广义Fibonacci数的一些恒等式

利用非数学归纳法,以及广义Fibonacci数的性质,得到了广义Fibonacci数的一些求和公式.     

n-Colour self-inverse compositions

MacMahon’s definition of self-inverse composition is extended ton-colour self-inverse composition. This introduces four new sequences which satisfy the same recurrence relation with different initial conditions like the famous Fibonacci and Lucas sequences. For these new sequences explicit formulas, recurrence relations, generating functions and a summation formula are obtained. Two new binomial identities with combinatorial meaning are also given.     

The plane wave expansion, infinite integrals and identities involving spherical Bessel functions

This paper shows that the plane wave expansion can be a useful tool in obtaining analytical solutions to infinite integrals over spherical Bessel functions and the derivation of identities for these functions. The integrals are often used in nuclear scattering calculations, where an analytical result can provide an insight into the reaction mechanism. A technique is developed whereby an integral over several special functions which cannot be found in any standard integral table can be broken down into integrals that have existing analytical solutions.     

Minkowski identities for hypersurfaces in constant sectional curvature manifolds

We give a new proof of the generalized Minkowski identities relating the higher degree mean curvatures of orientable closed hypersurfaces immersed in a given constant sectional curvature manifold. Our methods rely on a fundamental differential system of Riemannian geometry introduced by the author. We develop the notion of position vector field, which lies at the core of the Minkowski identities.     

Several Expressions of Dirichlet L-function at Positive Integers

In this paper, by making use of Abel's theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet L-function at positive integers by means of some finite sums of different types. Some special cases as well as immediate consequences of the results presented here are also considered.     

On the Applications of the Linear Recurrence Relationships to Pseudoprimes

We present here some results on the applications of linear recursive sequences of order $2$ to the Fermat pseudoprimes, Fibonacci pseudoprimes, and Dickson pseudoprimes.     

Novice facilitators’ changes in practices: From launching to managing discussions about mathematics teaching

Novice facilitators of professional development (PD) programs for mathematics teachers often face challenges in leading productive discussions and achieving the goals of these programs. Although research in this area is gradually accumulating, not much is known about how novice facilitators address these challenges and change their practices accordingly. This paper presents case studies of two novice facilitators of PD programs in two different countries. The analyses look at their work over one year, to illustrate the changes in their practices while managing discussions. The results show that although the facilitators operated in different contexts, their practices and their processes of change resembled, suggesting that these processes are not idiosyncratic. We argue that novice facilitators’ changes in practices correspond to changes in their resources, orientations, goals, and identities and that PD program teams can support these changes.