More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

Deposition kinetics of the γ′ phase in N36T2YU2 steel

Electron microscopy is reported for the deposition in this steel; quantitative results are given on the particle size of the phase deposited during a continuous and uninterrupted decomposition. The deposition of the phase occurs in one stage, while the two stages in the variation in the mechanical properties arise from features of the interaction of dislocations with the phase particles. There appears to be only a small energy barrier to the generation of phase particles. Spherulites are formed in regions of interrupted decomposition. The effects of quenching temperature on the deposition mechanism are discussed.Translated from Izvestiya VUZ, Fizika, No. 3, pp. 41–45, March, 1973.     

Symmetries and half-sided modular inclusions of von Neumann algebras

LetN, be a von Neumann algebras on a Hilbert space , a common cyclic and separating vector. Assume to be cyclic and also separating forN . Denote by , _N , _N the modular operators to (, ), (N, ), resp (N , ). Assume now ^-it N ^it N for allt 0. (Such type of inclusions ((N U, ) , ) are called half-sided modular.) Then the modular groups ^it , _N ^ir , _N ^is ,t, r, s generate a unitary representation of the group S1(2, )/Z ₂ of positive energy.Another result is related to two half-sided modular inclusions (₁ , ) and (₂ , ). Under proper conditions the three modular groups ^it , ₁ ^ir , ₂ ^is ,t, r, s generate the three-dimensional subgroup of O(2, 1) of two commuting translations and the Lorentz transformation.Partly supported by the DFG, SFB 288 Differentialgeometrie und Quantenphysik.     

S0-S1 two photon absorption dynamics of organic dye solutions

The two-photon absorption cross-sections and excited-state absorption cross-sections of the dyes rhodamine 6G, methylene blue and fuchsin dissolved in methanol, and of the dyes safranine T, 1,3,3,1,3,3-hexamethylindocarbocyanine iodide (HMICI) and 1,3,1,3-tetramethyl-2,2-dioxopyrimidi-6,6-carbocyanine hydrogen sulphate (PYC) dissolved in hexafluoroisopropanol (HFIP) are determined. The excitation is achieved with picosecond light pulses of a passively mode-locked Nd-glass laser (_L = 1.054m). The influence of amplified spontaneous emission on the two-photon absorption dynamics is analysed.     

Vector two-point functions in maximally symmetric spaces

We obtain massive and massless vector two-point functions in maximally symmetric spaces (and vacua) of any number of dimensions. These include de Sitter space and anti-de Sitter space, and their Euclidean analogsS ⁿ andH ⁿ. Our method is based on a simple way of constructing every possible maximally symmetric bitensorT _a...bc...d(x, x) which carries tangent-space indicesa...b atx andc...d atx.     

A Monomial Basis for the Virasoro Minimal Series M(p,p′) : The Case 1<p′/p<2

Quadratic relations are given explicitly in two cases of chiral conformal field theory, and monomial bases of the representation spaces are constructed by using the Fourier components of the intertwiners. The first case is the (2,1) primary fields for the (p,p)-minimal series M_r,s (1rp–1,1sp–1) for the Virasoro algebra where 1<p/p<2. We restrict ourselves to the case p3, for which the (2,1) primary field exists. The second case is the intertwiners corresponding to the two-dimensional representation for the level k integrable highest weight modules V() (0k) for the affine Lie algebra      

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     

Dielectric constant characterization of large-area substrates in millimeter wave band

A possibility of the dielectric constant measurement for substrates with permittivity=+i without an essential restriction on their area has been shown experimentally. The method uses frequency measurement of quasioptical dielectric resonator (QDR) with two slots oriented along the QDR radius with a dielectric substrate in one of them. Taking QDR of teflon in 8mm waveband as an example it is found that measurable values of can ran up 15 _q , where _q is the QDR material permittivity. Absolute error of the measurements is determined by an accuracy with which the permittivity of calibrated (standard) samples is known. The relative measuring error is determined by the accuracy of the QDR frequency measurement and can be quite a small. As an example the method is demonstrated forLaAlO ₃ single crystals.     

