In this paper, a standard congruence of higher degree of composite modulus is considered for study and after a thorough study, it is then formulated for its incongruent solutions. The established formula is tested and verified true by solving suitable examples. Formulation is the merit of the paper. This formulation made the study of the congruence of higher degree easy, simple and interesting. Mental calculation of solutions become possible due to this formulation. In the literature of earlier mathematics, no formulation is found for the solutions of the said congruence. Prof B M Roy "Rp-106: Formulation of Solutions of a Class of Standard Congruence of Composite Modulus of Higher Degree" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-1 , December 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29764.pdf Paper URL: https://www.ijtsrd.com/mathemetics/other/29764/rp-106-formulation-of-solutions-of-a-class-of-standard-congruence-of-composite-modulus-of-higher-degree/prof-b-m-roy
RP 108 Formulation of Solutions of Standard Congruence of Higher Degree modul...ijtsrd
In this study, the solutions of a standard congruence of higher degree modulo a multiple of composite power integer is considered for formulation and is formulated. The formula developed is proved and verified true. Oral calculation of solutions are also possible. Formulation is the merit of the paper. Prof B M Roy ""RP-108: Formulation of Solutions of Standard Congruence of Higher Degree modulo a Multiple of Composite Power Integer"" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-2 , February 2020,
URL: https://www.ijtsrd.com/papers/ijtsrd30151.pdf
Paper Url : https://www.ijtsrd.com/mathemetics/other/30151/rp-108-formulation-of-solutions-of-standard-congruence-of-higher-degree-modulo-a-multiple-of-composite-power-integer/prof-b-m-roy
RP 47 Formulation of a Class of Standard Congruence of Higher Degree Modulo a...ijtsrd
In this paper, the author considered a problem ""Formulation of solutions of a class of standard congruence of higher degree modulo a power of an odd prime integer"". It is studied rigorously and the solutions of the congruence are formulated. Illustrating suitable examples, the formula established is tested and verified true. No earlier formulation is found in the literature of mathematics for such congruence. Author has tried his best to find a formula for the solutions of the problem under consideration and succeed. It is the merit of the paper. Prof B M Roy ""RP-47: Formulation of a Class of Standard Congruence of Higher Degree Modulo a Power of an Odd Prime Integer"" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-2 , February 2020,
URL: https://www.ijtsrd.com/papers/ijtsrd29994.pdf
Paper Url : https://www.ijtsrd.com/mathemetics/other/29994/rp-47-formulation-of-a-class-of-standard-congruence-of-higher-degree-modulo-a-power-of-an-odd-prime-integer/prof-b-m-roy
Rp-99: Formulation of Standard Cubic Congruence of Composite Modulus- A Multi...ijtsrd
In this paper, two special standard cubic congruence of composite modulus of higher degree are considered for study to establish a formulation of the solutions of the congruence. The formulation of the solutions is established. The author's rigorous labour works efficiently and succeed to formulate the solutions of the congruence under consideration. This paper presents the author's successful efforts. The discovered formula is tested and verified true by illustrating different suitable examples. No effective method is found in the literature of mathematics for its solutions. Formulation is the merit of the paper. Formulation is proved time saving, easy and simple. The study of standard cubic congruence of composite modulus of higher degree is now an interesting subject of mathematics. Prof B M Roy "Rp-99: Formulation of Standard Cubic Congruence of Composite Modulus- A Multiple of the Power of the Modulus" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-1 , December 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29391.pdfPaper URL: https://www.ijtsrd.com/mathemetics/other/29391/rp-99-formulation-of-standard-cubic-congruence-of-composite-modulus--a-multiple-of-the-power-of-the-modulus/prof-b-m-roy
RP 74 Solving Three Special Types of Standard Congruence of Prime Modulus of ...ijtsrd
In this paper, three special classes of congruence of prime modulus of higher degree are considered for formulation and authors efforts established the formulae for solutions. The congruence were not formulated by earlier mathematicians. Due to this formulation, it becomes an easy task to solve the congruence of higher degree of prime modulus reducing the congruence to their equivalent quadratic congruence of prime modulus. Formulations of the congruence is the merit of the paper. Prof. B M Roy ""RP-74: Solving Three Special Types of Standard Congruence of Prime Modulus of Higher Degree"" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-3 , April 2019, URL: https://www.ijtsrd.com/papers/ijtsrd23488.pdf
Paper URL: https://www.ijtsrd.com/mathemetics/other/23488/rp-74-solving-three-special-types-of-standard-congruence-of-prime-modulus-of-higher-degree/prof-b-m-roy
Rp 91 Solving Some Standard Cubic Congruence of Prime Modulusijtsrd
In this paper, finding solutions of some classes of standard cubic congruence of prime modulus are considered for study and then formulated. Formulation of the solutions is proved time saving, simple and quick. It made the finding solutions of cubic congruence of prime modulus easy. Formulation is the merit of the paper. . Here, solvability condition is obtained. This saves time in calculation. This is the merit of the paper. Prof B M Roy ""Rp-91: Solving Some Standard Cubic Congruence of Prime Modulus"" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-4 , June 2019, URL: https://www.ijtsrd.com/papers/ijtsrd25117.pdf
Paper URL: https://www.ijtsrd.com/mathemetics/other/25117/rp-91--solving-some-standard-cubic-congruence-of-prime-modulus/prof-b-m-roy
RP 105 Formulation of Standard Quadratic Congruence of Composite Modulus A Pr...ijtsrd
In this paper, a standard quadratic congruence of composite modulus a product of twin primes, is formulated. Actually a formula is discovered to find all the solutions of the congruence. It is found that the method is simple and takes less time as compared to the existed method. A comparative study is made by solving a problem using existed method and Author's formulation. Formulation is proved time saving. Solutions can be obtained orally. This is the merit of the paper. Prof B M Roy "RP-105: Formulation of Standard Quadratic Congruence of Composite Modulus- A Product of Twin Primes" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26492.pdfPaper URL: https://www.ijtsrd.com/mathemetics/other/26492/rp-105-formulation-of-standard-quadratic-congruence-of-composite-modulus--a-product-of-twin-primes/prof-b-m-roy
In solving real life assignment problem, we often face the state of uncertainty as well as hesitation due to varies uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. In this paper, computationally a simple method is proposed to find the optimal solution for an unbalanced assignment problem under intuitionistic fuzzy environment. In conventional assignment problem, cost is always certain. This paper develops an approach to solve the unbalanced assignment problem where the time/cost/profit is not in deterministic numbers but imprecise ones. In this assignment problem, the elements of the cost matrix are represented by the triangular intuitionistic fuzzy numbers. The existing Ranking procedure of Varghese and Kuriakose is used to transform the unbalanced intuitionistic fuzzy assignment problem into a crisp one so that the conventional method may be applied to solve the AP . Finally, the method is illustrated by a numerical example which is followed by graphical representation and discussion of the finding.
