Functions and Analysis

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Recent Submissions

Any replacements are listed further down

[20] viXra:1202.0071 [pdf] submitted on 2012-02-21 22:27:58

A L-Topology of Banach Space and Separability of Lipschitz Dual Space

Authors: Choe Ryong Gil
Comments: 23 pages

In this paper we have introduced a new topology and a convergence in Banach space, which would be called a L-topology and a L-convergence. It is similar to the weak topology and weak convergence, but there are some essential differences. For example, the L-topology is stronger than weak topology, but weaker than the strong one. On the basis of the notion, we have considered the problem on the separability and reflexibility of Lipschitz (Lip-) dual space. Furthermore, we have introduced a new topology of Lip-dual space, which is similar to the weak* (W*-) topology of linear dual of Banach space and would be called an L*-topology, and we have considered the problems on the metrizability of L*-topology and on the L*-separability of Lip-dual space, too.
Category: Functions and Analysis

[19] viXra:1202.0069 [pdf] submitted on 2012-02-20 20:24:29

A L*-Convergence of Sequence of Nonlinear Lipschitz Functionals and Its Applications in Banach Spaces

Authors: Choe Ryong Gil
Comments: 18 pages

In this paper we have introduced a new concept on the convergence of a sequence of the nonlinear Lipschitz (Lip-) functionals, which would be called an L*-convergence, and we have considered its applications in Banach spaces. This convergence is very similar to the weak* (W*-) convergence of the sequence of the bounded linear functionals, but there are some differences. By the L*-convergence, we have considered the problem on the relations of the compactness between the Lip-operator and its Lip-dual operator, and we have obtained the mean ergodic theorems for the Lip-operator.
Category: Functions and Analysis

[18] viXra:1202.0060 [pdf] submitted on 2012-02-19 02:03:52

An Extension Theorem of Nonlinear Lipschitz Functional and Its Application in Banach Spaces

Authors: Choe Ryong Gil
Comments: 17 pages

In this paper we have obtained a new theorem that a nonlinear Lipschitz (Lip-) functional defined on the closed subset of Banach spaces can be extended to the whole space with Lip-continuity and maintenance of Lip-constant, which would be called an extension theorem (ET). This theorem is a generalization to the Lip-functional of the famous Hahn-Banach theorem on the bounded linear functional. By the ET, we have completely solved the open problem on the relation of the invertibility between the Lip-operator and its Lip-dual operator.
Category: Functions and Analysis

[17] viXra:1202.0015 [pdf] submitted on 2012-02-06 15:20:56

Volume of the Off-Center Spherical Pyramidal Trunk

Authors: Richard J. Mathar
Comments: 12 Pages. Includes complete C++ source listing.

The volume inside intersecting spheres may be computed by a standard method which computes a surface integral over all visible sections of the spheres. If the visible sections are divided in simple zonal sections, the individual contribution by each zone follows from basic analysis. We implement this within a semi-numerical program which marks the zones individually as visible or invisible.
Category: Functions and Analysis

[16] viXra:1112.0044 [pdf] submitted on 2011-12-15 09:36:44

On the Connectivity in One-Dimensional ad Hoc Wireless Networks with a Forbidden Zone

Authors: Xiaodong Hu, Evgeniy Grechnikov
Comments: 11 Pages.

This paper investigates the connectivity in one-dimensional ad hoc wireless networks with a forbidden zone. We derive the probability of the wireless networks which are composed of exactly m clusters by means of the methods of combinatorics and probability. The probability of connectivity, i.e. $m = 1$, can be obtained as a special case. Further, we explain how the transmission range of node affects the connectivity of the wireless network.
Category: Functions and Analysis

[15] viXra:1111.0105 [pdf] submitted on 28 Nov 2011

A Hamiltonian Operator Whose Zeros Are the Roots of the Riemann XI-Function

Authors: Jose Javier Garcia Moreta
Comments: 23 Pages.

