The enveloping algebra of a covariant system

In an earlier work, Doplicher, Kastler and Robinson have examined a mathematical structure consisting of a pair (A, G), whereA is aC*-algebra andG is a locally compact automorphism group ofA. We call such a structure a covariant system. The enveloping von Neumann algebraA(A, G) of (A, G) is defined as a *-algebra of operator valued functions (called options) on the space of covariant representations of (A, G). The system (A, G) is canonically embedded in, and in fact generates, the von Neumann algebraA(A, G). Further we show there is a natural one-to-one correspondence between the normal *-representations ofA(A, G) and the proper covariant representations of (A, G). The relation ofA(A, G) to the covarainceC*-algebraC*(A, G) is also examined.     

紫外激光等选育生淀粉糖化酶高产菌株及其应用

以紫外线、LiCl、5氟尿嘧啶、HNO₂为诱变剂,黑曲霉Sx为出发菌株,选育出生淀粉糖化酶酶活力提高12%的突变株黑曲霉S’x制取黑曲霉S’x的原生质体,用HeNe激光照射,经反复筛选得到突变株黑曲霉Sy,其酶活力较出发菌株提高51%,而酸性蛋白酶活力降低45%并对其在农作物秸杆的应用进行了研究.     

Relative compatibility in conventional quantum mechanics

The notion of relative compability is introduced, according to which compatibility is construed as relative to individual quantum states. The compatibility domain of two observablesA, B is defined to be the set com(A, B) of states relative to whichA andB are compatible. Three basic categories of relative compatibility are then defined according to the character of com(A, B): absolute compatibility (ordinary compatibility), absolute incompatibility, and partial compatibility. Then com(A, B) is seen to be a subspace of Hilbert space invariant underA andB; being a subspace, it corresponds to a quantum binary observable (projection), denotedc(A, B). IfA andB are themselves binary observables, thenc(A, B) is expressible as a quantum logical compound ofA andB using the lattice operations meet, join, and orthocomplement. This suggests extending the notion of relative compatibility to the theory of orthomodular lattices, as well as to more general lattice-theoretic formulations of quantum mechanics.     

Perturbations of Functions of Operators in a Banach Space

We consider an analytic function f of bounded operators A and [(A)\tilde]\tilde A represented by infinite matrices in a Banach space with a Schauder basis. Sharp inequalities for the norm of f(A)-f([(A)\tilde])f(A)-f(\tilde A) are established. Applications to differential equations are also discussed.     

A duality theorem for the automorphism group of a covariant system

In this paper we examine the covariant representation theory of a covariant system (A, G) introduced by Doplicher, Kastler and Robinson. (A is aC*-algebra andG is a locally compact group of automorphisms ofA.) We define the concept of left tensor product of two covariant representations. Loosely stated, our duality theorem says thatG is canonically isomorphic to the set of bounded operator valued maps on the set of covariant representations of the covariant system (A, G) which preserve direct sums, unitary equivalence and left tensor products. We further show that the enveloping von Neumann algebraA(A, G) of the covariant system (A, G) admits a (not necessarily injective) comultiplicationd such that (A(A, G),d) is a Hopf von Neumann algebra. The intrinsic group of this Hopf von Neumann algebra is canonically isomorphic and (strong operator topology) homeomorphic toG.     

Effective action in multidimensional (Super)gravities

In the present paper we have obtained unique effective action ford=5 gravity on the backgroundM ₄×s ₁, whereM ₄ is the Minkowski space,S ₁ is a one-sphere. The effective action is calculated forN=1d=11 supergravity on the backgroundR _n xT _11–n whereR _n is then-dimensional curved space, T_d is thed-dimensional torus. A mechanism of inducing the Einstein gravity with zero--term is proposed.We thank A. O. Barvinsky, E. S. Fradkin, I. V. Tyutin and A. A. Tseytlin for helpful discussions. We are grateful to L. G. Fonova for technical assistance.     

Greens functions,Hamiltonians and modular automorphisms

We demonstrate, under circumstances that allow the construction of a G(A, B; t) = w(As_t (B))G(A, B; t) = \omega (A\sigma _t (B))     

Sequential Product and Jordan Product of Quantum Effects

The quantum effects for a physical system can be described by the set E(H)\mathcal{E(H)} of positive operators on a complex Hilbert space H\mathcal{H} that are bounded above by the identity operator I. We denote the set of sharp effects by P(H){\mathcal{P(H) }}. For A,B ? E(H)A,B\in\mathcal{E(H)}, the operation of sequential product A°B=A^\frac12BA^\frac12A\circ B=A^{\frac{1}{2}}BA^{\frac{1}{2}} was proposed as a model for sequential quantum measurements. Denote by A*B=\fracAB+BA2A\ast B=\frac{AB+BA}{2} the Jordan product of A,B ? E(H)A,B\in\mathcal{E(H)}. The main purpose of this note is to study some of the algebraic properties of the Jordan product of effects. Many of our results show that algebraic conditions on A∗B imply that A and B commute for the usual operator product. And there are many common properties between Jordan product and sequential product of effects. For example, if A∗B satisfies certain associative laws, then AB=BA. Moreover, A*B ? P(H)A\ast B\in{\mathcal{P(H) }} if and only if A°B ? P(H)A\circ B\in{\mathcal{P(H)}}.     

