Double quantum transitions in free radicals

The observation of double quantum transitions on three kinds of free radicals (DPPH, DPANO, ultramarine) at temperatures of liquid nitrogen is described. Signals having an absorption and emission character were observed in the 12-5 MHz–18 MHz frequency band in the direction parallel to the external magnetic fieldH ₀ and their dependence on different parameters was studied.Bloch equations were solved for two mutually perpendicular high-frequency fields and expressions were found for the components of dynamic susceptibility in theH ₀ direction. The experiments agree with theory.The possibility of using double quantum transitions for measuring relaxation times is discussed.

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(DPPH, DPANO, ) . 12,5MHz–18MHz H ₀, ; . H ₀. . .

     

Extremal invariant states with a spectrum condition and Borchers' theorem

If the energy spectrum of an extremal invariant state is not the whole real line, it is shown that is either pure or uniquely decomposed into mutually disjoint pure states in the way that =^-1 F _{0 t} dt where is a pure state satisfying = with >0. Next we give a slightly generalized version of Borchers' theorem [1] on the innerness of some automorphism group of a von Neumann algebra with a spectrum condition.     

Geometric expansion of the boundary free energy of a dilute gas

We consider a dilute classical gas in a volume ^–1 which tends to ^d by dilation as 0. We prove that the pressurep(^–1) isC ^q in at =0 (thermodynamic limit), for anyq, provided the boundary isC ^q and provided the Ursell functionsu _n (x ₁, ...,x _n) admit moments of degreeq and have nice derivatives.     

Manifestation of Extracoordination in the Resonance Raman Spectra of Water‐Soluble Cation Co‐Porphyrins

Resonance Raman spectra (RRS) of Co(II) and Co(III)5,10,15,20tetrakis(4Nmethylpyridinium)porphyrin ((Co^II(TmpyP4), and Co^III(TMPyP4)) in aqueous solutions at different pH as well as in organic solvents (methanol, ethanol, DMSO, DMF) are obtained. The increased sensitivity of the oscillation frequencies ₂, ₄, ₈, and ₆ — the markers of the oxidation state of a metal — to the nature of an axial ligand has been revealed. For Co^III(TmpyP4), the shifts of the indicated frequencies in extracoordination have turned out to be twofold larger than those for Co^II(TmpyP4). The spectral effects observed are related to different electron influence of the extraligands on the system of the porphyrin ring. In the case of Co(III)porphyrin, interaction of the d orbitals of the metal and the e _g ^*orbitals of the macrocycle is more efficient since its ionic radius is smaller than for the Co(II)complex. For Co^III(TmpyP4), a linear correlation between the oscillation frequencies ₂, ₄, ₈, and ₆ and the experimental Gutmann parameters characterizing the electronacceptor properties of solvents is found.     

The crystal structure of copper dipyridine dibromide Cu(C5H5N)2Br2

The X-ray structural analysis of copper dipyridine dibromide was carried out. The substance is monoclinic, its space group isP2₁/n, having the lattice constantsa=8.30 kXU,b=17.72 kXU,c=4.04 kXU,=96°,Z=2. The localization of the heavy atoms was carried out by means of the projections of the Patterson functionsP(u, v) andP(v, w), which provided the bases for determining the signs of the majority of structure factors. The projections of the electron density(x, y) and(y, z) were calculated on the basis of these data. The positions of the atoms were refined three times by methods of differential syntheses and by geometrical analysis. The structure of CuPy₂Br₂ is very close to that of CuPy₂Cl₂ [1], [2], differing from it primarily in the orientation of the symmetry elements with respect to the crystallographic axes. In both structures the copper atom is octahedrally coordinated with four halogen and two nitrogen atoms. The nitrogen atoms and two bromine atoms are bound to the copper covalently in the structure of the bromine derivative, as follows from the length of the bonds (Cu-N 1.99 kXU, Cu-Br, 2.46 kXU), while the remaining two bromine atoms are bound to the copper by weaker bonds and mediate the chain formation of molecules in the direction of thec axis.

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Cu(C₅H₅N)₂Br₂

. , 2₁/ ==8,30 kX,b=17,72 kX,=4,04 kX,=96°,z=2. (, v) P(v, w), . (, ) (, z). . CuPy₂Br₂ u₂1₂, . . , (-N 1,99 kX, u-r 2,46 kX), .

