共查询到20条相似文献,搜索用时 15 毫秒
1.
Zbigniew Grande 《Mathematica Slovaca》2013,63(4):793-798
Let f: ?2 → ? be a function with upper semicontinuous and quasi-continuous vertical sections f x (t) = f(x, t), t, x ∈ ?. It is proved that if the horizontal sections f y (t) = f(t, y), y, t ∈ ?, are of Baire class α (resp. Lebesgue measurable) [resp. with the Baire property] then f is of Baire class α + 2 (resp. Lebesgue measurable and sup-measurable) [resp. has Baire property]. 相似文献
2.
《Mathematical and Computer Modelling》1997,25(2):109-116
This work deals with the guidance and control of a system which is composed of a rolling cylinder and a controlled slender rod that is pivoted, through its center of mass, about the cylinder's center. Given a finite time interval [0, tf], and let P1 and P2 be two points in the (X, Y)-plane. The problem dealt with here is to find a closed-loop control law for the cylinder-rod system such that:
- 1.(i) the cylinder center will move from P1 to P2 during [0, tf] and will come to rest at P2, and
- 2.(ii) the rod will rotate from an angle ψ21 to ψ22 during [0, tf] and will stop to rotate at t = tf.
3.
S. K. Sachdev 《Journal of Optimization Theory and Applications》1983,39(1):19-34
The nonlinear initial-value problemu″(t)+f(t,u(t))=0,u(t 0)+bu′(t 0)=c,t 0≥0,b≤0,c≥0, is considered for positive solutions on [t 0, ∞). Existence of positive solutions is proved without the hypothesis thatf(t, ω)≥0 (or ≤0), using the lattice fixed point theorem. A monotonicity condition inf(t, ω) is used to prove the uniqueness of the solution of the initial-value problem. Whenf(t, ω)≥0 (or ≤0), uniqueness is also obtained under a sublinearity condition onf(t, ω). 相似文献
4.
《Mathematical and Computer Modelling》1997,25(11):67-74
This work deals with the guidance and control of a riderless bicycle (see Figure 1). Given two points P1 and p2 in the horizontal plane and a finite time interval [0, tf]. Denote by (x1,y1,z1) the coordinates of the center of the bicycle's rear wheel. Based on a simplified dynamical model of the bicycle, and by using the concept of path controllability, control laws are derived for the bicycle's pedalling moment and directional moment such that (x1,y1) will move from p1 to P2 during the time interval [0, tf]. 相似文献
5.
Hong-Xu Li 《Journal of Mathematical Analysis and Applications》2004,298(2):693-709
In this paper, we present an existence theorem of almost periodic solutions of second-order neutral delay-differential equations with piecewise constant arguments of the form (x(t)+x(t−1))″=qx([t])+f(t), where [·] denotes the greatest integer function, q is a nonzero constant, and f(t) is almost periodic. 相似文献
6.
N. A. Izobov 《Differential Equations》2013,49(10):1211-1226
For the lower sigma-exponent of the linear differential system ? = A(t)x, x ∈ R n , t ≥ 0, defined by the formula Δσ(A) ≡ infλ[Q]≤-σ λ 1(A + Q), σ > 0, on the basis of the lower characteristic exponents λ 1(A+Q) of perturbed linear systems with Lyapunov exponents λ[Q] ≤ ?σ < 0 of perturbations Q, we prove the following general form as a function of the parameter σ > 0. For any nondecreasing bounded function f(σ) of the parameter σ ∈ (0,+∞) that coincides with a constant on some infinite interval (σ 0,+∞), σ 0 ≥ 0, and satisfies the Lipschitz condition on the complementary interval (0, σ 0], we prove the existence of a linear system with coefficient matrix A f (t) bounded on the half-line [0,+∞) whose lower sigma-exponent Δσ(A f ) coincides with the function f(σ) on the entire interval (0,+∞). 相似文献
7.
We find conditions for the existence and uniqueness of almost periodic solutions of second-order neutral delay-differential equations with almost periodic time dependence of the form (x(t)+px(t−1))″=qx([t])+f(t); here [·] is the greatest integer function, p and q are nonzero constants, and f(t) is Bohr almost periodic. 相似文献
8.
Stacey Muir 《Journal of Mathematical Analysis and Applications》2008,348(2):862-871
For two complex-valued harmonic functions f and F defined in the open unit disk Δ with f(0)=F(0)=0, we say f is weakly subordinate to F if f(Δ)⊂F(Δ). Furthermore, if we let E be a possibly infinite interval, a function with f(⋅,t) harmonic in Δ and f(0,t)=0 for each t∈E is said to be a weak subordination chain if f(Δ,t1)⊂f(Δ,t2) whenever t1,t2∈E and t1<t2. In this paper, we construct a weak subordination chain of convex univalent harmonic functions using a harmonic de la Vallée Poussin mean and a modified form of Pommerenke's criterion for a subordination chain of analytic functions. 相似文献
9.
