Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

Phase transformations in Cu-Sn alloys containing Ni,Al, Ge,and In

After quenching from 700C and aging, Cu-Sn alloys containing Ni and Al were found to have a precipitation of-solid solution, with a DO₃ type of ordering, of metastable ,, and phases. It was established that the phase has an 4 type of ordering while the phase has the Cu₃Ti type. Observations revealed that Cu-Sn-Al alloys contained two phases, and, with an identical structure but with different ratios of electron concentration per atom.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 34–37, April, 1981.     

Slowing down of retrieval in the hopfield model

The variation of the convergence time, as a function of the storage capacity is studied numerically for systems ranging in size fromN=1000 toN=16,000 neurons. is found to increase likeexp[–A(_c–)] as one nears the critical storage capacity _c =0.142=0.002.     

Interacting spinor and scalar fields: Exact self-consistent solutions in Bianci I space

Exact self-consistent solutions of the equations that describe a system of interacting spinor and massless scalar fields with the interaction Lagrangian L_int=_,^,(S), where (S) is an arbitrary function of the invariant S=, are obtained in Bianci I space. The possibility of excluding the initial singularity is studied for the case of a power-law function (S), and isotropic expansion of the space as t is established.Russian University of International Amity. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 53–58, July, 1995.     

Localization in general one dimensional random systems,I. Jacobi matrices

We consider random discrete Schrödinger operators in a strip with a potentialV (n, ) (n a label in and a finite label across the strip) andV an ergodic process. We prove thatH ₀+V has only point spectrum with probability one under two assumptions: (1) Theconditional distribution of {V (n,)} _n=0,1;all conditioned on {V } _n0,1;all has an absolutely continuous component with positive probability. (2) For a.e.E, no Lyaponov exponent is zero.Research partially supported by USNSF grant MCS-81-20833     

Quantum Observables,Lie Algebra Homology and TQFT

Let us consider a Lie (super)algebra G spanned by T where T are quantum observables in BV formalism. It is proved that for every tensor c^... that determines a homology class of the Lie algebra G the expression c^...T...T is again a quantum observable. This theorem is used to construct quantum observables in the BV sigma model. We apply this construction to explain Kontsevich's results about the relation between homology of the Lie algebra of Hamiltonian vector fields and topological invariants of manifolds.     

Structure investigations on the hot-working behaviour of steel

Structure changes occurring in hot-deformation of the austenite of steel, the - phase transformation of which takes place above room temperature, cannot directly be studied with quenched specimens. However, within certain limits a microstructure characterization is possible by means of investigation of carefully selected model alloys and/or by analysis of the microstructure inheritance associated with a martensitic - transition of the hot-worked austenite. Application of both procedures is demonstrated with results which were obtained in investigations of the hot-working behaviour of low-alloy spring steel and an Fe-Ni-C model alloy.     

A Rigorous Derivation of a Linear Kinetic Equation of Fokker–Planck Type in the Limit of Grazing Collisions

We rigorously derive a linear kinetic equation of Fokker–Planck type for a 2-D Lorentz gas in which the obstacles are randomly distributed. Each obstacle of the Lorentz gas generates a potential V( ), where V is a smooth radially symmetric function with compact support, and >0. The density of obstacles diverges as ^– , where >0. We prove that when 0< <1/8 and =2+1, the probability density of a test particle converges as 0 to a solution of our kinetic equation.     

On the Virial Theorem for the Relativistic Operator of Brown and Ravenhall,and the Absence of Embedded Eigenvalues

A virial theorem is established for the operator proposed by Brown and Ravenhall as a model for relativistic one-electron atoms. As a consequence, it is proved that the operator has no eigenvalues greater than max(2Z - )mc², where is the fine structure constant, for all values of the nuclear charge Z below the critical value Z_c: in particular, there are no eigenvalues embedded in the essential spectrum when Z 3/4 . Implications for the operators in the partial wave decomposition are also described.     

