Rotating filters permit wide range of optical pyrometry

Gear-driven dual filter disks of graduated density vary linearly with respect to rotation, allowing a wide range of photographic pyrometry. this technique is applicable in metallurgy, glass, plastics and refractory research, and crystallography

qq-graded Heisenberg algebras and deformed supersymmetries

The notion of $q$-grading on the enveloping algebra generated by products of q-deformed Heisenberg algebras is introduced for $q$ complex number in the unit disc. Within this formulation, we consider the extension of the notion of supersymmetry in the enveloping algebra. We recover the ordinary $\mathbb{Z}_2$ grading or Grassmann parity for associative superalgebra, and a modified version of the usual supersymmetry. As a specific problem, we focus on the interesting limit $q\to -1$ for which the Arik and Coon deformation of the Heisenberg algebra allows to map fermionic modes to bosonic ones in a modified sense. Different algebraic consequences are discussed.Comment: 2 figure

q-Analogue of Shock Soliton Solution

By using Jackson's q-exponential function we introduce the generating function, the recursive formulas and the second order q-differential equation for the q-Hermite polynomials. This allows us to solve the q-heat equation in terms of q-Kampe de Feriet polynomials with arbitrary N moving zeroes, and to find operator solution for the Initial Value Problem for the q-heat equation. By the q-analog of the Cole-Hopf transformation we construct the q-Burgers type nonlinear heat equation with quadratic dispersion and the cubic nonlinearity. In q -> 1 limit it reduces to the standard Burgers equation. Exact solutions for the q-Burgers equation in the form of moving poles, singular and regular q-shock soliton solutions are found.Comment: 13 pages, 5 figure

Formation of the high-affinity agonist state of the α1-adrenergic receptor at cold temperatures does not require a G-protein

AbstractTwo methods were employed to uncouple hepatic α1-adrenergic receptors from their associated G-protein (termed Gp) in order to determine wether locking of the α1-receptor in a high-affinity agonist state at cold temperatures (2°C) represents formation of a ternary complex. Uncoupling is defined as the inability to observe the GppNHp-sensitive, high-affinity agonist state of the receptor in [3H]prazosin competition binding studies performed at 25°C. The first method for achieving uncoupling involved brief alkalinization and resulted in greater 95% loss of several G-proteins. The second method involved proteolytic cleavage of either part or all of the α1-receptor coupling domain from the binding domain. Following either treatment, receptors were converted to the high-affinity agonist state at 2°C. Thus, while formation of the high-affinity state of the receptor at higher temperatures may require Gp, formation of this state at 2°C does not require Gp or even the entire α1-adregenic receptor

Uniqueness of the mass in the radiating regime

The usual approaches to the definition of energy give an ambiguous result for the energy of fields in the radiating regime. We show that for a massless scalar field in Minkowski space-time the definition may be rendered unambiguous by adding the requirement that the energy cannot increase in retarded time. We present a similar theorem for the gravitational field, proved elsewhere, which establishes that the Trautman-Bondi energy is the unique (up to a multiplicative factor) functional, within a natural class, which is monotonic in time for all solutions of the vacuum Einstein equations admitting a smooth ``piece'' of conformal null infinity Scri.Comment: 8 pages, revte

Normal Ordering for Deformed Boson Operators and Operator-valued Deformed Stirling Numbers

The normal ordering formulae for powers of the boson number operator $\hat{n}$ are extended to deformed bosons. It is found that for the `M-type' deformed bosons, which satisfy $a a^{\dagger} - q a^{\dagger} a = 1$, the extension involves a set of deformed Stirling numbers which replace the Stirling numbers occurring in the conventional case. On the other hand, the deformed Stirling numbers which have to be introduced in the case of the `P-type' deformed bosons, which satisfy $a a^{\dagger} - q a^{\dagger} a = q^{-\hat{n}}$, are found to depend on the operator $\hat{n}$. This distinction between the two types of deformed bosons is in harmony with earlier observations made in the context of a study of the extended Campbell-Baker-Hausdorff formula.Comment: 14 pages, Latex fil

Lattice Green Function (at 0) for the 4d Hypercubic Lattice

The generating function for recurrent Polya walks on the four dimensional hypercubic lattice is expressed as a Kampe-de-Feriet function. Various properties of the associated walks are enumerated.Comment: latex, 5 pages, Res. Report 1

(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

Boost-rotation symmetric type D radiative metrics in Bondi coordinates

The asymptotic properties of the solutions to the Einstein-Maxwell equations with boost-rotation symmetry and Petrov type D are studied. We find series solutions to the pertinent set of equations which are suitable for a late time descriptions in coordinates which are well adapted for the description of the radiative properties of spacetimes (Bondi coordinates). By calculating the total charge, Bondi and NUT mass and the Newman-Penrose constants of the spacetimes we provide a physical interpretation of the free parameters of the solutions. Additional relevant aspects on the asymptotics and radiative properties of the spacetimes considered, such as the possible polarization states of the gravitational and electromagnetic field, are discussed through the way