Quantum Yang-Mills on a Riemann surface

We obtain the quantum expectations of gauge-invariant functions of the connection on aG=SU(N) product bundle over a Riemann surface of genusg. We show that the spaceA/G _m of connections modulo those gauge transformations which are the identity at one point is itself a principal bundle with affine linear fiber. The base space Path^2g G consists of 2g-tuples of paths inG subject to a relation on their endpoint values. Quantum expectations are iterated path integrals over first the fiber then over Path^2g G, each with respect to the push-forward toA/G _m of the measuree ^–S(A) D A. Here,S(A) denotes the Yang-Mills action onA. We exhibit a global section ofA/G _m to define a choice of origin in each fiber, relative to which the measure on the fiber is Gaussian. The induced measure on Path^2g G is the product of Wiener measures on the component paths, conditioned to preserve the endopoint relation. Conformal transformations of the metric onM act by reparametrizing these paths. We explicitly compute the partition function in the general case and the expectations of functions of certain products of Wilson loops in the caseg=1.Research supported in part by DOE grant DE-FGO2-88ER25066     

Ab initio CI study of the vibrational structure of the 1 1Σ− (1 1 A″)←X and 1 1Δ (2 1 A′, 2 1 A″)←X electronic transitions in HCN and DCN

The results of an ab initio CI study of the vibrational/vibronic structure of the 1 ¹Σ^? (1 ¹ A″)←X and 1 ¹Δ (2 ¹ A′, 2 ¹ A″)←X electronic transitions in HCN and DCN are presented. Calculated band positions and intensity distributions within the band progressions are compared with corresponding experimental data. While the theoretical results for the 1A″←X transition reproduce well the structure of the observed A-X spectrum, they place doubt on the Bickel-Innes interpretation of the B-X band system in terms of transitions to the same excited electronic state but accompanied by excitation of a single quantum of the C?H stretching vibrational mode.     

A cylindrically symmetric inhomogeneous cosmological model with electromagnetic field

A cylindrically symmetric inhomogeneous cosmological model with electromagnetic field for perfect fluid distributions is obtained. To get a determinate solution, a supplementary conditionA=(BC) ⁿ between metric potentials is used whereA, B, andC are functions of bothx andt andn is a constant. Some physical and geometrical properties of the model and behavior of electromagnetic field tensors are also discussed.     

Gleason's Theorem for Rectangular JBW-Triples

A JBW^*-triple B is said to be rectangular if there exists a W^*-algebra A and a pair (p,q) of centrally equivalent elements of the complete orthomodular lattice P(A)\mathcal{P}(A) of projections in A such that B is isomorphic to the JBW^*-triple pAq. Any weak^*-closed injective operator space provides an example of a rectangular JBW^*-triple. The principal order ideal CP(A)_(p,q)\mathcal{C}\mathcal{P}(A)_{(p,q)} of the complete ^*-lattice CP(A)\mathcal{C}\mathcal{P}(A) of centrally equivalent pairs of projections in a W^*-algebra A, generated by (p,q), forms a complete lattice that is order isomorphic to the complete latticeI(B)\mathcal{I}(B) of weak^*-closed inner ideals in B and to the complete lattice S(B)\mathcal{S}(B) of structural projections on B. Although not itself, in general, orthomodular, CP(A)_(p,q)\mathcal{C}\mathcal{P}(A)_{(p,q)} possesses a complementation that allows for definitions of orthogonality, centre, and central orthogonality to be given. A less familiar notion in lattice theory, that is well-known in the theory of Jordan algebras and Jordan triple systems, is that of rigid collinearity of a pair (e₂,f²) and (e₂,f²) of elements of CP(A)_(p,q)\mathcal{C}\mathcal{P}(A)_{(p,q)}. This is defined and characterized in terms of properties of P(A)\mathcal{P}(A). A W^*-algebra A is sometimes thought of as providing a model for a statistical physical system. In this case B, or, equivalently, pAq, may be thought of as providing a model for a fixed sub-system of that represented by A. Therefore, CP(A)_(p,q)\mathcal{C}\mathcal{P}(A)_{(p,q)} may be considered to represent the set consisting of a particular kind of sub-system of that represented by pAq. Central orthogonality and rigid collinearity of pairs of elements of CP(A)_(p,q)\mathcal{C}\mathcal{P}(A)_{(p,q)} may be regarded as representing two different types of disjointness, the former, classical disjointness, and the latter, decoherence, of the two sub-systems. It is therefore natural to consider bounded measures m on CP(A)_(p,q)\mathcal{C}\mathcal{P}(A)_{(p,q)} that are additive on centrally orthogonal and rigidly collinear pairs of elements. Using results of J.D.M. Wright, it is shown that, provided that neither of the two hereditary sub-W^*-algebras pAp and qAq of A has a weak^*-closed ideal of Type I², such measures are precisely those that are the restrictions of bounded sesquilinear functionals {_m on pAp 2 qAq with the property that the action of the centroid Z(B) of B commutes with the adjoint operation. When B is a complex Hilbert space of dimension greater than two, this result reduces to Gleason's Theorem.     