We give Lyapunov exponents of solutions to linear differential equations of the form x′=Ax+f(t), where A is a complex matrix and f(t) is a τ-periodic continuous function. Notice that f(t) is not “small” as t→∞. The proof is essentially based on a representation [J. Kato, T. Naito, J.S. Shin, A characterization of solutions in linear differential equations with periodic forcing functions, J. Difference Equ. Appl. 11 (2005) 1-19] of solutions to the above equation. 相似文献
10.
A Liouville-Green (or WKB) asymptotic approximation theory is developed for the class of linear second-order matrix differential equations Y″=[f(t)A+G(t)]Y on [a,+∞), where A and G(t) are matrices and f(t) is scalar. This includes the case of an “asymptotically constant” (not necessarily diagonalizable) coefficient A (when f(t)≡1). An explicit representation for a basis of the right-module of solutions is given, and precise computable bounds for the error terms are provided. The double asymptotic nature with respect to both t and some parameter entering the matrix coefficient is also shown. Several examples, some concerning semi-discretized wave and convection-diffusion equations, are given. 相似文献
11.
12.
J. Bourgain 《Israel Journal of Mathematics》1992,77(1-2):1-16
We study the almost everythere convergence to the initial dataf(x)=u(x, 0) of the solutionu(x, t) of the two-dimensional linear Schrödinger equation Δu=i? t u. The main result is thatu(x, t) →f(x) almost everywhere fort → 0 iff ∈H p (R2), wherep may be chosen <1/2. To get this result (improving on Vega’s work, see [6]), we devise a strategy to capture certain cancellations, which we believe has other applications in related problems. 相似文献
13.
《Applied Mathematics Letters》2000,13(1):115-120
Existence results are presented for the singular Volterra integral equation y(t) = h(t) + ∫0t k(t, s) f(s, y(s)) ds, for t ∈ [0,T]. Here f may be singular at y = 0. As a consequence new results are presented for the nth order singular initial value problem. 相似文献
14.
《Mathematical and Computer Modelling》1997,25(3):69-79
Some necessary conditions are established for the nonoscillation of solutions of the second-order neutral delay differential equation [a(t)(x (t) + p(t)x(t − τ)′]′ + q(t)f(x(t − σ)) = 0. Using these results, we obtain some oscillation criteria for the above equation. 相似文献
15.
He-Xi Ye 《Discrete Mathematics》2009,309(4):1001-3257
Let f(t,k) be the maximum diameter of graphs obtained by deleting t edges from a (t+1)-edge-connected graph with diameter k. This paper shows for t≥4, which corrects an improper result in [C. Peyrat, Diameter vulnerability of graphs, Discrete Appl. Math. 9 (3) (1984) 245-250] and also determines f(2,k)=3k−1 and f(3,k)=4k−2 for k≥3. 相似文献
16.
Let fs,t(m,n) be the number of (0,1) - matrices of size m x n such that each row has exactly s ones and each column has exactly t ones (sm = nt). How to determine fs,t(m,n)? As R. P. Stanley has observed (Enumerative CombinatoricsⅠ(1997), Example 1.1.3), the determination of fs,t(m, n) is an unsolved problem, except for very small s, t. In this paper the closed formulas for f2,2(n,n), f3,2(m,n), f4,2(m,n) are given. And recursion formulas and generating functions are discussed. 相似文献
17.
We present the geometric construction of some classical iterative methods that have global convergence and “infinite” speed of convergence when they are applied to solve certain nonlinear equations f(t)=0. In particular, for nonlinear equations with the degree of logarithmic convexity of f′, Lf′(t)=f′(t)f?(t)/f″(t)2, is constant, a family of Newton-type iterative methods of high orders of convergence is constructed. We see that this family of iterations includes the classical iterative methods. The convergence of the family is studied in the real line and the complex plane, and domains of semilocal and global convergence are located. 相似文献
18.
《Mathematical and Computer Modelling》2004,39(4-5):457-471
Several oscillation criteria are given for the second-order damped nonlinear differential equation (a(t)[y′(t)]σ′i +p(t)[y′(t)]σ +q(t)f(y(t)) = 0, where σ > 0 is any quotient of odd integers, a ϵ C(R, (0, ∞)), p(t) and q(t) are allowed to change sign on [to, ∞), and f ϵ Cl (R, R) such that xf (x) > 0 for x≠0. Our results improve and extend some known oscillation criteria. Examples are inserted to illustrate our results. 相似文献
19.
Zhi-Qiang Zhu 《Journal of Mathematical Analysis and Applications》2007,335(2):751-762
In this paper, we give an analogue of the Arzela-Ascoli theorem on time scales. Then, we establish the existence of nonoscillatory solutions to the neutral dynamic equation Δ[x(t)+p(t)x(g(t))]+f(t,x(h(t)))=0 on a time scale. To dwell upon the importance of our results, three interesting examples are also included. 相似文献