Support properties of the free measure for Boson fields

Let μ be the measure onI′ (? ^d ) corresponding to the Gaussian process with mean zero and covariance (f,(?Δ+1)^?1 g) onI (? ^d ). It is proven that the set $$( - \Delta _{d - 1} + 1)^{d/4 - \tfrac{1}{2} + \alpha } (1 + x^2 )^{d/4} [\log (2 + x^2 )]^\beta L^2 (\mathbb{R}^d )$$ has μ measure one if α>0 and β>1/2 and μ measure zero if α>0 and β<1/2; here Δ _d?1 is the Laplacian in anyd?1 dimensions whend>1 and Δ₀=Δ.     

A new ℋ -space formalism

The equations governing geometrical objects in ? space are written in terms of operators adapted to families of left shear-freeσ ⁰= 0) cross sections of complexified null infinity (C I ⁺). The concept of ?-conformai weight (HCW) is introduced, and a derivative operatorI _a ^′ , which is closely connected with the covariant derivative but which (unlike the covariant derivative) maps objects having well-defined HCW to other such objects, is defined. A function ?, derived from the Gaussian curvature of left shear-free slicings ofC I ⁺ and having a well-defined HCW, is shown to contain all the curvature information for ? space.     

Demonstration of the origins of cooperativity within SU2×L 6 mapping over\left\{ {I\tilde H_\upsilon } \right\} Liouvillian carrier subspaces characterising the MQ-NMR cluster [A]6(L 6) and its\{ |kq\upsilon :[\tilde \lambda ] > > \} tensorial bases

The fundamental mappings over carrier subspace and substructures associated with \(\{ |kq\upsilon > > \} \) augmented spin algebras of Liouville space, and their mapping onto a subduced symmetry, are derived for [A]₆(L ₆) spin clusters within the combinatorial context of Rota-Cayley algebra over a field. Use of suitable lexical sets of combinatorialp-tuples (number partitions) over {|IM(M ₁?M _n )>}M, followed by the subsequent use ofL _n inner tensor product (ITP) algebra, allows the substructure of Liouville space to be derived. For SU2×L ₆ mapping over the simply-reducible \(\left\{ {I\tilde H_\upsilon } \right\}\) carrier subspaces, the \(D^k \left( {\tilde U} \right) \times \tilde \Gamma ^{\left[ {\tilde \lambda } \right]} \left( \upsilon \right)\) (L ₆) dual irreps, also arise as a consequence of the Liouville space recoupling termsv≡{k ₁?k _n } being distinct labels for \(\left\{ {I\tilde H_\upsilon } \right\}\) which are themselves amenible to combinatorial analysis within the concept of Rota-Cayley algebra. Hence, theL _n -induced symmetry aspects of multiquantum NMR density matrix formalisms and their dual \(\{ |kq\upsilon :[\tilde \lambda ] > > \} \) tensorial bases of spin cluster problems are derived and the nature of the cooperative, aspect between the individual symmetries comprising the duality is demonstrated, i.e. in the context of the operator bases of Liouville space. These practical arguments correlate, well with those based on an augmented boson pattern algebra derived from a Heisenburg algebra for superoperators, ?_±,?₀. An earlier, treatment of conventional Hilbert space SU2×L ₆ dualitycould only be realised in terms of standard SU2 boson algebra. Since the recoupling Rota-‘field’v for Liouville space is an explicit aspect of the dual mapping, a direct demonstration of cooperativity exists.     

Neutrino-induced deuteron disintegration in an experiment at the Krasnoyarsk nuclear reactor

The results of studying antineutrino interactions with deuterons (CCD and NCD reactions) and hydrogen (CCP) at the Krasnoyarsk underground reactor with the Deuteron detector are presented. The cross sections for NCD and CCD were measured with a precision of 9%. For CCP, the precision is 3%: σ _expt ^NCD =(3.35±0.31)×10^?44 cm²/fission ²³⁵U, σ _expt ^NCD =(1.08±0.09)×10^?44 cm²/fission ²³⁵U, and σ _expt ^NCD =(6.39±0.19)×10^?43 cm²/fission ²³⁵U. The precision of the experimental results is close to the theoretical one and is in good agreement with other experiments. The limit on the parameters of antineutrino oscillations into the sterile state was obtained: Δm ²≤4.7×10^?2 eV² for sin²(2?)=1.0 (68% C.L.). A comparison of the measured and theoretical cross section gives us the neutron-neutron scattering length of a _nn(S)=?17±6 fm in the approach of zero momentum transfers. The weak neutral current constant is in good agreement with the prediction of the Standard Model: G _A ^NC =G _A ^CC /0.932±0.056.     

