JOURNAL OF NEW RESEARCHES IN MATHEMATICS
Year:2019 | Volume:5 | Issue:20 |Papers Count:16

Suppose that A is a C^*-algebra. We consider the class of A-linear mappins between two inner product A-modules such that for each two orthogonal vectors in the domain space their values are orthogonal in the target space. In this paper, we intend to determine A-linear mappings that preserve orthogonality. For this purpose, suppose that E and F are two inner product A-modules and A+ is the set of all positive elements of A. We show that an A-linear mapping T: E→ F preserves orthogonality if and only if there exists a∈ A+ such that ⟨ Tx, Ty⟩ = a^2 ⟨ x, y⟩ for each x, y∈ E. At first recall that two vector x, y∈ E are ordinary orthogonal if ⟨ x, y⟩ =0 and then we introduce the notion of orthogonality in an inner product A-module in three ways and show that an A-linear mapping between two inner product A-modules preserves the ordinary orthogonality if and only if it preserves each one of the new orthogonality.

In this paper, without using the classification of finite simple groups, we determine the structure of finite simple groups whose Sylow 3-subgroups are of the order 9. More precisely, we classify finite simple groups whose Sylow 3-subgroups are elementary abelian of order 9.

The quadrics are all surfaces that can be expressed as a second degree polynomial in x, y and z. We study the Gauss map G of quadric surfaces in the 3-dimensional Euclidean space R^3 with respect to the so called L_1 operator ( Cheng-Yau operator □ ) acting on the smooth functions defined on the surfaces. For any smooth functions f defined on the surfaces, L_f=tr(P_1o hessf), where P_1 is the 1-th Newton transformation associated to the second fundamental form of the surface and hessf denotes the self-adjoint linear operator metrically equivalent to the Hessian of, L_1G=(L_1G_1, L_1G_2, L_1G_3), G=(G_1, G_2, G_3). As a result, we establish the classification theorem that the only quadric surfaces with Gauss map G satisfying L_1G=AG for some 3×3 matrix A are the spheres and flat ones. Furthermore, the spheres are the only compact quadric surfaces with Gauss map G satisfying L_1G=AG for some 3×3 matrix A.

In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractional derivative method and the Riemann-Liouville fractional integral method. In the both method, a set of linear or nonlinear algebraic equations are achieved using collocation technique. Tow presented methods are implemented on some test problems. Numerical results explain the high performance of tow methods. Note that all calculations have been done by Mathematica software. Numerical results show that it should be used the first method when the exact solution of differential equation is a polynomial and the second method should be used when the exact solution of differential equation is a transcendental function.

One of the most important topic that consider in recent years by researcher is absolute value equation (AVE). The absolute value equation seems to be a useful tool in optimization since it subsumes the linear complementarity problem and thus also linear programming and convex quadratic programming. This paper introduce a new method for solving absolute value equation. To do this, we transform absolute value equation to linear system and then demonstrate efficient augmented Lagrangian method to solve the linear system. Also this paper is considered a class of two-point boundary value problems and introduced a new method to solve them. In this paper is shown that this class of problems is equivalent to absolute value equation. To illustrate the feasibility and effectiveness our method we generate random problems and solve them also solve a class of two-point boundary value problems. In section numerical results, we consider the efficiency of the proposed method. Computational results show that convergence to high accuracy often occurs in short time.

In this research, a two-dimensional model of pulsatile blood flow through a tapered artery with a non-symmetric stenosis is simulated. The blood flow as a cross fluid is modeled in an elastic cylindrical tube with an axially non-symmetric stenosis and a time-dependent geometry. The velocity of blood flow is compared within an elastic artery and an inelastic artery. Mild stenosis approximation is applied to simplify the governing equations. By applying an appropriate coordinate transformation, a cosine elastic artery turns into a rectangular and rigid artery. Using the finite difference method the Navier-Stokes equations governing the dynamics of the blood flow are numerically solved for velocity field. The correctness of the proposed model is proved through a comparison between the obtained results the present study and the previously obtained ones by others. The blood flow characteristics including resistive impedances, volumetric flow rate, and wall shear stress are obtained via the axial velocity profile. Various Two-dimensional diagrams for different parameters of the velocity distribution are also provided.