RP 108 Formulation of Solutions of Standard Congruence of Higher Degree modul...ijtsrd
In this study, the solutions of a standard congruence of higher degree modulo a multiple of composite power integer is considered for formulation and is formulated. The formula developed is proved and verified true. Oral calculation of solutions are also possible. Formulation is the merit of the paper. Prof B M Roy ""RP-108: Formulation of Solutions of Standard Congruence of Higher Degree modulo a Multiple of Composite Power Integer"" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-2 , February 2020,
URL: https://www.ijtsrd.com/papers/ijtsrd30151.pdf
Paper Url : https://www.ijtsrd.com/mathemetics/other/30151/rp-108-formulation-of-solutions-of-standard-congruence-of-higher-degree-modulo-a-multiple-of-composite-power-integer/prof-b-m-roy
RP 47 Formulation of a Class of Standard Congruence of Higher Degree Modulo a...ijtsrd
In this paper, the author considered a problem ""Formulation of solutions of a class of standard congruence of higher degree modulo a power of an odd prime integer"". It is studied rigorously and the solutions of the congruence are formulated. Illustrating suitable examples, the formula established is tested and verified true. No earlier formulation is found in the literature of mathematics for such congruence. Author has tried his best to find a formula for the solutions of the problem under consideration and succeed. It is the merit of the paper. Prof B M Roy ""RP-47: Formulation of a Class of Standard Congruence of Higher Degree Modulo a Power of an Odd Prime Integer"" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-2 , February 2020,
URL: https://www.ijtsrd.com/papers/ijtsrd29994.pdf
Paper Url : https://www.ijtsrd.com/mathemetics/other/29994/rp-47-formulation-of-a-class-of-standard-congruence-of-higher-degree-modulo-a-power-of-an-odd-prime-integer/prof-b-m-roy
Rp-99: Formulation of Standard Cubic Congruence of Composite Modulus- A Multi...ijtsrd
In this paper, two special standard cubic congruence of composite modulus of higher degree are considered for study to establish a formulation of the solutions of the congruence. The formulation of the solutions is established. The author's rigorous labour works efficiently and succeed to formulate the solutions of the congruence under consideration. This paper presents the author's successful efforts. The discovered formula is tested and verified true by illustrating different suitable examples. No effective method is found in the literature of mathematics for its solutions. Formulation is the merit of the paper. Formulation is proved time saving, easy and simple. The study of standard cubic congruence of composite modulus of higher degree is now an interesting subject of mathematics. Prof B M Roy "Rp-99: Formulation of Standard Cubic Congruence of Composite Modulus- A Multiple of the Power of the Modulus" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-1 , December 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29391.pdfPaper URL: https://www.ijtsrd.com/mathemetics/other/29391/rp-99-formulation-of-standard-cubic-congruence-of-composite-modulus--a-multiple-of-the-power-of-the-modulus/prof-b-m-roy
RP 74 Solving Three Special Types of Standard Congruence of Prime Modulus of ...ijtsrd
In this paper, three special classes of congruence of prime modulus of higher degree are considered for formulation and authors efforts established the formulae for solutions. The congruence were not formulated by earlier mathematicians. Due to this formulation, it becomes an easy task to solve the congruence of higher degree of prime modulus reducing the congruence to their equivalent quadratic congruence of prime modulus. Formulations of the congruence is the merit of the paper. Prof. B M Roy ""RP-74: Solving Three Special Types of Standard Congruence of Prime Modulus of Higher Degree"" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-3 , April 2019, URL: https://www.ijtsrd.com/papers/ijtsrd23488.pdf
Paper URL: https://www.ijtsrd.com/mathemetics/other/23488/rp-74-solving-three-special-types-of-standard-congruence-of-prime-modulus-of-higher-degree/prof-b-m-roy
Rp 91 Solving Some Standard Cubic Congruence of Prime Modulusijtsrd
In this paper, finding solutions of some classes of standard cubic congruence of prime modulus are considered for study and then formulated. Formulation of the solutions is proved time saving, simple and quick. It made the finding solutions of cubic congruence of prime modulus easy. Formulation is the merit of the paper. . Here, solvability condition is obtained. This saves time in calculation. This is the merit of the paper. Prof B M Roy ""Rp-91: Solving Some Standard Cubic Congruence of Prime Modulus"" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-4 , June 2019, URL: https://www.ijtsrd.com/papers/ijtsrd25117.pdf
Paper URL: https://www.ijtsrd.com/mathemetics/other/25117/rp-91--solving-some-standard-cubic-congruence-of-prime-modulus/prof-b-m-roy
RP 105 Formulation of Standard Quadratic Congruence of Composite Modulus A Pr...ijtsrd
In this paper, a standard quadratic congruence of composite modulus a product of twin primes, is formulated. Actually a formula is discovered to find all the solutions of the congruence. It is found that the method is simple and takes less time as compared to the existed method. A comparative study is made by solving a problem using existed method and Author's formulation. Formulation is proved time saving. Solutions can be obtained orally. This is the merit of the paper. Prof B M Roy "RP-105: Formulation of Standard Quadratic Congruence of Composite Modulus- A Product of Twin Primes" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26492.pdfPaper URL: https://www.ijtsrd.com/mathemetics/other/26492/rp-105-formulation-of-standard-quadratic-congruence-of-composite-modulus--a-product-of-twin-primes/prof-b-m-roy
In solving real life assignment problem, we often face the state of uncertainty as well as hesitation due to varies uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. In this paper, computationally a simple method is proposed to find the optimal solution for an unbalanced assignment problem under intuitionistic fuzzy environment. In conventional assignment problem, cost is always certain. This paper develops an approach to solve the unbalanced assignment problem where the time/cost/profit is not in deterministic numbers but imprecise ones. In this assignment problem, the elements of the cost matrix are represented by the triangular intuitionistic fuzzy numbers. The existing Ranking procedure of Varghese and Kuriakose is used to transform the unbalanced intuitionistic fuzzy assignment problem into a crisp one so that the conventional method may be applied to solve the AP . Finally, the method is illustrated by a numerical example which is followed by graphical representation and discussion of the finding.
Rp 72 Formulation of Solutions of a Standard Cubic Congruence of Composite Mo...ijtsrd
In this study, a standard cubic congruence of composite modulus a multiple of four and power of three is considered. After a thorough study, formulation of the solutions of the said congruence are established in four different cases. It is found that the standard cubic congruence under consideration in case I has exactly three solutions for an odd positive integer and in case II, has six solutions for an even positive integer. In case III, it has nine solutions and in case IV, the congruence has exactly eighteen solutions. Formulations are the merit of the study. Prof B M Roy "Rp-72: Formulation of Solutions of a Standard Cubic Congruence of Composite Modulus-a Multiple of Four and Power of Three" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-3 , April 2020, URL: https://www.ijtsrd.com/papers/ijtsrd30762.pdf Paper Url :https://www.ijtsrd.com/mathemetics/other/30762/rp72-formulation-of-solutions-of-a-standard-cubic-congruence-of-composite-modulusa-multiple-of-four-and-power-of-three/prof-b-m-roy
RP 129 Formulation of a Special Type of Standard Quadratic Congruence of Comp...ijtsrd
In this current study, a very special type of standard quadratic congruence of composite modulus a product of two powered odd primes is considered for finding solutions. It is studied and solved in different cases. The author's effort made an easy way to find the solutions of the congruence under consideration. Such types of congruence are not formulated earlier. First time the author's effort came in existence. This is the merit of the paper. Prof B M Roy "RP-129: Formulation of a Special Type of Standard Quadratic Congruence of Composite Modulus- a Product of Two Powered Odd Primes" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-4 , June 2020, URL: https://www.ijtsrd.com/papers/ijtsrd30964.pdf Paper Url :https://www.ijtsrd.com/mathemetics/applied-mathematics/30964/rp129-formulation-of-a-special-type-of-standard-quadratic-congruence-of-composite-modulus%E2%80%93-a-product-of-two-powered-odd-primes/prof-b-m-roy
RP 163 Solving a Special Standard Quadratic Congruence Modulo an Even Multipl...YogeshIJTSRD
The author, here in this paper, presented a formulation for solving a special standard quadratic congruence modulo an even multiple of an odd positive integer. The established formula is tested and verified true by solving various numerical examples. The formulation works well and proved time saving. Prof B M Roy "RP-163: Solving a Special Standard Quadratic Congruence Modulo an Even Multiple of an Odd Positive Integer" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-3 , April 2021, URL: https://www.ijtsrd.com/papers/ijtsrd41116.pdf Paper URL: https://www.ijtsrd.com/mathemetics/applied-mathematics/41116/rp163-solving-a-special-standard-quadratic-congruence-modulo-an-even-multiple-of-an-odd-positive-integer/prof-b-m-roy
RP 75 Formulation of two Special Classes of Standard Congruence of Prime Modu...ijtsrd
In this paper, two special classes of congruence of prime modulus of higher degree are considered for formulation. Authors sincere efforts established the corresponding formulae for solutions. The congruence were not formulated earlier. Due to this formulation, it becomes an easy task to solve the said congruence orally when p is comparatively small. Formulations of the congruence is the merit of the paper. Prof. B M Roy ""RP-75: Formulation of two Special Classes of Standard Congruence of Prime Modulus of Higher Degree"" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-3 , April 2019, URL: https://www.ijtsrd.com/papers/ijtsrd23417.pdf
Paper URL: https://www.ijtsrd.com/mathemetics/other/23417/rp-75-formulation-of-two-special-classes-of-standard-congruence-of-prime-modulus-of-higher-degree/prof-b-m-roy
RP 64 A Review of Finding Solutions of Standard Cubic Congruence of Prime Mod...ijtsrd
In this paper, the solutions of a standard cubic congruence of prime modulus is discussed. Also, the condition of solvability is established. The literature of mathematics is silent for finding the solutions of such congruence. Even no method to solve such types of congruence is discussed. Here, solvability condition is obtained. The solvability condition makes it easy to find the solutions. It saves the time in calculation. This is the merit of the paper. Prof B M Roy "RP-64: A Review of Finding Solutions of Standard Cubic Congruence of Prime Modulus" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-3 , April 2020, URL: https://www.ijtsrd.com/papers/ijtsrd30421.pdf Paper Url :https://www.ijtsrd.com/mathemetics/other/30421/rp64-a-review-of-finding-solutions-of-standard-cubic-congruence-of-prime-modulus/prof-b-m-roy
RP 170 Formulating Solutions of a Special Class of Standard Cubic Congruence ...ijtsrd
In this research paper, the author has formulated the solutions of a standard cubic congruence of composite modulus modulo p2 multiple of 3n, n being a positive integer. It is found that the said congruence has exactly 3p incongruent solutions p being an odd prime positive integer. It seems that the earlier mathematicians didn’t study such types of congruence. First time a formulation of solutions is established by the author. Formulation is the merit of the paper as formulation of solutions has provided a simple procedure of finding the required solutions with an ease. Prof B M Roy "RP-170: Formulating Solutions of a Special Class of Standard Cubic Congruence Modulo p2 Multiple of 3n" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-4 , June 2021, URL: https://www.ijtsrd.compapers/ijtsrd42540.pdf Paper URL: https://www.ijtsrd.commathemetics/applied-mathamatics/42540/rp170-formulating-solutions-of-a-special-class-of-standard-cubic-congruence-modulo-p2-multiple-of-3n/prof-b-m-roy
