Main Probability Characteristics of the Queuing System Gκ|G|1

For the queuing system G |G|1 with batch arrivals of calls, we present the distributions of the following characteristics: the length of a busy period, queue length in transient and stationary modes of the queuing system, total idle time of the queuing system, virtual waiting time to the beginning of the service, input stream of calls, output stream of served calls, etc.     

Free groups in the smallest ideal of β G

Let G be an infinite group with cardinality κ embeddable into a direct sum of countable groups and let β G be the Stone-Čech compactification of G as a discrete semigroup. We show that the structural group of the smallest ideal of β G contains copies of the free group on generators. Supported by NRF grants FA2007041200005 and IFR2008041600015, respectively, and The John Knopfmacher Centre for Applicable Analysis and Number Theory.     

Non-parametric Estimation for the M/G/∞ Queue

Given an M/G/ queue with input rate and service-time distribution G, we consider the problem of estimating and G from data on the queue-length process Q = (Q_t). Our motivation is to study departures of G from exponentiality, following recent work of Bingham and Dunham (1997, Ann. Inst. Statist. Math., 49, 667–679).     

On the classification of first order Gödel logics

We characterize the recursively enumerable first order Gödel logics with △ with respect to validity and non-satisfiability. The finitely valued and four infinitely valued Gödel logics with △ are recursively enumerable, not-satisfiability is recursively enumerable if validity is recursively enumerable. This is in contrast to first order Gödel logics without △, where validity is recursively enumerable for finitely valued and two infinitely valued Gödel logics, not-satisfiability is recursively enumerable if validity is recursively enumerable or 0 isolated in the truth value set.     

Über einen Homomorphiesatz von G.Köthe

The main object of this paper is to generalize a homomorphism theorem of Köthe [5] for a wide class of not necessarily locally convex topological vector spaces. A sequence =(B_n) of balanced sets B_n in a vector space E(), such that the union of the B_n's equals E and such that B_n+B_nB_n+1 for all nN, is called an absorbent sequence. E() is called -locally topological, if it possesses an absorbent sequence =(B_n) of bounded sets and if a linear mapping A from E() into any other vector space is continuous if all restrictions are continuous at 0. It is shown, that a continuous linear mapping A from a vector space E() with an absorbant sequence of compact sets into a boundedly summing -locally topological space F() is a homomorphism if A(E) is closed in F().     

On the range of the derivative of Gâteaux-smooth functions on separable banach spaces

We prove that there exists a Lipschitz function froml ¹ into ℝ² which is Gateaux-differentiable at every point and such that for everyx, y εl ¹, the norm off′(x) −f′(y) is bigger than 1. On the other hand, for every Lipschitz and Gateaux-differentiable function from an arbitrary Banach spaceX into ℝ and for everyε > 0, there always exist two pointsx, y εX such that ‖f′(x) −f′(y)‖ is less thanε. We also construct, in every infinite dimensional separable Banach space, a real valued functionf onX, which is Gateaux-differentiable at every point, has bounded non-empty support, and with the properties thatf′ is norm to weak* continuous andf′(X) has an isolated pointa, and that necessarilya ε 0. This work has been initiated while the second-named author was visiting the University of Bordeaux. The second-named author is supported by grant AV 1019003, A1 019 205, GA CR 201 01 1198.     

Traveling wave solutions of nonlinear evolution equations via the enhanced (G′/G)-expansion method

In this article, an enhanced (G′/G)-expansion method is suggested to find the traveling wave solutions for the modified Korteweg de-Vries (mKDV) equation. Abundant traveling wave solutions are derived, which are expressed by the hyperbolic and trigonometric functions involving several parameters. The efficiency of this method for finding these exact solutions has been demonstrated. It is shown that the proposed method is effective and can be used for many other nonlinear evolution equations (NLEEs) in mathematical physics.     

The （G＇/G, 1/G）-expansion method and its application to travelling wave solutions of the Zakharov equations

The （G＇/G, 1/G）-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the （G＇/G）-expansion method proposed recently, is presented. By using this method abundant travelling wave so- lutions with arbitrary parameters of the Zakharov equations are successfully obtained. When the parameters are replaced by special values, the well-known solitary wave solutions of the equations are rediscovered from the travelling waves.     

Estimation of the Intensity of the Flow of Nonmonotone Refusals in the Queuing System (≤ λ)/G/m

We consider a queuing system ()/G/m, where the symbol () means that, independently of prehistory, the probability of arrival of a call during the time interval dtdoes not exceed dt. The case where the queue length first attains the level r m+ 1 during a busy period is called the refusal of the system. We determine a bound for the intensity ₁(t) of the flow of homogeneous events associated with the monotone refusals of the system, namely, ₁(t) = O( ^{r+ 1}₁ ^{m– 1} _{r– m+ 1}), where _k is the kth moment of the service-time distribution.     

Circular proofs for the Gödel-Löb provability logic

Sequent calculus for the provability logic GL is considered, in which provability is based on the notion of a circular proof. Unlike ordinary derivations, circular proofs are represented by graphs allowed to contain cycles, rather than by finite trees. Using this notion, we obtain a syntactic proof of the Lyndon interpolation property for GL.     

Instabilities in the Görtler model for wall bounded flows

The original Görtler model is analyzed with no-slip boundary conditions on the wall. These conditions have historically been the most difficult to treat. It is proved that the principle of exchange of stabilities holds, that is, the first unstable eigenvalue has imaginary part equal to zero. The techniques used involve factoring positive operators.     

Boundary-value problems for the wave equation with Lévy Laplacian in the Gâteaux class

We present the solutions of the initial-value problem in the entire space and the solutions of the boundary-value and initial-boundary-value problems for the wave equation

A Generalized （G＇/G）-Expansion Method to Find the Traveling Wave Solutions of Nonlinear Evolution Equations

In this article, we construct the exact traveling wave solutions for nonlinear evolution equations in the mathematical physics via the modified Kawahara equation, the nonlinear coupled KdV equations and the classical Boussinesq equations, by using a generalized （G＇/G）-expansion method, where G satisfies the Jacobi elliptic equation. Many exact solutions in terms of Jacobi elliptic functions are obtained.     

Tail asymptotics for the queue size distribution in the MAP/G/1 retrial queue

We consider a MAP/G/1 retrial queue where the service time distribution has a finite exponential moment. We derive matrix differential equations for the vector probability generating functions of the stationary queue size distributions. Using these equations, Perron–Frobenius theory, and the Karamata Tauberian theorem, we obtain the tail asymptotics of the queue size distribution. The main result on light-tailed asymptotics is an extension of the result in Kim et al. (J. Appl. Probab. 44:1111–1118, 2007) on the M/G/1 retrial queue.