Previous months: - 0903(1) - 1003(2) - 1004(2) - 1005(2) - 1007(1) - 1008(1)
[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.
[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)
[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)
[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)
[5] viXra:1004.0053 [pdf] submitted on 8 Mar 2010
Authors: Florentin Smarandache, Mircea Eugen Selariu
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.
[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.
[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
[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)
[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.
[3] 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.
[2] 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)
[1] 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)