Let wρ x : |x|exp −Q x , ρ > −1/2, where Q ∈ C2 : −∞,∞ → 0,∞ is an even function. In 2008 we have a relation of the orthonormal polynomial pn w2 ρ;x with respect to the weightw 2 ρ x ; p′ n x An x pn−1 x − Bn x pn x − 2ρnpn x /x, where An x and Bn x are some integrating functions for orthonormal polynomials pn w2 ρ;x . In this paper, we get estimates of the higher derivatives of An x and Bn x ,...

Let Y be a finite CW-complex of dimension at most three and P → Y an SO(3) bundle. Associated with P are its Stiefel–Whitney classes wi(P ) ∈ H i(Y ;Z/2), i = 1, 2, 3. Only one of them, namely, w2(P ) ∈ H (Y ;Z/2), will be of importance to us, for the reason that w1(P ) = 0 since P is orientable, and w3(P ) = Sq (w2(P )) by the Wu formula. The class w2(P ) can be defined as follows. Let {Uα } b...

ABSTRACT Accurate metallicities of RR Lyrae are extremely important in constraining period–luminosity–metallicity (PLZ) relationships, particularly the near-infrared. We analyse 69 high-resolution spectra Galactic stars from Southern African Large Telescope. measure 58 these with typical uncertainties 0.15 dex. All but one this sample has accurate ($\sigma _{\varpi }\lesssim 10{{\ \rm per\ cent...

Gastric emptying (GE) is an important determinant of postprandial blood glucose (BG), yet GE is delayed in anorexia nervosa (AN). This study aimed to characterise relationships between GE (13C-octanoate breath test), and BG responses to, a mixed-nutrient semi-solid meal in 22 female adolescent AN inpatients on admission (BL) and following 1 (W1) and 2 weeks (W2) of refeeding, and in 17 age-matc...

Two strings x and y are said to be Abelian equivalent if x is a permutation of y, or vice versa. If a string z satisfies z = xy with x and y being Abelian equivalent, then z is said to be an Abelian square. If a string w can be factorized into a sequence v1, . . . , vs of strings such that v1, . . . , vs−1 are all Abelian equivalent and vs is a substring of a permutation of v1, then w is said t...

LL-37 is the only antimicrobial peptide (AMP) of the human cathelicidin family. In addition to potent antimicrobial activity, LL-37 is known to have the potential to inhibit lipolysaccharide (LPS)-induced endotoxic effects. To provide the stability to proteolytic digestion and increase prokaryotic selectivity and/or antiendotoxic activity of two Lys/Trp-substituted 19-meric antimicrobial peptid...