نشریه پژوهشهای ریاضی
سال هفتم شماره 2 (پیاپی 17، تابستان 1400)

The fundamental role of algebraic properties in the development of the basics of computer science has led researchers to study the concepts of fuzzy automaton separatedness, connectedness, and reversibility on a large scale.In this paper, the general fuzzy automaton is investigated from an algebraic and topological point of view and the algebraic properties of this automaton is studied on the basis of Lattice-ordered monoid.On the other hand, the general fuzzy automaton is examined using the concepts of operators.These operators help us in the algebraic study of general fuzzy automata and provide us the necessary basis for the application of topological concepts. For this purpose, considering the definition of general fuzzy automaton, we define the LB-valued general fuzzy automaton in which B is lattice-ordered monoid consisting of propositions about general fuzzy automaton. Further, we define the LB–valued interior and Kuratowski clouser operators on the set of these automaton modes and then introduce the topological structures resulting from the related operators. A noteworthy point in this study is to search for algebraic and topological concepts for general fuzzy automata based on lattice-ordered monoid which rely on dependent monoid structures. Finally, some of the connectedness and seperatedness properties of the general LB-value fuzzy automaton are examined in this study while the proposed concepts are illustrated in details through examples. 

In this paper, we give a criterion for the density of a subspace of lip _{alpha} (X; S) when (X; d) is a compact metric space, S is a complex Banach space and 0 < alpha< 1. In the case where X = [a; b], we conclude that Lip1(X; S) is dense in lip _{alpha}(X; S). Also, using Bochner spaces and the duality we show that C1([a; b]; S), the space of continuously differentiable S-valued functions on [a; b], is dense in lip _{alpha} ([a; b]; S)..

In this study, we consider the differential equation with aftereffect under the separated boundary conditions on a finite interval. In fact, we consider the Sturm-Liouville operator disorganized by a Volterra integral operator. We obtain the numerical solution for the special case of the inverse aftereffect problem by applying Chebyshev interpolation method by calculating the solution of the integro-differential equations.In section 2, we show the asymptotic form of the solution and the eigenvalues of the problem and present the uniqueness theorem for the solution of the inverse aftereffect problem. In section 3, we approximate the function M in the special case contained, by using the method of Chebyshev interpolation and provide the numerical algorithm for solving the inverse aftereffect problem.

Preliminaries:

In this section, our goal is to show asymptotic form of the solution and the eigenvalues of the problem and to present the uniqueness theorem for the inverse aftereffect problem under the given boundary conditions.Numerical algorithmIn this section, we describe a numerical method based on Chebyshev interpolation method by using Chebyshev polynomials of the first kind for solving the inverse aftereffect problem by calculating the solution of the integro-differential equations.Since the solution of the integral equation is the solution of inverse problem, so it is sufficient that we solve the integral equation. We apply Chebyshev interpolation method for solving the integral equation. We use Chebyshev polynomials of the first kind as the basic functions for calculating the approximation of the function M and convert the integral equation to the system of the linear equations. We apply Matlab software program for drawing the figures.

In this study, we applied Chebyshev polynomials of the first kind to get the approximation of the solution of inverse problem for the special case of the aftereffect equation under the separated boundary conditions. Also, we provided some examples to calculate the numerical values of the function M and showed the stable numerical results in the presented examples.

In this paper, in the first part, the affine geometry is assumed as the main framework. Then we have a spacious explanation of necessary introduction in rather different subjects. In this part, statistical submanifolds of Sasakian statistical manifolds with constant -sectional curvature is considered as the pivotal topic. Afterwards, with a rather long process, we obtain an optimal inequalities between generalized normalized scalar curvature as an intrinsic property and 􀟜-Casorati curvature as an extrinsic property. In زthis result is existence of an inequality between normalized scalar curvature and Casorati curvature. In the second section, using Casorati curvature, with more capability than sectional curvature, we deduce some results about locally symmetric, quasi-umbilical hypersurfaces of real space forms of zero curvature. This yields an analytical and algebraic expression for locally symmetric, quasi-umbilical hypersurfaces that concludes the usability of affine geometry in using of softwares

In this paper, we introduce a Fréchet space  and define a measure of noncompactness on it.  For credit and the application to our theorems, in the application section of this paper, we present a theorem which shows the existence of solution of infinite system of nonlinear Volterra integral equations, and by using the technique of measures of noncompactness together Darbo fixed point theorem we guarantee the existence of solution in this Fréchet space . Finally, we present some examples which show the efficiency and applicability of our theorem.

In this paper, we discuss stochastic comparisons of active redundancy at component level versus system level. We also consider series systems in order to compare their lifetimes using the usual stochastic, the hazard rate and the reversed hazard rate orders, for two cases: (i) the spare and parent components are independent and have the same distribution, and then (ii) the spare and parent components are dependent and have not the same distribution. 

Survival analysis, and in particular survival distribution estimation, are important issues in the statistical sciences. Various parametric and nonparametric methods have been proposed to estimate the survival distribution. In this respect, the theoretical survival distributions are specified and their parameters are obtained by methods such as the maximum likelihood estimator and the Bayesian estimator and we can mention to nonparametric methods such as the Kaplan-Meier method, Cox regression and the life table. In addition, another important issue in survival analysis, especially in actuarial and biostatistics, is graduation of data for which smoothness and goodness of fit are two fundamental requirements.On the other hand, in the probability theory, there are two basic approaches to estimate probability distributions by using the concept of entropy: Maximum Entropy Principle (ME) and Minimum Kullback-Leibler Principle (MKL) or Minimum Cross Entropy Principle.In this paper, we examine the approach of the above two optimization models to estimate survival and probability distributions, especially for the classification of the data. In these studies, in addition to investigating parametric models, in order to achieve a compromise between the conditions of smoothness and goodness of fit, we apply a new entropy optimization model by defining an objective function combined from both of the two above principles and adjusting a coefficient that is used to ensure the degree of goodness of fitting and smoothing the estimates, as well as to show their priority in the classification of the data. We use this model to estimate the mortality probability distribution, particularly the column related to the mortality probability of a certain age ( qx) in life table. Finally, with the help of this method, we set the life table for Iranian women and men in 2011.

