stability for quadratic functional equation in the spaces of generalized functions in this paper we consider the general solution of quadratic functional equation f ax y f ax y f x y f x y 2 a2 1 f x for any integer a with a 1 0 1 moreover we reformulate and prove the hyers ulam rassias stability theorem of the above equation in the spaces of tempered distributions and fourier hyperfunctions the generalized hyers ulam stability originated from the th m rassias s stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

generalization of ulam stability problem for euler lagrange quadratic mappings in 1968 s m ulam proposed the problem when is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true in 1978 p m gruber proposed the ulam type problem suppose a mathematical object satisfies a certain property approximately is it then possible to approximate this object by objects satisfying the property exactly in this paper we solve the generalized ulam stability problem for non linear euler lagrange quadratic mappings satisfying approximately a mean equation and an euler lagrange type functional equations in quasi banach spaces and p banach spaces

probabilistic analysis of output cost of a heuristic search algorithm abstract by proposing a new restricted type of network model we compute the probability distribution of output costs generated by the heuristic search algorithm a of bagchi and mohanti a of nilsson in terms of the heuristic distribution

on the ulam stability of mixed type mappings on restricted domains in 1941 d h hyers solved the well known ulam stability problem for linear mappings in 1951 d g bourgin was the second author to treat the ulam problem for additive mappings in 1982 1998 we established the hyers ulam stability for the ulam problem of linear and nonlinear mappings in 1983 f skof was the first author to solve the ulam problem for additive mappings on a restricted domain in 1998 s m jung investigated the hyers ulam stability of additive and quadratic mappings on restricted domains in this paper we improve the bounds and thus the results obtained by s m jung in 1998 besides we establish the ulam stability of mixed type mappings on restricted domains finally we apply our recent results to the asymptotic behavior of functional equations of different types

search algorithms under different kinds of heuristics a comparative study three heuristic search algorithms called algorithms a b and c are presented their performance with the admissibility condition relaxed is compared using the following two criteria i number of node expansions and ii cost of solution found first a general comparison is made in this process some variations and extensions of c are also considered subsequently two types of heuristic estimates called proper and path dependent are defined and the algorithms are reexamined it is shown that on the whole a nilsson s algorithm and b martelli s algorithm are inferior to c which is a slightly modified version of b 7 references

graph search methods for non order preserving evaluation functions applications to job sequencing problems abstract graph search with a is frequently faster than tree search but a graph search operates correctly only when the evaluation function is order preserving in the non orderpreserving case no paths can be discarded and the entire explicit graph must be stored in memory such situations arise in one machine minimum penalty job sequencing problems when setup times are sequence dependent grec the unlimited memory version of a memory constrained search algorithm of the authors called mrec has a clear advantage over a in that it is able to find optimal solutions to such problems at the same time it is as efficient as a in solving graph search problems with order preserving evaluation functions experimental results indicate that in the non order preserving case grec is faster than both best first and depth first tree search and can solve problem instances of larger size than best first tree search

on the stability of functional equations in banach spaces the paper is devoted to some results on the problem of s m ulam for the stability of functional equations in banach spaces the problem was posed by ulam 60 years ago

best first search methods for constrained two dimensional cutting stock problems best first search is a widely used problem solving technique in the field of artificial intelligence the method has useful applications in operations research as well here we describe an application to constrained two dimensional cutting stock problems of the following type a stock rectangle s of dimensions l w is supplied there are n types of demanded rectangles r1 r2 rn with the ith type having length li width wi value vi and demand constraint bi it is required to produce from the stock rectangle s ai copies of ri 1 i n to maximize a1v1 a2v2 anvn subject to the constraints ai bi only orthogonal guillotine cuts are permitted all parameters are integers a best first tree search algorithm based on wang s bottom up approach is described that guarantees optimal solutions and is more efficient than existing methods

a generalization of the hyers ulam rassias stability of approximately additive mappings abstract in this paper we prove a generalization of the stability of approximately additive mappings in the spirit of hyers ulam and rassias

