Sueyoshi and Sekitani in 2007 presented a paper that explores the measurement of Returns to Scale under a possible occurrence of multiple solution in a reference set and a Supporting hyperplane. The occurrence of multiple solutions is classified into Type I and Type II. Type I is an occurrence of multiple solutions in a reference set. Type II is an occurrence of multiple solutions on a Supporting hyperplane passing on the reference set. In this paper we want to apply their method for estimating RTS under weight restrictions. For this goal we use tone's method for estimating RTS under weight restrictions.

We show that the approximate hyperplane series property consequence, we obtain that the class of spaces Y such that the pair (l1,Y) has the Bishop-Phelps-Bollobas property for operators is stable under finite lp-sums for 1≤p<∞. We also deduce that every Banach space of dimension at least 2 can be equivalently renormed to have the AHSp but to fail Lindenstrauss’ property b. We also show that every infinite-dimensional Banach space admitting an equivalent strictly convex norm also admits such an equivalent norm failing the AHSp.

DEA is the way of evaluating the performance of decision-making units on the basis of the degree of efficiency. Unfortunately, congestion has been known as a technical inefficiency for at least three decades just because of the lack of determining the congestion border. In this article, we have introduced the concept of the congestion hyperplane without considering the efficiency value. This has considerably reduced the calculation, and the congestion border has been determined. In addition, the existence of this hyperplane is ascertained. For this purpose, we determine the BCC-efficient DMUs. The normal vector of the hyperplane is denoted by these values. This hyperplane can pass from any of the BCC-efficient DMUs. Next, we have shown that the previous congestion methods are covered and improved by this hyperplane.

Data Envelopment Analysis (DEA) is an estimator. This estimator tries to assess a relationship between multiple inputs and multiple outputs, and an identified technology. In traditional DEA models, firms are classified into two divisions, efficient and inefficient. Efficient firms are considered as a reference for inefficient firms. In traditional DEA models, the efficiency improvement has been inspected for inefficient firms and efficient firms are assumed to be unchanged. Since the estimated technology is rationally smaller than the real technology or in other words, the estimated technology is always the subset of the true technology, we can expand it a little. Thus, we can improve efficient firms. This is done by creating some virtual DMUs. In this paper, an algorithm is proposed to expand the Production Possibility Set (PPS) and to improve efficient firms. To illustrate the proposed approach, numerical and applied examples are provided. The results are explained and discussed.

In a verifiable database scheme (VDB), a client with limited storage resources securely outsources its very large and dynamic database to an untrusted server such that any attempt to tamper with the data, or even any unintentional changes to the data, can be detected by the client with high probability. The latest work in this area has tried to add the secure search feature of single keyword and multiple keywords. In this paper, we intend to add a range query to the features of this database. The scheme presented in this article provides the requirements of a secure search, namely the completeness of the search result, the proof of the empty search result, the lack of additional information leakage and the freshness of the search results, as well as the database with public verifiability. In the proposed scheme, the computational complexity of the client is not changed significantly compared with the previous scheme, but the computational and storage complexity of the server has increased which is justifiable by its rich resources.

The production possibility set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. The frontier the production possibility set can be partitioned to strong defining hyperplanes and weak defining hyperplanes. These hyperplanes are useful in sensitivity and stability analysis, identifying the status of returns to scale of a DMU, incorporating performance into the efficient frontier analysis, and so on. In this paper, by using the basic concepts of Linear Algebra, we propose an algorithm for finding all strong and weak defining hyperplanes of PPS without solving any linear programming problems. The proposed method is applicable to both, PPS under constant and variable returns-to-scale assumptions. Two numerical examples are presented to explain the usage and effectiveness of the proposed algorithm. Our method can be easily implemented using existing packages for mathematical algorithm, such as python.

A jurisprudential research in Supporting foreign tourists English In today's world, the tourism industry is one of the fields that has received attention due to the groundwork for progress and the important role it plays in human social relationships. Since Islamic jurisprudence has entered into various fields of human life and specifies the duties of the obligees, the question of the upcoming research is what position should be taken in relation to this industry from the point of view of jurisprudence in the Islamic government. The author, with an interdisciplinary research of the type of analyticaldocumentary research with the method of collecting library information, is pursuing a jurisprudential examination of the Islamic government's encounter with the tourism industry in the light of Quranic and narrative documentation and the views of jurists in this field. Examining the Islamic verses and traditions shows that the importance of the Islamic religion to this issue is important, the most important components raised in this context are in the form of the rule of honoring human beings, the jurisprudential rule of conditions and harm, and the contract of safety. Therefore, jurisprudence, while accepting this industry, has approached its exclusive territory due to the necessity of public expediency in the field of cultural and economic prosperity of the Islamic government, and has also proposed solutions for the presence of foreign tourists and tourists in order to preserve the religious and cultural essence of the Islamic society.

. Since “obvious crimes”, the subject of article 45 of the code of criminal procedure is just presented by examples and there is not any specific criterion for it, the officer cannot use that definition as a default principle in suspicious cases. Thus, on one hand, with reference to the application of privacy in verbal arguments, Imam Khomeini’s fatwa in his 8-article command, and by scrutinizing the content of articles 56 and 57, the default principle, in dealing with obvious crimes that are suspected to be contrary to the public safety and security, is not to be pursued and not to be reported. On the other hand, these crimes, either based on the criterion of “necessitating being public” are not considered obvious or based on the criterion of “visibility” in all places, are considered obvious but the law of obvious crimes will not apply to them. Therefore, the agents’ acts will be illegal and will be subject to acquiring evidence through illegal means.