Polar derivatives of [closo-1-CB9H10]− and [closo-1-CB11H12]− anions as high Δε additives to a nematic host: a comparison of the CH2CH2 and COO linking groups

Liquid crystalline pyridinium zwitterions of [closo-1-CB9H10]− perform better as polar potential components of LCD materials than the sulfonium or [closo-1-CB11H12]− analogs on the basis of solubility and Maier–Meier analysis.

Generalizations of some Zygmund-type integral inequalities for polar derivatives of a complex polynomial

We prove some results for algebraic polynomials in the complex plane that relate the L-norm of the polar derivative of a complex polynomial and the polynomial under some conditions. The obtained results include several interesting generalizations of some Zygmund-type integral inequalities for polynomials and derive polar derivative analogues of some classical Bernsteintype inequalities for the sup-norms on the unit disk as well.

Black Ginseng

Black ginseng is a processed ginseng which prepared by  steaming and drying of white or red ginseng  for several times (usually 9). This process resulting in extensive changes in types and amounts of several secondary metabolites. Thus, primary ginsenosides (the main active inredients in ginseng) were transformed into less polar derivatives by steaming. In addition, apparent changes happened to other secondary metabolites such as the increasing  of phenolic compounds, reducing sugars and acidic polysaccharides as well as the decrease in concentrations of free amino acids and total polysaccharides. Furthermore, the presence of some Maillard reaction products like maltol was also engaged. These obvious chemical changes were associated with a noticeable superiority for black ginseng over white and red ginseng in most of the comparative biological studies including anticarcinogenic, immunomodulatory, anti-Inflammatory, antidiabetic, hepatoprotective, antioxidant and tonic effects.

Some integral inequalities for the polar derivative of polynomials

As a generalization of well-known result due to Turan [24] for polynomials having all their zeros in |z| ? 1, Malik [17] proved that, if P(z) is a polynomial of degree n, having all its zeros in |z| ? 1, then for any ? > 0, n{?2?0|P(ei?)|?d?}1/? ? {?2?0|1+ei?|?d?}1/? max |z|=1 |P?(z)|. We generalize the above inequality to polar derivatives, which as special cases include several known results in this area. Besides the paper contains some more results that generalize and sharpen several results known in this direction.

Duality between loci of complex polynomials and the zeros of polar derivatives

This work investigates the connections between the notion of a locus of a complex polynomial and the polar derivatives. Polar differentiation extends classical derivatives and provides additional flexibility. The notion of a locus was introduced in [8] and proved useful in providing sharp versions of several classical results in the area known as Geometry of Polynomials. The investigations culminated in the work [11]. A need was revealed for a unified treatment of bounded and unbounded loci of polynomials of degree at most n as well as a unified treatment of polar derivatives and ordinary derivatives. This work aims at providing such a framework.

Integral inequalities concerning polynomials with polar derivatives

Let P(z) be a polynomial of degree n and for any complex number α, let DαP(z) = nP(z) + (α − z)P 0 (z) denote the polar derivative of P(z) with respect to a complex number α. In this paper, we present an integral inequality for the polar derivative of a polynomial P(z). Our result includes as special cases several interesting generalizations of some Zygmund type inequalities for polynomials.