We give a possible interpretation of the Xi-function of Riemann as the Functional determinant for a certain Hamiltonian quantum operator in one dimension for a real-valued function V(x) , this potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function, through the paper we will assume that the reduced Planck constant is defined in units where and that the mass is
Category: Functions and Analysis

[14] viXra:1110.0075 [pdf] submitted on 30 Oct 2011

Mean Value Theorems for Local Fractional Integrals on Fractal Space

Authors: Guang-Sheng Chen
Comments: 6 pages.

In this paper, by some properties of Local fractional integral, we establish the generalized Mean value theorems for Local Fractional Integral.
Category: Functions and Analysis

[13] viXra:1106.0056 [pdf] submitted on 27 Jun 2011

The Introduction of Twist (The Skew) in the Mathematics

Authors: Mircea Selariu
Comments: 10 pages.

The article define a mathematic entity called twist, which generates, in this way, notion of straight line. Straight line becom thus a twist of eccentricity e = 0, and broken line (zigzag line) is a twist of s = ± 1.
Category: Functions and Analysis

[12] viXra:1106.0055 [pdf] submitted on 26 Jun 2011

The Calculus Relation Determination, with Whatever Precision, of Complete Elliptic Integral of the First Kind.

Authors: Mircea Selariu
Comments: 10 pages.

These papers show a calculus relation ( 50 ) of complete elliptic integral K(k) with minimum 9 precise decimals and the possibility to obtain a more precisely relation.. It results by application Landen's method, of geometrical-arithmetical average, not for obtain a numerical value but to obtain a compute algebraically relation after 5 steps of a geometrical transformation, called "CENTERED PROCESS".
Category: Functions and Analysis

[11] viXra:1106.0014 [pdf] submitted on 9 Jun 2011

Is Zero to the Zero Power Equal to One?

Authors: Ron Bourgoin
Comments: 4 pages

Sometimes in physics we end up with a function that resembles f(x)=00, where for example we have a radius that goes to zero and an exponent goes to zero in k/r n , where k is a constant. Is 00 in such cases equal to unity?
Category: Functions and Analysis

[10] viXra:1009.0047 [pdf] submitted on 13 Sep 2010

Summary of the Zeta Regularization Method Applied to the Calculation of Divergent Series Σn5 and Divergent Integrals ∫x5dx

Authors: Jose Javier Garcia Moreta
Comments: 13 pages.

We study a generalization of the zeta regularization method applied to the case of the regularization of divergent integrals ... (see paper for full abstract)
Category: Functions and Analysis

[9] viXra:1008.0025 [pdf] submitted on 9 Aug 2010

Survey on Singularities and Differential Algebras of Generalized Functions :A Basic Dichotomic Sheaf Theoretic Singularity Test

Authors: Elemér E Rosinger
Comments: 166 pages

It is shown how the infinity of differential algebras of generalized functions is naturally subjected to a basic dichotomic singularity test regarding their significantly different abilities to deal with large classes of singularities. In this respect, a review is presented of the way singularities are dealt with in four of the infinitely many types of differential algebras of generalized functions. These four algebras, in the order they were introduced in the literature are : the nowhere dense, Colombeau, space-time foam, and local ones. And so far, the first three of them turned out to be the ones most frequently used in a variety of applications. The issue of singularities is naturally not a simple one. Consequently, there are different points of view, as well as occasional misunderstandings. In order to set aside, and preferably, avoid such misunderstandings, two fundamentally important issues related to singularities are pursued. Namely, 1) how large are the sets of singularity points of various generalized functions, and 2) how are such generalized functions allowed to behave in the neighbourhood of their point of singularity. Following such a two fold clarification on singularities, it is further pointed out that, once one represents generalized functions - thus as well a large class of usual singular functions - as elements of suitable differential algebras of generalized functions, one of the main advantages is the resulting freedom to perform globally arbitrary algebraic and differential operations on such functions, simply as if they did not have any singularities at all. With the same freedom from singularities, one can perform globally operations such as limits, series, and so on, which involve infinitely many generalized functions. The property of a space of generalized functions of being a flabby sheaf proves to be essential in being able to deal with large classes of singularities. The first and third type of the mentioned differential algebras of generalized functions are flabby sheaves, while the second type fails to be so. The fourth type has not yet been studied in this regard.
Category: Functions and Analysis

[8] viXra:1007.0005 [pdf] submitted on 5 Jul 2010

A Conjecture About the Riemann XI-Function ξ(1/2 + Iz) and Functional Determinants

Authors: Jose Javier Garcia Moreta
Comments: 7 pages.

