Abstract:
In this short article, we have studied the controllability result for neutral impulsive differential inclusions with nonlocal conditions by using the fixed point theorem for condensing multi-valued map due to Martelli [1]. The system considered here follows the P.D.E involving spatial partial derivatives with α-norms.

Abstract:
In this article, we study the exact controllability of an abstract model described by the controlled generalized Hammerstein type integral equation $$ x(t) = int_0^t h(t,s)u(s)ds+ int_0^t k(t,s,x)f(s,x(s))ds, quad 0 leq t leq T less than infty, $$ where, the state $x(t)$ lies in a Hilbert space $H$ and control $u(t)$ lies another Hilbert space $V$ for each time $t in I=[0,T]$, $T$ greater than 0. We establish the controllability result under suitable assumptions on $h, k$ and $f$ using the monotone operator theory.

Abstract:
A stronger concept of complete (exact) controllability which we call Trajectory Controllability is introduced in this paper. We study the Trajectory Controllability of an abstract nonlinear integro-differential system in the finite and infinite dimensional space setting. We will then discuss how approximations to these problems can be found computationally using finite difference methods and optimization. Examples will be presented in one, two and three dimensions.

Abstract:
Mathematical models based on advanced
differential equations are utilized to analyze the glucose-insulin regulatory
system, and how it affects the detection of Type I and Type II diabetes. In
this paper, we have incorporated several models of prominent mathematicians in
this field of work. Three of these models are single time delays, where either
there is a time delay of how long it takes insulin produced by the pancreas to
take effect, or a delay in the glucose production after the insulin has taken
effect on the body. Three other models are two-time delay models, and based on
the specific models, the time delay takes place in some sort of insulin
production delay or glucose production delay. The intent of this paper is to
use these multiple delays to analyze the glucose-insulin regulatory system, and
how if it is not properly working at any point, the high risk of diabetes
becomes a reality.

Abstract:
This paper discusses the mathematical
modeling for the mechanics of solid using the distribution theory of Schwartz
to the beam bending differential Equations. This problem is solved by the use
of generalized functions, among which is the well known Dirac delta function.
The governing differential Equation is Euler-Bernoulli beams with jump
discontinuities on displacements and rotations. Also, the governing
differential Equations of a Timoshenko beam with jump discontinuities in slope,
deflection, flexural stiffness, and shear stiffness are obtained in the space
of generalized functions. The operator of one of the governing differential
Equations changes so that for both Equations the Dirac Delta function and its
first distributional derivative appear in the new force terms as we present the
same in a Euler-Bernoulli beam. Examples are provided to illustrate the
abstract theory. This research is useful to Mechanical Engineering, Ocean
Engineering, Civil Engineering, and Aerospace Engineering.

Abstract:
Many single and three-phase converters are well developed, and covered up in most of electric markets. It is used in many applications in power systems and machine drives. However, an exact definite output signal from the dc side still not recognized. The waveforms of output voltage and current demonstrate an imperfect dc signal and constitute losses, harmonic distortion, low power factor, and observed some ripples. An approximately perfect rectifier bridge is the aim of this research. Perhaps it gives the ability to identify the parameters of the converter to obtain, as much as possible, a perfect dc signal with less ripple, high power factor and high efficiency. Design is implemented by simulation on Power Simulator PSIM, and practically, a series regulator LM723 is applied to provide regulating output voltage. Comparisons of both simulation and hardware results are made to observe differences and similarities.

The paper provides mathematical analysis of sensitivity of different combination rules in the DS/AHP method when an alternative is added to the set of decision alternatives while solving foresight problems. Different cases of rank reversals are defined and two sets of conditions for these cases using the method DS/AHP are considered. Rank reversals are illustrated when the DS/AHP method is used to solve practical problem of critical technologies of energy conservation and power efficiency evaluation in Ukraine. It is shown that the DS/AHP method is not sensitive to exclusion (or addition) of an irrelevant decision alternative from (or to) the set of decision alternatives.

Abstract:
One of the problems in the development of mathematical theory of the genetic code (summary is presented in [1], the detailed—to [2]) is the problem of the calculation of the genetic code. Similar problem in the world is unknown and could be delivered only in the 21st century. One approach to solving this problem is devoted to this work. For the first time a detailed description of the method of calculation of the genetic code was provided, the idea of which was first published earlier [3]), and the choice of one of the most important sets for the calculation was based on an article [4]. Such a set of amino acid corresponds to a complete set of representation of the plurality of overlapping triple gene belonging to the same DNA strand. A separate issue was the initial point, triggering an iterative search process all codes submitted by the initial data. Mathematical analysis has shown that the said set contains some ambiguities, which have been founded because of our proposed compressed representation of the set. As a result, the developed method of calculation was reduced to two main stages of research, where at the first stage only single-valued domains were used in the calculations. The proposed approach made it possible to significantly reduce the amount of computation at each step in this complex discrete structure.

Abstract:
The disclosure of many secrets of the genetic code was facilitated by the fact that it was carried out on the basis of mathematical analysis of experimental data: the diversity of genes, their structures and genetic codes. New properties of the genetic code are presented and its most important integral characteristics are established. Two groups of such characteristics were distinguished. The first group refers to the integral characteristics for the areas of DNA, where genes are broken down in pairs and all 5 cases of overlap, allowed by the structure of DNA, were investigated. The second group of characteristics refers to the most extended areas of DNA in which there is no genetic overlap. The interrelation of the established integral characteristics in these groups is shown. As a result, a number of previously unknown effects were discovered. It was possible to establish two functions in which all the over-understood codons in mitochondrial genetic codes (human and other organizations) participate, as well as a significant difference in the integral characteristics of such codes compared to the standard code. Other properties of the structure of the genetic code following from the obtained results are also established. The obtained results allowed us to set and solve one of the new breakthrough problems—the calculation of the genetic code. The full version of the solution to this problem was published in this journal in August 2017.

Abstract:
This work investigates in-depth the effects of variation of the compositional ratio of the absorber layer in Cu(In,Ga)Se2 (CIGS) thin-film solar cells. Electrical simulations were carried out in order to propose the most suitable gallium double-grading profile for the high efficiency devices. To keep the model as close as possible to the real behavior of the thin film solar cell a trap model was implemented to describe the bulk defects in the absorber layer. The performance of a solar cell with a standard CIGS layer thickness (2 μm) exhibits a strong dependence on the front grading height (decreasing band gap toward the middle of the CIGS layer). An absolute gain in the efficiency (higher than 1%) is observed by a front grading height of 0.22. Moreover, simulation results show that the position of the plateau (the region characterized by the minimum band gap) should be accurately positioned at a compositional ratio of 20% Ga and 80% In, which corresponds to the region where a lower bulk defect density is expected. The developed model demonstrates that the length of the plateau is not playing a relevant role, causing just a slight change in the solar cell performances. Devices with different absorber layer thicknesses were simulated. The highest efficiency is obtained for a CIGS thin film with thicknesses between 0.8 and 1.1 μm.