نشریه پژوهشهای ریاضی
سال نهم شماره 2 (پیاپی 25، تابستان 1402)

A generalization of the continuous economic model is proposed for random markets. In this model, agents interact by pairs and exchange their money in a random way, in general, with possibly non- constant total amount of “money”. This model takes the form of an iterated nonlinear map of the distribution of wealth. We show the only way to reach equilibrium fixed point distribution is the agents to share their money without expansion or contraction factor. Furthermore, it is proved the higher momenta of the distribution exist and the iteration of higher momenta becomes stable under some specific conditions.

In this article, the Zariski topology is extended as the Zariski-countable topology. This imposes a new kind of manifolds using the countable-complement topology that the algebraic varieties are the analytic case of them. The advantage of this work is to convert any non-countable field to a topological field by Zariski-countable topology. This conversion is not possible by the usual Zariski topology.

Integro-Differential-Algebraic Equations arise in many in real world applications, in particular those related to the memory kernel identification problem in heat conduction, viscoelasticity, etc.  The main focus of this paper is to present a numerical method based on the iterative regularization algorithms. Owing to the ill-posed behavior of these equations, we are looking for iterative type methods including the regularization schemes in order to fixed the difficulties which may arise in their numerical solvability. Of particular interest would be on the Landweber iteration which is developed for its efficiency and fast performance to solve linear inverse equations as well as many ill-posed problems. Typically, the discretized form of these problems leads to a large, sparse and ill-conditioned linear system of equations. As the regularity of the solution is closely related to regularity of kernels, degree of smoothness and properties of the integral operator, we assume throughout the paper that all the functions are satisfied in the regular conditions.
The proposed

In this paper, a hybrid algorithm is developed in terms of the Landweber type iterative regularization and the Galerkin procedure.  The problems have been first discretized by a Galerkin type method with piecewise constant functions as basis functions. We then start from a suitable initial value and experimentally choose the regularization parameter. The proposed method terminates when the maximum number of iterations is reached or a stopping rule is satisfied. The strategy will be accomplished rather fast which leads to efficient and fast numerical algorithm.

Experimental

The validity and accuracy of the proposed algorithm are demonstrated through some illustrative examples. To clarify our results, we consider some test problems from the previously work and report the numerical results for different values of the number of nodes and iteration number.  We also reported the CPU time for each kernel evaluation.
It should be noted that, the iterative methods based on Landweber algorithm typically can cause a semi-convergence phenomenon, which means the error initially decreases while after some iterations begin to increase. This behavior depends on different factors such as level of the noise, the relaxation parameter and the starting point.  Under these crucial issues, the iterative algorithms may lead to fast or slow semi-convergence which indicates the key role of verification the semi-convergence.  Our experimental results show that the regularization parameter is important either in postponing the semi-convergence or decreasing the divergence. If it is chosen too large, it gives an over-smoothed solution which may lacks the desired solution, otherwise it yields a solution that is unnecessarily, and possibly severely contaminated by propagated error.

Here, the numerical solution of semi-explicit Integro-differential algebraic equations, using a hybrid algorithm based on iterative regularization method is presented. The efficiency and accuracy of the algorithm are experimentally discussed. The main advantages of the proposed method are the low computational complexity and its convenient numerical implementation. The intrinsic property of the method is stipulated by its ability to efficiently control the number of iterations by varying the regularization parameter and subdivisions.

The Kragujevac trees  where are used in molecular graphs have been studed by researchers of graph Theory in last years. In this paper, we study  the characteristic polynomial and spectrum of adjacency and Laplacian matrices of regular Kragujevac trees. As application of our obtained results, we compute a upper bound for spectral redius, energy of graph and kirchhoff index of  Kragujevac trees.

For i=1,2, let Xi be a compact Hausdorff space and Ai be a uniformly closed subalgebra of CR(Xi) which contains the constant functions and separates the points of Xi. In this paper, we describe surjections T:expA1→expA2 preserving specific subdistances.