RP 144 Formulation of Solutions of a Very Special Class of Standard Quadratic...ijtsrd
In this paper, the author considered a very special type of standard quadratic congruence of composite modulus for its formulation of solutions. It is found that such a congruence has exactly 4p solutions, p being an odd prime present in the modulus of the congruence. These solutions are formulated by the author. First time a formula is derived and hence the solutions can be obtained orally. The literature of mathematics remains silent in case of formulation of such congruence. Formulation is the merit of the paper. Prof B M Roy "RP-144: Formulation of Solutions of a Very Special Class of Standard Quadratic Congruence of Composite Modulus modulo a Multiple of Powered Even Prime by a Powered Odd Prime" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-6 , October 2020, URL: https://www.ijtsrd.com/papers/ijtsrd35718.pdf Paper Url: https://www.ijtsrd.com/mathemetics/applied-mathamatics/35718/rp144-formulation-of-solutions-of-a-very-special-class-of-standard-quadratic-congruence-of-composite-modulus-modulo-a-multiple-of-powered-even-prime-by-a-powered-odd-prime/prof-b-m-roy
RP 166 Solving Some Special Standard Cubic Congruence of Composite Modulus mo...ijtsrd
Here in this paper, ten special type of standard cubic congruence of composite modulus are studied for their solutions. It is found that each of the cubic congruence under consideration has a single solution. The solution can be obtained orally as the solution is given in the problems. No extra effort is necessary to find the solution. Prof B M Roy "RP-166: Solving Some Special Standard Cubic Congruence of Composite Modulus modulo a Multiple of an Odd Prime" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-4 , June 2021, URL: https://www.ijtsrd.compapers/ijtsrd42321.pdf Paper URL: https://www.ijtsrd.commathemetics/applied-mathamatics/42321/rp166-solving-some-special-standard-cubic-congruence-of-composite-modulus-modulo-a-multiple-of-an-odd-prime/prof-b-m-roy
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
RP 165 Solving Some Special Classes of Standard Cubic Congruence of Composite...YogeshIJTSRD
In this paper, a special class of standard cubic congruence of composite modulus is studied and formulated the solutions. The discussion is presented here. This cubic congruence has three types of solutions. In first case, it has exactly 3 incongruent solutions in second case, it has nine incongruent solutions and in third case it has twenty seven incongruent solutions. First time a suitable formulation is available for a class of standard cubic congruence. So, formulation is the merit of the paper. Prof B M Roy "RP-165: Solving Some Special Classes of Standard Cubic Congruence of Composite Modulus" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-3 , April 2021, URL: https://www.ijtsrd.com/papers/ijtsrd39816.pdf Paper URL: https://www.ijtsrd.com/mathemetics/applied-mathematics/39816/rp165-solving-some-special-classes-of-standard-cubic-congruence-of-composite-modulus/prof-b-m-roy
Rp 72 Formulation of Solutions of a Standard Cubic Congruence of Composite Mo...ijtsrd
In this study, a standard cubic congruence of composite modulus a multiple of four and power of three is considered. After a thorough study, formulation of the solutions of the said congruence are established in four different cases. It is found that the standard cubic congruence under consideration in case I has exactly three solutions for an odd positive integer and in case II, has six solutions for an even positive integer. In case III, it has nine solutions and in case IV, the congruence has exactly eighteen solutions. Formulations are the merit of the study. Prof B M Roy "Rp-72: Formulation of Solutions of a Standard Cubic Congruence of Composite Modulus-a Multiple of Four and Power of Three" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-3 , April 2020, URL: https://www.ijtsrd.com/papers/ijtsrd30762.pdf Paper Url :https://www.ijtsrd.com/mathemetics/other/30762/rp72-formulation-of-solutions-of-a-standard-cubic-congruence-of-composite-modulusa-multiple-of-four-and-power-of-three/prof-b-m-roy
RP 129 Formulation of a Special Type of Standard Quadratic Congruence of Comp...ijtsrd
In this current study, a very special type of standard quadratic congruence of composite modulus a product of two powered odd primes is considered for finding solutions. It is studied and solved in different cases. The author's effort made an easy way to find the solutions of the congruence under consideration. Such types of congruence are not formulated earlier. First time the author's effort came in existence. This is the merit of the paper. Prof B M Roy "RP-129: Formulation of a Special Type of Standard Quadratic Congruence of Composite Modulus- a Product of Two Powered Odd Primes" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-4 , June 2020, URL: https://www.ijtsrd.com/papers/ijtsrd30964.pdf Paper Url :https://www.ijtsrd.com/mathemetics/applied-mathematics/30964/rp129-formulation-of-a-special-type-of-standard-quadratic-congruence-of-composite-modulus%E2%80%93-a-product-of-two-powered-odd-primes/prof-b-m-roy
RP 163 Solving a Special Standard Quadratic Congruence Modulo an Even Multipl...YogeshIJTSRD
The author, here in this paper, presented a formulation for solving a special standard quadratic congruence modulo an even multiple of an odd positive integer. The established formula is tested and verified true by solving various numerical examples. The formulation works well and proved time saving. Prof B M Roy "RP-163: Solving a Special Standard Quadratic Congruence Modulo an Even Multiple of an Odd Positive Integer" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-3 , April 2021, URL: https://www.ijtsrd.com/papers/ijtsrd41116.pdf Paper URL: https://www.ijtsrd.com/mathemetics/applied-mathematics/41116/rp163-solving-a-special-standard-quadratic-congruence-modulo-an-even-multiple-of-an-odd-positive-integer/prof-b-m-roy
RP 75 Formulation of two Special Classes of Standard Congruence of Prime Modu...ijtsrd
In this paper, two special classes of congruence of prime modulus of higher degree are considered for formulation. Authors sincere efforts established the corresponding formulae for solutions. The congruence were not formulated earlier. Due to this formulation, it becomes an easy task to solve the said congruence orally when p is comparatively small. Formulations of the congruence is the merit of the paper. Prof. B M Roy ""RP-75: Formulation of two Special Classes of Standard Congruence of Prime Modulus of Higher Degree"" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-3 , April 2019, URL: https://www.ijtsrd.com/papers/ijtsrd23417.pdf
Paper URL: https://www.ijtsrd.com/mathemetics/other/23417/rp-75-formulation-of-two-special-classes-of-standard-congruence-of-prime-modulus-of-higher-degree/prof-b-m-roy
RP 64 A Review of Finding Solutions of Standard Cubic Congruence of Prime Mod...ijtsrd
In this paper, the solutions of a standard cubic congruence of prime modulus is discussed. Also, the condition of solvability is established. The literature of mathematics is silent for finding the solutions of such congruence. Even no method to solve such types of congruence is discussed. Here, solvability condition is obtained. The solvability condition makes it easy to find the solutions. It saves the time in calculation. This is the merit of the paper. Prof B M Roy "RP-64: A Review of Finding Solutions of Standard Cubic Congruence of Prime Modulus" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-3 , April 2020, URL: https://www.ijtsrd.com/papers/ijtsrd30421.pdf Paper Url :https://www.ijtsrd.com/mathemetics/other/30421/rp64-a-review-of-finding-solutions-of-standard-cubic-congruence-of-prime-modulus/prof-b-m-roy
RP 170 Formulating Solutions of a Special Class of Standard Cubic Congruence ...ijtsrd
In this research paper, the author has formulated the solutions of a standard cubic congruence of composite modulus modulo p2 multiple of 3n, n being a positive integer. It is found that the said congruence has exactly 3p incongruent solutions p being an odd prime positive integer. It seems that the earlier mathematicians didn’t study such types of congruence. First time a formulation of solutions is established by the author. Formulation is the merit of the paper as formulation of solutions has provided a simple procedure of finding the required solutions with an ease. Prof B M Roy "RP-170: Formulating Solutions of a Special Class of Standard Cubic Congruence Modulo p2 Multiple of 3n" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-4 , June 2021, URL: https://www.ijtsrd.compapers/ijtsrd42540.pdf Paper URL: https://www.ijtsrd.commathemetics/applied-mathamatics/42540/rp170-formulating-solutions-of-a-special-class-of-standard-cubic-congruence-modulo-p2-multiple-of-3n/prof-b-m-roy
RP 144 Formulation of Solutions of a Very Special Class of Standard Quadratic...ijtsrd
In this paper, the author considered a very special type of standard quadratic congruence of composite modulus for its formulation of solutions. It is found that such a congruence has exactly 4p solutions, p being an odd prime present in the modulus of the congruence. These solutions are formulated by the author. First time a formula is derived and hence the solutions can be obtained orally. The literature of mathematics remains silent in case of formulation of such congruence. Formulation is the merit of the paper. Prof B M Roy "RP-144: Formulation of Solutions of a Very Special Class of Standard Quadratic Congruence of Composite Modulus modulo a Multiple of Powered Even Prime by a Powered Odd Prime" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-6 , October 2020, URL: https://www.ijtsrd.com/papers/ijtsrd35718.pdf Paper Url: https://www.ijtsrd.com/mathemetics/applied-mathamatics/35718/rp144-formulation-of-solutions-of-a-very-special-class-of-standard-quadratic-congruence-of-composite-modulus-modulo-a-multiple-of-powered-even-prime-by-a-powered-odd-prime/prof-b-m-roy
RP 166 Solving Some Special Standard Cubic Congruence of Composite Modulus mo...ijtsrd
Here in this paper, ten special type of standard cubic congruence of composite modulus are studied for their solutions. It is found that each of the cubic congruence under consideration has a single solution. The solution can be obtained orally as the solution is given in the problems. No extra effort is necessary to find the solution. Prof B M Roy "RP-166: Solving Some Special Standard Cubic Congruence of Composite Modulus modulo a Multiple of an Odd Prime" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-4 , June 2021, URL: https://www.ijtsrd.compapers/ijtsrd42321.pdf Paper URL: https://www.ijtsrd.commathemetics/applied-mathamatics/42321/rp166-solving-some-special-standard-cubic-congruence-of-composite-modulus-modulo-a-multiple-of-an-odd-prime/prof-b-m-roy
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
RP 165 Solving Some Special Classes of Standard Cubic Congruence of Composite...YogeshIJTSRD
In this paper, a special class of standard cubic congruence of composite modulus is studied and formulated the solutions. The discussion is presented here. This cubic congruence has three types of solutions. In first case, it has exactly 3 incongruent solutions in second case, it has nine incongruent solutions and in third case it has twenty seven incongruent solutions. First time a suitable formulation is available for a class of standard cubic congruence. So, formulation is the merit of the paper. Prof B M Roy "RP-165: Solving Some Special Classes of Standard Cubic Congruence of Composite Modulus" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-3 , April 2021, URL: https://www.ijtsrd.com/papers/ijtsrd39816.pdf Paper URL: https://www.ijtsrd.com/mathemetics/applied-mathematics/39816/rp165-solving-some-special-classes-of-standard-cubic-congruence-of-composite-modulus/prof-b-m-roy
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...mathsjournal
The main purpose of this research is to find out the best method through iterative methods for solving the
nonlinear equation. In this study, the four iterative methods are examined and emphasized to solve the
nonlinear equations. From this method explained, the rate of convergence is demonstrated among the 1st
degree based iterative methods. After that, the graphical development is established here with the help of
the four iterative methods and these results are tested with various functions. An example of the algebraic
equation is taken to exhibit the comparison of the approximate error among the methods. Moreover, two
examples of the algebraic and transcendental equation are applied to verify the best method, as well as the
level of errors, are shown graphically.