We give a possible interpretation of the Xi-function of Riemann as the Functional determinant det (E - H) for a certain Hamiltonian quantum operator in one dimension ... (see paper for full abstract)
Category: Functions and Analysis

[7] viXra:1005.0075 [pdf] submitted on 19 May 2010

The Theory of Distributions Applied to Divergent Integrals of the Form (See Paper for Equation)

Authors: Jose Javier Garcia Moreta
Comments: 9 pages

In this paper we review some results on the regularization of divergent integrals of the form ... (see paper for full abstract)
Category: Functions and Analysis

[6] viXra:1005.0071 [pdf] submitted on 17 May 2010

Product of Distributions and Zeta Regularization of Divergent Integrals ∫ Xm-Sdx and Fourier Transforms

Authors: Jose Javier Garcia Moreta
Comments: 9 pages

Using the theory of distributions and Zeta regularization we manage to give a definition of product for Dirac delta distributions, we show how the fact of one can be define a coherent and finite product of dDirac delta distributions is related to the regularization of divergent integrals ... (see paper for full abstract)
Category: Functions and Analysis

[5] viXra:1004.0053 [pdf] submitted on 8 Mar 2010

Immediate Calculation of Some Poisson Type Integrals Using Supermathematics Circular ex-Centric Functions

Authors: Florentin Smarandache, Mircea Eugen Șelariu
Comments: 10 pages

This article presents two methods, in parallel, of solving more complex integrals, among which is the Poisson's integral, in order to emphasize the obvious advantages of a new method of integration, which uses the supermathematics circular ex-centric functions. We will specially analyze the possibilities of easy passing/changing of the supermathematics circular ex-centric functions of a centric variable α to the same functions of ex-centric variable &theta. The angle α is the angle at the center point O(0,0), which represents the centric variable and θ is the angle at the ex-center E(k,ε), representing the ex-centric variable. These are the angles from which the points W1 and W2 are visible on the unity circle - resulted from the intersection of the unity/trigonometric circle with the revolving straight line d around the ex-centric E(k,&epsilon) - from O and from E, respectively.
Category: Functions and Analysis

[4] viXra:1004.0014 [pdf] submitted on 8 Mar 2010

A Triple Inequality with Series and Improper Integrals

Authors: Florentin Smarandache
Comments: 4 pages

As a consequence of the Integral Test we find a triple inequality which bounds up and down both a series with respect to its corresponding improper integral, and reciprocally an improper integral with respect to its corresponding series.
Category: Functions and Analysis

[3] viXra:1003.0166 [pdf] submitted on 6 Mar 2010

A Recurrence Method for Generalizing Known Scientific Results

Authors: Florentin Smarandache
Comments: 4 pages

A great number of articles widen known scientific results (theorems, inequalities, math/physics/chemical etc. propositions, formulas), and this is due to a simple procedure, of which it is good to say a few words
Category: Functions and Analysis

[2] viXra:1003.0105 [pdf] submitted on 10 Mar 2010

Orthogonal Polynomials, Moment Problem and the Riemann XI-Function ξ(1/2 + Iz)

Authors: Jose Javier Garcia Moreta
Comments: 12 Pages.

