On the Variety Generated by Bounded Pseudo-BCK-Algebras

In the paper we prove that the equational class V(bp\mathbb BCK)\mathcal{V}(bp\mathbb {BCK}) generated by the class bp\mathbbBCKbp\mathbb{BCK} of all bounded pseudo-BCK-algebras is generated by its simple members. As a matter of fact, we prove that simple members of V(bp\mathbbBCK)\mathcal {V}(bp\mathbb{BCK}) just coincide with relative simple bounded pBCK-algebras. Moreover, as a byproduct we show that every simple bounded pBCK-algebra can be embedded into a simple integral residuated lattice.     

Simple Current Actions of Cyclic Groups

Permutation actions of simple currents on the primaries of a Rational Conformal Field Theory are considered in the framework of admissible weighted permutation actions. The solution of admissibility conditions is presented for cyclic quadratic groups: an irreducible WPA corresponds to each subgroup of the quadratic group. As a consequence, the primaries of a RCFT with an order n integral or half-integral spin simple current may be arranged into multiplets of length k² (where k is a divisor of n) or 3k² if the spin of the simple current is half-integral and k is odd.Mathematical Subject Classifications (2000). 81T40.Work supported by grant OTKA TS044839.     

Dimers on the kagome lattice I: Finite lattices

We report exact results on the enumeration of close-packed dimers on a finite kagome lattice with general asymmetric dimer weights under periodic and cylindrical boundary conditions. For symmetric dimer weights, the resulting dimer generating functions reduce to very simple expressions, and we show how the simple expressions can be obtained from the consideration of a spin-variable mapping.     

A modified Ashcroft pseudopotential: application to aluminium

Unified study of the different properties of metals clearly reveals the inadequacy of the empty-core Ashcroft pseudopotential even in the case of simple metals. In the present paper we propose a modification of the one-parameter Ashcroft pseudopotential by assuming the parameterr _c to be wave vector-dependent. This introduces a simple modification of the electron-ion pseudopotential in the reciprocal space. The corresponding potential in the configuration space shows that the abrupt change in the Coulomb potential atr=r _c is replaced by a continuous change spread over a small region near the core boundary. The present model has been used to make a unified study of Al and is found to be a significant improvement over the simple Ashcroft model. The agreement between the calculated and experimental values is found to be quite satisfactory.     

Simple algebras and Drinfeld doubles

The Drinfeld double structure underlying all the Cartan series of simple Lie algebras is discussed. The two solvable algebras that allow its definition are constructed enlarging each simple algebra of rank n with a central Abelian algebra of dimension n. In these solvable algebras, isomorphic to the two Borel subalgebras, a pairing can be built. The complete machinery of Drinfeld doubles is described in all details. This offers a new approach to the explicit construction of canonical quantum deformation of simple algebras and fixes uniquely, independently and differently from known conventions, canonical bases for all of them. The Drinfeld doubles for A _n and C _n are explicitly written. The full quantization of su(3) is discussed in terms of standard commutators as the A ₂ Drinfeld double requires. The text was submitted by the authors in English.     

Advanced metal alloy systems for massive high-current photocathodes

The physical principles of precise alloying are formulated with the aim of increasing the low quantum efficiency (QE) of suitable simple metals (Mg, Al, Cu) as well as of decreasing their electron work function (e φ) in the UV spectral range. The new approach provides valuable information for elucidating the origin of photoemission enhancement in bulk metal-based alloy systems. Bulk in-situ nanoclustering promises to be the most effective way of producing a much higher QE and a lower e φ in simple metals. In this article we show that the quantum efficiency of the metal-based alloys Mg–Ba, Al–Li, and Cu–BaO is considerably higher than the simple metals Mg, Al, and Cu, respectively.     

Correlation functions in the Itzykson-Zuber model

Then-point function for the integral over unitary matrices with Itzykson-Zuber measure is reduced to the integral over the Gelfand-Tzetlin table; the integrand (for genericn) is given by linear exponential times the rational function. Forn=2 and in some cases forn>2 later in fast is the polynomial and this allows to give an explicit and simple expression for all 2-point and a set ofn-point functions. For the most generaln-point function a simple linear differential equation is constructed.     