A Review Article on Fixed Point Theory and Its Applicationijtsrd
The theory of fixed point is one of the most important and powerful tools of the modern mathematics not only it is used on a daily bases in pure and applied mathematics but it is also solving a bridge between analysis and topology and provide a very fruitful are of interaction between the two. The theory of fixed points belongs to topology, a part of mathematics created at the end of the nineteenth century. The famous French mathematician H. Poincare 1854 1912 was the founder of the fixed point approach. He had deep insight into its future importance for problems of mathematical analysis and celestial mechanics and took an active part in its development. Dr. Brajraj Singh Chauhan "A Review Article on Fixed Point Theory & Its Application" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26431.pdfPaper URL: https://www.ijtsrd.com/mathemetics/applied-mathematics/26431/a-review-article-on-fixed-point-theory-and-its-application/dr-brajraj-singh-chauhan
International Journal of Engineering and Science Invention (IJESI)inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online
Similar to Rp-106: Formulation of Solutions of a Class of Standard Congruence of Composite Modulus of Higher Degree (20)
‘Six Sigma Technique’ A Journey Through its Implementationijtsrd
The manufacturing industries all over the world are facing tough challenges for growth, development and sustainability in today’s competitive environment. They have to achieve apex position by adapting with the global competitive environment by delivering goods and services at low cost, prime quality and better price to increase wealth and consumer satisfaction. Cost Management ensures profit, growth and sustainability of the business with implementation of Continuous Improvement Technique like Six Sigma. This leads to optimize Business performance. The method drives for customer satisfaction, low variation, reduction in waste and cycle time resulting into a competitive advantage over other industries which did not implement it. The main objective of this paper ‘Six Sigma Technique A Journey Through Its Implementation’ is to conceptualize the effectiveness of Six Sigma Technique through the journey of its implementation. Aditi Sunilkumar Ghosalkar "‘Six Sigma Technique’: A Journey Through its Implementation" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64546.pdf Paper Url: https://www.ijtsrd.com/other-scientific-research-area/other/64546/‘six-sigma-technique’-a-journey-through-its-implementation/aditi-sunilkumar-ghosalkar
Edge Computing in Space Enhancing Data Processing and Communication for Space...ijtsrd
Edge computing, a paradigm that involves processing data closer to its source, has gained significant attention for its potential to revolutionize data processing and communication in space missions. With the increasing complexity and data volume generated by modern space missions, traditional centralized computing approaches face challenges related to latency, bandwidth, and security. Edge computing in space, involving on board processing and analysis of data, offers promising solutions to these challenges. This paper explores the concept of edge computing in space, its benefits, applications, and future prospects in enhancing space missions. Manish Verma "Edge Computing in Space: Enhancing Data Processing and Communication for Space Missions" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64541.pdf Paper Url: https://www.ijtsrd.com/computer-science/artificial-intelligence/64541/edge-computing-in-space-enhancing-data-processing-and-communication-for-space-missions/manish-verma
Dynamics of Communal Politics in 21st Century India Challenges and Prospectsijtsrd
Communal politics in India has evolved through centuries, weaving a complex tapestry shaped by historical legacies, colonial influences, and contemporary socio political transformations. This research comprehensively examines the dynamics of communal politics in 21st century India, emphasizing its historical roots, socio political dynamics, economic implications, challenges, and prospects for mitigation. The historical perspective unravels the intricate interplay of religious identities and power dynamics from ancient civilizations to the impact of colonial rule, providing insights into the evolution of communalism. The socio political dynamics section delves into the contemporary manifestations, exploring the roles of identity politics, socio economic disparities, and globalization. The economic implications section highlights how communal politics intersects with economic issues, perpetuating disparities and influencing resource allocation. Challenges posed by communal politics are scrutinized, revealing multifaceted issues ranging from social fragmentation to threats against democratic values. The prospects for mitigation present a multifaceted approach, incorporating policy interventions, community engagement, and educational initiatives. The paper conducts a comparative analysis with international examples, identifying common patterns such as identity politics and economic disparities. It also examines unique challenges, emphasizing Indias diverse religious landscape, historical legacy, and secular framework. Lessons for effective strategies are drawn from international experiences, offering insights into inclusive policies, interfaith dialogue, media regulation, and global cooperation. By scrutinizing historical epochs, contemporary dynamics, economic implications, and international comparisons, this research provides a comprehensive understanding of communal politics in India. The proposed strategies for mitigation underscore the importance of a holistic approach to foster social harmony, inclusivity, and democratic values. Rose Hossain "Dynamics of Communal Politics in 21st Century India: Challenges and Prospects" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64528.pdf Paper Url: https://www.ijtsrd.com/humanities-and-the-arts/history/64528/dynamics-of-communal-politics-in-21st-century-india-challenges-and-prospects/rose-hossain
Assess Perspective and Knowledge of Healthcare Providers Towards Elehealth in...ijtsrd
Background and Objective Telehealth has become a well known tool for the delivery of health care in Saudi Arabia, and the perspective and knowledge of healthcare providers are influential in the implementation, adoption and advancement of the method. This systematic review was conducted to examine the current literature base regarding telehealth and the related healthcare professional perspective and knowledge in the Kingdom of Saudi Arabia. Materials and Methods This systematic review was conducted by searching 7 databases including, MEDLINE, CINHAL, Web of Science, Scopus, PubMed, PsycINFO, and ProQuest Central. Studies on healthcare practitioners telehealth knowledge and perspectives published in English in Saudi Arabia from 2000 to 2023 were included. Boland directed this comprehensive review. The researchers examined each connected study using the AXIS tool, which evaluates cross sectional systematic reviews. Narrative synthesis was used to summarise and convey the data. Results Out of 1840 search results, 10 studies were included. Positive outlook and limited knowledge among providers were seen across trials. Healthcare professionals like telehealth for its ability to improve quality, access, and delivery, save time and money, and be successful. Age, gender, occupation, and work experience also affect health workers knowledge. In Saudi Arabia, healthcare professionals face inadequate expert assistance, patient privacy, internet connection concerns, lack of training courses, lack of telehealth understanding, and high costs while performing telemedicine. Conclusions Healthcare practitioners telehealth perceptions and knowledge were examined in this systematic study. Its collection of concerned experts different personal attitudes and expertise would help enhance telehealths implementation in Saudi Arabia, develop its healthcare delivery alternative, and eliminate frequent problems. Badriah Mousa I Mulayhi | Dr. Jomin George | Judy Jenkins "Assess Perspective and Knowledge of Healthcare Providers Towards Elehealth in Saudi Arabia: A Systematic Review" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64535.pdf Paper Url: https://www.ijtsrd.com/medicine/other/64535/assess-perspective-and-knowledge-of-healthcare-providers-towards-elehealth-in-saudi-arabia-a-systematic-review/badriah-mousa-i-mulayhi
The Impact of Digital Media on the Decentralization of Power and the Erosion ...ijtsrd
The impact of digital media on the distribution of power and the weakening of traditional gatekeepers has gained considerable attention in recent years. The adoption of digital technologies and the internet has resulted in declining influence and power for traditional gatekeepers such as publishing houses and news organizations. Simultaneously, digital media has facilitated the emergence of new voices and players in the media industry. Digital medias impact on power decentralization and gatekeeper erosion is visible in several ways. One significant aspect is the democratization of information, which enables anyone with an internet connection to publish and share content globally, leading to citizen journalism and bypassing traditional gatekeepers. Another aspect is the disruption of conventional media industry business models, as traditional organizations struggle to adjust to the decrease in advertising revenue and the rise of digital platforms. Alternative business models, such as subscription models and crowdfunding, have become more prevalent, leading to the emergence of new players. Overall, the impact of digital media on the distribution of power and the weakening of traditional gatekeepers has brought about significant changes in the media landscape and the way information is shared. Further research is required to fully comprehend the implications of these changes and their impact on society. Dr. Kusum Lata "The Impact of Digital Media on the Decentralization of Power and the Erosion of Traditional Gatekeepers" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64544.pdf Paper Url: https://www.ijtsrd.com/humanities-and-the-arts/political-science/64544/the-impact-of-digital-media-on-the-decentralization-of-power-and-the-erosion-of-traditional-gatekeepers/dr-kusum-lata
Online Voices, Offline Impact Ambedkars Ideals and Socio Political Inclusion ...ijtsrd
This research investigates the nexus between online discussions on Dr. B.R. Ambedkars ideals and their impact on social inclusion among college students in Gurugram, Haryana. Surveying 240 students from 12 government colleges, findings indicate that 65 actively engage in online discussions, with 80 demonstrating moderate to high awareness of Ambedkars ideals. Statistically significant correlations reveal that higher online engagement correlates with increased awareness p 0.05 and perceived social inclusion. Variations across colleges and a notable effect of college type on perceived social inclusion highlight the influence of contextual factors. Furthermore, the intersectional analysis underscores nuanced differences based on gender, caste, and socio economic status. Dr. Kusum Lata "Online Voices, Offline Impact: Ambedkar's Ideals and Socio-Political Inclusion - A Study of Gurugram District" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64543.pdf Paper Url: https://www.ijtsrd.com/humanities-and-the-arts/political-science/64543/online-voices-offline-impact-ambedkars-ideals-and-sociopolitical-inclusion--a-study-of-gurugram-district/dr-kusum-lata
Problems and Challenges of Agro Entreprenurship A Studyijtsrd
