Semiempirical QSAR study and ligand receptor interaction of estrogens

Softness values E_n of estrogen derivatives and softness values E_m of receptor lysine, histidine, tyrosine and cysteine have been evaluated by Klopman equation. The required parameters for the solution of Klopman equation have been calculated with the help of PM3 method. The difference E_nm between E_n and E_m has been derived for QSAR study. The estrogen derivatives have been divided into four different sets on the basis of their structural similarities, and their biological activity taken from literature in terms of relative binding affinity (RBA). The QSAR study shows that, E_nm values provide good relationship with biological activity.     

Coherent states of theq-Weyl algebra

New coherent states of theq-Weyl algebraAA –qA A = 1,0 <q < 1, are constructed. They are defined as eigenstates of the operatorA which is the lowering operator for nonhighest weight representations describing positive energy states. Depending on whether the positive spectrum is discrete or continuous, these coherent states are related either to the bilateral basic hypergeometric series or to some integrals over them. The free particle realization of theq-Weyl algebra whenA A d²/dx² is used for illustrations.On leave of absence from the Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia.     

The collapse of the wave function

Probability distributions are seen to be observer dependent. The probability function can be put into an observer-dependent form. This eliminates the acausal behavior of the collapse of the wave function.     

The chiral determinant and the eta invariant

For { _y },y, a one parameter family of invertible Weyl operators of possibly non-zero index acting on spinors over an even dimensional compact manifoldX, we express the phase of the chiral determinant det _– in terms of the invariant of a Dirac operator acting on spinors over ×X.Supported in part by NSF Grant No. PHY-82-15249Supported in part by NSF Grant PHY 8605978 and the Robert A. Welch Foundation     

Representation theory of generalized deformed oscillator algebras

The representation theory of the generalized deformed oscillator algebras (GDOA's) is developed. GDOA's are generated by the four operators {1, a, a , N}. Their commutators and Hermiticity properties are those of the boson oscillator algebra, except for [a, a ] _q = G(N), where [a, b] _q = ab – q ba and G(N) is a Hermitian, analytic function. The unitary irreductible representations are obtained by means of a Casimir operator C and the semi-positive operator a a. They may belong to one out of four classes: bounded from below (BFB), bounded from above (BFA), finite-dimentional (FD), unbounded (UB). Some examples of these different types of unirreps are given.     

Long-range correlations at depinning transitions

Semi-infinite systems are considered with long-range surface fields B _z ^–(1+r) for large distancesz from the surface. The influence of such fields on the global phase diagram and on the critical singularities of depinning transitions is studied within Landau theory. For |B|0, the correlation length diverges as b ^–1/2 withb=|Bln|B^–(1+r). For finiteB, t ^v withv =(2+r)/(2+2r) wheret measures the distance from bulk coexistence. In the latter case, a Ginzburg criterion leads to the upper critical dimensiond ^*=(2+3r)/(2+r).     

On the Hamiltonian interpolation of near-to-the identity symplectic mappings with application to symplectic integration algorithms

We reconsider the problem of the Hamiltonian interpolation of symplectic mappings. Following Moser's scheme, we prove that for any mapping , analytic and -close to the identity, there exists an analytic autonomous Hamiltonian system, H such that its time-one mapping _H differs from by a quantity exponentially small in 1/. This result is applied, in particular, to the problem of numerical integration of Hamiltonian systems by symplectic algorithms; it turns out that, when using an analytic symplectic algorithm of orders to integrate a Hamiltonian systemK, one actually follows exactly, namely within the computer roundoff error, the trajectories of the interpolating Hamiltonian H, or equivalently of the rescaled Hamiltonian K=^-1H, which differs fromK, but turns out to be ⁵ close to it. Special attention is devoted to numerical integration for scattering problems.     

