40 research outputs found
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
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
On Orbits of the Ring Zmn under Action of the Group SL(m, Zn)
We consider the action of the finite matrix group SL(m,Zn ) on the ring Zmn. We determine orbits of this action for n arbitrary natural number. It is a generalization of the task which was studied by A. A. Kirillov for m = 2 and n prime number
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
Gaussian cubature arising from hybrid characters of simple Lie groups
Lie groups with two different root lengths allow two mixed sign homomorphisms
on their corresponding Weyl groups, which in turn give rise to two families of
hybrid Weyl group orbit functions and characters. In this paper we extend the
ideas leading to the Gaussian cubature formulas for families of polynomials
arising from the characters of irreducible representations of any simple Lie
group, to new cubature formulas based on the corresponding hybrid characters.
These formulas are new forms of Gaussian cubature in the short root length case
and new forms of Radau cubature in the long root case. The nodes for the
cubature arise quite naturally from the (computationally efficient) elements of
finite order of the Lie group.Comment: 23 pages, 3 figure
Influence of Moisture Content on the Application of ND and MD Tests to Various Species of Timber Elements
Variations in environmental conditions can affect the structural performance of
timber components and constructions. Especially in case of historic masonry buildings, where
timber elements can be found either in roof or floor structures, intrinsic defects (e.g., knots,
cracks, degradation), as well as the surrounding environmental conditions (e.g., temperature
and moisture) can play an important role in the assessment of the mechanical response of the
elements. In this connection, non-destructive (ND) and minor-destructive (MD) procedures are
used to investigate the onsite conditions of wood, which are commonly based on either tool
penetration resistance or wave transmission devices. In the paper, the influence of moisture
content (MC) measured with various devices on a series of both old and new timber elements
was compared. The elements made of various wood species (mainly red fir, but also white fir,
pine and larch) were subjected to laboratory ND and MD testing by three research groups.
Results showed the low influence of the MC on MD tests (i.e., resistance drilling and pin
penetration) in comparison to the ND (i.e., sonic/ultrasonic) ones. Correlation relationships
are provided, which illustrate and approximatively quantify the effect of MC for the
experimentally investigated conditions and test equipment
Effect of environmental conditions on species composition of macrophytes – study from two distinct biogeographical regions of Central Europe
The relationship between macrophytes and environmental conditions of lotic and lentic
habitats was studied within two distinct biogeographical regions (Pannonian and
Carpathian) represented by two model areas (Borská nížina lowland and Turčianska kotlina
basin) in 2011. Altogether, 72 taxa of macrophytes were found within both studied
biogeographical regions, while almost a third of them grew only in one from the regions.
Species-environmental variables relationship was studied by Canonical Correspondence
Analysis (forward selection), which revealed that three and seven environmental variables
explaining 10.35% and 24.45% of variance of species data had significant effect on species
composition of macrophytes in the Pannonian and Carpathian region, respectively. Flow
regime and the portion of fine substrate on the bottom are the main drivers of species
composition-environmental condition relationships and explained 3.57% and 6.21% of
variance in the Pannonian and Carpathian region, respectively. However, the highest values
of pure effect on species composition was detected in case of Altitude (Pannonian region;
3.81%) and Connectivity (Carpathian region; 3.19). Based on the variation partitioning,
landscape variables (including geographical variables; Pannonian region; 6.8%) and
hydrological variables (including morphological variables of the bottom; Carpathian
region; 11.3%) explained a bigger portion of the variability of macrophytes in regions
than the other groups of environmental variables