A Study on Gaps between Integers Having a Common Divisor with an Odd Semiprime | Chapter 6 | Mathematics and Computer Science: Research Updates Vol. 4

This paper elucidates the distribution law of integers that share a common divisor with an odd semiprime N = pq, where p and q are odd primes satisfying λp < q < (λ+1)p, and λ is a positive integer. It demonstrates that within the interval [1,N-1], the gaps between multiples of p or q exhibit symmetric behavior ranging from 0 to p - 1. Specifically, each gap from 0 to p - 2 appears exactly twice in a symmetric manner, while the gap p - 1 occurs precisely q - p - 1 times across p distinct subintervals. Among these p subintervals, q - λp - 1 subintervals each contain λ gaps of size p - 1, while the remaining subintervals each contain λ - 1 gaps of size p - 1. From a positional perspective, there are either λ or λ + 1 multiples of p between two adjacent multiples of q, with exactly λ multiples of p appearing both before the first multiple of q and after the last multiple of q. These findings can significantly facilitate the design of algorithms for identifying the divisors of unfactorized composite integers.

 

Author (s) Details

 

Xingbo Wang
Guangzhou College of Applied Science and Technology, Guangzhou City, 511370, PRC and Foshan University, Foshan City, 528000, PRC.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcsru/v4/4832

Effect of Hydrostatic Pressure on the Structural, Electronic and Magnetic Properties of Ga0.75Cr0.25P: First Principle Calculations | Chapter 6 | Current Research Progress in Physical Science Vol. 6

The doping of transition metal atoms in nonmagnetic semiconductor material results in the formation of Dilute Magnetic Semiconductors (DMS) that can be promising candidates for the spintronics industry. GaP belongs to the III-V semiconductor category and is a soft semiconductor in nature. In this paper, the investigation of the effect of hydrostatic pressure on the structural, electronic and magnetic properties of Ga_0.75Cr_0.25P ternary alloy in the Zinc-Blende (B3) phase at 0 GPa to 26 GPa pressure range has been done using the first principle calculations as implemented in Spanish Initiative for Electronic Simulations with Thousands of Atoms (SIESTA) code. The theoretical investigation of the electronic and magnetic properties of this compound represents that the compound is a half-metallic ferromagnet and shows 100% spin polarization at different values of pressure. It is found that the band gap increases with an increase in pressure as spin-polarized band structures experience changes with applied pressure. The calculated results show that the lattice constant and volume of the compound decrease along with an increase in induced local magnetic moments values on non-magnetic gallium and phosphorus atoms with applied pressure.  Due to the p-d hybridization of Cr-3d and P-3p states, there is an induction of local magnetic moments on the non-magnetic Ga and P atoms. The total magnetic moment of compounds remains the same, but the induced local magnetic moment value on non-magnetic Ga and P increases along with a decrease in Cr with applied pressure.

 

Author (s) Details

 

Kirandish Kaur
Guru Nanak College, Sri Muktsar Sahib (152026), India.

 

Suresh Sharma
DAV College, Abohar (152116), India.

 

Please see the book here:- https://doi.org/10.9734/bpi/crpps/v6/3105

Intensive Cultivation of Mango Using Ultra-High Density Planting (UHDP), and Drip and Fertigation Technologies for Higher Productivity | Chapter 7 | Research Advances and Challenges in Agricultural Sciences Vol. 1

 Chance of arable land for reaching mango cultivation has been a disadvantage over the years. Seeing the continual increase in human state and land use pressure in the country, there is restricted scope to expand the region. India has the largest extent under Mango crop; however the productivity is individual of lowest with the mango growing countries. The reasons for depressed yields are many: large number doddering orchards, traditional forms of cultivation, mainly rain-fed or with sporadic flow irrigation all the while fruit development, weak attention to the baldachin, nutrition, pest and afflictions, and lack of use of Good Land Practices (GAP), lack of awareness between farmers of up-to-date techniques like  calculating-irrigation and fertigation, Integrated  Blight Management (IPM), Joined Nutrition Management (INM), and up-to-date post-harvest management systems. The observations and the results of experiments carried out have proved that to get best benefits of UHDP in several mango cultivars, the strict devotion to the following important facets of practices are required. The Research and Development group of Jain Irrigation completed activity a number of field trials, accompanying high and extreme-high density estate techniques in mango and reliable to determine, irrigation and manure requirement utilizing drip technology and established the results of soil and leaf analysis for focus yields, and crop regulation by optimum awning management and use of Placobutrazol (PBZ) for early uniform and balanced flowering. They understood, IPM, Global-GAP and patterned, a package of practices for mango cultivars, under extreme density (4.5 m X 4.5 m) and ultra- extreme density mango (3 m X 2 m). The composite mango result technology thus grown over a period of 14 age in the R,D&D farm of JISL is now extended to many growers in the country.The mango yields raised two to three times, the maturation period for the  first harvest was reduced to  three to four  age, the quality of crops were good for export  and develop was regular even  in lacking-bearing  cultivars like Alphonso and Himampasand. JISL is the only organization in the country that has invested completely a large funds and backed its research and enlargement team in educating laborers in improved agro-methods and expose them to most recent technologies.

Author(s) Details:

P. Soman,
Research, Development and Demonstration Farms, Jain Irrigation Systems Ltd., Udumalpet, Tirupur District, Tamil Nadu-642 154, India.

A. U. Chaudhari,
Research, Development and Demonstration Farms, Jain Irrigation Systems Ltd., Udumalpet, Tirupur District, Tamil Nadu-642 154, India.

B. Krishna,
Research, Development and Demonstration Farms, Jain Irrigation Systems Ltd., Udumalpet, Tirupur District, Tamil Nadu-642 154, India.

V. R. Balasubramanyam,
Research, Development and Demonstration Farms, Jain Irrigation Systems Ltd., Udumalpet, Tirupur District, Tamil Nadu-642 154, India.

Please see the link here: https://stm.bookpi.org/RACAS-V1/article/view/12957