Since Diophantine equations play an important role in solving important real-world problems such as business investment problems, network flow problems, pole placement problems, and data privacy problems, researchers are increasingly interested in developing new techniques for analyzing the nature and solutions of the various Dio phantine equations. In this study we investigate the Diophantine problem 22x+40y = z2, where x, y, z are non-negative integers, and discover that it does not have a non-negative integer solution.
In continuation of the ongoing long term research work of the first author on the detailed mathematical and statistical analysis of thebudgetoftheBangaloreMunicipalCorporation(see,A.Sathyavathihttps://ssrn.com/abstract=4403863,https:/ssrn.com/abstract=4461494, https://ssrn.com/abstract=4518454 and https://ssrn. com/abstract=4568499), we carry ahead our previous study (A. Sathyavathi and L. M. Upadhyaya, Possible regression models for the municipal finances of the municipal corpo rations of various Indian states, Bull. Pure Appl. Sci. Sect. E Math. Stat. 42E(1), 72–93 (2023))to propose some possible regression models to account for the observed trends of the revenue receipts and the revenue expenditures of the municipal corporations of the various Indian States including the Union Territory of Chandigarh for the 2018-19 Bud get Estimates, which pertains to the data of finances of municipal corporations of the various Indian States during the financial year 2018-2019. We also present the com parisons of our different models for each of the categories of our present explorations. The entire data used by us in this study is gratefully taken by us from the Report on Municipal Finances which was published by the Reserve Bank of India recently on 10 November, 2022 (see,https://m.rbi.org.in/scripts/AnnualPublications.aspxhead=Report%20on%20Municipal%20Finances,https://rbidocs.rbi.org.in/rdocs/Publications/ PDFs/RMF101120223A34C4F7023A4A9E99CB7F7FEF6881D0.PDF). We find that a Polyno mial Degree 4 model best describes the financial data and in addition we also give a Rational Model and an Exponential Association 2 model for describing the trend of fi nances for the municipal corporations of India during the year 2018-19 in the Budget Estimates category and we also present our computational results of the Polynomial De gree 4 Model and the Rational Model using MATLAB.
This paper aims to investigate the solution of non-linear Volterra integral equation of the second kind by using the Rishi transform. The solutions of two numerical problems in compact form are determined by applying the Rishi transform, which sug gests that the Rishi transform can be used as a tool for solving these and the other types of related real world problems across various disciplines.
A detailed proof of the incorrectness of the foundations of the differential calculus is proposed. The correct methodological basis for the proof is the unity of formal logic and rational dialectics. The proof leads to the following irrefutable statement: differential calculus represents a gross error in mathematics and physics. The proof of this statement is based on the following irrefutable results: (1) the standard theory of infinitesimals and the theory of limits underlying the differential calculus are gross errors. The main error is that infinitesimal (infinitely decreasing) quantities do not take on numerical values in the process of tending to zero. The number “zero” is not a permissible value of infinitesimal quantity. The concepts of “infinitesimal quantity”, “movement”, “process of tendency”, and “limit of tendency” are meaningless concepts in mathematics: they are not mathematical concepts because the mathematical formalism does not contain movement (process); (2) the concepts of “increment of argument” and “increment of function” are the starting point of the differential calculus. The gross error is that the increment of argument is not defined. An indefinite (undefined, uncertain, ambiguous, undetermined) increment of an argument is a meaningless quantity (concept); (3) the definition of the derivative of a function is a gross error. The derivative is the limit of the ratio of the function increment to the argument increment under the following conditions: (a) the argument increment is not equal to zero; (b) the increment of the argument tends to zero and reaches the value “zero”. In this case, the following logical contradiction arises: the increment of the argument is both not equal to zero and equal to zero; (4) the differentials of the argument and the function - as infinitesimal quantities - do not take on numerical values. This means that the differentials of quantities have neither quantitative nor qualitative determinacy. In this case, the differentials of quantities are meaningless symbols. The geometric and physical interpretations of the derivative are a gross error; (5) the definition of the total differential of a function of two (many) variables is a gross error because the definition contains a formal-logical contradiction, i.e. the definition as the sum of partial differentials does not satisfy the formal-logical law of the lack (absence) of contradiction; (6) the theory of proportions completely refutes the theory of differential calculus. Thus, differential calculus does not satisfy the criterion of truth and is not correct scien tific (mathematical) theory.
In this paper, we investigate the generalized Hyers-Ulam-Stability of additive and quartic functional equations in modular spaces with and without the △2-condition using the direct method and also in 2-Banach Spaces.
In this paper, we introduce the k-Horn’s hypergeometric function H9,k and we investigate its limit formulas, integral representations, differentiation formulas, infinite sums, recursion formulas, the Laplace, Mellin, fractional Fourier, double Laplace and double Mellin transforms for the k-Horn’s hypergeometric function H9,k. Finally, we discuss the fractional integration and the k-fractional differentiation .
In the present paper we introduce a new generalized type of metric spaces called the right quasi-metric spaces. We state and prove convergence theorems to a fixed point for any map in these spaces. Finally, we give applications of our results. These results generalize the corresponding results in M. A. Ahmed and F. M. Zeyada (On con vergence of a sequence in complete metric spaces and its applications to some iterates of quasi-nonexpansive mappings, J. Math. Anal. Appl., 274(1), 458–465, 2002).
A graph with q edges is called antimagic if its edges can be labeled with 1,2,…,q without repetition such that the sums of the labels of the edges incident to each vertex are distinct. A graph which admits an antimagic labeling is called an antimagic graph. In this paper, we prove that the Pumpkin graph admit antimagic labeling.