A μSR study of spin density wave condensation in Cr85Mo15

Zero field SR spectra from Cr₈₅Mo₁₅ are well described by the sum of a lightly damped (0.02s^–1<₁<0.2s^–1) and a heavily damped (2s^–1<₂<15s^–1) exponential. The temperature dependence of these components is discussed in relation to the condensation of the incommensurate spin density wave and the onset of the antiferromagnetic state in this Cr-like alloy below T_N=120K. Evidence is presented for the nucleation of the spin density wave at temperatures greater than 1.5T_N.     

Clifford algebras and Hestenes spinors

This article reviews Hestenes' work on the Dirac theory, where his main achievement is a real formulation of the theory within thereal Clifford algebra Cl _1,3 M₂ (H). Hestenes invented first in 1966 hisideal spinors and later 1967/75 he recognized the importance of hisoperator spinors Cl _1,3 ⁺ M₂ (C).This article starts from the conventional Dirac equation as presented with matrices by Bjorken-Drell. Explicit mappings are given for a passage between Hestenes' operator spinors and Dirac's column spinors. Hestenes' operator spinors are seen to be multiples of even parts of real parts of Dirac spinors (real part in the decompositionC Cl _1,3 andnot inC M₄ (R)=M₄ (C)). It will become apparent that the standard matrix formulation contains superfluous parts, which ought to be cut out by Occam's razor.Fierz identities of bilinear covariants are known to be sufficient to study the non-null case but are seen to be insufficient for the null case ₀=0, ₀₀₁₂₃=0. The null case is thoroughly scrutinized for the first time with a new concept calledboomerang. This permits a new intrinsically geometric classification of spinors. This in turn reveals a new class of spinors which has not been discussed before. This class supplements the spinors of Dirac, Weyl, and Majorana; it describes neither the electron nor the neutron; it is awaiting a physical interpretation and a possible observation.Projection operators P_±, _± are resettled among their new relatives in End(Cl _1,3 ). Finally, a new mapping, calledtilt, is introduced to enable a transition from Cl _1,3 to the (graded) opposite algebra Cl _3,1 without resorting to complex numbers, that is, not using a replacement i.     

Infrared lattice bands of some pearls

From analysis of anisotropical lattice bands properties of 50 reflection spectra both of the CO stretching and bending bands measured from some pearl (Ca⁺⁺CO ₃ ^–– or Ca⁺⁺HCO ₃ ^–– layer) we discussed following subjects.i) Quantized properties present both in reflectivity and in energy. ii) classifications of the Optical Activity. iii) Polar distributions of the CO₃ oscillators in Ca⁺⁺CO ₃ ^–– surface mono-layer. iv) Force constants of these oscillators. v) Step variation of the dipolemoment and their influences to the degree of Optical Activity. vi) Two types of hysteresis loops of the values of Y_N (M_2Jbend ()/M_1Jstret. ()) derived from the oscillators which are at innert-state, at weak active-state and at active-state.     

Замечание К теории по степенного возникновения подви жных слоев в плазме инертных газов

[1] t _B , t _B . , t _B , . .

---

A note on the theory of the successive production of moving striations in the plasma of inert gases

Approximate expressions are derived on the basis of Pekárek's theoretical paper [1] for the period of the maximum t_B of a wave packet produced by the passage of a wave of stratification before the aperture of a photomultiplier, and for its time width in the half-height t_B. The relaxation time of a wave of stratification, following from the theory [1], can thus be calculated by means of the experimentally measured velocity of motion of the maximum of a wave packet u and its width t_B. The calculation is supplemented by numerical data on the magnitude of errors committed by using approximate expressions.

     

Mean-Field Critical Behavior for the Contact Process

The contact process is a model of spread of an infectious disease. Combining with the result of ref. 1, we prove that the critical exponents take on the mean-field values for sufficiently high dimensional nearest-neighbor models and for sufficiently spread-out models with d>4:()– _c as _c and ()( _c–)^–1 as _c, where () and () are the spread probability and the susceptibility of the infection respectively, and _c is the critical infection rate. Our results imply that the upper critical dimension for the contact process is at most 4.     

