Abstract:
For $0\leq \alpha <1$, the sharp radii of starlikeness and convexity of order $\alpha$ for functions of the form $f(z)=z+a_2z^2+a_3z^3+...$ whose Taylor coefficients $a_n$ satisfy the conditions $|a_2|=2b$, $0\leq b\leq 1$, and $|a_n|\leq n $, $M$ or $M/n$ ($M>0$) for $n\geq 3$ are obtained. Also a class of functions related to Carath\'eodory functions is considered.

Abstract:
The $n$th partial sum of an analytic function $f(z)=z+\sum_{k=2}^\infty a_k z^k$ is the polynomial $f_n(z):=z+\sum_{k=2}^n a_k z^k$. A survey of the univalence and other geometric properties of the $n$th partial sum of univalent functions as well as other related functions including those of starlike, convex and close-to-convex functions are presented.

Abstract:
The delivery of poorly water-soluble drugs has been the subject of much research, as approximately 40% of new chemical entities are hydrophobic in nature. One area in which published literature is lacking is the field of Nano emulsions. This review gives a conceptual idea about Nanoemulsion system. It provides reservoir vehicles for transdermal systems and controlled drug delivery systems or hydrolytically unstable drugs. The design and development of new drug delivery systems with the intention of enhancing the efficacy of existing drugs is an ongoing process in pharmaceutical research. It is necessary for a pharmaceutical solution to contain a therapeutic dose of the drug in a volume convenient for administration.The main difference between emulsions and Nanoemulsions lies in the size and shape of the particles dispersed in the continuous phase: these are at least an order of magnitude smaller in the case of Nanoemulsions (10-200 nm) than those of conventional emulsions (1-20 μm). Also, whereas emulsions consist of roughly spherical droplets of one phase dispersed into the other, nanoemulsions constantly evolve between various structures ranging from droplet-like swollen micelles to bicontinuous structures, making the usual “oil in water” and “water in oil” distinction sometimes irrelevant. Nanoemulsions are formed when and only when the interfacial tension at the oil/water interface is brought to a very low level and the interfacial layer is kept highly flexible and fluid. These two conditions are usually met by a careful and precise choice of the components and of their respective proportions, and by the use of a “co-surfactant” which brings flexibility to the oil/water interface. These conditions lead to a thermodynamically optimised structure, which is stable as opposed to conventional emulsions and does not require high input of energy (i.e. through agitation) to be formed.

Abstract:
The present paper deals botanical description and new distributional record for an epiphytic Orchid species Eria exilis Hook.f. So far, this species has been recorded in Western Ghats of Kerala, Karnataka and Tamil Nadu. This is the first report to occur the Eria exilis in Eastern Ghats of Tamil Nadu. The paper is provided photographs, habitat ecology, phenology and distributional ranges to this tiny endemic Orchid species for facilitating the identification and conservation measures.

Abstract:
In 1984, Clunie and Sheil-Small proved that a sense-preserving harmonic function whose analytic part is convex, is univalent and close-to-convex. In this paper, certain cases are discussed under which the conclusion of this result can be strengthened and extended to fully starlike and fully convex harmonic mappings. In addition, we investgate the properties of functions in the class $\mathcal{M}(\alpha)$ $(|\alpha|\leq 1)$ consisting of harmonic functions $f=h+\overline{g}$ with $g'(z)=\alpha zh'(z)$, $\RE (1+{zh''(z)}/{h'(z)})>-{1}/{2} $ $ \mbox{for} |z|<1 $. The coefficient estimates, growth results, area theorem and bounds for the radius of starlikeness and convexity of the class $\mathcal{M}(\alpha)$ are determined. In particular, the bound for the radius of convexity is sharp for the class $\mathcal{M}(1)$.

Abstract:
A subclass of complex-valued close-to-convex harmonic functions that are univalent and sense-preserving in the open unit disc is investigated. The coefficient estimates, growth results, area theorem, boundary behavior, convolution and convex combination properties for the above family of harmonic functions are obtained.

Abstract:
By using the theory of first-order differential subordination for functions with fixed initial coefficient, several well-known results for subclasses of univalent functions are improved by restricting the functions to have fixed second coefficient. The influence of the second coefficient of univalent functions is evident in the results obtained.

Abstract:
Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent analytic functions. The notion of harmonic Alexander integral operator is introduced. Also, the radius of convexity for certain families of harmonic functions is determined.

Abstract:
The hereditary property of convexity and starlikeness for conformal mappings does not generalize to univalent harmonic mappings. This failure leads us to the notion of fully starlike and convex mappings of order \alpha, (0\leq \alpha<1). A bound for the radius of fully starlikeness and fully convexity of order \alpha is determined for certain families of univalent harmonic mappings. Convexity is not preserved under the convolution of univalent harmonic convex mappings, unlike in the analytic case. Given two univalent harmonic convex mappings f and g, the problem of finding the radius r_{0} such that f*g is a univalent harmonic convex mapping in |z|

Abstract:
For given two harmonic functions $\Phi$ and $\Psi$ with real coefficients in the open unit disk $\mathbb{D}$, we study a class of harmonic functions $f(z)=z-\sum_{n=2}^{\infty}A_nz^{n}+\sum_{n=1}^{\infty}B_n\bar{z}^n$ $(A_n, B_n \geq 0)$ satisfying \[\RE \frac{(f*\Phi)(z)}{(f*\Psi)(z)}>\alpha \quad (0\leq \alpha <1, z \in \mathbb{D});\] * being the harmonic convolution. Coefficient inequalities, growth and covering theorems, as well as closure theorems are determined. The results obtained extend several known results as special cases. In addition, we study the class of harmonic functions $f$ that satisfy $\RE f(z)/z>\alpha$ $(0\leq \alpha <1, z \in \mathbb{D})$. As an application, their connection with certain integral transforms and hypergeometric functions is established.