A comprehensive approach to an equation of state for hard spheres and Lennard-Jones fluids

We present a simple method of obtaining various equations of state for hard sphere fluid in a simple unifying way.We will guess equations of state by using suitable axiomatic functional forms (n=1,2,3,4,5) for surface tension S n m (r),r ≥ d/2 with intermolecular separation r as a variable,where m is an arbitrary real number (pole).Among the equations of state obtained in this way are Percus-Yevick,scaled particle theory and Carnahan-Starling equations of state.In addition,we have found a simple equation of state for the hard sphere fluid in the region that represents the simulation data accurately.It is found that for both hard sphere fluids as well as Lennard-Jones fluids,with m=3/4 the derived equation of state (EOS) gives results which are in good agreement with computer simulation results.Furthermore,this equation of state gives the Percus-Yevick (pressure) EOS for the m=0,the Carnahan-Starling EOS for m=4/5,while for the value of m=1 it corresponds to a scaled particle theory EOS.     

W-Algebra W(2, 2) and the Vertex Operator Algebra $${L(\frac{1}{2},\,0)\,\otimes\, L(\frac{1}{2},\,0)}$$

In this paper the W-algebra W(2, 2) and its representation theory are studied. It is proved that a simple vertex operator algebra generated by two weight 2 vectors is either a vertex operator algebra associated to an irreducible highest weight W(2, 2)- module or a tensor product of two simple Virasoro vertex operator algebras. Furthermore, we show that any rational, C ₂-cofinite and simple vertex operator algebra whose weight 1 subspace is zero, weight 2 subspace is 2-dimensional and with central charge c = 1 is isomorphic to . Supported by NSF grants and a research grant from the Committee on Research, UC Santa Cruz.     

Quantization and representation theory of finiteW algebras

In this paper we study the finitely generated algebras underlyingW algebras. These so called finiteW algebras are constructed as Poisson reductions of Kirillov Poisson structures on simple Lie algebras. The inequivalent reductions are labeled by the inequivalent embeddings ofsl ₂ into the simple Lie algebra in question. For arbitrary embeddings a coordinate free formula for the reduced Poisson structure is derived. We also prove that any finiteW algebra can be embedded into the Kirillov Poisson algebra of a (semi)simple Lie algebra (generalized Miura map). Furthermore it is shown that generalized finite Toda systems are reductions of a system describing a free particle moving on a group manifold and that they have finiteW symmetry. In the second part we BRST quantize the finiteW algebras. The BRST cohomology is calculated using a spectral sequence (which is different from the one used by Feigin and Frenkel). This allows us to quantize all finiteW algebras in one stroke. Examples are given. In the last part of the paper we study the representation theory of finiteW algebras. It is shown, using a quantum version of the generalized Miura transformation, that the representations of finiteW algebras can be constructed from the representations of a certain Lie subalgebra of the original simple Lie algebra. As a byproduct of this we are able to construct the Fock realizations of arbitrary finiteW algebras.     

Casimir Elements for Some Graded Lie Algebras and Superalgebras

We consider a class of Lie algebras L such that L admits a grading by a finite Abelian group so that each nontrivial homogeneous component is one-dimensional. In particular, this class contains simple Lie algebras of types A, C and D where in C and D cases the rank of L is a power of 2. We give a simple construction of a family of central elements of the universal enveloping algebra U(L). We show that for the A-type Lie algebras the elements coincide with the Gelfand invariants and thus generate the center of U(L). The construction can be extended to Lie superalgebras with the additional assumption that the group grading is compatible with the parity grading.     

Permion spectrum in a confined SU(n) quark model

An explicit form of a colour-singlet Fermion field is constructed from the operator solution of SU(n) Thirring model where the quark-fields are known to be confined in LSZ sense. In simple cases of massless quarks these ferions are free with zero mass and can be expressed as the antisymmetric composites of constituent quark fields. This simple exercise suggests an alternative to conventional two-dimensional QCD which seems to confine all Fermion including baryons by Schwinger mechanism.     

New investigations of technical rhodium and iridium catalysts in homogeneous phase employing para-hydrogen induced polarization

It is shown that the para-hydrogen induced polarization (PHIP) phenomenon in homogenous solution containing the substrate styrene is also observable employing simple inorganic systems of the form MCl₃·xH₂O (M=Rh, Ir) as catalyst. Such observation confirms that already very simple metal complexes enable the creation of PHIP signal enhancement in solution. This opens up new pathways to increase the sensitivity of NMR and MRT by PHIP enhancement using cost-effective catalysts and will be essential for further mechanistic studies of simple transition metal systems.     

