The finite <Emphasis Type=Italic>p</Emphasis>-groups with <Emphasis Type=Italic>p</Emphasis> conjugacy classes of non-normal subgroups

Let ν(G) be the number of conjugacy classes of non-normal subgroups of a finite group G. The finite groups for which ν(G) ≤ 2 were determined by Dedekind and by Schmidt in the early times of group theory. On the other hand, if G is a finite p-group, La Haye and Rhemtulla have proved that either ν(G) ≤ 1 or ν(G) ≥ p. In this note, we determine all finite p-groups satisfying ν(G) = p for p > 2.     

On cyclic <Emphasis Type=Italic>p</Emphasis>-gonal Riemann surfaces with several <Emphasis Type=Italic>p</Emphasis>-gonal morphisms

Let p be a prime number, p > 2. A closed Riemann surface which can be realized as a p-sheeted covering of the Riemann sphere is called p-gonal, and such a covering is called a p-gonal morphism. If the p-gonal morphism is a cyclic regular covering, the Riemann surface is called a cyclic p-gonal Riemann surface. Accola showed that if the genus is greater than (p − 1)² the p-gonal morphism is unique. Using the characterization of p-gonality by means of Fuchsian groups we show that there exists a uniparametric family of cyclic p-gonal Riemann surfaces of genus (p − 1)² which admit two p-gonal morphisms. In this work we show that these uniparametric families are connected spaces and that each of them is the Riemann sphere without three points. We study the Hurwitz space of pairs (X, f), where X is a Riemann surface in one of the above families and f is a p-gonal morphism, and we obtain that each of these Hurwitz spaces is a Riemann sphere without four points.     

The <Emphasis Type=Italic>p</Emphasis>-adic quantum differential

We propose the Fredholm module structure on the space L₂(ℙ¹(ℚ_p)). We study the properties of the corresponding quantum Connes differential.     

<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)     

A generalization of Hardy spaces <Emphasis Type=Italic>H</Emphasis><Superscript><Emphasis Type=Italic>p</Emphasis></Superscript> by using atoms

Let X = （X, d,μ） The purpose of this paper is to be a space of homogeneous type in the sense of Coifman and Weiss. generalize the definition of Hardy space H^P（X） and prove that the generalized Hardy spaces have the same property as H^P（X）. Our definition includes a kind of Hardy- Orlicz spaces and a kind of Hardy spaces with variable exponent. The results are new even for the R^n case. Let （X, δ, μ） be the normalized space of （X, d, μ） in the sense of Macias and Segovia. We also study the relations of our function spaces for （X, d, μ） and （X, δ,μ）.     

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.      

Two sided norm estimate of the Bergman projection on <Emphasis Type=Italic>L</Emphasis><Superscript><Emphasis Type=Italic>p</Emphasis></Superscript> spaces

We give some explicit values of the constants C ₁ and C ₂ in the inequality C ₁/sin(π/p) ⩽ |P| _p ⩽ C ₂/sin(π/p) where |P| _p denotes the norm of the Bergman projection on the L ^p space. Partially supported by MNZZS Grant No. ON144010.     

On <Emphasis Type=Italic>l</Emphasis><Subscript>2,<Emphasis Type=Italic>p</Emphasis></Subscript>-circle numbers

Circle numbers are defined to reflect the Euclidean area-content and, for p ≠ 2, suitably defined non-Euclidean circumference properties of the l _2,p -circles, p ∈ [1, ∞]. The resulting function is continuous, increasing, and takes all values from [2, 4]. The actually chosen dual l _2,p -geometry for measuring the arc-length is closely connected with a generalization of the method of indivisibles of Cavalieri and Torricelli in the sense that integrating such arc-lengths means measuring area content. Moreover, this approach enables one to look in a new way into the co-area formula of measure theory which says that integrating Euclidean arc-lengths does not yield area content except for p = 2. The new circle numbers play a natural role, e.g., as norming constants in geometric measure representation formulae for p-generalized uniform probability distributions on l _2,p -circles.     

