Abstract: Renewable energy has an enormous importance for social development and it access to energy which is closely linked with economic uplift of the community. The oil-containing seeds of Jatropha curcas plant, a shrub prevalent in many countries, were recently rediscovered as a possible feedstock for biodiesel production. Jatropha plants is affected by many type of pest, among them there are some major pests (less than ten type) which are responsible for flower and fruit abortion. Nuclear Polyhedrosis Virus (NPV) are belonging to the family of Baculovirus, which are often host specific and usually fatal for the pests invading Jatropha crop. This virus spreads among the pest only and the infected pest can replicate virus. The predator consumes the infected prey only due to tradeoff cost which is beneficial to the plant irrespective of the degree of infection. Taking account of the ecological and functional relation among the pest, predator, virus and the plant, we formulate a five dimensional nonlinear system for Jatropha pest management with application of viral pesticide and extermination of natural pest of Jatropha. In the present work we applied the pesticide in a singlefoliar application and notice that the pest extermination is not fully achieved. Hence, we apply the same pesticide in a periodic interval till pest exist in the system. We hypothesize that impulsively spraying of viral pesticide may help to eradicate the pest of Jatropha. Our model is rigorously tested under strict analytical and numerical exploratory analysis reveals the short periodic application of pesticide is most beneficial for the health of the plant. The numerical results are also supported by our analytical findings.

Abstract: The effect of throughflow and temperature modulation on rotating porous medium is investigated. Weakly nonlinear flow model is considered to study heat transfer with oscillatory mode of convection. Heat transfer is measured in terms of the Nusselt number, which is governed by the non-autonomous complex Ginzburg-Landau equation. Both concepts of rotation and throughflow are used as an external mechanism to regulate heat transfer. The amplitude and frequency of modulation show significant effect on heat transport. Throughflow has duel effect on heat transfer depending its direction. The outflow enhances and inflow diminishes the heat transfer. Similarly high rotation rates promotes heat transfer and low rotation rates diminish heat transfer. Further, the effect of modulation on mean Nusselt number is discussed. The results computed numerically using Runge-Kutta-Fehlberg Method.

Abstract: The objective of the manuscript is to minimize the set of sufficient conditions for triple triangle matrices by using sequence space $A_k$ and the concept of absolutely $k^{th}$ power conservative of matrix. Hence, we gave a generalized theorem on an absolute summability factor with sufficient conditions. In this theorem, we prove the boundness of lower triangle infinite matrix (having non-zero principal diagonal entries) on $A_k^3$ i.e. T $\in B(A_k^3)$.

Abstract: In this paper we study the existence of solutions for some strongly nonlinear Dirichlet problems with natural growth condition on the non-linearity and $L^1$ data in the context of Musielak spaces, we also give a proof of a Poincare-type inequality in these spaces.

Abstract: This aim of this paper is threefold. A survey of trigonometric-hyperbolic function methods for constructing solitary wave solutions of nonlinear equations. Further analysis of the sine-Gordon expansion method. Studying the solution of the generalized PHI-four equation and the generalized regularized long wave equation by using a special transformation derived from the Sine-Gordon equation.

Abstract: In this article, a new method called the Natural Decomposition Transform Method (NDTM) is introduced. We use this method to obtain exact solutions for three different types of nonlinear partial differential equations (NLPDEs). The NDTM is based on the Natural transform method (NTM) and the Adomian decomposition method (ADM). The theoretical analysis of the NDTM is investigated for some equations and is calculated with easily computable terms. The results we obtained are compared with existing solutions obtained by other methods. One can conclude that the method is easy to use and efficient. Most of the symbolic and numerical computations were performed using Mathematica software.

Abstract: Control of chemical processes in presence of strong online nonlinearities and extreme sensitivity to disturbances is a major challenge. For the successful operation of any complex chemical process, it is desirable to understand its dynamic characteristics. A good understanding of the dynamics of chemical processes effectively results in efficient control system design. The controller designed for nonlinear complex chemical processes should have the capability to supress the effect of practical variations that occur in the process. One of the most common choice is PID (Proportional Integral Derivative) controller, but PID controller finds it difficult to deal with the perturbations that appear in complex nonlinear processes. This paper presents cascade control methodology for the control of a nonlinear exothermic chemical reactor. Continuous Stirred Tank Reactors (CSTR) are the example of complex nonlinear dynamical chemical reactor systems which are used in chemical industries.

Abstract: In this paper, we study the existence of approximate controllability of random impulsive semilinear control system under sufficient condition with non-densely defined system Finally, examples are given to illustrate the applications of the abstract results

Abstract: In this paper, a new analytical method to linear and nonlinear partial differential equation called the Natural Homotopy Perturbation Method (NHPM) is introduced. The new analytical method is a combination of the Natural Transform Method (NTM) and a well known analytical method, Homotopy Perturbation Method (HPM). The proposed analytical method avoids round off errors, linearization, transformation or taking some restrictive assumptions. Exact solution of linear and nonlinear partial differential equation are successfully obtained using the new analytical method, and the results are compared with the results of the existing methods. The high simplicity, efficiency, and accuracy of the new analytical method are clearly demonstrated.

Abstract: This paper is mainly concerned the global asymptotic stability of the zero solution of a class of nonlinear neutral differential equations in C¹. By converting the nonlinear neutral differential equation into an equivalent integral equation, our main results are obtained via the Banach contraction mapping principle, which generalize the work of Liu and Yan l .

