In this paper a new approach is developed for analyzing the discontinuous Galerkin method for hyperbolic equations. For a model problem in R2, the method is shown to converge at a rate 0(hn+l) when applied with nth degree polynomial approximations over a semiuniform triangulation, assuming sufficient regularity in the solution.

Let T(n) denote the number of arithmetic operations needed to evaluate the normalized derivatives P ^ ( t ) / i ! , i = 0,...,n, for an nth degree polynomial p(t) over the field of complex numbers. We show 1 2 T(n) ^ — c n log n + lower order terms where c may be taken as 12.

Commutativity has the same inherent limitations as compatibility. Then, it is worth conceiving simple concurrency control techniques. We propose a restricted form of commutativity which increases parallelism without incurring a higher overhead than compatibility. Advantages of our proposition are: (1) commutativity of operations is determined at compile-time, (2) runtime checking is as efficien...

In this paper, we consider the finitely presented groups Gm and K(s, l) as follows; Gm = 〈a, b|a = b = 1, [a, b] = [a, b], [a, b] = [a, b]〉 K(s, l) = 〈a, b|ab = ba, ba = ab〉; and find the n-commutativity degree for each of them. Also we study the concept of n-abelianity on these groups, where m,n, s and l are positive integers, m,n ≥ 2 and g.c.d(s, l) = 1.

This work reviews from a unified viewpoint the concepts underlying “nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems” (nth-CASAM-L) and Nonlinear (nth-CASAM-N) methodologies. The practical application of nth-CASAM-L methodology is illustrated an OECD/NEA reactor physics benchmark, while nth-CASAM-N nonlinear model dynamics that...

In this paper, we study the nth-bias optimality problem for finite continuous-time Markov decision processes (MDPs) with a multichain structure. We first provide nth-bias difference formulas for two policies and present some interesting characterizations of an nth-bias optimal policy by using these difference formulas. Then, we prove the existence of an nth-bias optimal policy by using nth-bias...

It is shown that coherence conditions for monoidal categories concerning associativity are analogous to coherence conditions for symmetric strictly monoidal categories, where associativity arrows are identities. Mac Lane’s pentagonal coherence condition for associativity is decomposed into conditions concerning commutativity, among which we have a condition analogous to naturality and a degener...

It is shown that coherence conditions for monoidal categories concerning associativity are analogous to coherence conditions for symmetric strictly monoidal categories, where associativity arrows are identities. Mac Lane’s pentagonal coherence condition for associativity is decomposed into conditions concerning commutativity, among which we have a condition analogous to naturality and a degener...

It is shown that all the assumptions for symmetric monoidal categories flow out of a unifying principle involving natural isomorphisms of the type (A ∧B) ∧ (C ∧D) → (A ∧ C) ∧ (B ∧D), called medial commutativity. Medial commutativity in the presence of the unit object enables us to define associativity and commutativity natural isomorphisms. In particular, Mac Lane’s pentagonal and hexagonal coh...