Occupation times for the finite buffer fluid queue with phase-type ON-times

In this short communication we study a fluid queue with a finite buffer. The performance measure we are interested in is the occupation time over a finite time period, i.e., the fraction of time the workload process is below some fixed target level. Using an alternating renewal sequence, we determine the double transform of the occupation time; the occupation time for the finite buffer M/G/1 queue with phase-type jumps follows as a limiting case.     

Minimisers of the Allen–Cahn equation and the asymptotic Plateau problem on hyperbolic groups

We investigate the existence of non-constant uniformly-bounded minimal solutions of the Allen–Cahn equation on a Gromov-hyperbolic group. We show that whenever the Laplace term in the Allen–Cahn equation is small enough, there exist minimal solutions satisfying a large class of prescribed asymptotic behaviours. For a phase field model on a hyperbolic group, such solutions describe phase transitions that asymptotically converge towards prescribed phases, given by asymptotic directions. In the spirit of de Giorgi's conjecture, we then fix an asymptotic behaviour and let the Laplace term go to zero. In the limit we obtain a solution to a corresponding asymptotic Plateau problem by Γ-convergence.     

A class of permutation quadrinomials

In this paper, we investigate the permutation behavior of a class of quadrinomials. Each term of these quadrinomials has a Niho-type exponent, and two sets of coefficient triples making the quadrinomials to be permutations are obtained. We use a substitution to transform the permutation problem into the root distribution problem in the unit circle of certain quadratic and cubic equations.     

The cancellation property of rings

A ring R is said to have the finitely generated cancellation property provided that the module isomorphism R⊕B?R⊕C implies B?C for any finitely generated R-modules B and C. It is proved that R has this property is equivalent to the existence of the cancellation matrices over R. Moreover, the structure of such matrices is investigated and finite weakly stable rings are characterized in terms of their cancellation matrices.     

Risk-sensitive finite-horizon piecewise deterministic Markov decision processes

This paper deals with risk-sensitive piecewise deterministic Markov decision processes, where the expected exponential utility of a finite-horizon reward is to be maximized. Both the transition rates and reward functions are allowed to be unbounded. Feynman–Kac’s formula is developed in our setup, using which along with an approximation technique, we establish the associated Hamilton–Jacobi–Bellman equation and the existence of risk-sensitive optimal policies under suitable conditions.     

An efficient approach for dual sourcing inventory systems with Tailored Base-Surge policies

Nowadays most companies use dual sourcing strategies to manage supply chains. Recently, a practical policy called the Tailored Base-Surge (TBS) policy has been proposed to manage the system, and shown to perform well. We study a dual sourcing inventory system with i.i.d. demands and TBS policies. Using the techniques of MacLaurin series analysis, we develop an efficient method to calculate the moments of the inventory position, the bullwhip effect, and performance measures. Numerical experiments show that our method works well.     

Cultivating a research imperative: Mentoring mathematics at Stockholms Högskola, 1882–1887

Though the central role of Gösta Mittag-Leffler in the promotion of specialized, research-oriented mathematics at Stockholms Högskola is widely acknowledged, the specific social and technical means by which he sought to cultivate a fledgling research community there during the early- to mid-1880s have received little attention. In particular, a detailed study of the relationship of his own research activity to that of his first Swedish students is absent from the existing literature.Through the juxtaposition of their research activities and unpublished correspondence, this paper explores Mittag-Leffler's active and deliberate efforts to engage his students Ivar Bendixson and Edvard Phragmén in open problems within his own research agenda, support them through his institutional connections, and instill within them norms concerning research ideologies, practices of communication and criticism, and frameworks for shared knowledge. It also illuminates the extent to which his teachings took root in at least one student to emerge from his program, who would perpetuate the mathematical practices set in place by his teacher and set forth on the international stage to promote his newly-acquired system of values.     

Weak Galerkin finite element methods combined with Crank-Nicolson scheme for parabolic interface problems

This article is devoted to the a priori error estimates of the fully discrete Crank-Nicolson approximation for the linear parabolic interface problem via weak Galerkin finite element methods (WG-FEM). All the finite element functions are discontinuous for which the usual gradient operator is implemented as distributions in properly defined spaces. Optimal order error estimates in both $L^{\infty}(H^1)$ and $L^{\infty}(L^2)$ norms are established for lowest order WG finite element space $({\cal P}_{k}(K),\;{\cal P}_{k-1}(\partial K),\;\big[{\cal P}_{k-1}(K)\big]^2)$. Finally, we give numerical examples to verify the theoretical results.     

素数幂、双素数幂阶元的共轭类长的个数为4的 有限群的结构

设群G为一个有限群.如果群G中素数幂、双素幂阶元的共轭类长的集合为{1,p~a,m,p~bm},那么群G是可解的,其中ab为正整数,p为素数且与m互素.进一步,给出了群G/Z(G)的结构,这是对文"Chen R F,Zhao X H.A criterion for a group to have nilpotent p-complements[J].Monatsh Math,2016,179(2):221-225"中定理A主要结论的一个推广.     

Stochastic consistency and stochastic stability in mean square sense for Cauchy advection problem

This work deals with the construction of finite difference solutions of random advection Cauchy type partial differential equation containing uncertainty through the coefficient of the velocity. Under appropriate hypothesis on the velocity random variable, we establish that the constructed random finite difference solution is mean square consistent and mean square stable over the whole real line. In addition, the main statistical functions, such as the mean, of the approximate solution stochastic process generated by truncation of the exact finite difference solution are given. Finally, we apply the proposed technique to several illustrative examples which show our discussing for the mean square stability.