| viXra.org > Functions and Analysis > 2208 |
 |
 |
| viXra.org > Functions and Analysis > 2208 |
|
|
[11] viXra:2208.0160 [pdf] submitted on 2022-08-29 20:55:58
Authors: Saburou Saitoh
Comments: 8 Pages. In this paper, we shall consider norm inequalities for one dimensional Sobolev Hilbert spaces by using the theory of reproducing kernels as fundamental inequalities.
In this paper, we shall consider norm inequalities for one dimensional Sobolev Hilbert spaces by using the theory of reproducing kernels as fundamental inequalities.
Category: Functions and Analysis
[10] viXra:2208.0138 [pdf] submitted on 2022-08-25 15:40:25
Authors: Theophilus Agama
Comments: 5 Pages. This paper is a multivariate analogue of Jensen's inequality.
In this note we prove a multivariate analogue of Jensen's inequality via the notion of the local product and associated space.
Category: Functions and Analysis
[9] viXra:2208.0111 [pdf] submitted on 2022-08-19 17:21:48
Authors: Richard J. Mathar
Comments: 8 Pages.
The integrals R_{n,n}$ obtained by Atkinson and van Steenwijkfor the resistance between points of an infinite set ofunit resistors on the triangular latticeobey P-finite recurrences. The main causeof these are similarities uncovered by partial integrations of theirintegral representations with algebraic kernels. All R_{n,p} resistancesto points with integer coordinates n and p relative to an originin the lattice can be derived recursively.
Category: Functions and Analysis
[8] viXra:2208.0089 [pdf] submitted on 2022-08-16 22:59:11
Authors: Marcello Colozzo
Comments: 18 Pages.
The Riemann hypothesis is proved through a theorem on the nature of points critics of the real part and the imaginary part u(x, y), v(x, y) of a holomorphic function having the same zeros of the Riemann zeta function. Precisely, the zeros of thesefunctions are saddle points, and furthermore in these points the partial derivatives of odd order. From this derives a system of infinite identities that are check if and only if the real part of the zeros of the zeta function is equal to 1/2.
Category: Functions and Analysis
[7] viXra:2208.0050 [pdf] submitted on 2022-08-10 00:49:08
Authors: Saburou Saitoh
Comments: 4 Pages.
We introduce an interesting example of conformal mappings (Joukowski transform) from the view point of the division by zero calculus. We give an interpretation of the identity, for a larger than b larger than 0 frac{rho + 1/rho}{rho - 1/rho} = frac{a}{b}, quad rho = sqrt{frac{a+b}{a - b}}, for the case a=b.
Category: Functions and Analysis
[6] viXra:2208.0046 [pdf] submitted on 2022-08-09 00:43:00
Authors: Michael C. I. Nwogugu
Comments: 10 Pages. The copyright license-type for this article is CC-BY-NC-ND.
Liptai, Németh, et. al. (2020) supposedly proved that in the diophantine equation (3^a−1)(3^b−1)=(5^c−1)(5^d−1) in positive integers and where a≤b and c≤d, the only solution to the title equation is (a,b,c,d)=(1,2,1,1). This article analyzes the Complexity of, and introduces properties of the equations (3^a−1)(3^b−1)=(5^c−1)(5^d−1) and g^u=f^v, new "Existence Conditions", new theories of "Rational Equivalence", and a new theorem pertaining to the equation g^u=f^v. The class of equations of the type [(X^a−1)(X^b−1)=(Y^c−1)(Y^d−1)] (the "Rational-Equivalence Equation") includes the equation (3^a−1)(3^b−1)=(5^c−1)(5^d−1). This article also introduces simple Java codes for finding solutions to this class of equations for positive-integers up to (10)^2457600000 (and even greater positive-integers depending on available computing power).
Category: Functions and Analysis
[5] viXra:2208.0019 [pdf] replaced on 2022-10-29 19:20:21
Authors: Joseph Bakhos
Comments: 7 Pages. Published December 18, 2022: Applied Mathematical Sciences, Vol. 16, 2022, no. 12, 665-677 doi: 10.12988/ams.2022.917217 Link: http://www.m-hikari.com/ams/ams-2022/ams-9-12-2022/p/bakhosAMS9-12-2022.pdf
Methods approximating the square root of a number use recursive sequences. They do not have a simpleformula for generating the seed value for the approximation, so instead they use various algorithms for choosing the first term of the sequences. Section 1 introduces a new option, based upon the number of digits of the radicand, for selecting the first term. This new option works well at all scales. This first term will then be used in a traditional recursive sequence used to approximate roots. Section 2 will apply the method shown in Section 1 to approximate pi using Archimedes’ method, which then no longer requires different algorithms at different scales for seed values. Section 3 will introduce new recursive sequences for approximating rootsusing Pythagorean triples. Section 4 will then use the same new method to approximate pi.
