Chordal Komatu–Loewner equation for a family of continuously growing hulls

In this paper, we discuss the chordal Komatu–Loewner equation on standard slit domains in a manner applicable not just to a simple curve but also a family of continuously growing hulls. Especially a conformally invariant characterization of the Komatu–Loewner evolution is obtained. As an application, we prove a sort of conformal invariance, or locality, of the stochastic Komatu–Loewner evolution ${\mathrm{SKLE}}_{\sqrt{6},?b_{\mathrm{BMD}}}$ in a fully general setting, which solves an open problem posed by Chen et al. (2017).     

A general theory of almost convex functions

Let be the standard -dimensional simplex and let . Then a function with domain a convex set in a real vector space is -almost convex iff for all and the inequality

holds. A detailed study of the properties of -almost convex functions is made. If contains at least one point that is not a vertex, then an extremal -almost convex function is constructed with the properties that it vanishes on the vertices of and if is any bounded -almost convex function with on the vertices of , then for all . In the special case , the barycenter of , very explicit formulas are given for and . These are of interest, as and are extremal in various geometric and analytic inequalities and theorems.

     

Standardization of Crude Extract of Neem Seed Kernels (Azadirachta indica A. Juss) and Commercial Neem Based Formulations Using HPTLC and Extended Length Packed-Columns SFC Method

Two chromatographic techniques are described for the separation and quantitative determination of azadirachtin A and B, salannin, and nimbin present in the crude extract of neem seed kernels and commercial neem based formulations. The high performance thin-layer chromatography (HPTLC) separation of markers was carried out on Merck TLC aluminium sheets of silica gel 60 F254 using ethylacetate-benzene (7.0: 3.0, v/v) as mobile phase. The other technique was based on extended length packed column supercritical fluid chromatographic (PC-SFC) separation of the markers using Cyano column (250 mm × 4.6 mm I.D, S-5.0 μ) and Kromasil 100 NH₂ column (250 mm × 4.6 mm I.D, 5.0 μ) connected in series. The detection was carried out using photodiode array detector at 338 K using methanol-modified carbon dioxide (10%) as the mobile phase at flow rate of 2.0 mL min⁻¹. The current study assesses the effect of extending column length during PC-SFC experiment to obtain maximum resolution between a number of unknown components and known markers present in neem seed extracts. Both the chromatographic methods were validated in terms of precision, robustness, recovery, limits of detection and quantitation. The analysis of variance (ANOVA) and Student’s t-test were applied to correlate the results of quantitative determination of markers by means of HPTLC and PC-SFC method.     

Optimal coverage of convex regions

The problem of the coverage of convex regions with polygons and quadratic configurations of minimal volume is considered. The regions are presented as inequality constraints of a linear or nonlinear programming problem. It is shown that the problem of the optimal coverage with an arbitrary polygon can be reduced to a convex one of coverage with a multidimensional rectangle. If, however, rotation of the coordinate system is allowed, an additional nonconvex problem must be solved. It is also shown that, to find the minimal covering hypersphere or hyperellipsoid, one has to solve two convex programming problems. Algorithms and examples illustrating the feasibility of the proposed methods are presented.This work was supported by funds for the promotion of research at the Technion under Contract No. 190-515.The authors would like to express their indebtedness to Prof. Aharon Ben-Tal from Technion and to Prof. L. C. W. Dixon of the Hatfield Polytechnic for several valuable suggestions on an earlier draft of this paper.     

Generating Random Points (or Vectors) Controlling the Percentage of them that Are Extreme in their Convex (or Positive) Hull

This paper presents a technique to generate random data in dimensional space m such that their convex (or positive) hull contains a specific percentage of extreme points (or vectors), determined by the analyst or generator of the data. The methodology strives to remove symmetry, regularity, or predictability, which may be desirable in data used to test or compare algorithms or heuristics. There are numerous applications for this methodology.Mathematics Subject Classifications (2000) 65C10, 52B11, 52B55.     

