Limiting behavior of certain mixtures of distributions

U — [0, 1] Y — . X=[1–U ^1/v /Y], U Y.     

О Сходимости Лагранжева Интерполирования В Некоторых Множествах Функций

.      

On the Cesàro summability of orthogonal sequences

(C, ). , . 0<<1. 1) - ( _k ), _k =a _k , (C, ), . 2) , , (C, ) ; _k = =¦a _k ¦.     

About generalized ideals in a distributive lattice

Let L be a distributive lattice characterized by a ternary operation (, ,), where (a,b,c)=(ab)(bc)(ac)=(ab)(ac)(bc), a,b,cL. The note considers convex sublattices of L, called generalized ideals of L generated by the operation (, ,). Some remarks have been stated about the graph of a distributive lattice.     

On Shikata's distance between differentiable structures

Shikata proved: there is a number (n) with the following property: If two compact homeomorphic n-dimensional manifolds have a distance less than (n), then they are diffeomorphic. We improve the known lower bound (n!)^–n for (n) to 1/3n ^–2.This work was done under the program Sonderforschungsbereich Theoretische Mathematik (SFB 40) at Bonn University while Shikata was SFB-guest at Bonn.     

A generalization ofH μ-spaces and Hankel transforms

-H _,M,a H _,b . - — H _,M H . . , H ,–1/2, H _,H,a H ^,1/a H _,M H . , .     

Elastic properties of honeycomb sandwich plates with nontraditional cell forms

A method for correcting the elastic properties of honeycomb sandwich plates by changing the cell shape is described. Compact and convenient analytical expressions (1) are proposed for calculating the reduced elastic parameters of the honeycomb sandwich plates. The acceptable range of changes in the size of the honeycombs is restricted by the cell elongation region [0.5;2] and the region of variation of the angle between cell walls [/6; 5/6]. The results of the calculation experiment showed that the traditional cell shape (=/3, =1) is not effective as an optimum structure (Table 1).Institute of Transport Systems and Technologies (Transmag), National Academy of Sciences of Ukraine, Dnepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 187–191, March–April, 1997.     

Behavior on rays of Dirichlet series of slow growth

The topic under consideration is the behavior on the rays arg z=, ¦¦ < /2, of an entire function F represented by a Dirichlet series, absolutely convergent in the whole plane, with exponents _n > 0 such that n= , n +, where q(r) is a proximate order and Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 12, pp. 1603–1613, December, 1991.     

Zum Einbettungsproblem für Markoff-Prozesse

Every elementary Markov process with a polish state space and with a discrete set of time parameter dense in ₊, whose finite dimensional distributions are derived from a semigroup (K _t) of Markov kernels continuous in 0 ₊ and whose initial distribution satisfies K _t, can be imbedded in an elementary Markov process with the same state space and with parameter set ₊ so that the corresponding finite dimensional distributions are equal.     

Quasigraded lie algebras,Kostant-Adler scheme,and integrable hierarchies

Using special anisotropic quasigraded Lie algebras, we obtain a number of new hierarchies of integrable nonlinear equations in partial derivatives admitting zero-curvature representations. Among them are an anisotropic deformation of the Heisenberg magnet hierarchy, a matrix and vector generalization of the Landau—Lifshitz hierarchies, new types of matrix and vector anisotropic chiral-field hierarchies, and other types of anisotropic hierarchies.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 2, pp. 329–345, February, 2005.     

Ergodic properties of Poisson processes with almost periodic intensity

Summary We discuss in this paper a non-homogeneous Poisson process A driven by an almost periodic intensity function. We give the stationary version A ^* and the Palm version A ⁰ corresponding to A ^*. Let (T _i ,i) be the inter-point distance sequence in A and (T _i ⁰ ,i) in A ⁰. We prove that forj, the sequence (T _i+j,i) converges in distribution to (T _i ⁰ ,i). If the intensity function is periodic then the convergence is in variation.     

Turán's extremal problem in random graphs: Forbidding odd cycles

For 0<1 and graphsG andH, we writeGH if any -proportion of the edges ofG span at least one copy ofH inG. As customary, we writeC ^k for a cycle of lengthk. We show that, for every fixed integerl1 and real >0, there exists a real constantC=C(l, ), such that almost every random graphG _{n, p} withp=p(n)Cn ^–1+1/2l satisfiesG _n,p1/2+ C ^2l+1. In particular, for any fixedl1 and >0, this result implies the existence of very sparse graphsG withG _1/2+ C ^2l+1.The first author was partially supported by NSERC. The second author was partially supported by FAPESP (Proc. 93/0603-1) and by CNP_q (Proc. 300334/93-1). The third author was partially sopported by KBN grant 2 1087 91 01.     

