Photoelasticity in quasicrystals

The maximum number of non-vanishing and independent second order photoelastic coefficients required by the seven pentagonal and the two icosahedral point groups 5(C₅), (S₁₀), (C_5h ), m2(D_5h ), 52(D₅), 5m(C_5v ), 2m(D_5d ); 235(I), 2/m (I _h )—that describe the quasicrystals symmetry groups in two and three dimensions—is obtained. The schemes of non-vanishing and independent coefficients have been calculated and listed. Finally the results of this group-theoretical study are briefly discussed.     

Combined constraints on modified Chaplygin gas model from cosmological observed data: Markov Chain Monte Carlo approach

We use the Markov Chain Monte Carlo method to investigate a global constraints on the modified Chaplygin gas (MCG) model as the unification of dark matter and dark energy from the latest observational data: the Union2 dataset of type supernovae Ia (SNIa), the observational Hubble data (OHD), the cluster X-ray gas mass fraction, the baryon acoustic oscillation (BAO), and the cosmic microwave background (CMB) data. In a flat universe, the constraint results for MCG model are, W_bh² = 0.02263^+0.00184_-0.00162 (1s)^+0.00213_-0.00195 (2s){\Omega_{b}h^{2}\,{=}\,0.02263^{+0.00184}_{-0.00162} (1\sigma)^{+0.00213}_{-0.00195} (2\sigma)}, B_s = 0.7788^+0.0736_-0.0723(1s)^+0.0918_-0.0904 (2s){B_{s}\,{=}\,0.7788^{+0.0736}_{-0.0723}(1\sigma)^{+0.0918}_{-0.0904} (2\sigma)}, a = 0.1079^+0.3397_-0.2539 (1s)^+0.4678_-0.2911 (2s){\alpha\,{=}\,0.1079^{+0.3397}_{-0.2539} (1\sigma)^{+0.4678}_{-0.2911} (2\sigma)}, B = 0.00189^+0.00583_-0.00756(1s)^+0.00660_-0.00915 (2s){B\,{=}\,0.00189^{+0.00583}_{-0.00756}(1\sigma)^{+0.00660}_{-0.00915} (2\sigma)}, and H₀=70.711^+4.188_-3.142 (1s)^+5.281_-4.149(2s){H_{0}=70.711^{+4.188}_{-3.142} (1\sigma)^{+5.281}_{-4.149}(2\sigma)}.     

Deformed Algebras from Elliptic sl(N) Algebras

We extend to the sl(N)sl(N) case the results that we previously obtained on the construction of W_q,p{\cal W}_{q,p} algebras from the elliptic algebra A_q,p([^(sl)](2)_c){\cal A}_{q,p}(\widehat{sl}(2)_{c}). The elliptic algebra \elp\elp at the critical level c= m N has an extended center containing trace-like operators t(z). Families of Poisson structures indexed by N(Nу)/2 integers, defining q-deformations of the W_N{\cal W}_{N} algebra, are constructed. The operators t(z) also close an exchange algebra when (-p^\sfrac12)^NM = q^-c-N(-p^\sfrac{1}{2})^{NM} = q^{-c-N} for M ? \ZZM\in\ZZ. It becomes Abelian when in addition p= q^Nh, where h is a non-zero integer. The Poisson structures obtained in these classical limits contain different q-deformed W_N{\cal W}_{N} algebras depending on the parity of h, characterizing the exchange structures at p p q^Nh as new W_q,p(sl(N)){\cal W}_{q,p}(sl(N)) algebras.     

