It has been thirty years since Perona and Malik (PM) introduced the nonlinear diffusion equation in image processing and analysis. The problem's complexity was to find a suitable and adaptive diffusion function that smooths away noise or textures while Preserving sharp edges of a sufficiently smooth intensity. This paper provides a new two-dimensional analysis of the PM diffusion equation to examine its behavior during scales and an explicit formula to select the right diffusion function adequately. In this context, we study the PM equation at the zero crossings of the first and second directional derivatives of a sufficiently smooth function in the gradient direction.

All of the old paper-based land documents should be transformed to digital georeferenced form. In digitization of parcels to be able to be imported into a cadastral system, the area of the digital form of the polygon should be in concordance with the analog document. However, during the digitization process, geometric properties, such as area, changes. Preserving the dimensions and area prevents the contradiction in documents and, registration and trading quarrels. In order to solve this problem, angles of the polygon vertexes are considered as observations by keeping the dimensions fixed and a method based on the least-square adjustment is proposed. Executing the invented process, the required concordance is acquired. For checking this method, a paper map having six parcels each with about one thousand m2 area in 1: 1000 scale is scanned and digitized by Preserving area and dimensions. Results showed that the mean, maximum and minimum movement by using adjusting method is in average 19. 31, 26. 96 and 10. 50 respectively that is acceptable from the land registration aspect because of map scale and cadastral law about cultivation and national parcels.

A B S T R A C T Transformations such as globalization, the contiguity of geographical spaces, as well as developments in the field of military technologies have transformed the issue of defense as the main factor for the survival of countries. Because the transformation from hard to soft war and then the smart war in recent decades has changed the approaches to defense. These transformations have led to the development of discussions about defense purposes. Meanwhile, Middle East countries have a prominent position and importance in terms of defense due to their special conditions. This article has tried to investigate the basic dimensions affecting the defense of foreign countries with descriptive and analytical methods, using library and field findings and Smart-PLS software. The results of the current research show that the effective components in the current research include 130 items that are placed in the form of 15 dimensions. The importance of these dimensions in defense of the Middle East countries is, respectively, geopolitical dimension with a 0.43 score, military dimension with a 0.41 score, economic dimension with a 0.41 score, political dimension with a 0.39 score, hydrology dimension with a 0.34 score, security dimension with a 0.32 score, social dimension with a 0.29 score, demographic dimension with a 0.28 score, cultural dimension with a 0.26 score, scientific-health dimension with a 0.25 score, geomorphological dimension with a 0.25 score, mathematical dimension with a 0.2 score, climatic dimension with a 0.2 score, biological dimension with a 0.2 score and soil dimension with a 0.18 score. Extended Abstract Introduction Security and defense are among the most vital issues for the preservation and survival of countries. In fact, defense and military affairs are necessary for countries' independence and political, cultural and economic development. Among them, geography and political geography are prominent fields that directly affect defense issues. Actions taken by a country in dimensions (political, military, economic, etc.) in order to maintain security and territorial integrity, guarantee independence and protection of its people against any enemy attack, will organize the geographical (spatial) environment, wise and appropriate distribution of critical places and sensitive centers and infrastructures are identified by taking into account the threats and the correct use of environmental capacities in political, economic, social, cultural, etc. dimensions, and as a result, it can lead to stability and stability in the country's geographical space. The design of defense planning model according to the economic, cultural, political and environmental features in the new era when countries are facing external and internal threats as a sub-branch of territorial planning has received the attention and importance of officials and governance systems in order to be able to reduce these threats with accurate and systematic planning in the geographical space, defense planning is not separate from the flow of national and regional planning. It is important to pay attention to it based on the type and amount of external and internal threats to governance. Due to the expansion of the security circle, the government is not only responsible for creating military security. However, it must also exercise part of its authority in the direction of territorial management. On the other hand, there has been a transformation in the form of threats and wars based on changes and the movement from hard to soft war and finally, smart war is the basis for reviewing and recognizing the components that can be used in defense of countries, including the Middle East countries, have a prominent position and importance. Despite the internal differences between countries, the Middle East has commonalities and connections that can directly affect the overall defense of this geographical space.   Methodology In terms of type and purpose, the current research is fundamentally applied. Also, it is descriptive and analytical in terms of nature. This research, in addition to the correct and realistic depiction of the defense situation of the Middle East countries, it is tried to provide a suitable model for the defense of the countries. The sources used in the current research are library and field sources (questionnaires). According to the subject of the current research, the statistical population of this research is a collection of people, experts and elites who have sufficient knowledge, experience and expertise regarding the research topic, which is the design of the defense model, according to the nature of the Delphi pattern model, at least the statistical population based on the sources should be between twenty and fifty people to reach statistical saturation. The number of selected samples included 51 people who were identified in the form of a non-random sampling pattern and introduced as a statistical sample in the framework of the Delphi model. Due to the qualitative nature of this research, it has been tried to use the Delphi model in the framework of the targeted non-random model. Therefore, based on these cases, the current research has selected the maximum statistical population of 51 elites, experts, and opinionated people in this field. In this research, to evaluate the research hypotheses in the form of the hardness equations model, the partial least squares method and the SMART-PLS software, which is a variance-based path modeling technique and provides the possibility of checking the theory and metrics simultaneously, have been exerted.   Results and discussion In this research, approaches such as political, military, cultural, etc., in the field of land use have been discussed. In the meantime, the defense of countries as an emerging approach is significant. According to the developments in geographical spaces, such as the evolution of military-defense technologies, the connection of geographical spaces to each other and most importantly, the movement from hard and soft war to smart war has witnessed a transformation and wide attention in a way that countries are suited to these developments are trying to prepare the geographical space of their country in terms of defense. Therefore, the defense planning of the Middle East countries as a geographical region has great importance from a geopolitical and strategic point of view, which indicates that the countries of this region face threats and complex defense-security issues in different ways.   Conclusion The results of the present research show that the defense planning in developing countries should be considered according to their characteristics, considering all 15 dimensions, which include 130 components. In the design of the defense planning of these countries, attention should be paid to the weight and importance of the shaping dimensions. In general, it can be said that the defense planning of the Middle East countries is proportional to the geographical features of these countries and on the other hand, considering the developments in the field of threats and moving from hard to smart war, 15 dimensions should be considered for the defense of these countries.   Funding There is no funding support.   Authors’ Contribution Authors contributed equally to the conceptualization and writing of the article. All of the authors approved thecontent of the manuscript and agreed on all aspects of the work declaration of competing interest none.   Conflict of Interest Authors declared no conflict of interest.   Acknowledgments  We are grateful to all the scientific consultants of this paper.

