Forward–Backward–Half Forward Dynamical Systems for Monotone Inclusion Problems with Application to v-GNE

Journal of Optimization Theory and Applications - In this paper, the first-order forward–backward–half forward dynamical systems associated with the inclusion problem consisting of...     

Self-Duality of Polytopes and its Relations to Vertex Enumeration and Graph Isomorphism

We study the complexity of determining whether a polytope given by its vertices or facets is combinatorially isomorphic to its polar dual. We prove that this problem is Graph Isomorphism hard, and that it is Graph Isomorphism complete if and only if Vertex Enumeration is Graph Isomorphism easy. To the best of our knowledge, this is the first problem that is not equivalent to Vertex Enumeration and whose complexity status has a non-trivial impact on the complexity of Vertex Enumeration irrespective of whether checking Self-duality turns out to be strictly harder than Graph Isomorphism or equivalent to Graph Isomorphism. The constructions employed in the proof yield a class of self-dual polytopes that are interesting on their own. In particular, this class of self-dual polytopes has the property that the facet-vertex incident matrix of the polytope is transposable if and only if the matrix is symmetrizable as well. As a consequence of this construction, we also prove that checking self-duality of a polytope, given by its facet-vertex incidence matrix, is Graph Isomorphism complete, thereby answering a question of Kaibel and Schwartz.     

Weyl group multiple Dirichlet series constructed from quadratic characters

We construct multiple Dirichlet series in several complex variables whose coefficients involve quadratic residue symbols. The series are shown to have an analytic continuation and satisfy a certain group of functional equations. These are the first examples of an infinite collection of unstable Weyl group multiple Dirichlet series in greater than two variables having the properties predicted in [2].     

Steady state analysis of an M/G/1 queue with two phase service and Bernoulli vacation schedule under multiple vacation policy

This paper examines the steady state behaviour of a batch arrival queue with two phases of heterogeneous service along and Bernoulli schedule vacation under multiple vacation policy, where after two successive phases service or first vacation the server may go for further vacations until it finds a new batch of customer in the system. We carry out an extensive stationary analysis of the system, including existence of stationary regime, queue size distribution of idle period process, embedded Markov chain steady state distribution of stationary queue size, busy period distribution along with some system characteristics.     

Directed transverse flow and its disappearance for asymmetric reactions

We study the directed transverse flow for mass asymmetry reactions. This is done by keeping the target fixed and varying the projectile mass from ⁴He to ¹³¹Xe. We find that directed transverse flow is sensitive to the mass of the projectile. We also study the disappearance of flow at a particular impact parameter called Geometry of Vanishing Flow (GVF) for such mass asymmetry reactions. Our results indicate that GVF is sensitive to the beam energy as well as to the mass of the projectile.     

A possible connection between neutrino mass generation and the lightness of a NMSSM pseudoscalar

One of the interesting properties of the NMSSM is that it can accommodate a light pseudoscalar of order 10 GeV. However, such scenarios are challenged by several experimental constraints, especially those related to the fermionic decays of the pseudoscalar. In this Letter, we extend the NMSSM field content by two gauge singlets, with lepton numbers +1 and −1. This serves the twin purpose of generating neutrino masses via the inverse seesaw mechanism and keeping the option of a very light pseudoscalar experimentally viable by opening dominant invisible decay channels of the pseudoscalar which help it evade the existing bounds.     

Conformally flat tilted Bianchi Type-V cosmological models in general relativity

We have investigated two conformally flat tilted Bianchi Type-V cosmological models in general relativity. To get a determinate solution, we have assumed a supplementary conditionA =B ⁿ between metric potentials wheren is a constant. The behaviour of the model forn = 2 is discussed in detail. Various physical and geometrical aspects of the models are also discussed.     

Proximity Approach to Study the Fusion Barriers for Proton and Helium Induced Reactions

By using various proximity potentials, the fusion barrier heights and positions are calculated for proton and helium induced reactions with targets in the mass range 51≤ A ≤130 and 12≤ A ≤233, respectively. The calculated fusion barriers are parameterized by using the relations RB^Par = aX1 ＋ b and VB^Par = cX2, where X1 and X2 are A2^1/3 and Z1Z2/RB^Par, respectively. The values of the constants a, b and c are different for different versions of proximity potentials. We find that the parameterized forms derived by using Proximity 1977 yield values closer to the empirical data in proton as well as helium induced reactions and can be used further to estimate directly the barrier parameters for the fusion reactions of proton and helium with any target.     

Monte Carlo calculation of electron spectra produced in water phantoms by 20 keV-1 GeV photons

Abstract

A Monte Carlo calculation for the energy spectra of electrons and positrons produced in infinite and semiinfinite water phantoms by photons ranging in energies from 20 keV to 1 GeV are presented. The dominant processes considered are the photoelectric effect, Auger effect, Compton effect, pair, and triplet production. Bremsstrahlung produced by electrons and positrons with energies greater than 1 MeV is also included. The effect of multiple Compton scattering, not considered in the earlier calculation, for the infinite phantom for photon energies higher than 2 MeV has been incorporated. For a semi-infinite phantom, multiple Compton scattering and backscattering through the top are considered. The results are compared with the earlier calculations for the first-collision spectrum. It is found that the inclusion of multiple Compton scattering significantly increases the average number of electrons/cm³ per photon/cm² at all energies considered whereas bremsstrahlung reduces the number of high energy electrons and produces more low energy electrons in the spectrum.