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1.
We consider a complete nonnegative biminimal submanifold M (that is, a complete biminimal submanifold with λ≥0) in a Euclidean space EN. Assume that the immersion is proper , that is, the preimage of every compact set in EN is also compact in M. Then, we prove that M is minimal. From this result, we give an affirmative partial answer to Chen’s conjecture. For the case of λ<0, we construct examples of biminimal submanifolds and curves. 相似文献
2.
Employing one- plus two-body random matrix ensembles for bosons, temperature and entropy are calculated, using different definitions, as a function of the two-body interaction strength λ for a system with 10 bosons (m=10) in five single-particle levels (N=5). It is found that in a region λ∼λt, different definitions give essentially the same values for temperature and entropy, thus defining a thermalization region. Also, (m,N) dependence of λt has been derived. It is seen that λt is much larger than the λ values where level fluctuations change from Poisson to GOE and strength functions change from Breit–Wigner to Gaussian. 相似文献
3.
Suppose that the sphere Sn has initially a homogeneous distribution of mass and let G be the Lie group of orientation preserving projective diffeomorphisms of Sn. A projective motion of the sphere, that is, a smooth curve in G, is called force free if it is a critical point of the kinetic energy functional. We find explicit examples of force free projective motions of Sn and, more generally, examples of subgroups H of G such that a force free motion initially tangent to H remains in H for all time (in contrast with the previously studied case for conformal motions, this property does not hold for H=SOn+1). The main tool is a Riemannian metric on G, which turns out to be not complete (in particular not invariant, as happens with non-rigid motions), given by the kinetic energy. 相似文献
4.
Denise A. do Nascimento Minos A. Neto J. Ricardo de Sousa Josefa T. Pacobahyba 《Journal of magnetism and magnetic materials》2012
In this paper we study the critical behavior of a two-sublattice Ising model on an anisotropic square lattice in both uniform longitudinal (H ) and transverse (Ω) fields by using the effective-field theory. The model consists of ferromagnetic interaction Jx in the x direction and antiferromagnetic interaction Jy in the y direction in the presence of the H and Ω fields. We obtain the phase diagrams in the H–T and Ω–T planes changing values of the Ω and H parameters, respectively for fixed value at λ=Jx/Jy=1. At null temperature, the ground state phase diagram in the Ω–H plane for several values of λ parameter is analyzed. In the particular case of λ=1 we compare our results with mean-field theory (MFT) and was not observed reentrant behavior around of the critical field Hc/Jy=2.0 for Ω=0 by using EFT. 相似文献
5.
A curve α immersed in the three-dimensional sphere S3 is said to be a Bertrand curve if there exists another curve β and a one-to-one correspondence between α and β such that both curves have common principal normal geodesics at corresponding points. The curves α and β are said to be a pair of Bertrand curves in S3. One of our main results is a sort of theorem for Bertrand curves in S3 which formally agrees with the classical one: “Bertrand curves in S3 correspond to curves for which there exist two constants λ≠0 and μ such that λκ+μτ=1”, where κ and τ stand for the curvature and torsion of the curve; in particular, general helices in the 3-sphere introduced by M. Barros are Bertrand curves. As an easy application of the main theorem, we characterize helices in S3 as the only twisted curves in S3 having infinite Bertrand conjugate curves. We also find several relationships between Bertrand curves in S3 and (1,3)-Bertrand curves in R4. 相似文献
6.
Large flocks of wild beings can have coordinated motion with neither leading center nor global information. The Vicsek model and its new versions explained such collective behavior of self-propelled agents with the mechanism of un-weighted influence of neighbors and global visual field (GVF), which may not always fit the reality. In the present work, we take both exponential (λ) neighbor weight (ENW) and restricted visual field (RVF) into account, and investigate the combinatory effect of them. Based on this mechanism, in most cases of our simulation, stationary direction consensus Va exhibits a maximum or decreases with VF, and a minimum convergence time Tmin appears in RVF, which demonstrates that GVF is not necessary for coordinated motion, while RVF matched ENW would be reasonable. Moreover, we simulated various recipes for optimizing Va and T in unfavorable cases, and found critical points separating inverse λ-dependent variations of T. The present work may be useful in improving the efficiency of direction consensus of large flocks of artificial individuals besides the understanding of biological collective motion in nature. 相似文献
7.
In this paper we show that for a compact minimal hypersurface M of constant scalar curvature in the unit sphere S6 with the shape operator A satisfying ‖A‖2>5, there exists an eigenvalue λ>10 of the Laplace operator of the hypersurface M such that ‖A‖2=λ−5. This gives the next discrete value of ‖A‖2 greater than 0 and 5. 相似文献
8.
We examine the scaling regime for the detrended fluctuation analysis (DFA)—the most popular method used to detect the presence of long-term memory in data and the fractal structure of time series. First, the scaling range for DFA is studied for uncorrelated data as a function of time series length L and the correlation coefficient of the linear regression R2 at various confidence levels. Next, a similar analysis for artificial short series of data with long-term memory is performed. In both cases the scaling range λ is found to change linearly—both with L and R2. We show how this dependence can be generalized to a simple unified model describing the relation λ=λ(L,R2,H) where H (1/2≤H≤1) stands for the Hurst exponent of the long range autocorrelated signal. Our findings should be useful in all applications of DFA technique, particularly for instantaneous (local) DFA where a huge number of short time series has to be analyzed at the same time, without possibility of checking the scaling range in each of them separately. 相似文献
9.
