Abstract:
Let , denote the class of all normalized analytic functions in the unit disc such that for some with , and . Let , , denote the Pascu class of -convex functions given by the analytic condition which unifies the classes of starlike and convex functions. The aim of this paper is to find conditions on so that the integral transform of the form carry functions from into . As for the applications, for specific values of , it is found that several known integral operators carry functions from into . The results for a more generalized operator related to are also given. 1. Introduction Let denote the class of all functions analytic in the open unit disc with the normalization , and let be the class of functions that are univalent in . A function is said to be starlike or convex , if maps conformally onto the domains, respectively, starlike with respect to origin and convex. Note that in , if follows from the well-known Alexander theorem (see [1] for details). A useful generalization of the class is the class that has the analytic characterization and . Various generalizations of classes and are abundant in the literature. One such generalization is the following. A function is said to be in the Pascu class of -convex functions of order if [2] or in other words This class is denoted by . Even though this class is known as Pascu class of -convex functions of order , since we use the parameter for another important class, we denote this class by , , and we remark that, in the sequel, we only consider the class . Clearly, and , which implies that this class is a smooth passage between the classes of starlike and convex functions. The main objective of this work is to find conditions on the nonnegative real valued integrable function satisfying , such that the operator is in the class . Note that this operator was introduced in [3]. To investigate this admissibility property, the class to which the function belongs is important. Let , where？？ , , and , denote the class of all normalized analytic functions in the open unit disc such that for some . This class and its particular cases were considered by many authors so that the corresponding operator given by (3) is univalent and in for some particular values of , , , and . This work was motivated in [3] by studying the conditions under which and was generalized in [4] by studying the case . Similar situation for the convex case, namely, , was initiated in [5]. After several generalizations by many authors, recently, the conditions under which were obtained in [6] and the corresponding results for the convex case so

Abstract:
We carryout a comparative study of spin distributions defined over the sphere for bipartite quantum spin assemblies. We analyse Einstein-Podolsky-Rosen-Bohm (EPRB) spin correlations in a spin-s singlet state using these distributions. We observe that in the classical limit EPRB spin distributions turn out to be delta functions, thus reflecting the perfect anticorrelation property of two spin vectors associated with a spin-s singlet state.

Abstract:
For $\alpha\geq 0$, $\delta>0$, $\beta<1$ and $\gamma\geq 0$, the class $\mathcal{W}_{\beta}^\delta(\alpha,\gamma)$ consist of analytic and normalized functions $f$ along with the condition \begin{align*} {\rm Re\,} e^{i\phi}(\dfrac{}{}(1\!-\!\alpha\!+\!2\gamma)\!({f}/{z})^\delta +(\alpha\!-\!3\gamma\!+\!\gamma[\dfrac{}{}(1-{1}/{\delta})({zf'}/{f})+ {1}/{\delta}(1+{zf''}/{f'})]).\\ .\dfrac{}{}({f}/{z})^\delta \!({zf'}/{f})-\beta)>0, \end{align*} where $\phi\in\mathbb{R}$ and $|z|<1$, is taken into consideration. The class $\mathcal{S}^\ast_s(\zeta)$ be the subclass of the univalent functions, defined by the analytic characterization ${\rm Re}{\,}({zf'}/{f})>\zeta$, for $0\leq \zeta< 1$, $0<\delta\leq\frac{1}{(1-\zeta)}$ and $|z|<1$. The admissible and sufficient conditions on $\lambda(t)$ are examined, so that the generalized and non-linear integral transforms \begin{align*} V_{\lambda}^\delta(f)(z)= (\int_0^1 \lambda(t) ({f(tz)}/{t})^\delta dt)^{1/\delta}, \end{align*} maps the function from $\mathcal{W}_{\beta}^\delta(\alpha,\gamma)$ into $\mathcal{S}^\ast_s(\zeta)$. Moreover, several interesting applications for specific choices of $\lambda(t)$ are discussed, that are related to some well-known integral operators.

