<Emphasis Type="Italic">m</Emphasis>-Dissipativity of Some Gradient Systems with Measurable Potential

We consider the operator in L ²(B, ν) and in L ¹(B, ν) with Neumann boundary condition, where U is an unbounded function belonging to for some q ∈(1, ∞), B is the possibly unbounded convex open set in where U is finite and ν(dx) = C exp (−2U (x))dx is a probability measure, infinitesimally invariant for N ₀. We prove that the closure of N ₀ is a m-dissipative operator both in L ²(B, ν) and in L ¹(B, ν). Moreover we study the properties of ergodicity and strong mixing of the measure ν in the L ² case.      

A Moderate Deviation Principle for <Emphasis Type="Italic">m</Emphasis>-Dependent Random Variables with Unbounded <Emphasis Type="Italic">m</Emphasis>

In this paper, a theorem on the moderate deviation principle for random arrays under m-dependence with unbounded m is established. This partially extends the results of Chen (Stat. Probab. Lett. 35:123–134, 1997). As an application, the moderate deviation principle for the truncation estimator of the variance in the analysis of time series is obtained.      

On the number of Diophantine <Emphasis Type="Italic">m</Emphasis>-tuples

A set of m positive integers is called a Diophantine m-tuple if the product of any two of them is one less than a perfect square. It is known that there does not exist a Diophantine sextuple and that there are only finitely many Diophantine quintuples. On the other hand, there are infinitely many Diophantine m-tuples for m=2, 3 and 4. In this paper, we derive asymptotic estimates for the number of Diophantine pairs, triples and quadruples with elements less than given positive integer N. The author was supported by the Ministry of Science and Technology, Republic of Croatia, grants 0037110 and 037-0372781-2821.     

<Emphasis Type="Italic">m</Emphasis> Components-admissible solutions of systems of higher-order partial differential equations on <Emphasis Type="Italic">C</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

Using value distribution theory and techniques in several complex variables,we investigate the problem of existence of m components-admissible solutions of a class of systems of higher-order partial differential equations in several complex variables and estimate the number of admissible components of solutions.Some related results will also be obtained.     

Approximations for the <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">GI</Emphasis>/<Emphasis Type="Italic">N</Emphasis>+<Emphasis Type="Italic">GI</Emphasis> type call center

In this paper, we propose approximations to compute the steady-state performance measures of the M/GI/N+GI queue receiving Poisson arrivals with N identical servers, and general service and abandonment-time distributions. The approximations are based on scaling a single server M/GI/1+GI queue. For problems involving deterministic and exponential abandon times distributions, we suggest a practical way to compute the waiting time distributions and their moments using the Laplace transform of the workload density function. Our first contribution is numerically computing the workload density function in the M/GI/1+GI queue when the abandon times follow general distributions different from the deterministic and exponential distributions. Then we compute the waiting time distributions and their moments. Next, we scale-up the M/GI/1+GI queue giving rise to our approximations to capture the behavior of the multi-server system. We conduct extensive numerical experiments to test the speed and performance of the approximations, which prove the accuracy of their predictions.      

Intrinsic normalizations of a nonholonomic hypersurface with <Emphasis Type="Italic">m</Emphasis>-dimensional generators in affine space <Emphasis Type="Italic">A</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

We consider some intrinsic normalizations of a nonholonomic hypersurface with m-dimensional generators in the n-dimensional affine spaced. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 3, pp. 532–562, October–December, 2007.     

The existence and uniqueness of solution and the convergence of a multi-step iterative algorithm for a system of variational inclusions with (<Emphasis Type="Italic">A</Emphasis>, <Emphasis Type="Italic">η</Emphasis>, <Emphasis Type="Italic">m</Emphasis>)-accretive operators

In this paper, we introduce and study a new system of variational inclusions with (A, η, m)-accretive operators which contains variational inequalities, variational inclusions, systems of variational inequalities and systems of variational inclusions in the literature as special cases. By using the resolvent technique for the (A, η, m)-accretive operators, we prove the existence and uniqueness of solution and the convergence of a new multi-step iterative algorithm for this system of variational inclusions in real q-uniformly smooth Banach spaces. The results in this paper unifies, extends and improves some known results in the literature.      