Beta-decay asymmetries in polarized12B and12N and theG-parity non-conservation

The decay asymmetries (A) in polarized¹²B and¹²N have been measured as a function of -ray energies (E). The coefficients _± inA = ±P(p/E) (1+_± E) have been determined to be _–(¹²B) =+(0.31±0.06)%/MeV and ₊(¹²N) = –(0.21±0.07)%/MeV. The experimental value, _––₊=(0.52±0.09)%/MeV, is larger than the prediction according to conservation of vector current which includes no second-class current, _––_{+ CVC}0.27%/MeV, and indicates the existence of the second-class induced-tensor current.This work has been done in collaboration with I. Tanihata and J. Göring.     

The room-temperature decomposition of metastable phases precipitated in the Al-Zn alloys at 200 °C

The room-temperature decomposition of metastable phases in the Al-Zn alloys (from 25 to 50 wt. % Zn) was studied by the transmission electron microscopy and X-ray diffraction. Metastable phases, i.e. G.-P. zones, _R-and -phases, were grown at 200 °C and their decomposition into equilibrium -phase at 20 °C was investigated. Ageing times comprised 1 to 999 days.Both the decomposition mechanism and the rate of decomposition of coherent phases were found to be dependent on the particle sizes and their density reached at 200 °C. The local vacancy supersaturation around the -nucleus in a dense system of G.-P. zones leads to an enhanced growth rate of such nucleus and thus to the formation of one large -precipitate at the expense of several neighbouring G.-P. zones. The elastic stress field around this -particle promotes the further nucleation and growth of -precipitates and leads to their gradual spread throughout the matrix. The decomposition of intermediately sized _Rprecipitates results in the development of -precipitates of comparable sizes nucleated on the array of misfit dislocations at the periphery of _R-precipitates. The cooperative effect between neighbouring particles does not influence the decomposition of large _R-precipitated which split then into several smaller -particles. The rate of G.-P. zones or _R to -decomposition increases with the increasing sizes of transition precipitates and with the zinc content of the alloy. The kinetics of to -decomposition was found to be independent both on the annealing time at 200 °C and on the investigated alloy composition. This can be attributed to the constant density of misfit dislocations as nucleation sites for -precipitates along the -matrix interface and to the large mutual separation of -precipitates in all these alloys.In conclusion we would like to express our thanks to Doc. Dr. V.Syneek, CSc. for his valuable discussions and to Ing. V.íma for the preparation of Al-Zn alloys. Our thanks are also due to Mr. Z.iký for his help in the X-ray diffraction measurement and to P.Vyhlídka for the careful chemical analyses of the investigated alloys.     

Nelson's symmetry and the infinite volume behavior of the vacuum inP(φ)2

LetH _l be the Hamiltonian in aP()₂ theory with sharp space cutoff in the interval (–l/2,l/2). LetE _l =inf(H _l ), (l)=–E _l /l, and let _l be the vacuum forH _l . discuss properties of (l) and _l . In particular, asl, there are finite constants <0 and such that (l), ((l)–)l, and hence (l)=+/l+o(l ^–1). Moreover exp(–c ₁ l) _{l 1}exp(–c ₂ l) forc ₁,c ₂ positive constants, where _{l 1} is theL ¹(Q, d₀) norm of ₁ with respect to the Fock vacuum measure. We also present a new proof of recent estimates of Glimm and Jaffe on local perturbations ofH _l in the infinite volume limit.Research sponsored by AFOSR under Contract No. F44620-71-C-0108.On leave from Istituto di Fisica Teorica, Universitá di Napoli and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli.A. Sloan Foundation Fellow.     

Radiative and nonradiative transitions to an unstable state

In this paper an expression is obtained, which enables us to treat radiative and nonradiative transitions in complex molecular systems, when the final state is unstable. Expressions are give for the matrix elements E/v and E|d/dR|v , where the stable state is described by a solution with a Morse potential, and the unstable state by a solution with a Hulthen potential. The possibility of the concrete realization of such transitions is discussed in the example of excimers.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 10, pp. 70–75, October, 1974.     

