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991.
Let G=(V,E) be a (directed) graph with vertex set V and edge (arc) set E. Given a set P of source-sink pairs of vertices of G, an important problem that arises in the computation of network reliability is the enumeration of minimal subsets of edges (arcs) that connect/disconnect all/at least one of the given source-sink pairs of P. For undirected graphs, we show that the enumeration problems for conjunctions of paths and disjunctions of cuts can be solved in incremental polynomial time. Furthermore, under the assumption that P consists of all pairs within a given vertex set, we also give incremental polynomial time algorithm for enumerating all minimal path disjunctions and cut conjunctions. For directed graphs, the enumeration problem for cut disjunction is known to be NP-complete. We extend this result to path conjunctions and path disjunctions, leaving open the complexity of the enumeration of cut conjunctions. Finally, we give a polynomial delay algorithm for enumerating all minimal sets of arcs connecting two given nodes s1 and s2 to, respectively, a given vertex t1, and each vertex of a given subset of vertices T2. 相似文献
992.
Qin-long Wang Yi-rong Liu 《应用数学学报(英文版)》2007,23(3):451-466
In this paper, we study the appearance of limit cycles from the equator and isochronicity of infinity in polynomial vector fields with no singular points at infinity. We give a recursive formula to compute the singular point quantities of a class of cubic polynomial systems, which is used to calculate the first seven singular point quantities. Further, we prove that such a cubic vector field can have maximal seven limit cycles in the neighborhood of infinity. We actually and construct a system that has seven limit cycles. The positions of these limit cycles can be given exactly without constructing the Poincare cycle fields. The technique employed in this work is essentially different from the previously widely used ones. Finally, the isochronous center conditions at infinity are given. 相似文献
993.
In this article, by introducing characteristic singular integral operator and associate singular integral equations (SIEs), the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu. 相似文献
994.
Alain Lascoux 《Bulletin des Sciences Mathématiques》2006,130(4):354-359
Eliminating the arbitrary coefficients in the equation of a generic plane curve of order n by computing sufficiently many derivatives, one obtains a differential equation. This is a projective invariant. The first one, corresponding to conics, has been obtained by Monge. Sylvester, Halphen, Cartan used invariants of higher order. The expression of these invariants is rather complicated, but becomes much simpler when interpreted in terms of symmetric functions. 相似文献
995.
S. Sarkar A. D. Thakur C. V. Tomy G. Balakrishnan D. McK Paul S. Ramakrishnan A. K. Grover 《Pramana》2006,66(1):193-207
New experimental data are presented on the scan rate dependence of the magnetization hysteresis width ΔM(H) (∞ critical current densityJ
c(H)) in isothermalMH scans in a weakly pinned single crystal of Ca3Rh4Sn13, which displays second magnetization peak (SMP) anomaly as distinct from the peak effect (PE). We observe an interesting
modulation in the field dependence of a parameter which purports to measure the dynamical annealing of the disordered bundles
of vortices injected through the sample edges towards the destined equilibrium vortex state at a givenH. These data, in conjunction with the earlier observations made while studying the thermomagnetic history dependence inJ
c(H) in the tracing of the minor hysteresis loops, imply that the partially disordered state heals towards the more ordered state
between the peak field of the SMP anomaly and the onset field of the PE. The vortex phase diagram in the given crystal of
Ca3Rh4Sn13 has been updated in the context of the notion of the phase coexistence of the ordered and disordered regions between the
onset field of the SMP anomaly and the spinodal line located just prior to the irreversibility line. A multi-critical point
and a critical point in the (H,T) region of the Bragg glass phase have been marked in this phase diagram and the observed behavior is discussed in the light
of recent data on multi-critical point in the vortex phase diagram in a single crystal of Nb. 相似文献
996.
R. Srinivasan 《Pramana》2006,66(1):3-30
Rotating dilute Bose-Einstein condensates (BEC) of alkali atoms offer a testing ground for theories of vortices in weakly
interacting superfluids. In a rotating super-fluid, quantised vortices, with a vorticity h/m, form above a critical velocity.
Such vortices have been generated in BEC of alkali atoms by different techniques such as (a) wave function engineering of
a two-component BEC, (b) decay of solitons, (c) rotation of a thermal cloud before cooling it below the condensation temperature,
(d) stirring with an ‘optical’ spoon, (e) rotating a deformation in the anisotropic trap in which the condensate is trapped
and (f) by creating Berry phase by adiabatically reversing the axial magnetic field. Since the core of a vortex is a fraction
of a micrometer in diameter, it cannot be directly imaged optically. The condensate with vortices is allowed to ballistically
expand till the size increases by one order before the vortices are imaged. Surface wave spectroscopy and the change in aspect
ratio of a rotating cloud are the other techniques used. Studies have been made on the creation and dynamics of single vortex
and on systems with more than a hundred vortices. Results have been obtained on vortex nucleation, stability of vortex structures,
nature of the vortex lattice and defects in such a lattice. Important results are: (a) evidence exists that vortex nucleation
takes place by a surface mode instability; but this is not the only mechanism; (b) the vortex lattice is perfectly triangular
right up to the edge; (c) in the initial stages of rotation of the cloud a tangled web of vortices is seen; it takes a few
hundred milliseconds before the vortices arrange themselves in a lattice; this time appears to be independent of temperature;
(d) the decay of vortices appears to arise from the transfer of energy to the rotating thermal component and is dependent
on temperature; (e) defects in the lattices such as dislocations and grain boundaries are seen; (f) transverse oscillations
(Tkachenko modes) of the vortex lattice have been observed; and (g) giant vortices have been produced. These will be discussed. 相似文献
997.
We study the transversal spin–spin correlations in the non-equilibrium steady state of the XY chain constructed by coupling a finite cutout of the chain to the two infinite parts to its left and right acting as thermal reservoirs at different temperatures. We prove that the spatial decay of these correlations is at least exponentially fast. 相似文献
998.
This paper is concerned with the spectral analysis of a one-velocity transport operator with Maxwell boundary condition in
L
1-space. After a detailed spectral analysis it is shown that the associated Cauchy problem is governed by a C
0-semigroup. Next, we discuss the irreducibility of the transport semigroup. In particular, we show that the transport semigroup
is irreducible. Finally, a spectral decomposition of the solutions into an asymptotic term and a transient one which will
be estimated for smooth initial data is given. 相似文献
999.
The constitutive behavior of porous materials (including the yield loci, the void growth rate, the macro stress-strain relation
and the strain to localization instability) is examined based on the lower bound approach proposed by the present authors.
These results are then compared with the experimental and the finite element results as well as those predicted by Gurson's
equations. Emphasis is placed on approaching the real behavior from the upper and the lower bound analysis. Calculation is
also made on the influence of void nucleation on the critical strain to instability and a modified strain-controlled nucleation
criterion is proposed. Finally the instability and fracture of AISI4340 steel in plane strain tension is examined and comparison
is made between theoretical and experimental results. 相似文献
1000.
This paper develops a mathematical model of the ring-spinning process that takes into account its non-stationary nature. A complex system of differential equations is obtained, which from a mathematical point of view constitutes a ‘free-boundary’ problem. Its solution involves definition of suitable boundary conditions related to the mechanical characteristics of the process and of the spinning machine itself. The boundary conditions which determine the solution are pointed out. A numerical solution of the system of differential equations can be obtained by the Finite-Segments method, as shown in an example. 相似文献