مجله پژوهش های نوین در ریاضی
پیاپی 29 (فروردین و اردیبهشت 1400)

In this paper, Chelyshkov expansion approach is presented for solving Volterra fractional order integro-differential equations with Caputo derivative. By means of the properties of Chelyshkov polynomials and numerical integral formula , the solution of fractional integro-differential equations reduced to the solution of algebraic equations. Then, by solving the system of algebraic equations, the solution of the differential-integral equation is presented as a function in the terms of Chelyshkov polynomials. Accuracy and error analysis have been investigated and since the accuracy of the obtained results for fractional integro-differential equations depends on the number of selected Chelyshkov polynomials therefore, with the increase in the number of Chelyshkov polynomials, we can achieve desirable accuracy step by step. All calculations are done by MATLAB software. Also, the numerical results of based on Chelyshkov polynomials method are compared with the results of some of the available methods for the validity, accuracy and efficiency of the technique.

‎For the study of atomic systems, first introduced by Feichtinger et al. Gavruta presented K-frames on Hilbert spaces. K-frames are a kind of frames in sense that the lower frame bound only holds for the elements in the range of the K, where K is a bounded linear operator in Hilbert space. C*-algebra whose topology is induced by a family of continuous C*-seminorms instead of a C*-norm is called pro-C*-algebra. Hilbert pro-C*-modules are generalizations of Hilbert spaces by allowing the inner product to take values in a pro-C*-algebra rather than in the field of complex numbers. In this paper, the sequences whose elements are adjointable operators from pro-C*-algebra into Hilbert pro-C*-module is called the sequence of multipliers. We introduce the concept atomic systems and K-frame of multipliers in Hilbert pro-C*-modules and for more information, we give an example of K-frames. We obtain a condition that sequences of multipliers is frame, also we investigate the relationship between atomic systems and K-frames with each other and the frame of multipliers. If K is a bounded operator with certain conditions then every K-frame of multipliers is a frame of multipliers in Hilbert pro-C*-module. Also, we investigate some of the properties of these concepts, such as the combination of operators with K-frames in Hilbert pro-C*-module.

In this paper, the notion of mp-residuated lattice, as a subclass of residuated lattices in which every prime filter contains a unique minimal prime filter, is introduced and investigated. For a residuated lattice A, the notion of ω-filter is introduced and it is shown that Ω(A), the set of ω-filters of A, is a bounded distributive lattice. Also, it is observed that γ(A), the set of coannulets of A, is a sublattice of Ω(A). Then for each prime filter P of A, the notion of the divisor filter D(P) as an important tool in investigating of minimal prime filters of A is introduced and it is proved that a prime filter P is minimal prime if and only if P=D(P). Finally, by the notion of ω-filters, as an extension of divisor filters, a fundamental characterization of mp-residuated lattices is given and it is shown that a residuated lattice is mp if and only if the set of its ω-filters is a sublattice of the lattice of its filters.

The estimation of unknown parameters of two-parameter Rayleigh distribution based on Type-II progressive censoring with binomial removals is studied. Maximum likelihood estimators of the parameters and their confidence intervals are derived. By applying Markov Chain Monte Carlo techniques, Bayes estimators, and corresponding highest posterior density confidence intervals of parameters are obtained. The expected time required to complete the life test under this censoring scheme is investigated. Monte Carlo simulations are performed to compare the performances of the different methods, and one data set is analyzed for illustrative purposes.

Some researchers deals to estimation of some of the influences factors in efficiency score in which the DMU, maintains or improves its current efficiency level. This problems are considered in a general framework which is called inverse DEA. This paper studies the inverse data envelopment analysis. The issue of input or output estimation has been examined with improvement in unit efficiency.Therefore, in this paper, by increasing the level of undesirable inputs and the level of desired outputs of decision-making units along with improvements in the efficiency of the decision-maker, the level of changes in the level of desired inputs and the level of undesirable outputs is estimated. To do this, we consider the data as Interval data and then use the inverse DEA method using a multi-objective linear programming model (MOLP), so that the unit performance under evaluation is improved. The following is an applied example of the proposed method.

In 1969, DeMarr proved that a commuting family of non-expansive mappings on a nonempty convex compact subset of a Banach space has a fixed point. Takahashi extended DeMarr’s theorem to the case of discrete amenable semi-groups. In recent years, considerable research has been devoted to the theory of fixed points as well as common fixed points. In the case of semi-topological semi-groups (that is, a semi-group with a Hausdorff topology such that the multiplication is separately continuous), Lau and Zhang studied DeMarr’s theorem under more general conditions for example in the case of the amenability of the space of almost periodic functions as well as the space of weakly almost periodic functions. In this paper, we study several fixed point properties of the mean non-expansive semi-topological semi-groups acting on nonempty convex weakly compact subsets of a locally convex space as well as give extensions of the results of Lau and Zhang.

In recent years, fourth-order differential equations in mathematical physics have been considered by many researchers. These applications include Micro Electro Mechanical systems, thin film theory, surface diffusion on solids, flow in Hele-Shaw cells and phase field models of multiphase systems.[ 9, 20] The importance of studying such equations is due to the justification of many physical examples using mathematical modeling, which can be seen mostly in the field of Newtonian fluids and elastic mechanics, in particular, electrological fluids (smart liquids). See [11, 21] for more details.In this paper, using variational methods, sufficient conditions for the existence of at least two weak non-trivial solutions of a fourth-order elliptic boundary value problem with the Rubin boundary conditions are investigated. Our analysis mainly relies on the variational arguments based on the mountain pass lemma and some recent theory on the generalized Lebesgue–Sobolev spaces. Our work starting point is the paper "Continuous spectrum of a fourth-order nonhomogenous elliptic equation with variable exponent" by A. Ayoujil, A.R. El Amrouss of [3] where the authors considered the problem (1) with the Navier boundary conditions. This paper's guarantee the exsitence of at least two nontrivial weak solutions for the problem (1) with Robin boundary conditions.More precisely, by applying Ambrosetti and Rabinowitz’s mountain pass theorem and under appropriate conditions, we show that there exists a positive number λ_*such that the problem (1) has at least two nontrivial weak solutions.