Fano resonance and wave transmission through a chain structure with an isolated ring composed of defects

We consider a discrete model that describes a linear chain of particles coupled to an isolated ring composed of N defects. This simple system can be regarded as a generalization of the familiar Fano-Anderson model. It can be used to model discrete networks of coupled defect modes in photonic crystals and simple waveguide arrays in two-dimensional lattices. The analytical result of the transmission coefficient is obtained, along with the conditions for perfect reflections and transmissions due to either destructive or constructive interferences. Using a simple example, we further investigate the relationship between the resonant frequencies and the number of defects N, and study how to affect the numbers of perfect reflections and transmissions. In addition, we demonstrate how these resonance transmissions and refections can be tuned by one nonlinear defect of the network that possesses a nonlinear Kerr-like response.     

Cut-down method in the inductive limit decomposition of non-commutative tori,III: A complete answer in 3-dimension

We use the cut-down method and a multi-dimensional continued fraction approximation to prove that any simple 3-torus is an inductive limit of direct sums of four circle algebras. Consequently, simple 3-tori are classified by the orderedK ₀-group with distinguished order unit.     

Algorithmic information and simplicity in statistical physics

Applications of algorithmic information theory to statistical physics rely (a) on the fact that average conditional algorithmic information can be approximated by Shannon information and (b) on the existence ofsimple states described by short programs. More precisely, given a list ofN states with probabilities 0<p ₁ ≤ ... ≤ p _N , the average conditional algorithmic informationĪ to specify one of these states obeys the inequalityH≤ Ī<H+O(1), whereH=−Σp _j log₂ p _j andO(1) is a computer-dependent constant. We show how any universal computer can be slightly modified in such a way that (a) the inequality becomesH≤ Ī<H+1 and (b) states that are simple with respect to the original computer remain simple with respect to the modified computer, thereby eliminating the computer-dependent constant from statistical physics.     

Transport in cooperativeT−(e+t) Jahn-Teller systems

A cooperative electron-phonon system is considered which exhibits a triply degenerate electronic ground state in each unit cell. As a model substance a simple cubic crystal is taken where each Jahn-Teller molecule has an octahedral surrounding. TheT electronic ground state is linearly coupled toe andt type vibrations with thee coupling dominating. By a unitary transformation the electron-phonon system is approximately decoupled. The remaining cooperative electron-electron system displays transport properties which are discussed in terms of a modified Maradudin formalism. Thermal conductivity is calculated by linear response theory. It is shown that in the transformed picture the phonon heat current approximately is independent from the pseudo spin heat current and the total thermal conductivity is given as a simple superposition of both contributions.Supported by a grant from the Deutsche Forschungsgemeinschaft     

Simple and Efficient PML Algorithm for Truncating Nonlinear FDTD Domains Based on the Z -Transform Method

Based on the Z-transform method, a simple, efficient and unsplit-field implementation of the Stretched Coordinate Perfectly Matched Layer (SC-PML) is proposed for truncating the nonlinear dispersive Finite Difference Time Domain (FDTD) lattices. In addition, the nonlinear FDTD formulations using the Z-transform method are reformulated with the advantage of a simple derivative process. The proposed algorithm is validated through two numerical examples carried out in one dimensional and two dimensional domains which include Lorentz dispersion as well as Kerr and Raman nonlinearities.     

New hierarchies of knot polynomials from topological Chern-Simons gauge theory

In this Letter, we report on a study of the expectation values of Wilson loops in D=3 topological Chern-Simons theory associated with the fundamental representation of the simple Lie algebras SO(n) and Sp(n). The skein relations satisfied by these expectation values are derived by conformal field-theory techniques. New hierarchies of invariant polynomials for knots in S ³ can be derived from these relations (at least) up to ten crossings. The N=3 Akutsu-Wadati polynomials are a special case with G=SO(3). The expectation value of the Wilson loops for a couple of simple unknotted circles is identified to the Weyl character.Work supported in part by U.S. National Science Foundation Grant PHY8706501.Work supported in party by Chinese National Science Foundation through Nankai University.