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A complex symplectic structure on a Lie algebra h is an integrable complex structure J with a closed non-degenerate (2,0)-form. It is determined by J and the real part Ω of the (2,0)-form. Suppose that h is a semi-direct product g?V, and both g and V are Lagrangian with respect to Ω and totally real with respect to J. This note shows that g?V is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of Ω and J are isomorphic. 相似文献
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We investigate the geometry of the moduli space of N vortices on line bundles over a closed Riemann surface Σ of genus g>1, in the little explored situation where 1≤N<g. In the regime where the area of the surface is just large enough to accommodate N vortices (which we call the dissolving limit), we describe the relation between the geometry of the moduli space and the complex geometry of the Jacobian variety of Σ. For N=1, we show that the metric on the moduli space converges to a natural Bergman metric on Σ. When N>1, the vortex metric typically degenerates as the dissolving limit is approached, the degeneration occurring precisely on the critical locus of the Abel–Jacobi map of Σ at degree N. We describe consequences of this phenomenon from the point of view of multivortex dynamics. 相似文献
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The distance d(i,j) between any two vertices i and j in a graph is the number of edges in a shortest path between i and j. If there is no path connecting i and j, then d(i,j)=∞. In 2001, Latora and Marchiori introduced the measure of efficiency between vertices in a graph (Latora and Marchiori, 2001) [1]. The efficiency between two vertices i and j is defined to be ∈i,j=j. In this paper, we investigate the efficiency of star-like networks, and show that networks of this type have a high level of efficiency. We apply these ideas to an analysis of the Metropolitan Atlanta Rapid Transit Authority (MARTA) Subway system, and show this network is 82% as efficient as a network where there is a direct line between every pair of stations. 相似文献
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Intertwining operators for infinite-dimensional representations of the Sklyanin algebra with spins ? and −?−1 are constructed using the technique of intertwining vectors for elliptic L-operator. They are expressed in terms of elliptic hypergeometric series with operator argument. The intertwining operators obtained (W-operators) serve as building blocks for the elliptic R-matrix which intertwines tensor product of two L-operators taken in infinite-dimensional representations of the Sklyanin algebra with arbitrary spin. The Yang–Baxter equation for this R-matrix follows from simpler equations of the star–triangle type for the W-operators. A natural graphic representation of the objects and equations involved in the construction is used. 相似文献
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We calculate low scale gravity effects on the cross section for neutrino–nucleon scattering at center of mass energies up to the Greisen–Zatsepin–Kuzmin (GZK) scale, in the eikonal approximation. We compare the cases of an infinitely thin brane embedded in n=5 compactified extra-dimensions, and of a brane with a physical tension MS=1 TeV and MS=10 TeV. The extra dimensional Planck scale MD is set at 103 GeV and 2×103 GeV. We also compare our calculations with neutral current standard model calculations in the same energy range, and compare the thin brane eikonal cross section to its saddle point approximation. New physics effects enhance the cross section by orders of magnitude on average. They are quite sensitive to MS and MD choices, though much less sensitive to n. 相似文献
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Let X be a smooth complex projective curve and S⊂X a finite subset. We show that an orthogonal or symplectic parabolic Higgs bundle on X with parabolic structure over S admits a Hermitian–Einstein connection if and only if it is polystable. 相似文献
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The effect of green/red asymmetry is studied for the single-car traffic model proposed in [B.A. Toledo, V. Muñoz, J. Rogan, C. Tenreiro, J.A. Valdivia, Modeling traffic through a sequence of traffic lights, Phys. Rev. E 70 (1) (2004) 016107], on two different signal synchronization strategies, namely, all signals in phase, and a green wave. The asymmetry is characterized by the parameter g=tgr/T, where tgr is the green time and T the signal period. Although the car dynamics turns simpler or more complex, as compared with the equivalent situation for the symmetric case g=0.5, critical behavior around resonance is shown to be preserved. However, unlike the case g=0.5, critical exponents at both sides of the resonance are not equal and depend on g. Analytical expressions for them are found, and shown to be both consistent with simulation results and independent of the distribution of distances between signals for the green wave case. Also, it is found that the green wave strategy is more robust to changes in g, with respect to the synchronized lights strategy, in the sense that larger departures from g=0.5 are needed to have noticeable effects on the car dynamics. 相似文献