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The authors thank M. Serátor for supplying the crystal samples and for initiating the work, the management of the Institute of Technical Physics, Czechoslovak Academy of Sciences, in Prague and especially Dr. A. Línek for making it possible to calculate some of the Fourier maps on the special computer Elika and finally A. lechtová for carefully calculating the Fourier maps and structure factors.

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The first stage of this work was reported on at the 3rd State Conference on Inorganic Chemistry, held in Bratislava from June 29th to July 4th, 1959.     

Measurement of the reaction γp → K0Σat photon energies up to 2.6 GeV⋆

The reaction p K⁰⁺ was measured in the photon energy range from threshold up to 2.6 GeV with the SAPHIR detector at the electron stretcher facility, ELSA, in Bonn. Results are presented on the reaction cross-section and the polarization of the ⁺ as a function of the kaon production angle in the centre-of-mass system, cos^c.m._K, and the photon energy. The cross-section is lower and varies less with photon energy and kaon production angle than that of p K⁺⁰. The ⁺ is polarized predominantly at cos^c.m._K 0. The data presented here are more precise than previous ones obtained with SAPHIR and extend the photon energy range to higher values. They are compared to isobar model calculations.     

Differential algebras for quantum groups of type B, C, and D

We study higher order bicovariant differential calculi on the quantum groups O_q(N) and Sp _q (N). We show that the second antisymmetrizer exterior algebra _u is the quotient of the universal exterior algebra _u by the principal ideal generated by . Here denotes the unique up to scalars biinvariant 1-form. Moreover is central in _u and _u is an inner differential calculus. We show that the quadratic dual to the left-invariant algebra _{s L} is isomorphic to the reflection equation algebra. Let be an arbitrary left-covariant first order differential calculus. We show that the dimension of the space of left-invariant 2-forms in the universal exterior algebra equals the number of linearly independent quadratic-linear relations in the quantum tangent space.     

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.     

On the existence of invariant,absolutely continuous measures

Let (, , ) be a measure space with normalized measure,f: a nonsingular transformation. We prove: there exists anf-invariant normalized measure which is absolutely continuous with respect to if and only if there exist >0, and , 0<<1, such that (E)< implies (f ^–k(E))< for allk0.     

Representations of state space transformations by Markov kernels

Every convex subset of a locally convex Hausdorff space (X, ) is equipped with the (-algebra generated by its-relatively open subsets. Within the set () of probability measures on two particular convex subsets are considered: (a) the set ^s () of probability measures with a separable support, and (b) the set ^c () of probability measures with a compact convex support. If is the base of a cone inX, then there exists an affine barycenter map from ^c () onto whose composition with the natural embedding of in ^c () yields the identity map on , and every-continuous affine transformation of can be represented by an affine transformation of ^c () that is induced by a Markov kernel. If (X, ) is a Banach space and is a closed, bounded, generating cone base inX that is contained in a hyperplane, then analogous results are obtained with respect to ^s (). Since the state spaces considered in noncommutative measure theory are cone bases and every change in time of an empirical system can be thought of as an affine transformation of the associated state space (Schrödinger picture), the existence of these representation theorems implies that the time evolution of general empirical systems can be described by dynamical concepts borrowed from classical probability theory.     

The paramagnetic state (μ+e−) in silicon and tellurium at high temperature

The paramagnetic state (⁺e^–) in Si and Te was observed in a longitudinal magnetic field. The mean lifetimes of these states were obtained: _Si = 1.45(3) s, _Te = 12.5(8) s at 290 K, _Te = 12(2) s at 250 K.     

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.     

Spatial Spectrum of Artificial Ionospheric Irregularities Induced by Powerful HF Radiowaves