Noting calls for contextualizing Agro entrepreneurs problems and challenges of the agro entrepreneurs and for greater attention to the Role of entrepreneurs in agro entrepreneurship research, we conduct a systematic literature review of extent research in agriculture entrepreneurship to overcome the study objectives of complications of agro entrepreneurs through various factors, Development of agriculture products is a key factor for the overall economic growth of agro entrepreneurs Agro Entrepreneurs produces firsthand large scale employment, utilizes the labor and natural resources, This research outlines the problems of Weather and Soil Erosions, Market price fluctuation, stimulates labor cost problems, reduces concentration of Price volatility, Dependency on Intermediaries, induces Limited Bargaining Power, and Storage and Transportation Costs. This paper mainly devoted to highlight Problems and challenges faced for the sustainable of Agro Entrepreneurs in India. Vinay Prasad B "Problems and Challenges of Agro Entreprenurship - A Study" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64540.pdf Paper Url: https://www.ijtsrd.com/other-scientific-research-area/other/64540/problems-and-challenges-of-agro-entreprenurship--a-study/vinay-prasad-b
Comparative Analysis of Total Corporate Disclosure of Selected IT Companies o...ijtsrd
Disclosure is a process through which a business enterprise communicates with external parties. A corporate disclosure is communication of financial and non financial information of the activities of a business enterprise to the interested entities. Corporate disclosure is done through publishing annual reports. So corporate disclosure through annual reports plays a vital role in the life of all the companies and provides valuable information to investors. The basic objectives of corporate disclosure is to give a true and fair view of companies to the parties related either directly or indirectly like owner, government, creditors, shareholders etc. in the companies act, provisions have been made about mandatory and voluntary disclosure. The IT sector in India is rapidly growing, the trend to invest in the IT sector is rising and employment opportunities in IT sectors are also increasing. Therefore the IT sector is expected to have fair, full and adequate disclosure of all information. Unfair and incomplete disclosure may adversely affect the entire economy. A research study on disclosure practices of IT companies could play an important role in this regard. Hence, the present research study has been done to study and review comparative analysis of total corporate disclosure of selected IT companies of India and to put forward overall findings and suggestions with a view to increase disclosure score of these companies. The researcher hopes that the present research study will be helpful to all selected Companies for improving level of corporate disclosure through annual reports as well as the government, creditors, investors, all business organizations and upcoming researcher for comparative analyses of level of corporate disclosure with special reference to selected IT companies. Dr. Vaibhavi D. Thaker "Comparative Analysis of Total Corporate Disclosure of Selected IT Companies of India" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64539.pdf Paper Url: https://www.ijtsrd.com/other-scientific-research-area/other/64539/comparative-analysis-of-total-corporate-disclosure-of-selected-it-companies-of-india/dr-vaibhavi-d-thaker
The Impact of Educational Background and Professional Training on Human Right...ijtsrd
This study investigated the impact of educational background and professional training on human rights awareness among secondary school teachers in the Marathwada region of Maharashtra, India. The key findings reveal that higher levels of education, particularly a master’s degree, and fields of study related to education, humanities, or social sciences are associated with greater human rights awareness among teachers. Additionally, both pre service teacher training and in service professional development programs focused on human rights education significantly enhance teacher’s knowledge, skills, and competencies in promoting human rights principles in their classrooms. Baig Ameer Bee Mirza Abdul Aziz | Dr. Syed Azaz Ali Amjad Ali "The Impact of Educational Background and Professional Training on Human Rights Awareness among Secondary School Teachers" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64529.pdf Paper Url: https://www.ijtsrd.com/humanities-and-the-arts/education/64529/the-impact-of-educational-background-and-professional-training-on-human-rights-awareness-among-secondary-school-teachers/baig-ameer-bee-mirza-abdul-aziz
A Study on the Effective Teaching Learning Process in English Curriculum at t...ijtsrd
“One Language sets you in a corridor for life. Two languages open every door along the way” Frank Smith English as a foreign language or as a second language has been ruling in India since the period of Lord Macaulay. But the question is how much we teach or learn English properly in our culture. Is there any scope to use English as a language rather than a subject How much we learn or teach English without any interference of mother language specially in the classroom teaching learning scenario in West Bengal By considering all these issues the researcher has attempted in this article to focus on the effective teaching learning process comparing to other traditional strategies in the field of English curriculum at the secondary level to investigate whether they fulfill the present teaching learning requirements or not by examining the validity of the present curriculum of English. The purpose of this study is to focus on the effectiveness of the systematic, scientific, sequential and logical transaction of the course between the teachers and the learners in the perspective of the 5Es programme that is engage, explore, explain, extend and evaluate. Sanchali Mondal | Santinath Sarkar "A Study on the Effective Teaching Learning Process in English Curriculum at the Secondary Level of West Bengal" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd62412.pdf Paper Url: https://www.ijtsrd.com/humanities-and-the-arts/education/62412/a-study-on-the-effective-teaching-learning-process-in-english-curriculum-at-the-secondary-level-of-west-bengal/sanchali-mondal
The Role of Mentoring and Its Influence on the Effectiveness of the Teaching ...ijtsrd
This paper reports on a study which was conducted to investigate the role of mentoring and its influence on the effectiveness of the teaching of Physics in secondary schools in the South West Region of Cameroon. The study adopted the convergent parallel mixed methods design, focusing on respondents in secondary schools in the South West Region of Cameroon. Both quantitative and qualitative data were collected, analysed separately, and the results were compared to see if the findings confirm or disconfirm each other. The quantitative analysis found that majority of the respondents 72 of Physics teachers affirmed that they had more experienced colleagues as mentors to help build their confidence, improve their teaching, and help them improve their effectiveness and efficiency in guiding learners’ achievements. Only 28 of the respondents disagreed with these statements. With majority respondents 72 agreeing with the statements, it implies that in most secondary schools, experienced Physics teachers act as mentors to build teachers’ confidence in teaching and improving students’ learning. The interview qualitative data analysis summarized how secondary school Principals use meetings with mentors and mentees to promote mentorship in the school milieu. This has helped strengthen teachers’ classroom practices in secondary schools in the South West Region of Cameroon. With the results confirming each other, the study recommends that mentoring should focus on helping teachers employ social interactions and instructional practices feedback and clarity in teaching that have direct measurable impact on students’ learning achievements. Andrew Ngeim Sumba | Frederick Ebot Ashu | Peter Agborbechem Tambi "The Role of Mentoring and Its Influence on the Effectiveness of the Teaching of Physics in Secondary Schools in the South West Region of Cameroon" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64524.pdf Paper Url: https://www.ijtsrd.com/management/management-development/64524/the-role-of-mentoring-and-its-influence-on-the-effectiveness-of-the-teaching-of-physics-in-secondary-schools-in-the-south-west-region-of-cameroon/andrew-ngeim-sumba
Design Simulation and Hardware Construction of an Arduino Microcontroller Bas...ijtsrd
This study primarily focuses on the design of a high side buck converter using an Arduino microcontroller. The converter is specifically intended for use in DC DC applications, particularly in standalone solar PV systems where the PV output voltage exceeds the load or battery voltage. To evaluate the performance of the converter, simulation experiments are conducted using Proteus Software. These simulations provide insights into the input and output voltages, currents, powers, and efficiency under different state of charge SoC conditions of a 12V,70Ah rechargeable lead acid battery. Additionally, the hardware design of the converter is implemented, and practical data is collected through operation, monitoring, and recording. By comparing the simulation results with the practical results, the efficiency and performance of the designed converter are assessed. The findings indicate that while the buck converter is suitable for practical use in standalone PV systems, its efficiency is compromised due to a lower output current. Chan Myae Aung | Dr. Ei Mon "Design Simulation and Hardware Construction of an Arduino-Microcontroller Based DC-DC High-Side Buck Converter for Standalone PV System" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64518.pdf Paper Url: https://www.ijtsrd.com/engineering/mechanical-engineering/64518/design-simulation-and-hardware-construction-of-an-arduinomicrocontroller-based-dcdc-highside-buck-converter-for-standalone-pv-system/chan-myae-aung
Sustainable Energy by Paul A. Adekunte | Matthew N. O. Sadiku | Janet O. Sadikuijtsrd
Energy becomes sustainable if it meets the needs of the present without compromising the ability of future generations to meet their own needs. Some of the definitions of sustainable energy include the considerations of environmental aspects such as greenhouse gas emissions, social, and economic aspects such as energy poverty. Generally far more sustainable than fossil fuel are renewable energy sources such as wind, hydroelectric power, solar, and geothermal energy sources. Worthy of note is that some renewable energy projects, like the clearing of forests to produce biofuels, can cause severe environmental damage. The sustainability of nuclear power which is a low carbon source is highly debated because of concerns about radioactive waste, nuclear proliferation, and accidents. The switching from coal to natural gas has environmental benefits, including a lower climate impact, but could lead to delay in switching to more sustainable options. “Carbon capture and storage” can be built into power plants to remove the carbon dioxide CO2 emissions, but this technology is expensive and has rarely been implemented. Leading non renewable energy sources around the world is fossil fuels, coal, petroleum, and natural gas. Nuclear energy is usually considered another non renewable energy source, although nuclear energy itself is a renewable energy source, but the material used in nuclear power plants is not. The paper addresses the issue of sustainable energy, its attendant benefits to the future generation, and humanity in general. Paul A. Adekunte | Matthew N. O. Sadiku | Janet O. Sadiku "Sustainable Energy" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64534.pdf Paper Url: https://www.ijtsrd.com/engineering/electrical-engineering/64534/sustainable-energy/paul-a-adekunte
