Let D be a set of n pairwise disjoint unit disks in the plane. 8 We describe how to build a data structure for D so that for any point 9 set P containing exactly one point from each disk, we can quickly find 10 the onion decomposition (convex layers) of P . 11 Our data structure can be built in O(n logn) time and has linear size. 12 Given P , we can find its onion decomposition in O(n log k) ti...

Many abstractions of program dependences have already been proposed such as the Dependence Distance the Dependence Di rection Vector the Dependence Level or the Dependence Cone These di erent abstractions have di erent precision The min imal abstraction associated to a transformation is the abstrac tion that contains the minimal amount of information necessary to decide when such a transformati...

Classical (real) hedgehogs can be regarded as the geometrical realiza-tions of formal di¤erences convex bodies in R n+1. Like bodies, identi…ed with their support functions. Adopting a pro-jective viewpoint, we prove that any holomorphic function h : C n ! 'support function' complex hedgehog H In same vein, introduce notion evolute such 2 , and natural (but apparently hitherto unknown) curvatur...

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

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Despite their impor tance in assess ing the impact of pol i cies, out come eval u a tions—and in par tic u lar ran dom ized exper i ments—are rel a tively rare. The ratio nal iza tions used to jus tify the absence of out come eval u a tions include such asser tions as “we know our pro grams are work ing,” “they can’t pos si bly harm any one,” and “if they only help one kid they’re worth it.” Us...

the aim of this paper is to prove some inequalities for p-valent meromorphic functions in thepunctured unit disk δ* and find important corollaries.

Abstract Funding Acknowledgements Type of funding sources: None. Background Dynamic substrate changes play a key role in facilitating conduction delay and re-entry ventricular tachycardia (VT) circuits. Extrastimuli pacing can unmask functional channels demonstrated by dynamic delay, which may the VT circuit. We have previously developed sense protocol mapping, using short coupled single extras...