ORTHOGONAL POLYNOMIALS AND DETERMINANT FORMULAS OF FUNCTION-VALUED PADE-TYPE APPROXIMATION USING FOR SOLUTION OF INTEGRAL EQUATIONS

To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation are explicitly given.

Rough Integrals Generated by Function Rough Sets

The concepts of the lower approximation integral,the upper approximation integral and rough integrals are given on the basis of function rough sets.Based on these concepts,the relation of the lower approximation integrals,the relation of the upper approximation integrals,the relation of rough integrals,and the double median theorem of rough integrals are discussed.Rough integrals have finite contraction characteristic and finite extension characteristic.

APPROXIMATION OF SINGULAR INTEGRALS BY INTERPOLATING SPLINES

In this paper we are mainly concerned with the approximation of the following type of singular Integrals: where w(t)≥0 is a weight function, f(x) a real continuous function on [a, b], satisfying certain smooth conditions, and the integral is of Canchy principal value.

APPROXIMATION BY INTEGRAL TYPE MEYER-KONIG-ZELLER OPERATORS ON A SIMPLEX

Letbe a simplex in The integral type Meyer-Komg-Zeller operators are constructed on the simplex T, and the degree of approximation of these operators for L'-functions is obtained.

RESTRICTED NONLINEAR APPROXIMATION AND SINGULAR SOLUTIONS OF BOUNDARY INTEGRAL EQUATIONS

This paper studies several problems , which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterizations of functions in Besom spaces B(?)(0,1) with 0<σ<∞ and (1+σ)-1<γ<∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.

APPROXIMATION OF SPHERICAL MEANS OF MULTIPLE FOURIER INTEGRALS AND FOURIER SERIES ON SET OF FULL MEASURE

In this paper we consider the approximation for functions in some subspaces of L^2 by spherical means of their Fourier integrals and Fourier series on set of full measure. Two main theorems are obtained.

Asymptotic Analysis Methods for Structural Reliability

Applying Laplace asymptotic approximation of integral, asymptotic analysis methods of structural reliability are proposed in generalized and orthogonal random space. Analytic results show that the proposed methods are simple in calculation and accurate enough for problems of continuous random variables.

LOCAL SALINE APPROXIMATION METHODS FOR SINGULAR PRODUCT INTEGRATION

The purpose of this paper is to propose and study local spline approximation methods for singular product integration,for which;i)the precision degree is the highest possible using splint approximation; ii) the nodes fan be assumed equal to arbitrary points,where the integrand function f is known; iii) the number of the requested evaluations of f at the nodes is low,iv) a satisfactory convergence theory can be proved.

Unsteady Rotative Flow of Non-Newtonian Fluid in an Annular Pipe

This paper .Studies power law no-Newtonian fluid rotative flow. in an annularpipe. The governing equation is nonlinear one, we linearized the governing equationby assuming that partial factor is at state. With Laplace transform we obtain ananalytical solution of the problem In the paper several groups of curves are given.these curves reflect the temporal change law and. spatial distribution of fluid velocity.In addition.we study the effection of power law index on the flow field the resultindicates that when the power law index n < l. the flow velocity is highly sensitive tothe index. and this fact is importanl in related engineering decisions.

Identifying Malaria Hotspots Regions in Ghana Using Bayesian Spatial and Spatiotemporal Models

Background:Malaria remains a significant public health concern in Ghana,with varying risk levels across different geographical areas.Malaria affects millions of people each year and imposes a substantial burden on the health care system and population.Accurate risk estimation and mapping are crucial for effectively allocating resources and implementing targeted interventions to identify regions with disease hotspots.This study aimed to identify regions exhibiting elevated malaria risk so that public health interventions can be implemented,and to identify malaria risk predictors that can be controlled as part of public health interventions for malaria control.Methods:The data on laboratory-confirmed malaria cases from 2015 to 2021 were obtained from the Ghana Health Service and Ghana Statistical Service.We studied the spatial and spatiotemporal patterns of the relative risk of malaria using Bayesian spatial and spatiotemporal models.The malaria risk for each region was mapped to visually identify regions with malaria hotspots.Clustering and heterogeneity of disease risks were established using correlated and uncorrelated structures via the conditional autoregressive and Gaussian models,respectively.Parameter estimates from the marginal posterior distribution were estimated within the Integrated Nested Laplace Approximation using the R software.Results:The spatial model indicated an increased risk of malaria in the North East,Bono East,Ahafo,Central,Upper West,Brong Ahafo,Ashanti,and Eastern regions.The spatiotemporal model results highlighted an elevated malaria risk in the North East,Upper West,Upper East,Savannah,Bono East,Central,Bono,and Ahafo regions.Both spatial and spatiotemporal models identified the North East,Upper West,Bono East,Central,and Ahafo Regions as hotspots for malaria risk.Substantial variations in risk were evident across regions(H=104.9,P<0.001).Although climatic and economic factors influenced malaria infection,statistical significance was not established.Conclusions:Malaria risk was clustered and varied among regions in Ghana.There are many regions in Ghana that are hotspots for malaria risk,and climate and economic factors have no significant influence on malaria risk.This study could provide information on malaria transmission patterns in Ghana,and contribute to enhance the effectiveness of malaria control strategies.

A New Method for Analyzing VOCs Emission from Dry Materials

An approximate integral method for volatile compounds emission from plate is presented in this paper. The gas-phase mass transfer resistance was neglected for simplifying computation. Compared to Laplace Transformation Method, the method suggested is simple, and emission flux, chamber concentration of volatile compounds and concentration distribution of volatile compounds in the material can be determined conveniently. Results of the present method show good agreement with experimental data. The influence of CO, D, K and N on concentration of total volatile organic compounds （TVOC） in the air is also calculated.

Freezing of Water in a Slab with Boundary Conditions of the Third Kind

Predictions for freezing heat transfer in a slab with convective boundary conditions at the cold surfaceare obtained from heat balance integral approximations, which consider conduction as the only modeof heat transfer in both the solid and liquid and consider durations of precooling and freezing in theheat transfer process. The thermal penetration dimensionless parameter or is presented to distinguishtwO cases of freezing, and analytical results for α≥ 1 are given in this paper. An experimental investigation on freezing of water is reported for comparison with the one-dimensional conduction model toshow that experimental modeling for freezing heat transfer with convective boundary conditions usingPeltter devices is feasible. The comparison also demonstrated that the freezing rate in this case wasdecreased by natural convection in the liquid just as freezing with boundary conditions of the first kindand phase change approximately proceeds linearly with time rather than with square root of time atthe initiation of freezing.