Connection Considerations of Gravitational Field in Finsler Spaces

Some alternative connection structures of the Finslerian gravitational field are considered by modifying the independent variables (x,y) (x: point and y: vector) in various ways. For example, (x ^k ,y ⁱ ) (k,i = 1,2,3,4) are changed to (x ^k ,y ⁰) (y ⁰: scalar) or (x ⁰,y ⁱ ) (x ⁰: time axis); (x ^k ,y ⁱ ) are generalized to (x ^k ,y ⁱ ,p _i ) (p _i : covector dual to y ⁱ ) or (x ^k ,y ⁱ ,q _a ) (q _a : covector different from p _i ); (x ^k ,y ⁱ ) are further generalized to (x ^k ,y ^(a)i ) (a = 1,2,…,m), (y ^(a): (a)th vector), etc.     

Electric Dipole Oscillator Strength and Radiative Lifetimes in the Magnesium Isoelectronic Sequence

Oscillator strengths for the singlet 3sns(¹S)-3smp(¹P); (n, m = 3-7), 3snp(¹P)-3smd(¹D); (n = 4-7, m = 3-6) and the triplet 3sns(³S)-3smp(³P); (n = 4-7, m = 3-7), 3snp(³P)-3smd(³D); (n = 4-7, m = 3-6) transitions in the Mg I sequence are calculated in LS-coupling scheme. The Coulomb approximation is used in calculating the radial part of the wave functions, while the angular part is determined using the Racah technique. Lifetimes of the upper 3sns(³S, ¹S); (n = 4-7) and 3snp(³P, ¹P); (n = 3-7) excited states are obtained and compared with the available experimental data.     

Systematic measurements of M X-ray components X-ray fluorescence cross-sections for the elements with 77 ≤ Z ≤ 92 by employing laboratory source based energy dispersive X-ray fluorescence setup

The differential X-ray fluorescence (XRF) cross-sections for (Mξ₂, Mξ₁, Mδ₁), (Mδ₂, Mα_1,2 M₅-O₃), (Mβ, M₄-O_2,3), (Mγ, Mm₂, M₃-N₄, M₅-O_2,3), (Mm₁, M₃-N_6,7, M₃-O_4,5) and (Mm_2, M₂-N₆) group of M X-rays components have been measured for the elements with 77 ≤ Z ≤ 92 following photoionization by Mn K X-rays (E_Kαβ = 5.96 keV) obtained from ⁵⁵Fe radioisotope. The measurements were performed in annular source geometry at 126° emission angle using a low-energy Ge (LEGe) detector. The measured cross-section values are compared with theoretical values calculated using available sets of M_i (i = 1–5) photoionization cross-sections, radiative emission rates (F_ij), Coster-Kronig (f_ij), and fluorescence (ω_i) yields. The measured XRF cross-sections for the (Mξ₂, Mξ₁, Mδ₁), (Mm₁, M₃-N_6,7) and (Mm₂, M₂-N₆) groups of X-rays agree with the theoretical values within the experimental errors. The (Mβ, M₄-O_2,3) group of X-rays exhibit agreement with theoretical values within experimental uncertainty for all the elements under investigation except ₇₉Au and ₈₀Hg. The XRF cross-section for the (Mδ₂, Mα_1,2) group of X-rays are in general higher by ~20% for the elements with Z = 77–83 and exhibit agreement for the ₉₀Th and ₉₂U elements. For the (Mγ, Mm₂, M₃-N₄) X-ray group, the measured values are generally higher than the theoretical values, but the deviations are within experimental uncertainties. The large deviation in measured XRF cross-section for different M X-ray components from the theoretical ones are attributed to (i) poor separation of M X-ray components (ii) contribution of self-resonant Raman scattering (RRS) process and (iii) self-fluorescence of M₅ subshell by M_i subshell X-rays (i = 1–3).     