Coreflectivity of E-Monads and Algebraic Hulls

Let Xbe a category with a given(E,M)-factorization structure for morphisms, M Mono X. In general, an arbitrary endofunctor T of X fails badly to preserve the E-class. If T carries a monad structure, then T(E) E implies that the corresponding category of Eilenberg–Moore-algebras admits (E,M)-factorizations and vice versa. In order to get T as close as possible to this nice algebraic behaviour, a couniversal modification T T with (E) E is constructed in two different ways using mild and natural assumptions on E and M, respectively. T inherits its monad structure from T. In case of T = U F, F U, the Eilenberg–Moore-category of T contains a universal (E,M-algebraic hull (completion) of U [2, 3]. There are further applications to varietal hulls [4] and to function spaces.     

Adsorption of Cr(VI) using activated neem leaves: kinetic studies

In the present study, adsorbent is prepared from neem leaves and used for Cr(VI) removal from aqueous solutions. Neem leaves are activated by giving heat treatment and with the use of concentrated hydrochloric acid (36.5 wt%). The activated neem leaves are further treated with 100 mmol of copper solution. Batch adsorption studies demonstrate that the adsorbent prepared from neem leaves has a significant capacity for adsorption of Cr(VI) from aqueous solution. The parameters investigated in this study include pH, contact time, initial Cr(VI) concentration and adsorbent dosage. The adsorption of Cr(VI) is found to be maximum (99%) at low values of pH in the range of 1-3. A small amount of the neem leaves adsorbent (10 g/l) could remove as much as 99% of Cr(VI) from a solution of initial concentration 50 mg/l. The adsorption process of Cr(VI) is tested with Langmuir isotherm model. Application of the Langmuir isotherm to the system yielded maximum adsorption capacity of 62.97 mg/g. The dimensionless equilibrium parameter, R _L, signifies a favorable adsorption of Cr(VI) on neem leaves adsorbent and is found to be between 0.0155 and 0.888 (0<R _L<1). The adsorption process follows second order kinetics and the corresponding rate constant is found to be 0.00137 g/(mg) (min).     

Some properties of two subclasses of k-fold symmetric functions associated with Srivastava-Attiya operator

In the present paper, by using the Srivastava-Attiya operator, we define two new subclasses of k-fold symmetric analytic functions. Some interesting properties of these subclasses such as integral representations, extreme points, close convex hulls and subordinations are obtained, which generalize and refine some previous results.     

Linear functionals and the duality principle for harmonic functions

Let ${\mathcal H}$ be the class of complex‐valued harmonic functions in the unit disk |z| < 1 and ${\mathcal H}_1$ the set of all functions $f\in {\mathcal H}$ such that f(0) = 0, f_z(0) = 1 and $f_{\overline{z}}(0)=0$. For $V \subset {\mathcal H}_1$, its dual V* is where * denotes the Hadamard product for harmonic functions. The set V is a dual class if V = W* for some $W \subset {\mathcal H}_1.$ In the present paper, the duality principle is extended to ${\mathcal H}_1$ by means of the Hadamard product. Counterparts of the dual classes are introduced and their structural properties studied.     

Investigation on the effect of RF air plasma and neem leaf extract treatment on the surface modification and antimicrobial activity of cotton fabric

A thorough investigation on the antimicrobial activity of RF air plasma and azadirachtin (neem leaf extract) treated cotton fabric has been dealt with in this paper. The cotton fabric was given a RF air plasma treatment to improve its hydrophilicity. The process parameters such as electrode gap, time of exposure and RF power have been varied to study their effect in improving the hydrophilicity of the cotton fabric and they were optimized based on the static immersion test results. The neem leaf extract (azadirachtin) was applied on fabric samples to impart antimicrobial activity. The antimicrobial efficacy of the samples have been analysed and compared with the efficacy of the cotton fabric treated with the antimicrobial finish alone. The investigation reveals that the RF air plasma has modified the surface of the fabric, which in turn increased the antimicrobial activity of the fabric when treated with azadirachtin. The surface modification due to RF air plasma treatment has been analysed by comparing the FTIR spectra of the untreated and plasma treated samples. The molecular interaction between the fabric, azadirachtin and citric acid which was used as a cross linking agent to increase the durability of the antimicrobial finish has also been analysed using FTIR spectra.