JOURNAL OF NEW RESEARCHES IN MATHEMATICS
Year:2018 | Volume:4 | Issue:13 |Papers Count:10

Discriminant analysis is a classification method that can predict the group membership of a newly sampled observation. In discriminant analysis, classification of new observed data has an uncertainty. In this paper, the confidence degree is introduced to determine the confidence of classification of new observed data. Then, a Monte Carlo-based sensitivity analysis is applied to an assessment of the influence of financial variables on the overall variance in defined confidence degree. The variables that have a dominant influence on the confidence of new observed data are identified. The result show that in changing classification of the new branch of banks, the uncertainties in the long-term deposits and loans granted variables are more significant than the uncertainties in other bank’ s variables in decision making. Also, the personnel, non-benefit deposit and non-performing loans variables have little effect. The results open the door to better making decision on establishing a new bank’ s branches.

Data envelopment analysis (DEA) is a relatively new data oriented approach to evaluate performance of a set of peer entities called decision-making units (DMUs) that convert multiple inputs into multiple outputs. Within a relative limited period, DEA has been converted into a strong quantitative and analytical tool to measure and evaluate performance. In an article written by Toloo et al. (2009), they proposed a new DEA model to find the most efficient association rule in data mining. Considering several criteria, they created an algorithm for ranking association rules using this model. In the present article, we show that their model only selects an optimistic efficient association rule randomly and it is completely dependent on solution or software, which is used for solving problems. In addition, it shows that their proposed algorithm can only rank optimistic efficient rules randomly and it is not able to rank optimistic non-efficient DMUs. We mention other disadvantages and propose a new approach “ DEA with double frontiers” to create a complete ranking of association rules. A numerical example will explain some contents of the paper.

Let η be a line bundle on a smooth curve X with η ^2=0 such that π _η , the double covering induced by η is an etale morphism. Assume also that X_η be the Prym-canonical model of X associated to K_X. η and Q is a rank 4 quadric containing X_η . After stablishing the projective normality of the prym-canonical models of curves X with Clifford index 2, we obtain in this paper a sufficient condition for Q to be a tangent cone. Under some circumstances, we obtain an inverse to this sufficient condition. We make our study complete by presenting an example of a curve of genus 7 and gonality 4 in chapter 4. The importance of our example stems from its elementary nature and the fact that it is generalizable.

In this paper, we study the tensor commutativity degree of pair of finite groups. Erdos introduced the relative commutativity degree and studied its properties. Then, Mr. Niroomand introduced the tensor relative commutativity degree, calculated tensor relative degree for some groups, and studied its properties. Also, he explained its relation with relative commutativity degree. In this paper, we give a brief explanation of the tensor commutativity degree and could introduce relations for this tensor commutativity degree. We proved some relations, including the relation among tensor commutativity degree of subgroups of a group. In addition, we introduced some boundaries for groups having special properties.

In this paper, using sub-supersolution argument, we prove an existence result on positive solution for an ecological model under certain conditions. It also describes the dynamics of the fish population with natural predation and constant yield harvesting. The assumptions are that the ecosystem is spatially homogeneous and the herbivore density is a constant which are valid assumptions for managed grazing systems. This term saturates to c at high levels of vegetation density as the grazing population is a constant. This model tries to capture the phenomena of bistability and hysteresis and provide qualitative and quantitative information for ecosystem managements. This model has also been applied to describe the dynamics of fish populations. This model describes grazing of a fixed number of grazers on a logistically growing species. The general logistic function is characterized by a declining growth rate per capita function (Equation) Here P is the population, r > 0 is the growth rate and is positive constant[21]. But there are some ecosystems where the growth rate per capita may achieve its peak at a positive density. This is called the Allee effect This effect can be caused by shortage of mates, lack of effective pollinations predator saturation and cooperative behaviors. In this pape, we restrict ourselves to logistic models.

In this paper, the new concept of non-autonomous iterated function system is introduced and also shown that non-autonomous iterated function system IFS(f_(1, ∞ )^0, f_(1, ∞ )^1) is topologically transitive for the metric space of X whenever the system has average shadowing property and its minimal points on X are dense. Moreover, such a system is topologically transitive, whenever, there is a point like z∈ U for each open and invariant set U from X so that N(z, U) has a positive upper density. It is also shown that topological transitivity is result of properties of shadowing and chain transitivity. The relation between average shadowing property, topological transitivity and chaotic non-autonomous iterated function system is studied. Moreover, it is also demonstrated that the first two conditions for the definition of chaos results the third condition. The topological mixing of such a system is obtained from shadowing property and chain mixing. Finally, we evaluated that the dynamical system (X, f) has Li-York e chaos under special conditions.

