Comparing the VGCG model as the unification of dark sectors with observations

Current observations indicate that 95% of the energy density in the universe is the unknown dark component.The dark component is considered composed of two fluids:dark matter and dark energy.Or it is a mixture of these two dark components,i.e.,one can consider it an exotic unknown dark fluid.With this consideration,the variable generalized Chaplygin gas(VGCG)model is studied with not dividing the unknown fluid into dark matter and dark energy parts in this paper.By using the Markov Chain Monte Carlo method,the VGCG model as the unification of dark sectors is constrained,and the constraint results on the VGCG model parameters are,n=0.00057+0.0001+0.0009-0.0006-0.0006,α=0.0015+0.0003+0.0017-0.0015-0.0015and B s=0.778+0.016+0.030-0.016-0.035,obtained by the cosmic microwave background data from the 7-year WMAP full data points,the baryon acoustic oscillation data from Sloan Digital Sky Survey(SDSS)and 2-degree Field Galaxy Redshift(2dFGRS)survey,and the Union2 type Ia supernova data with systematic errors.At last,according to the evolution of deceleration parameter it is shown that an expanded universe from deceleration to acceleration can be obtained in VGCG cosmology.     

Axial Anomaly and the Triality Symmetry of Leptons and Hadrons

We apply the supersymmetric model of É. Cartan to the pseudoscalar meson decay into two photons, \({\pi_0\to\gamma\gamma}\) , \({\eta\to\gamma\gamma}\) and \({\eta'\to\gamma\gamma}\) . In the book of É. Cartan published in 1966, Dirac spinors ^t (A, B) and ^t (C, D) and vector fields E and E′ were introduced and five supersymmetric transformations G ₂₃, G ₁₂, G ₁₃, G ₁₂₃ and G ₁₃₂ were considered. The Pauli spinor is treated as a quaternion and the Dirac spinor is treated as an octonion. In the pseudoscalar meson decay, when the two final vector fields belong to the same group (EE or E′E′), we call the diagram rescattering diagram. When they belong to different groups (EE′), the diagram is called twisted diagram. Assuming the triality selection rules of octonions, dark matter is interpreted as matter emitting photons in a different triality sector than that of electromagnetic probes in our world.     

Quantum deformation of compactified Minkowski space

The quantum GrassmanianG(2|0; ? _q ^4|0 ) of “quantum 2-planes ? _q ^2|0 in the quantum 4-plane ? _q ^4|0 ”, which provides aq-deformation of compactified complexified Minkowski space, is proposed. A quantum analogue of classical Plücker embedding of the usual GrassmanianG(2; ?²) into a non-degenerate quadric in ??⁵ is found.     

An experimental study of anti-phase boundaries contrast of Fe-Si alloys in superlattice reflexions

Thin foils of ordered alloys of different composition are studied by transmission electron microscopy. The contrast on antiphase boundaries 1/4a ₀ ^′ 〈111〉, 1/2a ₀ ^′ 〈100〉 is compared with contrast theories. It is shown that the dependence of the contrast profile on the deviation parameter from the Bragg reflexion position and the thickness of the foil for oblique boundaries is qualitatively in agreement with the theory. On nearly perpendicular boundaries the observed dependence of contrast is qualitatively the same for higher silicon contents. For lower silicon contents, however, only dark contrast (in the dark field image) is observed for all values of the deviation parameter and foil thickness. This behaviour of nearly perpendicular boundaries at lower silicon contents is explained by the existence of a disordered layer of finite thickness in the boundary. The disordered layer also causes the anomalous contrast of 1/2a ₀ ^′ 〈100〉 boundaries in S₂ reflexions for which zero contrast is predicted by the theory. In contrast to the idealized model of a boundary of this type with disordered second nearest neighbours only, the experiments show also some disorder of the first nearest neighbours. Finally, examples of complicated fringe contrast are shown which can possibly be interpreted as many-beam cases with superlattice and fundamental reflexions excited simultaneously.     

