Narrow Results

This paper deals with global compactness and the multiplicity of positive solutions to problems of the type

Due to the essential difficulty of establishing an appropriate variational framework on a suitable working space, how to apply the critical point theory for showing the existence and multiplicity of periodic solutions of continuous-time difference equations remains a completely open problem. New ideas including gluing arguments are introduced in this work to overcome such a difficulty. This enables us to employ the critical point theory to construct uncountably many periodic solutions for a class of superlinear continuous-time difference equations without assuming symmetry properties on the nonlinear terms. The obtained solutions are piecewise differentiable in some cases, distinguishing continuous-time difference equations from ordinary differential equations qualitatively. To the best of our knowledge, this is the first time in the literature that the critical point theory has been used for such types of problems. Our work may open an avenue for studying discrete nonlinear systems with continuous time via the critical point theory.

In this paper we prove that a rational surface singularity with divisor class group ℤ/(2) is a rational double point. This generalizes a result by Brieskorn: if the divisor class group of a rational singularity is trivial then it is the E₈ singularity [3].

We also prove several inequalities involving the integers e, δ, m_i, , where is the fundamental cycle. The proof of this result uses ideas from Minkowski's theory of reduction of positive-definite quadratic forms. We also give some interesting counterexamples to some of the related questions in this context.

Let $P$ be a minimal parabolic subgroup of a real reductive Lie group $G$ and $H$ a closed subgroup of $G$. Then it is proved by Kobayashi and Oshima that the regular representation $C^{\infty }(G/H)$ contains each irreducible representation of $G$ at most finitely many times if the number of $H$-orbits on $G/P$ is finite. Moreover, they also proved that the multiplicities are uniformly bounded if the number of $H_{ℂ}$-orbits on $G_{ℂ}/B$ is finite, where $G_{ℂ},H_{ℂ}$ are complexifications of $G,H$, respectively, and $B$ is a Borel subgroup of $G_{ℂ}$. In this paper, we prove that the multiplicities of the representations of $G$ induced from a parabolic subgroup $Q$ in the regular representation on $G/H$ are uniformly bounded if the number of $H_{ℂ}$-orbits on $G_{ℂ}/Q_{ℂ}$ is finite. For the proof of this claim, we also show the uniform boundedness of the dimensions of the spaces of group invariant hyperfunctions using the theory of holonomic ${{𝒟}}_X$-modules.

Some properties: average multiplicity, average momentum and average transverse momentum of light nuclei (without identification), produced in ¹²CC collisions at 4.2A GeV/c are studied as a function of centrality. An unexpected change in the behavior of these properties is observed within the same region of centrality, where the multiplicity of the produced light nuclei is increased. These measurements are compared with models, Cascade and Fritiof predictions, which fail to account for the observed effect. It is suggested that the inclusion of nuclear coalescence effect may explain the difference between the measurements and the predictions.

Centrality definition in A + A collisions at colliders such as RHIC and LHC suffers from a correlated systematic uncertainty caused by the efficiency of detecting a p + p collision ($50\pm 5\%$ for PHENIX at RHIC). In A + A collisions where centrality is measured by the number of nucleon collisions, $N_{\mathrm{\text{coll}}}$, or the number of nucleon participants, $N_{\mathrm{\text{part}}}$, or the number of constituent quark participants, $N_{\mathrm{\text{qp}}}$, the error in the efficiency of the primary interaction trigger (Beam–Beam Counters) for a p + p collision leads to a correlated systematic uncertainty in $N_{\mathrm{\text{part}}}$, $N_{\mathrm{\text{coll}}}$ or $N_{\mathrm{\text{qp}}}$ which reduces binomially as the A + A collisions become more central. If this is not correctly accounted for in projections of A + A to p + p collisions, then mistaken conclusions can result. A recent example is presented in whether the mid-rapidity charged multiplicity per constituent quark participant $(d{N}_{\mathrm{\text{ch}}}/d\eta )/N_{\mathrm{\text{qp}}}$ in Au + Au at RHIC was the same as the value in p + p collisions.

