To study the relationship between the linear statistical models we used methods of linear algebra, Hilbert spaces and statistics. It was found that there is a linear relationship between linear statistical models which is expressed by a matrix equality. Several corollaries are derived and discussed, and a new interpretation is proposed for the parameters of linear statistical model. The given relation between the linear statistical models may be useful for both theoretical analysis of statistical models and interpretation of applied statistical models, in particular, to analyze the impact of confounders.

Robustness of secure software is directly associated with better market and refining relations between customers and software vendors. Nowadays robustness of secure software is an assessment tool to find healthier market room by way of developing highly integrated quotient between customers and vendors. Software security risk management is a very highly appealing phenomenon to control security through establishing expensive countermeasures of security hazards and by controlling them. Existing approaches for security risk management are merely available which are having direct or indirect impact with the simple implementations through planning, development of established security requirements for modifications and execution of security design policies. This paper examines the associated security risks of software through different inputs of security risk management procedure. This review may be helpful to discover the new pitches of risk management techniques of software security controls at design level for high quality secure product. A contribution is made after reviewing views of authors in this paper in the form of a checklist for security risk evaluation and management at software design phase.

This paper deals with the problem of computing optimal ordering policies for the probabilistic fixed lifetime inventory model with continuous demand rate. We proposed a probabilistic fixed lifetime inventory model with continuous demand rate. The necessary condition for minimizing the expected proposed cost model was derived. The condition is also sufficient because the model is convex in S. The optimal ordering policies for this probabilistic fixed lifetime inventory system with continuous demand rate were given. The objective of the study is to examine decisions regarding when to order or not. This was investigated under some conditions. The operating characteristics obtained in this article are very significant because, for practical problems, available mathematically optimal solutions to the fixed lifetime inventory problem cannot be realized due to their computational complexity arising from the fact that exact formulation of the problem requires information on the age distribution of the items in inventory and the corresponding quantity of items of each age. Hence there is a gap between theoretical results and practical requirements for computational results. We have been able to bridge the gap between theoretical results and practical requirements for computational results. We computed the ordering cost, expected holding cost, expected shortage cost and expected outdates cost, and these computations were applied to determine the expected cost for the fixed lifetime inventory system. The expected cost model with Set- up Cost and without Set- up Cost were useful costs for the determination of the optimal ordering policy for this type of inventory system Finally, organization may like to operate under a given aspiration scenario, values of inventory level that satisfy such condition are identified and are used in the cost function to determine optimal operating conditions, this will go a long way to reduce waste and holding cost.

The main purpose of the present article is to give a brief description of the “golden” number theory and new properties of natural numbers following from it, in particular, Z-property, D-property, Φ -code, F-code, L-code. These properties are of big theoretical interest for number theory and can be used in computer science.

The article is written in popular form and is intended for a wide circle of mathematicians (including mathematics students) and specialists in computer science, who are interested in the histories of mathematics and new ideas in the development of number theory and its applications in computer science.

for every x in [1]. In this paper, the conditions under which composite multiplication operator becomes k-*paranormal operator, k-quasi-*paranormal operator and (n,k) -quasi-*paranormal operator, have been obtained in terms of Radon-Nikodym derivative .

The poor performance of students in Mathematical Science based programmes in Nigerian Universities is partly as a result of the tools and data used in the admission process into tertiary institutions. In this paper, a comparative analysis on three rule base cases using fuzzy logic was made on the Post University Matriculation Examination (PUME) results of the current 400 Level students in Mathematical Sciences programmes of Kaduna State University, Kaduna. The results reveal that the CGPA of students that had very good performance in Mathematics and Physics in their PUME are higher as compared to those that score fail in either Physics or Mathematics but were offered admissions into Mathematical Sciences programmes. The percentage pass from the aggregate method is 41% while that for fuzzy logic approach is 59%.

In this work, the second order nonlinear ordinary differential equation is implemented as an auxiliary equation. For illustration, the generalized Hirota-Satsuma coupled KdV equations are considered for constructing traveling wave solutions by applying a new extension of so called (G'/G) method. As a result, many new traveling wave solutions have been generated with many arbitrary parameters. The obtained solutions also show the wider applicability of this new extended method for handling nonlinear evolution equations. The numerical results are also described in the figures.