1st Kind Research Articles

Jacobi wavelet operational matrix of fractional integration for solving fractional integro-differential equation

In this paper, we first define generalized shifted Jacobi polynomial on interval and then use it to define Jacobi wavelet. Then, the operational matrix of fractional integration for Jacobi wavelet is being derived to solve fractional differential equation and fractional integro-differential equation. This method can be seen as a generalization of other orthogonal wavelet operational methods, e.g. Legendre wavelets, Chebyshev wavelets of 1st kind, Chebyshev wavelets of 2nd kind, etc. which are special cases of the Jacobi wavelets. We apply our method to a special type of fractional integro-differential equation of Fredholm type.

ОБ ОСОБЕННОСТЯХ ИДЕНТИФИКАЦИИ НЕОДНОРОДНЫХ ПОРОУПРУГИХ ХАРАКТЕРИСТИК ПОЛОГО ЦИЛИНДРА

The coefficient inverse problem of finding poroelastic characteristics of ingomogeneous hollow cylinder is considered. Direct problem poroelasticity for the cylinder is solved by a method of adjustment. As additional information for solving the inverse problem appears measured displacement or pressure at the outer edge of the cylinder. To solve the inverse problem, based on the linearization method derived operator relations, establishing a relationship between a desired and measured characteristics. Poroelastictic characteristics restored in two phases. The first phase was an initial approximation. The second stage amendments to the recoverable characteristics are determined from the solution of Fredholm integral equations of the 1st kind. For solutions of Fredholm integral equations of the 1st kind used method of A.N. Tikhonov. Concrete examples of the reconstruction of the characteristics of inhomogeneous poroelastic cylinder are given. Keywords: poroelasticity, inverse problem, hollow cylinder, integral equations.

On reconstruction of thermalphysic characteristics of functionally graded hollow cylinder

An inverse coefficient problem of thermal conductivity for a functionally graded hollow cylinder is considered. After applying the Laplace transform, the direct thermal conductivity problem is solved by using two methods: (1) based on a reduction to the Fredholm integral equation of the 2nd kind; (2) by means of the Galerkin method. A comparison of the direct problem solving techniques is provided. The nonlinear inverse problem is solved on the basis of an iterative process; at every step of the latter the linear Fredholm integral equation of the 1st kind is solved. Results of the computational experiments on a reconstruction of variation laws of thermal conductivity and specific volumetric heat capacity are presented.

A numerical study on dual-phase-lag model of bio-heat transfer during hyperthermia treatment

The success of hyperthermia in the treatment of cancer depends on the precise prediction and control of temperature. It was absolutely a necessity for hyperthermia treatment planning to understand the temperature distribution within living biological tissues. In this paper, dual-phase-lag model of bio-heat transfer has been studied using Gaussian distribution source term under most generalized boundary condition during hyperthermia treatment. An approximate analytical solution of the present problem has been done by Finite element wavelet Galerkin method which uses Legendre wavelet as a basis function. Multi-resolution analysis of Legendre wavelet in the present case localizes small scale variations of solution and fast switching of functional bases. The whole analysis is presented in dimensionless form. The dual-phase-lag model of bio-heat transfer has compared with Pennes and Thermal wave model of bio-heat transfer and it has been found that large differences in the temperature at the hyperthermia position and time to achieve the hyperthermia temperature exist, when we increase the value of τT. Particular cases when surface subjected to boundary condition of 1st, 2nd and 3rd kind are discussed in detail. The use of dual-phase-lag model of bio-heat transfer and finite element wavelet Galerkin method as a solution method helps in precise prediction of temperature. Gaussian distribution source term helps in control of temperature during hyperthermia treatment. So, it makes this study more useful for clinical applications.

Неопределенность 1-го рода в восстановительной медицине

So far, the fact that statistically significance differences between samples (sets of parameters of the body xi) before the treatment and after the treatment led to the conclusion of non effective treatment. However, in the framework of the theory of chaos and self-organization the assessment of the significant differences can be carried out without going through statistical methods, based on the analysis parameters of quasi-attractors or using neural emulators. In this report the authors present examples of uncertainties of the 1st kind in regenerative medicine and introduce new technologies to resolve these uncertainties. A procedure for finding differences between samples and determining the parameters of the order (the most important diagnostic features) based methods neurocomputing. The effectiveness of this approach in the evaluation of the effectiveness treatment effects of abnormalities in the body during acute stroke in a kinesotherapy is presented. The authors proved ineffective stochastics and opportunities neurocomputing in the task of system synthesis

The methodical framework of the development of adequate model of estimation of credit risk of the bank

It was considered the modern methods of assessment of credit risk which are used by the foreign banks, in particular, their essence, advantages and disadvantages were discovered in this article. It was proposed and characterized the criteria of judgmental estimate adequacy of the models intended for analysis and forecast of borrower creditworthiness assessment, in particular such criteria as general accuracy of the model, the errors of 1st and 2nd kind, ROC – curve and GINI index.