In this paper we study a set of orthogonal Polynomials with respect a certain given measure related to the Taylor series expansion of the Xi-function , this paper is based on a previous conjecture by Carlon and Gaston related to the fact that Riemann Hypothesis (with simple zeros) is equivalent to the limit for a certain set of orthogonal Polynomials, we study the 'Hamburger moment problem' for even 'n' and 0 for n odd here the moments are related to the power series expansion of Xi-function , we also give the integral representation for the generating function , in terms of the Laplace transform of , and in the end of the paper we study the connection of our orthogonal polynomial set with the Kernel , through all the paper we will use the simplified notation (see paper for abstract with equations)
Category: Functions and Analysis

[1] viXra:0903.0007 [pdf] submitted on 28 Mar 2009

The Exact Analytic Solution of Blasius Equation

Authors: Chun-Xuan Jiang
Comments: recovered from sciprint.org

We find Blasius function to satisfy the boundary condition f(∞) = 1 and obtain the exact analytic soultion of Blasius equation.
Category: Functions and Analysis

Recent Replacements

[18] viXra:1106.0055 [pdf] replaced on 27 Jun 2011

The Calculus Relation Determination, with Whatever Precision, of Complete Elliptic Integral of the First Kind.

Authors: Mircea Selariu
Comments: 10 pages. v1 in Romanian, v2 in English.

These papers show a calculus relation ( 50 ) of complete elliptic integral K(k) with minimum 9 precise decimals and the possibility to obtain a more precisely relation.. It results by application Landen's method, of geometrical-arithmetical average, not for obtain a numerical value but to obtain a compute algebraically relation after 5 steps of a geometrical transformation, called "CENTERED PROCESS".
Category: Functions and Analysis

[17] viXra:1009.0047 [pdf] replaced on 23 Feb 2011

Summary of the Zeta Regularization Method Applied to the Calculation of Divergent Series Σn5 and Divergent Integrals ∫x5dx

Authors: Jose Javier Garcia Moreta
Comments: 19 pages.

We study a generalization of the zeta regularization method applied to the case of the regularization of divergent integrals ... (see paper for full abstract)
Category: Functions and Analysis

[16] viXra:1009.0047 [pdf] replaced on 11 Feb 2011

Summary of the Zeta Regularization Method Applied to the Calculation of Divergent Series Σn5 and Divergent Integrals ∫x5dx

Authors: Jose Javier Garcia Moreta
Comments: 18 pages.

We study a generalization of the zeta regularization method applied to the case of the regularization of divergent integrals ... (see paper for full abstract)
Category: Functions and Analysis

[15] viXra:1009.0047 [pdf] replaced on 8 Nov 2010

Summary of the Zeta Regularization Method Applied to the Calculation of Divergent Series Σn5 and Divergent Integrals ∫x5dx

Authors: Jose Javier Garcia Moreta
Comments: 14 pages.

We study a generalization of the zeta regularization method applied to the case of the regularization of divergent integrals ... (see paper for full abstract)
Category: Functions and Analysis

[14] viXra:1008.0025 [pdf] replaced on 12 Aug 2010

Survey on Singularities and Differential Algebras of Generalized Functions :A Basic Dichotomic Sheaf Theoretic Singularity Test

Authors: Elemér E Rosinger
Comments: 184 pages

It is shown how the infinity of differential algebras of generalized functions is naturally subjected to a basic dichotomic singularity test regarding their significantly different abilities to deal with large classes of singularities. In this respect, a review is presented of the way singularities are dealt with in four of the infinitely many types of differential algebras of generalized functions. These four algebras, in the order they were introduced in the literature are : the nowhere dense, Colombeau, space-time foam, and local ones. And so far, the first three of them turned out to be the ones most frequently used in a variety of applications. The issue of singularities is naturally not a simple one. Consequently, there are different points of view, as well as occasional misunderstandings. In order to set aside, and preferably, avoid such misunderstandings, two fundamentally important issues related to singularities are pursued. Namely, 1) how large are the sets of singularity points of various generalized functions, and 2) how are such generalized functions allowed to behave in the neighbourhood of their point of singularity. Following such a two fold clarification on singularities, it is further pointed out that, once one represents generalized functions - thus as well a large class of usual singular functions - as elements of suitable differential algebras of generalized functions, one of the main advantages is the resulting freedom to perform globally arbitrary algebraic and differential operations on such functions, simply as if they did not have any singularities at all. With the same freedom from singularities, one can perform globally operations such as limits, series, and so on, which involve infinitely many generalized functions. The property of a space of generalized functions of being a flabby sheaf proves to be essential in being able to deal with large classes of singularities. The first and third type of the mentioned differential algebras of generalized functions are flabby sheaves, while the second type fails to be so. The fourth type has not yet been studied in this regard.
Category: Functions and Analysis

