oundary One-Point Function of the Rational Six-Vertex Model with Partial Domain Wall Boundary Conditions: Explicit Formulas and Scaling Properties

We consider the six-vertex model with the rational weights on an s by N square lattice with partial domain wall boundary conditions. We study the one-point function at the boundary where the free boundary conditions are imposed. For a finite lattice, it can be computed by the quantum inverse scattering method in terms of determinants. In the large N limit, the result boils down to an explicit terminating series in the parameter of the weights. Using the saddle-point method for an equivalent integral representation, we show that as s next tends to infinity, the one-point function demonstrates a step-wise behavior; at the vicinity of the step it scales as the error function. We also show that the asymptotic expansion of the one-point function can be computed from a second-order ordinary differential equation.

Approximations of Tangent Polynomials, Tangent –Bernoulli and Tangent – Genocchi Polynomials in terms of Hyperbolic Functions

Asymptotic approximations of Tangent polynomials, Tangent-Bernoulli, and Tangent-Genocchi polynomials are derived using saddle point method and the approximations are expressed in terms of hyperbolic functions. For each polynomial there are two approximations derived with one having enlarged region of validity.

Shell-structure and asymmetry effects in level densities

Level density [Formula: see text] is derived for a nuclear system with a given energy [Formula: see text], neutron [Formula: see text], and proton [Formula: see text] particle numbers, within the semiclassical extended Thomas–Fermi and periodic-orbit theory beyond the Fermi-gas saddle-point method. We obtain [Formula: see text], where [Formula: see text] is the modified Bessel function of the entropy [Formula: see text], and [Formula: see text] is related to the number of integrals of motion, except for the energy [Formula: see text]. For small shell structure contribution one obtains within the micro–macroscopic approximation (MMA) the value of [Formula: see text] for [Formula: see text]. In the opposite case of much larger shell structure contributions one finds a larger value of [Formula: see text]. The MMA level density [Formula: see text] reaches the well-known Fermi gas asymptote for large excitation energies, and the finite micro-canonical limit for low excitation energies. Fitting the MMA [Formula: see text] to experimental data on a long isotope chain for low excitation energies, due mainly to the shell effects, one obtains results for the inverse level density parameter [Formula: see text], which differs significantly from that of neutron resonances.

On the Deficiency of the Ott-Clemmow Modified Saddle-Point Method in the Sommerfeld Half-Space Problem

Preprint of a submitted article.

On the Deficiency of the Ott-Clemmow Modified Saddle-Point Method in the Sommerfeld Half-Space Problem

Preprint of a submitted article.

A complete analytical solution to the integro-differential model describing the nucleation and evolution of ellipsoidal particles

In this paper, a complete analytical solution to the integro-differential model describing the nucleation and growth of ellipsoidal crystals in a supersaturated solution is obtained. The asymptotic solution of the model equations is constructed using the saddle-point method to evaluate the Laplace-type integral. Numerical simulations carried out for physical parameters of real solutions show that the first four terms of the asymptotic series give a convergent solution. The developed theory was compared with the experimental data on desupersaturation kinetics in proteins. It is shown that the theory and experiments are in good agreement.

Saddle Point Approximation of Mutual Information for Finite-Alphabet Inputs over Doubly Correlated MIMO Rayleigh Fading Channels

Given the mutual information of finite-alphabet inputs cannot be calculated concisely and accurately over fading channels, this paper proposes a new method to calculate the mutual information. First, the applicability of the saddle point method is studied, and then the mutual information is estimated by the saddle point approximation method with known channel state information. Furthermore, we induce the expectation of mutual information over doubly correlated multiple-input multiple-output (MIMO) Rayleigh fading channels. The validity of the saddle point approximation method is verified by comparing the numerical results of the Monte Carlo method and the saddle point approximation method under different doubly correlated MIMO fading channel scenarios.

Quantum gravity, group field theory (GFT), and combinatorics

This chapter is the first chapter of the book dedicated to the study of the combinatorics of various quantum gravity approaches. After a brief introductory section to quantum gravity, we shortly mention the main candidates for a quantum theory of gravity: string theory, loop quantum gravity, and group field theory (GFT), causal dynamical triangulations, matrix models. The next sections introduce some GFT models such as the Boulatov model, the colourable and the multi-orientable model. The saddle point method for some specific GFT Feynman integrals is presented in the fifth section. Finally, some algebraic combinatorics results are presented: definition of an appropriate Conne–Kreimer Hopf algebra describing the combinatorics of the renormalization of a certain tensor GFT model (the so-called Ben Geloun–Rivasseau model) and the use of its Hochschild cohomology for the study of the combinatorial Dyson–Schwinger equation of this specific model.

Approximate analytical solution of the integro-differential model of bulk crystallization in a metastable liquid with mass supply (heat dissipation) and crystal withdrawal mechanism

This paper is devoted to an approximate analytical solution of an integro-differential model describing the process of nucleation and growth of particles in crystallizers, taking into account the thermal-mass exchange with the environment and the removal of product crystals from the metastable medium. The method developed in this work for solving model equations (kinetic equation for the particle size distribution function and balance equations for temperature/impurity concentration) is based on using the saddle point method for calculating the Laplace-type integral. It is shown that the degree of metastability of the liquid decreases with time at a fixed value of the mass inflow from the outside (heat flow to the outside). The crystal size distribution function has the form of an irregular bell-shaped curve, which increases with the intensification of heat and mass exchange with the environment.

Application of Intuitionistic Neutrosophic Soft Sets in Decision Making Based on Game Theory

The main objective of the paper is to introduce intuitionistic neutrosophic soft sets(INSSs) and their properties in the study of game theory. Earlier, in 2018, Anjan et al. introduced the notion of intuitionistic fuzzy soft game theory. So, here an attempt has been made to extend the earlier concept by introducing intuitionistic neutrosophic soft game theory. We also define two-person intuitionistic neutrosophic soft games (TP-INS-games) and extend them to N-person-INS-games. Finally, with the help of the intuitionistic neutrosophic soft saddle point method, we give an application in a real decision-making problem.