Стохастика и хаос в оценке параметров порядка в восстановительной медицине

The basis of the third global paradigm of theory of chaos and self-organization, which focuses on the assessment of the chaotic dynamics of the state vector of complex biological systems using multi-dimensional phase space of states. The paper presents a comparative description of the effectiveness of the traditional stochastic methods and methods of calculating the parameters of quasi-attractors. It is showed the difference in efficiency (low) of stochastics, which leads to the uncertainty of the 1st kind, and methods of multidimensional phase spaces, providing the solution of system synthesis. Volumes quasi-attractors with kinesotherapy in patients with acute stroke increased 5.3 times in the initial stage of treatment, and then falling off sharply. It is discussed the need for parallel applications and stochastic methods and methods of theory of chaos and self-organization in the study of complex medical and biological systems.

Application of the Abel equation of the 1st kind to inflation analysis of non-exactly solvable cosmological models

In this paper we revisit the relationship between the Einstein--Friedman and the Abel equations to demonstrate how it might be applied to the inflationary analysis in a flat Friedman universe filled with a real-valued scalar field. The analysis is performed for three distinct cases of polynomial potentials. As a result of a numeric integration of Abel equation, the necessary and sufficient conditions for both slow-rolling and inflation proper are estimated with respect to the initial value of the field. In addition, the relationship between the slow-rolling condition and the inflation is ascertained.

Ecological and economical efficiency of monitoring systems for oil and gas production on the shelf

Requirements for signals’ reliability of monitoring systems (with respect to the errors of the 1st and 2nd kinds, i.e., false alarms and skipping of danger) are deduced from the ratio of expenditures of different kinds (of exploitation expenses and losses due to accidents). The expressions obtained in the research may be used for economic foundations (and optimization) of specifications for monitoring systems. In cases when optimal parameters are not available, the sufficient condition of monitoring systems economical efficiency is presented.

On the Hypersurface of a Finsler Space with the Special Metric α+ βn+1 (α-β)n

In the present paper, we consider a n−dimentional Finsler space Fn = (Mn,L) with (α,β)−metric L(α,β) = α + βn+1 (α−β)n which is a generalization of the metric α + β2 (α−β) considered in [9] and the hypersurface of Fn with bi(x) = ∂ib being the gradient of a scalar function b(x). We find the conditions for this hypersurface to be a hyperplane of 1st kind, 2nd kind and we also show that this hypersurface is a hyperplane of 3rd kind if and only if it is a hyperplane of f irst kind.

On an inverse problem for inhomogeneous thermoelastic rod

In recent years, different fields of engineering have been increasingly incorporating functionally graded materials with variable physical properties that significantly improve a quality of elements of designs. The efficiency of practical application of thermoelastic inhomogeneous materials depends on knowledge of exact laws of heterogeneity, and to define them it is necessary to solve coefficient inverse problems of thermoelasticity.In the present research a scheme of solving the inverse problem for an inhomogeneous thermoelastic rod is presented. Two statements of the inverse problem are considered: in the Laplace transform space and in the actual space. The direct problem solving is reduced to a system of the Fredholm integral equations of the 2nd kind in the Laplace transform space and an inversion of the solutions obtained on the basis of the theory of residues. The inverse problem solving is reduced to an iterative procedure, at its each step it is necessary to solve the Fredholm integral equation of the 1st kind; to solve it the Tikhonov method is used. Specific examples of a reconstruction of variable characteristics required are given.

A note on spacelike surfaces in Minkowski 3-space

We characterize and classify spacelike surfaces endowed with a canonical principal direction in Minkowski 3-space E13. Under the maximality condition, a new characterization for the catenoid of the 1st kind is obtained.

A nonlocal problem for a hyperbolic equation with integral conditions of the 1st kind with time-dependent kernels

We consider a nonlocal problem with integral conditions of the 1st kind. The main goal is to prove the unique solvability of this problem under the assumption that kernels of nonlocal conditions depend both on spatial and time variables. To this end we propose a technique based on the proved equivalence between the nonlocal problem with integral conditions of the 1st kind and a nonlocal problem with integral conditions of the 2nd kind in a special form. We formulate requirements to the initial data guaranteeing the unique existence of a generalized solution to the stated problem.

Economic optimization of specifications for geoecological monitoring systems

The problem of incomparability of errors of 1st and 2nd kind (of false alarm and of missing of real danger) became solved after degrees of ecological disasters began to be expressed monetary. Requirements to reliability of monitoring systems (MS) signals are deduced from ratio of expenses of different kind. The sufficient condition of MS economic efficiency is resulted also. These results should be considered by working out specifications on MS.