chaotic dynamics of coherent structures abstract a variety of chaotic flows evolving in relatively high dimensional spaces are considered it is shown through the use of an optimal choice of basis functions which are consequence of the karhunen loeve procedure that an accurate description can be given in a relatively low dimensional space particular examples of this procedure which are presented are the ginzburg landau equation turbulent convection in an unbounded domain and turbulent convection in a bounded domain

refinements of generalized triangle inequalities abstract in this paper we discuss refinements of the well known triangle inequality and it is reverse inequality for strongly integrable functions with values in a banach space x we also discuss refinement of a generalized triangle inequality of the second kind for l p functions for both cases the attainability of the equality is also investigated

on the stability of euler lagrange type cubic mappings in quasi banach spaces abstract in this paper we solve the generalized hyers ulam rassias stability problem for euler lagrange type cubic functional equations f a x y f x a y a 1 a 1 2 f x f y a a 1 f x y for mappings f x y in quasi banach spaces and for fixed integers a with a 0 1 in addition we also present a counterexample that does not satisfy the stability based on ulam s question

solution of the ulam stability problem for euler lagrange quadratic mappings abstract in 1940 s m ulam proposed at the university of wisconsin theproblem give conditions in order for a linear mapping near an approximately linear mapping to exist in 1968 s u ulam proposed the moregeneral problem when is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true in 1978 p m gruber proposed theulam type problem suppose a mathematical object satisfies a certain property approximately is it then possible to approximate this object by objects satisfying the property exactly according to p m gruber this kind of stability problems is of particular interest in probability theory and in the case of functional equations of different types in 1982 1996 we solved the above ulam problem or equivalently the ulam type problem for linear mappings and established analogous stability problems in this paper we first introduce new quadratic weighted means and fundamental functional equations and then solve the ulam stability problem for non linear euler lagrange quadratic mappings q x y satisfying a mean equation and functional equation formula for all 2 dimensional vectors x1 x2 x2 withxa normed linear space y a real complete normed linear space and any fixed pair a1 a2 of realsaiand any fixed pair m1 m2 of positive realsmi i 1 2 formula

ulam stability problem for quadratic mappings of euler lagrange abstract the purpose of this paper is to solve the stability problem of ulam for an approximate mapping f a b of the following quadratic functional equation of euler lagrange a b aq x a b bq y q ax by abq x y for all x y a with a and b linear spaces

on approximation of approximately linear mappings by linear mappings abstract assume a is a normed linear space b is a banach space and f a b is a mapping approximately linear we solve the following ulam problem give conditions in order for a linear mapping near an approximately linear mapping to exist

characterization of a generalized triangle inequality in normed spaces abstract for a normed linear space x and p 0 we characterize all n tuples 1 n r n for which the generalized triangle inequality of the second type x 1 x n p x 1 p 1 x n p n holds for any x 1 x n x we also characterize 1 n r n for which the reverse of the inequality above holds

heuristic search through islands abstract a heuristic search strategy via islands is suggested to significantly decrease the number of nodes expanded algorithm i which searches through a set of island nodes island set is presented assuming that the island set contains at least one node on an optimal cost path this algorithm is shown to be admissible and expands no more nodes than a for cases where the island set does not contain an optimal cost path or any path algorithm i a modification of algorithm i is suggested this algorithm ensures a suboptimal cost path which may be optimal and in extreme cases falls back to a

inconsistent heuristics in theory and practice in the field of heuristic search it is usually assumed that admissible heuristics are consistent implying that consistency is a desirable attribute the term inconsistent heuristic has at times been portrayed negatively as something to be avoided part of this is historical early research discovered that inconsistency can lead to poor performance for a nodes might be re expanded many times however the issue has never been fully investigated and was not re considered after the invention of ida this paper shows that many of the preconceived notions about inconsistent heuristics are outdated the worst case exponential time of inconsistent heuristics is shown to only occur on contrived graphs with edge weights that are exponential in the size of the graph furthermore the paper shows that rather than being something to be avoided inconsistent heuristics often add a diversity of heuristic values into a search which can lead to a reduction in the number of node expansions inconsistent heuristics are easy to create contrary to the common perception in the ai literature to demonstrate this a number of methods for achieving effective inconsistent heuristics are presented pathmax is a way of propagating inconsistent heuristic values in the search from parent to children this technique is generalized into bidirectional pathmax bpmx which propagates values from a parent to a child node and vice versa bpmx can be integrated into ida and a when inconsistent heuristics are used with bpmx experimental results show a large reduction in the search effort required by ida positive results are also presented for a searches