Light meson mass dependence of the positive-parity heavy-strange mesons

We calculate the masses of the resonances D_s0^*(2317)\ensuremath D_{s0}^{\ast}(2317) and D_s1(2460)\ensuremath D_{s1}(2460) as well as their bottom partners as bound states of a kaon and a D^(*)\ensuremath D^{(\ast)} - and B^(*)\ensuremath B^{(\ast)} -meson, respectively, in unitarized chiral perturbation theory at next-to-leading order. After fixing the parameters in the D_s0^*(2317)\ensuremath D_{s0}^{\ast}(2317) channel, the calculated mass for the D_s1(2460)\ensuremath D_{s1}(2460) is found in excellent agreement with experiment. The masses for the analogous states with a bottom quark are predicted to be M_B^*s0=(5696±40)\ensuremath M_{B^{\ast}_{s0}}=(5696\pm 40) MeV and M_Bs1=(5742±40)\ensuremath M_{B_{s1}}=(5742\pm 40) MeV in reasonable agreement with previous analyses. In particular, we predict M_Bs1-M_Bs0^*=46±1\ensuremath M_{B_{s1}}{-}M_{B_{s0}^{\ast}}=46\pm 1 MeV. We also explore the dependence of the states on the pion and kaon masses. We argue that the kaon mass dependence of a kaonic bound state should be almost linear with slope about unity. Such a dependence is specific to the assumed molecular nature of the states. We suggest to extract the kaon mass dependence of these states from lattice QCD calculations.     

Mechanical and electronic properties of endofullerene Ne@C60 studied via structure distortions

Elastic, strength, electronic properties and vibrational spectra of Ne@C₆₀ (I _h) in its ground electronic state (X ¹A_g) were investigated with density functional theory at B3PW91/6-31G level via structure distortions. The elastic properties were obtained from the potential energy curves (PECs) in all of the five independent distortional directions of the molecule with symmetries of 1. D _5d, 2. D _3d, 3. D _2h, 4. C _2h(1) and 5. C _2h(2). PECs were examined where the structure of Ne@C₆₀ was destroyed. The necessary energies to destroy the structure were thus obtained, which illuminated the stability of Ne@C₆₀. PECs were found to be anisotropic and were accurately fitted to polynomials. Elongations in the direction of D _5d and compression in D _2h encountered potential energy surface cross-linkages, which might be considered as a single electron pump for further application in the design of single electron devices. Time-dependent B3PW91/6-31G analysis predicted significant electronic spectra changes associated with structure distortions. Similarities and differences of the properties were compared with those in C₆₀ and He@C₆₀.     

Gleason's Theorem for Rectangular JBW-Triples

A JBW^*-triple B is said to be rectangular if there exists a W^*-algebra A and a pair (p,q) of centrally equivalent elements of the complete orthomodular lattice P(A)\mathcal{P}(A) of projections in A such that B is isomorphic to the JBW^*-triple pAq. Any weak^*-closed injective operator space provides an example of a rectangular JBW^*-triple. The principal order ideal CP(A)_(p,q)\mathcal{C}\mathcal{P}(A)_{(p,q)} of the complete ^*-lattice CP(A)\mathcal{C}\mathcal{P}(A) of centrally equivalent pairs of projections in a W^*-algebra A, generated by (p,q), forms a complete lattice that is order isomorphic to the complete latticeI(B)\mathcal{I}(B) of weak^*-closed inner ideals in B and to the complete lattice S(B)\mathcal{S}(B) of structural projections on B. Although not itself, in general, orthomodular, CP(A)_(p,q)\mathcal{C}\mathcal{P}(A)_{(p,q)} possesses a complementation that allows for definitions of orthogonality, centre, and central orthogonality to be given. A less familiar notion in lattice theory, that is well-known in the theory of Jordan algebras and Jordan triple systems, is that of rigid collinearity of a pair (e₂,f²) and (e₂,f²) of elements of CP(A)_(p,q)\mathcal{C}\mathcal{P}(A)_{(p,q)}. This is defined and characterized in terms of properties of P(A)\mathcal{P}(A). A W^*-algebra A is sometimes thought of as providing a model for a statistical physical system. In this case B, or, equivalently, pAq, may be thought of as providing a model for a fixed sub-system of that represented by A. Therefore, CP(A)_(p,q)\mathcal{C}\mathcal{P}(A)_{(p,q)} may be considered to represent the set consisting of a particular kind of sub-system of that represented by pAq. Central orthogonality and rigid collinearity of pairs of elements of CP(A)_(p,q)\mathcal{C}\mathcal{P}(A)_{(p,q)} may be regarded as representing two different types of disjointness, the former, classical disjointness, and the latter, decoherence, of the two sub-systems. It is therefore natural to consider bounded measures m on CP(A)_(p,q)\mathcal{C}\mathcal{P}(A)_{(p,q)} that are additive on centrally orthogonal and rigidly collinear pairs of elements. Using results of J.D.M. Wright, it is shown that, provided that neither of the two hereditary sub-W^*-algebras pAp and qAq of A has a weak^*-closed ideal of Type I², such measures are precisely those that are the restrictions of bounded sesquilinear functionals {_m on pAp 2 qAq with the property that the action of the centroid Z(B) of B commutes with the adjoint operation. When B is a complex Hilbert space of dimension greater than two, this result reduces to Gleason's Theorem.     

