مجله پژوهش های نوین در ریاضی
پیاپی 34 (بهمن و اسفند 1400)

One of the most important factors for the economic development of countries is the insurance industry.A closer look at the economies of Developed Countries shows that the insurance industry has a significant contribution in the economic development of these countries. The insurance industry needs to accept the risk in order to carry out any insurance activity. In the other word, the insurance companies create tranquillity in the society by accepting the risk. On the other hand, the insurance companies need to access to the powerful risk analysis tools in order to manage the potential risks. Data envelopment analysis (DEA) is one of the most important techniques to identify the risk resources. Hence, data envelopment analysis is widely used in the insurance industry. This study uses the dataset of the car insurance policies of Saman Insurance Company during the years 2018-2019. First, we identify the effective indicators and examine the properties of these indicators to classify them into input and output groups. Finally, we use data envelopment analysis to propose a model for predictionthe risk of insurers (in terms of existence of damage risk or absence of damage risk). This model can be used in the future policies of the insurance company. For example, the insurance companies can use the results of data envelopment analysis to adjust the premiums received from different insurers and increase the satisfaction for insurers and their profitability by creating a rating system based on the insurers 'risk.

Data Envelopment Analysis (DEA) is one of the best tools for evaluating the performance of decision-making units. Traditional DEA fails to measure efficient and inefficient units and evaluate the performance of network systems, and traditional models of DEA do not pay attention to internal structures and intermediate values. For this reason, in recent years, DEA model, known as network Data Envelopment Analysis models, have been introduced, this models eliminated this deficiency by considering intermediate values. In this paper, DEA based on network two-stage and slack variables and triangular intuitionistic fuzzy data is used to identify the efficiency of units. At first, the two-stage DEA model is introduced and then the model is transformed based on intuitionistic fuzzy coefficients and variables and finally it is converted to crisp two-stage structures by arithmetic operators on intuitionistic fuzzy data. The importance of this model is to measure the values of slack variables, which based on the Tone and Tsutsui model optimizes the intermediate values for inefficient units and ultimately shows better inefficiency. Finally, the optimized intermediate values are considered in the proposed model and thus are improved the overall efficiency of the system.

One of the most important and fundamental factors in the life of living things is water. Therefore, water pollution is a major environmental problem and prevent water pollution and providing smart methods for water treatment is so important. Equipping engineering sciences with intelligent tools and artificial intelligence in the diagnose quality of wastewater treatments can reduce the errors of the methods. This paper presents a simple and hybrid neural network with statistical logistic regression method for modelling of the output quality of wastewater treatment. The proposed intelligent method plays an important role in the quality of wastewater treatment and can be used by artificial intelligence researchers and environmental engineers. Comparison of the predicted results by simple neural network and hybrid one showed that the efficiency of the hybrid model and it is suitable for our purpose. results of research proved that the new method has the highest efficiency with minimum errors.

Let H be a Hilbert space. For each f∈H, we define a multiplication operator M_φ by M_φ (f)=φf. Let φ be an entire function. For each f belongs to the Fock space F^2, the composition operator C_φ is defined by C_φ (f)=f∘φ. For entire functions ψ, φ and f∈F^2, the weighted composition operator C_(ψ,φ) on F^2 are given by C_(ψ,φ) (f)=ψ.(f∘φ). Let T be a bounded operator on H, the set W(T)={⟨Tf,f⟩:‖f‖=1} is called the numerical range of T. In this paper, we find the point spectrum of some operators C_(ψ_1,φ_1 )+C_(ψ_2,φ_2 ), when φ_1 and φ_2 have the some fixed point. Moreover, we obtain an invariant subspace for the operator (C_(ψ_1,φ_1 )+C_(ψ_2,φ_2 ) )^*. Then by these results, for compact operators C_(ψ_1,φ_1 ) and C_(ψ_2,φ_2 ), we find the spectrum of C_(ψ_1,φ_1 )+C_(ψ_2,φ_2 ). Then for φ_1 and φ_2 which have the some fixed point, we investigate the numerical range of C_(ψ_1,φ_1 )+C_(ψ_2,φ_2 ).

* The formulas are not displayed correctly.

Cardiovascular system is a permanent source of information which incorporate to declaration of Cardiovascular diseases. The existence of available valid data is the main part of any research study. Today, in the field of human life study, experimental data by means of different issues are always deviated from their actual values not only in measurement errors but also it is appeared due to the measuring concept. Composing of heart signal, as a real example of signals, with noise signal causes ambiguity in which classical available methods become disable in correct processing and interpretation of these signals. This paper is focused on proposing an algorithm in signal noise reduction of heart sound signal at pre-processing step. This novel de-noising method of heart sound signal is established on arbitrary order fuzzy partial differential equations. Fuzzification is done due to eliminating of absolute boundaries. The propose algorithm of noise reduction is examined by adding Gaussian white noise to the normal heart sound signal without any noise. De-noising method is implemented after presenting the model concept. Attaining the (FFPDE) filter is including the following steps: the filter matrix is defined after using the backward Euler scheme to discretize the fuzzy differential equation. The results indicated that using of fuzzy fractional partial differential equations was completely effective in de-noising of heart sound signals.