Production and loss of N 2 + , Ne+ and Ne 2 + during the decay period of plasmas produced in neon-nitrogen mixtures

Studies of the time dependencies of the number density of N ₂ ⁺ , Ne⁺ and Ne ₂ ⁺ ions have been made during the decay period of plasmas produced in neon containing various concentrations of nitrogen molecules. Reaction rate constants were obtained for N ₂ ⁺ +N₂+Ne→N ₄ ⁺ +Ne((1.2±0.2)×10^?29 cm⁶ sec^?1) and Ne⁺+N₂→N ₂ ⁺ + Ne ((2.9±0.3) × 10^?12 cm³ sec^?1). The ambipolar diffusion coefficient of N ₂ ⁺ in neon was found to beD _a p _o =350±20 cm² sec^?1 Torr.     

Estimation of higher-order magnetic spin interactions of Fe(III) and Gd(III) ions doped in α-alumina powder with multifrequency EPR

Fe(III) and Gd(III) ions in α-alumina (A1₂O₃) exhibit spin states ofS = 5/2 andS = 7/2 respectively. The magnitude of the zero-field interaction (ZFI) (D = 0.10?0.15 cm^?1) gives rise to an inter Kramers doublet splitting in the same order of magnitude as the X-band electron paramagnetic resonance (EPR) quantum (0.3 cm^?1). It is demonstrated that through a careful step-by-step analysis and spectral simulation of EPR spectra taken at D-band (130 GHz), Q-band (35 GHz), and X-band (9 GHz) at room temperature, the (relative) sign and magnitude of the ZFI parameters, b ₂ ⁰ , b ₄ ⁰ , and b ₄ ³ , can be reliably estimated.     

Temperature dependence of Mn2+ EPR in Sn2P2S6 near the phase transition

The X-band EPR spectrum of Mn²⁺ in Sn₂P₂S₆ was studied in the temperature rangeT=223–363 K. At room temperature the spin-Hamiltonian constants areg=2.00±0.01,B ₂ ⁰ =(163±3)·10^?4 cm^?1,B ₂ ² =(159±3)·10^?4 cm^?1,A=?(75±1)·10^?4 cm^?1. The effect of the invariance in temperature of the resonance magnetic fields in the narrow temperature rangeT=337–340 K and the model of the paramagnetic centre are discussed. According to EPR data a phase transition occurs atT=337 K. This transition from the paraelectric phase to the ferroelectric one is accompanied by a dramatic change in value of the spin-Hamiltonian constantB ₂ ⁰ .     

Compact QEPAS sensor for trace methane and ammonia detection in impure hydrogen

A compact two-gas sensor based on quartz-enhanced photoacoustic spectroscopy (QEPAS) was developed for trace methane and ammonia quantification in impure hydrogen. The sensor is equipped with a micro-resonator to confine the sound wave and enhance QEPAS signal. The normalized noise-equivalent absorption coefficients (1σ) of 2.45×10^?8 cm^?1?W/ $\sqrt{}$ Hz and 9.1×10^?9 cm^?1?W/ $\sqrt{}$ Hz for CH₄ detection at 200 Torr and NH₃ detection at 50 Torr were demonstrated with the QEPAS sensor configuration, respectively. The influence of water vapor on the CH₄ channel was also investigated.     

