Stability of Perturbed Set Differential Equations Involving Causal Operators in Regard to Their Unperturbed Ones considering Difference in Initial Conditions

We investigate the stability of solutions of perturbed set differential equations with causal operators in regard to their corresponding unperturbed ones considering the difference in initial conditions (time and position) by utilizing Lyapunov functions and Lyapunov functionals.

IMPACT OF ENVIRONMENTAL CONTAMINANTS ON THE REPRODUCTION OF NON-TARGET INSECT DROSOPHILA MELANOGASTER

Recent researches show that Drosophila flies infertility is affected by Environmental contaminants, chemicals, Solid industrial wastes, heavy metals, Benzene. The rate of infertility of these flies is increasing day by day with the increase in industrialization and with the increasing use of pesticides, insecticides, and other harmful chemicals. Albeit different reasons have been theorized for the developing fruitlessness rate and mutation rate, ecological contaminants, and these synthetic substances are possibly significant causal operators related to this change. These substance pollutants are far and wide all through our current circumstance and presentation of these are avoidable nowadays on the Drosophila flies. The general commitment of natural and artificial contaminants, benzene, heavy metals, octopamine, and different perilous synthetics and mutagens to fruitlessness is known, and a few examinations including word occupational introduction, along with results from creature tests, recommend that ecological toxins antagonistically influence ripeness. We inspected the antagonistic impacts of natural introduction on the richness and related conceptive results. Natural impurities canvassed in this survey incorporate weighty metals, natural solvents, pesticides, and hormonal disturbing synthetics. It is trusted that this survey will feature the requirement for additional examination here. Here, in this study Drosophila is used as a model organism for testing the hazards of these environmental contaminants.

Method vs. Metaphysics

This article discusses Descartes’s preferred focus on morally and theologically neutral subjects and points out the impact of this focus on the scientific status of theology. It does so by linking Descartes’s method to his transformation of the notion of substance. Descartes’s Meditations centred around epistemological questions rather than non-human intelligences or the life of the mind beyond this world. Likewise, in his early works, Descartes consistently avoided referring to causal operators. Finally, having first redefined the notion of substance in the Principia, Descartes would completely abandon making use of this notion in his later years. Indeed, in contrast to many authors before and after him, Descartes never showed any interest in the long-established metaphysical interpretation of substances as being causal factors of natural change. With God, nature, and mind commonly serving as instances of substantial causality, Descartes’s philosophy had a huge impact on the place of God in science and discreetly excluded theology as a subject to which his method might be applied.

Impulsive Evolution Equations with Causal Operators

In this paper, we establish sufficient conditions for the existence of mild solutions for certain impulsive evolution differential equations with causal operators in separable Banach spaces. We rely on the existence of mild solutions for the strongly continuous semigroups theory, the measure of noncompactness and the Schauder fixed point theorem. We consider the impulsive integro-differential evolutions equation and impulsive reaction diffusion equations (which could include symmetric kernels) as applications to illustrate our main results.

On the solvability of causal functional inclusions with infinite delay

In the present article we develop the results of works devoted to the study of problems for functional differential equations and inclusions with causal operators, in case of infinite delay. In the introduction of the article we substantiates the relevance of the research topic and provides links to relevant works A. N. Tikhonov, C. Corduneanu, A. I. Bulgakov, E. S. Zhukovskii, V. V. Obukhovskii and P. Zecca. In section two we present the necessary information from the theory of condensing multivalued maps and measures of noncompactness, also introduced the concept of a multivalued causal operator with infinite delay and illustrated it by examples. In the next section we formulate the Cauchy problem for functional inclusion, containing the composition of multivalued and single-valued causal operators; we study the properties of the multiopera-tor whose fixed points are solutions of the problem. In particular, sufficient conditions under which this multioperator is condensing on the respective measures of noncompacness. On this basis, in section four we prove local and global results and continuous dependence of the solution set on initial data. Next the case of inclusions with lower semicontinuous causal multioperators is considered. In the last section we generalize some results for semilinear differential inclusions and Volterra integrodifferential inclusions with infinite delay.