robustness of acoustic analogies for predicting mixing layer noise acoustic analogies for the prediction of flow noise are exact rearrangements of the flow equations n q 0 into a nominal sound source s q and sound propagation operator c such that l q s q in practice the sound source is typically modeled and the propagation operator inverted to make predictions because the rearrangement is exact any sufficiently accurate model of the source will yield the correct sound and so other factors must determine the merits of any particular formulation using data from a two dimensional mixing layer direct numerical simulation we evaluate the robustness of several formulations to different errors intentionally introduced into the source the motivation is that because s cannot be perfectly modeled analogies that are less sensitive to errors in s are preferable our assessment is made within the framework of goldstein s generalized acoustic analogy a uniform base flow yields a lighthill like analogy which we evaluate against a formulation in which the base flow is the actual mean flow of the direct numerical simulation and also against a globally parallel base flow that gives a lilley like analogy the more complex mean flow formulations are found to be significantly more robust to errors in the energetic turbulent fluctuations but the advantage is less clear when errors are introduced at smaller scales

generalized best first search strategies and the optimality of a this paper reports several properties of heuristic best first search strategies whose scoring functions depend on all the information available from each candidate path not merely on the current cost g and the estimated completion cost h it is shown that several known properties of a retain their form with the minmax of f playing the role of the optimal cost which helps establish general tests of admissibility and general conditions for node expansion for these strategies on the basis of this framework the computational optimality of a in the sense of never expanding a node that can be skipped by some other algorithm having access to the same heuristic information that a uses is examined a hierarchy of four optimality types is defined and three classes of algorithms and four domains of problem instances are considered computational performances relative to these algorithms and domains are appraised for each class domain combination we then identify the strongest type of optimality that exists and the algorithm for achieving it the main results of this paper relate to the class of algorithms that like a return optimal solutions i e admissible when all cost estimates are optimistic i e h h on this class a is shown to be not optimal and it is also shown that no optimal algorithm exists but if the performance tests are confirmed to cases in which the estimates are also consistent then a is indeed optimal additionally a is also shown to be optimal over a subset of the latter class containing all best first algorithms that are guided by path dependent evaluation functions

solution of hyers ulam stability problem for generalized pappus equation abstract the purpose of this paper is to solve the stability problem of ulam for an approximate mapping f x y of the following generalized pappus equation n 2 q x m y m n q x n y m n n q x m q n y for all x y x with x and y linear spaces

and or graph heuristic search methods two new marking algorithms for and or graphs called cf and cs are presented for admissible heuristics cs is not needed and cf is shown to be preferable to the marking algorithms of martelli and montanari when the heuristic is not admissible the analysis is carried out with the help of the notion of the first and second discriminants of an and or graph it is proved that in this case cf can be followed by cs to get optimal solutions provided the sumcost criterion is used and the first discriminant equals the second estimates of time and storage requirements are given other cost measures such as maxcost are also considered and a number of interesting open problems are enumerated

on compressibility assumptions in aeroacoustic integrals a numerical study with subsonic mixing layers two assumptions commonly made in predictions based on lighthill s formalism are investigated a constant density in the quadrupole expression and the evaluation of the source quantity from incompressible simulations numerical predictions of the acoustic field are conducted in the case of a subsonic spatially evolving two dimensional mixing layer at re 400 published results of the direct noise computation dnc of the flow are used as reference and input for hybrid approaches before the assumptions on density are progressively introduced divergence free velocity fields are obtained from an incompressible simulation of the same flow case exhibiting the same hydrodynamic field as the dnc for the tested values of the mach number hybrid predictions reproduce correctly the reference acoustic field validating both assumptions in the source region however in the observer region the inclusion of flow effects in the lighthill source term is not preserved which is illustrated through a comparison with the kirchhoff wave extrapolation formalism and with the use of a convected green function in the integration process