In this paper, a numerical method based on the finite element method and the least square scheme with the Tikhonov regularization method for nonlinear inverse diffusion problem is presented. For this propose, first finite element method and basis functions will be used to discretize the variational form of the problem; then the least square scheme and Tikhonov regularization method are proposed to correct diffusion. It is assumed that no prior information is available on the functional form of the unknown diffusion coefficient in the present study, and so, it is classified as the function estimation in inverse calculation. Numerical result shows that a good estimation on the unknown functions of the inverse problem can be obtained.

Introduction and preliminaries Hilbert C∗-modules were firrst introduced in the work of I. Kaplansky.Hilbert C*-modules are the natural  generalization that of Hilbert spaces arising by replacing of the field of scalars C by a C∗-algebra. Let us recall some basic facts about the Hilbert C∗-modules. Let A be a C∗-algebra. An right inner product A-module is a linear space X which is a right A-module (with compatible scalar multiplication: λ(x.a) =(λx).a = x.(λa) for x ∈ X, a ∈ A, λ ∈ C), together with a map (x, y)→   : X × X → A such that for all x, y, z ∈ X, a ∈ A, α, β ∈ C.

In this paper, we present a generalization of well-posedness for a system of split multi-valued variational inequalities with set-valued maps and establish a metric characterization for them. Moreover, we show that the strong well-posedness is equivalent to the existence and uniqueness of solution for a split multi-valued variational inequality.

The cable equation is one the most fundamental mathematical models in the neuroscience, which describes the electro-diffusion of ions in denderits. New findings indicate that the standard cable equation is inadequate for describing the process of electro-diffusion of ions. So, recently, the cable model has been modified based on the theory of fractional calculus. In this paper, the two dimensional time fractional nonlinear cable equation as an improved mathematical model in neuronal dynamics, is investigated numerically. An efficient and powerful computational technique based on the combination of time integration scheme and local weak form meshfree method has been formulated and implemented to solve the underlying problem. An implicit difference scheme with second order accuracy is used to discretize the model in the temporal direction. Then a meshless method based on the local Petrov-Galerkin technique is employed to fully discretize the model. The proposed numerical technique is performed to approximate the solutions of three examples. Presented results through the Tables and figures confirm the high efficiency and accuracy of the method.

Suppose    is a finite measure space, E is a Banach lattice, and  is the space of all Bochner integrable E valued functions. In this note, we show that is a KB-space or has the sequential Fatou property if and only if so is E Among this, some results about Bochner integral convergence in  using order structure of, have been proved, as well.

This paper, inspired by recent advances in the application of the multilevel Monte-Carlo (MLMC) approach to Lévy driven assets, is based on the valuation of financial derivatives. First, using the weak Euler method the numerical estimate of the underlying asset, which satisfies a multi-dimensional stochastic differential equation with Lévy noise, is calculated and then applying the weak multilevel Monte-Carlo method the expected price is obtained. In this paper, as an improvement of Belomestny’s work and with a new approach in the theory, we express and prove the convergence theorems in spacefor and not only 2. We also seek to implement the weak MLMC algorithm for nonlinear equations with dependent components and . In the end, we show numerical experiments when applied to different types of processes with call options.

This manuscript deals with a Shannon wavelet regularization method to solve the inverse Cauchy problem associated with the Helmholtz equation which uses to identify the radiation wave of an infinite “strip” domain. In view of Hadamard, the proposed problem extremely suffers from an intrinsic ill-posedness, i.e., the exact solution of this problem is computationally impossible to measure since any measurement or numerical computation is polluted by inevitable errors. To retrieve the solution, a regularization scheme based on Shannon wavelet is developed. The regularized solution is restored by Shannon wavelet projection on elements of Shannon multiresolution analysis. Furthermore, the concepts of convergence rate and stability of the proposed scheme are investigated and some new optimal stable estimates of the so-called Holder-Logarithmic type are rigorously derived by imposing an a priori information controlled by Sobolev scale.  The computational performance of the proposed method effectively confirms the applicability and validity of our qualitative analysis.

The natural and practical condition numbers for summation of complex numbers are introduced. These numbers measure the effect of loss of significant digits on the round-off error when computing a sum in floating point arithmetic. The relationship between the natural and practical condition numbers and their size are studied. It is shown that the practical condition number is equal to one when all the summands lie in one of the quadrants of the complex plane. Also, an upper bound for the natural condition number is obtained when the summands lie in a sector with an angle less than or equal to pi/2..

The judgment post stratification is a method of stratification of observation by using a key variable, such that stratification will be done after selecting the sample. In this paper, this method will use in two stage cluster sampling. In other words, instead of simple random sampling without replacement, we use the judgment post stratification method and the generalized judgment post stratification method in second stage of two stage cluster sampling, and obtain new estimators of the population mean. Finally, the proposed estimators are compared to usual two stage cluster simple random sampling estimator of the population mean by Monte Carlo simulation studies on a set of real data and generated data from symmetric and asymmetric distributions. The results of simulation study show that, in most cases, the proposed estimators have better performance than the mean of two stage cluster simple random sample.