Mathematical Researches

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projective Ricci curvature. Then we characterize isotropic projective Ricci curvature of Randers metrics. we also show that Randers metrics are PRic-reversible if and only if they are PRic-quadratic../files/site1/files/0Abstract2.pdf

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      An important class of Finsler metric is named Kropina metrics which is defined by Riemannian metric α and 1-form β  which have many applications in physic, magnetic field and dynamic systems. In this paper, conformal transformations of χ-curvature and H-curvature of Kropina metrics are studied and the conditions that preserve this quantities are investigated. Also it is shown that in the special cases the  conformal transformations reduced to homothetic transformations.  ./files/site1/files/62/14Abstract.pdf     
 

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An R-module M is called Almost uniserial module, if any two non-isomorphic submodules of M are linearly ordered by inclusion. In this paper, we investigate some properties of Almost uniserial modules. We show that every finitely generated Almost uniserial module over a Noetherian ring, is torsion or torsionfree. Also the construction of a torsion Almost uniserial modules whose first nonzero Fitting ideal is a product of maximal ideals, is invetigated and torsion Almost uniserial modules over an integral domain and a UFD are characterized../files/site1/files/71/3.pdf

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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 ( q_x) in life table. Finally, with the help of this method, we set the life table for Iranian women and men in 2011../files/site1/files/72/8Abstract.pdf
 

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   Randers metrics are the most important class of Finsler metrics which is defined by a Riemannian metric  and a 1-form  as    . In this paper, the concept of geodesic circle preserve transformations in  Finslerian space is studied and the weak Einstein  Randers metrics have been investigated. Further we prove this condition for Randers metric of weak isotropic flag curvature and weak isotropic Berwald curvature.
 
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In 2016, Prof. Shen et al. studied one of the most important warped structures of Finsler metrics and investigated Einstein type of the metrics. In this paper, we first compute the E-curvature of the metrics and characterize Finsler warped product metrics with isotropic E-curvature.

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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.

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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.

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Introduction
        Let a  be an ideal of Noetherian ring R  and M,N  be finitely generated R -modules. Recall that, for each i≥0 , i-th generalized local cohomology module M, N with respect to a  is defined by
HaiM,N≔limn Hai(M/anM,N).
Also, recall that  cda,M,N,  the cohomological dimension of R-modules M and N with respect to an ideal a  of a commutative Noetherian ring R  is
supi∈N0: Hai M,N≠0.
An important problem concerning local cohomology is determining the set of attached prime ideals of the top local cohomology modules. This problem has been studied by several authors. In this paper, we study attached prime ideals of top local cohomology modules.
 Material and methods
   In this paper, we first obtain some subsets of the set of attached prime ideals of top local cohomology module. By using these, we obtain a result about finiteness of  top local cohomology modules.

Results and discussion
    Let R  be a Noetherian ring and a  be an ideal of  R . Let M  and N  be non-zero finitely generated R -modules.  Assume that  pdM=d<∞ , cda,N=c<∞ . We will prove that 
i) p∈SuppRN:  cda,R/p=c, dimRp=c⊆AttR(HacN),
ii)  AttR(Had+cM,N)⊆p∈SuppRN:  cda,M,R/p=d+c,
iii) p∈SuppRN :cda,M,Rp=d+c,dimRp=c ⊆AttR(Had+cM,N).
Conclusion
    Let M  and N  be non-zero finitely generated R -modules.  Assume that  pdM=d<∞ , cda,N=c<∞.  The following conclusions were drawn from this research.
 •  If  (R,m)   is a Noetherian local ring such that   Had+cM,N≠0  then Had+cM,N  is not of finite length.      
  •  If R is a Noetherian domain, then under certain conditions we have 
AttR(Had+cM,N)=AttR(HacN) .
 

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In this paper, using a new method based on the generalized hat functions, we solve a class of fractional delay differential equations in which the fractional derivative is considered in the sense of Caputo. First, we introduce the generalized hat functions and their corresponding operational matrices. Then, in order to solve the considered problem, the existing functions are approximated using the basis functions. By employing the properties of generalized hat functions, the Caputo fractional derivative and the Riemann-Liouville fractional integral, a system of algebraic equations is obtained which by solving it, the unknown coefficients are determined. By substituting the resulting values, an approximation of the solution of the problem is obtained. In addition, the computational complexity of the resulting system is investigated. In continue, an error analysis of the method is given. Finally, the accuracy and efficiency of the proposed method are shown by presenting two examples.