Magnetoexciton absorption in coupled quantum wells

A Mott exciton in coupled quantum wells in a transverse magnetic field H is considered. An expression for the exciton spectrum in an arbitrary magnetic field for large separations D between quantum wells containing an electron (e) and a hole (h) is given. The exciton spectrum in a strong magnetic field for different Landau levels at arbitrary D has been calculated. Changes in the parameter D/l, where is the magnetic length, cause rearrangement of the magnetoexciton dispersion curves ℰ(P), where P is the conserved “magnetic” momentum, which is a function of the separation between the electron and hole in the plane of the quantum wells. Off-center (“roton”) extrema occur only for D/l,<(D/l)_cr, where (D/l)_cr is a function of the exciton quantum numbers n and m. The magnetoexciton effective mass in states with magnetic quantum number m=0 monotonically increases with H and D, while in states with m≠0 it is a nonmonotonic function of D/l. The probability of generating an exciton in coupled quantum wells increases with H. Absorption of electromagnetic radiation due to transitions between excitonic levels in coupled quantum wells is discussed. For an exciton containing a heavy hole the oscillator strengths increase with H and the oscillator strengths decrease. Zh. éksp. Teor. Fiz. 112, 1791–1808 (November 1997)     

Local exponential estimates for h-pseudodifferential operators and tunneling for Schrödinger, Dirac, and square root Klein-Gordon operators

We consider the class of matrix h-pseudodifferential operators Op _h (a) with symbols a = (a _ij ) _i,j=1 ^N , where the coefficients a _ij ∈ C ^∞(? _x ⁿ × ? _ξ ⁿ ? C(0, 1] satisfy the estimates |? _x ^β g6 _ξ ^α α _ij (x, ξ, h)| ? C _αβ 〈ξ〉 ^m and 〈ξ〉 = (1 + |ξ|²)^1/2 for every multi-indices α, β. We also assume that a _ij (x, ξ) is analytically continued with respect to ξ to a tube domain ? ⁿ + i $ \mathcal{B} We consider the class of matrix h-pseudodifferential operators Op _h (a) with symbols a = (a _ij ) _i,j=1^N, where the coefficients a _ij ∈ C ^∞(ℝ _x ⁿ × ℝ _ξ ⁿ ⊗ C(0, 1] satisfy the estimates |ϖ _x ^β g6 _ξ ^α α _ij (x, ξ, h)| ⩽ C _αβ 〈ξ〉 ^m and 〈ξ〉 = (1 + |ξ|²)^1/2 for every multi-indices α, β. We also assume that a _ij (x, ξ) is analytically continued with respect to ξ to a tube domain ℝ ⁿ + i , where is a bounded domain in ℝ ⁿ containing the origin. The main results of the paper are the local estimates for solutions of h-pseudodifferential equations. Let H _h ^s (ℝ ⁿ , ℂ ^N ) be the space of distributions with values in ℂ ^N which is equipped with the norm , let Ω ⊂ ℝ ⁿ be a bounded open set, let v ∈ C ^∞(ℝ ⁿ ), let ▿v(x) ∈ for any x ∈ Ω, and let . Let u _h (∈ H _h ^s (ℝ ⁿ ,‒ ^N )) be a solution of the equation Op _h (α)u = 0. In this case, for every ϕ ∈ C ₀^∞ (Ω) such that ϕ(x) = 1 on Supp v and for a sufficiently small h ₀ > 0, there exists a constant C > 0 such that the following estimate holds for every h ∈ (0, h ₀]:

