The analytical solutions for the general-four-wave-mixing hyperpolarizabilities chi(3)[-(omega1 + omega2 + omega3);omega1,omega2,omega3] on infinite chains under both Su-Shrieffer-Heeger and Takayama-Lin-Liu-Maki models of trans-polyacetylene are obtained through the scheme of dipole-dipole correlation. Analytical expressions of dc Kerr effect chi(3)(-omega;0,0,omega), dc-induced second-harmoni...

 The category of the title is called $mathcal{W}$. This has all free objects $F(I)$ ($I$ a set). For an object class $mathcal{A}$, $Hmathcal{A}$ consists of all homomorphic images of $mathcal{A}$-objects. This note continues the study of the $H$-closed monoreflections $(mathcal{R}, r)$ (meaning $Hmathcal{R} = mathcal{R}$), about which we show ({em inter alia}): $A in mathcal{A}$ if and  only if...

     In this article we introduce the notion of textit{Fractal $omega$-operad} emerging from  a natural $omega$-operad associated to any coglobular object in the category of higher operads in Batanin's sense, which in fact is a coendomorphism $omega$-operads. We have in mind coglobular object of higher operads which algebras are kind of higher transformations. It follows that this natural $omeg...

A weakly nonlinear oscillator of natural frequency omega(0) and damping ratio delta is driven by an amplitude-modulated force of dimensionless amplitude epsilon, carrier frequency omega, and modulation frequency omega(1). Each of (omega - omega(0))/omega(0), omega(1)/omega(0), and delta is O(epsilon(2/3)) as epsilon --> 0. The response in this resonant neighborhood is a slowly modulated sine wa...

conclusions our results showed that vitamin e plus omega free fatty acids decrease the severity of mastodynia better than vitamin e alone. results vitamin e plus omega free fatty acids are more effective than the use of vitamin e alone in decreasing mastodynia. significant difference was seen between the cardiff breast score (cbs) of the vitamin e group compared to vitamin e - omega group (p < ...

the aim of this research was to investigate the effect of 8 weeks of aerobic training and omega-3 fatty acid supplementation on plasma sicam-1 in elderly men. in this study, 36 male non-athletes (aged between 50 and 70) were selected through available method and randomly divided into 4 groups (9 subjects per group): aerobic training+omega-3 supplement, aerobic training+placebo, omega-3 suppleme...