. The class of strongly Ɵcl - continuous functions is considered in this paper. Studying about basic properties of strongly Ɵcl - continuous functions, it is observed that these properties are similar to the properties of continuous functions. We denote by Scl(X)  the ring of all real valued strongly Ɵcl - continuous functions on a topological space X . It is proved that if the range of a strongly  Ɵcl- continuous function f  is a T1 - space, then f  is constant on quasi – components of its domain. Using this fact, we prove that for every topological space X , there is an ultra- Hausdorff  space Y  such that Scl(X) is isomorphic to C(Y).The behavior of these functions in relation to separation axioms is studied. We show that if f is a strongly Ɵcl - continuous function from a topological space X  to a T0 - space Y , then X  is  ultra-Hausdorff. Topological properties of direct and inverse image of spaces with certain topological properties under strongly Ɵcl - continuous functions are investigated. Among them, it is proved that the image of every cl-closure compact space under a strongly Ɵcl - continuous function is compact. Finally the properties of the graphs of strongly Ɵcl - continuous functions are discussed. It is proved that for every compact and Hausdorff space Y , strong Ɵcl - continuity of the function f from X to Y is equivalent to Ɵcl - closedness of  the graph of f relative to X .

Usually, the traditional estimation methods is used to estimate Parameters of the linear regression model, such as least-squared error method. Sometimes the researcher has information about the unknown intercept parameter as a guess that is called as non-sample prior information. In this article, a preliminary test estimator for the intercept parameter of the simple linear regression according to the non-sample prior information is introduced and the value of its risk function under the reflected normal loss function is investigated. Also, the behavior of shrinkage pretest estimator is compared with respect to the least-squares estimator using a simulation. The intervals where the shrinkage pretest estimator has the least risk compared to the least-squares estimator presented. The results show that the shrinkage pretest estimator outperforms the least-squares estimator when non-sample prior information is close to the real value. Also, the optimum value of the significant level of test is determined using max-min method. Then, proposed estimators are compared using a real data set.

‎General ‎relativity ‎is ‎model ‎of ‎nature, ‎especially, ‎of ‎gravity.‎‎ ‎Its ‎cent‎ral ‎assumption ‎is‎ that space, time, and gravity are all aspects of a single entity, ‎cal‎led ‎space-‎time, which is modeled by a 4-dimensional Lorentzian manifold. It analyzes ‎space-‎time, electromagnetism, matter, and their mutual ‎infl‎uences. ‎But ‎the ‎effects ‎of ‎matter ‎and ‎electromagnetism ‎are ‎added ‎to ‎the ‎model ‎in a‎ ‎way‎ ‎which ‎is ‎not ‎directly ‎related ‎to ‎geometry ‎of ‎space-time ‎manifold. ‎In ‎fact, ‎in‎fluences ‎of ‎matter ‎and ‎electromagnetism ‎fields ‎are ‎added ‎to ‎theory ‎under ‎notion ‎of ‎stress-energy ‎tensor. ‎Hence, considering non-symmetric metrics extends this geometry and make a good apparatus to describe other physical quantities.

In this paper, we consider the geometry of a non-symmetric semi-Riemannian metric on a manifold M. A special class of such metrics contains a semi-Riemannian metric and a symplectic structure on M, simultaneously. Similar to the Levi-Civita connections in semi-Riemannain manifold, we define a new connection which is torsion free and compatible with our symplectic structure. With the help of semi-Riemannian metric, we define and compute the Rcci and scalar curvature of this new connection.

Using a natural Lagrangian (which is a generalization of Hilbert-Einstein action) and calculus of variations we derive some new field equations. The equations show that the symmetric part of semi-Riemannain metrics is directly related to gravity and the symplectic part is capable of describing quantities related to matter. 

