共查询到20条相似文献,搜索用时 15 毫秒
1.
The aim of this paper is double. First, we point out that the hypothesis D( t1) D( t2) = D( t2) D( t1) imposed in [1] can be removed. Second, a constructive method for obtaining analytic-numerical solutions with a prefixed accuracy in a bounded domain Ω( t0, t1) = [0, p] × [ t0, t1], for mixed problems of the type ut( x, t) − D( t) uxx( x, t) = 0, 0 < x < p, t> 0, subject to u(0, t) = u( p, t) = 0 and u( x,0) = F( x) is proposed. Here, u( x, t) and F( x) are r-component vectors, D( t) is a Cr × r valued analytic function and there exists a positive number δ such that every eigenvalue z of (1/2) ( D( t) + D( t) H) is bigger than δ. An illustrative example is included. 相似文献
2.
In this paper we study the behavior of the beta-spline functions in the case the parameter β 2( i) is negative. We prove that a negative value
exists so that if
, the beta-spline functions Ni( u) are positive. Moreover, if the control vertices are such that x0 xm−1, we have proved that the design curve keeps the properties already proved in the case β 2( i) 0. 相似文献
3.
For arbitrary equally sized square complex matrices A and Q ( Q Hermitian), the paper provides a complete algebraic test for verifying the existence of a Hermitian solution X of the nonstrict Lyapunov inequality A*X + XA + Q 0. If existing, we exhibit how to construct a solution. Our approach involves the validation problem for the linear matrix inequality Σ j=1k ( Aj*XjBj + Bj*Xj*Aj) + Q> 0 in Xj, for which we provide an algebraic solvability test and a construct solutions if the kernels of Aj or, dually, those of Bj form an isotonic sequence. 相似文献
4.
A conforming finite element formulation of the equations governing composite multilayered plates using Reddy's higher-order theory is presented. The element has eight degrees of freedom, u0, v0, w, ∂ w/∂ x, ∂ w/∂ y, ∂ 2w/∂ x∂ y, γ x, γ y, per node. The transverse displacement of the present element is described by a modified bicubic displacement function while the in-plane displacements and shear-rotations are interpolated quadraticly. The element is evaluated for its accuracy in the analysis of static, vibration, and buckling of anisotropic rectangular plates with different lamination schemes and boundary conditions. The conforming finite element described here for the higher-order theory gives fairly accurate results for displacements, stresses, buckling loads, and natural frequencies. 相似文献
5.
This paper describes some new techniques for the rapid evaluation and fitting of radial basic functions. The techniques are based on the hierarchical and multipole expansions recently introduced by several authors for the calculation of many-body potentials. Consider in particular the N term thin-plate spline, s( x) = Σ j=1N djφ( x− xj), where φ( u) = | u| 2log| u|, in 2-dimensions. The direct evaluation of s at a single extra point requires an extra O( N) operations. This paper shows that, with judicious use of series expansions, the incremental cost of evaluating s( x) to within precision ε, can be cut to O(1+|log ε|) operations. In particular, if A is the interpolation matrix, ai,j = φ( xi− xj, the technique allows computation of the matrix-vector product Ad in O( N), rather than the previously required O( N2) operations, and using only O( N) storage. Fast, storage-efficient, computation of this matrix-vector product makes pre-conditioned conjugate-gradient methods very attractive as solvers of the interpolation equations, Ad = y, when N is large. 相似文献
6.
Let A be an alphabet and ƒ be a right infinite word on A. If ƒ is not ultimately periodic then there exists an infinite set { vii0} of (finite) words on A such that ƒ= v0v1… vi…, { vii1} is a biprefix code and vi≠ vj for positive integers i≠ j. 相似文献
7.
We show that given any family of asymptotically stabilizable LTI systems depending continuously on a parameter that lies in some subset [ a1, b1]××[ ap, bp] of
, there exists a C0 time-varying state feedback law v( t, x) (resp. a C0 time-invariant feedback law v( x)) which robustly globally exponentially stabilizes (resp. which robustly stabilizes, not asymptotically) the family. Further, if these systems are obtained by linearizing some nonlinear systems, then v( t, x) locally exponentially stabilizes these nonlinear systems. Finally, v( t, x) globally exponentially stabilizes any time-varying system which switches “slowly enough” between the given LTI systems. 相似文献
8.
The paper presents sufficient conditions for the existence of positive solutions of the equation x″( t) + q( t) f( t, x( t), x′( t)) = 0 with the Dirichlet conditions x(0) = 0, x(1) = 0 and of the equation ( p( t) x′( t))′ + p( t) q( t) f( t, x( t), p( t) x′( t)) = 0 with the boundary conditions lim t→o+ p( t) x′( t) = 0, x(1) = 0. Our nonlinearity f is allowed to change sign and f may be singular at x = 0. The proofs are based on a combination of the regularity and sequential techniques and the method of lower and upper functions. 相似文献
9.