The modified Korteweg-de Vries equation on the quarter plane with t-periodic data

We study the modified Korteweg-de Vries equation posed on the quarter plane with asymptotically t-periodic Dirichlet boundary datum u(0,t) in the sense that u(0,t) tends to a periodic function g?₀ (t) with period τ as t → ∞. We consider the perturbative expansion of the solution in a small ε > 0. Here we show that if the unknown boundary data u_x(0,t) and u_xx(0,t) are asymptotically t-periodic with period τ which tend to the functions g?₁ (t) and g?₂ (t) as t → ∞, respectively, then the periodic functions g?₁ (t) and g?₂ (t) can be uniquely determined in terms of the function g?₀ (t). Furthermore, we characterize the Fourier coefficients of g?₁ (t) and g?₂ (t) to all orders in the perturbative expansion by solving an infinite system of algebraic equations. As an illustrative example, we consider the case of a sine-wave as Dirichlet datum and we explicitly determine the coefficients for large t up to the third order in the perturbative expansion.     

An exact formulation of the Blume-Emery-Griffiths model on a two-fold Cayley tree model

A two-fold Cayley tree graph with fully q-coordinated sites is constructed and the spin-1 Ising Blume-Emery-Griffiths model on the constructed graph is solved exactly using the exact recursion equations for the coordination number q = 3. The exact phase diagrams in (kT/J, K/J ) and (kT/J, D/J) planes are obtained for various values of constants D/J and K/J, respectively, and the tricritical behavior is found. It is observed that when the negative biquadratic exchange (K) and the positive crystal-field (D) interactions are large enough, the tricritical point disappears in the (kT/J, K/J) plane. On the other hand, the system always exhibits a tricritical behavior in the phase diagram of (kT/J, D/J) plane. Received 8 June 2001 and Received in final form 28 September 2001     

On Bilinear Invariant Differential Operators Acting on Tensor Fields on the Symplectic Manifold

Abstract

Let M be an n-dimensional manifold, V the space of a representation ρ : GL(n) → GL(V). Locally, let T (V ) be the space of sections of the tensor bundle with fiber V over a sufficiently small open set U ? M, in other words, T (V ) is the space of tensor fields of type V on M on which the group Diff(M) of diffeomorphisms of M naturally acts. Elsewhere, the author classified the Diff(M)-invariant differential operators D : T (V ₁) ? T (V ₂) → T (V ₃) for irreducible fibers with lowest weight. Here the result is generalized to bilinear operators invariant with respect to the group Diff_ω(M) of symplectomorphisms of the symplectic manifold (M, ω). We classify all first order invariant operators; the list of other operators is conjectural. Among the new operators we mention a 2nd order one which determins an “algebra” structure on the space of metrics (symmetric forms) on M.     

AES and ELS study of titanium oxidation in high vacuum

In the present work, results of the interaction of O₂ with polycrystalline titanium using AES, and ELS techniques, are presented. Changes in the shapes of Ti(LMV) and Ti(LMM) transitions and in the Ti(LM)O(V)/Ti(LMV) and Ti(LMV) Ti(LMM) amplitude ratios as well as a shift of the 34 eV loss peak [Ti(3p level], are studied as function of the oxygen exposure.At O₂ pressures equal or less than 10^–6 Pa and exposure up to 2000 L(O₂) (weak oxidation), the Ti(LM)O(V)/Ti(LMV) and Ti(LMV)/Ti(LMM) ratios show three clearly distinct regions: (i) up to 20L there is a chemisorbed phase with the Ti(LMV)/Ti(LMM) ratio remaining constant and a fast linear increase in the Ti(LM)O(V)/Ti(LMM) ratio. (ii) At exposures higher than 20L the oxidation begins being characterized by a linear variation of the Ti(LM)O(V)/Ti(LMV) and Ti(LMV)/Ti(LMV) ratios, with positive and negative slopes, respectively. (iii) At 125L there is a change in both slopes but no stable value is achieved, despite the O(KLL)/Ti(LMM) ratio remains constant. Hence, it can be concluded that TiO is the final oxide obtained after that treatment, from features like the shape of the transitions and a maximum shift of 3eV of the Ti(3p) level, complemented with ESD experiments.On the other hand, experiments at pressures higher than 10^–4Pa with or without the surfaces at 900K (strong oxidation) indicate that the most likely final oxide is TiO₂.Work presented to the IXIVC-VICSS. Madrid (1983)     

Inverse resonance scattering for Jacobi operators

The Jacobi operator (Jf) _n = a _n−1 f _n−1 +a _n f _n+1 + b _n f _n on ℤ with real finitely supported sequences (a _n − 1) _n∈ℤ and (b _n ) _n∈ℤ is considered. The inverse problem for two mappings (including their characterization): (a _n , b _n , n ∈ ℤ) → {the zeros of the reflection coefficient} and (a _n , b _n , n ∈ ℤ) → {the eigenvalues and the resonances} is solved. All Jacobi operators with the same eigenvalues and resonances are also described.     