Let $B(H)$ be the $C^*$-algebra of all bounded linear operators on a complex Hilbert spaces $H$.  Ando, Li and Mathias introduced a generalized geometric mean for $n$ positive definite operators. This geometric mean $G(A_{1},A_{2},dots ,A_{n})$ of any $n$-tuple of positive definite operators $mathbb{A}=(A_1,dots,A_n)$ is defined by induction.(i) $G(A_{1},A_{2})$ =$A_{1}sharp A_{2}$ (ii) Assume that the geometric mean any $(n-1)$-tuple of operators is defined. Let [G ((A_j)_{jneq i })= G(A_{1},A_{2},dots,A_{i-1},A_{i+1},dots,A_{n}), ] and let sequences ${mathbb{A}_{i}^{(r)}} _{r=1}^{infty}$ be $mathbb{A}_{i}^{(1)}= A_{i}$ and $ mathbb{A}_{i}^{(r+1)}=G((mathbb{A}_{j}^{(r)})_{jneq i }) $. If there exists $ lim_{rrightarrowinfty}{mathbb{A}_{i}^{(r)}} $, and it does not depend on $i$. Hence the geometric mean of $n$-operators is defined by begin{equation*} lim_{rrightarrowinfty}{mathbb{A}_{i}^{(r)}} = G((mathbb{A}))=G(A_{1},A_{2},dots,A_{n}) text{ for } i= 1,dots,n. end{equation*} We shall show a reverse inequality for the generalized geometric mean defined by Ando-Li-Mathias for $n$ positive definite operators, as follows: Let $Phi$ be a unital positive linear map on $B(H)$ and $r(A)$ be the spectral radius of $A$, then begin{align*} Phi(G(A_1,dots,A_n))geqleft(frac{2h}{1+h^2}right)^{n-1}G(Phi(A_1),dots,Phi(A_n)), end{align*} where $R(A_i, A_j)=max{r(A_i^{-1}A_j) ,r(A_j^{-1}A_i)}$ and $h=min_{i,j} R(A_i, A_j)$.The Karcher mean, also called the Riemannian mean, Recently it has been used in a diverse variety of settings:diffusion tensors in medical imaging and radar, covariance matrices in statistics, kernels in machine learning andelasticity. We also give a reverse inequality for the weighted power mean of $n$ positive definite operators involving unital positive linear maps.

* The formulas are not displayed correctly.

Performance evaluation of the production systems by considering data related to different time periods is one of the most important issues of production theory. In this paper, a new method for measuring the aggregative efficiency of multi-period production systems using the data envelopment analysis (DEA) technique is proposed. The provided approach could be considered as extension of the radial methods in the literature. An extended Russell based model is presented for the first time to measure aggregative efficiency with respect to the time intervals of the production stages. One of the useful features of the proposed model is that the inefficiency of the existing aggregative approach is detected in one step without need to account for the second stage of optimizing slack variables. Some properties and advantages of the new model is discussed. Finally, to illustrate the applicability of the new approach, two practical examples are investigated and analyzed. The results show the good performance of the proposed method.

Let R be commutative Noetherian ring with identity (not necessarily local), M and N be nonzero finitely generated R- modules. Let K be a semidualizing R-module and χ_n be a subcategory of G_K- perfect R-modules of grade n . In this paper, we study the theory of linkage of module with respect to χ_n. Also, we generalize a number of statements about horizontally linked modules to linked modules with respect to χ_n. In particular, we define the reduce grade of R-module M then for linked module with respect to χ_n, over a commutative Noetherian local ring R, the connection of its reduced grade and depth of its linked module is discussed. As a consequence, over a Cohen-Macaulay local ring, we determine the attached primes of the local cohomology module〖 H〗_m^(〖cd〗_m (M)) (M), in terms of the depth of its linked module. Finally, under certain conditions, it is shown that some relation between relative reduce grade of M and relative reduce grade of its linked module.Keywords: Linkage of modules, Semidualizing module, G_K-dimension.

* The formulas are not displayed correctly.

The quantum calculus or q-calculus begins with F. H. Jackson in the early twentieth century, but only recently it has aroused interest, due to high demand of mathematics that is modeling quantum computing and it has been an important subject for applied sciences . The quantum calculus is one of the applied and inter disciplinary sciences, which is more important than the classical calculus because in the standard calculus the definition of the derivative depends on the existence of limit but the quantum derivative in quantum calculus works without the definition of limit and for this reason the work with a quantum calculus is numerically faster and easier than the standard calculus. In this paper, fuzzy quantum derivative, fuzzy quantum fractional derivative in Caputo sense by using generalized Hukuhara difference and fuzzy quantum fractional integral of the Riemann-Liouville type are introduced, then the related theorems and properties are provided in details.These results occur in many applications as physics, quantum theory, number theory, statistical mechanics, etc.