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Geometrical characterizations are given for the tensor R⋅S, where S is the Ricci tensor of a (semi-)Riemannian manifold (M,g) and R denotes the curvature operator acting on S as a derivation, and of the Ricci Tachibana tensor ∧g⋅S, where the natural metrical operator ∧g also acts as a derivation on S. As a combination, the Ricci curvatures associated with directions on M, of which the isotropy determines that M is Einstein, are extended to the Ricci curvatures of Deszcz associated with directions and planes on M, and of which the isotropy determines that M is Ricci pseudo-symmetric in the sense of Deszcz. 相似文献
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Let M be a symplectic symmetric space, and let ?:M→V be an extrinsic symplectic symmetric immersion in the sense of Krantz and Schwachhöfer (2010) [7], i.e., (V,Ω) is a symplectic vector space and ? is an injective symplectic immersion such that for each point p∈M, the geodesic symmetry in p is compatible with the reflection in the affine normal space at ?(p). 相似文献
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Even though the one-dimensional (1D) Hubbard model is solvable by the Bethe ansatz, at half-filling its finite-temperature T>0 transport properties remain poorly understood. In this paper we combine that solution with symmetry to show that within that prominent T=0 1D insulator the charge stiffness D(T) vanishes for T>0 and finite values of the on-site repulsion U in the thermodynamic limit. This result is exact and clarifies a long-standing open problem. It rules out that at half-filling the model is an ideal conductor in the thermodynamic limit. Whether at finite T and U>0 it is an ideal insulator or a normal resistor remains an open question. That at half-filling the charge stiffness is finite at U=0 and vanishes for U>0 is found to result from a general transition from a conductor to an insulator or resistor occurring at U=Uc=0 for all finite temperatures T>0. (At T=0 such a transition is the quantum metal to Mott-Hubbard-insulator transition.) The interplay of the η-spin SU(2) symmetry with the hidden U(1) symmetry beyond SO(4) is found to play a central role in the unusual finite-temperature charge transport properties of the 1D half-filled Hubbard model. 相似文献
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The random-crystal field spin-1 Blume–Capel model is investigated by the lowest approximation of the cluster-variation method which is identical to the mean-field approximation. The crystal field is either turned on randomly with probability p or turned off with q=1−p in a bimodal distribution. Then the phase diagrams are constructed on the crystal field (Δ)–temperature (kT/J) planes for given values of p and on the (kT/J,p) planes for given Δ by studying the thermal variations of the order parameters. In the latter, we only present the second-order phase transition lines, because of the existence of irregular wiggly phase transitions which are not good enough to construct lines. In addition to these phase transitions, the model also yields tricritical points for all values of p and the reentrant behavior at lower p values. 相似文献
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We introduce a network evolution process motivated by the network of citations in the scientific literature. In each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already in the network. This set includes m “ambassador” nodes and l of each ambassador’s descendants where m and l are random variables selected from any choice of distributions pl and qm. The process mimics the tendency of authors to cite varying numbers of papers included in the bibliographies of the other papers they cite. We show that the degree distributions of the networks generated after a large number of iterations are scale-free and derive an expression for the power-law exponent. In a particular case of the model where the number of ambassadors is always the constant m and the number of selected descendants from each ambassador is the constant l, the power-law exponent is (2l+1)/l. For this example we derive expressions for the degree distribution and clustering coefficient in terms of l and m. We conclude that the proposed model can be tuned to have the same power law exponent and clustering coefficient of a broad range of the scale-free distributions that have been studied empirically. 相似文献
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Let E→M be a holomorphic vector bundle over a compact Kähler manifold (M,ω). We prove that if E admits a ω-balanced metric (in X. Wang’s terminology (Wang, 2005 [3])) then it is unique. This result together with Biliotti and Ghigi (2008) [14] implies the existence and uniqueness of ω-balanced metrics of certain direct sums of irreducible homogeneous vector bundles over rational homogeneous varieties. We finally apply our result to show the rigidity of ω-balanced Kähler maps into Grassmannians. 相似文献
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The deviation δQW of the weak charge from its standard model prediction due to the mixing of the W boson with the charged bilepton Y as well as of the Z boson with the neutral Z′ and the real part of the non-Hermitian neutral bilepton X in the economical 3–3–1 model is established. Additional contributions to the usual δQW expression in the extra U(1) models and the left–right models are obtained. Our calculations are quite different from previous analyzes in this kind of the 3–3–1 models and give the limit on mass of the Z′ boson, the Z–Z′ and W–Y mixing angles with the more appropriate values: MZ′>564 GeV, −0.018<sinφ<0 and |sinθ|<0.043. 相似文献