Cross-section measurements of (n, 2n) and (n, p) reactions on 124,126,128,130,131,132Xe in the 14 MeV region and theoretical calculations of their excitation functions

The reaction cross-sections of ¹²⁴Xe(n, 2n)¹²³Xe, ¹²⁶Xe(n, 2n)¹²⁵Xe, ¹²⁸Xe(n, 2n)¹²⁷Xe, ¹³⁰Xe(n, 2n)^129mXe, ¹³²Xe(n, 2n)^131mXe, ¹³⁰Xe(n, p)¹³⁰I, ¹³¹Xe(n, p)¹³¹I, and ¹³²Xe(n, p)¹³²I were measured at the 13.5, 13.8, 14.1, 14.4, and 14.8 MeV neutron energies. The monoenergetic neutrons were generated via the ³H(d,n)⁴He reaction at the China Academy of Engineering Physics using the K-400 Neutron Generator with a solid ³H-Ti target. A high-purity germanium detector was employed to measure the activities of the product. The reactions ⁹³Nb(n, 2n)^92mNb and ²⁷Al(n, α)²⁴Na were adopted for neutron flux calibration. The cross sections of the (n, 2n) and (n, p) reactions of the xenon isotopes were obtained within the 13–15 MeV neutron energy range. These cross-sections were then compared with the IAEA-exchange format (EXFOR) database-derived experimental data, together with the evaluation results of the CENDL-3, ENDF/B-VIII.0, JENDL-4.0, RUSFOND, and JEFF-3.3 data libraries, as well as the theoretical excitation function obtained using the TALYS-1.95 code. The cross-sections of the reactions (except for the ¹²⁴Xe(n, 2n)¹²³Xe and ¹³²Xe(n, p)¹³²I) at 13.5, 13.8, and 14.1 MeV are reported for the first time in this study. The obtained results are beneficial in providing better cross-section constraints for the reactions in the 13–15 MeV region, thus improving the quality of the corresponding database. Meanwhile, these data can also be used for the verification of relevant nuclear reaction model parameters.     

Raman studies and optical properties of some (PbO)x(Bi2O3)0.2(B2O3)0.8−x glasses

Five (PbO)_x(Bi₂O₃)_0.2(B₂O₃)_0.8−x glasses, where x = 0, 0.2, 0.3, 0.4 and 0.6, were prepared. The dilatometric glass transition temperature (T_g) was found in the region 470 (x = 0)≥ T_g ( °C) ≥ 347 (x = 0.6), and the density (ρ) varied within 4.57 (x = 0) ≤ ρ (g/cm³) ≤ 8.31 (x = 0.6). Raman spectra indicated the conversion of BO₃ to BO₄ entities for low x values but for x > 0.3, namely, for x → 0.6, back‐conversion occurred, most probably. From the measurements of the optical transmission on very thin bulk samples, the room temperature optical gap values (E_g) were determined to be in the range 4.03 (x = 0)≥ E_g (eV) ≥ 3.08 (x = 0.6). The temperature (T) dependence of the optical gap (E_g(T)) in the region 300 ≤ T(K) ≤ 600 was examined and approximated by a linear relationship of the form of E_g(T) = E_g(0)− γT, where γ × 10⁻⁴(eV/K) varied from 5.1 to 6.8. The non‐linear refractive index (n₂) was estimated from the optical gap values and it was found to correspond to the n₂ values calculated from the experimental third‐order non‐linear optical susceptibility taken from the literature. Copyright © 2008 John Wiley & Sons, Ltd.     

Weak electric and magnetic form factors for semileptonic baryon decays in a relativistic quark model

Weak electric and magnetic form factors for semileptonic baryon decays are calculated in a relativistic quark model based on the Dirac equation with the independent-quark confining potential of the formV _q(r)=1/2(1+γ ⁰)(a ² r+V ₀). The values obtained for (g ₂/g ₁) are not very much different from the nonrelativistic results of Donoghue and Holstein. The values of (g ₁/f ₁) extracted from our model calculations of (f ₂/f ₁) in the Cabibbo limit compare well with the experimental values. The values of (f ₂/f ₁) for various semileptonic transitions are also estimated incorporating phenomenologically the effect of nonzerog ₂ in the ratio (g ₁/f ₁). It is found that the SU(3)-symmetry breaking does not generate significant departures in (f ₂/f ₁) values from the corresponding Cabibbo predictions.     

