The singular values of the logarithmic potential transform on bound states spaces of Landau Hamiltonian

The singular values of the logarithmic potential transform on the generalized Bergmann space is calculated explicitly, too behavior in infinityComment: 16 page

Reduction principle for functionals of strong-weak dependent vector random fields

We prove the reduction principle for asymptotics of functionals of vector random fields with weakly and strongly dependent components. These functionals can be used to construct new classes of random fields with skewed and heavy-tailed distributions. Contrary to the case of scalar long-range dependent random fields, it is shown that the asymptotic behaviour of such functionals is not necessarily determined by the terms at their Hermite rank. The results are illustrated by an application to the first Minkowski functional of the Student random fields. Some simulation studies based on the theoretical findings are also presented.Comment: 31 pages, 5 figure

Reduction principle for functionals of vector random fields

We prove a version of the reduction principle for functionals of vector long-range dependent random fields. The components of the fields may have different long-range dependent behaviours. The results are illustrated by an application to the first Minkowski functional of the Fisher-Snedecor random fields. Simulation studies confirm the obtained theoretical results and suggest some new problems.Comment: 21 pages, 5 figure

External vertices for crystals of type A

We show that a vertex in the reduced crystal is i-external for a residue i if the defect is less than the absolute value of the i-component of the hub. We demonstrate the existence of a bound on the degree after which all vertices of a given defect d are external in at least one i-string. Combining this with the Chuang-Rouquier categorification for the simple modules of the cyclotomic Hecke algebras of type A and rank e, this would imply a version of Donovan's Conjecture for the cyclotomics. For e=2, we calculate an approximation to this bound.Comment: two figure

External Littelmann paths for crystals of type A

For the Kashiwara crystal of a highest weight representation of an affine Lie algebra of type A and rank e, with highest weight $\Lambda$, there is a labeling by multipartitions and by piecewise linear paths in the real weight space called Littelmann paths. Both labelings are constructed recursively, but since Kashiwara demonstrated that the crystals are isomorphic, there is a bijection between the labels. We choose a multicharge $(k_1,\dots,k_r)$, with $0 \leq k_1\leq k_2....\leq k_r \leq e-1$. We put $k_i$ in the node at the upper left corner of partition $i$ of the multipartition and let the residues from $\mathbb Z/ e \mathbb Z$ increase across rows and decrease down columns. For e=2, we call a multipartition residue-homogeneous if all nonzero rows end in nodes of the same residue and partitions with the same corner residue have first rows of the same parity. It is strongly residue homogeneous if each partition ends in a triangle of whose side has length one less than the first row of the next partition. In this paper we show that each such multipartition corresponds to a Littelmann path which is unidirectional in the sense that the projection of the the main part of the path to the coordinates of the fundamental weights consists of long paths all lying in either the second or fourth quadrant, separated by oscillating paths with a fixed integer oscillator. The path corresponding to such a multipartition can be constructed non-recursively using only integers describing the structure of the multipartition.Comment: 33 pages, 2 figures; removed case of level 1, broadened definition of strongly residue homogeneous, gave parameters for structure of Littelmann pat

On Some q-Analogues of the Natural Transform and Further Investigations

Some q-analogues of classical integral transforms have recently been investigated by many authors in diverse citations. The q-analogues of the Natural transform are not known nor used. In the present paper, we are concerned with definitions and investigations of the q-theory of the Natural transform and some applications. We present two types of q-analogues of the cited transform on given sets and get results of the nominated analogues for certain class of functions of special type. We declare here that given results are new and they complement recent known results related to q-Laplace and q-Sumudu transforms. Over and above, we present some supporting examples to illustrate effectiveness of the given results .Comment: 16 Page

Spin-Peierls Dimerization of a s=1/2 Heisenberg Antiferromagnet on Square Lattice

