Identities of symmetry for Euler polynomials arising from quotients of fermionic integrals invariant under S_3

In this paper, we derive eight basic identities of symmetry in three variables related to Euler polynomials and alternating power sums. These and most of their corollaries are new, since there have been results only about identities of symmetry in two variables. These abundance of symmetries shed new light even on the existing identities so as to yield some further interesting ones. The derivations of identities are based on the $p$-adic integral expression of the generating function for the Euler polynomials and the quotient of integrals that can be expressed as the exponential generating function for the alternating power sums.Comment: No comment

Effect of epitaxial strain on ferroelectric polarization in multiferroic BiFeO3 films

Multiferroic BiFeO3 epitaxial films with thickness ranging from 40 nm to 960 nm were grown by pulsed laser deposition on SrTiO3 (001) substrates with SrRuO3 bottom electrodes. X-ray characterization shows that the structure evolves from angularly-distorted tetragonal with c/a ~ 1.04 to more bulk-like distorted rhombohedral (c/a ~ 1.01) as the strain relaxes with increasing thickness. Despite this significant structural evolution, the ferroelectric polarization along the body diagonal of the distorted pseudo-cubic unit cells, as calculated from measurements along the normal direction, barely changes.Comment: Legend in Fig.3 corrected and et

Folding machineries displayed on a cation-exchanger for the concerted refolding of cysteine- or proline-rich proteins

<p>Abstract</p> <p>Background</p> <p><it>Escherichia coli </it>has been most widely used for the production of valuable recombinant proteins. However, over-production of heterologous proteins in <it>E. coli </it>frequently leads to their misfolding and aggregation yielding inclusion bodies. Previous attempts to refold the inclusion bodies into bioactive forms usually result in poor recovery and account for the major cost in industrial production of desired proteins from recombinant <it>E. coli</it>. Here, we describe the successful use of the immobilized folding machineries for <it>in vitro </it>refolding with the examples of high yield refolding of a ribonuclease A (RNase A) and cyclohexanone monooxygenase (CHMO).</p> <p>Results</p> <p>We have generated refolding-facilitating media immobilized with three folding machineries, mini-chaperone (a monomeric apical domain consisting of residues 191–345 of GroEL) and two foldases (DsbA and human peptidyl-prolyl <it>cis-trans </it>isomerase) by mimicking oxidative refolding chromatography. For efficient and simple purification and immobilization simultaneously, folding machineries were fused with the positively-charged consecutive 10-arginine tag at their C-terminal. The immobilized folding machineries were fully functional when assayed in a batch mode. When the refolding-facilitating matrices were applied to the refolding of denatured and reduced RNase A and CHMO, both of which contain many cysteine and proline residues, RNase A and CHMO were recovered in 73% and 53% yield of soluble protein with full enzyme activity, respectively.</p> <p>Conclusion</p> <p>The refolding-facilitating media presented here could be a cost-efficient platform and should be applicable to refold a wide range of <it>E. coli </it>inclusion bodies in high yield with biological function.</p

Solutions of xqk+⋯+xq+x=ax^{q^k}+\cdots+x^{q}+x=a in GF2nGF{2^n}

Though it is well known that the roots of any affine polynomial over a finite field can be computed by a system of linear equations by using a normal base of the field, such solving approach appears to be difficult to apply when the field is fairly large. Thus, it may be of great interest to find an explicit representation of the solutions independently of the field base. This was previously done only for quadratic equations over a binary finite field. This paper gives an explicit representation of solutions for a much wider class of affine polynomials over a binary prime field