Reliability formula &; limit law of the failure time of “<Emphasis Type="Italic">m</Emphasis>-consecutive-<Emphasis Type="Italic">k</Emphasis>-out-of-<Emphasis Type="Italic">n</Emphasis>:<Emphasis Type="Italic">F</Emphasis> system”

An “m-consecutive-k-out-of-n:F system” consists of n components ordered on a line; the system fails if and only if there are at least m nonoverlapping runs of k consecutive failed components. In this paper, we give a recursive formula to compute the reliability of such a system. Thereafter, we state two asymptotic results concerning the failure time Z _n of the system. The first result concerns a limit theorem for Z _n when the failure times of components are not necessarily with identical failure distributions. In the second one, we prove that, for an arbitrary common failure distribution of components, the limit system failure distribution is always of the Poisson class.      

The flatness properties of <Emphasis Type="Italic">S</Emphasis>-poset <Emphasis Type="Italic">A</Emphasis>(<Emphasis Type="Italic">I</Emphasis>) and Rees factor <Emphasis Type="Italic">S</Emphasis>-posets

Let S be a pomonoid and I a proper right ideal of S. In a previous paper, using the amalgamated coproduct A(I) of two copies of _S S over I, we were able to solve one of the problems posed in S. Bulman-Fleming et al. (Commun. Algebra 34:1291–1317, 2006). In the present paper, we investigate further flatness properties of A(I). We also solve another problem stated in the paper cited above. Namely, we determine the condition under which Rees factor S-posets have property (P _w ). Research supported by nwnu-kjcxgc-03-18.     

<Emphasis Type="Italic">∂</Emphasis>-operations and <Emphasis Type="Italic">H</Emphasis><Subscript><Emphasis Type="Italic">V</Emphasis></Subscript>-fields

The hyperoperations, called theta-operations （δ）, are motivated from the usual property, which the derivative has on the derivation of a product of functions. Using any map on a set, one can define δ-operations. In this paper, we continue our study on the δ-operations on groupoids, rings, fields and vector spaces or on the corresponding hyperstructures. Using δ-operations one obtains, mainly, Hwstructures, which form the largest class of the hyperstructures. For representation theory of hyperstructures, by hypermatrices, one needs special Hv-rings or Hy-fields, so these hyperstructures can be used. Moreover, we study the relation of these δ-structures with other classes of hyperstructures, especially with the Hv-structures.     

Consecutive customer losses in regular and oscillating <Emphasis Type="Italic">M</Emphasis><Superscript><Emphasis Type="Italic">X</Emphasis></Superscript>/<Emphasis Type="Italic">G</Emphasis>/1/<Emphasis Type="Italic">n</Emphasis> systems

We derive fast recursions to compute the probability that k or more consecutive customer losses take place during a busy period of a queue, the so called k-CCL probability, for regular and oscillating M ^X /G/1/n systems.     

Localization of <Emphasis Type="Italic">LM</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>-algebras

The aim of this paper is to define the localization LM _n -algebra of an LM _n —algebra L with respect to a topology F on L; in Section 5 we prove that the maximal LM _n -algebra of fractions (defined in [3]) and the LM _n -algebra of fractions relative to an Λ—closed system (defined in Section 2) are LM _n -algebras of localization.     

A novel proof of the existence of solutions for a new system of generalized mixed quasi-variational-like inclusions involving (<Emphasis Type="Italic">A</Emphasis>, <Emphasis Type="Italic">η</Emphasis>, <Emphasis Type="Italic">m</Emphasis>)-accretive operators

In this paper, we introduce a new system of generalized mixed quasi-variational-like inclusions with (A, η, m)-accretive operators and relaxed cocoercive mappings. By using the fixed point theorem of Nadler, we prove the existence of solutions for this general system of generalized mixed quasi-variational-like inclusions and its special cases. The results in this paper unify, extend and improve some known results in the literature. The novel proof method is simpler than those iterative algorithm approach for proving the existence of solutions of all classes of system of set-valued variational inclusions in the literature.     

