Search results for "degree"

A code to evaluate prolate and oblate spheroidal harmonics

1998

Abstract We present a code to evaluate prolate ( P n m ( x ), Q n m ( x ); n ≥ m , x > 1) and oblate ( P n m ( ix ), Q n m ( ix ); n ≥ m , x > 0) spheroidal harmonics, that is, spherical harmonics ( n and m integers) for real arguments larger than one and for purely imaginary arguments. We start from the known values (in closed form) of P m m and P m +1 m and we apply the forward recurrence relation over n up to a given degree n = N Max . The Wronskian relating P 's and Q 's, together with the evaluation of the continued fraction for Q m+N staggeredMax m / Q m+N staggeredMax -1 m , allows the calculation of Q m+N staggeredMax m and Q m+N staggeredMax -1 m . Backward recurrence is then appli…

$n$-th relative nilpotency degree and relative $n$-isoclinism classes

2011

P. Hall introduced the notion of isoclinism between two groups more than 60 years ago. Successively, many authors have extended such a notion in different contexts. The present paper deals with the notion of relative n-isoclinism, given by N. S. Hekster in 1986, and with the notion of n-th relative nilpotency degree, recently introduced in literature.

Counting degree sequences of spanning trees in bipartite graphs: A graph‐theoretic proof

2019

Groups whose real irreducible characters have degrees coprime to p

2012

Abstract In this paper we study groups for which every real irreducible character has degree not divisible by some given odd prime p .

The exact bounds for the degree of commutativity of a p-group of maximal class, I

2002

Abstract The first major study of p-groups of maximal class was made by Blackburn in 1958. He showed that an important invariant of these groups is the ‘degree of commutativity.’ Recently (1995) Fernandez-Alcober proved a best possible inequality for the degree of commutativity in terms of the order of the group. Recent computations for primes up to 43 show that sharper results can be obtained when an additional invariant is considered. A series of conjectures about this for all primes have been recorded in [A. Vera-Lopez et al., preprint]. In this paper, we prove two of these conjectures.

Error Bounds for the Numerical Evaluation of Integrals with Weights

1988

This paper is concerned with a procedure of obtaining error bounds for numerically evaluated integrals with weights. If \( - \infty \mathop < \limits_ = a < b\mathop < \limits_ = \infty \), w integrable over [a,b] and positive almost everywhere, then an approximation of \({I_W}f: = \int\limits_a^b {w\left( t \right)f\left( t \right)dt} \) by a quadrature rule \({Q_n}f: = \sum\limits_{i = 0}^n {{\alpha _i}f\left( {{t_i}} \right)} \) is leading to the error Enf ≔ Iwf ‒ Qnf. An algorithm is derived for the computation of bounds for |Enf| depending on the smoothness of the integrand f and on the degree of exactness of Q. As initial values this algorithm needs moments of the weighting function w…

Low Degree of Separation Does Not Guarantee Easy Coordination

2012

In the times of increased global competition, software companies are forced to search for more effective development practices and often team up with onshore and offshore partners to develop faster and better products. In this paper we empirically explore a highly distributed onshore development project with a complex coordination structure. Our findings demonstrate that onshore development projects are not protected from coordination and communication challenges and task allocation complexities. Previously reported qualitative findings regarding organizational problems in this paper are supplemented with quantitative measurements of the true coordination delays and additional analysis of c…

Splineapproximationen von beliebigem Defekt zur numerischen L�sung gew�hnlicher Differentialgleichungen. Teil III

1980

In the first part [5] a general procedure is presented to obtain polynomial spline approximations of arbitrary defect for the solution of the initial value problem of ordinary differential equations. The essential result is a divergence theorem in dependence of the polynomial degree and the defect of the spline functions. In this second part the convergent procedures are investigated and two convergence theorems are proved. Furthermore the question is treated, whether the convergent procedures are appropriate for the numerical solution of stiff equations. The paper is finished by a convergence theorem for a procedure producing spline approximations in a natural way by the discrete approxima…

Network structure and optimal technological innovation

2019

The role of networks in the emergence, diffusion and evolution of technological innovations has attracted much theoretical and empirical attention. Yet, much of the work has explored the role of undirected and homogeneous networks. In real cases, many networks are directed. The flow of information, benefits or observations is directed from one node towards another node. Real networks are also heterogeneous, for example, few nodes have a high degree while many others have a low degree. In this article, we report on the results of an evolutionary agent-based model in which a group of agents, in our case firms, collectively search a complex (rugged) technological landscape and observe each oth…

How Low Can Approximate Degree and Quantum Query Complexity Be for Total Boolean Functions?

2012

It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of approximate degree and bounded-error quantum query complexity. We show that for these measures the correct lower bound is Omega(log n / loglog n), and we exhibit quantum algorithms for two functions where this bound is achieved.