((1))

We apply estimate (1) to local tunnel exponential estimates for the behavior as h → 0 of the eigenfunctions of matrix Schr?dinger, Dirac, and square-root Klein-Gordon operators. To the memory of Professor V. A. Borovikov     

The newly observed open-charm states in quark model

Comparing the measured properties of the newly observed open-charm states D(2550), D(2600), D(2750), D(2760), D _s1(2710), D _sJ (2860), and D _sJ (3040) with our predicted spectroscopy and strong decays in a constituent quark model, we find that (1) the D(2 ¹ S ₀) assignment to D(2550) remains open for its too broad width determined by experiment; (2) the D(2600) and D _s1(2710) can be identified as the 2 ³ S ₁–1 ³ D ₁ mixtures; (3) if the D(2760) and D(2750) are indeed the same resonance, they would be the D(1 ³ D ₃); otherwise, they could be assigned as the D(1 ³ D ₃) and D^￠₂(1D)D^{\prime}_{2}(1D), respectively; (4) the D _sJ (2860) could be either the D _s1(2710)’s partner or the D _s (1 ³ D ₃); and (5) both the D _s1(2P) and D^￠_s1(2P)D^{\prime}_{s1}(2P) interpretations for the D _sJ (3040) seem likely. The E1 and M1 radiative decays of these sates are also studied. Further experimental efforts are needed to test the present quarkonium assignments for these new open-charm states.     

Real forms of extended Kac–Moody symmetries and higher spin gauge theories

We consider the relation between higher spin gauge fields and real Kac–Moody Lie algebras. These algebras are obtained by double and triple extensions of real forms \mathfrakg₀{\mathfrak{g}_0} of the finite-dimensional simple algebras \mathfrakg{\mathfrak{g}} arising in dimensional reductions of gravity and supergravity theories. Besides providing an exhaustive list of all such algebras, together with their associated involutions and restricted root diagrams, we are able to prove general properties of their spectrum of generators with respect to a decomposition of the triple extension of \mathfrakg₀{\mathfrak{g}_0} under its gravity subalgebra \mathfrakgl(D,\mathbb R){\mathfrak{gl}(D,\mathbb {R})} . These results are then combined with known consistent models of higher spin gauge theory to prove that all but finitely many generators correspond to non-propagating fields and there are no higher spin fields contained in the Kac–Moody algebra.     

Charged Higgs observability through associated production with W ± at a muon collider

The observability of a charged Higgs boson produced in association with a W boson at future muon colliders is studied. The analysis is performed within the MSSM framework. The charged Higgs is assumed to decay to $t\bar{b}We study $B_{s}^{0} \to J/\psi f_{0}(980)$ decays, the quark content of f ₀(980) and the mixing angle of f ₀(980) and ??(600). We calculate not only the factorizable contribution in the QCD factorization scheme but also the nonfactorizable hard spectator corrections in QCDF and pQCD approach. We get a result consistent with the experimental data of $B_{s}^{0} \to J/\psi f_{0}(980)$ and predict the branching ratio of $B_{s}^{0}$ ?CJ/???. We suggest two ways to determine f ₀?C?? mixing angle ??. Using the experimental measured branching ratio of $B_{s}^{0} \to J/\psi f_{0}(980)$ , we can get the f ₀?C?? mixing angle ?? with some theoretical uncertainties. We suggest another way to determine the f ₀?C?? mixing angle ?? using both experimental measured decay branching ratios $B_{s}^{0} \to J/\psi f_{0}(980) (\sigma)$ to avoid theoretical uncertainties.     