Experimental study of the energy dependence of the reaction rate coefficients of the reaction CH 3 + with N2O and NH3

The kinetics of the reaction of CH ₃ ⁺ ions with N₂O and NH₃ has been investigated in He and Ar buffers using Selected Ion Flow Drift Tube technique (SIFDT). Both studied reactions proceed with nearly collisional rate at near thermal energies. The rate coefficient of the reaction of CH ₃ ⁺ with N₂O is decreasing more than one order of magnitude (from 1.2×10^?9cm³s^?1 up to 8×10^?11cm³s^?1) with reactant ion/reactant neutral average centre-of-mass kinetic energy (E _r) increasing from near thermal up to 2 eV. The dominant product of this reaction is the isomer HCO⁺ (≥94%) and the minor product is CH₃O⁺. The reaction of CH ₃ ⁺ with NH₃ has two binary channels with the dominant product ion CH₂NH ₂ ⁺ (>70%) and the minor product ion NH ₄ ⁺ (≈10%) and three body association channel with product CH₃NH ₃ ⁺ (≈20% at 0.32 Torr). The rate coefficient of this reaction is decreasing nearly by one order of magnitude with increasingE _r from near thermal up to 0.8eV, forE _r>0.8 eV the rate coefficient increases with increasingE _r. The experimental results are interpreted in terms of a simple model assuming the reactions to proceed via the formation of long-lived collision complexes.     

EPR study of the ferroelectric phase transition in chromium-doped DMAAS

X-band electron paramagnetic resonance (EPR) investigations of single crystals of Cr³⁺-doped dimethylammonium aluminium sulphate hexahydrate are presented from 100 K to room temperature. The crystal undergoes a phase transition at 152 K from the ferroelastic to the ferroelectric phase. The spin-Hamiltonian parameters have been determined for both phases. The spin-Hamiltonian parameters in the ferroelectric phase are:g=1.980±0.003,b ₂ ⁰ =(1140±15)·10^?4 cm^?1,b ₂ ² =(214±10)·10^?4 cm^?1. Remarkable EPR line width changes confirm the order-disorder character of the ferroelectric phase transition on a microscopic level and demonstrate that the dimethylammonium reorientation freezing-out is the prime reason for this transition.     

FastJet user manual

FastJet is a C++ package that provides a broad range of jet finding and analysis tools. It includes efficient native implementations of all widely used 2??1 sequential recombination jet algorithms for pp and e ⁺ e ^? collisions, as well as access to 3rd party jet algorithms through a plugin mechanism, including all currently used cone algorithms. FastJet also provides means to facilitate the manipulation of jet substructure, including some common boosted heavy-object taggers, as well as tools for estimation of pileup and underlying-event noise levels, determination of jet areas and subtraction or suppression of noise in jets.     

Fourth-order zero-field splitting parameters of [Mn(cyclam)Br2]Br determined by single-crystal W-band EPR

Single-crystal W-band (95 GHz) electron paramagnetic resonance (EPR) studies have been performed at 20 K and at room temperature on a tetragonal Mn(III) compound with potential application as a building block for high-spin clusters. The observed EPR spectra correspond to an anisotropic high-spinS = 2 ground state and have been attributed to equivalent centers related by four-fold symmetry. Accurate values for the spin Hamiltonian parameters were obtained from the analysis of the data at both temperatures. At 20 K the contribution of fourth-order zero-field splitting terms was shown to be significant, with parameter values B ₄ ⁰ = 0.0009(3) cm^?1, B ₄ ² = 0.0006(2) cm^?1 and B ₄ ⁴ = 0.0017(3) cm^?1, to be considered together with the second-order parametersD = ?1.1677(7) cm^?1 andE= ?0.0135(6) cm^?1.     

Unitarity constraints for new physics induced by dim-6 operators

We compute the helicity amplitudes for bosonboson scattering at high energy due to the operatorsO _BΦ,O _WΦ andO _UB , and we derive the corresponding unitarity bounds. Thus, we provide relations between the couplings of these operators and the corresponding New Physics thresholds, where either unitarity is saturated or new degrees of freedom are excited. We compare the results with those previously obtained for the operatorsO _W andO _UW and we discuss their implications for direct and indirect tests at present and future colliders. The present treatment completes the study of the unitarity constraints for all blind bosonic operators.     