Restriction Site Mapping is one of the interesting tasks in Computational Biology. A DNA strand can be thought of as a string on the letters A, T, C, and G. When a particular restriction enzyme is added to a DNA solution, the DNA is cut at particular restriction sites. The goal of the restriction site mapping is to determine the location of every site for a given enzyme. In partial digest method, all pairwise distances between restriction sites are produced. Mathematically, given pairwise distances between n points on a line segment, the goal is to find that points. This problem has been named Partial Digest Problem(PDP). In this paper we present a new model for PDP using generalized network flows. Since complexity class of this problem is one of the most important open problems in bioinformatics (there is no polynomial algorithm and no proof for Np-completeness) reducing to a network flow problem create a new viewpoint to challenge with this problem.

This paper examines the issue of handling outputs in DEA that occur at different stages in time. In some situations, the output set occur at the different period of time, meaning that the produced outputs at the first period of time impact on the production of outputs of next time. This problem setting gives rise to the phenomenon of time-staged outputs. Specifically, the two outputs occur at different points in time, meaning that one of them plays a dual role. In other words, the dual-role measure is considered as either the output of the first stage and simultaneously as input for another time period. This paper demonstrates a modification of the joint technology in order to yield the maximum efficiency of the evaluated units. A real case on ten business schools has been illustrated. This real example is applied to emphasize that the suggested structure can handle this situation appropriately.

Wireless Sensor Networks (WSNs) are consist of independent distributed sensors with storing, processing, sensing and communication capabilities to monitor physical or environmental conditions. There are number of challenges in WSNs because of limitation of battery power, communications, computation and storage space. In the recent years, computational intelligence approaches such as evolutionary algorithms and swarm intelligence are applied successfully to solve many problems in WSNs. Most important of these problems are data aggregation, energy-aware routing, duty cycle scheduling, security and localization. These problem are in form of distributed so distributed approaches are required to solve them. Reinforcement learning is one of the most widely used and most effective methods of computational intelligence. In this paper, we used the reinforcement learning to solve multicast Quality of Service (QoS) routing. The simulation results showed that reinforcement learning is a suitable approach to solve this problem. The algorithm is implemented easy, it has the great flexibility in topology changes and it leads to optimized results. Distributed reinforcement learning provides compatibility mechanisms that show the intelligence behavior in complicate and dynamic environment such as WSNs. Using reinforcement learning, sensors behave autonomously, independently and flexibly during topology and scenario changes.

Controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator on abstract Hilbert spaces. Fusion frames and g-frames generalize frames. Hilbert C*-modules form a wide category between Hilbert spaces and Banach spaces. Hilbert C*-modules are generalizations of Hilbert spaces by allowing the inner product to take values in a C*-algebra rather than in the field of complex numbers. In this paper, we define and characterize controlled g-frames and controlled fusion frames in Hilbert C*-modules. These are generalization of controlled frames in Hilbert C*-modules and also controlled g-frames and controlled fusion frames in Hilbert spaces. We show, similar in Hilbert space, every controlled g-frame in Hilbert C*-module is an usual g-frame. Also we study the relation between controlled fusion frames and fusion frames in Hilbert C*-modules. Finally we present a sufficient condition on a family of closed submodules to be a controlled fusion frame.

n this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α , β )-metric admits no concurrent vector fields. We also prove that an L-reducible Finsler metric admitting a concurrent vector field reduces to a Landsberg metric. In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α , β )-metric admits no concurrent vector fields. We also prove that an L-reducible Finsler metric admitting a concurrent vector field reduces to a Landsberg metric. In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α , β )-metric admits no concurrent vector fields. We also prove that an L-reducible Finsler metric admitting a concurrent vector field reduces to a Landsberg metric. In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α , β )-metric admits no concurrent vector fields. We also prove that an L-reducible Finsler metric admitting a concurrent vector field reduces to a Landsberg metric.

This paper proposes a new method based on the ideal input vector to estimate inputs of a given decision making unit (DMU) when some or all of its outputs are increased to maintain its current efficiency level. In other words, this paper studied the following question: How much would be the increase in the inputs of the DMU if the decision maker increases certain outputs to a particular unit in which the DMU maintains its current efficiency level? In this study, unlike other proposed methods, the above question was addressed using just the single-objective linear programming (LP) problems. The problem of estimation of inputs was investigated based on the non-radial models. Necessary and sufficient conditions are proposed for estimation of inputs using just the single-objective LP problems. In addition, the level of deficiency (if any exists) in each of the output components is specified. An example with real data is presented to illustrate our proposed method.