Riesz <Emphasis Type="Italic">s</Emphasis>-Equilibrium Measures on <Emphasis Type="Italic">d</Emphasis>-Rectifiable Sets as <Emphasis Type="Italic">s</Emphasis> Approaches <Emphasis Type="Italic">d</Emphasis>

Let A be a compact set in of Hausdorff dimension d. For s ∈ (0,d) the Riesz s-equilibrium measure μ ^s is the unique Borel probability measure with support in A that minimizes

(<Emphasis Type="Italic">s</Emphasis>, <Emphasis Type="Italic">t</Emphasis>, <Emphasis Type="Italic">d</Emphasis>)-bi-Koszul algebras

The paper focuses on the 1-generated positively graded algebras with non-pure resolutions and mainly discusses a new kind of algebras called(s,t,d)-bi-Koszul algebras as the generalization of bi-Koszul algebras. An(s,t,d)-bi-Koszul algebra can be obtained from two periodic algebras with pure resolutions. The generation of the Koszul dual of an(s,t,d)-bi-Koszul algebra is discussed. Based on it,the notion of strongly(s,t,d)-bi-Koszul algebras is raised and their homological properties are further discussed.     

<Emphasis Type="Italic">A</Emphasis><Subscript>1</Subscript> weights and <Emphasis Type="Italic">d</Emphasis>-homogeneous measures on ahlfors <Emphasis Type="Italic">d</Emphasis>-regular space

Let X be an Ahlfors d-regular space and mad-regular measure on X . We prove that a measure μ on X is d-homogeneous if and only if μ is mutually absolutely continuous with respect to m and the derivative Dmμ(x) is an A1 weight. Also, we show by an example that every Ahlfors d-regular space carries a measure which is d-homogeneous but not d-regular.     

Rate of convergence to stationarity of the system <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">N</Emphasis>/<Emphasis Type="Italic">N</Emphasis>+<Emphasis Type="Italic">R</Emphasis>

We consider the M/M/N/N+R service system, characterized by N servers, R waiting positions, Poisson arrivals and exponential service times. We discuss representations and bounds for the rate of convergence to stationarity of the number of customers in the system, and study its behaviour as a function of R, N and the arrival rate λ, allowing λ to be a function of N.     

On edge-antipodal <Emphasis Type="Italic">d</Emphasis>-polytopes

A convex d-polytope in ℝ ^d is called edge-antipodal if any two vertices that determine an edge of the polytope lie on distinct parallel supporting hyperplanes of the polytope. We introduce a program for investigating such polytopes, and examine those that are simple.      

The <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">G</Emphasis>/1+<Emphasis Type="Italic">G</Emphasis> queue revisited

We consider an M/G/1 queue with the following form of customer impatience: an arriving customer balks or reneges when its virtual waiting time, i.e., the amount of work seen upon arrival, is larger than a certain random patience time. We consider the number of customers in the system, the maximum workload during a busy period, and the length of a busy period. We also briefly treat the analogous model in which any customer enters the system and leaves at the end of his patience time or at the end of his virtual sojourn time, whichever occurs first.     

Eigenvalues of the Manifold Sp（n）/U（n）

In this paper, we give the eigenvalues of the manifold Sp(n)/U(n). We prove that an eigenvalue λ _s (f ₂, f ₂, …, f _n ) of the Lie group Sp(n), corresponding to the representation with label (f ₁, f ₂, ..., f _n ), is an eigenvalue of the manifold Sp(n)/U(n), if and only if f ₁, f ₂, …, f _n are all even.     

The Dedekind Completion of <Emphasis Type="Italic">d</Emphasis>-Algebras

It is shown that the multiplication in an Archimedean d-algebra A can be extended to a multiplication in the Dedekind completion A of A such that A becomes a d-algebra with respect to this extended multiplication. This answers a question posed by Huijsmans in Studies in Economic Theory (Vol. 2, Springer, Berlin, 1991).     

Further Results for the Queueing System <Emphasis Type="Italic">M</Emphasis><Superscript><Emphasis Type="Italic">x</Emphasis></Superscript>/<Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">c</Emphasis>

For the multi-channel bulk-arrival queue, M ^x /M/c, Abol'nikov and Kabak independently obtained steady state results. In this paper the results of these authors are extended, corrected and simplified. A number of measures of efficiency are calculated for three cases where the arrival group size has: (i) a constant value, (ii) a geometric distribution, or (iii) a positive Poisson distribution. The paper also shows how to calculate fractiles for both the queue length and the waiting time distribution. Examples of extensive numerical results for certain measures of efficiency are presented in tabular and chart form.     

The <Emphasis Type="Italic">p</Emphasis>-harmonic approximation and the regularity of <Emphasis Type="Italic">p</Emphasis>-harmonic maps

We extend to the degenerate case , Simons approach to the classical regularity theory of harmonic maps of Schoen & Uhlenbeck, by proving a p-Harmonic Approximation Lemma. This allows to approximate functions with p-harmonic functions in the same way as the classical harmonic approximation lemma (going back to De Giorgi) does via harmonic functions. Finally, we show how to combine this tool with suitable regularity estimates for solutions to degenerate elliptic systems with a critical growth right hand side, in order to obtain partial -regularity of p-harmonic maps.Received: 2 November 2002, Accepted: 10 July 2003, Published online: 4 September 2003Mathematics Subject Classification (2000): 35J70, 49N60, 49Q60     

<Emphasis Type="Italic">X</Emphasis>-decomposable finite groups for <Emphasis Type="Italic">X</Emphasis>={1, <Emphasis Type="Italic">m</Emphasis>, <Emphasis Type="Italic">m</Emphasis> + 1, <Emphasis Type="Italic">m</Emphasis> + 2}

A normal subgroup N of a finite group G is called n-decomposable in G if N is the union of n distinct G-conjugacy classes. We study the structure of nonperfect groups in which every proper nontrivial normal subgroup is m-decomposable, m+1-decomposable, or m+2-decomposable for some positive integer m. Furthermore, we give classification for the soluble case.     