[13] viXra:1007.0005 [pdf] replaced on 13 Nov 2011

A Hamiltonian Operator Whose Zeros Are the Roots of the Riemann XI-Function

Authors: Jose Javier Garcia Moreta
Comments: 20 pages.

We give a possible interpretation of the Xi-function of Riemann as the Functional determinant det(E-H) for a certain Hamiltonian quantum operator in one dimension (see paper) for a real-valued function V(x), this potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function, through the paper we will assume that the reduced Planck constant is defined in units where h-bar = 1 and that the mass is 2m = 1
Category: Functions and Analysis

[12] viXra:1007.0005 [pdf] replaced on 3 Nov 2011

A Hamiltonian Operator Whose Zeros Are the Roots of the Riemann XI-Function

Authors: Jose Javier Garcia Moreta
Comments: 19 pages.

We give a possible interpretation of the Xi-function of Riemann as the Functional determinant det(E-H) for a certain Hamiltonian quantum operator in one dimension (see paper) for a real-valued function V(x), this potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function, through the paper we will assume that the reduced Planck constant is defined in units where h-bar = 1 and that the mass is 2m = 1
Category: Functions and Analysis

[11] viXra:1007.0005 [pdf] replaced on 4 Oct 2011

A Hamiltonian Operator Whose Zeros Are the Roots of the Riemann XI-Function

Authors: Jose Javier Garcia Moreta
Comments: 16 pages.

We give a possible interpretation of the Xi-function of Riemann as the Functional determinant det(E-H) for a certain Hamiltonian quantum operator in one dimension (see paper) for a real-valued function V(x), this potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function, through the paper we will assume that the reduced Planck constant is defined in units where h-bar = 1 and that the mass is 2m = 1
Category: Functions and Analysis

[10] viXra:1007.0005 [pdf] replaced on 28 Jun 2011

A Hamiltonian Operator Whose Zeros Are the Roots of the Riemann XI-Function

Authors: Jose Javier Garcia Moreta
Comments: 14 pages.

We give a possible interpretation of the Xi-function of Riemann as the Functional determinant det(E-H) for a certain Hamiltonian quantum operator in one dimension (see paper) for a real-valued function V(x), this potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function, through the paper we will assume that the reduced Planck constant is defined in units where h-bar = 1 and that the mass is 2m = 1
Category: Functions and Analysis

[9] viXra:1007.0005 [pdf] replaced on 2 May 2011

A Hamiltonian Operator Whose Zeros Are the Roots of the Riemann XI-Function

Authors: Jose Javier Garcia Moreta
Comments: 18 pages.

We give a possible interpretation of the Xi-function of Riemann as the Functional determinant det(E-H) for a certain Hamiltonian quantum operator in one dimension (see paper) for a real-valued function V(x), this potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function, through the paper we will assume that the reduced Planck constant is defined in units where h-bar = 1 and that the mass is 2m = 1
Category: Functions and Analysis

[8] viXra:1007.0005 [pdf] replaced on 5 Apr 2011

A Hamiltonian Operator Whose Zeros Are the Roots of the Riemann XI-Function

Authors: Jose Javier Garcia Moreta
Comments: 16 pages.

We give a possible interpretation of the Xi-function of Riemann as the Functional determinant det(E-H) for a certain Hamiltonian quantum operator in one dimension (see paper) for a real-valued function V(x), this potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function, through the paper we will assume that the reduced Planck constant is defined in units where h-bar = 1 and that the mass is 2m = 1
Category: Functions and Analysis

[7] viXra:1007.0005 [pdf] replaced on 10 Mar 2011

A Hamiltonian Operator Whose Zeros Are the Roots of the Riemann XI-Function ξ(1/2 + Iz)

Authors: Jose Javier Garcia Moreta
Comments: 15 pages.

