1 if n = 1 0 if n is not square-free (−1) t if n is a product of t distinct primes. Its behavior is central in the theory of prime numbers. For example, the " orthogonality " of µ and the function 1, meaning that (2)

Large and complex models can often benefit from parallel execution on multiple machines. In the Möbius modeling environment, this is especially true of models for which the user wants to examine several independent configurations or parameterizations. A Remote Job Server with the capability to securely forward jobs to remote workstations or securely submit jobs via a standard batch submission s...

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Abstract. A divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2,... | |} V such that an edge uv is assigned the label 1 if ( ) | ( ) f u f v or ( ) | ( ) f v f u and the label 0 otherwise, then number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a divisor cordial labeling is called a divisor cordial graph. ...

See examples in Fig. 1(b). Many graph algorithms use an st-orientation. For instance, graph drawing algorithms [3], [4], [17], [19], [22], routing algorithms [1], [13] and partitioning algorithms [14]. Given a biconnected graph G and its two vertices s and t, one can find an st-orientation of G in O(m + n) time [5], [6], [22]. Note that if G is not biconnected then G may have no st-orientation....

A path graph is the intersection graph of subpaths of a tree. In 1970, Renz asked for a characterization of path graphs by forbidden induced subgraphs. We answer this question by determining the complete list of graphs that are not path graphs and are minimal with this property. 2009 Wiley Periodicals, Inc. J Graph Theory 62: 369–384, 2009

We prove that for any class of finite or countable graphs closed under taking subgraphs, and such that every finite graph in the class has a number of edges linearly bounded in terms of the number of vertices, the edge set quantifications can be replaced by vertex set quantifications in Monadic secondorder formulas. This result extends to hypergraphs of bounded rank.

A graph that contains a Hamiltonian cycle is called a Hamiltonian graph. In this paper we compute the first and the second geometric – arithmetic indices of Hamiltonian graphs. Then we apply our results to obtain some bounds for fullerene.

Moebius syndrome consists of congenital complete or partial facial nerve palsy with or without paralysis of other cranial nerves (most commonly an abducens paralysis) and often associated with other malformations of the limbs and orofacial structures. The first description of congenital facial diplegia was given by von Graaefe in 18801 and this was soon followed by other reports. Moebius2 3 dre...

This article presents a new method to sample on manifolds, based the Dirichlet distribution. The proposed strategy allows completely respect underlying manifold around which data are observed, and do massive sampling with low computational effort. can be very helpful, for instance, in neural networks training process, as well uncertainty analysis stochastic optimization. Due its simplicity effi...