Existence and asymptotic properties of aerotaxis model with the Fokker–Planck type diffusion

In this paper, we consider Fokker–Planck type diffusion aerotaxis equations which resemble the usual aerotaxis equations. In view of well-posedness, its own special diffusion structure enables us to take advantage. In two dimensions, we show the existence of global classical solutions under some appropriate conditions. In addition, the stabilization property of the solution is studied, as time approaches infinity. In three dimensions, we prove the existence of global weak solutions.     

On the Ulam stability of Jensen and Jensen type mappings on restricted domains

In 1941 Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 Bourgin was the second author to treat this problem for additive mappings. In 1982-1998 Rassias established the Hyers-Ulam stability of linear and nonlinear mappings. In 1983 Skof was the first author to solve the same problem on a restricted domain. In 1998 Jung investigated the Hyers-Ulam stability of more general mappings on restricted domains. In this paper we introduce additive mappings of two forms: of “Jensen” and “Jensen type,” and achieve the Ulam stability of these mappings on restricted domains. Finally, we apply our results to the asymptotic behavior of the functional equations of these types.     

非平凡正规子群的阶相同的有限群

本文研究了非平凡正规子群的阶相同的有限群. 给出了非平凡正规子群唯一的可解群的结构. 对非可解群的情况, 我们也给出了它的刻画.     

On the Ulam stability of mixed type mappings on restricted domains

In 1941 D.H. Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 D.G. Bourgin was the second author to treat the Ulam problem for additive mappings. In 1982-1998 we established the Hyers-Ulam stability for the Ulam problem of linear and nonlinear mappings. In 1983 F. Skof was the first author to solve the Ulam problem for additive mappings on a restricted domain. In 1998 S.M. Jung investigated the Hyers-Ulam stability of additive and quadratic mappings on restricted domains. In this paper we improve the bounds and thus the results obtained by S.M. Jung, in 1998. Besides we establish the Ulam stability of mixed type mappings on restricted domains. Finally, we apply our recent results to the asymptotic behavior of functional equations of different types.     

Capacitated emergency facility siting with multiple levels of backup

In many service systems, the primary objective is to provide continuous service and/or service within a prespecified time interval. In the public sector, emergency service systems fit into this category. In the private sector, systems providing repair service to critical production facilities and computers constitute another example. In these systems, the concept of multiple service facilities providing backup to each other becomes an important element in the design process. In this paper, we study the capacitated facility siting problem with multiple levels of backup coverage. The problem is formulated as a mathematical program; an efficient solution procedure is developed and computational experiments are reported.     

Projective modules and Hilbert spaces with a Nevanlinna-Pick kernel

In this paper we solve a mapping problem for a particular class of Hilbert modules over an algebra multipliers of a diagonal Nevanlinna-Pick (NP) kernel. In this case, the regular representation provides a multiplier norm which induces the topology on the algebra. In particular, we show that, in an appropriate category, a certain class of Hilbert modules are projective. In addition, we establish a commutant lifting theorem for diagonal NP kernels.

     

某些算子代数的可加导子

本文主要研究非Ｉｎ型因子ＶｏｎＮｅｕｍａｎｎ代数的Ｎｅｓｔ子代数及两元生成格自反代数的可加导子的自动线性性和连续性问题．通过给出一个含无限维交换ＶｏｎＮｅｕｍａｎｎ子代数的代数上可加导子定理，证明了非Ｉｎ型因子ＶｏｎＮｅｕｍａｎｎ代数的Ｎｅｓｔ子代数上的可加导子是线性的，从而是自动连续的．这推广并简化证明了作者［１］中的主要结果．对于在非自伴算子代数研究中起重要的两元生成格自反代数，给出了所有可加导子是线性导子的充分必要条件．     

Schadenreservierung im Licht stochastischer Prozesse

In this article loss-reserves are handled with the methods and models for financial assets. In particular, the stochastic processes number of payments and size of the payment are modelled by an (inhomogeneous) poisson-process resp. an geometric brownian motion. In this model the cumulative payments are given by the stochastic integral. In an first step the conditional expectation, i.?e. the best estimator, of the payment-process is derived, where in an second step this expression is approximated by observations. Furthermore, the mean-square-error and an estimator of this expression is given.     

Summatory Functions of Digital Sums Occurring in Cryptography

Morain and Olivos gave two algorithms that allow fast exponentiation in elliptic curve cryptosystems. These algorithms are based on representations of integers in certain redundant binary number systems. In this paper we consider the weight and the sum of digits function of these representations. In particular, we give formulas for their summatory functions. In the proofs we use the Mellin-Perron formula. In order to apply this formula, we have to compute the analytic continuation of a class of Dirichlet series.     