A Modified Generalized Chaplygin Gas as the Unified Dark Matter–Dark Energy Revisited

A modified generalized Chaplygin gas (MGCG) is considered as the unified dark matter–dark energy revisited. The character of MGCG is endued with the dual role, which behaves as matter at early times and as a quiessence dark energy at late times. The equation of state for MGCG is p?=???αρ/(1?+?α)????(z)ρ ^???α /(1?+?α) , where $\vartheta(z)=-[\,\rho_{\,\rm 0c}(1+z)^{3}]\,^{(1+\alpha)}(1-\Omega_{\,\rm 0B})^{\alpha}\{\alpha\Omega_{\,\rm 0DM}+ \Omega_{\,\rm 0DE}[\,\omega_{\,\rm DE}+\alpha(1+\omega_{\rm DE})](1+z)^{3\omega_{\rm DE}(1+\alpha)}\}$ . Some cosmological quantities, such as the densities of different components of the universe Ω _i (i, respectively, denotes baryons, dark matter, and dark energy) and the deceleration parameter q, are obtained. The present deceleration parameter q ₀, the transition redshift z _T, and the redshift z _eq, which describes the epoch when the densities in dark matter and dark energy are equal, are also calculated. To distinguish MGCG from others, we then apply the Statefinder diagnostic. Later on, the parameters (α and ω _DE) of MGCG are constrained by combination of the sound speed $c^{2}_{\rm s}$ , the age of the universe t ₀, the growth factor m, and the bias parameter b. It yields $\alpha=-3.07^{+5.66}_{-4.98}\times10^{-2}$ and $\omega_{\rm DE}=-1.05^{+0.06}_{-0.11}$ . Through the analysis of the growth of density perturbations for MGCG, it is found that the energy will transfer from dark matter to dark energy which reach equal at z _eq～0.48 and the density fluctuations start deviating from the linear behavior at z～0.25 caused by the dominance of dark energy.     

Asymptotic analysis of perturbed dust cosmologies to second order

Nonlinear perturbations of Friedmann–Lemaitre cosmologies with dust and a cosmological constant $\Lambda >0$ Λ > 0 have recently attracted considerable attention. In this paper our first goal is to compare the evolution of the first and second order perturbations by determining their asymptotic behaviour at late times in ever-expanding models. We show that in the presence of spatial curvature K or a cosmological constant, the density perturbation approaches a finite limit both to first and second order, but the rate of approach depends on the model, being power law in the scale factor if $\Lambda >0$ Λ > 0 but logarithmic if $\Lambda =0$ Λ = 0 and $K<0$ K < 0 . Scalar perturbations in general contain a growing and a decaying mode. We find, somewhat surprisingly, that if $\Lambda >0$ Λ > 0 the decaying mode does not die away, i.e. it contributes on an equal footing as the growing mode to the asymptotic expression for the density perturbation. On the other hand, the future asymptotic regime of the Einstein–de Sitter universe ( $K=\Lambda =0$ K = Λ = 0 ) is completely different, as exemplified by the density perturbation which diverges; moreover, the second order perturbation diverges faster than the first order perturbation, which suggests that the Einstein–de Sitter universe is unstable to perturbations, and that the perturbation series do not converge towards the future. We conclude that the presence of spatial curvature or a cosmological constant stabilizes the perturbations. Our second goal is to derive an explicit expression for the second order density perturbation that can be used to study the effects of including a cosmological constant and spatial curvature.     

Dielectric relaxation phenomena of rigid polar liquid molecules under giga hertz electric field

The dielectric relaxation phenomena of rigid polar liquid molecules chloral and ethyltrichloroacetate (j) in benzene, n-hexane and n-heptane (i) under 4.2, 9.8 and 24.6 GHz electric fields at 30°C are studied to show the possible existence of double relaxation times τ ₂ and τ ₁ for rotations of the whole and the flexible parts of molecules. The probability of showing double relaxation is more in aliphatic solvents indicating their nonrigidity. The symmetric and asymmetric distribution parameters γ and δ are obtained from X _ij ^′ /X _0ij and X _ij ^″ /X _0ij and w _j →0 where X _ij ^′ and X _ij ^″ are real and imaginary parts of the complex orientational susceptibility X _i ^* and X _0ij is the low frequency susceptibility which is real. X _ij ’s are involved with the measured dielectric relative permittivities ε _ij ^′ , ε _in ^″ , ε _0ij and ε _∞ij of solutions. The theoretical weighted contributions c ₁ and c ₂ towards dielectric dispersions by Fröhlich’s method are compared with the experimental ones obtained from the graphical variation of X _ij ^′ /X _0ij and X _ij ^″ /X _0ij with weight fractions w _j ’s at w _j → 0. The measured dipole moments μ ₂ and μ ₁ of the whole and the flexible part of a polar molecule in terms of the linear coefficients β’s of X _ij ^′ ’s with w _j ’s and the estimated τ ₂ and τ ₁ reveal their associations with aliphatic solvents. The theoretical dipole moments μ _theo’s from the available bond angles and bond moments of the substituent polar groups of the molecules with the estimated μ’s suggest the mesomeric, inductive and electromeric effects in them under GHz electric field.     

