On the Harmonic Measure and Capacity of Rational Lemniscates

We study the lemniscates of rational maps. We prove a reflection principle for the harmonic measure of rational lemniscates and we give estimates for their capacity and the capacity of their components. Also, we prove a version of Schwarz’s lemma for the capacity of the lemniscates of proper holomorphic functions.     

Computational Fluid Dynamic Design of Jet Stirred Reactors for Measuring Intrinsic Kinetics of Gas‐Phase and Gas‐Solid Reactions

Nonreactive and reactive computational fluid dynamic simulations were applied to optimize the design of a laboratory scale jet stirred reactor for measuring intrinsic kinetics of gas‐phase and gas‐solid reactions, i.e. kinetics determined by chemical steps only and not by heat or mass transfer. In the past these reactors were designed and tested based on empirical design criteria and residence time distribution experiments. This work shows that these do not always capture important local effects that are vital for kinetic studies. First the degree of macro–mixing was evaluated for three different geometries (down case, 45° case and 90° case) by performing in silico residence time distribution experiments at 900 K, showing that with these type of experiments only minor differences are observed. However, the ethane steam cracking simulations revealed major differences, with the 45° case being the most uniform in terms of temperature and the 90° case being by far the worst. The species nonuniformity in all geometries was acceptable and was in some cases even partly masked by important shortcut streams such as those observed in the 90° case. The existing gradients on the substrate surface are sufficiently small to be neglected in modeling efforts. As temperature is the major parameter determining the rate of the surface reactions, the 45° case is suggested as the best geometry for measuring intrinsic kinetics.     

Monotonicity of some functions involving the gamma and psi functions

Let , where is Euler's gamma function. We determine conditions for the numbers so that the function is strongly completely monotonic on . Through this result we obtain some inequalities involving the ratio of gamma functions and provide some applications in the context of trigonometric sum estimation. We also give several other examples of strongly completely monotonic functions defined in terms of and functions. Some limiting and particular cases are also considered.

     

A Positive Functional Bound for Certain Sine Sums

The positivity of the sine sums

On a monotonic trigonometric sum

By establishing a cosine analogue of a result of Askey and Steinig on a monotonic sine sum, this paper sharpens and unifies several results associated with Young's inequality for the partial sums of k ^–1 cosk.     

Probability and expectation inequalities

Summary This paper introduces a mathematical framework within which a wide variety of known and new inequalities can be viewed from a common perspective. Probability and expectation inequalities of the following types are considered: (a)P(ZA) P(ZA) for some class of setsA, (b)k(Z)k(Z) for some class of functionsk, and (c)l(Z)k(Z) for some class of pairs of functionsl andk. It is shown, sometimes using explicit constructions ofZ andZ, that, in several cases, (a) (b) (c); included here are cases of normal and elliptically contoured distributions. A case where (a) (b) (c) is studied and is expressed in terms ofn monotone functions for (some of) which integral representations are obtained. Also, necessary and sufficient conditions for (c) are given.Research supported by the Air Force Office of Scientific Research under Grants AFOSR-75-2796 and AFOSR-80-0080Research supported by the National Science Foundation under Grants MCS78-01240 and MCS81-00748     

Simultaneous determination of the flavonoid aglycones diosmetin and hesperetin in human plasma and urine by a validated GC/MS method: in vivo metabolic reduction of diosmetin to hesperetin

Diosmetin and hesperetin are the aglycones of the flavonoid glycosides diosmin and hesperidin which occur naturally in citrus fruit. A GC/MS method for the simultaneous determination of diosmetin and hesperetin in human plasma and urine has been developed and validated. The method was linear in the 2-300 ng/mL concentration range for both diosmetin and hesperetin in plasma and urine (r > 0.999). The precision of the method was better than 6.01 and 7.16% for diosmetin and hesperetin, respectively, and the accuracy was 96.76-100.40% and 95.00-105.50% for diosmetin and hesperetin, respectively. The lower limit of quantitation was found to be 2 ng/mL for both analytes in plasma and urine. Recovery of diosmetin, hesperetin and internal standard naringenin was greater than 82.5%. The method has been applied for the determination of diosmetin and hesperetin in plasma and urine samples obtained from a healthy male subject following a single oral 1000 mg dose of the flavonoid glycoside diosmin. The presence of hesperetin in plasma and urine samples indicates the metabolic reduction of diosmetin to its flavanone analogue hesperetin through reduction of the 2,3 double bond of the C-ring by the enzymes of bacteria of the intestinal microflora.     

A Sharp Inequality for a Trigonometric Sum

We prove that the inequality $$-\frac{1}{2}\leq {\sum\limits_{k=1}^{n}} \left( \frac{{\rm cos}(2kx)}{2k - 1}+\frac{{\rm sin}((2k - 1)x)}{2k} \right)$$ holds for all natural numbers n and real numbers x with ${x \in [0, \pi]}$ . The sign of equality is valid if and only if n =  1 and x =  π /2.     

Updating Insights into the Catalytic Domain Properties of Plant Cellulose synthase (CesA) and Cellulose synthase-like (Csl) Proteins

The wall is the last frontier of a plant cell involved in modulating growth, development and defense against biotic stresses. Cellulose and additional polysaccharides of plant cell walls are the most abundant biopolymers on earth, having increased in economic value and thereby attracted significant interest in biotechnology. Cellulose biosynthesis constitutes a highly complicated process relying on the formation of cellulose synthase complexes. Cellulose synthase (CesA) and Cellulose synthase-like (Csl) genes encode enzymes that synthesize cellulose and most hemicellulosic polysaccharides. Arabidopsis and rice are invaluable genetic models and reliable representatives of land plants to comprehend cell wall synthesis. During the past two decades, enormous research progress has been made to understand the mechanisms of cellulose synthesis and construction of the plant cell wall. A plethora of cesa and csl mutants have been characterized, providing functional insights into individual protein isoforms. Recent structural studies have uncovered the mode of CesA assembly and the dynamics of cellulose production. Genetics and structural biology have generated new knowledge and have accelerated the pace of discovery in this field, ultimately opening perspectives towards cellulose synthesis manipulation. This review provides an overview of the major breakthroughs gathering previous and recent genetic and structural advancements, focusing on the function of CesA and Csl catalytic domain in plants.