For a class of skew-normal matrix distributions, the density function, moment generating function and independent conditions are obtained. The noncentral skew Wishart distribution is defined and the necessary and sufficient conditions under which a quadratic form is noncentral skew Wishart distributed random matrix are established. A new version of Cochran’s theorem is given. For illustration, ...

Skew heaps are an amazingly simple and lightweight implementation of priority queues. They were invented by Sleator and Tarjan [1] and have logarithmic amortized complexity. This entry provides executable and verified functional skew heaps. The amortized complexity of skew heaps is analyzed in the AFP entry Amortized Complexity.

We extend the Siegel-Weil formula to all quaternion dual pairs. Applications include the classification problem of skew hermitian forms over a quaternion algebra over a number field and a product formula for the weighted average of the representation numbers of a skew hermitian form by another skew hermitian form.

This paper presents a study of skew — highly variable task runtimes — in MapReduce applications. We describe various causes and manifestations of skew as observed in real world Hadoop applications. Runtime task distributions from these applications demonstrate the presence and negative impact of skew on performance behavior. We discuss best practices recommended for avoiding such behavior and t...

New sufficient conditions and necessary conditions are developed for two skew diagrams to give rise to the same skew Schur function. The sufficient conditions come from a variety of new operations related to ribbons (also known as border strips or rim hooks). The necessary conditions relate to the extent of overlap among the rows or among the columns of the skew diagram.

In this paper we generalize coding theory of cyclic codes over finite fields to skew polynomial rings over finite rings. Codes that are principal ideals in quotient rings of skew polynomial rings by two sided ideals are studied. Next we consider skew codes of endomorphism type and derivation type. And we give some examples. Mathematics Subject Classification: Primary 94B60; Secondary 94B15, 16D25

In this survey paper we define partial actions of groups on algebras and give several related results. For any partial action a partial skew group ring is defined. This partial skew group ring is not always associative. Conditions under which associativity holds are studied. Several other questions are considered like, for example, enveloping actions and properties of partial skew group rings.

Structured rational matrices such as symmetric, skew-symmetric, Hamiltonian, skew-Hamiltonian, Hermitian, and para-Hermitian arise in many applications. Linearizations of rational...

1. C. B. Boyer, History of Analytic Geometry, Scripta Mathematica, New York, 1956. 2. J. L. Coolidge, The origin of analytic geometry, Osiris 1 (1936) 231–250, also available at www.jstor. org. 3. M. Ghomi and B. Solomon, Skew loops and quadric surfaces, Comment. Math. Helv. 4 (2002) 767–782. 4. J.-P. Sha and B. Solomon, No skew branes on non-degenerate hyperquadrics, Math. Zeit. 257 (2002) 225...

In wireless sensor networks, time synchronization is a critical problem. In this paper, we propose SLTP, a Scalable Lightweight Time-synchronization Protocol for wireless sensor networks. By using passive clustering and linear regression SLTP can reduce the energy consumption of network nodes and also decrease the overhead of creating and maintaining the clusters. Moreover SLTP uses linear regr...