Thermochromic Polymeric Films for Applications in Active Intelligent Packaging—An Overview

The need for passive sensors to monitor changes in temperature has been critical in several packaging related applications. Most of these applications involve the use of bar codes, inks and equipment that involve constant complex electronic manipulation. The objective of this paper is to explore solutions to temperature measurements that not only provide product information but also the condition of the product in real time, specifically shelf-life. The study will explore previously proposed solutions as well as plans for modified approaches that involve the use of smart polymers as temperature sensors.

ON THE UNIQUENESS VIOLATION OF THE DIRICHLET PROBLEM SOLUTION FOR SECOND-ORDER SYSTEMS

The study of the issues of the correct posedness of boundary value problems for differential equations and systems occupies an important place in modern research. When considering correctness, the question of unique solvability of this problem is of paramount importance. In particular, the problem of violation of the uniqueness of the solution of boundary value problems for general differential equations in bounded domains with algebraic boundary is of interest. The property of nontrivial solvability of the homogeneous Dirichlet problem for incorrectly elliptic equations of the second order was first pointed out by A. V. Bitsadze, having constructed an example of an equation with constant complex obtained a condition for the violation of the uniqueness of the solution to the Dirichlet problem in the unit disc for a hyperbolic equation in the case when the slope angles of the characteristics differ in sign. V. P. Burskii, considering the homogeneous Dirichlet problem in the unit disc for second-order equations with constant complex coefficients and a homogeneous non-degenerate symbol, obtained a criterion for nontrivial solvability in the form of π-irrationality of the angle between the characteristics. In this paper, we investigate the question of violation of the uniqueness of the solution of the homogeneous Dirichlet problem for a system of typeless second-order partial differential equations in a model domain – a circle. The original system is written in the form of an equation with commuting matrix coefficients. The permutability condition allows one to obtain a necessary and sufficient condition for the nontrivial solvability of the problem under consideration in the form of equality to zero of the determinant, the elements of which are expressed in terms of the coefficients of the equation. This form of writing the criterion allows one to construct examples of systems for which the kernel of the Dirichlet problem is nontrivial and infinite-dimensional. The study was based on the integral condition for the connection of associated boundary L-traces, as well as a functional scheme, the application of which reduces the expansion of a matrix function in a Fourier series to a standard expansion of each of its elements. A theorem of nontrivial solvability of the homogeneous Dirichlet problem is proved.

Julia Set with Trigonometric Function

Julia sets are generated by initializing a complex number z = x + yi where z is then iterated using the iteration function fc (z)= zn 2 + c, where n indicates the number of iteration and c is a constant complex number. Recently, study of cubic Julia sets was introduced in Noor Orbit (NO) with improved escape criterions for cubic polynomials. In this paper, we investigate the complex dynamics of different functions and apply the iteration function to generate an entire new class of Julia sets. Here, we introduce different types of orbits on cubic Julia sets with trigonometric functions. The two functions to investigate from Julia sets are sine and cosine functions.

Shifting in optoelectronic properties from pure K2O and Rb2O compounds to their V- and Cr-doped alloys

First principle calculations within the density functional theory (DFT) have been used in this approach to study the electronic and optical properties of vanadium (V) and chromium (Cr) doped K2O and Rb2O compounds. Based on the structure properties reported in our previous work, the study of electronic and optoelectronic properties of V- and Cr-doped K2O and Rb2O alloys have been vastly investigated. K2O and Rb2O are found to be semiconductors while their V- and Cr-alloys are metallic in nature. The optical functions like complex dielectric constant, complex index of refraction, absorption coefficient, and reflectivity of these alloys are computed and compared with those of pure K2O and Rb2O compounds. It has been shown that due to TM-doping (TM = V and Cr transition metals), many distinguished peaks appeared in the lower energy part (infrared) of the spectrum. The negative value of [Formula: see text] ([Formula: see text]) in this energy range confirmed the metallic behavior of these alloys. Furthermore, the frequency-dependent optical conductivity is also predicted in the entire spectrum, where it increases with increasing photon energy for all the studied alloys. The significant results of [Formula: see text] ([Formula: see text]) predict that all these compounds are useful in different optoelectronic applications in a wide part of the spectrum (between 13 eV and 27 eV).

Dynamics of quasiregular mappings with constant complex dilatation

The study of quadratic polynomials is a foundational part of modern complex dynamics. In this article, we study quasiregular counterparts to these in the plane. More specifically, let $h:\mathbb{C}\rightarrow \mathbb{C}$ be an $\mathbb{R}$-linear map and consider the quasiregular mapping $H=g\circ h$, where $g$ is a quadratic polynomial. By studying $H$ and via the Böttcher-type coordinate constructed in A. Fletcher and R. Fryer [On Böttcher coordinates and quasiregular maps. Contemp. Math.575 (2012), 53–76], we are able to obtain results on the dynamics of any degree-two mapping of the plane with constant complex dilatation. We show that any such mapping has either one, two or three fixed external rays, that all cases can occur and exhibit how the dynamics changes in each case. We use results from complex dynamics to prove that these mappings are nowhere uniformly quasiregular in a neighbourhood of infinity. We also show that in most cases, two such mappings are not quasiconformally conjugate on a neighbourhood of infinity.

IMAGING A NANOSTRUCTURE BY THE LYAPUNOV EXPONENT COMPUTATION

A model of the AFM (atomic force microscope) with certain tip-nanostructure interaction, cantilever elasticity and damping of its oscillations is proposed. Stable and unstable motion of the AFM tip interacting with the graphene sheet is investigated by the Lyapunov exponent computation. In our approximation, a hundred Si atoms (top of the AFM tip) interact with C atoms of the nanostructure. Тhis interaction is described by Lennard-Jones potential, and the distance between the top and the center of the cantilever mass is a constant. Complex influence of the initial tip-nanostructure distance and nanostructure size on stability has been examined. We discuss a possible new mode of the AFM operation based on the Lyapunov exponent computation. Maxima and minima of the Lyapunov exponent show where certain parts of the elementary cells are placed.

Spotting Environmental Drivers

The only constant in life is change, and business organizations are not different. Environmental uncertainties made transition to knowledge-based economies made establishment of effective CKM mechanisms within companies crucial to business competitiveness. This chapter examines the importance of business environmental conditions in driving an organizational change, viz. CKM. The basic premise of the chapter is that business organizations need to strive to adapt to opportunities as well as challenges brought by constant, complex, rapid, and discontinuous environmental uncertainties. In their quest for SCA, organizations need to leverage their DCCs in scanning environmental drivers for CKM as well as in the crafting a holistic CKM strategy.