Convergence to steady state of solutions of the euler equations,I

In this paper we analyze the convergence to steady state of solutions of the compressible and the incompressible isentropic Euler equations in two space dimensions. In the compressible case, the original equations do not converge. We replace the equation of continuity with an elliptic equation for the density, obtaining a new set of equations, which have the same steady solution. In the incompressible case, the equation of continuity is replaced by a Poisson equation for the pressure. In both cases, we linearize the equations around a steady solution and show that the unsteady solution of the linearized equations converges to the steady solution, if the steady solution is sufficiently smooth. In the proof we consider how the energy of the time dependent part developes with time, and find that it decrease exponentially.     

A review of open queueing network models of manufacturing systems

In this paper we review open queueing network models of manufacturing systems. The paper consists of two parts. In the first part we discuss design and planning problems arising in manufacturing. In doing so we focus on those problems that are best addressed by queueing network models. In the second part of the paper we describe developments in queueing network methodology. We are primarily concerned with features such as general service times, deterministic product routings, and machine failures — features that are prevalent in manufacturing settings. Since these features have eluded exact analysis, approximation procedures have been proposed. In the second part of this paper we review the developments in approximation procedures and highlight the assumptions that underlie these approaches.     

ISOMORPHISMS OF CIRCULANT DIGRAPHS OF DEGREE 3

Abstract. In this paper, we introduce a new approach to characterize the isomor-phisms of circulant digraphs. In terms of this method, we completely determine the isomorphic classes of circulant digraphs of degree 3. In psrticular, we characterize those circulant digraphs of degree 3 which don‘‘t satisfy JkdAm‘‘s conjectttre.     

The Andrews–Sellers family of partition congruences

In 1994, James Sellers conjectured an infinite family of Ramanujan type congruences for 2-colored Frobenius partitions introduced by George E. Andrews. These congruences arise modulo powers of 5. In 2002 Dennis Eichhorn and Sellers were able to settle the conjecture for powers up to 4. In this article, we prove Sellers’ conjecture for all powers of 5. In addition, we discuss why the Andrews–Sellers family is significantly different from classical congruences modulo powers of primes.     

当极限方程有奇性时高阶线性常微分方程柯西问题解的渐近式*

本文研究当极限方程有奇性时,高阶线性常微分方程柯西问题解的渐近式.为了构造解的渐近式,我们把区域分为三个小区域,在每个小区域,微分方程的解是不同的.     

The quadratic convergence of the topological epsilon algorithm for systems of nonlinear equations

In this work we consider the topological epsilon algorithm for solving systems of nonlinear equations. In section 2, a sufficient condition for its quadratic convergence is given. In section 3, some geometrical remarks about this condition are made.     

应用复合极值理论计算VaR1

本文介绍了一种复合极值理论,并将其应用到VaR的计算上。实际中大的损失发生的频率也是风险的一种度量,在应用复合极值理论方法计算VaR时,我们第一次将在一定时期内金融资产的损失率超过一定阈值的次数的分布和收益率的分布结合了起来,对欧元/人民币、日元/人民币两种汇率进行了VaR的计算,经过实证分析,得到了一些有意义的结果。     

Differentialgleichungen in Jordantripelsystemen

In the first section we summarize some properties of Jordan triples. Then we state some rules about differential calculus of rational functions. In the second section we generalize results about norms and traces of Jordan algebras. In the next section we define a group of birational functions belonging to a Jordan triple and characterize this group by differential equations. A special form of these differential equations was given by M. Koecher (see [3], page 44, Theorem 2.1.). In the last section we give some examples. In particular one obtains the exceptional group E₆ as a homomorphic image of a transformation group.     

Properties of two Shannon’s ciphers

In 1949 Shannon published the famous paper “Communication theory of secrecy systems” where he briefly described two ciphers, but did not investigate their properties. In this note we carry out information-theoretical analysis of these ciphers. In particular, we propose estimations of the cipher equivocation and the probability of correct deciphering without key.     

Complex Dynamics in a Hysteretic Relay Feedback System with Delay

Relay feedback systems are used to control engineering devices. In practice the switching between different functional forms of the system is never instantaneous, but takes place after a small delay. In this paper we analyse the dynamics and bifurcations of a representative example of such systems. In the absence of delay, negative feedback results only in unimodal symmetric limit cycles, but positive feedback can lead to aperiodic trajectories and chaos. In the presence of delay, the system can behave as an equivalent system without delay, provided that the delay is small in a sense which we define precisely. For larger delays, we identify a new bifurcation phenomenon, an event collision, where the delayed switching manifold intersects the relay hysteretic lines. In this case the dynamics become much more complicated.