We give a possible interpretation of the Xi-function of Riemann as the Functional determinant det(E-H) for a certain Hamiltonian quantum operator in one dimension () for a real-valued function V(x) , this potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function, through the paper we will assume that the reduced Planck constant is defined in units where h-bar = 1 and that the mass is 2m = 1
Category: Functions and Analysis

[6] viXra:1007.0005 [pdf] replaced on 18 Nov 2010

A Conjecture About the Riemann XI-Function ξ(1/2 + Iz) and Functional Determinants

Authors: Jose Javier Garcia Moreta
Comments: 13 pages.

We give a possible interpretation of the Xi-function of Riemann as the Functional determinant det (E - H) for a certain Hamiltonian quantum operator in one dimension ... (see paper for full abstract)
Category: Functions and Analysis

[5] viXra:1007.0005 [pdf] replaced on 3 Aug 2010

A Conjecture About the Riemann XI-Function ξ(1/2 + Iz) and Functional Determinants

Authors: Jose Javier Garcia Moreta
Comments: 10 pages.

We give a possible interpretation of the Xi-function of Riemann as the Functional determinant det (E - H) for a certain Hamiltonian quantum operator in one dimension ... (see paper for full abstract)
Category: Functions and Analysis

[4] viXra:1007.0005 [pdf] replaced on 27 Jul 2010

A Conjecture About the Riemann XI-Function ξ(1/2 + Iz) and Functional Determinants

Authors: Jose Javier Garcia Moreta
Comments: 9 pages.

We give a possible interpretation of the Xi-function of Riemann as the Functional determinant det (E - H) for a certain Hamiltonian quantum operator in one dimension ... (see paper for full abstract)
Category: Functions and Analysis

[3] viXra:1005.0071 [pdf] replaced on 20 Jun 2011

Product of Distributions and Zeta Regularization of Divergent Integrals ∫ Xm-Sdx and Fourier Transforms

Authors: Jose Javier Garcia Moreta
Comments: 13 pages

Using the theory of distributions and Zeta regularization we manage to give a definition of product for Dirac delta distributions, we show how the fact of one can be define a coherent and finite product of Dirac delta distributions is related to the regularization of divergent integrals ... (see paper for full abstract)
Category: Functions and Analysis

[2] viXra:1005.0071 [pdf] replaced on 15 Jan 2011

Product of Distributions and Zeta Regularization of Divergent Integrals ∫ Xm-Sdx and Fourier Transforms

Authors: Jose Javier Garcia Moreta
Comments: 13 pages

Using the theory of distributions and Zeta regularization we manage to give a definition of product for Dirac delta distributions, we show how the fact of one can be define a coherent and finite product of Dirac delta distributions is related to the regularization of divergent integrals ... (see paper for full abstract)
Category: Functions and Analysis

[1] viXra:1003.0166 [pdf] replaced on 20 Mar 2010

A Self-Recurrence Method for Generalizing Known Scientific Results

Authors: Florentin Smarandache
Comments: 7 pages

A great number of articles widen known scientific results (theorems, inequalities, math/physics/chemical etc. propositions, formulas), and this is due to a simple procedure, of which it is good to say a few words: Let suppose that we want to generalizes a known mathematical proposition P(a) , where a is a constant, to the proposition P(n) , where n is a variable which belongs to subset of N . To prove that P is true for n by recurrence means the following: the first step is trivial, since it is about the known result P(a) (and thus it was already verified before by other mathematicians!). To pass from P(n) to P(n + 1) , one uses too P(a) : therefore one widens a proposition by using the proposition itself, in other words the found generalization will be paradoxically proved with the help of the particular case from which one started! We present below the generalizations of Hölder, Minkovski, and respectively Tchebychev inequalities.
Category: Functions and Analysis