共查询到20条相似文献,搜索用时 15 毫秒
1.
R. Ayala L.M. Fernández J.A. Vilches 《Bulletin of the Brazilian Mathematical Society》2009,40(2):225-235
We get a characterization theorem for equivalent discrete Morse functions defined on simplicial complexes in terms of their
gradient vector field. As a consequence, we also characterize them in the 1-dimensional case by using critical elements.
The authors are partially supported by the P.A.I. project (Junta de Andalucia, SPAIN, 2009/FQM-189 and 327) and by the MEC-FEDER
grants MTM2007-61284 and MTM2007-65726 (MEC, SPAIN, 2007). 相似文献
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In Nicolaescu (2008) [7] the number of non-homologically equivalent excellent Morse functions defined on S2 was obtained in the differentiable setting. We carried out an analogous study in the discrete setting for some kinds of graphs, including S1, in Ayala et al. (2009) [1]. This paper completes this study, counting excellent discrete Morse functions defined on any infinite locally finite graph. 相似文献
3.
Fan C. Meng 《Operations Research Letters》2008,36(3):377-380
In this note some new characterization results for multistate systems are obtained. In particular, a new characterization of the Natvig class of multistate systems is presented, which provides us an easy-to-use method of classifying multistate systems. Examples are given to illustrate our results. 相似文献
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In 1968, Vizing conjectured that, if G is a Δ-critical graph with n vertices, then α(G)?n/2, where α(G) is the independence number of G. In this note, we verify this conjecture for n?2Δ. 相似文献
5.
Vugar E. Ismailov 《Applicable analysis》2013,92(11):2245-2260
In this paper, we consider the problem of approximation of continuous multivariate functions by neural networks with a bounded number of neurons in hidden layers. We prove the existence of single-hidden-layer networks with bounded number of neurons, which have approximation capabilities not worse than those of networks with arbitrarily many neurons. Our analysis is based on the properties of ridge functions. 相似文献
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Algorithmic thinking is emerging as an important competence in mathematics education, yet research appears to be lagging this shift in curricular focus. The aim of this generative study is to examine how students use the cognitive skills of algorithmic thinking to design algorithms. Task-based interviews were conducted with four pairs of Year 12 students (n = 8) to analyze how they used decomposition and abstraction to specify the projects, designed algorithms to solve scheduling problems by first devising fundamental operations and then using algorithmic concepts to account for complex and special cases of the problems, and tested and debugged their algorithms. A deductive-inductive analytical process was used to classify students’ responses according to the four cognitive skills to develop sets of subskills to describe how the students engaged these cognitive skills. 相似文献
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In this paper, general functional equations of rooted essential maps on surfaces (orientable and nonorientable) are deduced and their formal solutions are presented. Further, three explicit for- mulae for counting essential maps on S2,N3 andN4 are given. In the same time, some known results can be derived. 相似文献
9.
We study a flow-shop problem, where each of the jobs is limited to no more than two operations. One of these operations is common for all the jobs, and is performed on the same (”critical”) machine. Reflecting many applications, jobs are assumed to be processed in blocks on the critical machine. All the jobs share a common due-date, and the objective is minimum weighted number of tardy jobs. We prove that the problem is NP-hard. Then we formulate the problem as an integer program, and introduce a pseudo-polynomial dynamic programming algorithm, proving that the problem is NP-hard in the ordinary sense. We also propose an efficient heuristic, which is shown numerically to produce very close-to-optimal schedules. Finally, we show that the special case of identical weights is polynomially solvable. 相似文献
10.