We have studied the anisotropic two-dimensional nearest-neighbor Ising model with competitive interactions in both uniform longitudinal field H and transverse magnetic field Ω. Using the effective-field theory (EFT) with correlation in cluster with N=1 spin we calculate the thermodynamic properties as a function of temperature with values H and Ω fixed. The model consists of ferromagnetic interaction Jx in the x direction and antiferromagnetic interaction Jy in the y direction, and it is found that for H/Jy∈[0,2] the system exhibits a second-order phase transition. The thermodynamic properties are obtained for the particular case of λ=Jx/Jy=1 (isotropic square lattice). 相似文献
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11.
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
12.
We present new axially symmetric half-monopole configuration of the SU(2)×U(1) Weinberg–Salam model of electromagnetic and weak interactions. The half-monopole configuration possesses net magnetic charge 2π/e which is half the magnetic charge of a Cho–Maison monopole. The electromagnetic gauge potential is singular along the negative z-axis. However the total energy is finite and increases only logarithmically with increasing Higgs field self-coupling constant λ1/2 at sin2θW=0.2312. In the U(1) magnetic field, the half-monopole is just a one dimensional finite length line magnetic charge extending from the origin r=0 and lying along the negative z-axis. In the SU(2) ’t Hooft magnetic field, it is a point magnetic charge located at r=0. The half-monopole possesses magnetic dipole moment that decreases exponentially fast with increasing Higgs field self-coupling constant λ1/2 at sin2θW=0.2312. 相似文献
13.
We discuss three Hamiltonians, each with a central-field part H0 and a PT-symmetric perturbation igz. When H0 is the isotropic Harmonic oscillator the spectrum is real for all g because H is isospectral to H0+g2/2. When H0 is the Hydrogen atom then infinitely many eigenvalues are complex for all g. If the potential in H0 is linear in the radial variable r then the spectrum of H exhibits real eigenvalues for 0<g<gc and a PT phase transition at gc. 相似文献
14.
We discuss space-time symmetric Hamiltonian operators of the form H=H0+igH′, where H0 is Hermitian and g real. H0 is invariant under the unitary operations of a point group G while H′ is invariant under transformation by elements of a subgroup G′ of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0<g<gc, where gc is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H may exhibit real or complex eigenvalues for g>0. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries. 相似文献
15.
We consider a Schrödinger-type differential expression HV=∇∗∇+V, where ∇ is a Hermitian connection on a Hermitian vector bundle E over a complete Riemannian manifold (M,g) with metric g and positive smooth measure dμ, and V is a locally integrable section of the bundle of endomorphisms of E. We give a sufficient condition for m-accretivity of a realization of HV in L2(E). 相似文献
16.
In [L. Lebtahi, Lie algebra on the transverse bundle of a decreasing family of foliations, J. Geom. Phys. 60 (2010), 122–133], we defined the transverse bundle Vk to a decreasing family of k foliations Fi on a manifold M. We have shown that there exists a (1,1) tensor J of Vk such that Jk≠0, Jk+1=0 and we defined by LJ(Vk) the Lie Algebra of vector fields X on Vk such that, for each vector field Y on Vk, [X,JY]=J[X,Y]. 相似文献
17.
We investigate complete spacelike hypersurfaces in Lorentz–Minkowski space with two distinct principal curvatures and constant mth mean curvature. By using Otsuki’s idea, we obtain the global classification result. As their applications, we obtain some characterizations for hyperbolic cylinders. We prove that the only complete spacelike hypersurfaces in Lorentz–Minkowski (n+1)-spaces (n≥3) of nonzero constant mth mean curvature (m≤n−1) with two distinct principal curvatures λ and μ satisfying inf(λ−μ)2>0 are the hyperbolic cylinders. We also obtain a global characterization for hyperbolic cylinder Hn−1(c)×R in terms of square length of the second fundamental form. 相似文献
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19.
We study reduction of generalized complex structures. More precisely, we investigate the following question. Let J be a generalized complex structure on a manifold M, which admits an action of a Lie group G preserving J. Assume that M0 is a G-invariant smooth submanifold and the G-action on M0 is proper and free so that MG?M0/G is a smooth manifold. Under what condition does J descend to a generalized complex structure on MG? We describe a sufficient condition for the reduction to hold, which includes the Marsden–Weinstein reduction of symplectic manifolds and the reduction of the complex structures in Kähler manifolds as special cases. As an application, we study reduction of generalized Kähler manifolds. 相似文献
20.
S.A. Leonel Amanda Castro Oliveira B.V. Costa Pablo Zimmermann Coura 《Journal of magnetism and magnetic materials》2006
Generally, in literature, easy-axis single ion anisotropy and easy-axis exchange anisotropy was treated in indistinct way. In this work we propose to perform a comparative study of the effects of these two easy-axis anisotropies on the behavior of the magnetization and the critical temperature (Tc) in the 2D classical Heisenberg antiferromagnetic model. In order to study the low-temperature thermodynamics of this model, we should consider the contribution of anisotropic spin waves, using a self-consistent harmonic approximation (SCHA) theory. We compare the predictions of SCHA with numerical simulations on L×L square lattices using Monte Carlo (MC) simulations, which include effects due to all thermodynamically allowed excitations. Our SCHA results are in good agreement with our MC simulations results and have shown that the strong K limit gives two different Ising-like behavior. In the exchange anisotropic case, the dependence of Tc on anisotropic parameter K becomes linear and in the single-ion anisotropic case, Tc becomes independent of K. Also, using MC simulations and finite size scaling, we show that the critical exponents in the two anisotropic case are compatible with the 2D Ising values α=0.125 and γ=1.75. 相似文献