In this paper we establish a mathematical model for the assessment of the human cognition, in particular, the student ability to learn in different practical cases. The method allows us to obtain quantitative and qualitative estimates to a group of undergraduates for their acquired knowledge. We illustrate the theory by a practical example. A qualitative analysis to the obtained data is presented.

In this work, the Cantor-Schroeder-Bernstein theoremt is addressed. The main goal and contribution of this presentation consists in giving an easy proof which can be easily understood by students without a strong mathematical foun- dation. I have employed it successfully in my Discrete Mathematics course for Computer Science students at the Instituto Politecnico Nacional.

Let G be a finite non-abelian group and let be a set of elements of G. Let A be the set of commuting elements in , i.e A = {v ∈ : vg = gv,g ∈ G}. In this paper, we extend the work on centralizer graph by defining a new graph called the isotropy graph, denoted as iso. The vertices of this graph are proper isotropy groups. In other words, |V ( iso)| = StabG()−A, where StabG() is the number of stabilizers under group action of G on and A is the number of improper isotropy groups under group action on a set. Two vertices are connected by an edge if their cardinalities are identical.

Encryption schemes can be derived from the units which are known as invertible elements in a group ring. Besides there are many studies on units in group rings in the literature, we can also see some studies of units in terms of applicability to cryptography and coding theory. In this work, we shall establish the relations between units and RSA problem. Our motivation is to construct a much stronger public key cryptosystem. It is clear that we must consider a mathematical hard problem to do this. Thus, we investigate some interesting properties of units which are no deterministic algorithm in general. Our notations follow (8).

The reliable solution of nonlinear parameter estimation problems is an important computation problem in chemical engineering. The present paper is devoted to an application of a nonlinear solving process to a system of transcendent equations. In such systems we may define the values of the parameters �12 and �21 to the Wilson equation on the base of the activity coefficientsat infinite dilution. The Wilson equation was used in the mathematical model for prediction of mixture flash point temperature.

An integral of some rational functions involving a square root of a quadratic of a single cosine function is reduced to elliptic integrals and elementary functions if any. For simplicity interval of integration is limited to be real and finite, although parameters may be complex. Restrictions of the dependency on parameters for the interval of integration is shown.

The aim of this paper is to develop monotone iterative scheme using the notion of upper-lower solutions for weakly coupled system of finite difference equations which corresponds to weakly coupled system of semilinear time degenerate parabolic Dirichlet initial boundary value problem (IBVP). Using upper and lower solutions as distinct initial iterations, two monotone convergent sequences from linear system are constructed. It is shown that these two sequences converge monotonically from above and below to maximal and minimal solutions respectively which lead to the existence-comparison and uniqueness results for the solution of the discrete nonlinear Dirichlet IBVP. Positivity lemma is the main ingredient used in the proof of these results. AMS Subject Classification: 65Q10

New class of spaces is introduced in this paper as a generalization of countably compact spaces called nearly countably compact spaces. Some character- izations and results about this new class of spaces are also presented. We give a definition of more generalized kind of spaces and we call it nearly regular countably compact spaces. Also, we study the effect of some mappings on the nearly countably compact spaces.

In this paper, we study the existence of solutions for a fractional bound- ary value problem involving Hadamard type fractional differential equations and three-point boundary conditions. Our analysis is based on Krasnoselskii-Zabreiko's fixed point theorem. As an application, we discuss a Hadamard type boundary value problem with fractional integral boundary conditions. We emphasize that our re- sults are new in the context of Hadamard fractional calculus and are well illustrated with the aid of examples.