CALCULATING THE SMARANOACHE FUNCTION WITHOUT FACTORISING

This paper presents an alternative algorithm for use when S is to be calculated for all integers up to n. The integers are synthesised by combining all the prime powers in the range up to n

Differentially Addressable Cavities within Metal-Organic Cage-Cross-Linked Polymeric Hydrogels

Here we report a new class of hydrogels formed by polymers that are cross-linked through subcomponent self-assembled metal–organic cages. Selective encapsulation of guest molecules within the cages creates two distinct internal phases within the hydrogel, which allows for contrasting release profiles of related molecules depending on their aptitude for encapsulation within the cages. The hydrogels were fabricated into microparticles via a droplet-based microfluidic approach and proved responsive to a variety of stimuli, including acid and competing amine or aldehyde subcomponents, allowing for the triggered release of cargo

Constraints on gluon evolution at small x

The BFKL and the unified angular-ordered equations are solved to determine the gluon distribution at small $x$. The impact of kinematic constraints is investigated. Predictions are made for observables sensitive to the gluon at small $x$. In particular comparison is made with measurements at the HERA electron-proton collider of the proton structure function $F_2 (x, Q^2)$ as a function of $\ln Q^2$, the charm component, $F_2^c(x,Q^2)$ and diffractive $J/\psi$ photoproduction.Comment: 17 LaTeX pages and 9 postscript figure

Properties of the BFKL equation and structure function predictions for HERA

The general properties of the Lipatov or BFKL equation are reviewed. Modifications to the infrared region are proposed. Numerical predictions for the deep-inelastic electron-proton structure functions at small $x$ are presented and confronted with recent HERA measurements.Comment: 21 pages, 11 figures, Latex file, Durham preprint DTP 92/2

Molecular-orbital theory for the stopping power of atoms in the low velocity regime:the case of helium in alkali metals

A free-parameter linear-combination-of-atomic-orbitals approach is presented for analyzing the stopping power of slow ions moving in a metal. The method is applied to the case of He moving in alkali metals. Mean stopping powers for He present a good agreement with local-density-approximation calculations. Our results show important variations in the stopping power of channeled atoms with respect to their mean values.Comment: LATEX, 3 PostScript Figures attached. Total size 0.54

The ergogenic effect of beta-alanine combined with sodium bicarbonate on high-intensity swimming performance

We investigated the effect of beta-alanine (BA) alone (study A) and in combination with sodium bicarbonate (SB) (study B) on 100- and 200-m swimming performance. In study A, 16 swimmers were assigned to receive either BA (3.2 g·day−1 for 1 week and 6.4 g·day−1 for 4 weeks) or placebo (PL; dextrose). At baseline and after 5 weeks of supplementation, 100- and 200-m races were completed. In study B, 14 were assigned to receive either BA (3.2 g·day−1 for 1 week and 6.4 g·day−1 for 3 weeks) or PL. Time trials were performed once before and twice after supplementation (with PL and SB), in a crossover fashion, providing 4 conditions: PL-PL, PL-SB, BA-PL, and BA-SB. In study A, BA supplementation improved 100- and 200-m time-trial performance by 2.1% (p = 0.029) and 2.0% (p = 0.0008), respectively. In study B, 200-m time-trial performance improved in all conditions, compared with presupplementation, except the PL-PL condition (PL-SB, +2.3%; BA-PL, +1.5%; BA-SB, +2.13% (p < 0.05)). BA-SB was not different from BA-PL (p = 0.21), but the probability of a positive effect was 78.5%. In the 100-m time-trial, only a within-group effect for SB was observed in the PL-SB (p = 0.022) and BA-SB (p = 0.051) conditions. However, 6 of 7 athletes swam faster after BA supplementation. The probability of BA having a positive effect was 65.2%; when SB was added to BA, the probability was 71.8%. BA and SB supplementation improved 100- and 200-m swimming performance. The coingestion of BA and SB induced a further nonsignificant improvement in performance

Low Energy Chiral Lagrangian in Curved Space-Time from the Spectral Quark Model

We analyze the recently proposed Spectral Quark Model in the light of Chiral Perturbation Theory in curved space-time. In particular, we calculate the chiral coefficients $L_1, ..., L_{10}$, as well as the coefficients $L_{11}$, $L_{12}$, and $L_{13}$, appearing when the model is coupled to gravity. The analysis is carried for the SU(3) case. We analyze the pattern of chiral symmetry breaking as well as elaborate on the fulfillment of anomalies. Matching the model results to resonance meson exchange yields the relation between the masses of the scalar, tensor and vector mesons, $M_{f_0}=M_{f_2}=\sqrt{2} M_V= 4 \sqrt{3 /N_c} \pi f_\pi$. Finally, the large-$N_c$ limit suggests the dual relations in the vector and scalar channels, $M_V=M_S= 2 \sqrt{6 /N_c} \pi f_\pi$ and $^{1/2}_S = < r^2 >^{1/2}_V = 2 \sqrt{N_c} / f_\pi = 0.59 {\rm fm}$.Comment: 18 pages, no figure