In this work, we present a completely geometric theory of gravity. The Riemannian geometry, which is usually used to formulate gravitational theories adds the notion of matter to space time manifold as the way which is not directly related to geometry of the theory. In this framework, we retrieve Einstein’s field equation and we will show that the distribution of matter in space-time is directly related to symplectic part of our geometry

The concept of non-abelian tensor product in algebraic k-theory, algebraic topology, and homotopy theory has its roots. Later in group theory, this concept gained attention. In this article, we introduce the concept of non-abelian exterior product, which has a weaker structure compared to the non-abelian tensor product. Additionally, by introducing exterior n-auto Bell groups, exterior n-auto Levi groups, and exterior n-auto Kappe groups, we prove some properties of these groups. Among them, we prove that if G is an exterior n-auto Bell group, then G/L^_3(G) has a finite exponent dividing 2n(n-1).

Operational risk is one of the identified risks in organizations, especially in banks, and Basel committees on banking supervision pay special attention to it. In this paper, the mathematical model based on the advanced operational risk model is considered to calculate the probability of survive as a partial Volterra integro-differentail equation. This equation has been solved numerically by applying the finite differences method with trapezoidal rule to estimate its integral part and the effect of changing the model parameters on the output of the problem has been investigated. In addition, the stability and convergence of the method are discussed and its numerical results are presented.

In this paper, we consider a collection ℵ of normal subgroups with closed finite intersection property of a group G. We define a uniformity on the Rees matrix semigroup S from G. So, we study the topological properties of this uniform topology. In particular, we show that if the normal subgroups are closed arbitrary intersection property, then the uniformity is compelete. Finally, if normal subgroups are closed finite intersection property, then we construct a completion.

As application of compound distributions in the study of longevity data, in this paper the compound distribution of inverse Weibull Geometric is investigated. The presence of parameters of scale, shape and failure rate in this distribution, their study in terms of estimation and hypothesis testing is of particular importance. However, since the phenomenon of censorship is also considered in the study of lifetime data, so the parameters under the type-II of censorship are estimated using the maximum likelihood and Bayesian estimation. In Bayesian estimation, the parameters under different loss functions are estimated based on appropriate prior distributions, then the symmetric confidence interval and HPD are presented by simulation and the estimators are compared using statistical criteria. Finally, the goodness of fit of model is presented by the real data.

In financial markets, volatility decreases with rising stock prices. The constant elasticity of variance (CEV) model is a good model to show this inverse relationship between stock price and its volatility in the market. In this paper, we assume that stock price dynamics follows the CEV model. But this model cannot show the trend memory effect in financial markets. Given that fractional derivatives are suitable tools for describing the trend memory effect, they can interpret and express the hereditary characteristics of the options well. Hence, under the assumption that the price change of the underlying asset follows a fractal transmission system, we investigate the pricing of the European option. The main objective of this paper is to numerically solve the time-fractional Black-Scholes equation based on the meshless local Petrov-Galerkin (MLPG) and implicit finite difference methods for discretizing the option price and time variable, respectively. In this study, MLPG type 2 (MLPG2) is developed based on the moving Kriging interpolation method to construct shape functions that have the Kronecker delta property, and the Kronecker delta is the test function. Also, we analyze the stability of the proposed method using the matrix method. Numerical examples show the accuracy and efficiency of the method.

In this paper, we explicitly investigate the Schwarz boundary value problem of complex partial differential equations for an inhomogeneous Cauchy-Riemann equation on a polygon domain with distinct points of the equilateral triangle. By applying the technique of parquet reflection and selecting an arbitrary point of the equilateral triangle and its repeated reflections in all parts of the boundary, full page of complex spaces covered. In addition, the fundamental tool for solving the Schwarz boundary value problem from the complex partial differential equations for the Cauchy-Riemann equation is the Cauchy–Pompeiu integral representation formula. Thus, using the technique of parquet reflection and the Cauchy–Pompeiu integral representation formula, we accurately calculate the Schwarz-Poisson integral representation formula on the equilateral triangle and its different boundary portions. We also consider boundary behaviors of the Schwarz-type operator. Finally, we give an exact answer for the Schwarz boundary value problem of complex partial differential equations for an inhomogeneous Cauchy-Riemann equation on the equilateral triangle.