Equilibrium and pre-equilibrium emissions in proton-induced reactions on <Superscript>203,205</Superscript>Tl

In this study, the excitation functions for the reactions ²⁰³Tl(p, n)²⁰³Pb, ²⁰⁵Tl(p, 3n)²⁰³Pb, ²⁰³Tl(p, 2n)²⁰²Pb, ²⁰⁵Tl(p, 4n)²⁰²Pb, ²⁰³Tl(p, 3n)²⁰¹Pb, ²⁰⁵Tl(p, 5n)²⁰¹Pb, ²⁰³Tl(p, 4n)²⁰⁰Pb and ²⁰⁵Tl(p, 6n)²⁰⁰Pb have been calculated using pre-equilibrium and equilibrium reaction mechanisms. Calculated results based on hybrid model, geometry-dependent hybrid model and cascade-exciton model have been compared with the experimental data.      

Clusters of cycles

A cluster of cycles (or (r,q)-polycycle) is a simple planar 2-connected finite or countable graph G of girth r and maximal vertex-degree q, which admits an (r,q)-polycyclic realization P(G) on the plane. An (r,q)-polycyclic realization is determined by the following properties: (i) all interior vertices are of degree q; (ii) all interior faces (denote their number by p_r) are combinatorial r-gons; (iii) all vertices, edges and interior faces form a cell-complex.An example of (r,q)-polycycle is the skeleton of (r^q), i.e. of the q-valent partition of the sphere, Euclidean plane or hyperbolic plane by regular r-gons. Call spheric pairs (r,q)=(3,3),(4,3),(3,4),(5,3),(3,5). Only for those five pairs, P((r^q)) is (r^q) without exterior face; otherwise, P((r^q))=(r^q).Here we give a compact survey of results on (r,q)-polycycles. We start with the following general results for any (r,q)-polycycle G: (i) P(G) is unique, except of (easy) case when G is the skeleton of one of the five Platonic polyhedra; (ii) P(G) admits a cell-homomorphism f into (r^q); (iii) a polynomial criterion to decide if given finite graph is a polycycle, is presented.Call a polycycle proper if it is a partial subgraph of (r^q) and a helicene, otherwise. In [ARS Comb. A 29 (1990) 5], all proper spheric polycycles are given. An (r,q)-helicene exists if and only if p_r>(q−2)(r−1) and (r,q)≠(3,3). We list the (4,3)-, (3,4)-helicenes and the number of (5,3)-, (3,5)-helicenes for first interesting p_r. Any outerplanar (r,q)-polycycle G is a proper (r,2q−2)-polycycle and its projection f(P(G)) into (r^2q−2) is convex. Any outerplanar (3,q)-polycycle G is a proper (3,q+2)-polycycle.The symmetry group Aut(G) (equal to Aut(P(G)), except of Platonic case) of an (r,q)-polycycle G is a subgroup of Aut((r^q)) if it is proper and an extension of Aut(f(P(G))), otherwise. Aut(G) consists only of rotations and mirrors if G is finite, so its order divides one of the numbers 2r, 4 or 2q. Almost all polycycles G have trivial AutG.Call a polycycle G isotoxal (or isogonal, or isohedral) if AutG is transitive on edges (or vertices, or interior faces); use notation IT (or IG, or IH), for short. Only r-gons and non-spheric (r^q) are isotoxal. Let T^*(l,m,n) denote Coxeter’s triangle group of a triangle on S², E² or H² with angles π/l, π/m, π/n and let T(l,m,n) denote its subgroup of index 2, excluding motions of 2nd kind. We list all IG- or IH-polycycles for spheric (r,q) and construct many examples of IH-polycycles for general case (with AutG being above two groups for some parameters, including strip and modular groups). Any IG-, but not IT-polycycle is infinite, outerplanar and with same vertex-degree, we present two IG-, but not IH-polycycles with (r,q)=(3,5),(4,4) and AutG=T(2,3,∞)PSL(2,Z), T^*(2,4,∞). Any IH-polycycle has the same number of boundary edges for each its r-gon. For any r≥5, there exists a continuum of quasi-IH-polycycles, i.e. not isohedral, but all r-gons have the same 1-corona.On two notions of extremal polycycles:

1. We found for the spheric (r,q) the maximal number n_int of interior points for an (r,q)-polycycle with given p_r; in general case, (p_r/q)≤n_int<(rp_r/q) if any r-gon contains an interior point.