Abstract: In this paper, we prove the existence and uniqueness of integral solutions for non-densely defined impulsive Volterra integrodifferential equations with infinite delay by using the theory of integrated semigroup and fixed point theorems. Further, we give an example in support of the abstract results we obtained.

Abstract: In epidemiology or in eco-epidemiology, the mode of disease transmission is one of the most important factors, and the rate is highly influenced by seasonal factors like temperature, rainfall, humidity, etc. These environmental factors are likely to be of time periodic. Seasonality in effective contact rate is common in natural population, and less efforts are being paid so far on the eco-epidemiological systems. The present investigation aims at to study the dynamics by changing the constant transmission rate into periodic transmission rate. The basic reproduction number (R0) in periodic environment is analytically derived by spectral radius and thereby the conditions of the persistence, and the extinction of a disease are derived in terms of basic reproduction numbers. The conditions for existence of positive periodic solution and its global stability are also derived analytically. Numerical simulations are carried out to illustrate the analytical findings. Our main findings are that the periodic transmission rate plays an important role in the persistence and the recurrence of a disease in the population.

Abstract: — For fractional order systems that their measurements have multiple time delay, the discrete time Fractional Kalman Filter (FKF) is developed. Reorganized innovation approach is extended for converting the multiple time delay measurement to delay-free system. Then, the optimal solution is obtained by solving the discrete Riccati equation. A numerical example is given to clarify the efficiency of the proposed scheme.

Abstract: Let $G=(V,E)$ be a graph, $k$ is a positive integer and let $S=(U,X)$ be a semigraph. A subset $D\subseteq V$ is called a $k-$strong(weak) dominating set of the graph $G$ if every vertex $v\in V-D$ is strongly(weakly) dominated by at least $k$ vertices of $D$. The $k-$strong(weak)domination number $\gamma_k^s ~(\gamma_k^w)$ is the minimum cardinality of $k-$strong(weak) dominating set of $G$. A subset $D \subseteq U$ is called $k-$ strong(weak) adjacent dominating set of semigraph $S$ if every vertex $u\in U-D$ is strongly(weakly) adjacent dominated by at least $k$ vertices of $D$. The minimum cardinality of a $k-$ strong adjacent dominating set, a $k-$ weak adjacent dominating set are respectively denoted as $\gamma_k^{s,a}(S)$ and $\gamma_k^{w,a}(S)$. In this paper, we determine $\gamma_k^s $ and $\gamma_k^w $ for standard graphs. Also, we establish bounds on the above domination parameters for graphs and semigraphs. We prove that the $k-$strong(weak) domination problem is NP-complete for general graphs.

Abstract: This paper deals with the unsteady free convection and mass transfer boundary layer flow past accelerated infinite vertical porous flat plate with suction. The velocity field, temperature field and concentration distribution have been solved analytically by using Homotopy analysis method. The flow phenomenon has been characterized with the help of flow parameters such as suction parameter , porosity parameter , Grashof number , Schmidt number and Prandlt number . The analytical results are presented graphically. This type of problem is significantly relevant to geophysical and astrophysical studies.

Abstract: This paper deals with the effect of mass and radiative heat transfer on free convective flow of a viscous incompressible optically thick fluid towards a vertical surface has been investigated. The nonlinear non-dimensional, similarity-transformed boundary-layer equations of the problem are solved analytically. The resulting equations are solved analytically by using Homotopy analysis method. The velocity field, temperature field and concentration distribution have been discussed and the analytical results are presented graphically. This type of problem is significantly relevant to geophysical and astrophysical studies.

Abstract: An Analytical Modular Dynamics (AMD) model of tree stand growth with discounting is investigated using KCC-Theory. Jacobi stability of carbon production is proved. A formal (DEBT) energy expression for the seasonal carbon cycle, obtained and data from the Serto of Northeastern Brazil, is utilized to calibrate the model

Abstract: With the rapid growth of smartphones and music gadgets, various companies exploit the user needs towards music by various cloud-based music platforms. In this article log- based recommendation system is proposed, in which recommendation is done using locally stored log files. The system is capable of recommending the next most suitable song. In this research considering MP3 ID3 format for dynamic playlist generation. The results of experiments conducted on MP3 ID3 song dataset accurately generate song playlist and satisfactorily update log file for the specific user and it leads to higher performance of the system. Moreover, the demonstrated log based recommender system can be applied to various other similar domains like movies, books, news recommendation.

Abstract: This paper investigates the existence of the equilibriums, their stability and possible bifurcations in a longitudinal flight with constant forward velocity and high angle of attack. The theoretical framework is the general mathematical model describing the movements of a rigid aircraft around its center of mass [1]. Necessary or sufficient conditions concerning the existence of equilibriums, their stability and possible bifurcations are given. The analysis follows and extends the results reported in the paper [2]. Numerical illustrations are given.

Abstract: Main aim of present paper is to survey results on multiplicative perturbation of generators of continuous & analytic semi-groups in Hilbert and Banach spaces. Few open problems in that direction are suggested. We as well mention a partial integro-differential equation of age dependent population dynamics, which leads to a problem in multiplicative perturbation of generators of analytic semi-group.

Abstract: The concept of L-limited set is used to characterize several classes of operators. As consequence, we give a dual characterisation of the Dunford-Pettis* property of a Banach space (resp., weak Dunford-Pettis* of a Banach lattice).