remarks on the periodic boundary value problems for first order differential equations this paper is concerned with the existence of solutions and the monotone method of first order periodic boundary value problems when the lower and upper solutions and violate the boundary conditions 0 2 and 0 2 using the topological degree theory two existence theorems are established under weaker conditions than the one side lipschitz conditions an example is given which illustrates that pbvp may not have solutions between and without further restrictions to f t u the monotone method is also discussed with some new results

on the synchronizability and detectability of random ppm sequences the problem of synchronization and detection of random pulse position modulation ppm sequences is investigated under the assumption of perfect slot synchronization maximum likelihood ppm symbol synchronization and receiver algorithms are derived that make decisions based on both soft and hard data these algorithms are seen to be easily implementable the author derives bounds on the symbol error probability and the probability of false synchronization that indicate the existence of a severe performance floor which can be the limiting factor in the overall system performance the performance floor is inherent in the ppm format and random data and becomes more serious as the ppm alphabet size q is increased a way to eliminate the performance floor is suggested by inserting special ppm symbols in the random data stream

locally connected models for julia sets let p be a polynomial with a connected julia set j we use continuum theory to show that it admits a finest monotone map onto a locally connected continuum j p i e a monotone map j j p such that for any other monotone map j j there exists a monotone map h with h then we extend onto the complex plane c keeping the same notation and show that monotonically semiconjugates p c to a topological polynomial g c c if p does not have siegel or cremer periodic points this gives an alternative proof of kiwi s fundamental results on locally connected models of dynamics on the julia sets but the results hold for all polynomials with connected julia sets we also give a characterization and a useful sufficient condition for the map not to collapse all of j into a point

periodic boundary value problems for a class of functional differential equations in this paper we show that the method of upper and lower solutions coupled with the monotone iterative technique is valid to obtain constructive proofs of existence of solutions for nonlinear periodic boundary value problems of functional differential equations without assuming properties of monotonicity in the nonlinear part

monotone method for second order delayed differential equations with boundary value conditions in this paper we investigate the existence of extremal solutions of boundary value problems for second order differential equations with delayed arguments we show that a lower and upper solution method has been applied successfully to such problems an one sided lipschitz condition with corresponding constants is important assumption in our research

multiple positive solutions of periodic boundary value problems for second order impulsive differential equations abstract this paper is devoted to study the existence of multiple positive solutions for the second order periodic boundary value problem with impulse effects the main results here are the generalization of jiang daqing jiang on the existence of positive solutions to second order periodic bvps acta math sci 18 1998 31 35 for ordinary differential equations existence is established via the theory of fixed point index in cones

first order functional difference equations with nonlinear boundary value problems the monotone iterative method is used to show that corresponding difference problems with boundary conditions have extremal solutions in the region bounded by lower and upper solutions it is important to indicate that the right hand sides of problems depend on r delayed arguments difference inequalities of such types are also discussed two examples satisfying the assumptions are presented

on boundary value problems for singular second order functional differential equations abstract positive solutions to the boundary value problem y f x y w x 0 y x y x x a x 0 y x y x x 1 x b are obtained by applying the schauder fixed point theorem where w x is a continuous function defined on 0 1 and f x y is a function defined on 0 1 0 which satisfies certain restrictions and may have singularity at y 0 the result corrects and improves an existence theorem due to erbe and kong j comput appl math 53 1994 377 388

practical codes for photon communication in a recent paper pierce studied the problems of communicating at optical frequencies using photon counting techniques and concluded that at low temperatures we encounter insuperable problems of encoding long before we approach channel capacity in this paper it is shown that even assuming a noiseless model for photon communication for which capacity measured in nats photon is infinite it is unlikely that a signaling efficiency of even 10 nats photon could be achieved practically on the positive side it is shown that pulse position modulation plus reed solomon coding yields practical results in the range of 2 to 3 nats photon

second order functional differential equations with past present and future dependence abstract in this paper we obtain a result on existence of extremal quasisolutions and solutions for second order functional differential equations with functional boundary conditions and past present and future dependence in order to do that we develop a generalized monotone method in presence of lower and upper solutions some examples of application are provided too

monotone method for first order functional differential equations we study periodic boundary value problems relative to a general class of first order functional differential equations for this class of problems we develop the monotone iterative technique our formulation is very general including delay differential equations functional differential equations with maxima and integro differential equations but the case where the operator defining the functional dependence is not necessarily lipschitzian is also considered

solvability of three point boundary value problems for second order differential equations with deviating arguments the monotone iterative technique is used to boundary problems for second order ordinary differential equations with deviating arguments corresponding results are formulated when the problem has extremal solutions or weakly coupled extremal quasi solutions

