The aim of the current paper is to study a partially described inverse eigenvalue problem of  a specific symmetric  matrix, and prove some properties of such matrix. The problem includes the construction of the matrix by  the  minimal eigenvalue of all  leading principal submatrices  and eigenpair $(\lambda_2^{(n)},x)$ such that $ \lambda_2^{(n)}$ is the maximal eigenvalue of the required matrix. We investigate  conditions for the solvability of the problem, and finally an algorithm and  its numerical results are presented.

Background and Objective: In recent years, DNA microarray technology has become a central tool in genomic research. Using this technology, which made it possible to simultaneously analyze expression levels for thousands of genes under different conditions, massive amounts of information will be obtained. While traditional clustering methods, such as hierarchical and K-means clustering have been shown to be useful in analyzing microarray data, they have some limitations. These methods assume that a gene or an experimental condition can be assigned to only one cluster and a gene belongs to a group of genes that are coexpressed under all conditions. Therefore, to overcome these shortcomings, biclustering methods are used. The purpose of this paper was to evaluate the efficiency of a biclustering method in analyzing yeast gene expression data.Materials and Methods: In this study, Large Average submatrices (LAS) method has been used to analyze the yeast Saccharomyces cerevisiae expression dataset, provided by Gasch et al. (2000). The dataset contains 2993 genes and 173 different experimental conditions. In this study, the software packages such as LAS, JMP and GOAL has been used for analyzing data.Results: Results showed that the LAS method is able to produce biologically and statistically relevant biclusters.Conclusion: This study showed that LAS can be used to discover biologically significant subsets of genes under subsets of conditions for microarray data analysis.

The purpose of this research is to investigate the factors affecting the formation of leading schools, so that it can be used in Iran's education. For this purpose, first, according to the research background and theoretical foundations, a conceptual framework was presented in the field of the components of an efficient and progressive school. Due to the nature of the subject, this research is an applied and developmental research and its method is of a mixed type, and includes quantitative and qualitative methods. According to the obtained information, the statistical population is about 3000 people. The sample size is estimated to be 344 people using Morgan's table. Stratified sampling method was used for sampling in this research, and 84 managers and 260 teachers participated in this study. The tool of this research is a researcher-made questionnaire. To analyze the data and answer the research questions, the correlation coefficient test and factor analysis were used. The results of the research showed that the components of management and leadership, research factors, educational factors, human resources, budget and infrastructure, technology and equipment are the main components of the formation of leading schools, and the component of educational factors has the largest contribution.

The inverse eigenvalue problem involves constructing a matrix based on its spectral information, along with providing conditions on the input data to determine the solvability of the problem. In this paper, we focus on a specific instance of the inverse eigenvalue problem, known as IEPSP, to generate symmetric pentadiagonal matrices using two pairs of eigenvalues from the desired matrix and an additional eigenvalue from each of its leading principal submatrices. Additionally, we explore a non-negative formulation of the inverse eigenvalue problem to produce a matrix that has non-negative elements. We present sufficient conditions for problem solvability, propose an algorithm, and provide several numerical examples to validate the results.

The problem of constructing a matrix by its spectral information is called inverse eigenvalue problem (IEP) which arises in a variety of applications. In this paper, we study an IEP for arrowhead matrices in different cases. The problem involves constructing of the matrix by some eigenvalues of each of the leading principal submatrices and one eigenpair. We will also investigate this problem and its variants in the cases of matrix entries being real, nonnegative, positive definite, complex and equal diagonal entries. To solve the problems, a new method to establish a relationship between the IEP and properties of symmetric and general form of matrices is developed. The necessary and sufficient conditions of the solvability of the problems  are obtained. Finally, some numerical examples are presented.

Theory of undisclosed principal is a particular theory of law of common law system. This is accepted in the Law of common Law system against some of lawyers dissented with it. In the passing regulations of agency of Geneva international sale dated 1983 was effective and the foregoing convention is subject to this regulations. This theory is not consistent with fundamental and basic principles.In the law of common law, undisclosed principal have right to intervene in contract of agent which is concluded for his or her without writing his or her name. This intervention is subject to election of third party. Also until when undisclosed principal is not appeared, all payments and receivements to agent, is payment and receivement to principal. This theory have little analogous with 196 article of Iran civil code in the respect of the intervention , altogether both are from two adverse law system, Notwithstanding in the Iranian law system the right of election in the agent contract by the third party is not recognized. Because Iranian commercial law is subject from roman - Germany law system, theory of undisclosed principal cannot accepted and the undisclosed principal have not the right of intervention.Articles of 5 and 6 insurance act and articles 357 and 367, 388 commercial Code in the foregoing debates denote this object.

In this paper, we consider an inverse eigenvalue problem (IEP) for constructing a special kind of acyclic matri-ces. The problem involves the reconstruction of matri-ces whose graph is a banana tree. This is performed by using the minimal and maximal eigenvalues of all lead-ing principal submatrices of the required matrix. The necessary and su cient conditions for the solvability of the problem is derived. An algorithm to construct the solution is provided.