Let A and B be standard operator algebras on Banach spaces X and Y, respectively. Let ϕ, : A →,B be a bijective map. In this paper, we show that ϕ,is completely Preserving quadratic operator in both directions if and only if ϕ,is 2-quadratic Preserving operator in both directions and if and only if ϕ,is either an isomorphism or (in the complex case) a conjugate isomorphism.

The target of this paper is to present partial fuzzy metric-Preserving functions and characterize the functions $f:[0,1]\to[0,1]$ with this aspect. We give a characterization for partial fuzzy  metric-Preserving functions considering the different t-norms. Also, we show that the topology induced by partial fuzzy metric does not preserve under these functions with  an example. Then we  give a characterization of those partial fuzzy metric-Preserving functions which preserve completeness and contractivity under some conditions. Finally, we discussed the relation between fuzzy  metric Preserving and partial fuzzy Preserving functions.

The family of the Prophet (SAW) are the highest authority next to the Noble Quran as the Prophet recommended at the last moment of his life, saying 'I leave you with two successors, Allah's Book - a long rope between the Heaven and the earth, or between the Heaven to the earth - and my family; they will not be separated till they return back to me at the Pool (Hawd)'.The Almighty God has chosen them for the guidance and leadership of the Muslim after the Prophet (SAW).(AS), the fifth Imam and leader after the Prophet (SAW), held the control of the ark of guidance at the time when the social and political conditions had changed from that of the earliest Imams: therefore he was able to teach his knowledge to those eager and to open the doors of different sciences.In this article, we are about to mention some of his scholastic activities and his recommendations about recording, memorizing and writing hadith.