Dimerization of a spin-half Heisenberg antiferromagnet on a square lattice is investigated by taking unexpanded exchange couplings. Several dimerized configurations are considered some of which are shown to have lower ground state energies than others. In particular, the lattice deformations resulting in alternate strong and weak couplings along both the principal axes of a square lattice are shown to result in a larger gain in energy. In addition, a `columnar' configuration is shown to have a lower ground state energy and a faster increase in the energy gap parameter than a `staggered' configuration. The inclusion of unexpanded exchange coupling leads to a power law behaviour for the magnetic energy gain and the spin-Peierls gap, which is qualitatively different from that reported earlier. Instead of varying as $\delta ^x$, the two quantities are shown proportional to $\delta ^\nu / |ln \delta|.$ It is thus proposed that the logarithmic correction, that was regarded as an outcome of including umklapp processes for small distortions, can also be a direct consequence of using an un-truncated spin-spin exchange interaction. The calculations, which employ the coupled cluster method, lead to a conclusion result that the dimerization of a spin-half Heisenberg antiferromagnet on a sqaure lattice is unconditional.Comment: 10 pages, Latex, 6 figures, The revised results bring out a different power law behaviour for the spin-Peierls transition. They also show that plaquette configuration is the most stable mode of dimerization of a spin-half Heisenberg antiferromagne

Thermal chaotic mixing: comparison of constant wall temperature and constant heat flux boundary conditions

In a recent paper (El Omari and Le Guer, IJHMT, 53, 2010) we have investigated mixing and heat transfer enhancement in a mixer composed of two circular rods maintained vertically in a cylindrical tank. The rods and tank can rotate around their revolution axes while their surfaces were maintained at a constant temperature. In the present study we investigate the differences in the thermal mixing process arising from the utilization of a constant heat flux as a boundary condition. The study concerns a highly viscous fluid with a high Prandtl number $Pr = 10,000$ for which this chaotic mixer is suitable. Chaotic flows are obtained by imposing temporal modulations of the rotational velocities of the walls. By solving numerically the flow and energy equations, we studied the effects of different stirring protocols and flow configurations on the efficiency of mixing and heat transfer. For this purpose, we used different statistical indicators as tools to characterize the evolution of the fluid temperature and its homogenization. Fundamental differences have been reported between these two modes of heating or cooling: while the mixing with an imposed temperature results in a homogeneous temperature field, with a fixed heat flux we observe a constant difference between the maximal and minimal temperatures that establish in the fluid; the extent of this difference is governed by the efficiency of the mixing protocol

Thermal properties of ferrimagnetic systems

The heat capacity of some ferrimagnets has additional structures like a shoulder in the Schottky-like peak, or emergence of a second peak when an external magnetic field is applied. It is shown here that as long as spin wave-spin wave interactions are ignored in a ferrimagnet, the ferromagnetic and antiferromagnetic elementary excitation spectra give rise to two independent heat capacity peaks, one enveloped by the other, which add up to give the peak for the total system. Taking this into account helps understand the additional structures in the peaks. Moreover, the classification of ferrimagnets into predominantly antiferromagnetic, ferromagnetic, or a mixture of the two is shown to be validated by studying them under additional influences like dimerization and frustration. Because these two are shown to influence the ferromagnetic and antiferromagnetic dispersion relations - and hence the quantities like heat capacity and magnetic susceptibility - by different amounts, the characterisation of ferrimagnetic systems ($1,1/2$), ($3/2,1$) and ($3/2,1/2$) is brought out more clearly. Both these influences enhance antiferromagnetic character.Comment: 13 pages, latex, 11 postscript figure

Dimerization of Ferrimagnets on Chains and Square Lattices

A linear spin wave analysis of dimerization of alternating Heisenberg system with spins $s_{1}$ and $s_{2}$ on linear chain as well as square lattice is presented. Among the several possible dimerized configurations considered in two dimensions the plaquette configuration is found to be energetically the most favored one. Inclusion of a variable nearest neighbor exchange coupling $J(a)=\frac{J}{a}$ leads to a uniform power law behavior: that is to say, the same $\delta$-dependence is found (i) in chains as well as in square lattices; (ii) in systems consisting of different pairs of spins $s_{1}$ and $s_{2}$; (iii) for the magnetic energy gain, the energy gap, the energy of the gapped magnetic excitation mode as well as for the sublattice magnetization; (iv) for all the configurations of the square lattice; and (v) in the entire range of $\delta :$ $(0\leq \delta <1)$. The variable exchange coupling also allows \ the energy of the gapped excitation spectrum to be $\delta$-dependent even in the linear spin wave theory.Comment: 10 pages, 14 Postscript figures, RevTex forma