Sign change of the function <Emphasis Type=Italic>S</Emphasis>(<Emphasis Type=Italic>t</Emphasis>) on short intervals

A theorem for the sign variation of the argument of the Riemann zeta function S(t) in the interval (t − A, t + A) with A = 4.39 ln ln ln ln T for each t, T ≤ t ≤ T + H excluding values from the set E with the measure mes(E) = O(H(ln ln T)⁻¹(ln ln ln T)^−0,5) is proved.     

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.     

About <Emphasis Type=Italic>I</Emphasis>(<Emphasis Type=Italic>J</Emphasis>)-approximately continuous functions

A generalization of density point with respect to category and I(J)-density topology has been presented in [5]. This papers deals with some basic properties of the corresponding I(J)-approximately continuous functions and gives answer when these functions are of the first Baire class and when they are Darboux functions.     

On the structure of theta lifts of discrete series for dual pairs (<Emphasis Type=Italic>Sp</Emphasis>(<Emphasis Type=Italic>n</Emphasis>),<Emphasis Type=Italic>O</Emphasis>(<Emphasis Type=Italic>V</Emphasis>))

The purpose of this paper is to prove some fundamental results on the structure of theta lifts of discrete series.     

Completeness properties of the pseudocompact-open topology on <Emphasis Type=Italic>C</Emphasis>(<Emphasis Type=Italic>X</Emphasis>)

This is a study of the completeness properties of the space C _ps (X) of continuous real-valued functions on a Tychonoff space X, where the function space has the pseudocompact-open topology. The properties range from complete metrizability to the Baire space property. Dedicated to Professor Robert A. McCoy     

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.      

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.      

Topological properties of the multifunction space <Emphasis Type=Italic>L</Emphasis>(<Emphasis Type=Italic>X</Emphasis>) of cusco maps

A set-valued mapping F from a topological space X to a topological space Y is called a cusco map if F is upper semicontinuous and F(x) is a nonempty, compact and connected subset of Y for each x ∈ X. We denote by L(X), the space of all subsets F of X × ℝ such that F is the graph of a cusco map from the space X to the real line ℝ. In this paper, we study topological properties of L(X) endowed with the Vietoris topology. The second author is supported by the SPM fellowship awarded by the Council of Scientific and Industrial Research, India.     

Some properties of compatibility function based on <Emphasis Type=Italic>T</Emphasis>-operation

In this paper, the concept of compatibility function is proposed for fuzzy value with respect to a kind of the binomial operations which is called t-operation. Besides the continuity of compatibility function on three kinds of metric spaces are discussed, respectively.     

Joint continuity of <Emphasis Type=Italic>K</Emphasis><Subscript><Emphasis Type=Italic>h</Emphasis></Subscript><Emphasis Type=Italic>C</Emphasis>-functions with values in moore spaces

We introduce the notion of categorical cliquish mapping and show that, for each K _h C-mapping f: X × Y → Z, where X is a topological space, Y is a space with the first axiom of countability, and Z is a Moore space, with categorical-cliquish horizontal y-sections f _y , the sets C _y (f) are residual G _δ-type sets in X for every y ∈ Y. Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 11, pp. 1539–1547, November, 2008.     

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.     

Improved Full-Newton Step <Emphasis Type=Italic>O</Emphasis>(<Emphasis Type=Italic>nL</Emphasis>) Infeasible Interior-Point Method for Linear Optimization

We present several improvements of the full-Newton step infeasible interior-point method for linear optimization introduced by Roos (SIAM J. Optim. 16(4):1110–1136, 2006). Each main step of the method consists of a feasibility step and several centering steps. We use a more natural feasibility step, which targets the μ ⁺-center of the next pair of perturbed problems. As for the centering steps, we apply a sharper quadratic convergence result, which leads to a slightly wider neighborhood for the feasibility steps. Moreover, the analysis is much simplified and the iteration bound is slightly better.     

Some remarks on <Emphasis Type=Italic>S</Emphasis>-paracompact spaces

Some characterizations of S-paracompact spaces are given. We introduce a class of S-expandable spaces and study topological properties of S-expandable spaces. The second author acknowledges the support from the NSFC (No. 10571081) and the Natural Science Foundation of Jingsu Higher Education Institutions of China (Grant No. 07KJB110055).     

On the code generated by the incidence matrix of points and hyperplanes in <Emphasis Type=Italic>PG</Emphasis>(<Emphasis Type=Italic>n</Emphasis>,<Emphasis Type=Italic>q</Emphasis>) and its dual

In this paper, we study the p-ary linear code C(PG(n,q)), q = p ^h , p prime, h ≥ 1, generated by the incidence matrix of points and hyperplanes of a Desarguesian projective space PG(n,q), and its dual code. We link the codewords of small weight of this code to blocking sets with respect to lines in PG(n,q) and we exclude all possible codewords arising from small linear blocking sets. We also look at the dual code of C(PG(n,q)) and we prove that finding the minimum weight of the dual code can be reduced to finding the minimum weight of the dual code of points and lines in PG(2,q). We present an improved upper bound on this minimum weight and we show that we can drop the divisibility condition on the weight of the codewords in Sachar’s lower bound (Geom Dedicata 8:407–415, 1979). G. Van de Voorde’s research was supported by the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen).     

Cluster analysis model with <Emphasis Type=Italic>T</Emphasis>-fuzzy data

With T-fuzzy data definition, properties and weigh-and-measure formula given and dimension unified by the aid of normal standardization, first, the author discusses Min-Max (resp. Max-Min) transitive closure as well as α (or β) threshold value principle with a shortcut method produced for the cluster. Besides, he establishes a cluster analysis model with T-fuzzy data, and gains an access to T-fuzzy data and two approaches to non-fuzzifying. Finally, he shows results generally in coincident with practice, by an example in this paper.     

Three-webs <Emphasis Type=Italic>W</Emphasis>(1, <Emphasis Type=Italic>n</Emphasis>, 1) and associated systems of ordinary differential equations

We consider a three-web on a smooth manifold formed by two n-parameter families of curves and a one-parameter family of hypersurfaces. For such webs, we define a family of adapted frames, find the systemof structure equations, and study the differential-geometric objects that arise in differential neighborhoods up to the third order. We prove that each system of ordinary differential equations (SODE) uniquely defines a three-web. This allows us to describe properties of a SODE in terms of the corresponding three-web. In particular, we characterize autonomous SODE.     

Expectation values of scaling fields in <Emphasis Type=Italic>Z</Emphasis><Subscript><Emphasis Type=Italic>N</Emphasis></Subscript> Ising models

We compute exact vacuum expectation values of physically relevant scaling fields in the perturbed Z_N parafermionic models. Our algebraic method is based on analyzing vertex operators in the corresponding off-critical lattice model. The results coincide with the expressions derived by perturbed conformal field theory methods. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 3, pp. 557–583, March, 2008