278 research outputs found
Тракторобудування в Україні в контексті світового розвитку
В данній статті автором зроблена спроба відобразити шлях розвитку галузі тракторобудування
України від зародження і до 80-х років ХХ століття на фоні розвитку тракторобудування
провідних країн світу.In this article the author makes the attempt to display a way of development of tractor construction in
Ukraine from origin and to the 80th years of ХХ century on the background of leading countries of the
world tractor construction development
Symplectic duality of Symmetric Spaces
We show that between symmetric spaces of different types there exists a bi-symplectic map. We compute the duality map explicitely by using the theory of Jordan Algebra
A tour on Hermitian symmetric manifolds
Hermitian symmetric manifolds are Hermitian manifolds which are homogeneous
and such that every point has a symmetry preserving the Hermitian structure.
The aim of these notes is to present an introduction to this important class of
manifolds, trying to survey the several different perspectives from which
Hermitian symmetric manifolds can be studied.Comment: 56 pages, expanded version. Written for the Proceedings of the
CIME-CIRM summer course "Combinatorial Algebraic Geometry". Comments are
still welcome
Congruences concerning Jacobi polynomials and Ap\'ery-like formulae
Let be a prime. We prove congruences modulo for sums of the
general form and
with . We also consider the
special case of the former sum, where the congruences hold
modulo .Comment: to appear in Int. J. Number Theor
Spherical designs and lattices
In this article we prove that integral lattices with minimum <= 7 (or <= 9)
whose set of minimal vectors form spherical 9-designs (or 11-designs
respectively) are extremal, even and unimodular. We furthermore show that there
does not exist an integral lattice with minimum <=11 which yields a 13-design.Comment: The final publication is available at
http://link.springer.com/article/10.1007%2Fs13366-013-0155-
Multiple CSLs for the body centered cubic lattice
Ordinary Coincidence Site Lattices (CSLs) are defined as the intersection of
a lattice with a rotated copy of itself. They are useful for
classifying grain boundaries and have been studied extensively since the mid
sixties. Recently the interests turned to so-called multiple CSLs, i.e.
intersections of rotated copies of a given lattice , in particular
in connection with lattice quantizers. Here we consider multiple CSLs for the
3-dimensional body centered cubic lattice. We discuss the spectrum of
coincidence indices and their multiplicity, in particular we show that the
latter is a multiplicative function and give an explicit expression of it for
some special cases.Comment: 4 pages, SSPCM (31 August - 7 September 2005, Myczkowce, Poland
The flavor symmetry in the standard model and the triality symmetry
A Dirac fermion is expressed by a 4 component spinor which is a combination
of two quaternions and which can be treated as an octonion. The octonion
possesses the triality symmetry, which defines symmetry of fermion spinors and
bosonic vector fields.
The triality symmetry relates three sets of spinors and two sets of vectors,
which are transformed among themselves via transformations , and . If the electromagnetic (EM) interaction is
sensitive to the triality symmetry, i.e. EM probe selects one triality sector,
EM signals from the 5 transformed world would not be detected, and be treated
as the dark matter. According to an astrophysical measurement, the ratio of the
dark to ordinary matter in the universe as a whole is almost exactly 5. We
expect quarks are insensitive to the triality, and triality will appear as
three times larger flavor degrees of freedom in the lattice simulation.Comment: 16 pages 8 figures, To be published in International Journal of
Modern Physics
Coincidence rotations of the root lattice
The coincidence site lattices of the root lattice are considered, and
the statistics of the corresponding coincidence rotations according to their
indices is expressed in terms of a Dirichlet series generating function. This
is possible via an embedding of into the icosian ring with its rich
arithmetic structure, which recently (arXiv:math.MG/0702448) led to the
classification of the similar sublattices of .Comment: 13 pages, 1 figur
Unified N=2 Maxwell-Einstein and Yang-Mills-Einstein Supergravity Theories in Four Dimensions
We study unified N=2 Maxwell-Einstein supergravity theories (MESGTs) and
unified Yang-Mills Einstein supergravity theories (YMESGTs) in four dimensions.
As their defining property, these theories admit the action of a global or
local symmetry group that is (i) simple, and (ii) acts irreducibly on all the
vector fields of the theory, including the ``graviphoton''. Restricting
ourselves to the theories that originate from five dimensions via dimensional
reduction, we find that the generic Jordan family of MESGTs with the scalar
manifolds [SU(1,1)/U(1)] X [SO(2,n)/SO(2)X SO(n)] are all unified in four
dimensions with the unifying global symmetry group SO(2,n). Of these theories
only one can be gauged so as to obtain a unified YMESGT with the gauge group
SO(2,1). Three of the four magical supergravity theories defined by simple
Euclidean Jordan algebras of degree 3 are unified MESGTs in four dimensions.
Two of these can furthermore be gauged so as to obtain 4D unified YMESGTs with
gauge groups SO(3,2) and SO(6,2), respectively. The generic non-Jordan family
and the theories whose scalar manifolds are homogeneous but not symmetric do
not lead to unified MESGTs in four dimensions. The three infinite families of
unified five-dimensional MESGTs defined by simple Lorentzian Jordan algebras,
whose scalar manifolds are non-homogeneous, do not lead directly to unified
MESGTs in four dimensions under dimensional reduction. However, since their
manifolds are non-homogeneous we are not able to completely rule out the
existence of symplectic sections in which these theories become unified in four
dimensions.Comment: 47 pages; latex fil
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