2. All non-extendible (r,q)-polycycles (i.e. not a proper subgraph of another (r,q)-polycycle) are (r^q), four special ones, (possibly, but we conjecture their non-existence) some other finite (3,5)-polycycles, and, for any (r,q)≠(3,3),(3,4),(4,3), a continuum of infinite ones.

On isometric embedding of polycycles into hypercubes Q_m, half-hypercubes and, if infinite, into cubic lattices Z_m, : for (r,q)≠(5,3),(3,5), there are exactly three non-embeddable polycycles (including (4³)−e, (3⁴)−e); all non-embeddable (5,3)-polycycles are characterized by two forbidden sub-polycycles with p₅=6.     

Dimer state in the two-dimensional anisotropic alternated-exchange Heisenberg model

An analysis is made of the two-dimensional Heisenberg model with S=1/2, anisotropic exchange interaction between nearest neighbors, and alternating exchange in two directions, [100] and [010] (corresponding to condensation of the (π, π) mode) and in one direction [100] (corresponding to condensation of the (π, 0) mode). The quantum Monte Carlo method is used to calculate the thermodynamic characteristics and the spin correlation functions which are used as the basis to determine the boundary of stability of an anisotropic antiferromagnetic with respect to alternation of exchange δ=(1−J ^x,y /J ^z )^0.4 in the (π,π) model and δ=(1−J ^x,y /J ^z )^0.31 in the (π,0) model. In the (π,0) model a disordered quantum state exists in the range (1−J ^x,y /J ^z )^0.31<δ<(0.3–0.35). The energy (E−0.68)=0.36δ ^1.80(6) and 0.21 δ ^2.0(5), the energy gap between the ground and excited states H _c (δ)=1.96δ ^2.(1), 1.8(1) (δ−0.35(3))^0.67(2) were determined as a function of the alternation of exchange in the (π,π)-and (π,0) models, respectively. Fiz. Tverd. Tela (St. Petersburg) 40, 1080–1085 (June 1998)     

Microorganisms baroinactivation of germinated mung bean (green gram) seeds

It is possible to describe the pressure degradation of microorganisms as being analogous to thermal inactivation. Equation for baroinactivation is derived from thermal death time (TDT) model D _p = D _pref 10^{(pref-p)/z _p} , where D _pref is decimal reduction time at the reference pressure (min), p _ref is the reference pressure (MPa), z _p is the pressure increase (MPa) required to reduce the D _p value by a factor of 10. This method was used for the calculation of baroinactivation model parameters of the total number of microorganisms of pressurized germinated mung bean (green gram) seeds (Vigna radiata (L.) Wilczek). Microbial contamination of germinated mung bean (green gram) seeds can be effectively decreased by treatment at a high pressure of 400 MPa, time of pressurization 5 min.     

Low-temperature elastic constants and piezoelectric coefficients of langasite (La3Ga5SiO14)

A complete set of elastic constants C _ij and piezoelectric coefficients e _ij of a La₃Ga₅SiO₁₄ (langasite) single crystal was determined from 5.5 to 275.5?K by resonant ultrasound spectroscopy. Unlike a conventional crystal, the elastic constants C _ij of the langasite crystal showed three types of temperature dependence: (i) monotonic elastic stiffening upon cooling (C ₄₄ and C ₁₄); (ii) monotonic elastic softening (C ₆₆); and (iii) a stiffening-to-softening transition below 150?K (C ₁₁, C ₁₂, C ₁₃ and C ₃₃). In addition, a strong correlation between C ₆₆ and the piezoelectric coefficient e ₁₁ was confirmed. Group theoretical lattice dynamics analysis revealed that the novel phenomena of elastic softening and strong correlation are explained on the basis of two types of optical mode internal displacements which have the totally symmetric A ₁ and doubly degenerated E symmetries in the point group D ₃.     

