1,389 research outputs found
(Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms
Four families of special functions, depending on n variables, are studied. We
call them symmetric and antisymmetric multivariate sine and cosine functions.
They are given as determinants or antideterminants of matrices, whose matrix
elements are sine or cosine functions of one variable each. These functions are
eigenfunctions of the Laplace operator, satisfying specific conditions at the
boundary of a certain domain F of the n-dimensional Euclidean space. Discrete
and continuous orthogonality on F of the functions within each family, allows
one to introduce symmetrized and antisymmetrized multivariate Fourier-like
transforms, involving the symmetric and antisymmetric multivariate sine and
cosine functions.Comment: 25 pages, no figures; LaTaX; corrected typo
Six types of functions of the Lie groups O(5) and G(2)
New families of -functions are described in the context of the compact
simple Lie groups O(5) and G(2). These functions of two real variables
generalize the common exponential functions and for each group, only one family
is currently found in the literature. All the families are fully characterized,
their most important properties are described, namely their continuous and
discrete orthogonalities and decompositions of their products.Comment: 25 pages, 13 figure
Image Sampling with Quasicrystals
We investigate the use of quasicrystals in image sampling. Quasicrystals
produce space-filling, non-periodic point sets that are uniformly discrete and
relatively dense, thereby ensuring the sample sites are evenly spread out
throughout the sampled image. Their self-similar structure can be attractive
for creating sampling patterns endowed with a decorative symmetry. We present a
brief general overview of the algebraic theory of cut-and-project quasicrystals
based on the geometry of the golden ratio. To assess the practical utility of
quasicrystal sampling, we evaluate the visual effects of a variety of
non-adaptive image sampling strategies on photorealistic image reconstruction
and non-photorealistic image rendering used in multiresolution image
representations. For computer visualization of point sets used in image
sampling, we introduce a mosaic rendering technique.Comment: For a full resolution version of this paper, along with supplementary
materials, please visit at
http://www.Eyemaginary.com/Portfolio/Publications.htm
Spectral collocation methods
This review covers the theory and application of spectral collocation methods. Section 1 describes the fundamentals, and summarizes results pertaining to spectral approximations of functions. Some stability and convergence results are presented for simple elliptic, parabolic, and hyperbolic equations. Applications of these methods to fluid dynamics problems are discussed in Section 2
Three variable exponential functions of the alternating group
New class of special functions of three real variables, based on the
alternating subgroup of the permutation group , is studied. These
functions are used for Fourier-like expansion of digital data given on lattice
of any density and general position. Such functions have only trivial analogs
in one and two variables; a connection to the functions of is shown.
Continuous interpolation of the three dimensional data is studied and
exemplified.Comment: 10 pages, 3 figure
A well-posed optimal spectral element approximation for the Stokes problem
A method is proposed for the spectral element simulation of incompressible flow. This method constitutes in a well-posed optimal approximation of the steady Stokes problem with no spurious modes in the pressure. The resulting method is analyzed, and numerical results are presented for a model problem
High granularity tracker based on a Triple-GEM optically read by a CMOS-based camera
The detection of photons produced during the avalanche development in gas
chambers has been the subject of detailed studies in the past. The great
progresses achieved in last years in the performance of micro-pattern gas
detectors on one side and of photo-sensors on the other provide the possibility
of making high granularity and very sensitive particle trackers. In this paper,
the results obtained with a triple-GEM structure read-out by a CMOS based
sensor are described. The use of an He/CF (60/40) gas mixture and a
detailed optimization of the electric fields made possible to obtain and very
high GEM light yield. About 80 photons per primary electron were detected by
the sensor resulting in a very good capability of tracking both muons from
cosmic rays and electrons from natural radioactivity
On E-functions of Semisimple Lie Groups
We develop and describe continuous and discrete transforms of class functions
on a compact semisimple, but not simple, Lie group as their expansions into
series of special functions that are invariant under the action of the even
subgroup of the Weyl group of . We distinguish two cases of even Weyl groups
-- one is the direct product of even Weyl groups of simple components of ,
the second is the full even Weyl group of . The problem is rather simple in
two dimensions. It is much richer in dimensions greater than two -- we describe
in detail transforms of semisimple Lie groups of rank 3.Comment: 17 pages, 2 figure
Four dimensional Lie symmetry algebras and fourth order ordinary differential equations
Realizations of four dimensional Lie algebras as vector fields in the plane
are explicitly constructed. Fourth order ordinary differential equations which
admit such Lie symmetry algebras are derived. The route to their integration is
described.Comment: 12 page
- …