Concepts for Sudan Survey Act Implementations Executive Regulations and Stand...ijtsrd
This paper aims to outline the executive regulations, survey standards, and specifications required for the implementation of the Sudan Survey Act, and for regulating and organizing all surveying work activities in Sudan. The act has been discussed for more than 5 years. The Land Survey Act was initiated by the Sudan Survey Authority and all official legislations were headed by the Sudan Ministry of Justice till it was issued in 2022. The paper presents conceptual guidelines to be used for the Survey Act implementation and to regulate the survey work practice, standardizing the field surveys, processing, quality control, procedures, and the processes related to survey work carried out by the stakeholders and relevant authorities in Sudan. The conceptual guidelines are meant to improve the quality and harmonization of geospatial data and to aid decision making processes as well as geospatial information systems. The established comprehensive executive regulations will govern and regulate the implementation of the Sudan Survey Geomatics Act in all surveying and mapping practices undertaken by the Sudan Survey Authority SSA and state local survey departments for public or private sector organizations. The targeted standards and specifications include the reference frame, projection, coordinate systems, and the guidelines and specifications that must be followed in the field of survey work, processes, and mapping products. In the last few decades, there has been a growing awareness of the importance of geomatics activities and measurements on the Earths surface in space and time, together with observing and mapping the changes. In such cases, data must be captured promptly, standardized, and obtained with more accuracy and specified in much detail. The paper will also highlight the current situation in Sudan, the degree to which survey standards are used, the problems encountered, and the errors that arise from not using the standards and survey specifications. Kamal A. A. Sami "Concepts for Sudan Survey Act Implementations - Executive Regulations and Standards" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd63484.pdf Paper Url: https://www.ijtsrd.com/engineering/civil-engineering/63484/concepts-for-sudan-survey-act-implementations--executive-regulations-and-standards/kamal-a-a-sami
Towards the Implementation of the Sudan Interpolated Geoid Model Khartoum Sta...ijtsrd
The discussions between ellipsoid and geoid have invoked many researchers during the recent decades, especially during the GNSS technology era, which had witnessed a great deal of development but still geoid undulation requires more investigations. To figure out a solution for Sudans local geoid, this research has tried to intake the possibility of determining the geoid model by following two approaches, gravimetric and geometrical geoid model determination, by making use of GNSS leveling benchmarks at Khartoum state. The Benchmarks are well distributed in the study area, in which, the horizontal coordinates and the height above the ellipsoid have been observed by GNSS while orthometric heights were carried out using precise leveling. The Global Geopotential Model GGM represented in EGM2008 has been exploited to figure out the geoid undulation at the benchmarks in the study area. This is followed by a fitting process, that has been done to suit the geoid undulation data which has been computed using GNSS leveling data and geoid undulation inspired by the EGM2008. Two geoid surfaces were created after the fitting process to ensure that they are identical and both of them could be counted for getting the same geoid undulation with an acceptable accuracy. In this respect, statistical operation played an important role in ensuring the consistency and integrity of the model by applying cross validation techniques splitting the data into training and testing datasets for building the geoid model and testing its eligibility. The geometrical solution for geoid undulation computation has been utilized by applying straightforward equations that facilitate the calculation of the geoid undulation directly through applying statistical techniques for the GNSS leveling data of the study area to get the common equation parameters values that could be utilized to calculate geoid undulation of any position in the study area within the claimed accuracy. Both systems were checked and proved eligible to be used within the study area with acceptable accuracy which may contribute to solving the geoid undulation problem in the Khartoum area, and be further generalized to determine the geoid model over the entire country, and this could be considered in the future, for regional and continental geoid model. Ahmed M. A. Mohammed. | Kamal A. A. Sami "Towards the Implementation of the Sudan Interpolated Geoid Model (Khartoum State Case Study)" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd63483.pdf Paper Url: https://www.ijtsrd.com/engineering/civil-engineering/63483/towards-the-implementation-of-the-sudan-interpolated-geoid-model-khartoum-state-case-study/ahmed-m-a-mohammed
Activating Geospatial Information for Sudans Sustainable Investment Mapijtsrd
Sudan is witnessing an acceleration in the processes of development and transformation in the performance of government institutions to raise the productivity and investment efficiency of the government sector. The development plans and investment opportunities have focused on achieving national goals in various sectors. This paper aims to illuminate the path to the future and provide geospatial data and information to develop the investment climate and environment for all sized businesses, and to bridge the development gap between the Sudan states. The Sudan Survey Authority SSA is the main advisor to the Sudan Government in conducting surveying, mappings, designing, and developing systems related to geospatial data and information. In recent years, SSA made a strategic partnership with the Ministry of Investment to activate Geospatial Information for Sudans Sustainable Investment and in particular, for the preparation and implementation of the Sudan investment map, based on the directives and objectives of the Ministry of Investment MI in Sudan. This paper comes within the framework of activating the efforts of the Ministry of Investment to develop technical investment services by applying techniques adopted by the Ministry and its strategic partners for advancing investment processes in the country. Kamal A. A. Sami "Activating Geospatial Information for Sudan's Sustainable Investment Map" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd63482.pdf Paper Url: https://www.ijtsrd.com/engineering/information-technology/63482/activating-geospatial-information-for-sudans-sustainable-investment-map/kamal-a-a-sami
Educational Unity Embracing Diversity for a Stronger Societyijtsrd
In a rapidly changing global landscape, the importance of education as a unifying force cannot be overstated. This paper explores the crucial role of educational unity in fostering a stronger and more inclusive society through the embrace of diversity. By examining the benefits of diverse learning environments, the paper aims to highlight the positive impact on societal strength. The discussion encompasses various dimensions, from curriculum design to classroom dynamics, and emphasizes the need for educational institutions to become catalysts for unity in diversity. It highlights the need for a paradigm shift in educational policies, curricula, and pedagogical approaches to ensure that they are reflective of the diverse fabric of society. This paper also addresses the challenges associated with implementing inclusive educational practices and offers practical strategies for overcoming barriers. It advocates for collaborative efforts between educational institutions, policymakers, and communities to create a supportive ecosystem that promotes diversity and unity. Mr. Amit Adhikari | Madhumita Teli | Gopal Adhikari "Educational Unity: Embracing Diversity for a Stronger Society" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64525.pdf Paper Url: https://www.ijtsrd.com/humanities-and-the-arts/education/64525/educational-unity-embracing-diversity-for-a-stronger-society/mr-amit-adhikari
Integration of Indian Indigenous Knowledge System in Management Prospects and...ijtsrd
The diversity of indigenous knowledge systems in India is vast and can vary significantly between different communities and regions. Preserving and respecting these knowledge systems is crucial for maintaining cultural heritage, promoting sustainable practices, and fostering cross cultural understanding. In this paper, an overview of the prospects and challenges associated with incorporating Indian indigenous knowledge into management is explored. It is found that IIKS helps in management in many areas like sustainable development, tourism, food security, natural resource management, cultural preservation and innovation, etc. However, IIKS integration with management faces some challenges in the form of a lack of documentation, cultural sensitivity, language barriers legal framework, etc. Savita Lathwal "Integration of Indian Indigenous Knowledge System in Management: Prospects and Challenges" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd63500.pdf Paper Url: https://www.ijtsrd.com/management/accounting-and-finance/63500/integration-of-indian-indigenous-knowledge-system-in-management-prospects-and-challenges/savita-lathwal
DeepMask Transforming Face Mask Identification for Better Pandemic Control in...ijtsrd
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Streamlining Data Collection eCRF Design and Machine Learningijtsrd
Efficient and accurate data collection is paramount in clinical trials, and the design of Electronic Case Report Forms eCRFs plays a pivotal role in streamlining this process. This paper explores the integration of machine learning techniques in the design and implementation of eCRFs to enhance data collection efficiency. We delve into the synergies between eCRF design principles and machine learning algorithms, aiming to optimize data quality, reduce errors, and expedite the overall data collection process. The application of machine learning in eCRF design brings forth innovative approaches to data validation, anomaly detection, and real time adaptability. This paper discusses the benefits, challenges, and future prospects of leveraging machine learning in eCRF design for streamlined and advanced data collection in clinical trials. Dhanalakshmi D | Vijaya Lakshmi Kannareddy "Streamlining Data Collection: eCRF Design and Machine Learning" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd63515.pdf Paper Url: https://www.ijtsrd.com/biological-science/biotechnology/63515/streamlining-data-collection-ecrf-design-and-machine-learning/dhanalakshmi-d
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2. International Journal of Trend in Scientific Research and Development (IJTSRD) @ www.ijtsrd.com eISSN: 2456-6470
@ IJTSRD | Unique Paper ID – IJTSRD29764 | Volume – 4 | Issue – 1 | November-December 2019 Page 968
ݔ ≡ ܽିାଵ
. ܽିଵ
± ܽ ሺ݉ܽ ݀ሻ
≡ ܽ
± ܽ ሺ݉ ݉݀ሻܽ
ሻ
≡ 0 ± ܽ ሺ݉ܽ ݀
ሻ
≡ ±ܽ ሺ݉ܽ ݀
ሻ ,
which are the same solutions as for k=0. Similarly, it can
also be seen that for next higher values of k, the
corresponding solutions repeats as for k=1,
2,……………….,ሺܽିଵ
− 1ሻ.