Complements to various Stone-Weierstrass theorems forC *-algebras and a theorem of Shultz

J. Glimm's Stone-Weierstrass theorem states that ifA is aC ^*-algebra,P(A) is the set of pure states ofA, andB is aC ^*-subalgebra which separates , thenB=A. We show that ifB is aC ^*-subalgebra ofA andx an element ofA such that any two elements of which agree onB agree also onx, thenxB. Similar complements are given to other Stone-Weierstrass theorems. A theorem of F. Shultz states that ifxA ^**, the enveloping von Neumann algebra ofA, and ifx, x ^*, x, andxx ^* are uniformly continuous onP(A){0}, then there is an element ofA which agrees withx onP(A). We show that the hypotheses onx ^*x andxx ^* can be dropped.     

Midpoints in gyrogroups

The obscured Thomas precessionof the special theory of relativity (STR) has been soared into prominence by exposing the mathematical structure, called a gyrogroup,to which it gives rise [A. A. Ungar, Amer. J. Phys.59,824 (1991)], and the role that it plays in the study of Lorentz groups [A. A. Ungar, Amer. J. Phys.60,815 (1992); A. A. Ungar, J. Math. Phys.35,1408 (1994); A. A. Ungar, J. Math. Phys.35,1881 (1994)]. Thomas gyrationresults from the abstraction of Thomas precession.As such, its study sheds light on relativistic velocity spaces and their symmetries which are concealed in Thomas precession. In order to uncover new properties of relativistic gyrogroups, we employ in this article the group theoretic concepts of divisible groupsand two-torsion free groupsto construct midpointsin gyrogroups. Systems of successive midpoints then describe straight gyrolinesand suggest a new, natural distance function that involves a Thomas gyration. These, in turn, reveal a new, interesting geometry that underlies relativistic velocity spaces. In this resulting gyrogeometrythe straight gyrolines form geodesics under a distance function which turns out to be the Poincaré hyperbolic distance function relaxed by a Thomas gyration. These geodesics do obey the parallel axiom of Euclidean geometry. Ironically, (i) attempts to understand the parallel postulate of Euclidean geometry gave rise to hyperbolic geometry in which the parallel postulate disappears;(ii) hyperbolic geometry gave rise to Einstein's STR; (iii) Einstein's STR established the bizarre and counterintuitive relativistic effect called Thomas precession, the abstraction of which is called Thomas gyration; and (iv) Thomas gyration now repairs in this article the Poincaré distance function of hyperbolic geometry to the point where the parallel postulate reappears.     

Nonlinear optical effects for plasma diagnostics

Experimental investigations show that the 1/f noise intensityC and the contact resistanceR can be used to analyse contacts. The simply prepared contacts are fritted by discharging a capacitor, resulting in a multi-spot contact. A model relatesC andR to a number of contact spotsk with radiusa. More impulse-frittings at increasing energies decreaseC andR, thus enhancing the values ofk anda. From experimentalC vsR plots two regions are determined for GaAs: A fritting (a=constant) and A+B fritting (a∝k). Calculated values ofk are in good agreement with the number of peaks or pits formed by etching the semiconductor surface. From experimentalC vsW orR vsW curves, withW the cumulative impulse-fritting energy, the conclusion can be made thatka ³ is proportional toW.     

