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The prime principle is the mathematical foundations for clusters and nanostructures - ALL IS THE STABLE NUMBER (Ai mathematics)

Chun-Xuan. Jiang

P. O. Box142-206 , Beijing 100854, P. R. China

jiangchunxuan2@163.com

Abstract: Why we have five fingers. We suggest two principles: (1) the prime principle and (2) the symmetric principle. We prove that 1, 3, 5, 7, 11, 23, 47, and 2, 4, 6, 10, 14, 22, 46, 94 are the most stable numbers, which are the basic building-blocks in clusters and nanostructures. The prime principle is the mathematical foundations for clusters and nanostructures . All is the stable number.

[Chun-Xuan. Jiang. The prime principle is the mathematical foundations for clusters and nanostructures - ALL IS THE STABLE NUMBER (Ai mathematics). J Am Sci 2026;22(6):1-4]. ISSN 1545-1003 (print); ISSN 2375-7264 (online). http://www.jofamericanscience.org. 01. doi:10.7537/marsjas220626.01

Keywords: prime principle; mathematical foundation; cluster; nanostructures

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Study on the Reliability Evaluation of the Web-Based Software

¹Dr. Rajeev Yadav and ²GulshanKumar

¹Professor, Department of Computer Science, SunRise University, Alwar, Rajasthan (India)

²Research Scholar, Department of Computer Science, SunRise University, Alwar, Rajasthan (India)

Email-gulshan-_dixit@rediff.com

Abstract: The simulator developed in this chapter has been executed for 100000 number of simulation runs in order to compute system reliability for web-based software. The results obtained for web-based software reliability corresponding to different data sets of values of web page reliability. It is found that the system reliability increases as the web page reliability increases. The simulator described in his chapter will be of great importance to evaluate the reliability of web based software. The transition probabilities of web pages which are not connected directly are considered as zero when ideal transition probabilities for the web pages are entered. Each state is prone to failure to some extent, thereby making the web software imperfect. The simulator is executed using various combinations of reliabilities of web pages and it is found that the system reliability is sensitive to the reliability of individual web pages. It is depicted from the graph plotted between web page reliability and web-based software reliability. It is also evident that the web-based software reliability increases as the number of simulation runs increases from the results.  This simulator can be used as an access tool by the software quality assurance team for estimating the reliability of web-based system. The reliability evaluation will act as a metric of amount the software quality assurance needs for meeting software project quality objectives.

[Dr. Rajeev Yadav and GulshanKumar. Study on the Reliability Evaluation of the Web-Based Software. J Am Sci 2026;22(6):5-11]. ISSN 1545-1003 (print); ISSN 2375-7264 (online). http://www.jofamericanscience.org. 02. doi:10.7537/marsjas220626.02

Keywords: Software; Simulators; Web; Reliabiity

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Establish the North East Monsoon Time Scale and break out the mysteries of the North East monsoon

Gangadhar

H.No.5-30-4/1, Saibabanagar, Jeedimetla, Hyderabad, India-500055

Email:  gangadhar19582058@gmail.com

Abstract:  There are many mysteries and unsolved issues in the monsoonal climate and Weather systems that cannot explain and solve. I proposed and designed the Basics of Monsoon Time Scales for all world global, regional, local monsoon systems along with countries for unraveling the mysteries of climate, weather, monsoons; studying the characteristics of mechanism of climate, weather and monsoons and exercising the benefits of mankind and development of monsoonal climate and weather sciences.  According to the researches and studies on the Monsoon Time Scales, it is known that there will be major global climate changes in the coming years "i.e"  heavy rains, floods and storms etc. will occur until about 2075 and there will be droughts and famines etc. until about 2150. Through the establishment of Monsoon Time Scales, we can know the future consequences of the climate changes. Plans can be made accordingly. So, scientists can establish the Monsoon Time Scale and predict what is going to happen in the monsoonal climate in the coming years roughly. I call on the world scientists to design and establish the Monsoon Time Scales following the Basics of Monsoon Time Scales outlined below, based on the India Monsoon Time Scale which is successfully proved out in practice. North East monsoon is a key system in  global monsoon systems. I have conducted many scientific researches on this monsoon system  and as a part these researches, I proposed and designed the Basics of North East Monsoon Time Scale  which can help to study the past, present and future conditions of the North East monsoon.  In the current year 2022, the pre-path of Indian summer monsoon was traveling upwards and reached to the 29th June. Below this, the main-path of Indian summer monsoon also traveled upwards parallel to the pre-path of Indian summer monsoon with a difference of about 30 days and reached to the 29th July, As it moves further up, changes in the climate are likely increasing and there are more chances of heavy rains and floods in the coming years.

[Gangadhar. Establish the North East Monsoon Time Scale and break out the mysteries of the North East monsoon. J Am Sci 2026;22(6):12-96]. ISSN 1545-1003 (print); ISSN 2375-7264 (online). http://www.jofamericanscience.org. 03. doi:10.7537/marsjas220626.03

Keywords:   Ecological Forecasting Time Scales(1965-70); A New Model of Cosmology (1970-80); Basics of Geoscope (1980-87); Basics of Monsoon Time Scales (1987-91); Astro-Climatic Numerical Periodic Tables (1991-2000); Designs of Geoscope (2000-2015); Designs of Global Monsoon Time Scales (2015-still)

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