Cyclotomic Hecke Algebras of <Emphasis Type="Italic">G</Emphasis>(<Emphasis Type="Italic">r</Emphasis>, <Emphasis Type="Italic">p</Emphasis>, <Emphasis Type="Italic">n</Emphasis>)

In this note, we find a monomial basis of the cyclotomic Hecke algebra \({\mathcal{H}_{r,p,n}}\) of G(r,p,n) and show that the Ariki-Koike algebra \({\mathcal{H}_{r,n}}\) is a free module over \({\mathcal{H}_{r,p,n}}\), using the Gröbner-Shirshov basis theory. For each irreducible representation of \({\mathcal{H}_{r,p,n}}\), we give a polynomial basis consisting of linear combinations of the monomials corresponding to cozy tableaux of a given shape.     

A study of (<Emphasis Type="Italic">x</Emphasis>(<Emphasis Type="Italic">q</Emphasis> + 1), <Emphasis Type="Italic">x</Emphasis>; 2, <Emphasis Type="Italic">q</Emphasis>)-minihypers

In this paper, we study the weighted (x(q + 1), x; 2, q)-minihypers. These are weighted sets of x(q + 1) points in PG(2, q) intersecting every line in at least x points. We investigate the decomposability of these minihypers, and define a switching construction which associates to an (x(q + 1), x; 2, q)-minihyper, with x ≤ q ² − q, not decomposable in the sum of another minihyper and a line, a (j(q + 1), j; 2, q)-minihyper, where j = q ² − q − x, again not decomposable into the sum of another minihyper and a line. We also characterize particular (x(q + 1), x; 2, q)-minihypers, and give new examples. Additionally, we show that (x(q + 1), x; 2, q)-minihypers can be described as rational sums of lines. In this way, this work continues the research on (x(q + 1), x; 2, q)-minihypers by Hill and Ward (Des Codes Cryptogr 44:169–196, 2007), giving further results on these minihypers.     

The Center of <Emphasis Type="Italic">Dist</Emphasis> (<Emphasis Type="Italic">GL</Emphasis>(<Emphasis Type="Italic">m</Emphasis>|<Emphasis Type="Italic">n</Emphasis>)) in Positive Characteristic

The purpose of this paper is to investigate central elements in distribution algebras D i s t(G) of general linear supergroups G = G L(m|n). As an application, we compute explicitly the center of D i s t(G L(1|1)) and its image under Harish-Chandra homomorphism.     

On the directions problem in <Emphasis Type="Italic">AG</Emphasis>(<Emphasis Type="Italic">n</Emphasis>, <Emphasis Type="Italic">q</Emphasis>)

We prove that if q = p ^h , p a prime, do not exist sets U í AG(n,q){U {\subseteq} AG(n,q)}, with |U| = q ^k and 1 < k < n, determining N directions where

The isogeny conjecture for <Emphasis Type="Italic">A</Emphasis>-motives

We prove the isogeny conjecture for A-motives over finitely generated fields K of transcendence degree ≤1. This conjecture says that for any semisimple A-motive M over K, there exist only finitely many isomorphism classes of A-motives M′ over K for which there exists a separable isogeny M′→M. The result is in precise analogy to known results for abelian varieties and for Drinfeld modules and will have strong consequences for the \mathfrak p{\mathfrak {p}}-adic and adelic Galois representations associated to M. The method makes essential use of the Harder–Narasimhan filtration for locally free coherent sheaves on an algebraic curve.     

<Emphasis Type="Italic">M</Emphasis><Superscript><Emphasis Type="Italic">X</Emphasis></Superscript>/<Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">c</Emphasis> Queue with catastrophes and state-dependent control at idle time

We consider an M ^X /M/c queue with catastrophes and state-dependent control at idle time. Properties of the queues which terminate when the servers become idle are first studied. Recurrence, equilibrium distribution, and equilibrium queue-size structure are studied for the case of resurrection and no catastrophes. All of these properties and the first effective catastrophe occurrence time are then investigated for the case of resurrection and catastrophes. In particular, we obtain the Laplace transform of the transition probability for the absorbing M ^X /M/c queue.     

On the Diophantine Queueing System, <Emphasis Type="Italic">D/D</Emphasis><Superscript><Emphasis Type="Italic">a,b</Emphasis></Superscript><Emphasis Type="Italic">/</Emphasis>1

This paper considers the solution of a deterministic queueing system. In this system, the single server provides service in bulk with a threshold for the acceptance of customers into service. Analytic results are given for the steady-state probabilities of the number of customers in the system and in the queue for random and pre-arrival epochs. The solution of this system is a prerequisite to a four-point approximation to the model GI/G ^a,b /1. The paper demonstrates that the solution of such a system is not a trivial problem and can produce interesting results. The graphical solution discussed in the literature requires that the traffic intensity be a rational number. The results so generated may be misleading in practice when a control policy is imposed, even when the probability distributions for the interarrival and service times are both deterministic.     

Discreteness criteria in <Emphasis Type="Italic">PU</Emphasis> (1, <Emphasis Type="Italic">n</Emphasis>; <Emphasis Type="Italic">C</Emphasis>)

In this paper, we study the discreteness for non-elementary subgroups in PU (1, n; C), and several discreteness criteria are obtained.