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Any replacements are listed further down
[20] viXra:1202.0071 [pdf] submitted on 2012-02-21 22:27:58
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
[18] viXra:1106.0055 [pdf] replaced on 27 Jun 2011
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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