The measurement of organizational efficiency has always been discussed by various researchers. Data envelopment analysis, taking the inputs and outputs of the decision-making units into account, makes it possible to calculate the relative efficiency for each unit. Many organizations have a two-stage structure, and their performance in successive periods depends on each other. In evaluating such a structure, partial and periodic efficiency must be calculated. Early models and network and dynamic models are not able to calculate this performance alone. Models of existing dynamic networks are also unable to provide a projection for inefficient units or solve all challenges. In this study, by defining the PPS, an input-oriented dynamic two-stage DEA was developed.  In this model, the optimal value of the intermediate and carryover variables is determined by the next stage and period, and the stages and periods become efficient backward from the last stage of the last period. In addition to the total structure, the model makes efficient all stages and periods and only becomes an efficient unit if it is efficient in all stages and periods. It was also proved that the projection of the unit to be evaluated is partial, periodic, and total efficient. How to use the model to calculate efficiency was expressed by a practical three periodical example.

In this paper, we introduce a double projection algorithm based on extragradient method for solving the variational inequality problems and we prove the convergence theorem of proposed algorithm. One of the parameters that determine the efficiency and accuracy of the projection method is a properly selected step size. This selection is based on the contractive properties of operator which is projected on the feasible region. For example, if the Lipschitz constant is not known, we have trouble choosing step size of the algorithm. The proposed algorithm eliminates the need to know the Lipschitz constant and provides a method that facilitates step size selection.We formulate the asymmetric traffic equilibrium problem as a variational inequality on the path flows space. According to the decomposable structure of the feasible set of this model, we obtain the traffic network equilibrium state, by using the proposed algorithm. Finally, we present the numerical results of using this algorithm on the Sioux-Falls test traffic network.

Let A be a Banach algebra and X be a Banach A-bimodule. A mapping D:A--->X is called a cubic derivation if, for all a,bin A we have D(ab)=a^3D(b)+D(a)b^3 . The mapping D:A--->X is called a cubic homogenous map if we have D(lambda a)=lambda^3 D(a) for all ain A and lambdain C. In this paper, we define linear-cubic map and linear-cubic derivation as follows. We say the cubic homogenous map D:A--->X is a linear-cubic map if we have D(lambda a+b)=lambda^3D(a)+D(b) , for all a,bin A and lambdain C and moreover if D:A--->X is a cubic derivation, then we call it a linear-cubic derivation. In this paper, we characterize linear-cubic derivations on various class of Banach algebras such as Banach algebras obtained by theta-Lau product, module extensions of Banach algebras and amalgamated Banach algebras. For characterizing, we define theta-cubic derivation and module cubic mappings. For Banach algebra Atimes_theta B , where thetainsigma(A)cup{0} and A is unital, we show that D:A--->X is a linear-cubic derivation if and only if there are theat -cubic derivation D_B,A:B--->A and linear-cubic derivations D_A:A--->A and D_B:B---> B such that for any (a,b)in Atimes_theta B, be as follows D(a,b)=(D_A(a)+D_B,A(b),D(b)) and these mappings satisfy in the given condition. We obtain similar results for module extensions of Banach algebras and amalgamated Banach algebras.

* The formulas are not displayed correctly.

A weak odd dominating set in a graph is a subset B of vertices for which there exists a distinct set of vertices C such that every vertex in B has an odd number of neighbors in C. κ(G) denotes the size of the largest weak odd dominating set and κ'(G) the size of the smallest non weak odd dominating set. One of main motivation for studying the weak odd dominating set is their role in the design of graph-based quantum secret sharing protocols. Graph G of order n corresponds to a secret sharing protocol whose threshold is κ_Q (G)=max(κ(G),n- κ'(G)). In this paper we prove a lower bound for the largest weak odd dominating set in trees proving a conjecture for trees. Also, we present an upper bound for the largest weak odd dominating set in trees in terms of the order and the number of leaves and we improve some previous bounds.

* The formulas are not displayed correctly.

Mathematical program with equilibrium constraints is one of the optimization problems whose constraints are used to model certain equilibria in the applications of engineering sciences and economics. Our main aim in the present paper is to investigate the necessary optimality conditions and create a Wolfe type dual problem for such problems. To investigate these conditions, we consider non smooth and non convex optimization problem with equilibrium constraints and suppose that all functions are not necessarily differentiable or convex. For this optimization problem, using the notion of convexificator, which is viewed as a generalization of the idea of subdifferential, we remind some constraint qualifications, stationary conditions, and generalized convexity. Finally, weak duality theorem and strong duality theorem are established under appropriate generalized convexity assumptions and a constraint qualification for an optimization problem with equilibrium constraints based on the notion of convexificators. We also illustrate some of our results by an example.