A solution spectrum of the nonlinear Schrödinger equation. II

It was shown in a previous communication that the nonlinear Schrödinger equation exhibits a spectrum of eigenfunctions of the form = _k,A _k (coshkx) ^–k and = _k B _k (coshkx) ^–k–1sinhkx, and the corresponding eigenvalues of the energy are related to a band structure with a characteristic energy gap as a significant feature. In the present paper, it is shown that a further spectrum exists exhibiting the general structure = _k=0 A _k(cosh kx)^–k–1/2and = _k=0 B_k(cosh kx)^–k–3/2sinhkx and yielding also a band structure. An extension of the solution spectrum to a nonlinear Klein-Gordon equation and a nonlinear Dirac equation does not imply essential difficulties, and the corresponding characteristic band structure has to be related to a mass spectrum.     

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.     

Bounded perturbations of dynamics

If and are one-parameter automorphism groups of a von Neumann algebraM is said to be a bounded perturbation of if _t – _t 0 ast0. We give a complete characterization of the bounded perturbations of . In particular, we show that if can be implemented by a strongly continuous one-parameter group with self-adjoint generator (Hamiltonian)H, then can be implemented in the same way and the corresponding HamiltonianH can be chosen to be of the formH=VHV ^–1+h, whereV is a unitary ofM andh=h*M.On leave of absence from II. Institut für Theoretische Physik, Universität Hamburg, D-2000 Hamburg 50, Federal Republic of Germany     

пРИМЕНЕНИЕ МЕтОДА ОтНОшЕНИь к ОпРЕДЕДЕНИУ сОстАВльУЩЕИ σx НАпРьжЕНИь

In this paper the possibility is analyzed of using the ratio method to determine the biaxial stress component _x in an arbitrary direction from two photographs, one taken with the primary beam incident perpendicularly and rotating film holder and the second photograph with the primary beam incident obliquely and film holder stacionary or oscillating in a small angular range. A relation is derived for the value of _x based on measurements of the diameters of the diffraction circles in the corresponding azimut, and a relation for estimating the magnitude of the percentual error of the value of _x thus determined as compared with the real value of _x .It is shown in the case of aluminium in three typical stress states (circularly symmetrical stress distribution, unaxial state, torsional stress) that the error in determining _x , caused by using the ratio method, is quite unimportant for application in technical practice and is much smaller than when applying the ratio methods to the determination of the sum of the two principal stresses from one photograph taken with the primary beam incident perpendicularly. The application of the ratio method for determining _x gives simultaneously the possibility of using this method for solving the general problem, i.e. of determining the two principal stresses as to their magnitude and direction.     

Triple Fluorescence of Substituted Benzanilides in Solution and in Solid States

The competitive triple fluorescence of benzanilide is studied by steady-state fluorescence investigations in dependence on the solvent polarity and the para-substitution of the aniline core as well as by comparison with the fluorescence behavior of 4-methoxy-N-methylbenzanilide. The normal fluorescence of benzanilide S₁(LE) S₀ appears at _max = 345 nm, whereas a superposition of proton transfer (PT) fluorescence S₁(PT) S₀(PT) and intramolecular charge transfer (ICT) flu-orescence S₁(ICT) S₀(FC) is responsible for the long-wavelength fluorescence in the 500-nm region. Different possibilities for the formation of the PT and ICT states are discussed. Investigations of the fluorescence behavior of benzanilides both in solution and as crystals in dependence on the para-substitution of the benzanilide moiety support the PT/ICT model.     

Small perturbations ofC*-dynamical systems

It is shown that if is the generator of a strongly continuous oneparameter group of *-automorphisms of aC*-algebraA and is an unbounded *-derivation ofA with the same domain as , then + is also a generator for all sufficiently small real numbers .     

Is It Possible to Study the Wave Function of 2S Vector Mesons at HERA?