Group invariance and <Emphasis Type=Italic>L</Emphasis><Superscript><Emphasis Type=Italic>p</Emphasis></Superscript>-bounded operators

The Hilbert and Riesz transforms can be characterized up to scalar as the translation invariant operators that satisfy additionally certain relative invariance of conformal transformation groups. In this article, we initiate a systematic study of translation invariant operators from group theoretic viewpoints, and formalize a geometric condition that characterizes specific multiplier operators uniquely up to scalar by means of relative invariance of affine subgroups. After providing some interesting examples of multiplier operators having “large symmetry”, we classify which of these examples can be extended to continuous operators on L ^p (R ⁿ ) (1 < p < ∞). T. Kobayashi was partially supported by Grant-in-Aid for Scientific Research 18340037, Japan Society for the Promotion of Science. A. Nilsson was partially supported by Japan Society for the Promotion of Science.     

A necessary condition for non-abelian finite <Emphasis Type=Italic>p</Emphasis>-groups with second centre of order <Emphasis Type=Italic>p</Emphasis><Superscript>2</Superscript>

Let G be a non-abelian finite p-group such that |Z ₂(G)| = p ². In this paper we prove that each maximal subgroup M ≠ C _G (Z ₂(G)) is non-abelian and has cyclic centre.     

Nearly <Emphasis Type=Italic>H</Emphasis>-closed spaces

For a subset M of a topological space X, the θ-closure {ie626-01} M is defined as the set of all x ∈ X such that any closed neighborhood of x intersects M. A Urysohn space X is said to be U-closed if, whenever X ∪ {ξ} is a Urysohn space obtained from X by adding one point ξ, the point ξ is isolated in X ∪ {ξ}. The θ-closure operator is applied to study compactness-type properties of (weakly) U-and H-closed and closed-hereditarily U-and H-closed spaces. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 48, General Topology, 2007.     

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.     

Analog of <Emphasis Type=Italic>L</Emphasis><Superscript><Emphasis Type=Italic>p</Emphasis></Superscript> with a subadditive measure

For a subadditive fuzzy measure (not assumed finite), a Minkowski type triangle inequality, with Choquet integrals in place of Lebesgue integrals, is shown to hold. It is immediate that the set of functions for which a certain positive power of the absolute values have finite Choquet integrals is closed under addition, leading to a linear space analogous to the Lebesgue space L ^p , with a metric related to the integral of that power. Under the additional condition that the subadditive fuzzy measure is inner continuous (Sugeno), the space is shown to be complete. Consequences of the Minkowski type inequality are illustrated in two specific instances.      

An <Emphasis Type=Italic>L</Emphasis><Subscript><Emphasis Type=Italic>p</Emphasis></Subscript>-Theory of SPDEs on Lipschitz Domains

Stochastic partial differential equations are considered on Lipschitz domains. Existence and uniqueness results are given in weighted Sobolev spaces, and Hölder estimates of the solutions are also obtained. The number of derivatives of the solutions can be any real number, in particular, it can be negative and fractional. It is allowed that the coefficients of the equations blow up near the boundary.     

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.     

Solutions of <Emphasis Type=Italic>p</Emphasis>-adic string equations

We review several purely mathematical results concerning boundary value problems for nonlinear pseudodifferential equations for p-adic closed and open strings in the tree approximation in the case d = 1. For the solutions of these problems, we present formulas establishing the relations between the numbers of their zeros, the multiplicities of the zeros, and the numbers indicating how many times the solutions change sign.     

A polynomial <Emphasis Type=Italic>p</Emphasis>-adic dynamical system

We completely describe the Siegel discs and attractors for the p-adic dynamical system f(x) = x ²ⁿ⁺¹ + axⁿ⁺¹ on the space of complex p-adic numbers.