Disentangling q-Exponentials: A General Approach

We revisit the q-deformed counterpart of the Zassenhaus formula, expressing the Jackson q-exponential of the sum of two non-q-commuting operators as an (in general) infinite product of q-exponential operators involving repeated q-commutators of increasing order, E_q(A+B) = E_q0(A)E_q1 (B) _i=2 E_qi. By systematically transforming the q-exponentials into exponentials of series and using the conventional Baker–Campbell–Hausdorff formula, we prove that one can make any choice for the bases ^qi, i=0, 1, 2, ..., of the q-exponentials in the infinite product. An explicit calculation of the operators C _i in the successive factors, carried out up to sixth order, also shows that the simplest q-Zassenhaus formula is obtained for ₀ = ₁ =1, and ₂ = 2, and ₃ = 3. This confirms and reinforces a result of Sridhar and Jagannathan, on the basis of fourth-order calculations.     

Singular behavior of the density of states and the Lyapunov coefficient in binary random harmonic chains

We study the integrated density of statesH( ²) of a chain of harmonic oscillators with a binary random distribution of the masses. We show in particular that there is a dense set of values of the squared frequency for which the differenceH( ²+)-H( ²) has a singularity of the type ¦¦², multiplied by a periodic function of ln ¦¦, where the exponent and the period depend continuously on ². In the region where < 1/2,H is not differentiate on a dense set of points. The same type of singularities is also present in the Lyapunov coefficient.     

Space-and time-resolved diffusion-limited binary reaction kinetics in capillaries: experimental observation of segregation,anomalous exponents,and depletion zone

An experimental investigation of one-dimensional, diffusion-limited A+BC chemical reactions is reported. The persistence of reactant segregation and the formation of a depletion zone is observed and expressed in terms of the universal time exponents: (motion of the boundary zone), (width of instantaneous product formation zone), (rate of instantaneous local formation of product), (rate of instantaneous global formation of product), etc. There is good agreement with the recently predicted and/or simulated values:=1/2,=1/6,=2/3,=1/2, in contrast to classical predictions (=0,=1/2,=0,=–1/2). Furthermore, classically the segregation would not be preserved and there would be no formation of a depletion zone and no motion (just dissipation) of the reaction zone. We also discuss the relations to electrode oxidation-reduction reactions, i.e., A+CC where C is a catalyst, electrode, or trap.     

TheS=1/2 Heisenberg antiferromagnet on the triangular lattice: Exact results and spin-wave theory for finite cells

We study the ground state properties of theS=1/2 Heisenberg antiferromagnet (HAF) on the triangular lattice with nearest-neighbour (J) and next-nearest neighbour (J) couplings. Classically, this system is known to be ordered in a 120° Néel type state for values-<1/8 of the ratio of these couplings and in a collinear state for 1/8<<1. The order parameter and the helicity /gC of the 120° structure are obtained by numerical diagonalisation of finite periodic systems of up toN=30 sites and by applying the spin-wave (SW) approximation to the same finite systems. We find a surprisingly good agreement between the exact and the SW results in the entire region-<<1/8. It appears that the SW theory is still valid for the simple triangular HAF (=0) although the sublattice magnetisation is substantially reduced from its classical value by quantum fluctuations. Our numerical results for the order parameterM of the collinear order support the previous conjecture of a first order transition between the 120° and the collinear order at 1/8.     

Mössbauer effect study of the Β-FeOOH to α-Fe2O3 phase transformation

-FeOOH was precipitated from a chloride solution. Mössbauer spectra were taken at room temperature (RT) and at 4.2 K in zero field and in external magnetic fields. Samples aged for successively longer time periods were studied. They contain -FeOOH and -Fe₂O₃, the Mössbauer spectra of which show superparamagnetic behavior. The transformation into -Fe₂O₃ is already induced by aging in the mother solution at 100 C. A final heat treatment at 350 C leads to the complete transformation into -Fe₂O₃ and to an increase of the crystallite size.     

A natural scalar field in the einstein gravitational theory

In a Riemannian space-time, the difference between the third-order tensor potentialH of the Riemann tensor (presented in a precedent paper) and the Lanczos generating function of the Weyl tensor is here shown to be characterized by a vectorV , obtained by contractionH . The significant role of such a vector, in the context of general relativity, is then discussed. Particular attention is paid to the scalar potential which characterizes the irrotational part ofV : such a scalar field satisfies a space-time wave equation of the Poisson type. Weak fields are also considered: in the particular case of a static metric, the scalar is found to be proportional to the classic Newtonian potential.This work was done in the sphere of activity of the C.N.R. Groups for mathematical research.