We present a short review of anomalous properties in diffractive photo- and electroproduction of radially excited V(2S) vector mesons. Using the color dipole generalized Balitsky-Fadin-Kuraev-Lipatov phenomenology we analyze anomalous Q ² and energy dependence of the production cross section, V(2S)/V(1S) production ratio, the diffraction slope and anomalous t-behavior of the differential cross section d/dt. The origin of these anomalies is based on the interplay of the nodal structure of V(2S) radial wave function with the energy and dipole size dependence of the dipole cross section and the diffraction slope. We analyze how a different pattern of anomalous behavior of V(2S) production leads to a different position of the node in the wave function and discuss how that node position can be extracted from the data at HERA.     

Direct observation of the second-order Stark effect of theX-B transition in molecular iodine

The second-order Stark shift of the components of the hyperfine structure of the transition¹ _g ⁺ ( = 0,j = 13, 15) ³ _ou ⁺ ( = 43,j = 12, 16) (of molecular iodine have been studied by means of saturated absorption spectroscopy in an external cell with the I₂ vapour located in an electric field. The anisotropic polarizabilities of the upper and lower levels together with the difference between the isotropic polarizabilities of the levels of the transition have been obtained.     

Mixed-valence states in TCNQ salts of monoalkylbiferrocenes and their mixed crystals with dialkyl derivative

TCNQ salts of 1-monoalkylbiferrocenes showed a temperature-independent trapped-valence state as expected for the unsymmetrical structure of cations. On the other hand, mixed crystals of 1-monobutyl- and 1.1-dibutylbiferrocenium⁺(TCNQ) ₃ ^– showed a temperature dependence of the mixed-valence states, showing that the lattice affects the mixed-valence states.     

Electrodynamics Under a Possible Alternative to the Lorentz Transformation

A generalization of the classical electrodynamics for systems in absolute motion in presented using a possible alternative to the Lorentz transformation. The main hypothesis assumed in this work are: a) The inertial transformations relate two inertial frames: the privileged frame S and the moving frame S with velocity v with respect to S. b) The transformation of the fields from S to the moving frame S is given by H = a(H – v × D) and E = a(E + v × B), where a is a matrix whose elements depend of the absolute velocity of the system. c) The constitutive relations in the moving frame S are given by D = E, B = H and J = E. It is found that Maxwell's equations, which are transformed to the moving frame, take a new form depending on the absolute velocity of the system. Moreover, differing from classical electrodynamics, it is proven that the electrodynamics proposed explains satisfactorily the Wilson effect.     

Effect of hydrogen doping on the magnetic properties of Gd2CuO4

We report the results of ac-susceptibility and dc-magnetization measurements for H_yGd₂CuO₄ (0y0.54). It is shown thatH doping lowers the weak ferromagnetic component in the material. The distinct hysteresis loops observed atT=77 K for both non- and hydrogenated samples change its shape withy. The magnetic ordering temperatures T _N ^Cu and T _N ^Gd , as determined from the temperature dependencies of ac-susceptibility, remain unchanged with sample's hydrogenation. This result seems to indicate that extra electrons are not doped onto the Cu-O planes of Gd₂CuO₄. The frequency dependencies ofx(, T) andx(, T) for bothy=0 andy=0.15 samples are analysed., The maximums ofx andx found at about 200K are considered in terms of susceptibility dependence on the spin-lattice relaxation time (). The anomalies in ac-susceptibility found recently in Gd₂CuO₄ atT _a=8 K andT _b=9.5 K decrease significantly withy. Results are discussed in the context of available data on 214T-type compounds.     

Natural boundaries for area-preserving twist maps

We consider KAM invariant curves for generalizations of the standard map of the form (x, y)=(x+y, y+f(x)), wheref(x) is an odd trigonometric polynomial. We study numerically their analytic properties by a Padé approximant method applied to the function which conjugates the dynamics to a rotation +. In the complex plane, natural boundaries of different shapes are found. In the complex plane the analyticity region appears to be a strip bounded by a natural boundary, whose width tends linearly to 0 as tends to the critical value.