The potential for which E n 1 ′ 12=E n 2 ′ l1 in nonrelativistic quantum mechanics

The answer is provided to the question ‘What is the potential for which E _{n 1} ^′ l₂=E _{n 2} ^′ l₁ in nonrelativistic Quantum Mechanics?’     

Electromagnetic and weak interactions in stochastic space-time: A review

A scheme for a nonlocal theory of quantized fields based on the hypothesis of stochastic space is proposed. Within this scheme the gauge-invariant quantum electrodynamics of particles with spin 0, 1/2, 1 and four-fermion weak interactions are constructed, and nonlocal corrections to the anomalous magnetic moments of leptons and to the Lamb shift are calculated. Some consequences of the neutrino oscillations and the electromagnetic properties of neutrinos are considered in detail. Further the rare decayK _L ⁰ →Μ⁺Μ^? and the mass difference ofK _L ⁰ andK _S ⁰ mesons are investigated in this model. It is shown that the parameter of nonlocality (elementary lengthl) of weak interactions which can characterize a domain of unification of weak and electromagnetic interactions is ～10^?16 cm. The low-energy experiments imply that quantum electrodynamics is valid up to distances of order ～10^?15 cm.     

Pion photoproduction on197Au to ground and isomeric states in197Hg

The lifetime of the 331.3 keV 0 ₂ ⁺ state in¹⁰⁰Zr has been measured at the gas-filled recoil separator for fission products JOSEF. By observing the delayed coincidences between theβ-particles populating the level and theE0 conversion electrons from its decay into the ground state, a half-life of 3.37±0.30 ns has been obtained. From the measured lifetime and the relative intensities of the 0 ₂ ⁺ →0 ₁ ⁺ and 0 ₂ ⁺ →2 ₁ ⁺ transitions, values of 0.493±0.015 for theE0 strength parameterρ, and of 16 single particle units forB(E2,2 ₁ ⁺ → 0 ₂ ⁺ ) have been deduced. The enhanced nature of theE0 transitions suggests mixing of the 0 ₁ ⁺ and 0 ₂ ⁺ states which may be estimated by comparing the experimentalB(E2) values for the 2 ₁ ⁺ →0 ₁ ⁺ and 2 ₁ ⁺ →0 ₂ ⁺ transitions with the predictions of the asymmetric VMI model.     

Parametrization of two-body perturbation on atomic fine and hyperfine structure. The configuration (6p)3 in the bismuth atom

A method of simultaneous parametrization of one- and two-body interactions on atomic hyperfine structure of configurationl ^N is proposed and applied for the analysis of the configuration (6p)³ in the bismuth atom. For this purpose, the hyperfine structure splittings of the levels²D ₃ ^2/0 ,²D ₅ ^2/0 and²P ₁ ^2/0 were measured. The finally obtained values of HFS parameters are: for one-body parameters (in MHz):a _p ⁰¹ =2,537(9),a _p ¹² =5,182 (12),a′¹⁰=?2,019(10),b _p ⁰² =?3,198(53),b _p ¹¹ =2,816(54); for two-body parameters (in MHz):x _pp ^′/01 ,₂=284(3),x _pp ^′/12 ,₂=581(5),x _pf ^′/12 ,₂=170(70),x _pp ^′/02 ,₂=?359(36),x _pf ^′/02 ,₂=?33(100). The value of the quadrupole moment of the nucleus ₈₃ ²⁰⁹ Bi is also discussed.     