We present measurement results and spatial-spectrum shapes of the dependence of the relaxation time on the scale across the geomagnetic field for artificial ionospheric irregularities (AIIs) induced in the upper ionosphere by powerful HF radiation of the SURA heating facility. The irregularity diagnostics was based on observing amplitude scintillations of a 243-MHz beacon signal from a quasi-geostationary, solar-synchronous satellite and on measuring field-aligned scattering at frequencies 15 and 20 MHz. The satellite signal was received at the Kazan State University Observatory. The field-aligned scattering signals were received and analyzed by a bistatic HF radar based on the UTR-2 radio telescope located near Kharkov (Ukraine). It is shown that irregularities of the electron density, whose two-dimensional spectrum in the plane perpendicular to the geomagnetic field is the power law æ ^-p with index p2, are developed in the scale range 30–60 l 200–400 m. In this case, the relative fluctuations (N²)^1/2 of the electron density increase with decreasing scale l=2/æ. The estimate N²)^1/2 1–1.5% is obtained for a heating power of 150 MW and irregularity scales l 30–60 m at which the fluctuations are maximum. The measured dependence of the AII relaxation time, defined as the e-folding time of the amplitude-scintillation intensity, has the form _r l . If l 30–60 m, then the index is close to 2, whereas the effective diffusion coefficient D (2–3)· 10^-1 m²/s corresponds to the ambipolar cross-field diffusion coefficient in a magnetized plasma. The time _r for scales l 60–100 m is independent of l and increases with decreasing velocity of regular drift of the plasma. The Doppler-spectrum broadening (²)^1/2 0.6 Hz observed when receiving field-aligned scattered signals can be related to chaotic motions of plasma-density disturbances whose random drift velocities amount to (v²)^1/2 2–3 m/s for scales l 20 m at which the power-law index changes drastically.     

Particle polarizations in decays of5HeΛ and4HΛhypernuclei

Nucleon polarizations are examined in the hypernucleus decays⁵He, ⁴He + p + _–,⁴H, ³H + p + _–, and⁴H, ³He + n + _–. The effect of the strong interaction in the final state is taken into account. A significant role is predicted for the resonance interaction in the p-⁴He system in the formation of the proton polarization in the⁵He decay. It is also shown that in the⁴H, ³H + p + _– decay the proton-polarization components should attain significant magnitudes, while in the charge-exchange decay⁴H, ³He + n + _–, the neutron polarization is expected to be not too large.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 100–103, October, 1988.     

Fock representations of the affine Lie algebraA 1 (1)

The aim of this note is to show that the affine Lie algebraA ₁ ⁽¹⁾ has a natural family _, ,v of Fock representations on the spaceC[x _i,y _j;i andj ], parametrized by (,v) C ². By corresponding the highest weight _, of _, to each (,), the parameter spaceC ₂ forms a double cover of the weight spaceC₀C –₁ with singularities at linear forms of level –2; this number is (–1)-times the dual Coxeter number. Our results contain explicit realizations of irreducible non-integrable highest wieghtA ₁ ⁽¹⁾ -modules for generic (,v).     

On the Surface Pressure for the Edwards-Anderson Model

For the Edwards-Anderson model we introduce an integral representation for the surface pressure (per unit surface) in terms of a quenched moment of the bond-overlap on the surface. We consider free , periodic and antiperiodic ^* boundary conditions (by symmetry ⁽⁾=^(*)), and prove the bounds We show moreover that at high temperatures ⁽⁾ is close to ^2/4 and ⁽⁾ is close to ^2/4 uniformly in the volume .     

Four-wave mixing in CO via the C 1Σ+ (υ′=0) state

Coherent vacuum ultraviolet (VUV) radiation was generated by four-wave difference frequency mixing (_VUV=2₁–₂) of pulsed dye laser radiation in carbon monoxide (CO). The frequency ₁ was tuned to the C ¹⁺(=0)X ¹⁺(=0) two-photon transition, while the dye laser frequency ₂ was scaned around 17650 cm^–1 which corresponds to the A ¹(=7)«C ¹⁺(=0) transition energy. The VUV intensity was found to be strongly wavelength dependent. The analysis of the spectrum revealed (i) that the VUV intensity was enhanced by the rotational levels of the A ¹(=7) state and (ii) that the off-resonance excitation in the C ¹⁺(=0)X ¹⁺(=0) two-photon transition greatly contributed to the present four-wave mixing process. The effects of pumping laser detuning, saturation and foreign gases are briefly discussed.     

Energy spectrum and angular distribution of muons from the decay of heavy leptons produced in colliding electron-positron beams

On the basis of an arbitrary (V, A) structure of the neutral weak ¯ee and LL currents (L=^–, M⁰) a study is made of the processes of production in colliding electron-positron beams of pairs of heavy leptons with subsequent decays in accordance with the schemes e⁺e^––(µ^–v_µv) + ⁺( anything) and e⁺e^–M⁰(µ^–e⁺v_e) + M⁰( anything). The energy spectrum and asymmetry of the distribution of the produced muons are investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 66–70, February, 1981.     

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.     

К ВОПРОСУ O КРИТИЧЕСКО Й ЧАСТОТЕ ПРИ ПРЕРЫВИСТОМ ОСВЕ ЩЕНИИ

c , c n , n AgBr. .