From Nagumo [10], there have been many accomplishments on the study of the existence of solutions for boundary value problems (BVPs) using the theory of differential inequality (cf. [1–9, 11–17]). However, for the nth-order nonlinear differential equations with the nonlinear boundary conditions, results are very few. The authors made some attempts to solve the nth-order Robin problem [14]. Now ...

The Escherichia coli endonuclease III (Nth-Eco) protein is involved in the removal of damaged pyrimidine residues from DNA by base excision repair. It is an iron-sulphur enzyme possessing both DNA glycosylase and apurinic/apyrimidinic lyase activities. A database homology search identified an open reading frame in genomic sequences of Schizosaccharomyces pombe which encodes a protein highly sim...

Second-price auctions are designed to induce people to reveal their private preferences for a good. Laboratory evidence suggests that while these auctions do a reasonable job on aggregate, they fall short at the individual level, especially for bidders who are off-margin of the market-clearing price. Herein we introduce and explore whether a random nth-price auction can engage all bidders to bi...

Significant values of a combinatorial count need not fit the recurrence for the count. Consequently, initial values of the count can much outnumber those for the recurrence. So is the case of the count, Gl(n), of distance-l independent sets on the cycle Cn, studied by Comtet for l ≥ 0 and n ≥ 1 [sic]. We prove that values of Gl(n) are nth power sums of the characteristic roots of the correspond...

Abstract: In order that the nth-order Generalized Frequency Response Function (GFRF) for nonlinear systems described by a NARX model can be directly written into a more straightforward and meaningful form in terms of the first order GFRF and model parameters, the nth-order GFRF is now determined by a new mapping function based on a parametric characteristic. This can explicitly unveil the linea...

To a knot in 3-space, one can associate a sequence of Laurent polynomials, whose nth term is the nth colored Jones polynomial. The paper is concerned with the asymptotic behavior of the value of the nth colored Jones polynomial at eα/n, when α is a fixed complex number and n tends to infinity. We analyze this asymptotic behavior to all orders in 1/n when α is a sufficiently small complex number...

Let F be a field of characteristic zero and let ft,n be the stabilization homomorphism from the nth integral homology of SLt(F ) to the nth integral homology of SLt+1(F ). We prove the following results: For all n, ft,n is an isomorphism if t ≥ n+ 1 and is surjective for t = n, confirming a conjecture of C-H. Sah. fn,n is an isomorphism when n is odd and when n is even the kernel is isomorphic ...