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排序方式: 共有197条查询结果,搜索用时 125 毫秒
1.
We study a class of shape optimization problems for semi-linear elliptic equations with Dirichlet boundary conditions in smooth
domains in ℝ2. A part of the boundary of the domain is variable as the graph of a smooth function. The problem is equivalently reformulated
on a fixed domain. Continuity of the solution to the state equation with respect to domain variations is shown. This is used
to obtain differentiability in the general case, and moreover a useful formula for the gradient of the cost functional in
the case where the principal part of the differential operator is the Laplacian.
Online publication 23 January 2004. 相似文献
2.
J. Haslinger T. Kozubek K. Kunisch G. Peichl 《Journal of Mathematical Analysis and Applications》2004,290(2):665-685
This contribution combines a shape optimization approach to free boundary value problems of Bernoulli type with an embedding domain technique. A theoretical framework is developed which allows to prove continuous dependence of the primal and dual variables in the resulting saddle point problems with respect to the domain. This ensures the existence of a solution of a related shape optimization problem in a sufficiently large class of admissible domains. 相似文献
3.
Ming-Chien Yang 《Applied mathematics and computation》2010,216(12):3754-3760
The n-dimensional star graph Sn is an attractive alternative to the hypercube graph and is a bipartite graph with two partite sets of equal size. Let Fv and Fe be the sets of faulty vertices and faulty edges of Sn, respectively. We prove that Sn − Fv − Fe contains a fault-free cycle of every even length from 6 to n! − 2∣Fv∣ with ∣Fv∣ + ∣Fe∣ ? n − 3 for every n ? 4. We also show that Sn − Fv − Fe contains a fault-free path of length n! − 2∣Fv∣ − 1 (respectively, n! − 2∣Fv∣ − 2) between two arbitrary vertices of Sn in different partite sets (respectively, the same partite set) with ∣Fv∣ + ∣Fe∣ ? n − 3 for every n ? 4. 相似文献
4.
A stationary random field is often more complicated than a univariate stationary time series, since dependence for a random field extends in all directions, while there is only the natural distinction of past and future at any instant in a univariate time series. In this paper we start from a simple correlation structure, derive a class of stationary random fields with the simple correlation function and the simple spectral density function by using linear combinations of separable spatial correlation functions, and discuss a problem of embedding a lattice model into a continuous domain model. 相似文献
5.
We investigate GI
X
/M(n)//N systems with stochastic customer acceptance policy, function of the customer batch size and the number of customers in the
system at its arrival. We address the time-dependent and long-run analysis of the number of customers in the system at prearrivals
and postarrivals of batches and seen by customers at their arrival to the system, as well as customer blocking probabilities.
These results are then used to derive the continuous-time long-run distribution of the number of customers in the system.
Our analysis combines Markov chain embedding with uniformization and uses stochastic ordering as a way to bound the errors
of the computed performance measures.
相似文献
6.
Shahar Mendelson 《Random Structures and Algorithms》2005,27(1):25-45
We investigate a new notion of embedding of subsets of {?1,1}n in a given normed space, in a way which preserves the structure of the given set as a class of functions on {1, …, n}. This notion is an extension of the margin parameter often used in Nonparametric Statistics. Our main result is that even when considering “small” subsets of {?1, 1}n, the vast majority of such sets do not embed in a better way than the entire cube in any normed space that satisfies a minor structural assumption. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005 相似文献
7.
For a given polyhedron K(?)M,the notation RM(K)denotes a regular neigh- borhood of K in M.The authors study the following problem:find all pairs(m,k) such that if K is a compact k-polyhedron and M a PL m-manifold,then R_M(f(K))≌R_M(g(K))for each two homotopic PL embeddings f,g:K→M.It is proved that R_S~(k 2)(S~k)(?)S~k×D~2 for each k(?)2 and some PL sphere S~k(?)S~(k 2)(even for any PL sphere S~k(?)S~(K 2)having an isolated non-locally flat point with the singularity S~(k-1)(?) S~(k 1)such thatπ_1(S~(k 1)-S~(k-1))(?)Z). 相似文献
8.
We introduce the notion of sofic measurable equivalence relations. Using them we prove that Connes' Embedding Conjecture as well as the Measurable Determinant Conjecture of Lück, Sauer and Wegner hold for treeable equivalence relations. 相似文献
9.
The proposed all-optical 2-D switching networks are (i) M×N-gon prism switches (M2, N3) and (ii) 3-D grids of any geometry N3. For the routing we assume (1) the projection of the spatial architectures onto plane graphs (2) the embedding of the latter guest graphs into (in)complete host hypercubes (N=4) and generally, into N-cube networks (N3) and (3) routing by means of the cube algorithms of the host. By the embedding mainly faulty cubes (synonyms: injured cubes, incomplete cubes) arise which complicate the routing and analysis. The application of N-cube networks (i) extend the hypercube principles to any N3 (ii) increase the number of plane host graphs and (iii) reduce the incompleteness of the host cubes. Several different embeddings of the intersection graphs (IGs) of 2-D switching networks and several different routings are explained for N=4 and 6 by various examples. By the expansion of the grids (enlargement) internal waveguides (WGs) and internal switches are introduced which interact with the switches of the original 3-D grid without increasing the number of stages (NS). The embeddings by expansion apply to interconnection networks whereas dilation-2 embeddings (dilation ≡ distance of the nearest-neighbour nodes of the guest graph at the host) are rather suitable for the emulation of algorithms. Concepts for fault-tolerant routing and algorithm mapping are briefly explained. 相似文献
10.
Julia M. N. Brown 《Designs, Codes and Cryptography》2007,44(1-3):239-248
We give a nearfield-free definition of some finite and infinite incidence systems by means of half-points and half-lines and
show that they are projective planes. We determine a planar ternary ring for these planes and use it to determine the full
collineation group and to demonstrate some embeddings of these planes among themselves. We show that these planes include
all finite regular Hughes planes and many infinite ones. We also show that PG(3, q) embeds in Hu(q
4) (and show infinite versions of this embedding).
Dan Hughes 80th Birthday. 相似文献