Category: Functions and Analysis
[4] viXra:2208.0014 [pdf] submitted on 2022-08-04 01:26:25
Authors: Michael C. I. Nwogugu
Comments: 9 Pages.
This article proves that the Collatz Conjecture is valid for all positive integers. The main formula (and rules) for the Collatz Conjecture is as follows: f(n) = (n/2) or (3n+1).
Category: Functions and Analysis
[3] viXra:2208.0013 [pdf] submitted on 2022-08-04 01:27:41
Authors: Michael C. I. Nwogugu
Comments: 15 Pages.
Equity Based Incentives include Employee Stock Options (ESOs), and substantially change the traditional production/service function, because ESOs/EBIs have different psychological impacts (motivation, or de-motivation), can create intangible capital (ie. Social Capital, Reputational Capital and Human Capital), and create different economic payoffs. Although Game Theory is a flawed concept, it can be helpful in describing interactions in ESO/EBIs transactions. ESOs/EBIs involve a two-stage game; and there are no perfect Nash Equilibria for the two sub-games. The large number of actual and potential participants in these games significantly complicates resolution of equilibria and increases the dynamism of the game(s), given that players are more sensitive to each other’s moves in such games. This article: i) builds on but differs from Nwogugu (2004; 2006); ii) analyzes how ESOs/EBIs dynamics affect traditional assumptions of production functions (in both the manufacturing and service sectors), iii) develops new models of multi-dimensional/combined games (two-stage games, dynamic games and differential games) inherent in ESO/EBIs transactions, iv) illustrates some of the limitations of game theory.
Category: Functions and Analysis
[2] viXra:2208.0011 [pdf] submitted on 2022-08-04 01:29:17
Authors: Michael C. I. Nwogugu
Comments: 13 Pages. The copyright license-type for this article is CC-BY-NC-ND
The annual volumes of M&A transactions and cross-border M&A transactions around the world are significant and often have Multiplier Effects and Spillover Effects on national economies and households, and a wide range of financial/economic indicators. Similarly, the volumes of Strategic Alliances and Joint Ventures around the world are significant (worth more than US$15 trillion annually) and have Multiplier Effects and Cross-Border Spillover Effects. As noted in Nwogugu (2015), "Synthetic M&As" can be executed using Strategic Alliances or joint Ventures. Conversely Strategic Alliances or Joint Ventures can be structured to provide all the benefits of M&A transactions. This article analyzes critical Dynamical Systems, Nonlinearity, Networks and behavioral issues pertaining to the choice between a Strategic Alliance or joint venture on one hand, and an M&A transaction; and also introduces new decision models.
Category: Functions and Analysis
[1] viXra:2208.0010 [pdf] submitted on 2022-08-04 01:30:42
Authors: Michael C. I. Nwogugu
Comments: 31 Pages. The copyright license-type for this article is CC-BY-NC-ND
Some properties of the equations x2+y2+z2+v2= rXYZ, x2+y2+z2= rXYZ, x2+y2+z2+v2+u2=rXYZ, X2+Y2+Z2+V2= rXYZ, X2+Y2+Z2 = rXYZ, X2+Y2+Z2+V2 +U2 = rXYZ, Xi+Yi+Zi+Vi= rXYZ, x3+y3+z3=rXYZ, x3+y3+z3+x6+y6+z6=rXYZ, x6+y6+z6=rXYZ, [(x12+y12+z12)-(x6+y6+z6)]=rXYZ, and xi+yi+zi=rXYZ, (i is a positive integer), where x│X (ie. X is a multiple of x), y│Y, and z│Z are real numbers. This article also summarizes the relationships to Homotopy Theory, PDEs, Mathematical Cryptography and Analysis. The proofs are within the context of Sub-Rings. The additional common factor is that each of the variables x,y,z, v and dXYZ are multiples of (n-f), where n and f are real numbers. The solutions derived herein can be extended to other problems wherein (n-f) can take the form of polynomials/functions such as (6d-3), (14-5c), (ai-b2i), etc.. Some of the results are applicable where all variables are Integers.
Category: Functions and Analysis
| Third-Party Links: |
|