KNO scaling was put forward by Koba, Nielsen, and Olesen (KNO) in 1972. Although it is an important tool for explaining multiplicity distributions and formulated for the asymptotic energies, it has been applied at a finite energy range where its formulation is not self-consistent. A consistent generalization, known as KNO-G scaling, was done by Golokhvastov in 1977 to make it self-consistent. Then, KNO-G scaling has been successfully applied in many experiments and its validity has been reported. In this study, KNO-G scaling is tested in neutrino interactions. The charged hadron multiplicity of CHORUS, OPERA, NOMAD and DONUT, which are neutrino experiments, is compared and tested the KNO-G scaling. It is observed that neutrino data are consistent with KNO-G scaling. A fit is superimposed on the data sets and fit parameters are compared.

Let ℕ be the set of nonnegative integers and let I be an interval of positive rational numbers. Then is a numerical semigroup. In this paper we study the multiplicity of the numerical semigroups of the form , where a and b are integers such that 2 ≤ a < b. We also see the connection between the multiplicity and the Frobenius number of this type of semigroups.

In this paper we introduce the notion of m-irreducibility that extends the standard concept of irreducibility of a numerical semigroup when the multiplicity is fixed. We analyze the structure of the set of m-irreducible numerical semigroups, we give some properties of these numerical semigroups and we present algorithms to compute the decomposition of a numerical semigroup with multiplicity m into m-irreducible numerical semigroups.

In this work, we give parametrizations in terms of the Kunz coordinates of numerical semigroups with multiplicity up to $5$. We also obtain parametrizations of MED semigroups, symmetric and pseudo-symmetric numerical semigroups with multiplicity up to $5$. These parametrizations also lead to formulas for the number of numerical semigroups, the number of MED semigroups and the number of symmetric and pseudo-symmetric numerical semigroups with multiplicity up to $5$ and given conductor.

Let $(A,𝔪)$ be a commutative quasi-local ring (with identity $1\ne 0$), and let $I\subset 𝔪$ be an $A$-ideal such that $\ell (0{:}_{M}I)<\infty$. For $M$ an Artinian $A$-module of N-dimension $d$, we introduce the notion of Hilbert-coefficients of $I$ relative to $M$ and give several properties. When $M$ is a co-Cohen–Macaulay $A$-module, we establish the Northcott’s inequality for Artinian modules. As applications, we show some formulas involving the Hilbert coefficients and we investigate the behavior of these multiplicities when the module is the local cohomology module.

In this work, we study $A$-semigroups, that is, numerical semigroups which have no consecutive elements less than the Frobenius number. We give algorithms that allow computation of the whole set of $A$-semigroups with a given genus, multiplicity and Frobenius number and from this we study interesting families of $A$-semigroups which are Frobenius varieties, pseudo-varieties; R-varieties.

We investigate a class of nonlinear Schrödinger equations with a generalized Choquard nonlinearity and fractional diffusion. We obtain regularity, existence, nonexistence, symmetry as well as decays properties.

Concepts from statistical mechanics and ensemble theory are applied to study the characteristic properties of charged particle production in hadron–nucleus collisions at high energy. In the present study we utilize the predictions from different approaches using statistical mechanics. The Tsallis q-statistics is used to study the regularity in multiplicity distributions in hadron–nucleus collisions at high energies as one of the interesting options. Gamma distributions and a possible microcanonical generalization of Tsallis distribution have also been exploited to describe the data.

Study of the characteristic properties of charged particle production in hadron–nucleus collisions at high energies by utilizing the approaches from different statistical models is performed. Predictions from different approaches using the negative binomial distribution, shifted Gompertz distribution, Weibull distribution and the Krasznovszky–Wagner distribution are considered for a comparative study of the relative success of these models. These distributions derived from a variety of functional forms are based on either phenomenological parameterizations or some model of the underlying dynamics. Some of these have also been used to study the data at the Large Hadron Collider (LHC) for both proton–proton and nucleus–nucleus collisions. Various physical and derived observables have been used for the analysis.

We discuss existence, non-existence and multiplicity of positive solutions of the Dirichlet problem for the one-dimensional prescribed curvature equation

This paper studies the existence of positive solutions for a class of singular boundary value problems of p-Laplacian. By using Global Continuation Theorem and the fixed point index technique, criteria of the existence, multiplicity and nonexistence of positive solutions are established.

In this paper, we study the problem

We establish a precise connection between two elliptic quasilinear problems with Dirichlet data in a bounded domain of ℝ^N. The first one, of the form

In this paper, we are concerned with the semilinear elliptic problem