Electric properties of levels of 156Dy rotational bands

The nonadiabaticity of E0 transitions from 0 ₂ ⁺ states and 2 ₁ ⁺ bands in ¹⁵⁶Dy is examined within a phenomenological model that takes into account the mixing of K ^π = 0 ₁ ⁺ , 0 ₂ ⁺ , 0 ₃ ⁺ , 2 ₁ ⁺ states and 1⁺-bands. It is shown that the nonadiabaticity of E0 transitions is due primarily to the mixing of 0 ₂ ⁺ and 0 ₃ ⁺ bands.     

On the permutability of Bäcklund transformations: 1 infinitesimal Bäcklund transformations of the sine-Gordon equation

Letu′=B _a u be the Bäcklund transformation of the sine-Gordon equation, we prove that $$B_{a + \varepsilon } B_a^{ - 1} u = u + \varepsilon \sum\limits_{n = 0}^\infty {2D^{ - 1} } \frac{{\delta G_{n + 1} }}{{\delta u}}a^{2n} ,$$ where {G _n} is an infinite set of conserved densities of the sine-Gordon equation and η ⁿ ≡D ^?1δG _n /δu are just the symmetries obtained by Olver [17]. Basing upon this expansion, we prove the equivalence between the permutability of the infinitesimal Bäcklund transformations and the involution of the conserved densities of the sine-Gordon equation.     

New screening doublets in x-ray satellite spectra

Recent scrutiny of the relevant data available at present on x-ray satellite spectra in theK, L andM regions revealed the existence of two new satellite pairsα″α′ andα″α′ ₃ ′ in theKα satellite group, three pairsα′ ₂ α″,α′ ₂ α^VI andα? α ^IV in theLα satellite group, twoLβ ₂ satellite groups; viz.,β ₂ ^(b) (β ₂ ^I ,β ₂ ^II β ₂ ^(c) ) andβ ₂ ^(c) (β ₂ ^I β ₂ ^II ), two pairsγ′₁ γ′₂ andγ′₁ γ′_2′ in theLγ satellite group and also a pairβ _II β _III in theMβ satellites, which are all found to be governed by the screening doublet relationship,Δ(v/R)^1/2=constant.     

On the signatures of the canonical and the metrical energy densities of vector fields

The energy-density components Θ ₀ ⁰ andT ₀ ⁰ of the canonical and of the metrical energy-momentum tensors Θ _k ⁱ andT _k ⁱ for a statical field of vector mesons have opposite signatures: Θ ₀ ⁰ =H=?T ₀ ⁰ =?L. From this property some relativistic and field-theoretical theorems can be deduced in an elementary way.     

Investigation of N 2 + (C 2Σ u + → X 2Σ g + fluorescence excited through auger decay of the 1s −1π* resonance

A theoretical investigation of N ₂ ⁺ (C ²Σ _u ⁺ → X ²Σ _g ⁺ molecular fluorescence excited through the Auger decay of the 1s ^?1π* resonance is carried out. The fluorescence cross sections are calculated with due regard for the dependence of the matrix element of the C → X dipole transition on the internuclear distance, the interference between channels of excitation via different vibrational levels v _r of the 1s ^?1π* resonance, the rotational structure of the fluorescence band, and the predissociation of the N ₂ ⁺ C ²Σ _u ⁺ v′ ≥3) states. The calculated cross sections are in good agreement with the experimental results of recent measurements. The results of the calculations have demonstrated that the observed dependence of the cross section of the (C ²Σ _u ⁺ (v′) → X ²Σ _g ⁺ (v″) fluorescence on the excitation energy and the fluorescence wavelength for a group of bands with equal values of the difference Δv = v′ ? v″ is associated with transitions between the vibrational levels of the electronic states involved in the excitation and subsequent cascade decay of the 1s ^?1π* resonance: N₂ (v ₀ = 0) → N*₂(1s ^?1π*(v _r)) ? N ₂ ⁺ : (C ²Σ _u ⁺ (v′) → X ²Σ _g ⁺ (v″).     

