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1.
Adrian Butscher 《Annals of Global Analysis and Geometry》2009,36(3):221-274
Four constructions of constant mean curvature (CMC) hypersurfaces in
\mathbb Sn+1{\mathbb {S}^{n+1}} are given, which should be considered analogues of ‘classical’ constructions that are possible for CMC hypersurfaces in Euclidean
space. First, Delaunay-like hypersurfaces, consisting roughly of a chain of hyperspheres winding multiple times around an
equator, are shown to exist for all the values of the mean curvature. Second, a hypersurface is constructed which consists
of two chains of spheres winding around a pair of orthogonal equators, showing that Delaunay-like hypersurfaces can be fused
together in a symmetric manner. Third, a Delaunay-like handle can be attached to a generalized Clifford torus of the same
mean curvature. Finally, two generalized Clifford tori of equal but opposite mean curvature of any magnitude can be attached
to each other by symmetrically positioned Delaunay-like ‘arms’. This last result extends Butscher and Pacard’s doubling construction
for generalized Clifford tori of small mean curvature. 相似文献
2.
Double-periodic solutions of the Euler-Lagrange equation for the (1+1)-dimensional scalarϗ
4-theory are considered. The nonlinear term is assumed to be small, and the Poincaré method is used to seek asymptotic solutions
in the standing-wave form. The principal resonance problem, which arises for zero mass, is resolved if the leading-order term
is taken in the form of a Jacobi elliptic function.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 116, No. 2, pp. 182–192, August, 1998. 相似文献
3.
V. L. Kulakov Yu. M. Tarnopol’skii D. D. Mungalov A. I. Beyle 《Mechanics of Composite Materials》2000,36(3):199-206
The effective deformative characteristics of spatially reinforced composites made by spatial braiding along the generatrices
of a one-sheet hyperboloid are analyzed. The geometrical relationships determining the structure of a unit cell of a braided
composite are derived. The effective thermoelastic characteristics are calculated by the method of orientational averaging.
The dependences of the bending and torsional stiffnesses of thick-walled cylindrical rods — made by the method suggested and
by winding — on the braiding/winding angle are compared. The numerical estimations are given for rods made of carbon (CFRP)
and aramid (AFRP) epoxy plastics.
Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000).
Translated from Mekhanika Kompzitnykh Materialov, Vol. 36, No. 3, pp. 341–354, May–June, 2000. 相似文献
4.
V. R. Khalilov 《Theoretical and Mathematical Physics》1999,119(1):481-492
In the problem of a two-dimensional hydrogen-like atom in a magnetic field background, we construct quasi-classical solutions
and the energy spectrum of the Dirac equation in a strong Coulomb field and in a weak constant homogeneous magnetic field
in 2+1 dimensions. We find some “exact” solutions of the Dirac and Pauli equations describing the “spinless” fermions in strong
Coulomb fields and in homogeneous magnetic fields in 2+1 dimensions.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 1, pp. 105–118, April, 1999. 相似文献
5.
Based on a general multidimensional Riemann theta function and the super Hirota bilinear form, we extend the Hirota method
to construct explicit super quasiperiodic (multiperiodic) wave solutions of $
\mathcal{N} = 1
$
\mathcal{N} = 1
supersymmetric KdV-type equations in superspace. We show that the supersymmetric KdV equation does not have an N-periodic
wave solution with arbitrary parameters for N ≥ 2. In addition, an interesting influencing band occurs among the super quasiperiodic waves under the presence of a Grassmann
variable. We also observe that the super quasiperiodic waves are symmetric about this band but collapse along with it. We
present a limit procedure for analyzing the asymptotic properties of the super quasiperiodic waves and rigorously show that
the super periodic wave solutions tend to super soliton solutions under some “small amplitude” limits. 相似文献
6.
The paper is concerned with the ‘primal’ problem of maximizing a given quadratic pseudo-boolean function. Four equivalent
problems are discussed—the primal, the ‘complementation’, the ‘discrete Rhys LP’ and the ‘weighted stability problem of a
SAM graph’. Each of them has a relaxation—the ‘roof dual’, the ‘quadratic complementation,’ the ‘continuous Rhys LP’ and the
‘fractional weighted stability problem of a SAM graph’. The main result is that the four gaps associated with the four relaxations
are equal. Furthermore, a solution to any of these problems leads at once to solutions of the other three equivalent ones.
The four relaxations can be solved in polynomial time by transforming them to a bipartite maximum flow problem. The optimal
solutions of the ‘roof-dual’ define ‘best’ linear majorantsp(x) off, having the following persistency property: if theith coefficient inp is positive (negative) thenx
i=1 (0) in every optimum of the primal problem. Several characterizations are given for the case where these persistency results
cannot be used to fix any variable of the primal. On the other hand, a class of gap-free functions (properly including the
supermodular ones) is exhibited. 相似文献
7.