Ferromagnetic and antiferromagnetic ordering in the wurtzite-type diluted magnetic semiconductors

We determined the magnetic symmetry groups (Shubnikov groups) of the wurtzite-type crystals doped with magnetic atoms periodically distributed at cation sites. The magnetic groups of doped crystals with ferro- or antiferromagnetic properties arise from the P6₃ mc (C _6v ⁴), P3m1 (C _3v ¹), C _s ³ (Cm) or C ₁¹ (P1) ordinary space groups. Those arising from the P6₃ mc or P3m1 group can present macroscopic ferromagnetic polarization only along the wurtzite symmetry axis whereas those arising from the C _s ³ (Cm) group can present ferromagnetic polarization only in the symmetry plane and those arising from the C ₁¹ (P1) group can present polarization along any direction. Actual structures do not keep in general long-range order for magnetic atom distribution but the samples with macroscopic polarization should present local symmetries close to those listed above. Therefore, orientation of easy magnetization can provide information about the most frequent local symmetry.     

Thermal physical properties of the La0.825Sr0.175MnO3 single crystals

The heat capacity (C _P), the thermal diffusion (η), the thermal conductivity (κ), and the electrical resistance of the La_0.825Sr_0.175MnO₃ single crystal have been measured in the temperature range 80–350 K in magnetic fields to 40 kOe. Dependences C _P(T), κ(T), and η(T) have anomalies near T _C, which are suppressed in magnetic field. The minima in dependences κ(T) and η(T) near T _C are explained by the phonon scattering on fluctuations of the magnetic order parameter. Dependences κ(T) and η(T) have anomalies near T _S = 200 K related to the structural transition from the rhombohedral (R) to the orthorhombic (O*) phase.

     

Coherent inelastic processes on nuclei at ultrarelativistic energies

The coherent inelastic processes of the type a → b, which may take place in the interaction of hadrons and γ quanta with nuclei at very high energies (the nucleus remains the same), are theoretically investigated. For taking into account the influence of the nucleus matter, the optical model, based on the conception of the refraction index, is used. Analytical formulas for the effective cross section σ _coh (a → b) are obtained, taking into account that, at ultrarelativistic energies, the main contribution into σ _coh (a → b) is provided by very small transferred momenta in the vicinity of the minimal longitudinal momentum transferred to the nucleus. It is shown that the cross section σ _coh (a → b) may be expressed through the “forward” amplitudes of inelastic scattering f _a+N+b+N (0) and elastic scattering f _a+N+a+N(0), f _b+N+b+N(0) on a separate nucleon, and it depends on the ratios L _a /R and L _b /R (L _a and L _b are the mean lengths of the free path in the nucleus matter for the particles a and b, respectively, and R is the nucleus radius). In particular, when L _a /R ≫ 1, but L _b /R ≪ 1 (or L _a /R ≪ 1, but L _b /R ≫ 1), σ _coh (a → b) is equal to the ratio of the “forward” cross sections of inelastic scattering a + N → b + N and elastic scattering of the particle b (or a) on a nucleon, multiplied by the cross section of scattering on the “black” nucleus πR ². When both conditions L _a /R ≫ 1 and L _b /R ≫ 1 are satisfied, σ _coh (a → b) is proportional to the factor R ⁴/k ², where k is the initial energy of particle a in the laboratory frame. The text was submitted by the authors in English.     

Adsorption parameters of Cu and Ni on the {110} plane of W and Mo

This paper reports on the embedded-atom method (EAM, developed by Johnson) calculations of adsorption parameters for Cu and Ni on {110} unrelaxed substrates of Mo and W. The following are calculated: (i) the equilibrium height h _c of an adatom; (ii) the optimum coefficients W ₀ A _hk of a truncated Fourier representation of the adatom-substrate interaction potential; (iii) the desorption energies E _des ; and (iv) the activation energies Q of surface migration. It is shown that (a) the calculated values of E _des agree satisfactorily with available empirical data; (b) the scale factor W ₀ is approximately proportional to the bonding as measured by E _des , whereas the normalized coefficients A _hk are determined by the {110} substrate symmetry; (c) E _des and Q are respectively dominated by the embedding energy and pair potential of the EAM; and (d) W ₀ and E _des for an atom in a monolayer are only about half as much as the corresponding quantities for an isolated atom.