|
| 2001-10-15T14:58:41Z | | A Piece of the Lepton Theory from a Probability | | A masses of a leptons deduced from a representation of a probability density
vector by a spinors. A massive W and Z bosons and a massless A boson are
obtained from a transformations for which a density vector is invariant.
| | Gunn Alex Quznetsov |
| 2004-05-06T02:45:50Z | | Shapes and Positions of Black Hole Shadows in Accretion Disks and Spin
Parameters of Black Holes | | Can we determine a spin parameter of a black hole by observation of a black
hole shadow in an accretion disk? In order to answer this question, we make a
qualitative analysis and a quantitative analysis of a shape and a position of a
black hole shadow casted by a rotating black hole on an optically thick
accretion disk and its dependence on an angular momentum of a black hole. We
have found black hole shadows with a quite similar size and a shape for largely
different black hole spin parameters and a same black hole mass. Thus, it is
practically difficult to determine a spin parameter of a black hole from a size
and a shape of a black hole shadow in an accretion disk. We newly introduce a
bisector axis of a black hole shadow named a shadow axis. For a rotating black
hole a shape and a position of a black hole shadow are not symmetric with
respect to a rotation axis of a black hole shadow. So, in this case the minimum
interval between a mass center of a black hole and a shadow axis is finite. An
extent of this minimum interval is roughly proportional to a spin parameter of
a black hole for a fixed inclination angle between a rotation axis of a black
hole and a direction of an observer. In order to measure a spin parameter of a
black hole, if a shadow axis is determined observationally, it is crucially
important to determine a position of a mass center of a black hole in a region
of a black hole shadow.
| | Rohta Takahashi |
| 2005-02-19T23:20:22Z | | When a C*-algebra is a coefficient algebra for a given endomorphism | | The paper presents a criterion for a C*-algebra to be a coefficient algebra
associated with a given endomorphism
| | V. I. Bakhtin A. V. Lebedev |
| 1995-12-01T00:00:00Z | | Relative cohomology of Banach algebras | | Let $A$ be a Banach algebra, not necessarily unital, and let $B$ be a closed
subalgebra of $A$. We establish a connection between the Banach cyclic
cohomology group $ {\cal{HC}}^n(A)$ of $A$ and the Banach $B$-relative cyclic
cohomology group $ {\cal{HC}}^n_B(A) $ of $A$. We prove that, for a Banach
algebra $A$ with a bounded approximate identity and an amenable closed
subalgebra $B$ of $A$, up to topological isomorphism, ${\cal{HC}}^n(A) =
{\cal{HC}}^n_B(A) $ for all $n \ge 0$. We also establish a connection between
the Banach simplicial or cyclic cohomology groups of $A$ and those of the
quotient algebra $A/I$ by an amenable closed bi-ideal $I$. The results are
applied to the calculation of these groups for certain operator algebras,
including von Neumann algebras.
| | Zinaida A. Lykova |
| 2010-04-21T16:09:45Z | | On the Lower Central Series Quotients of a Graded Associative Algebra | | We continue the study of the lower central series L_i(A) and its successive
quotients B_i(A) of a noncommutative associative algebra A, defined by
L_1(A)=A, L_{i+1}(A)=[A,L_i(A)], and B_i(A)=L_i(A)/L_{i+1}(A). We describe
B_{2}(A) for A a quotient of the free algebra on two or three generators by the
two-sided ideal generated by a generic homogeneous element. We prove that it is
isomorphic to a certain quotient of Kaehler differentials on the non-smooth
variety associated to the abelianization of A.
| | Martina Balagovic Anirudha Balasubramanian |
| 2008-07-03T01:23:36Z | | Gorenstein Approximation, Dual Filtrations and Applications | | We give a two step method to study certain questions regarding associated
graded module of a Cohen-Macaulay (CM) module $M$ w.r.t an $\m$-primary ideal
$\A$ in a complete Noetherian local ring $(A,\m)$. The first step, we call it
Gorenstein approximation, enables us to reduce to the case when both $A$, $ \GA
= \bigoplus_{n \geq 0} \A^n/\A^{n+1} $ are Gorenstein and $M$ is a maximal CM
$A$-module. The second step consists of analyzing the classical filtration
$\{\Hom_A(M,\A^n) \}_{\nZ}$ of the dual $\Hom_A(M,A)$. We give many
applications of this point of view. For instance let $(A,\m)$ be
equicharacteristic and CM. Let $a(G_\A(A))$ be the $a$-invariant of $\GA$. We
prove:
1. $a(G_\A(A)) = -\dim A$ iff $\A$ is generated by a regular sequence.
2. If $\A$ is integrally closed and $a(G_\A(A)) = -\dim A + 1$ then $\A$ has
minimal multiplicity.
We give an example of a non-CM local ring $(R,\n)$ with $a(G_\n(R)) = -\dim
R$. We extend to modules a result of Ooishi relating symmetry of $h$-vectors.
| | Tony J. Puthenpurakal |
| 2002-09-11T18:41:35Z | | Maps between non-commutative spaces | | We examine maps between noncommutative projective spaces. A surjection of
graded rings A-->A/J induces a closed immersion Proj(A/J)-->Proj(A). A
homomorphism f:A-->B between graded rings induces an affine map U --> Proj(A)
from a non-empty open subspace U of Proj(B). If A^{(n)} is the n-th Veronese
subalgebra of a graded ring A there is a map Proj(A)-->Proj(A^{(n)}); we
identify open subspaces on which this map is an isomorphism. Applying these
results when A is (a quotient of) a weighted polynomial ring produces a
non-commutative resolution of (a closed subscheme of) a weighted projective
space.
| | S. Paul Smith |
| 2008-07-31T16:20:22Z | | On a theorem of Shkredov | | We show that if A is a finite subset of an abelian group with additive energy
at least c|A|^3 then there is a subset L of A with |L|=O(c^{-1}\log |A|) such
that |A \cap Span(L)| >> c^{1/2}|A|.
| | Tom Sanders |
| 2003-03-09T12:17:09Z | | Recognizing dualizing complexes | | Let A be a noetherian local commutative ring and let M be a suitable complex
of A-modules. This paper proves that M is a dualizing complex for A if and only
if the trivial extension A \ltimes M is a Gorenstein Differential Graded
Algebra. As a corollary follows that A has a dualizing complex if and only if
it is a quotient of a Gorenstein local Differential Graded Algebra.
| | Peter Jorgensen |
| 2003-05-01T17:56:46Z | | Smarandache semirings, semifields and semivector spaces | | Generally, in any human field, a Smarandache Structure on a set A means a
weak structure W on A such that there exists a proper subset B which is
embedded with a stronger structure S. By proper subset one understands a set
included in A, different from the empty set, from the unit element if any, and
from A. These types of structures occur in our every day's life, that's why we
study them in this book.
Thus, as three particular cases:
1) A Smarandache semiring is a semiring A such that a proper subset B of A is
a semifield (with respect to the same induced operation). 2) A Smarandache
semifield is a semifield A such that a proper subset B of A is a k-semi
algebra, with respect to the same induced operations and an external operator.
3) A Smarandache semivector space is a semivector space A (over a semifield B)
which is a Smarandache semigroup.
| | W. B. Vasantha Kandasamy |
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