Inclusive production ofK s 0 , K s 0 K s 0 andK *±(892) in\bar pp interactions at 3.0, 3.5, 4.0 and 4.5 GeV/c

InclusiveK _s ⁰ andK _s ⁰ K _s ⁰ production in \(\bar pp\) interactions at 3.0, 3.5, 4.0 and 4.5 GeV/c are studied. Cross sections ofK _s ⁰ , K _s ⁰ K _s ⁰ andK ^*±(892) are presented for each incident momentum. The production ofK _s ⁰ andK ^*±(892) through annihilation process is investigated. It is found that the annihilation process is dominant but decreases with incident momentum. The annihilation process is compared withe ⁺ e ^? interactions. Remarkable similarity between them is found in the \({{x_0 = 2E(K_s^0 )} \mathord{\left/ {\vphantom {{x_0 = 2E(K_s^0 )} {\sqrt s }}} \right. \kern-0em} {\sqrt s }}\) distribution. Events with two detectedK _s ⁰ 's are analyzed. The result shows theK _s ⁰ K _s ⁰ pairs are produced in the central region of c.m. system and there is a clearS ^* signal in theK _s ⁰ K _s ⁰ effective mass distribution.     

Semiempirical investigation of perturbations of the g factors of electronic-vibrational-rotational levels of hydrogen: III. The r 3Π g − and s 3Δ g − states of the H2 and D2 molecules

The g factors of rovibrational levels of the (4d)r ³Π _g ^? and (4d)s ³Δ _g ^? states of the H₂ and D₂ molecules have been obtained for the first time. These values were found within the nonadiabatic model taking into account the interaction of the 4dπ³Π_g and 4dδ³Δ_g states in the pure precession approximation using semiempirical values of the expansion coefficients of the wave function in an adiabatic basis, which was obtained for the first time for the states of the triplet 4d complex of terms of the hydrogen molecules, and the results of numerical calculation of the overlap integrals of the vibrational wave functions of these states. It is established that the interference effects of the interaction between the 4dπ³Π _g ^? and 4dδ³Δ _g ^? states lead to significant (up to 7 times for the r ³Π _g ^? state of the H₂ and D₂ molecules and 70 and 8 times for the s ³Δ _g ^? state of the H₂ and D₂ molecules, respectively) differences between the nonadiabatic values of the g factors and the corresponding adiabatic values. It is found that the perturbed values of the g factors are much closer to the values corresponding to the case of Hund’s d coupling of angular momenta than to the values corresponding to the b coupling. It is established that the perturbations of the g factors of rovibrational levels of the states of the 4d complex of terms are much greater (up to 2 times for the ³Π _g ^? states and 350 times for the ³Δ _g ^? states) than the perturbations of the same characteristics for the 3d complex of terms of the hydrogen molecule with the same vibrational and rotational quantum numbers.     

The decay of the Bethe-Salpeter kernel inP(ϕ)2 quantum field models

We extend methods of high temperature expansions to show that for even weakly coupledP(?)₂ quantum field models the Bethe-Salpeter kernel has 4 particle decay. More precisely ifK denotes the Euclidean Bethe-Salpeter kernel $$|K(x_1 ,x_2 ,x_3 ,x_4 )| \leqq Oe^{ - m_0 (1 - \varepsilon )d_2 } ,$$ wherex=(x ⁰,x ¹),d ₂=2|x ₁ ⁰ +x ₂ ⁰ ?x ₃ ⁰ ?x ₄ ⁰ |+|x ₁ ⁰ ?x ₂ ⁰ |+|x ₃ ⁰ ?x ₄ ⁰ | and ε(λ)→0 as λ→0. Our methods apply to otherr particle irreducible kernels.     

Multiplicities of charged particles prior to fission

Electric monopole transitions between the 0 ₂ ⁺ , 0 ₁ ⁺ and 2 ₂ ⁺ , 2 ₁ ⁺ levels in⁷⁶Se, populated in the decay of⁷⁶Br, were investigated by means of conversion electrons and gammaray spectroscopy. TheK-electron intensity ratios ofE0 andE2 transitions connecting the 0 ₂ ⁺ level to the 0 ₁ ⁺ and 2 ₁ ⁺ levels and of theE0 andE2 components in the 2 ₂ ⁺ →2 ₁ ⁺ transition were determined. The ratioX(E0/E2) of theE0 toE2 reduced transition probabilities and, from the available lifetimes, theE0 strength parameters ρ(E0) were deduced for the two transitions. The results are compared with the predictions of current models.