Two Workload Properties for Brownian Networks

As one approach to dynamic scheduling problems for open stochastic processing networks, J.M. Harrison has proposed the use of formal heavy traffic approximations known as Brownian networks. A key step in this approach is a reduction in dimension of a Brownian network, due to Harrison and Van Mieghem [21], in which the queue length process is replaced by a workload process. In this paper, we establish two properties of these workload processes. Firstly, we derive a formula for the dimension of such processes. For a given Brownian network, this dimension is unique. However, there are infinitely many possible choices for the workload process. Harrison [16] has proposed a canonical choice, which reduces the possibilities to a finite number. Our second result provides sufficient conditions for this canonical choice to be valid and for it to yield a non-negative workload process. The assumptions and proofs for our results involve only first-order model parameters.     

Natural aging and dynamic mechanical properties of polymer matrices

The influence of natural six-month aging at 293 K of two kinds of epoxy resins with different network density on their dynamical properties was studied. All the samples were examined by forced resonance oscillations at a frequency of 200 Hz in the range of 120–520 K. The components of the complex Young's modulus E, E, tan , and low-frequency velocity of sound were measured. The basic temperature transitions including T_g and the network density were determined from the experimental data. It was established that after aging of epoxy resins cured by the cross-linking agent meta-phenylenediamine their network density decreased (cold degradation). By using the cross-linking agent 2,6-diaminopyridine, and T_g increased. An attempt is made to explain the nature of this phenomenon.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Moscow State Technical University, Russia. Translated from Mechanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 407–412, May–June, 1998.     

Central limit theorem for complex measures

We prove two central limit theorems for real identically distribution random variables where the distribution is a complex-valued Borel measure . The results involve the weak convergence of the suitably scaledn-fold convolution of certain complex atomic or absolutely continuous measures of spectral radius 1 to ahypergaussian measure whose Fourier-Stieltjes transform is exp(–² for a positive integer . The proof uses a generalization of the method of characteristic functions. Counter-examples are given to rather more general statements that had appeared previously in the literature. This research arose in connection with problems related to general tauberian theorems on the line for complexvalued summability methods which are discussed at the end of the paper. Some interesting examples are given generalizing well-known theorems related to Euler and Borel summability.     

Implications of order reduction for implicit Runge-Kutta methods

Stability analysis of Runge-Kutta (RK) formulas was originally limited to linear ordinary differential equations (ODEs). More recently such analysis has been extended to include the behaviour of solutions to nonlinear problems. This extension led to additional stability requirements for RK methods. Although the class of problems has been widened, the analysis is still restricted to a fixed stepsize. In the case of differential algebraic equations (DAEs), additional order conditions must be satisfied [6] to achieve full classical ODE order and avoid possible order reduction. In this case too, a fixed stepsize analysis is employed. Such analysis may be of only limited use in quantifying the effectiveness of adaptive methods on stiff problems.In this paper we examine the phenomenon of order reduction and its implications on variable-step algorithms. We introduce a global measure of order referred to here as the observed order which is based on the average stepsize over the region of integration. This measure may be better suited to the study of stiff systems, where the stepsize selection algorithm will vary the stepsize considerably over the interval of integration. Observed order gives a better indication of the relationship between accuracy and cost. Using this measure, the observed order reduction will be seen to be less severe than that predicated by fixed stepsize order analysis.Supported by the Information Technology Research Centre of Ontario, and the Natural Science and Engineering Research Council of Canada.     

The convolution equation of Choquet and Deny on [IN]-groups

Let be a probability measure on a locally compact groupG. A real Borel functionf onG is called -harmonic if it satisfies the convolution equation *f=f. Given that isnonsingular with its translates, we show that the bounded -harmonic functions are constant on a class of groups including the almost connected [IN]-groups. If is nondegenerate and absolutely continuous, we solve the more general equation *= for positive measure on those groups which are metrizable and separable.Supported by Hong Kong RGC Earmarked Grant and CUHK Direct Grant     

On an application of infinitely divisible distributions to quadrature problems

— - , .     

The order of magnitude of the arithmetic means of double orthogonal series

, - , (C, 1,1), (C, 1,0) (C, 0,1)- . , , . - .

---

---

Dedicated to Academician S. M. Nikol'skii on his 80th birthday