In this paper we prove that every n-Jordan homomorphis varphi: mathcal {A} longrightarrowmathcal {B} from unital Banach algebras mathcal {A} into varphi-commutative Banach algebra mathcal {B} satisfiying the condition varphi (x^2)=0 Longrightarrow varphi (x)=0, xin mathcal {A}, is an n-homomorphism. In this paper we prove that every n-Jordan homomorphism varphi: mathcal {A} longrightarrowmathcal {B} from unital Banach algebras $mathcal{A} into varphi$-commutative Banach algebra $mathcal {B}. satisfiying the condition varphi (x^2)=0 Longrightarrow varphi (x)=0, xin mathcal {A}, is an n-homomorphism. This result was proved in cite {zivari1} for 3-Jordan homomorphism with the additional hypothesis that the Banach algebra mathcal {A} is unital, and it is extended for all nin mathbb {N} in cite {An}. Later, for nin lbrace 3, 4 rbrace, Theorem ref {T1} proved in cite {Bodaghi1} by considering an extra condition varphi (ab^2)= varphi (b^2a), (a, bin mathcal {A}). Some significant results concerning Jordan homomorphisms and their automatic continuity on Banach algebras obtained by the author in cite {zivari}, cite {zivari2} and cite {zivari3}. In this paper, under special hypotheses we prove that every n-Jordan homomorphism varphi from Banach algebra mathcal {A} into Banach algebra mathcal {B} is an n-homomorphism.

Let G be a simple connected graph. The transmission of any vertex v of a graph G is defined as the sum of distances of a vertex v from all other vertices in a graph G. Then the distance signless Laplacian matrix of G is defined as D^{Q}(G)=D(G)+Tr(G), where D(G) denotes the distance matrix of graphs and Tr(G) is the diagonal matrix of vertex transmissions of G. For a given minimum dominating set of a graph G, our aim in this paper is to define and study the so called minimum dominating distance signless Laplacian matrix, denoted by MDD^{Q}(G). We study some properties of the matrix MDD^{Q}(G). We also define the minimum dominating distance signless Laplacian energy of a graph G, denoted by EDD^{Q}(G), as the sum of the absolute values of the eigenvalues of MDD^{Q}(G), and give some upper and lower bounds for the energy and spectral radius of MDD^{Q}(G).

Let R be a commutative Noetherian ring. The k-torsionless modules are defined in [7] as a generalization of torsionless and reflexive modules, i. e., torsionless modules are 1-torsionless and reflexive modules are 2-torsionless. Some properties of torsionless, reflexive, and k-torsionless modules are investigated in this paper. It is proved that if M is an R-module such that G-dimR(M)<∞ , then M is k-torsionless if and only if Mp is k-torsionless for p∊ Spec(R) with depth (RP)≤ k-1, and dephRp (Mp)≥ k for p∊ Spec(R) with deph(Rp)≥ k. Furthermore, by Auslander-Bridger formula, we prove that M is k-torsionless if and only if Mp is k-torsionless for p∊ Spec(R) with depth (RP)≤ k-1, and G-dimRp(Mp)≤ depth(Rp)-k for p∊ Spec(R) with deph(Rp)≥ k. Also, it is shown that the class of maximal Cohen-Macaulay modules and the class of k-torsionless modules are equivalent over Gorenstein local ring with dimension k. Finally, we provide the necessary and sufficient conditions which led the tensor product of k-torsionless modules to be k-torsionless.

One of the fundamental problems in the classic DEA is lack of ability to distinguish unit's performance scores that is considered as a disadvantage. Recently, Parkan et al. [9] tried to address this problem. They proposed to assess each unit both optimistic and pessimistic views are taken into account. In contrast to traditional evaluation, one index is considered for each unit based on the lowest measured performance that is called robust efficiency. In this way, a new technology was made on the assumption of constant returns to scale. In this paper, the production technology with variable returns to scale assumptions made and the corresponding models are formulated as linear programming. Finally, it is shown that, the models based on the robust efficiency has more discriminatory power of the classic DEA.