Therefore, the required solutions are given by
ݔ ≡ ܽିାଵ
݇ ± ܽ ሺ݉ܽ ݀ሻ; k 0, 1, 2, … … … , ሺܽିଵ
− 1ሻ.
It is also seen that for a single value of k, the congruence
has two solutions and here k has ܽିଵ
values. Thus, total
number of solutions are definitely 2ܽିଵ
for even n.
Case-II: Let n be an odd positive integer and consider the
congruence under consideration: ݔ
≡ ܽ
ሺ݉ܽ ݀ሻ; ݉ >
݊.
Also consider that ݔ ≡ ܽିାଵ
݇ ± ܽ ሺ݉ܽ ݀ሻ
Then, ݔ
≡ ሺܽିାଵ
݇ ± ܽሻ
(mod ܽ
ሻ
≡ ±ܽ
+ ܽሺ… … ሻ ሺ݉ܽ ݀
ሻ
≡ ±ܽ
ሺ݉ܽ ݀
ሻ
Thus, ݔ ≡ ܽିାଵ
݇ ± ܽ ሺ݉ܽ ݀ሻ cannot be the solutions.
But if ݔ ≡ ܽିାଵ
݇ + ܽ ሺ݉ܽ ݀ሻ,
then , ݔ
≡ ܽ
ሺ݉ܽ ݀ሻ.
Thus, it can be said that ݔ ≡ ܽିାଵ
݇ + ܽ ሺ݉ܽ ݀ሻ
is a solution of the congruence.
But, if one has the value ݇ = ܽିଵ
,
then ݔ ≡ ܽିାଵ
݇ + ܽ ሺ݉ܽ ݀ሻ reduces to
ݔ ≡ ܽିାଵ
. ܽିଵ
+ ܽ ሺ݉ܽ ݀ሻ
≡ ܽ
+ ܽ ሺ݉ܽ ݀
ሻ
≡ 0 + ܽ ሺ݉ܽ ݀
ሻ
≡ ܽ ሺ݉ܽ ݀
ሻ ,
which is the same solution as for k=0. Similarly, it can also
be seen that for next higher values of k, the corresponding
solutions repeats as for k=1, 2,…….,ሺܽିଵ
− 1ሻ.
Therefore, the required solutions are given by
ݔ ≡ ܽିାଵ
݇ + ܽ ሺ݉ܽ ݀ሻ; k = 1, 2, … … . , ሺܽିଵ
− 1ሻ.
It is also seen that for a single value of k, the congruence
has one solution and here k has ܽିଵ
values. Thus, total
number of solutions are definitely ܽିଵ
for odd n.
If ݉ ≤ ݊, the solutions of the congruence are given by
ݔ
≡ ܽ
ሺ݉ܽ ݀ሻ ݓℎ݅ܿℎ ݅ݐ ݐ݈݊݁ܽݒ݅ݑݍ݁ ݏ
ݔ
≡ 0 ሺ݉ܽ ݀ሻ
and the solutions are given by:
ݔ ≡ ܽ ݐሺ݉ܽ ݀ሻ, .ݎ݁݃݁ݐ݊݅ ݊ܽ ܾ݃݊݅݁ ݐ
ILLUSTRATIONS
Consider the congruence ݔ
≡ 729 ሺ݉7812 ݀ሻ.
It can be written as ݔ
≡ 3
ሺ݉3 ݀ሻݐ݅ݓℎ ܽ = 3.
It is of the type
ݔ
≡ ܽ
ሺ݉ܽ ݀ሻ; ݉ > ݊ ݐ݅ݓℎ ݁.݊ ݎ݁݃݁ݐ݊݅ ݁ݒ݅ݐ݅ݏ ݊݁ݒ
It has 2ܽିଵ
= 2. 3ିଵ
= 2. 3ହ
= 2.243 = 486 ݏ݊݅ݐݑ݈ݏ as
n is even positive integer and the solutions are given by
ݔ ≡ ܽିାଵ
݇ ± ܽ ሺ݉ܽ ݀ሻ; ݇ = 0, 1, 2, … . . ሺܽହ
− 1ሻ.
≡ 3ିାଵ
݇ ± 3 ሺ݉3 ݀
ሻ
≡ 3ଶ
݇ ± 3 ሺ݉3 ݀
ሻ
9݇ 3 ሺ݉7812 ݀ሻ; ݇ 0, 1, 2, 3, 4, … ,10, … . . , 100, … … , ሺ243 −
1ሻ.
≡ 0 ± 3; 9 ± 3; 18 ± 3; 27 ± 3; 36 ± 3; … ; 90 3; … . . ; 900 ±
3; … … 2178 ± 3.
≡ 3, 2184; 6, 12; 15,21; 24, 30; 33, 39; … … . . ; 87, 93; … … ;
897, 903; … . . ; 2175, 2181 ሺ݉7812 ݀ሻ.
These are the required 486 solutions.
These solutions are verified and found true.
Consider the congruence ݔହ
≡ 243 ሺ݉927 ݀ሻ.
It can be written as: ݔହ
≡ 3ହ
ሺ݉3݀
ሻ.
It is of the type:
ݔ
≡ ܽሺ݉ܽ݀ሻ; ݉ > ݊ ݐ݅ݓℎ ݊ .ݎ݁݃݁ݐ݊݅ ݁ݒ݅ݐ݅ݏ ݀݀
The congruence has only ܽିଵ
= 3ହିଵ
= 3ସ
=
81 .ݏ݊݅ݐݑ݈ݏ
Solutions are given by
ݔ ≡ ܽିାଵ
݇ + ܽ ሺ݉ܽ ݀ሻ; ݇ = 0, 1, 2, 3,4, … … . ሺܽିଵ
−
1.
≡ 3ିସ
݇ + 3 ሺ݉3 ݀ሻ; ݇ = 0, 1, 2, 3, 4, … … … . 80.
≡ 3ଶ
݇ + 3 ሺ݉927 ݀ሻ
≡ 9݇ + 3 ሺ݉927 ݀ሻ
≡ 0 + 3; 9 + 3; 18 + 3; 27 + 3; 36 + 3; 45 + 3; 54 +
3; … … .711 + 3;
720 + 3 ሺ݉927 ݀ሻ.
≡ 3, 12, 21, 30, 39, 48, 57, … … … … 714, 723 ሺ݉927 ݀ሻ.
These are the required 81 solutions.
These solutions are verified and found true.
Consider one more example: It can be written as:
ݔ
≡ 3
ሺ݉3 ݀
ሻ.
It can be written as: ݔ
≡ 0 ሺ݉3 ݀
ሻ.
Then the solutions are given by
3. International Journal of Trend in Scientific Research and Development (IJTSRD) @ www.ijtsrd.com eISSN: 2456-6470
@ IJTSRD | Unique Paper ID – IJTSRD29764 | Volume – 4 | Issue – 1 | November-December 2019 Page 969
ݔ ≡ ܽ ݐሺ݉ܽ ݀ሻ, .ݎ݁݃݁ݐ݊݅ ݊ܽ ܾ݃݊݅݁ ݐ
≡ 3 ݐሺ݉3 ݀ሻ; ݐ = 1, 2, 3, … … ..
≡ 3, 6, 9, 12, 15, … … … ሺ݉927 ݀ሻ
COLCLUSION
Thus, it can be concluded that the standard congruence of
composite modulus of higher degree of the type:
ݔ
≡ ܽ
ሺ݉ܽ ݀ሻ; ݉ > ݊, has 2ܽିଵ
solutions, if ݊ is an even positive integer, given by
ݔ ≡ ܽିାଵ
݇ ± ܽ ሺ݉ܽ ݀ሻ; ݇ = 0, 1, 2, … . . ሺܽିଵ
− 1ሻ.
But the congruence has only ܽିଵ
solutions, if ݊ is an odd
positive integer, given by
ݔ ≡ ܽିାଵ
݇ + ܽ ሺ݉ܽ ݀ሻ; ݇ = 0, 1, 2, … . . ሺܽିଵ
− 1ሻ.
