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SecondOrder Functions and Theorems in ACL2
"... SOFT (‘SecondOrder Functions and Theorems’) is a tool to mimic secondorder functions and theorems in the firstorder logic of ACL2. Secondorder functions are mimicked by firstorder functions that reference explicitly designated uninterpreted functions that mimic function variables. Firstorder ..."
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SOFT (‘SecondOrder Functions and Theorems’) is a tool to mimic secondorder functions and theorems in the firstorder logic of ACL2. Secondorder functions are mimicked by firstorder functions that reference explicitly designated uninterpreted functions that mimic function variables. Firstorder
Verification of SecondOrder Functional Programs
"... Functional programming languages such as Haskell or ML allow the programmer to implement and to use higherorder procedures. A higherorder procedure gets a function as argument and applies this function to some values. For instance, procedure map applies a function to all elements of a list and ret ..."
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. In this thesis we show how the verification of secondorder functional programs can be supported by semiautomated theorem provers. Secondorder
On the Role of Deception in Second Order Functions
"... In this paper we study the behavior of genetic algorithms (GAs) on second order functions, more specially on random binary constraint satisfaction problems for which well studied instance generators can be found. We observe that deception does not play an important role in the search for a solution. ..."
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In this paper we study the behavior of genetic algorithms (GAs) on second order functions, more specially on random binary constraint satisfaction problems for which well studied instance generators can be found. We observe that deception does not play an important role in the search for a solution
A Remark On Second Order Functional Differential Systems
, 1992
"... It is proved that under some conditions the set of solutions to initial value problem for second order functional differential system on an unbounded interval is a compact R ffi set and hence nonvoid, compact and connected set in a Fr'echet space. The proof is based on a Kub'acek's ..."
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It is proved that under some conditions the set of solutions to initial value problem for second order functional differential system on an unbounded interval is a compact R ffi set and hence nonvoid, compact and connected set in a Fr'echet space. The proof is based on a Kub
SGA Search Dynamics on Second Order Functions
 Artificial Evolution 97
, 1998
"... . By comparing its search dynamics to that of a simple O(n 2 ) heuristic, we are able to analyze the behavior of the simple genetic algorithm on second order functions, whose optimization is shown to be an NPequivalent problem. It appears that both algorithms approach these fitness functions in t ..."
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Cited by 2 (2 self)
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. By comparing its search dynamics to that of a simple O(n 2 ) heuristic, we are able to analyze the behavior of the simple genetic algorithm on second order functions, whose optimization is shown to be an NPequivalent problem. It appears that both algorithms approach these fitness functions
Boundary value problems for systems of secondorder functional differential equations
 Proceedings of the 6th Colloquium on the Qualitative Theory of Differential Equations (Szeged
, 1999
"... Abstract. Systems of secondorder functional differential equations (x ′ (t)+L(x)(t)) ′ = F (x)(t) together with nonlinear functional boundary conditions are considered. Here L: ..."
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Abstract. Systems of secondorder functional differential equations (x ′ (t)+L(x)(t)) ′ = F (x)(t) together with nonlinear functional boundary conditions are considered. Here L:
TWO POSITIVE SOLUTIONS FOR SECONDORDER FUNCTIONAL AND ORDINARY BOUNDARYVALUE PROBLEMS
, 2005
"... In this paper we use a fixed point theorem due to Avery and Henderson to prove, under appropriate conditions, the existence of at least two positive solutions for a secondorder functional and ordinary boundaryvalue problem. ..."
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In this paper we use a fixed point theorem due to Avery and Henderson to prove, under appropriate conditions, the existence of at least two positive solutions for a secondorder functional and ordinary boundaryvalue problem.
ON MONOTONE SOLUTIONS FOR A NONCONVEX SECONDORDER FUNCTIONAL DIFFERENTIAL INCLUSION
"... The existence of monotone solutions for a secondorder functional differential inclusion is obtained in the case when the multifunction that define the inclusion is upper semicontinuous compact valued and contained in the Fréchet subdifferential of a φconvex function of order two. 1 ..."
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The existence of monotone solutions for a secondorder functional differential inclusion is obtained in the case when the multifunction that define the inclusion is upper semicontinuous compact valued and contained in the Fréchet subdifferential of a φconvex function of order two. 1
ANALYTIC SOLUTION OF CERTAIN SECONDORDER FUNCTIONAL DIFFERENTIAL EQUATION
, 2006
"... We consider the existence of analytic solutions of a certain class of iterative secondorder functional differential equation of the form x (x[r](z)) = c0z2 + c1(x(z))2 + (c2x[2](z))2 + ·· · + cm(x[m](z))2,m,r ≥ 0. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved. 1. ..."
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We consider the existence of analytic solutions of a certain class of iterative secondorder functional differential equation of the form x (x[r](z)) = c0z2 + c1(x(z))2 + (c2x[2](z))2 + ·· · + cm(x[m](z))2,m,r ≥ 0. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved. 1.
Oscillation of second order functional dynamic equations
 Int. J. Differential Equ. (Submitted
"... Abstract In this paper we investigate the oscillation of a second order nonlinear functional dynamic equation. Our results extend and improve many known results for oscillation of second order dynamic equations. Some examples are given to illustrate the main results. ..."
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Abstract In this paper we investigate the oscillation of a second order nonlinear functional dynamic equation. Our results extend and improve many known results for oscillation of second order dynamic equations. Some examples are given to illustrate the main results.
Results 1  10
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