A. V. Domrin 《Theoretical and Mathematical Physics》2008,156(3):1231-1246
Using a noncommutative version of the uniton theory, we study the space of those solutions of the noncommutative U(1) sigma
model that are representable as finite-dimensional perturbations of the identity operator. The basic integer-valued characteristics
of such solutions are their normalized energy e, canonical rank r, and minimum uniton number u, which always satisfy r ≤ e
and u ≤ e. Starting with the so-called BPS solutions (u = 1), we completely describe the sets of all solutions with r = 1,
2, e − 1, e (which forces u ≤ 2) and all solutions of small energy (e ≤ 5). The obtained results reveal a simple but nontrivial
structure of the moduli spaces and lead to a series of conjectures.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 3, pp. 307–327, September, 2008. 相似文献
8.
Stephen J. Sangwine 《Advances in Applied Clifford Algebras》2006,16(1):63-68
The roots of −1 in the set of biquaternions (quaternions with complex components, or complex numbers with quaternion real
and imaginary parts) are derived. There are trivial solutions (the complex operator, and any unit pure real quaternion), and
non-trivial solutions consisting of complex numbers with perpendicular pure quaternion real and imaginary parts. The moduli
of the two perpendicular pure quaternions are expressible by a single parameter by using a hyperbolic trigonometric identity. 相似文献
9.
A. B. Mitkevich 《Mechanics of Composite Materials》2005,41(6):497-504
Errors in the programs of winding pressure vessels can lead to an asymmetric reinforcement structure, which affects the equilibrium
shape of their domes and the tension in the left and right families of filaments. In this paper, equations determining the
equilibrium shape of the domes, the tension in filaments, and the shear stresses between layers are obtained. Examples with
winding trajectories in the form of geodesics and constant-deviation lines are considered. It is found that, for pressure
vessels, in the absence of external torque, the tension levels in filaments of the left and right families differ considerably.
It is also revealed that, for actual friction coefficients in winding, the shear stresses taken up by the binder are insignificant.
__________
Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 6, pp. 743–752, November–December, 2005. 相似文献
10.
V. P. Stavrov A. V. Markov A. V. Zhernovskii K. F. Friedrich 《Mechanics of Composite Materials》2000,36(3):249-254
The problem of compression of a unidirectional layer and shear of a polymer interlayer during winding of rings is considered.
The equations determining the dependence of the layer thickness and stresses on the parameters entering into the power flow
law for a prepreg and polymer matrix and on the basic parameters of the winding process—the initial tension of the prepreg,
its placement rate, and the radius of a mandrel—are derived. The ring thickness measurements obtained at various temperatures
and initial tension forces of plies confirm the adequacy of the model offered. It is found that the viscous properties of
the prepreg and matrix upon winding affect the relative change in the layer thickness to a greater extent than the stresses
in these layers. With increase in temperature and tension force upon winding, the effect of viscous deformations of the prepreg
and matrix increases. A decrease in viscosity and an increase in the tension force of the tape lead to a higher strength of
the ring in tension and interlaminar shear; however, the growing percolation of the polymer melt leads to a greater inhomogeneity
of the structure of the composite in the ring and to a lower reinforcing effect of the factors mentioned.
Presented at the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000).
Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 419–428, 2000. 相似文献
11.
It is proposed to employ a variable winding tension designed to give a required initial stress distribution. The program is constructed on the basis of solutions describing the loss of tension associated with winding and the softening of the resin during heat treatment. The problems are solved in the elastic formulation. Programs are obtained for three cases: constant tension in a ring sill on the mandrel, compensation of the stresses that develop after removal from the mandrel, and compensation of the thermoelastic stresses that develop during cooling.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 48–53, January–February, 1970. 相似文献
12.
Fred B. Weissler 《Israel Journal of Mathematics》1981,38(1-2):29-40
The existence and non-existence of global solutions and theL
p blow-up of non-global solutions to the initial value problemu′(t)=Δu(t)+u(t)
γ
onR
n are studied. We consider onlyγ>1. In the casen(γ − 1)/2=1, we present a simple proof that there are no non-trivial global non-negative solutions. Ifn(γ−1)/2≦1, we show under mild technical restrictions that non-negativeL
p solutions always blow-up inL
p norm in finite time. In the casen(γ−1)/2>1, we give new sufficient conditions on the initial data which guarantee the existence of global solutions.
Research partially supported by NSF grant MCS79-03636. 相似文献
13.
Haïm Brezis Jean Van Schaftingen 《Calculus of Variations and Partial Differential Equations》2007,30(3):369-388
We obtain boundary estimates for the gradient of solutions to elliptic systems with Dirichlet or Neumann boundary conditions
and L
1–data, under some condition on the divergence of the data. Similar boundary estimates are obtained for div–curl and Hodge
systems. 相似文献
14.