Boundary Concentration for Eigenvalue Problems Related to the Onset of Superconductivity

We examine the asymptotic behavior of the eigenvalue w(h) and corresponding eigenfunction associated with the variational problem m(h) o inf_{y ? H¹(W;C )} \fracò_W \abs(i?+hA)y² dx dy ò_W\absy² dx dy \mu(h)\equiv\inf_{\psi\in H^{1}(\Omega;{\bf C} )} \frac{\int_{\Omega } \abs{(i\nabla+h{\bf A})\psi}^{2}\,dx\,dy} {\int_{\Omega }\abs{\psi}^{2}\,dx\,dy} in the regime h>>1. Here A is any vector field with curl equal to 1. The problem arises within the Ginzburg-Landau model for superconductivity with the function w(h) yielding the relationship between the critical temperature vs. applied magnetic field strength in the transition from normal to superconducting state in a thin mesoscopic sample with cross-section W ì \R²\Omega\subset\R^{2}. We first carry out a rigorous analysis of the associated problem on a half-plane and then rigorously justify some of the formal arguments of [BS], obtaining an expansion for w while also proving that the first eigenfunction decays to zero somewhere along the sample boundary ?W\partial \Omega when z is not a disc. For interior decay, we demonstrate that the rate is exponential.     

C42+的几何构型和Jahn Teller效应

用从头计算法QCISD/6-311G得到了C₄²⁺分子的10种不同的几何构型,其中包括C_s,C_∞v,C_2v,D_2h,D_∞h,D_4h,D_2d,C_3v等不同的构型.计算表明C₄²⁺的T_d构型不能稳定存在,详细讨论了T_{d 关键词： 几何构型 4}²⁺')" href="#">C₄²⁺ Jahn Teller效应     

Interaction of sodium fullerene derivatives with trimethylchlorosilane

Soluble dimer compounds of the general formula [C₆₀(Me ₃Si)_n]₂ (where n = 3, 5, 7, or 9 and M _e = CH₃) and a soluble monomer compound, C₆₀(Me ₃Si)₁₂, are synthesized by the reaction of the compound C₆₀Na_n(THF)_x (where n = 4, 6, 8, 10, or 12 and THF = tetrahydrofuran) with trimethylchlorosilane Me ₃SiCl. The compounds synthesized are identified using IR and NMR spectroscopy and mass spectrometry. An irreversible endothermic effect exhibited by the [C₆₀(Me ₃Si)₇]₂ compound in the temperature range 448–570 K is revealed by dynamic adiabatic calorimetry. From analyzing the experimental results, it becomes possible for the first time to demonstrate the structural flexibility of the fullerene in the following sequence of reactions: $\begin{array}{*{20}c} {C_{60} \xrightarrow[{ - 12C_{10} H_8 }]{{ + 12NaC_{10} H_8 }}C_{60} Na_{12} \xrightarrow[{ - 12NaCl}]{{ + excess Me_3 SiCl}}C_{60} (Me_3 Si)_{12} \xrightarrow[{ - 12Me_3 SiCl}]{{ + HCl(gas)}}[C_{60} H_n ]\xrightarrow[{ - 1/2nH_2 }]{{hv}}C_{60} } \\ {C_{60} \xrightarrow[{ - 8C_{10} H_8 }]{{ + 8NaC_{10} H_8 }}C_{60} Na_8 \xrightarrow[{ - 8NaCl}]{{ + excess Me_3 SiCl}}[C_{60} (Me_3 Si)_7 ]_2 \xrightarrow{{573K}}\begin{array}{*{20}c} {products of the} \\ {transformation of + } \\ {Me_3 Si groups} \\ \end{array} C_{60^ - } } \\ \end{array} $      

Analysis of the <Emphasis Type="Italic">Y</Emphasis>(4140) and related molecular states with QCD sum rules

