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1.
The authors introduce and investigate various properties of a general class;,which unifies and extends several (known or new) subclasses of meromorphically multivalent functions. The properties and characteristics of this general class, which are presented here, include growth and distortion theorems; they also involve Hadamard products (or convolution) of functions belonging to the class Uk[p,α,β,A,B]. 相似文献
Uk[p,a,β,A,B]
p, k ε N {1, 2, 3,…,}; 0 α < p; β 0
−1 A < B 1; 0 < B 1)
2.
Y. Muroya 《Computers & Mathematics with Applications》2005,49(11-12):1913-1927
Consider the following separable nonlinear delay differential equation , where we assume that, there is a strictly monotone increasing function f(x) on (−∞, +∞) such that In this paper, to the above separable nonlinear delay differential equation, we establish conditions of global asymptotic stability for the zero solution. In particular, for a special wide class of f(x) which contains a case of f(x) = ex−1, we give more explicit conditions. Applying these, we offer conditions of global asymptotic stability for solutions of nonautonomous logistic equations with delays. 相似文献
3.
M. Jaberi Douraki Mehdi Dehghan Javad Mashreghi 《Computers & Mathematics with Applications》2008,56(1):186-198
We study the invariant interval, the character of semicycles, the global stability, and the boundedness of the difference equation where the initial conditions x−k,…,x−1,x0 are nonnegative, and p,q>0. 相似文献
4.
5.
We consider the equivalence relation in the space of time-invariant linear dynamical systems of the form under the full group action of state feedback/output injection transformations. As in the case of the reduction of a matrix to its Jordan canonical form, the reduction of a quadruple (A,B,C,D) defining a system as above to its canonical reduced form is an unstable operation. Following V.I. Arnold’s techniques, the starting point for the study of local perturbations is to obtain a miniversal deformation of a differentiable family of quadruples. In this paper, a “real” miniversal deformation and some applications are shown. 相似文献
6.
Jovan Stefanovski 《Systems & Control Letters》2002,46(3)
In this paper conditions for the nonlinear control systemto have a nonlinear feedback controlsuch that the nonlinear system takes a form of an affine systemare presented. All results require algebraic operations and differentiation of functions only. 相似文献
u=(x,v), vΩ′Rm′, m′m, 0Ω′
7.
In this paper, we are concerned with the delay difference equations of the form(*) (*)where pn ≥ 0 and k is a positive integer. We prove by using a new technique thatguarantees that all solutions of equation (*) oscillate, which improves many previous well-known results. In particular, our theorems also fit the case where Σn−1i=n−kpi ≤ kk+1/(k + 1)k+1. In addition, we present a nonoscillation sufficient condition for equation (*). 相似文献
yn+1 − yn + pnyn−k = 0, N = 0, 1, 2, …,
8.
Kamareddine and Nederpelt[9], resp. Kamareddine and Ríos [11] gave two calculi of explicit of substitutions highly influenced by de Bruijn's notation of the λ-calculus. These calculi added to the explosive pool of work on explicit substitution in the past 15 years. As far as we know, calculi of explicit substitutions: a) are unable to handle local substitutions, and b) have answered (positively or negatively) the question of the termination of the underlying calculus of substitutions. The exception to a) is the calculus of [9] where substitution is handled both locally and globally. However, the calculus of [9] does not satisfy properties like confluence and termination. The exception to b) is the λse-calculus of [11] for which termination of the se-calculus, the underlying calculus of substitutions, remains unsolved. This paper has two aims:
- (i) To provide a calculus à la de Bruijn which deals with local substitution and whose underlying calculus of substitutions is terminating and confluent.
- (ii) To pose the problem of the termination of the substitution calculus of [11] in the hope that it can generate interest as a termination problem which at least for curiosity, needs to be settled. The answer here can go either way. On the one hand, although the λσ-calculus [1] does not preserve termination, the σ-calculus itself terminates. On the other hand, could the non-preservation of termination in the λse-calculus imply the non-termination of the se-calculus?
References
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Z. Benaissa, D. Briaud, P. Lescanne and J. Rouyer-Degli, λυ, a calculus of explicit substitutions which preserves strong normalisation, Functional Programming 6 (5) (1996).
P.-L. Curien, Categorical Combinators, Sequential Algorithms and Functional Programming, Pitman (1986) Revised edition: Birkhäuser (1993).
Curien P-L, T. Hardin and A. Ríos, Strong normalisation of substitutions, Logic and Computation 6 (1996), pp. 799–817.
N.G. de Bruijn, Lambda-Calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser Theorem, Indag. Mat 34 (5) (1972), pp. 381–392. Abstract | Article | PDF (718 K)
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F. Kamareddine and R. Nederpelt, A useful λ-notation, Theoretical Computer Science 155 (1996), pp. 85–109. Abstract | PDF (1169 K)
| MathSciNet | View Record in Scopus | Cited By in Scopus (15)
F. Kamareddine and R.P. Nederpelt, On stepwise explicit substitution, International Journal of Foundations of Computer Science 4 (3) (1993), pp. 197–240. MathSciNet | Full Text via CrossRef
F. Kamareddine, and A. Ríos. A λ-calculus à la de Bruijn with explicit substitutions. Proceedings of PLILP'95. LNCS, 982:45–62, 1995.
F. Kamareddine and A. Ríos, Extending a λ-calculus with explicit substitution which preserves strong normalisation into a confluent calculus on open terms, Journal of Functional Programming 7 (4) (1997), pp. 420–495.
F. Kamareddine and A. Ríos, Bridging de Bruijn indices and variable names in explicit substitutions calculi, Logic Journal of the IGPL 6 (6) (1998), pp. 843–874. MathSciNet | Full Text via CrossRef
F. Kamareddine and A. Ríos, Relating the λσ- and λs-styles of explicit substitutions, Logic and Computation 10 (3) (2000), pp. 349–380. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus (11)
J.-W. Klop, Term rewriting systems, Handbook of Logic in Computer Science, II (1992).
S.L. Peyton-Jones, The Implementation of Functional Programming Languages, Prentice-Hall (1987).
A. Ríos. Contribution à l'étude des λ-calculs avec substitutions explicites. PhD thesis, Université de Paris 7, 1993.
H. Zantema, Termination of term rewriting: interpretation and type elimination, J. Symbolic Computation 17 (1) (1994), pp. 23–50. Abstract | PDF (885 K)
| MathSciNet | View Record in Scopus | Cited By in Scopus (48)
H. Zantema, Termination of term rewriting by semantic labelling, Fundamenta Informaticae 24 (1995), pp. 89–105. MathSciNet
相似文献
9.
We study the problem of semiglobally stabilizing uncertain nonlinear system
, with (A,B) in Brunowski form. We prove that if p1(z,u,t)u and p2(z,u,t)u are of order greater than 1 and 0, respectively, with “generalized” dilation δl(z,u)=(l1−nz1,…,l−1zn−1,zn,lu) and uniformly with respect to t, where zi is the ith component of z, then we can achieve semiglobal stabilization via arbitrarily bounded linear measurement feedback. 相似文献
Full-size image
10.
In this paper the quasilinear heat equation with the nonlinear boundary condition is studied. The blow-up rate and existence of a self-similar solution are obtained. It is proved that the rescaled function
v(y,t)=(T−t)1/(2p+α−2)u((T−t)(p−1)/(2p+α−2)y,t),