Note on the binomial partial difference equation

The new implicit finite difference scheme for two-sided space-time fractional partial differential equation

Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...

Note on the Convolution of Binomial Coefficients

We prove that, for every integer a, real numbers k and ℓ, and nonnegative integers n, i and j, i+j=n a i + k − ℓ i a j + ℓ j = i+j=n a i + k i a j j , by presenting explicit expressions for its value. We use the identity to generalize a recent result of Chang and Xu, and end the paper by presenting, in explicit form, the ordinary generating function of the sequence 2n+k n ∞ n=0 , where k ∈ R.

A cautionary note on exact unconditional inference for a difference between two independent binomial proportions.

Fisher's exact test for comparing response proportions in a randomized experiment can be overly conservative when the group sizes are small or when the response proportions are close to zero or one. This is primarily because the null distribution of the test statistic becomes too discrete, a partial consequence of the inference being conditional on the total number of responders. Accordingly, e...

Binomial Difference Ideals

In this paper, binomial difference ideals are studied. Three canonical representations for Laurent binomial difference ideals are given in terms of the reduced Gröbner basis of Z[x]-lattices, regular and coherent difference ascending chains, and partial characters over Z[x]-lattices, respectively. Criteria for a Laurent binomial difference ideal to be reflexive, prime, well-mixed, and perfect a...

A Note on Teaching Binomial Confidence Intervals