The presence of the neuronal-specific N1-Src splice variant of the C-Src tyrosine kinase is conserved through vertebrate evolution, suggesting an important role in complex nervous systems. Alternative splicing involving an N1-Src-specific microexon leads to a 5 or 6 aa insertion into the SH3 domain of Src. A prevailing model suggests that N1-Src regulates neuronal differentiation via cytoskelet...

Proof of Claim 1.1: Of course, we assume that {nj}j=1 are all distinct. Let n1 = 1. Then there must exist An2 such that An2 ∩An1 6= ∅. If not, then An1 ∩Aj = ∅ for all j 6= n1. Thus, An1 ⊆ Aj for all j 6= n1. Now, fix some j0 6= n1 such thatAj0 6= An1 . Then, sinceF is a σ-algebra, we have thatAk0 = A c j0 for some k0 6= n1. Thus, setting j = k0 6= n1, An1 ⊆ Ack0 = ( Acj0 )c = Aj0 . The only wa...

We give a fast elementary algorithm to get a small number n1 for an admissible q-properhypergeometric identity ∑ k F(n, k) = G(n), n ≥ n0 such that we can prove the identity by checking its correctness for n (n0 ≤ n ≤ n1). For example, we get n1 = 191 for the q-Vandermonde-Chu identity, n1 = 70 for a finite version of Jacobi’s triple product identity and n1 = 209 for an identity due to L.J. Rog...

We study a discrete time model of the growth of two species of plankton with competitive and allelopathic effects on each other N1(k + 1) = N1(k)exp{r1(k)− a11(k)N1(k)− a12(k)N2(k) − b1(k)N1(k)N2(k)}, N2(k + 1) = N2(k)exp{r2(k) − a21(k)N1(k) − a22(k) N2(k)− b2(k)N1(k)N2(k)}. A set of sufficient conditions is obtained for the existence of multiple positive periodic solutions for this model. The ...

By using the Newton interpolation formula, we generalize the recent identities on the Catalan triangle obtained by Miana and Romero as well as those of Chen and Chu. We further study divisibility properties of sums of products of binomial coefficients and an odd power of a natural number. For example, we prove that for all positive integers n1, . . . , nm, nm+1 = n1, and any nonnegative integer...

Schmidt decompositions of the quantum Fourier transform on C1 ⊗C2 are computed for all N1,N2 ≥ 2. The Schmidt decomposition is shown to be completely degenerate when N1 is a factor of N2 and when N1 > N2. This generalizes previous decompositions, found for N1 = N2 = 2 n [M. A. Nielsen, PhD Thesis, University of New Mexico (1998), Chapter 6; arXiv:quant-ph/0011036], and, more generally, for N1 =...

Earlier, a theory was introduced that enabled a method of scalable logic synthesis. In this method, given a circuit N1 and its partition into subcircuits N1 , i=1,..k, an optimized circuit N2 functionally equivalent to N1 is built by replacing each subcircuit N1 i with a toggle equivalent counterpart N2 . To implement this method in practice, one needs a procedure that, given a multi-output sub...