The iterative map xn+1 = rnxn (1 - xn) is investigated with rn changing periodically between two values A and B. Different periodicities are assumed, e.g., { rn} = { BABA …} or { rn} = { BBABA BBABA …}. The Lyapunov exponent (a measure of average stability) is displayed with high resolution on the A- B-plane. The resulting images have aesthetically appealing self-similar structures. Furthermore, these images allow with one glimpse the identification of a number of system properties: coexistence of attractors, superstable curves, order by alternation of chaotic processes, and chaos by periodic resetting from a stable into an unstable fixed point. 相似文献
10.
We call a function f in n variables an order-configuration function if for any x1,…, xn such that xi1 … xin we have f( x1,…, xn) = xt, where t is determined by the n-tuple ( i1,…, in) corresponding to that ordering. Equivalently, it is a function built as a minimum of maxima, or a maximum of minima. Well-known examples are the minimum, the maximum, the median, and more generally rank functions, or the composition of rank functions. Such types of functions are often used in nonlinear processing of digital signals or images (for example in the median or separable median filter, min-max filters, rank filters, etc.). In this paper we study the mathematical properties of order-configuration functions and of a wider class of functions that we call order-subconfiguration functions. We give several characterization theorems for them. We show through various examples how our concepts can be used in the design of digital signal filters or image transformations based on order-configuration functions. 相似文献
11.
A single-chip 3-D silicon vector sensor for magnetic-field measurement is presented. This triaxial device functionally integrates in a common transducer region two novel five-contacts parallel-field Hall elements for in-plane components Bx and By and four cross-coupled orthogonal triple Hall elements for the Bz component, perpendicular to the chip surface. The effective sensor volume is 150 μm×150 μm×100 μm. The main advantage of this 3-D vector magnetometer is the strongly reduced (with about 45%) channel cross-sensitivities. This is achieved by amperometric output mode of operation using an original read-out circuitry, keeping equal voltage conditions on the top of the chip with and without magnetic field. The sensitivities per channel reaches SA( Bx)= SA( By)=356 μA/T and SA( Bz)=260 μA/T at a supply current 10 mA, the measured equivalent offsets of the three channel outputs are 25/35 mT and the low frequency noise is mainly a 1/ f. The lowest detected magnetic induction of the three output channels is about 15/20 μT in the range 1≤ f≤ 10 2 Hz and the frequency response of the 3-D device together with the read-out electronics is at least 30 kHz. 相似文献
12.
A previous application of the Newton divided difference series of the displacement function Ez = (1 + Δ) z = e Dz, where the operators Δ and D are the variables, to purely exponential interpolation employing general-factorial differences and derivatives, {Pi; mi=0 (Δ - Si)} f(0) and {Pi; mi=0 ( D - ti)} f(0), in which the si's and ti's are distinct[1], is here extended to mixed polynomial-exponential interpolation where the si's and ti's are no longer distinct. 相似文献
13.
For each nonempty binary word w= c1c2cq, where ci{0,1}, the nonnegative integer ∑ i=1q ( q+1− i) ci is called the moment of w and is denoted by M( w). Let [ w] denote the conjugacy class of w. Define M([ w])={ M( u): u[ w]}, N( w)={ M( u)− M( w): u[ w]} and δ( w)=max{ M( u)− M( v): u, v[ w]}. Using these objects, we obtain equivalent conditions for a binary word to be an -word (respectively, a power of an -word). For instance, we prove that the following statements are equivalent for any binary word w with | w|2: (a) w is an -word, (b) δ( w)=| w|−1, (c) w is a cyclic balanced primitive word, (d) M([ w]) is a set of | w| consecutive positive integers, (e) N( w) is a set of | w| consecutive integers and 0 N( w), (f) w is primitive and [ w] St. 相似文献
14.
Consider the functions H( t):= t2 and h( u, v):= uv. The identity H( t)= h( t, t) shows that h is the restriction of h to the diagonal u= v in the uv-plane. Yet, in many ways, a bilinear function like h is simpler than a homogeneous quadratic function like H. More generally, if F(t) is some n-ic polynomial function, it is often helpful to study the polar form of F, which is the unique symmetric, multiaffine function ƒ( u1,…un) satisfying the identity F( t)= f( t,…, t). The mathematical theory underlying splines is one area where polar forms can be particularly helpful, because two pieces F and G of an n-ic spline meet at a point r with Ck parametric continuity if and only if their polar forms ƒ and g agree on all sequences of n arguments that contain at least n- k copies of r. The polar approach to the theory of splines emerged in rather different guises in three independent research efforts: Paul de Faget Casteljau called it ‘shapes through poles’; Carl de Boor called it ‘B-splines without divided differences’; and Lyle Ramshaw called it ‘blossoming’. This paper reviews the work of de Casteljau, de Boor, and Ramshaw in an attempt to clarify the basic principles that underly the polar approach. It also proposes a consistent system of nomenclature as a possible standard. 相似文献
15.