Abstract:
Let $\mathcal{W}_{\beta}^\delta(\alpha,\gamma)$ be the class of normalized analytic functions $f$ defined in the domain $|z|<1$ satisfying \begin{align*} {\rm Re\,} e^{i\phi}\left(\dfrac{}{}(1\!-\!\alpha\!+\!2\gamma)\!\left({f}/{z}\right)^\delta +\left(\alpha\!-\!3\gamma+\gamma\left[\dfrac{}{}\left(1-{1}/{\delta}\right)\left({zf'}/{f}\right)+ {1}/{\delta}\left(1+{zf''}/{f'}\right)\right]\right)\right.\\ \left.\dfrac{}{}\left({f}/{z}\right)^\delta \!\left({zf'}/{f}\right)-\beta\right)>0, \end{align*} with the conditions $\alpha\geq 0$, $\beta<1$, $\gamma\geq 0$, $\delta>0$ and $\phi\in\mathbb{R}$. Moreover, for $0<\delta\leq\frac{1}{(1-\zeta)}$, $0\leq\zeta<1$, the class $\mathcal{C}_\delta(\zeta)$ be the subclass of normalized analytic functions such that \begin{align*} {\rm Re}{\,}\left(1/\delta\left(1+zf''/f'\right)+(1-1/\delta)\left({zf'}/{f}\right)\right)>\zeta,\quad |z|<1. \end{align*} In the present work, the sufficient conditions on $\lambda(t)$ are investigated, so that the generalized integral transform \begin{align*} V_{\lambda}^\delta(f)(z)= \left(\int_0^1 \lambda(t) \left({f(tz)}/{t}\right)^\delta dt\right)^{1/\delta},\quad |z|<1, \end{align*} carries the functions from $\mathcal{W}_{\beta}^\delta(\alpha,\gamma)$ into $\mathcal{C}_\delta(\zeta)$. Several interesting applications are provided for special choices of $\lambda(t)$.

Abstract:
Let $\mathcal{W}_{\beta}^\delta(\alpha,\gamma)$ be the class of normalized analytic functions $f$ defined in the region $|z|<1$ and satisfying \begin{align*} {\rm Re\,} e^{i\phi}\left(\dfrac{}{}(1\!-\!\alpha\!+\!2\gamma)\!\left({f}/{z}\right)^\delta +\left(\alpha\!-\!3\gamma+\gamma\left[\dfrac{}{}\left(1-{1}/{\delta}\right)\left({zf'}/{f}\right)+ {1}/{\delta}\left(1+{zf"}/{f'}\right)\right]\right)\right.\\ \left.\dfrac{}{}\left({f}/{z}\right)^\delta \!\left({zf'}/{f}\right)-\beta\right)>0, \end{align*} with the conditions $\alpha\geq 0$, $\beta<1$, $\gamma\geq 0$, $\delta>0$ and $\phi\in\mathbb{R}$. For a non-negative and real-valued integrable function $\lambda(t)$ with $\int_0^1\lambda(t) dt=1$, the generalized non-linear integral transform is defined as \begin{align*} V_{\lambda}^\delta(f)(z)= \left(\int_0^1 \lambda(t) \left({f(tz)}/{t}\right)^\delta dt\right)^{1/\delta}. \end{align*} The main aim of the present work is to find conditions on the related parameters such that $V_\lambda^\delta(f)(z)\in\mathcal{W}_{\beta_1}^{\delta_1}(\alpha_1,\gamma_1)$, whenever $f\in\mathcal{W}_{\beta_2}^{\delta_2}(\alpha_2,\gamma_2)$. Further, several interesting applications for specific choices of $\lambda(t)$ are discussed.