If ݉ ≤ ݊, the solutions of the congruence are given by
ݔ
≡ ܽ
ሺ݉ܽ ݀ሻ; and the solutions are given by:
ݔ ≡ ܽ ݐሺ݉ܽ ݀ሻ, .ݎ݁݃݁ݐ݊݅ ݊ܽ ܾ݃݊݅݁ ݐ
MERIT OF THE PAPER
In this paper, a standard congruence of composite
modulus of higher degree is formulated successfully. The
formula established is proved true using suitable
examples. It is verified by illustrations. The solutions can
be obtained in a short time. It is proved time-saving.
Formulation is the merit of the paper.
REFERENCE
[1] H S Zuckerman at el, 2008, An Introduction to The
Theory of Numbers, fifth edition, Wiley student
edition, INDIA, ISBN: 978-81-265-1811-1.
[2] Thomas Koshy, 2009, “Elementary Number Theory
with Applications”, 2/e Indian print, Academic Press,
ISBN: 978-81-312-1859-4.
[3] Roy B M, Formulation of solutions of a special type of
standard congruence of prime modulus of higher
degree, International Journal of Advance Research,
Ideas and Innovations in Technology (IJARIIT), ISSN:
2454-132X, Vol-4, Issue-2, Mar-April-18.
[4] Roy B M, Formulation of solutions of a class of
congruence of prime-power modulus of higher
degree, International Journal of Innovative Science &
Research Technology (IJISRT), ISSN: 2456-2165, Vol-
03, Issue-04, April-18.
[5] Roy B M, Formulation of solutions of two special
congruence of prime modulus of higher degree,
International Journal of Science and Engineering
Development Research (IJSDR), ISSN: 2455-2631,
Vol-03, Issue-05, May-18.
[6] Roy B M, Solutions of a class of congruence of
multiple of prime-power modulus of higher degree,
International Journal of current Innovation in
Advanced Research (IJCIAR), ISSN: 2636-6282, Vol-
01, Issue-03, Jul-18.
[7] Roy B M, Formulation of a class of standard
congruence of higher degree modulo an odd prime-
square integer, International Journal of Science and
Engineering Development Research (IJSDR), ISSN:
2455-2631, Vol-04, Isue-01, Dec-18.
[8] Roy B M, Formulation of Two Special Classes of
Standard Congruence of Prime Higher Degree,
International Journal of Trend in Scientific Research
and development (IJTSRD), ISSN: 2456-6470, Vol-03,
Issue-03, April-19.
[9] Roy B M, Formulation of Solutions of a Special
Standard Cubic Congruence of Composite Modulus--
an Integer Multiple of Power of Prime, International
Journal of Advance Research, Ideas and Innovations
in Technology (IJARIIT), Vol-05, Issue-03, May-19.
[10] Roy B M, Solutions of three special classes of
congruence of prime modulus of higher degree,
International Journal of Scientific Research and
Development (IJSRED), ISSN: 2581-7175, Vol-02,
Issue-03, Jun-19.
![International Journal of Trend in Scientific Research and Development (IJTSRD)
Volume 4 Issue 1, December 2019
@ IJTSRD | Unique Paper ID – IJTSRD29764
Rp-106: Formulation
Congruence of Composite Modulus
M. Sc (Maths), Hon. Ph. D, Hon. D. Sc,
Jagat Arts, Commerce & I H P Science College, Goregaon
ABSTRACT
In this paper, a standard congruence of higher degree of composite
modulus is considered for study and after a thorough study,
formulated for its incongruent solutions. The established formula is tested
and verified true by solving suitable examples. Formulation is the merit of
the paper. This formulation made the study of the congruence of higher
degree easy, simple and interesting. Mental calculation of solutions become
possible due to this formulation. In the literature of earlier mathematics, no
formulation is found for the solutions of the said congruence.
KEYWORDS: Congruence of Higher Degree, Composite modulus
INRODUCTION
Many research papers on the formulation of quadratic,
cubic, bi-quadratic and congruence of higher degree of
prime and composite modulus have been published in
different reputed international journals by the author.
Even the author found a special type of congruence of
higher degree of composite modulus, yet not formulated. It
can be stated as:
ݔ
≡ ܽ
ሺ݉ܽ ݀ሻ; ܽ ് 0, ݉
The author wishes to consider such congruence and tried
to find a formulation of the congruence of composite
modulus of higher degree.
PROBLEM-STATEMENT
Here the problem is-
“To find a formulation of the congruence of higher degree
of composite modulus of the type:
ݔ
≡ ܽ
ሺ݉ܽ ݀ሻ; ܽ ് 0, ݉ ݊ ݅݊
Case-I: when n is even positive integer,
Case-II: when n is odd positive integer”.
LITERATURE-REVIEW
Many books of Number theory containing congruence of
higher degree are referred [1], [2]. No formulation of the
International Journal of Trend in Scientific Research and Development (IJTSRD)
2019 Available Online: www.ijtsrd.com
29764 | Volume – 4 | Issue – 1 | November-
Formulation of Solutions of a Class o
Composite Modulus of Higher Degree
Prof B M Roy
aths), Hon. Ph. D, Hon. D. Sc, Head, Department of Mathematics
Jagat Arts, Commerce & I H P Science College, Goregaon, Gondia, Maharashtra
In this paper, a standard congruence of higher degree of composite
modulus is considered for study and after a thorough study, it is then
formulated for its incongruent solutions. The established formula is tested
and verified true by solving suitable examples. Formulation is the merit of
the paper. This formulation made the study of the congruence of higher
nd interesting. Mental calculation of solutions become
possible due to this formulation. In the literature of earlier mathematics, no
formulation is found for the solutions of the said congruence.
Congruence of Higher Degree, Composite modulus, Formulation
How to cite this paper
"Rp-106: Formulation of Solutions of a
Class of Standard Congruence of
Composite Modulus of Higher Degree"
Published in
International
Journal of Trend in
Scientific Research
and Development
(ijtsrd), ISSN: 2456
6470, Volume
Issue-1, Decemb
2019, pp.967
www.ijtsrd.com/papers/ijtsrd29764.pdf
Copyright © 2019 by author(s) and
International Journal of Trend
Scientific Research and Development
Journal. This is an Open Access article
distributed under
the terms of the
Creative Commons
Attribution License (CC BY 4.0)
(http://creativecommons.org/licenses/
by/4.0)
formulation of quadratic,
quadratic and congruence of higher degree of
prime and composite modulus have been published in
different reputed international journals by the author.
Even the author found a special type of congruence of
of composite modulus, yet not formulated. It
݊".
The author wishes to consider such congruence and tried
to find a formulation of the congruence of composite
“To find a formulation of the congruence of higher degree
:ݏ݁ݏܽܿ ݓݐ
Many books of Number theory containing congruence of
higher degree are referred [1], [2]. No formulation of the
said congruence is found. Only the research papers on the
congruence of higher degree of the author published are
seen [3], [4],…… …….[9].
ANALYSIS & RESULT
Case-I: Let n be an even positive integer and
congruence under consideration:
ݔ
≡ ܽ
ሺ݉݀
Also consider that ݔ ≡ ܽିା
Then, ݔ
≡ ሺܽିାଵ
݇ േ ܽሻ
≡
ሺܽିାଵ
݇ሻ
݊ሺ ܽିାଵ
݇ሻିଵ
.
⋯ … … … . . േ ݊. ܽିାଵ
݇. ܽିଵ
≡ ܽ
ܽሺ… … ሻ ሺ݉ܽ ݀
ሻ
≡ ܽ
ሺ݉ܽ ݀
ሻ
Thus, it can be said that ݔ ≡ ܽ
a solution of the congruence.
But, if one has the value ݇ ൌ
then ݔ ≡ ܽିାଵ
݇ േ ܽ ሺ݉ ݀
International Journal of Trend in Scientific Research and Development (IJTSRD)
e-ISSN: 2456 – 6470
-December 2019 Page 967
of Standard
Higher Degree
Head, Department of Mathematics,
Maharashtra, India
How to cite this paper: Prof B M Roy
106: Formulation of Solutions of a
Class of Standard Congruence of
Composite Modulus of Higher Degree"
Published in
International
Journal of Trend in
Scientific Research
and Development
(ijtsrd), ISSN: 2456-
6470, Volume-4 |
1, December
2019, pp.967-969, URL:
www.ijtsrd.com/papers/ijtsrd29764.pdf
Copyright © 2019 by author(s) and
International Journal of Trend in
Scientific Research and Development
Journal. This is an Open Access article
distributed under
the terms of the
Creative Commons
Attribution License (CC BY 4.0)
http://creativecommons.org/licenses/
said congruence is found. Only the research papers on the
congruence of higher degree of the author published are
Let n be an even positive integer and consider the
congruence under consideration:
ሺ݉ܽ ݀ሻ; ݉ ݊.
ାଵ
݇ േ ܽ ሺ݉ܽ ݀ሻ
(mod ܽ
ሻ
. ܽ
.ሺିଵሻ
ଶ
ሺܽିାଵ
݇ሻିଶ
. ܽଶ
േ
ଵ
ܽ
ሺ݉ܽ ݀
ሻ
ܽିାଵ
݇ േ ܽ ሺ݉ܽ ݀ሻ is
a solution of the congruence.
ܽିଵ
,
ܽሻ reduces to
IJTSRD29764](https://image.slidesharecdn.com/186rp-106formulationofsolutionsofaclassofstandardcongruenceofcompositemodulusofhigherdegree-200110122956/85/Rp-106-Formulation-of-Solutions-of-a-Class-of-Standard-Congruence-of-Composite-Modulus-of-Higher-Degree-1-320.jpg)
