We present an external-memory algorithm to compute a well-separated pair decomposition (WSPD) of a given point set S in Rd in O(sort(N)) I/Os, where N is the number of points in S and sort(N) denotes the I/O-complexity of sorting N items. (Throughout this paper, we assume that the dimension d is fixed). As applications of the WSPD, we show how to compute a linear-size t-spanner for S within the...

In this paper N is a set with non empty elements. One can prove the following propositions: (1) For all sets x, y, z such that x 6= y and x 6= z holds {x, y, z}\{x} = {y, z}. (2) For every non empty non void AMI A over N and for every state s of A and for every object o of A holds s(o) ∈ ObjectKind(o). (3) Let A be a realistic IC-Ins-separated definite non empty non void AMI over N , s be a sta...

the augmented gravity model was employed to determine iran's trading model and agricultural export directions in the case of cross section analysis in 2005 for 64 countries which are considered as iran's main export market. besides, another explanatory variable named trade conformity index (tci) was added to the model. this index was employed to identify iran's trading model. als...

When does a sequence of spherical codes with “good” spherical cap discrepancy, and “good” separation also have “good” Riesz s-energy? For d > 2 and the Riesz s-energy for 0 < s < d, we consider asymptotically equidistributed sequences of S codes with an upper bound δ on discrepancy and a lower bound ∆ on separation. For such sequences, the difference between the normalized Riesz s-energy and th...

It is observed that strings in AdS5 × S and membranes in AdS7 × S exhibit long range phase interactions. Two well separated membranes dragged around one another in AdS acquire phases of 2π/N . The same phases are acquired by a well separated F and D string dragged around one another. The phases are shown to correspond to both the standard and a novel type of Aharonov-Bohm effect in the dual fie...

A summary of some recent studies in jet physics is given. Topics include leading particle production in light flavor events in e + e − annihilations, an analytical treatment of gluon and quark jets at the next-to-next-to-next-to-leading order (3NLO), and various studies performed at LEP and HERA involving separated gluon and quark jets. 1 Leading particle production in separated light quark eve...

Fix an algebraic space S, and let X and Y be separated Artin stacks of finite presentation over S with finite diagonals (over S). We define a stack HomS(X ,Y) classifying morphisms between X and Y. Assume that X is proper and flat over S, and fppf–locally on S there exists a finite finitely presented flat cover Z → X with Z an algebraic space. Then we show that HomS(X ,Y) is an Artin stack with...

Aimed at an audience of researchers and graduate students in computational geometry and algorithm design, this book uses the Geometric Spanner Network Problem to showcase a number of useful algorithmic techniques, data structure strategies, and geometric analysis techniques with many applications, practical and theoretical. The authors present rigorous descriptions of the main algorithms and th...

We construct Belyi maps having specified behavior at finitely many points. Specifically, for any curve C defined over Q, and any disjoint finite subsets S, T ⊂ C(Q), we construct a finite morphism φ : C → P such that φ ramifies at each point in S, the branch locus of φ is {0, 1,∞}, and φ(T ) ∩ {0, 1,∞} = ∅. This refines a result of Mochizuki’s. We also prove an analogous result over fields of p...