Elastic <Emphasis Type="Italic">Nd</Emphasis> scattering at intermediate energies as a tool for probing the short-range deuteron structure

A calculation of the deuteron polarization observables A _y ^d , A _yy , A _xx , A _xz and the differential cross section for elastic nucleon-deuteron scattering at incident deuteron energies 270 and 880 MeV in lab is presented. A comparison of the calculations with two different deuteron wave functions derived from the Bonn-CD NN-potential model and the dressed-quark-bag model is carried out. A model-independent approach, based on an optical-potential framework, is used in which a nucleon-nucleon T matrix is assumed to be local and taken on the energy shell, but still depends on the internal nucleon momentum in a deuteron. The text was submitted by the author in English.     

Magnetic anisotropy and magnetoelectric properties of Tb1 ? xErxFe3(BO3)4 ferroborates

Magnetic and magnetoelectric properties of ferroborate single crystals with complex composition (Tb_{1 − x} Er _x Fe₃(BO₃)₄, x = 0, 0.75) and with competing exchange Tb-Fe and Er-Fe interactions are investigated. Jumps in electric polarization, magnetostriction, and magnetization are observed as a result of spin-flop transitions, as well as a considerable decrease in the critical field upon an increase in the Er concentration, in a field H _c parallel to the c axis. The observed behavior of phase-transition fields is analyzed and explained using a simple model taking into account anisotropy in g factors and exchange splitting of funda-mental doublets of the easy-axis Tb³⁺ ion and easy-plane Er³⁺ ion. It is established that magnetoelectric and magnetostriction anomalies under spin-flop transitions are mainly controlled by the Tb subsystem. The Tb subsystem makes a nonmonotonic contribution ΔP _a (H _a , T) to polarization along the a axis: the value of ΔP _a reverses its sign and increases with temperature due to the contribution from the excited states of the Tb³⁺ ion. Original Russian Text ? A.K. Zvezdin, A.M. Kadomtseva, Yu.F. Popov, G.P. Vorob’ev, A.P. Pyatakov, V.Yu. Ivanov, A.M. Kuz’menko, A.A. Mukhin, L.N. Bezmaternykh, I.A. Gudim, 2009, published in Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2009, Vol. 136, No. 1, pp. 80–86.     

A metric topology for causally continuous completions

A metric topologyH(¯M) is introduced on the causal completion¯M of a causally continuous space-timeM. This metric topology is at least as coarse as the extended Alexandrov topologyA(¯M) on¯M. In bothH(¯M) andA(¯M), the original space-timeM is an open and dense subset. From the definition ofH(¯M), it follows that the causality on¯M is continuous at boundary points. IfM admits a compact Cauchy surface, thenH(¯M) andA(¯M) are the same.     

Study on the Supramolecular Interactions of p-Sulfonated Calix[4, 6, 8]arenes with Lomefloxacin

The supramolecular interactions between a homologous series of p-sulfonated calix[n]arenes (SCnA, n = 4, 6, 8) as hosts and lomefloxacin (LFLX) were studied by spectrofluorometry. LFLX was found to react with SCnA to produce stable complexes. The fluorescence intensity of the complexes decreased gradually with increasing SCnA concentration. The formation of complexes was further confirmed by ¹H NMR studies and molecular modeling calculations. Data of the stability constants and thermodynamic parameters of the obtained complex showed that the stability of the SC8A-LFLX complex is superior to that of SC6A-LFLX and SC4A-LFLX. A mechanism was proposed to explain the inclusion process.     

Magnetostriction and magnetization of the intermetallic compounds R Fe2 ? x Co x ( R = Tb, Dy, Er) with compensated magnetic anisotropy

The compounds Tb_0.35Dy_0.45Er_0.2Fe_{2 − x} Co _x (0 ≤ x ≤ 2) are synthesized in both polycrystalline and single-crystal states. The composition of the new multicomponent alloys with compensated magnetic anisotropy is calculated in the framework of the single-ion magnetic anisotropy model with allowance for the data on the temperature dependences of the magnetic anisotropy constants for RFe₂ single crystals. The synthesized compounds are characterized using metallographic, chemical, X-ray diffraction, and thermomagnetic methods. A combined analysis of the magnetic and magnetoelastic properties is also carried out. It is established that the high magnetostriction characteristics of the rare-earth intermetallic compounds Tb_0.35Dy_0.45Er_0.2Fe_{2 − x} Co _x with a structure of Laves phases are observed in the region of the spin-reorientational phase transition whose temperature can be varied by properly choosing the Co content. It is found that, in the room-temperature region, the magnetic susceptibility (dλ/dH) of the composition with x = 1.3 reaches levels in excess of the value of dλ/dH for terphenol D due to the compensation of magnetic anisotropy. Original Russian Text ? I.S. Tereshina, S.A. Nikitin, G.A. Politova, A.A. Opalenko, E.A. Tereshina, I.V. Telegina, 2009, published in Fizika Tverdogo Tela, 2009, Vol. 51, No. 1, pp. 85–90.