existence results for impulsive multivalued semilinear neutral functional differential inclusions in banach spaces in this paper the existence of mild solutions for first and second order impulsive semilinear neutral functional differential inclusions in banach spaces is investigated the results are obtained by using a fixed point theorem for condensing multivalued maps due to martelli and semigroup theory

computing point enclosures given a set of n rectangles in the plane the point enclosure query is the question to determine for any point p which rectangles of the set it is contained in it is the dual of the well known range query in computational geometry it is shown that the point enclosure query in the plane can be answered in 0 log n k time where k is the number of rectangles reported the solution makes use of a new data structure called the s tree the data structure can be generalized to obtain an efficient algorithm for the point enclosure problem in d dimensional space d 2

a global regularity result for some degenerate elliptic systems abstract we establish a caccioppoli type inequality for a second order degenerate elliptic systems of p laplacian type as a direct consequence exploiting classical campanato s approach and the hole filling technique due to widman we are able to prove a global regularity result on morrey s and l q spaces with q p

optimal computation of finitely oriented convex hulls abstract we define four versions of the convex hull of a simple finitely oriented polygon i e a polygon whose edge orientations all belong to some fixed finite set of angles and give optimal algorithms to find them two of these generalize the notions of the orthogonal convex hull of an orthogonal polygon and the traditional bounding box of a polygon three of the hulls have worst case time complexity n f and worst case space complexity n space where n is the number of edges of a given polygon and f 2 is the number of allowed orientations we also show that testing whether an arbitrary simple polygon is finitely oriented convex has worst case time and space complexity n f and n respectively

integral inequalities and mild solutions of semilinear neutral evolution equations abstract existence of mild solutions to semilinear neutral evolution equations with nonlocal conditions is proved the result is obtained by using fractional power of operators krasnoselski schaefer type fixed point theorem and by applying a modification of the bihari type inequality to the case of singular integral inequality an application to partial differential equations is given

global existence for semilinear evolution equations with nonlocal conditions abstract in this paper we study the global existence of solutions for semilinear evolution equations with nonlocal conditions via a fixed point analysis approach using the leray schauder alternative we derive conditions under which a solution exists globally

priority search trees let d be a dynamic set of ordered pairs x y over the set 0 1 cdots k 1 of integers consider the following operations applied to d 1 insert delete a pair x y into from d 2 given test integers x0 x1 and y1 among all pairs x y in d such that x0 leqq x leqq x1 and y leqq y1 find a pair whose x is minimal or maximal 3 given test integers x0 and x1 among all pairs x y in d such that x0 leqq x leqq x1 find a pair whose y is minimal 4 given test integers x0 x1 and y1 enumerate those pairs x y in d such that x0 leqq x leqq x1 and y leqq y1 using a new data structure that we call a priority search tree of which two variants are introduced operations 1 2 and 3 can be implemented in o log n time where n is the cardinality of d operation 4 is performed in at most o log n s time where s is the number of pairs enumerated the priority search tree occupies o n space priority seach tree algorithms can

regularity of solutions to degenerate p laplacian equations abstract we prove regularity results for solutions of the equation div a x u x u p 2 2 a x u 0 1 p where x x 1 x m is a family of vector fields satisfying hormander s condition and a is an m m symmetric matrix that satisfies degenerate ellipticity conditions if the degeneracy is of the form w x 2 p 2 a x w x 2 p 2 w a p then we show that solutions are locally holder continuous if the degeneracy is of the form k x 2 p 2 a x k x 2 p 2 k a p r h where depends on the homogeneous dimension then the solutions are continuous almost everywhere and we give examples to show that this is the best result possible we give an application to maps of finite distortion

sobolev morrey regularity of solutions to general quasilinear elliptic equations abstract we deal with the dirichlet problem for general quasilinear elliptic equations over reifenberg flat domains the principal part of the operator supports natural gradient growth and its x discontinuity is of small bmo type while the lower order terms satisfy controlled growth conditions with x behaviour modelled by morrey spaces we obtain a calderon zygmund type result for the gradient of the weak solution by proving that the solution gains sobolev morrey regularity from the data of the problem

controllability of neutral functional integrodifferential systems in banach spaces abstract sufficient conditions for controllability of neutral functional integrodifferential systems in a banach space are established the results are obtained by using the schaefer fixed point theorem an example is provided to illustrate the theory

existence of solutions of nonlinear neutral integrodifferential equations in banach spaces abstract in this paper we prove the existence of mild solutions of a nonlinear neutral integrodifferential equation in a banach space the results are obtained by using the schaefer fixed point theorem as an application the controllability problem for the neutral system is discussed