Neutron diffraction studies of the premartensitic transformation B2 → B19′ in Ti49Ni51 single crystals

We have studied structural changes in the high-temperature B2-phase in a large single crystal at temperatures near the premartensitic transformation B2 B19. We are the first to observe an extra 1/2 (110) reflection in neutron diffraction patterns taken along the [110]_B2 direction as the sample is cooled below 420 K, but still far from the martensite start temperature (M_s=180 K). This extra reflection heralds the formation of long-range order in atomic displacements with wave vectorq=(1/2±)[110]2/a. Premartensitic diffraction effects (caused by the development and correlation of lattice waves of atomic displacements with wave vectorsq ₁2/a[1/3, 1/3, 0] andq ₁2/1[1/3, 1/3] that were clearly visible in this same single crystal before the martensitic transformation B2 R, appeared at even lower temperatures with substantially lower intensities.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 56–61, January, 1995.     

Spin-orbit coupling in the chlorobenzene molecule

The possible ways of drawing of the intensity of the S₀ T* transition in the chlorobenzene molecule are investigated. The effective spin-orbit coupling of either S* or S* states with the T* state leads to the out-of-plane polarized component of phosphorescence in the chlorobenzene. The in-plane polarized component cannot be explained by the mechanism under consideration — by drawing of intensity of the S₀ S₀* transitions through spin-orbit coupling of first order.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 134–138, August, 1974.     

Feasibility of an experiment to determine the branching ratio for the emission of a heavy neutrino after muon capture in3He

The triton energy of the muon capture reaction ³He t+v, where ³ He is the ground state of muonic³He, has been measured in order to investigate a possible heavy v admixture into the flavour with high sensitivity. ³ He has been formed via the pd fusion reaction by stopping ^– in an ionization chamber (IC) filled with an H/D gas mixture of 3% D concentration at a pressure of 161 bar. In a first short experiment 650 triton events were observed yielding an upper limit for the -heavy v mixing strength of 2.3×10^–3 atE _0v=60 MeV.     

Gentle perturbations

By introducing a specific type of perturbation,A, in the Hamiltonian, we define a class of gently perturbed states, ,A, of a canonical ensemble, . The perturbations are chosen so as to preserve a relationship of the form ,A constant ×. Applications in ergodic theory and phase transitions are described.     

EPR and Thermoluminescence in ZnO Single Crystals with Anionic Vacancies

The radiation defects created in hydrothermal ZnO–Li single crystals by irradiating them with electrons, protons, and highenergy ions have been investigated. The anionic vacancies (Fcenters) in ZnO are established to be the centers of radiationless recombination of the charge carriers with a photoionization energy of 2.3 eV (a signal of the photoEPR with the gfactor for the F⁺center: g = 1.9948 and g = 1.9963). The anionic vacancies in the form of the F and F⁺ states are a good reference of the electron and hole processes. The [F_Li]^×centers that correspond to the oxygen vacancies localized near the point defects Li_Zn are detected. In the temperature range 530–660 K, ZnO crystals display thermally stimulated processes such as the healing of anionic vacancies (530–630 K) and the disappearance of the [F_Li]^×centers (610–660 K).     

Deformed harmonic oscillators: Coherent states and Bargmann representations

Generalizing the case of the usual harmonic oscillator, we look for Bargmann representations corresponding to deformed harmonic oscillators. Deformed harmonic oscillator algebras are generated by four operators a, a , N and the unity 1 such as [a, N] = a, [a , N] = –a , a a = (N) and aa = (N + 1). We discuss the conditions of existence of a scalar product expressed with a true integral on the space spanned by the e igenstates of a (or a ). We give various examples, in particular we consider functions that are linear combinations of q ^N, q ^–N and unity and that correspond to q-oscillators with Fock-representations or with non-Fock-representations.     

Some Remarks on a Nongeometrical Interpretation of Gravity and the Flatness Problem

In a nongeometrical interpretation of gravity,the metric g(x) = + (x)is interpreted as an effective metric, whereas(x) is interpreted as afundamental gravitational field, propagated in spacetime which isactually flat. Some advantages and disadvantages of suchan interpretation are discussed. The main advantage isa natural resolution of the flatness problem.