quasi solutions for generalized second order differential equations with deviating arguments this paper deal with boundary value problems for generalized second order differential equations with deviating arguments existence of quasi solutions and solutions are proved by monotone iterative method examples with numerical results are added

periodic boundary value problem for the second order impulsive functional differential equations this paper considers the existence of extreme solutions of the periodic boundary value problem for second order functional differential equations by using the method of lower and upper solutions coupled with monotone iterative technique

existence and approximation of solutions for nonlinear functional differential equations with periodic boundary value conditions abstract this paper is concerned with the existence and approximation of solutions for a class of first order functional differential equations with periodic boundary conditions we present a new comparison result and extend previous results

multi point boundary value problems for second order functional differential equations this paper is concerned with the existence of extreme solutions of multi point boundary value problem for a class of second order functional differential equations we introduce a new concept of lower and upper solutions by using the method of upper and lower solutions and monotone iterative technique we obtain the existence of extreme solutions

remarks on periodic boundary value problems for functional differential equations we extend some results on existence and approximation of solution for a class of first order functional differential equations with periodic boundary conditions we show the validity of the monotone iterative technique under weaker hypotheses and present some examples

periodic boundary value problems for delay differential equations with impulses existence and approximation of solutions for an impulsive delay differential equation with periodic boundary value conditions are presented we use comparison principles and monotone iterative techniques

existence results to delay fractional differential equations with nonlinear boundary conditions this paper concerns boundary value problems for delay fractional differential equations we formulate sufficient conditions under which such problems have extremal solutions in the corresponding region delay differential inequalities are also discussed examples are given to illustrate the effectiveness of the results

real laminations and the topological dynamics of complex polynomials abstract we characterize the laminations associated to complex polynomials with connected julia sets and without irrationally neutral cycles

periodic boundary value problems for the second order functional differential equations this paper considers the existence of extreme solutions of the periodic boundary value problems for second order functional differential equations a new concept of lower and upper solutions is introduced and we present a new comparison principle meanwhile we extend previous results

existence theorems for a class of nonlocal differential equations abstract a class of nonlocal second order ordinary differential equations of the form y x f x y x y x y x for continuous f and is studied the equation is supplemented with none one or two robin boundary conditions depending on whether the interval of interest i is finite semi infinite or infinite the only other restriction on the function is that it maps i into itself sufficient conditions for the existence of a solution are found which include the assumption of the existence of upper and lower solutions the upper and lower solutions provide bounds for the solution on i

maximum likelihood symbol synchronization for the direct detection optical on off keying channel the maximum likelihood symbol synchronization statistic is derived from noisy observations of randomly modulated on off keying data for the direct detection optical channel a similar statistic for the case when the transmitter sends a special pattern of alternating o s and 1 s for synchronization purposes only is also derived various approximations to the optimal statistic are introduced and their performance compared to the optimal one under a new criterion believed to be more appropriate for the poisson channel than the mean square error criterion routinely used with other channels it is shown that although the variable associated with symbol transitions is continuous the possible values of it that maximize the maximum likelihood ml statistic belong to a discrete set with relatively few elements

wandering orbit portraits we study a counting problem in holomorphic dynamics related to external rays of complex polynomials we give upper bounds on the number of external rays that land at a point z in the julia set of a polynomial provided that z has an infinite forward orbit

boundary value problems for singular second order functional differential equations abstract we consider general linear boundary value problems for equations of the form y f x y x 0 0 x x is continuous and f x y has a singularity at y 0 the results improve and extend earlier results for the case x x due to taliaferro 1979 and gatica 1989

existence of solutions of boundary value problems for differential equations with delayed arguments we study the existence and approximation of solution of boundary value problems for differential equations with delayed arguments sufficient conditions are established for the existence of a unique solution or extremal ones of the given problem a monotone iterative technique is applied

nonlinear boundary value problems for second order differential equations with causal operators in this paper we deal with second order differential equations with causal operators to obtain sufficient conditions for existence of solutions we use a monotone iterative method we investigate both differential equations and differential inequalities an example illustrates the results obtained

on monotone method for first and second order periodic boundary value problems and periodic solutions of functional differential equations abstract in this paper we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions of first and second order periodic boundary value problems and periodic solutions of functional differential equations we obtain some new results relative to the lower solution and upper solution with

boundary value problems for first order impulsive delay differential equations with a parameter in this paper by means of the method of upper and lower solutions and monotone iterative technique the existence of maximal and minimal solutions of the boundary value problems for first order impulsive delay differential equations is established