counting and reporting intersections of d ranges we present a solution to the problem of reporting and counting all pairs of intersecting or overlapping d ranges in a given set of n d ranges a d range is a rectilinearly oriented rectangular d dimensional box or brick the three dimensional case is presented in some detail and an 0 n log2 2 n k time and 0 n log2 2 n space algorithm is developed for the reporting problem where k is the number of reported intersecting pairs this gives an 0 n log2 2 n time and 0 n log 2 n space algorithm for the counting problem apart from its usefulness wherever a bounding boxes technique is used the development of the algorithm is of interest in its own right because of the data structures that are introduced and because of the technique used to reduce the time needed for preprocessing finally the algorithm is generalized to give an 0 2 d 1 n log 2 d n k time and an 0 2d 1n log 2 d n space algorithm for the d range intersection reporting problem for d 2 which again reduces to an 0 2d 1n log 2 d 1n time and 0 2d 1n log 2 d 2n space algorithm for the counting problem finally we sketch how the reporting problem can be carried out with the same space requirements as the counting problem the bounds presented are the best known to date

controllability of nonlinear neutral evolution integrodifferential systems sufficient conditions for controllability of nonlinear neutral evolution integrodifferential systems in a banach space are established the results are obtained by using the resolvent operators and the schaefer fixed point theorem an application to partial integrodifferential equation is given

approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces various sufficient conditions for approximate controllability of linear evolution systems in abstract spaces have been obtained but approximate controllability of semilinear control systems usually requires some complicated and limited assumptions in this paper we show the approximate controllability of the abstract semilinear deterministic and stochastic control systems under the natural assumption that the associated linear control system is approximately controllable the results are obtained using new properties of symmetric operators which are proved in this paper compact semigroups the schauder fixed point theorem and or the contraction mapping principle

dynamic c oriented polygonal intersection searching a set of polygons is called c oriented if the edges of all polygons are oriented in a constant number of previously defined directions the intersection searching problem is studied for such objects namely given a set of c oriented polygons p and a c oriented query polygon q find all polygons in p that intersect q it is shown that this problem can be solved in o log 2 n t time with o n log n space and o n log 2 n preprocessing where n is the cardinality of p and t the number of answers to a query furthermore the solution is extended to the cases in which p is a semidynamic or dynamic set of polygons whereas planar intersection searching can be carried out more efficiently for orthogonal objects e g rectangles it is expensive for arbitrary polygons this suggests that the c oriented solution be used in appropriate areas of application for instance in vlsi design

fundamentals of restricted orientation convexity abstract a restricted orientation convex set also called an o convex set is a set of points whose intersection with lines from some fixed set is empty or connected the notion of o convexity generalizes standard convexity and orthogonal convexity we explore some of the basic properties of o convex sets in two and higher dimensions we also study o connected sets which are restricted o convex sets with several special properties we introduce and investigate restricted orientation analogs of lines flats and hyperplanes and characterize o convex and o connected sets in terms of their intersections with hyperplanes we then explore properties of o connected curves in particular we show when replacing a segment of an o connected curve with a new curvilinear segment yields an o connected curve and when the catenation of several curvilinear segments forms an o connected segment we use these results to characterize an o connected set in terms of o connected segments joining pairs of its points that are wholly contained in the set we also identify some of the major properties of standard convex sets that hold for o convexity in particular we establish the following results the intersection of a collection of o convex sets is an o convex set every o connected curvilinear segment is a segment of some o connected curve for every two points of an o convex set there is an o convex segment joining them that is wholly contained in the set

gradient estimates via linear and nonlinear potentials we prove new potential and nonlinear potential pointwise gradient estimates for solutions to measure data problems involving possibly degenerate quasilinear operators whose prototype is given by pu in particular no matter the nonlinearity of the equations considered we show that in the case p 2 a pointwise gradient estimate is possible using standard linear riesz potentials the proof is based on the identification of a natural quantity that on one hand respects the natural scaling of the problem and on the other allows to encode the weaker coercivity properties of the operators considered in the case p 2 in the case p 2 we prove a new gradient estimate employing nonlinear potentials of wolff type

existence results for partial neutral functional differential equations with unbounded delay abstract we prove the existence of mild solutions for a partial neutral functional integrodifferential equation with unbounded delay using the leray schauder alternative

nonlocal cauchy problems for neutral functional differential and integrodifferential inclusions in banach spaces in this paper we investigate the existence of mild solutions on a compact interval to initial value problems for neutral functional differential and integrodifferential inclusions in banach spaces with nonlocal conditions the results are obtained by using a fixed point theorem for condensing maps due to martelli