Logical reasoning in any form is an important aspect of life; it is persuading or convincing others with logic through writing or speech, for example, scientists, politicians, businessmen, financiers, solicitors and many others do this. This paper points out the frequent inefficacy of logical presentations, arguments and debates per se in bringing about the correct and wonted outcomes. It describes the scenario of people frequently involved in fruitless arguments and debates, and shows why the application of logic, for example, in logical argument or debate, could not often achieve the desired outcomes, much of the time ending up with frustration, unhappiness, bad feelings and poor relationships. Scenarios from mathematics, which probably represents the most rigorous form of logical reasoning, and science are described as well. The paper also delves into the problems encountered in logical reasoning as well as some modes of reasoning. It would be difficult and might be impossible to reason with and convince someone with a closed mind-set, someone who has made up the mind not to be convinced, or even someone who is not intelligent enough to be convinced. The paper presents a resolution to this serious problem, which is important, as that would be conducive to peace and harmony. (Published
In this paper, authors have examined the Diophantine equation 8α + 67β = γ2, where α,β, γ are non-negative integers, for non-negative integer solutions. Authors used Catalan's conjecture for this purpose. Results of the present paper show that the Diophantine equation 8α + 67β = γ2, where α,β,γ are non-negative integers, has a unique solution in non-negative integers and this solution is given by (α, β, γ) = (1,0,3).
After the introduction of intuitionistic fuzzy sets by Atanassov K.T, many mathematical researchers have been devoted in the study of different aspects of this concept and they have been successful. The purpose of this paper is to introduce the notion of intuitionistic nil radicals of intuitionistic fuzzy ideals of hemirings. The author also investigated some of their properties.
This paper touches on the part played by the non-trivial zeros of the Riemann zeta function ζ, providing many important information and insights in the process, including some approaches to the Riemann hypothesis. (Published in Bulletin of Pure and Applied Sciences Section E Mathematics & Statistics Vol. 41E, No.1, January-June 2022.P.88-99) MSC. 11A41, 11A99
In an agricultural design of experiment the treatment received by a plot may affect the other response on the neighbouring plots of a same block or it may happen to affect the response on the following plot. For example of the second condition, the tall varieties may affect the other crops grown on the neighbouring plots by their shades. Bailey (2003) has developed such design concerned with the study of one sided neighbour effect, under the above mentioned second condition. This paper gives a new series of Universally Optimal One-Sided Circular Neighbour Balanced designs.
Odd graceful labeling was originally introduced by Gnanajothi [3] in 1991. The graph Gdemonstrates Odd graceful labeling as injecting β from V(G) → {0,1,2,… (2q - 1)} in such a way that whenever the label |β(x) - β(y)| is allocated to every edgexy, the derived edge labels are {1,3,5,…, (2q - 1). This paper demonstrates that the Super subdivision of the star and super subdivision of path permits odd graceful labeling.
The problems of Engineering and Science can easily represent by developing their mathematical models in the terms of integral equations. Various analytical and numerical methods are available that can be used for solving integral equations of different kinds. In this paper, authors have considered recently developed integral transform “Rishi Transform” for obtaining the exact solution of non-linear Volterra integral equation of first kind (NLVIEFK). Four numerical problems have considered for demonstrating the complete procedure of determining the exact solution. Results of these problems depict that Rishi transform is very effective integral transform and it provides the exact solution of NLVIEFK without doing complicated calculation work.
In this work, we have discuses and prove the different properties of the triple Laplace-Sumudu-Elzaki transform like linearity property, convolution theorems property, first shitting property, periodic function property, and the some applications to solve partial differential equations in three- dimensions.
Maximum Distance Separable (MDS) matrices offer ideal diffusion properties and are of great importance in design of block ciphers and hash functions. A rhotrix as defined by Sani, is a coupled matrix which when used in a cryptosystem provides double security. Many authors constructed MDS Rhotrices over finite fields using matrices which are cryptographically significant. Hankel matrices have wide range of applications in engineering, coding theory and cryptography. In the present paper, we define block rhotrix and block Hankel- like rhotrix. Further, we construct MDS block Hankel-like rhotrices using self-dual basis and conjugate elements of Fpn.
. The critical analysis of the starting point of the theory of complex numbers is proposed. The unity of formal logic and rational dialectics is methodological basis of the analysis. The analysis leads to the following main results: (1) the definition of a complex number contradicts to the laws of formal logic, because this definition is the union of two contradictory concepts: the concept of a real number and the concept of a non-real (imaginary) number - an image. The concepts of a real number and a non-real (imaginary) number are in logical relation of contradiction: the essential feature of one concept completely negates the essential feature of another concept. These concepts have no common feature (i.e. these concepts have nothing in common with each other), therefore one cannot compare these concepts with each other. Consequently, the concepts of a real number and a non-real (imaginary) number cannot be united and contained in the definition of a complex number. The concept of a complex number is a gross formal-logical error; (2) the real part of a complex number is the result of a measurement. But the non-real (imaginary) part of a complex number is not the result of a measurement. The non-real (imaginary) part is a meaningless symbol, because the mathematical (quantitative) operation of multiplication of a real number by a meaningless symbol is a meaningless operation. This means that the theory of complex number is not a correct method of calculation. Consequently, mathematical (quantitative) operations on meaningless symbols are a gross formal-logical error; (3) a complex number cannot be represented (interpreted) in the Cartesian geometric coordinate system, because the Cartesian coordinate system is a system of two identical scales (rulers). The standard geometric representation (interpretation) of a complex number leads to the logical contradictions if the scales (rulers) are not identical. This means that the scale of non-real (imaginary) numbers cannot exist in the Cartesian geometric coordinate system. Consequently, and (electromagnetism and electrical engineering, fluid quantum mechanics, relativity) represent a gross methodological error and lead to gross errors in mathematics and physics.