monotone iterative method for first order functional difference equations with nonlinear boundary value conditions in this paper we show that the method of monotone iterative coupled with the upper and lower solutions is valid to obtain constructive proofs to the existence of solutions for first order functional difference equations with nonlinear boundary value conditions an example is given to illustrate the results obtained

periodic boundary value problems of second order impulsive differential equations abstract this paper discusses periodic boundary value problems of second order impulsive differential equations by using schaeffer s fixed point theorem and monotone iterative technique some existence results are obtained

boundary value problems for first order differential equations of mixed type abstract we apply the monotone iterative method to formulate existence results for integro differential equations with nonlinear boundary conditions some results for integro differential inequalities are also given examples illustrate obtained results

discontinuous functional differential equations with delayed or advanced arguments we provide new results on the existence of extremal solutions for discontinuous differential equations with a deviated argument which can be either delayed or advanced the boundary condition is allowed to be discontinuous and to depend functionally on the unknown solution

an extended fatou shishikura inequality and wandering branch continua for polynomials abstract let p be a polynomial of degree d with julia set j p let n be the number of non repelling cycles of p by the famous fatou shishikura inequality n d 1 the goal of the paper is to improve this bound the new count includes wandering collections of non pre critical branch continua i e collections of continua or points q i j p all of whose images are pairwise disjoint contain no critical points and contain the limit sets of eval q i 3 external rays also we relate individual cycles which are either non repelling or repelling with no periodic rays landing to individual critical points that are recurrent in a weak sense a weak version of the inequality reads n n irr i eval q i 2 d 1 where n irr counts repelling cycles with no periodic rays landing at points in the cycle q i form a wandering collection b c of non pre critical branch continua 1 if b c is non empty and 0 otherwise

existence of solutions of boundary value problems for differential equations in which deviated arguments depend on the unknown solution this paper concerns differential equations with boundary conditions given are sufficient conditions under which such problems with deviated arguments have a unique solution in a corresponding sector to obtain existence results we apply a monotone iterative method

laminations in the language of leaves thurston defined invariant laminations i e collections of chords of the unit circle s called leaves that are pairwise disjoint inside the open unit disk and satisfy a few dynamical properties to be directly associated to a polynomial a lamination has to be generated by an equivalence relation with specific properties on s then it is called a q lamination since not all laminations are q laminations then from the point of view of studying polynomials the most interesting are those of them which are limits of q laminations in this paper we introduce an alternative definition of an invariant lamination which involves only conditions on the leaves and avoids gap invariance the new class of laminations is slightly smaller than that defined by thurston and is closed we use this notion to elucidate the connection between invariant laminations and invariant equivalence relations on s

jointly optimal receivers for the optical pulse position modulation channel jointly optimal receivers that make decisions in the absence of symbol synchronization are derived and analyzed for a pulse position modulation optical direct detection channel both receivers that observe the complete sample path count record data and receivers that observe histogram data are studied and approximations to them are derived it is seen that jointly optimal receivers are superior to conventional receivers that have separately designed synchronization and decision subsystems however their performance advantage is significant only at very low signal levels perhaps more significant is that an approximation to the jointly optimal receivers that is much easier to implement than an optimal separately synchronized receiver achieves nearly the same performance as the latter simulation results indicate that the much less complicated receivers that observe histogram data perform as well as receivers that observe the complete sample path at a rather small number of bins per slot

advanced differential equations with nonlinear boundary conditions we investigate the existence of solutions for advanced differential equations with nonlinear boundary conditions sufficient conditions when the problem has extremal solutions or a unique solution are formulated linear advanced differential inequalities are also discussed

existence of positive solutions for boundary value problem of second order fde abstract we use a fixed point theorem in cones to investigate the existence of positive solutions for boundary value problem of a second order functional differential equation fde with the form y t r t y t 0 0 y t y t t r t 0 y t y t n t 1 t 1 a where y t y t for a we allow that r t has the singularity at the endpoints t 0 and t 1 of 0 1 our results include the situations that f is either superlinear or sublinear

monotone iterative technique for second order delayed periodic problem in banach spaces in this paper we deal with the existence of periodic solutions for second order functional differential equation with delay in e u t f t u t u t t r where e is an ordered banach space f r e e e is a continuous function which is periodic in t and 0 is a constant we first build a new maximum principle for the periodic solutions of the corresponding linear equation with delay with the aid of this maximum principle under the assumption that the nonlinear function is quasi monotonicity we study the existence of the minimal and maximal periodic solutions for abstract delayed equation by combining perturbation method and monotone iterative technique of the lower and upper solutions