On <Emphasis Type="Italic">k</Emphasis>-Spaces and <Emphasis Type="Italic">k</Emphasis><Subscript><Emphasis Type="Italic">R</Emphasis></Subscript>-Spaces

In this note we study the relation between k _R -spaces and k-spaces and prove that a k _R -space with a σ-hereditarily closure-preserving k-network consisting of compact subsets is a k-space, and that a k _R -space with a point-countable k-network consisting of compact subsets need not be a k-space. This work was supported by the NSF of China (10271056).     

Analysis of GI<Superscript><Emphasis Type="Italic">X</Emphasis></Superscript>/<Emphasis Type="Italic">M</Emphasis>(<Emphasis Type="Italic">n</Emphasis>)//<Emphasis Type="Italic">N</Emphasis> systems with stochastic customer acceptance policy

We investigate GI ^X /M(n)//N systems with stochastic customer acceptance policy, function of the customer batch size and the number of customers in the system at its arrival. We address the time-dependent and long-run analysis of the number of customers in the system at prearrivals and postarrivals of batches and seen by customers at their arrival to the system, as well as customer blocking probabilities. These results are then used to derive the continuous-time long-run distribution of the number of customers in the system. Our analysis combines Markov chain embedding with uniformization and uses stochastic ordering as a way to bound the errors of the computed performance measures.      

Cc （X） Spaces with X Locally Compact

In this paper, we show, among other results, that if X is a [separable] locally compact space X [satisfying the first countability axiom] then the space Cc （X） has countable tightness [if and only if it has bounding tightness] if and only if it is Frechet-Urysohn, if and only if Cc （X） contains a dense （LM） subspace and if and only if X is a-compact.     

<Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>-mixed intersection bodies

In this paper the author first introduce a new concept of L _p -dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of L _p intersection body to L _p -mixed intersection body. Inequalities for L _p -dual mixed volumes of L _p -mixed intersection bodies are established and the results established here provide new estimates for these type of inequalities. This work was supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. Y605065) and the Foundation of the Education Department of Zhejiang Province of China (Grant No. 20050392)     

On locally <Emphasis Type="Italic">A</Emphasis>-convex <Emphasis Type="Italic">H</Emphasis>*-algebras

We endow any proper A-convex H*-algebra (E, τ) with a locally pre-C*-topology. The latter is equivalent to that introduced by the pre C*-norm given by Ptàk function when (E, τ) is a Q-algebra. We also prove that the algebra of complex numbers is the unique proper locally A-convex H*-algebra which is barrelled and Q-algebra.      

On <Emphasis Type="Italic">n</Emphasis> × <Emphasis Type="Italic">m</Emphasis>-valued Łukasiewicz-Moisil algebras

n×m-valued Łukasiewicz algebras with negation were introduced and investigated in [20, 22, 23]. These algebras constitute a non trivial generalization of n-valued Łukasiewicz-Moisil algebras and in what follows, we shall call them n×m-valued Łukasiewicz-Moisil algebras (or LM _n×m -algebras). In this paper, the study of this new class of algebras is continued. More precisely, a topological duality for these algebras is described and a characterization of LM _n×m -congruences in terms of special subsets of the associated space is shown. Besides, it is determined which of these subsets correspond to principal congruences. In addition, it is proved that the variety of LM _n×m -algebras is a discriminator variety and as a consequence, certain properties of the congruences are obtained. Finally, the number of congruences of a finite LM _n×m -algebra is computed.      

<Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>-nearest neighbor estimators of entropy

For estimating the entropy of an absolutely continuous multivariate distribution, we propose nonparametric estimators based on the Euclidean distances between the n sample points and their k _n -nearest neighbors, where {k _n : n = 1, 2, …} is a sequence of positive integers varying with n. The proposed estimators are shown to be asymptotically unbiased and consistent.