Ban(g)! Ban(g)! Dangerous Encounter - 1st Kind: Writing with Censorship

Ban(g)! Ban(g)! Dangerous Encounter - 1st Kind: Writing with Censorship

Correction and Verification of Dispersion and Loss of Plasmons on Metal Nano-Spheres

Rigorous verification has been performed on numerical and theoretical analyses of the dispersion and the loss of plasmonic resonance on Ag and Au nano-spheres. It is shown that the widely believed transcendental equation obtained from the Mie theory, which has been originally derived for dielectric spheres, must be modified for the analysis of metal nano-spheres whose permittivity has a negative real part; i.e., assumption of the field outside a sphere by the spherical Hankel function of the 1st kind must be altered to that by the spherical Hankel function of the 2nd kind . The complex resonance frequencies of the metal nano-spheres obtained both theoretically and numerically agree very well after the correction, whereas the solutions to the original equation in terms of fail, in particular, for the imaginary part. It is a fundamental and important problem; the analysis of metal spheres enables reliable clarification of the appropriate analysis methods and conditions not only from a dispersive nature (real part of the resonance frequency) but also from a dissipative nature (imaginary part of the resonance frequency). The plasmon resonance is then analyzed for various topologies of multiple-sphere clusters, and their resonance states have been characterized from the spectra in infrared to ultraviolet range.

Use of barrier functions for optimal correction of improper problems of linear programming of the 1st kind

Possibilities are investigated of the combined use of interior and exterior penalty functions for discovering the generalized (approximate) solutions of improper problems of linear programming of the 1st kind. Diagrams of algorithms, theorems of convergence, results of numerical experiments are presented.

Residual stresses in electron-beam coatings with a nitrogen-austenite matrix and structural mechanisms of their relaxation

The structure, distribution of elastic microdeformations related to the effect of residual stresses of the 1st and 2nd kind in nitrogen austenite coatings prepared by electron-beam overlaying and the mechanisms of relaxation of residual stresses in the substrate-coating system have been investigated. The state of stress is characterized by a change in sense over the coating thickness. An analysis of experimental data shows that the relaxation of residual stresses results in the formation of a structure with an enhanced density of dislocations. The main mechanism of relaxation of residual stresses in overlaid coatings is microtwinning and γ → ɛ transformation.

Application of inversion methods in solving ill-posed problems for magnetic parameter identification of steel hull vessel

Abstract Recovery of magnetic target parameters from magnetic sensor measurements has attracted wide interests and found many practical applications. However, difficulties present in identifying the permanent magnetization due to the complications of magnetization distributions over the ship body, and errors and noises of measurement data degrade the accuracy and quality of the parameter identification. In this paper, we use a two step sequential solutions to solve the inversion problem. In the first step, a numerical model is built and used to determine the induced magnetization of the ship. In the second step, we solve a type of continuous magnetization inversion problem by solving 2D Fredholm integral equation of the 1st kind. We use parallel computing which allows solve the inverse problem with high accuracy. In additional, Tikhonov regularization has been applied in solving the inversion problems. The proposed methods have been validated using simulation data with added noises.

Topological expansion of the β-ensemble model and quantum algebraic geometry in the sectorwise approach

We solve the loop equations of the $\beta$-ensemble model analogously to the solution found for the Hermitian matrices $\beta=1$. For \beta=1$, the solution was expressed using the algebraic spectral curve of equation $y^2=U(x)$. For arbitrary $\beta$, the spectral curve converts into a Schr\"odinger equation $((\hbar\partial)^2-U(x))\psi(x)=0$ with $\hbar\propto (\sqrt\beta-1/\sqrt\beta)/N$. This paper is similar to the sister paper~I, in particular, all the main ingredients specific for the algebraic solution of the problem remain the same, but here we present the second approach to finding a solution of loop equations using sectorwise definition of resolvents. Being technically more involved, it allows defining consistently the B-cycle structure of the obtained quantum algebraic curve (a D-module of the form $y^2-U(x)$, where $[y,x]=\hbar$) and to construct explicitly the correlation functions and the corresponding symplectic invariants $F_h$, or the terms of the free energy, in 1/N^2$-expansion at arbitrary $\hbar$. The set of "flat" coordinates comprises the potential times $t_k$ and the occupation numbers \widetilde{\epsilon}_\alpha$. We define and investigate the properties of the A- and B-cycles, forms of 1st, 2nd and 3rd kind, and the Riemann bilinear identities. We use these identities to find explicitly the singular part of $\mathcal F_0$ that depends exclusively on $\widetilde{\epsilon}_\alpha$.