In this article, we assume that there exist scalar D^*[`(D)]<sup>*</sup>{D}^{\ast}{\bar {D}}^{\ast}, D<sub>s</sub><sup>*</sup>[`(D)]_s^*{D}_{s}^{\ast}{\bar{D}}_{s}^{\ast}, B^*[`(B)]<sup>*</sup>{B}^{\ast}{\bar {B}}^{\ast} and B<sub>s</sub><sup>*</sup>[`(B)]_s^*{B}_{s}^{\ast}{\bar{B}}_{s}^{\ast} molecular states, and study their masses using the QCD sum rules. The numerical results indicate that the masses are about (250–500) MeV above the corresponding D ^*–[`(D)]<sup>*</sup>{\bar{D}}^{\ast}, D <sub>s</sub> <sup>*</sup>–[`(D)]_s^*{\bar {D}}_{s}^{\ast}, B ^*–[`(B)]<sup>*</sup>{\bar{B}}^{\ast} and B <sub>s</sub> <sup>*</sup>–[`(B)]_s^*{\bar {B}}_{s}^{\ast} thresholds, the Y(4140) is unlikely a scalar D_s^*[`(D)]<sub>s</sub><sup>*</sup>{D}_{s}^{\ast}{\bar{D}}_{s}^{\ast} molecular state. The scalar D<sup>*</sup>[`(D)]^*D^{\ast}{\bar{D}}^{\ast}, D_s^*[`(D)]<sub>s</sub><sup>*</sup>D_{s}^{\ast}{\bar{D}}_{s}^{\ast}, B<sup>*</sup>[`(B)]^*B^{\ast}{\bar{B}}^{\ast} and B_s^*[`(B)]<sub>s</sub><sup>*</sup>B_{s}^{\ast}{\bar{B}}_{s}^{\ast} molecular states maybe not exist, while the scalar D￠<sup>*</sup>[`(D)]^￠*{D'}^{\ast}{\bar{D}}^{\prime\ast}, D_s^￠*[`(D)]<sub>s</sub><sup>￠*</sup>{D}_{s}^{\prime\ast}{\bar{D}}_{s}^{\prime\ast}, B<sup>￠*</sup>[`(B)]^￠*{B}^{\prime\ast}{\bar{B}}^{\prime\ast} and B_s^￠*[`(B)]_s^￠*{B}_{s}^{\prime\ast}{\bar{B}}_{s}^{\prime\ast} molecular states maybe exist.     

A Monoidal Category for Perturbed Defects in Conformal Field Theory

Starting from an abelian rigid braided monoidal category C{\mathcal{C}} we define an abelian rigid monoidal category C_F{\mathcal{C}_F} which captures some aspects of perturbed conformal defects in two-dimensional conformal field theory. Namely, for V a rational vertex operator algebra we consider the charge-conjugation CFT constructed from V (the Cardy case). Then C = Rep(V){\mathcal{C} = {\rm Rep}(V)} and an object in C_F{\mathcal{C}_F} corresponds to a conformal defect condition together with a direction of perturbation. We assign to each object in C_F{\mathcal{C}_F} an operator on the space of states of the CFT, the perturbed defect operator, and show that the assignment factors through the Grothendieck ring of C_F{\mathcal{C}_F}. This allows one to find functional relations between perturbed defect operators. Such relations are interesting because they contain information about the integrable structure of the CFT.     

Highest Weight Modules Over Quantum Queer Superalgebra {U_q(\mathfrak {q}(n))}

In this paper, we investigate the structure of highest weight modules over the quantum queer superalgebra U_q(\mathfrak q(n)){U_q(\mathfrak {q}(n))}. The key ingredients are the triangular decomposition of U_q(\mathfrak q(n)){U_q(\mathfrak {q}(n))} and the classification of finite dimensional irreducible modules over quantum Clifford superalgebras. The main results we prove are the classical limit theorem and the complete reducibility theorem for U_q(\mathfrak q(n)){U_q(\mathfrak {q}(n))}-modules in the category O_q ^{3 0}{\mathcal {O}_{q}^{\geq 0}}.     

Maximum Solutions of Normalized Ricci Flow on 4-Manifolds

We consider the maximum solution g(t), t ∈ [0,  + ∞), to the normalized Ricci flow. Among other things, we prove that, if (M, ω) is a smooth compact symplectic 4-manifold such that and let g(t), t ∈ [0, ∞), be a solution to (1.3) on M whose Ricci curvature satisfies that |Ric(g(t))| ≤ 3 and additionally χ(M) = 3τ (M) > 0, then there exists an , and a sequence of points {x _j,k ∈ M}, j = 1, . . . , m, satisfying that, by passing to a subsequence,