Let P be a second-order, linear, elliptic operator with real coefficients which is defined on a noncompact and connected Riemannian manifold M. It is well known that the equation in M admits a positive supersolution which is not a solution if and only if P admits a unique positive minimal Green function on M, and in this case, P is said to be subcritical in M. If P does not admit a positive Green function but admits a global positive (super)solution, then such a solution is called a ground state of P in M, and P is said to be critical in M.We prove for a critical operator P in M, the existence of a Green function which is dominated above by the ground state of P away from the singularity. Moreover, in a certain class of Green functions, such a Green function is unique, up to an addition of a product of the ground states of P and . Under some further assumptions, we describe the behavior at infinity of such a Green function. This result extends and sharpens the celebrated result of P. Li and L.-F. Tam concerning the existence of a symmetric Green function for the Laplace–Beltrami operator on a smooth and complete Riemannian manifold M. 相似文献
11.
Tom Rackham 《Journal of Graph Theory》2011,68(2):129-136
A (k, 1)‐coloring of a graph is a vertex‐coloring with k colors such that each vertex is permitted at most 1 neighbor of the same color. We show that every planar graph has at least cρn distinct (4, 1)‐colorings, where c is constant and ρ≈1.466 satisfies ρ3 = ρ2 + 1. On the other hand for any ε>0, we give examples of planar graphs with fewer than c(? + ε)n distinct (4, 1)‐colorings, where c is constant and . Let γ(S) denote the chromatic number of a surface S. For every surface S except the sphere, we show that there exists a constant c′ = c′(S)>0 such that every graph embeddable in S has at least c′2n distinct (γ(S), 1)‐colorings. © 2010 Wiley Periodicals, Inc. J Graph Theory 28:129‐136, 2011 相似文献
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B. S. Kruglikov 《Mathematical Notes》1999,65(3):280-294
The paper contains the classification up to conjugation in the categoryC
k,k=1,...,∞, of complete nondegenerate divergence-free vector fieldson a compact surface (possibly with boundary) almost all
of whose trajectories are closed. The classification up to conjugation in given for arbitrary nondegenerate divergence-free
vector fields on the surfacesS
2,
,K
2,T
2,
, possibly with holes.
Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 336–353 March, 1999. 相似文献
14.
实Grassmann流形上的道路空间 总被引:1,自引:0,他引:1
G(n,m)表示R ̄n+m中全体n维子空间所构成的实Grassmann流形。本文首先找到p,q∈G(n,m)沿任何测地线均不共轭的充要条件,因此连接这样两点的测地线有可数条。通过计算得到编号为(k_1,k_2,…,k_n)的测地线指标λ(k_1,k_2…,k_n).最后根据Morse基本定理得到:设p,q是G(n,m),上沿任何测地线均不共轭的两点,则连接p,q的分段光滑道路空间同伦于一可数CW-复形,该复形中的胞腔可编号为(k_1,k_2,…,k_n),k_i为整数,且编号为(k_1,k_2,…,k_n的胞腔的维数为λ(k_1,k_2…,k_n)。 相似文献
15.
Liviu I. Nicolaescu 《Stochastic Processes and their Applications》2017,127(10):3412-3446
We prove a central limit theorem concerning the number of critical points in large cubes of an isotropic Gaussian random function on a Euclidean space. 相似文献
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Jian-Ming Peng Qi-Lei Yin Guo-lin Li He Liu Wei Wang 《Applied Mathematical Modelling》2013,37(14-15):7741-7751
The effect of actuator parameters on the critical flow velocity of the fluidic amplifier in liquid-jet hammers has been investigated numerically and experimentally. The flow in the fluidic amplifier and actuators coupled with the rigid body movement of the impacting body has been simulated using a commercial CFD software package, Fluent. The flow is modeled by the RNG-based κ–ε turbulence model and the incompressible Navier–Stokes equations. Dynamic layering method and a user-defined function written in C programming language are used to update the mesh in the simulations. The results show that, increasing the piston diameter decreases rapidly the critical flow velocity as the piston diameter is less than a certain value. The critical flow velocity increases sharply as the piston rod diameter is greater than a certain value, and increases nearly linearly with mass of the impacting body, and is independent on stroke length of the impacting body. The findings of the numerical investigations agree well with corresponding experimental results. 相似文献
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