In this paper, we prove that every multipliers on without order Banach algebra A is almost homomorophisms. Also we investigate the continuity of approximate multipliers and under special hypothesis we show that each approximate multiplier T:A⟶A is continuous.

In recent years the interest in studying the absolute value equation has been of great interest both theoretically and practically. The main reason for this is that various optimization problems, such as the complementary linear programming problem, can be written in the form of a robust equation that is easier to solve. The main purpose of this paper is to present a duplicate method for solving the equations of magnitude. Actually, in this paper, by introducing a scalar matrix, an improved generalized Newton method is proposed to solve the Absolute value equation. This new method is based on the methods of Mangserin [1] and Li [2]. In fact, if in the matrix A + αI-D, the value of the identity matrix coefficient is equal to zero, the Mangserin method and if the coefficient of the same matrix to one, the Li method is obtained. when all the singular values of the system matrix exceed one.

T h e iso clinism o f L i e algebra i s widely used i n the classification o f Lie algebra. This concept has a weaker structure than t h e concept o f the isomorphism. T h e iso clinism o f Lie algebra was first introduced by the Moneyhun and later it is generalized by others to n- iso clinism in Lie algebra, as well as, to the iso clinism in a pair of Lie algebra in the literature. In this paper, we study the n- isoclinism in Lie algebra and prove some of the features of the n- iso clinism in Lie algebra. For example, we prove that if L 1 and L 2 are two Lie algebras that the intersection of their centroid and F rattini algebra are zero, then, the iso clinism L 1 and L 2 are equivalent to their central factors.

A nontrivial graph is called nicely distance-balanced (nicely edge distance-balanced), whenever there exist positive integers γ_V (γ_E), such that for any adjacent vertices u and v in V(Γ), there are exactly γ_V vertices in V(Γ) (γ_E edges in E(Γ) that are closer to u than v, and exactly γ_V vertices in V(Γ) (γ_E edges in E(Γ)) that are closer to v than u. In this paper, we will prove that hyper cube Q_n and the folded cube F_n are nicely distance-balanced and Q_n is also nicely edge distance-balanced.A nontrivial graph is called nicely distance-balanced (nicely edge distance-balanced), whenever there exist positive integers γ_V (γ_E), such that for any adjacent vertices u and v in V(Γ), there are exactly γ_V vertices in V(Γ) (γ_E edges in E(Γ) that are closer to u than v, and exactly γ_V vertices in V(Γ) (γ_E edges in E(Γ)) that are closer to v than u. In this paper, we will prove that hyper cube Q_n and the folded cube F_n are nicely distance-balanced and Q_n is also nicely edge distance-balanced.

Although all managers seek to maximize the utility, most firms do not recognize the importance of inventory control and the use of warehouse inventory control systems as a management tool. On the other hand, in classical inventory control models, the parameters have to be determined, while in real world problems the parameters are mostly uncertain. Therefore, the models partially ignore the facts and as a result managers are reluctant to apply this kind of models. So, the present study seeks to answer the question of whether fuzzy inventory control models can overcome this defect, introduce parameters into the model more realistically and thus reduce total inventory cost and improve performance. In this paper, a model of fuzzy Economics Order Quantity (EOQ) was presented and evaluated with a numerical example. The findings confirmed the positive response to the above questions. Key words: Inventory Control Models, Economics Order Quantity, warehousing cost, ordering cost, fuzzy

In 1930, Kuratowski introduced the concept of measure of noncompactness. Later, Banas and Goebel generalized this concept axiomatically, which is more convenient in applications. The principal application of measures of noncompactness in fixed point theory is contained in the Darbo's fixed point theorem. This is a tool to investigate the existence and behaviour of solutions of many classes of integral equations such as Volterra, Fredholm and Uryson types. The technique of measure of noncompactness is applicable in several branches of nonlinear analysis. In particular, it is a very useful tool for several types of integral and integral-differential equations. In addition, the measure of noncompactness is also used in functional equations, fractional partial differential equations, ordinary and partial differential equations, operator theory and optimal control theory. The purpose of this article is to introduce a new measure of noncompactness in the Sobolev space W^(k,∞) (R^n). The results are obtained to solve integral-differential equations. Finally, by providing an example to show the efficiency of our results.

Determining the appropriate insurance premium for wealth insurance companies is important to increase revenue. In this paper, we want to optimize premium in order to increase the wealth insurance companies via optimal control theory based on choosing the appropriate risk. Determining appropriate premium, depending on the average market premium and such amount of losses, can lead to increase in the wealth of the insurance company. First, a dynamic model is expressed to describe the receipt of premium and the payment of losses. Then we introduce the premium variable as the problem control variable. In the next step, we define an appropriate objective function for the control variable and state variables in order to increase wealth and the proportionality of the premium to the average market premiume. Then, one of the principal variables is estimated by statistical methods and solves the control problem via the Pontryagin method. Finally, two numerical examples are presented.