On a More Accurate Half-Discrete Mulholland-Type Inequality Involving One Multiple Upper Limit Function

By the use of the weight functions, the symmetry property, and Hermite-Hadamard’s inequality, a more accurate half-discrete Mulholland-type inequality involving one multiple upper limit function is given. The equivalent conditions of the best possible constant factor related to multiparameters are studied. Furthermore, the equivalent forms, several inequalities for the particular parameters, and the operator expressions are provided.

A global random walk on grid algorithm for second order elliptic equations

We suggest in this paper a global random walk on grid (GRWG) method for solving second order elliptic equations. The equation may have constant or variable coefficients. The GRWS method calculates the solution in any desired family of m prescribed points of the gird in contrast to the classical stochastic differential equation based Feynman–Kac formula, and the conventional random walk on spheres (RWS) algorithm as well. The method uses only N trajectories instead of mN trajectories in the RWS algorithm and the Feynman–Kac formula. The idea is based on the symmetry property of the Green function and a double randomization approach.

Stability Analysis of a Mathematical Model of Hepatitis B Virus with Unbounded Memory Control on the Immune System in the Neighborhood of the Equilibrium Free Point

In the current paper, I research the influence of IL-2 therapy and I introduce the regulation by distributed feedback control with unbounded memory. The results of the stability analysis are presented. The proposed methodology in the article uses the properties of Cauchy matrix C(t,s), especially symmetry property, in order to study the behavior (stability) of the corresponding system of integro-differential equations.

Quasi-Arithmetic Type Mean Generated by the Generalized Choquet Integral

It is known that the quasi-arithmetic means can be characterized in various ways, with an essential role of a symmetry property. In the expected utility theory, the quasi-arithmetic mean is called the certainty equivalent and it is applied, e.g., in a utility-based insurance contracts pricing. In this paper, we introduce and study the quasi-arithmetic type mean in a more general setting, namely with the expected value being replaced by the generalized Choquet integral. We show that a functional that is defined in this way is a mean. Furthermore, we characterize the equality, positive homogeneity, and translativity in this class of means.

Comparison of Discrete Fourier Transform and Fast Fourier Transform with Reduced Number of Multiplication and Addition Operations

Fast Fourier Transform is an advanced algorithm for computing Discrete Fourier Transform efficiently. Although the results available from the operation of Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) are same, but exploiting the periodicity and symmetry property of phase factor Fast Fourier Transform computes the Discrete Fourier Transform using reduced number of multiplication and addition operations. The basic structure used in the operations of Fast Fourier Transform is the Butterfly structure. For the implementation of Fast Fourier Transform the two methods are used such as decimation in time (DIT) and decimation in frequency (DIF). Both the methods give same result but for decimation in time of Fast Fourier Transform bit reversed inputs are applied and for decimation in frequency of Fast Fourier Transform normal order inputs are applied, and the result is reversed again. In this paper, operations for DFT and FFT have been discussed and shown with examples. It is found that generalized formula for FFT have been described same in the books, but the expressions in the intermediate computations for the first decimation and second decimation are different in the various books of Digital Signal Processing. The expressions in the intermediate computation of FFT described in different books are broadly compared in this paper

Lifting Dual Connections with the Riemann Extension

Let (M,g) be a Riemannian manifold equipped with a pair of dual connections (∇,∇*). Such a structure is known as a statistical manifold since it was defined in the context of information geometry. This paper aims at defining the complete lift of such a structure to the cotangent bundle T*M using the Riemannian extension of the Levi-Civita connection of M. In the first section, common tensors are associated with pairs of dual connections, emphasizing the cyclic symmetry property of the so-called skewness tensor. In a second section, the complete lift of this tensor is obtained, allowing the definition of dual connections on TT*M with respect to the Riemannian extension. This work was motivated by the general problem of finding the projective limit of a sequence of a finite-dimensional statistical manifold.

Thermodynamic Theory of Diffusion and Thermodiffusion Coefficients in Multicomponent Mixtures

Transport coefficients (like diffusion and thermodiffusion) are the key parameters to be studied in non-equilibrium thermodynamics. For practical applications, it is important to predict them based on the thermodynamic parameters of a mixture under study: pressure, temperature, composition, and thermodynamic functions, like enthalpies or chemical potentials. The current study develops a thermodynamic framework for such prediction. The theory is based on a system of physically interpretable postulates; in this respect, it is better grounded theoretically than the previously suggested models for diffusion and thermodiffusion coefficients. In fact, it translates onto the thermodynamic language of the previously developed model for the transport properties based on the statistical fluctuation theory. Many statements of the previously developed model are simplified and amplified, and the derivation is made transparent and ready for further applications. The n(n+1)/2 independent Onsager coefficients are reduced to 2n+1 determining parameters: the emission functions and the penetration lengths. The transport coefficients are expressed in terms of these parameters. These expressions are much simplified based on the Onsager symmetry property for the phenomenological coefficients. The model is verified by comparison with the known expressions for the diffusion coefficients that were previously considered in the literature.