Comparison of electron spin polarization of P 870 + Qa a − observed in Zn2+-containing and Fe2+-depleted bacterial reaction centers

Recently, a general model has been developed to explain electron spin polarized (ESP) electron paramagnetic resonance (EPR) signals found in systems where radical pairs are formed sequentially. The photosynthetic bacterial reaction center (RC) is such a system in which we can experimentally vary parameters (lifetime, structure, and magnetic interactions in the sequentially formed radical pairs) that affect ESP development in order to test this model. In Fe²⁺-depleted transfer step from intermediate radical pair, P ₈₇₀ ⁺ Q _a ^? which is produced in an electron transfer step from intermediate radical pair, P ₈₇₀ ⁺ I^?. (P ₈₇₀ ⁺ is the oxidized primary donor, a special pair of bacteriochlorophyll molecules, I^? is the reduced bacteriopheophytin acceptor, and Q _a ^? is the reduced primary quinone acceptor.) The lifetime of P ₈₇₀ ⁺ I^? can be shortened relative to the lifetime of P ₈₇₀ ⁺ I^? in Fe²⁺-depleted RCs by substitution of Zn²⁺. We report the first observation of X-band and Q-band ESP EPR signals due to P ₈₇₀ ⁺ Q^? from bacterial reaction centers that contain Zn²⁺. Comparison of these signals to those observed from Fe²⁺-depleted bacterial reaction centers shows intensity differences and g-factor shifts. The results are discussed in terms of the general sequential radical pair model.     

Anticommutativity equation in topological quantum mechanics

We consider topological quantum mechanics as an example of topological field theory and show that its special properties lead to numerous interesting relations for topological correlators in this theory. We prove that the generating function ? for these correlators satisfies the anticommutativity equation (D?F)². We show that the commutativity equation [dB, dB]=0 can be considered as a special case of the anticommutativity equation.     

Estimate of the fraction of primary photons in the cosmic-ray flux at energies ∼1017 eV from the EAS-MSU experiment data

We reanalyze archival EAS-MSU data in order to search for events with an anomalously low content of muons with energies E _μ > 10 GeV in extensive air showers with the number of particles N _e ? 2 × 10⁷. We confirm the first evidence for a nonzero flux of primary cosmic gamma rays at energies E ～ 10¹⁷ eV. The estimated fraction of primary gamma rays in the flux of cosmic particles with energies E ? 5.4 × 10¹⁶ eV is ε_γ = (0.43 _?0.11 ^+0.12 )%, which corresponds to the intensity I _γ = (1.2 _?0.3 ^+0.4 ) × 10^?16 cm^?2 s^?1 sr^?1. The study of arrival directions does not favor any particular mechanism of the origin of the photon-like events.     

Electron paramagnetic resonance of Dy3+ ions in lead thiogallate single crystals

The results of electron paramagnetic resonance (EPR) studies of Dy³⁺ ions in lead thiogallate PbGa₂S₄ single crystals have been presented. It has been shown that the ground state of these ions corresponds to the lowest Stark sublevel Γ₆ of the term ⁶ H _15/2. The spectra are well described by the axially symmetric spin Hamiltonian with the effective spin S = 1/2 with the factors g _‖ = 15.06 and g _⊥ = 2.47. The Dy³⁺ ions substitute Pb²⁺ ions in the crystal lattice of PbGa₂S₄. The observed hyperfine structure has allowed to unambiguously interpret the EPR spectra. The hyperfine interaction constants of two odd isotopes of dysprosium in lead thiogallate single crystals have been found to be A _‖ = 675 × 10^?4 cm^?1 and A _⊥ = 111 × 10^?4 cm^?1 for ¹⁶³Dy and A _‖ = 472 × 10^?4 cm^?1 and A _⊥ = 77 × 10^?4 cm^?1 for ¹⁶¹Dy.     

Effective moment of inertia in132Ce,134Nd and136Nd

The effective moment of inertiaI _eff ⁽²⁾ of¹³²Ce,¹³⁴Nd and¹³⁶Nd produced in⁴⁰Ar induced reactions has been deduced from continuumγ-ray spectra measured by sum spectrometer methods. Results concerning the deformation of these nuclei are obtained by comparison of the experimental data and calculations in the frame of a cranking Nilsson — Strutinsky model.