Sudhasree Gadam 《Rendiconti del Circolo Matematico di Palermo》1992,41(2):209-220
We study the behaviour of the positive solutions to the Dirichlet problem IR
n
in the unit ball in IR
R
wherep<(N+2)/(N−2) ifN≥3 and λ varies over IR. For a special class of functionsg viz.,g(x)=u
0
p
(x) whereu
0 is the unique positive solution at λ=0, we prove that for certain λ’s nonradial solutions bifurcate from radially symmetric
positive solutions. WhenN=1, we obtain the complete bifurcation diagram for the positive solution curve. 相似文献
15.
Vladimir Protasov 《Journal of Fourier Analysis and Applications》2000,6(1):55-78
In this paper we analyze solutions of the n-scale functional equation Ф(x) = Σk∈ℤ
Pk Ф(nx−k), where n≥2 is an integer, the coefficients {Pk} are nonnegative and Σpk = 1. We construct a sharp criterion for the existence of absolutely continuous solutions of bounded
variation. This criterion implies several results concerning the problem of integrable solutions of n-scale refinement equations
and the problem of absolutely continuity of distribution function of one random series. Further we obtain a complete classification
of refinement equations with positive coefficients (in the case of finitely many terms) with respect to the existence of continuous
or integrable compactly supported solutions. 相似文献
16.
We study the global analytic properties of the solutions of a particular family of Painlevé VI equations with the parameters
β=γ=0, δ= and 2α=(2μ-1)2 with arbitrary μ, 2μ≠∈ℤ. We introduce a class of solutions having critical behaviour of algebraic type, and completely compute
the structure of the analytic continuation of these solutions in terms of an auxiliary reflection group in the three dimensional
space. The analytic continuation is given in terms of an action of the braid group on the triples of generators of the reflection
group. We show that the finite orbits of this action correspond to the algebraic solutions of our Painlevé VI equation and
use this result to classify all of them. We prove that the algebraic solutions of our Painlevé VI equation are in one-to-one
correspondence with the regular polyhedra or star-polyhedra in the three dimensional space.
Oblatum 19-III-1999 & 25-XI-1999?Published online: 21 February 2000 相似文献
17.
S. A. Nazarov 《Journal of Mathematical Sciences》1996,80(5):1989-2034
The asymptotic series for solutions of the mixed boundary-value problem for the Poisson equation in a domain, which is a junction
of singularly degenerating domains, are constructed. In this paper, which is the first part of the publication, the three-dimensional
problem (“wheel hub with spokes”) and the analogous two-dimensional problems are considered. The methods of matched and compound
asymptotic expansions are used. It is shown that a special self-adjoint extension of the operator of the limit problem in
the “hub” supplied by the straight-line segments (“limits of spokes”) can be chosen as an asymptotical model of the problem
in question; the extension parameters are to be some integral characteristics of the boundary-layer problems. Bibliography:
39 titles.
Translated from Trudy Seminara imeni I. G. Petrovskogo. No. 18, pp. 3–78, 1995. 相似文献
18.
We study the structure of optimal solutions for a class of constrained, second order variational problems on bounded intervals.
We show that, for intervals of length greater than some positive constant, the optimal solutions are bounded inC
1 by a bound independent of the length of the interval. Furthermore, for sufficiently large intervals, the ‘mass’ and ‘energy’
of optimal solutions are almost uniformly distributed. 相似文献
19.
Perfectly matched layers in 1-d : energy decay for continuous and semi-discrete waves 总被引:2,自引:1,他引:1
In this paper we investigate the efficiency of the method of perfectly matched layers (PML) for the 1-d wave equation. The
PML method furnishes a way to compute solutions of the wave equation for exterior problems in a finite computational domain
by adding a damping term on the matched layer. In view of the properties of solutions in the whole free space, one expects
the energy of solutions obtained by the PML method to tend to zero as t → ∞, and the rate of decay can be understood as a measure of the efficiency of the method. We prove, indeed, that the exponential
decay holds and characterize the exponential decay rate in terms of the parameters and damping potentials entering in the
implementation of the PML method. We also consider a space semi-discrete numerical approximation scheme and we prove that,
due to the high frequency spurious numerical solutions, the decay rate fails to be uniform as the mesh size parameter h tends to zero. We show however that adding a numerical viscosity term allows us to recover the property of exponential decay
of the energy uniformly on h. Although our analysis is restricted to finite differences in 1-d, most of the methods and results apply to finite elements
on regular meshes and to multi-dimensional problems.
This work started while the first author was visiting the Department of Mathematics of the Universidad Autónoma de Madrid,
in the frame of the European program “New materials, adaptive systems and their nonlinearities: modeling, control and numerical
simulation” HPRN-CT-2002-00284. The work was finished while both authors visited the Isaac Newton Institute of Cambridge within
the Program “Highly Oscillatory Problems”. 相似文献
20.
We consider solutions of a generalization of the Camassa-Holm hierarchy to 2+1 dimensions that include, in particular, the
well-known multipeakon solutions of the celebrated Camassa-Holm equation.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 2, pp. 295–301, August, 2005. 相似文献