Aggregation of Capital and Its Substitution with Energy

Controversy continues over the question of whether capital and energy are substitutes or complements. The authors find that the answer to the question partly depends on the aggregation of building capital and machinery capital into an aggregate input called capital. The authors' empirical results reject this aggregation. When building and machinery capital are treated as separate inputs, they find that machinery capital and energy are substitutes, while building capital and energy are complements. For policy purposes, this result implies that a rise in the price of energy will reduce building capital formation, while it will increase machinery capital formation.

A comprehensive computer program for predicting solar cell performance

Comprehensive computer program for predicting solar cell performanc

Exact Solution of Semi-Flexible and Super-Flexible Interacting Partially Directed Walks

We provide the exact generating function for semi-flexible and super-flexible interacting partially directed walks and also analyse the solution in detail. We demonstrate that while fully flexible walks have a collapse transition that is second order and obeys tricritical scaling, once positive stiffness is introduced the collapse transition becomes first order. This confirms a recent conjecture based on numerical results. We note that the addition of an horizontal force in either case does not affect the order of the transition. In the opposite case where stiffness is discouraged by the energy potential introduced, which we denote the super-flexible case, the transition also changes, though more subtly, with the crossover exponent remaining unmoved from the neutral case but the entropic exponents changing

Two parameter Deformed Multimode Oscillators and q-Symmetric States

Two types of the coherent states for two parameter deformed multimode oscillator system are investigated. Moreover, two parameter deformed $gl(n)$ algebra and deformed symmetric states are constructed.Comment: LaTeX v1.2, 14 pages with no figure

A double bounded key identity for Goellnitz's (big) partition theorem

Given integers i,j,k,L,M, we establish a new double bounded q-series identity from which the three parameter (i,j,k) key identity of Alladi-Andrews-Gordon for Goellnitz's (big) theorem follows if L, M tend to infinity. When L = M, the identity yields a strong refinement of Goellnitz's theorem with a bound on the parts given by L. This is the first time a bounded version of Goellnitz's (big) theorem has been proved. This leads to new bounded versions of Jacobi's triple product identity for theta functions and other fundamental identities.Comment: 17 pages, to appear in Proceedings of Gainesville 1999 Conference on Symbolic Computation

Q-power function over Q-commuting variables and deformed XXX, XXZ chains

We find certain functional identities for the Gauss q-power function of a sum of q-commuting variables. Then we use these identities to obtain two-parameter twists of the quantum affine algebra U_q (\hat{sl}_2) and of the Yangian Y(sl_2). We determine the corresponding deformed trigonometric and rational quantum R-matrices, which then are used in the computation of deformed XXX and XXZ Hamiltonians.Comment: LaTeX, 12 page

dS-AdS structures in the non-commutative Minkowski spaces

We consider a family of non-commutative 4d Minkowski spaces with the signature (1,3) and two types of spaces with the signature (2,2). The Minkowski spaces are defined by the common reflection equation and differ in anti-involutions. There exist two Casimir elements and the fixing of one of them leads to non-commutative "homogeneous" spaces $H_3$, $dS_3$, $AdS_3$ and light-cones. We present the quasi-classical description of the Minkowski spaces. There are three compatible Poisson structures - quadratic, linear and canonical. The quantization of the former leads to the considered Minkowski spaces. We introduce the horospheric generators of the Minkowski spaces. They lead to the horospheric description of $H_3$, $dS_3$ and $AdS_3$. The irreducible representations of Minkowski spaces $H_3$ and $dS_3$ are constructed. We find the eigen-functions of the Klein-Gordon equation in the terms of the horospheric generators of the Minkowski spaces. They give rise to eigen-functions on the $H_3$, $dS_3$, $AdS_3$ and light-cones.Comment: 31 pages, LateX, typos corrected, references adde

h analogue of Newton's binomial formula

In this letter, the $h$--analogue of Newton's binomial formula is obtained in the $h$--deformed quantum plane which does not have any $q$--analogue. For $h=0$, this is just the usual one as it should be. Furthermore, the binomial coefficients reduce to $\frac{n!}{(n-k)!}$ for $h=1$. \\ Some properties of the $h$--binomial coefficients are also given. \\ Finally, I hope that such results will contribute to an introduction of the $h$--analogue of the well--known functions, $h$--special functions and $h$--deformed analysis.Comment: 6 pages, latex Jounal-ref: J. Phys. A: Math. Gen. 31 (1998) L75

Quantum W-algebras and Elliptic Algebras

We define quantum W-algebras generalizing the results of Reshetikhin and the second author, and Shiraishi-Kubo-Awata-Odake. The quantum W-algebra associated to sl_N is an associative algebra depending on two parameters. For special values of parameters it becomes the ordinary W-algebra of sl_N, or the q-deformed classical W-algebra of sl_N. We construct free field realizations of the quantum W-algebras and the screening currents. We also point out some interesting elliptic structures arising in these algebras. In particular, we show that the screening currents satisfy elliptic analogues of the Drinfeld relations in U_q(n^).Comment: 26 pages, AMSLATE

(p,q)-Deformations and (p,q)-Vector Coherent States of the Jaynes-Cummings Model in the Rotating Wave Approximation

Classes of (p,q)-deformations of the Jaynes-Cummings model in the rotating wave approximation are considered. Diagonalization of the Hamiltonian is performed exactly, leading to useful spectral decompositions of a series of relevant operators. The latter include ladder operators acting between adjacent energy eigenstates within two separate infinite discrete towers, except for a singleton state. These ladder operators allow for the construction of (p,q)-deformed vector coherent states. Using (p,q)-arithmetics, explicit and exact solutions to the associated moment problem are displayed, providing new classes of coherent states for such models. Finally, in the limit of decoupled spin sectors, our analysis translates into (p,q)-deformations of the supersymmetric harmonic oscillator, such that the two supersymmetric sectors get intertwined through the action of the ladder operators as well as in the associated coherent states.Comment: 1+25 pages, no figure