We investigate time-constructible functions in one-dimensional cellular automata (CA). It is shown that (i) if a function t( n) is computable by an O( t( n)− n)-time Turing machine, then t( n) is time constructible by CA and (ii) if two functions are time constructible by CA, then the sum, product, and exponential functions of them are time constructible by CA. As an application, it is shown that if t1( n) and t2( n) are time constructible functions such that lim n→∞ t1( n)/ t2( n) = 0 and t1( n) n, then there is a language which can be recognized by a CA in t2( n) time but not by any CA in t1( n) time. 相似文献
16.
This paper presents an efficient algorithm for enumerating all minimal a- b separators separating given non-adjacent vertices a and b in an undirected connected simple graph G = ( V, E), Our algorithm requires O( n3Rab) time, which improves the known result of O( n4Rab) time for solving this problem, where ¦ V¦= n and Rab is the number of minimal a- b separators. The algorithm can be generalized for enumerating all minimal A- B separators that separate non-adjacent vertex sets A, B < V, and it requires O( n2( n − nA − nb) RAB) time in this case, where na = ¦ A¦, nB = ¦ B¦ and rAB is the number of all minimal A− B separators. Using the algorithm above as a routine, an efficient algorithm for enumerating all minimal separators of G separating G into at least two connected components is constructed. The algorithm runs in time O( n3R+Σ + n4RΣ), which improves the known result of O( n6RΣ) time, where Rσ is the number of all minimal separators of G and RΣR+Σ = ∑ 1i, v j) ER vivj (n( n − 1)/2 − m) RΣ. Efficient parallelization of these algorithms is also discussed. It is shown that the first algorithm requires at most O(( n/ log n) Rab) time and the second one runs in time O(( n/ log n) R+Σ+ n log nRΣ) on a CREW PRAM with O( n3) processors. 相似文献
17.
Let
be such that d1, pd=1, p02 and
. We are proving in this note a new criterion for the pair
to be a canonical number system. This enables us to prove that if p2,…, pd−1,∑ i=1dpi0 and p0>2∑ i=1d| pi|, then
is a canonical number system. 相似文献
18.
We formulate a class of difference schemes for stiff initial-value problems, with a small parameter ε multiplying the first derivative. We derive necessary conditions for uniform convergence with respect to the small parameter ε, that is the solution of the difference scheme uih satisfies | uih− u( xi)| Ch, where C is independent of h and ε. We also derive sufficient conditions for uniform convergence and show that a subclass of schemes is also optimal in the sense that | uih− u( xi)| C min ( h, ε). Finally, we show that this class contains higher-order schemes. 相似文献
19.
This paper presents a simple and robust method for computing the bisector of two planar rational curves. We represent the correspondence between the foot points on two planar rational curves C1( t) and C2( r) as an implicit curve
( t, r)=0, where
( t, r) is a bivariate polynomial B-spline function. Given two rational curves of degree m in the xy-plane, the curve
( t, r)=0 has degree 4 m−2, which is considerably lower than that of the corresponding bisector curve in the xy-plane. 相似文献
20.
For an ordered set W = { w1, w2,…, wk} of vertices and a vertex v in a connected graph G, the (metric) representation of v with respect to W is the k-vector r( v | W) = ( d( v, w1), d( v, w2),…, d( v, wk)), where d( x, y) represents the distance between the vertices x and y. The set W is a resolving set for G if distinct vertices of G have distinct representations. A new sharp lower bound for the dimension of a graph G in terms of its maximum degree is presented. A resolving set of minimum cardinality is a basis for G and the number of vertices in a basis is its (metric) dimension dim(G). A resolving set S of G is a minimal resolving set if no proper subset of S is a resolving set. The maximum cardinality of a minimal resolving set is the upper dimension dim+(G). The resolving number res(G) of a connected graph G is the minimum k such that every k-set W of vertices of G is also a resolving set of G. Then 1 ≤ dim(G) ≤ dim+(G) ≤ res(G) ≤ n − 1 for every nontrivial connected graph G of order n. It is shown that dim+(G) = res(G) = n − 1 if and only if G = Kn, while dim+(G) = res(G) = 2 if and only if G is a path of order at least 4 or an odd cycle. The resolving numbers and upper dimensions of some well-known graphs are determined. It is shown that for every pair a, b of integers with 2 ≤ a ≤ b, there exists a connected graph G with dim(G) = dim+(G) = a and res(G) = b. Also, for every positive integer N, there exists a connected graph G with res(G) − dim+(G) ≥ N and dim+(G) − dim(G) ≥ N. 相似文献
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