all of them. The usual approach has used Palais-Smale sequences. We show that all of them lead to Cerami sequences as well. Applications are given.     

树指标马氏链的一个强极限定理

树指标随机过程已成为近年来发展起来的概率论的研究方向之一.强极限定理一直是国际概率论界研究的中心课题之一.研究给出了一类非齐次树上马氏链的一个强极限定理.