Abstract:
For $\alpha\geq 0$, $\beta<1$ and $\gamma\geq 0$, the class $\mathcal{W}_{\beta}(\alpha,\gamma)$ satisfies the condition \begin{align*} {\rm Re\,} \left( e^{i\phi}\left((1-\alpha+2\gamma)f/z+(\alpha-2\gamma)f'+ \gamma zf''-\beta\right)\frac{}{}\right)>0, \quad \phi\in {\mathbb{R}},{\,}z\in {\mathbb{D}}; \end{align*} is taken into consideration. The Pascu class of $\xi$-convex functions of order $\sigma$ $(M(\sigma,{\,}\xi))$, having analytic characterization \begin{align*} {\rm Re\,}\frac{\xi z(zf'(z))'+(1-\xi)zf'(z)}{\xi zf'(z)+(1-\xi)f(z)}>\sigma,\quad 0\leq \sigma< 1,\quad z\in {\mathbb{D}}, \end{align*} unifies starlike and convex functions class of order $\sigma$.The admissible and sufficient conditions on $\lambda(t)$ are investigated so that the integral transforms \begin{align*} V_{\lambda}(f)(z)= \int_0^1 \lambda(t) \frac{f(tz)}{t} dt, \end{align*} maps the function from $\mathcal{W}_{\beta}(\alpha,\gamma)$ into $M(\sigma,{\,}\xi)$. Further several interesting applications, for specific choice of $\lambda(t)$ are discussed which are related to the classical integral transform.

Abstract:
An optical network is a type of data communication network built with optical fibre technology. It utilizes optical fibre cables as the primary communication medium for converting data and passing data as light pulses between sender and receiver nodes. The major issue in optical networking is disjoints that occur in the network. A polynomial time algorithm Wavelength Division Multiplexing-Passive Optical Networking (WDM-PON) computes disjoints of an optical network and reduces the count of disjoints that occur in the network by separating Optical Network Units (ONU) into several virtual point-to-point connections. The Arrayed Waveguide Grating (AWG) filter is included in WDM-PON to avoid the traffic in the network thereby increasing the bandwidth capacity. In case of a failure or disjoint Ant Colony Optimization (ACO) algorithm is used to find the optimized shortest path for re-routing. For enhanced security, modified Rivert Shamir Adleman (RSA) algorithm encrypts the message during communication between the nodes. The efficiency is found to be improved in terms of delay in packet delivery, longer optical reach, optimized shortest path, packet error rate.

Abstract:
Distributed generators are beneficial in reducing the losses effectively compared to other methods of loss reduction. In this paper optimal DG unit placement using fuzzy logic is discussed. The optimal size of the DG unit is calculated analytically using approximate reasoning suitable nodes are determined for DG unit placement. Voltage and power loss reduction indices of distribution system nodes are modeled by fuzzy membership functions. Fuzzy inference system containing a set of rules is used to determine the DG unit placement. DG units are placed with the highest suitability index. Simulation results show the advantage of optimal DG unit placement compared optimal capacitor unit placement. Compared to capacitor placement it is giving very good reduction not only in power loss but also it is improving voltage regulation.

Abstract:
In this study midstream urine samples were collected from urinary tract infected patients to isolate and identify UTI causing bacterial pathogens by biochemical methods. The identified strains were two gram-positive and five gram-negative bacterium. Out of these we have selected one gram-negative (Staphylococcus aureus) and three gram-positive (Escherichia coli, Pseudomonas aeruginosa and Klebsiella pneumoniae) bacteria for current study. The antibacterial effect of aqueous, hexane, chloroform, ethyl acetate and methanol extracts of Avicennia marina against UTI pathogens were studied. Most effective three extracts of A. marina were treated with charcoal. Out of three extracts methanol was confirmed as tremendous to act against bacterial isolates and it was characterized at two different concentrations and compared with chemical based antibiotics. The stability and antimicrobial efficacy of the extract of A. marina in different parameters such as temperature, pH, enzyme, surfactant, organic solvent was determined. In summary, the extract showed an excellent stability and effectiveness to temperature 50°C, pH 4, enzyme treatment using protease, surfactant (EDTA) and organic solvent (formaldehyde).