The “angle trisection-halting problem” impossibility analogy is fundamentally based on the obscure perception that; the classical geometric notion of constructability in Euclidean plane geometry corresponds to the modern theory of computability. Specifically, the difficulty of empirical trisectability of any angle has been viewed as analogous to the impossibility of solving the halting problem. The primary goal of this paper is to establish the inherent incompatibility between the geometric trisectioning of angles and the halting problem. The exposed proof concern the genetic solutions methodic characterization of the inconsistencies between the angle trisection problem and the halting problem. We show that regarding their attempts at solutions, the genetic trisectability of an arbitrary angle leads to solving the halting problem in geometric cryptographic schemes. It is upon the characteristic inconsistencies that we establish a provable refute of the validity of considering the practical applications of geometric cryptography as a solid source for cryptographic principles.

In a recent review paper related to energy storage, the authors noted that, in a bid to enhance the performance of the anode of a lithium-ion battery (LIB), that a part of the mechanism involved the ability of silicon (Si) and graphene oxide to bind, and that this process was aided by the ”mutual attraction of heterosexual charges” [1], a term or mechanism that was said to be derived from another paper [2]. A LIB, or any battery for that matter, does not have a bisexual, heterosexual or any sexual charge. It seems that this odd term and jargon neologism, or tortured phrase, was introduced as a result of mistranslation of an established term or jargon, ”opposite charges”. As such, it constitutes an error in need of correction. The wider implications for energy storage research such as LIBs, as well as for bibliometrics, are discussed.

The evolution of 4G networks has led to the development of different applications based on its powerful network capacity. Although, in the future with the presence of 5G (the fifth generation of network), the network of network, it is predicted that an incredible number of new services, with different business actors will be involved, are going to stem, exploit and explore. This paper briefly introduces the fifth generation of mobile network, 5G, in terms of capabilities, use cases and key enabling technologies, provides key concepts of information security, including availability, integrity and confidentiality. It also highlights the important of security in 5G landscape.

Methods to determine the environmental consequences of circular strategies may be a prerequisite for the circular economy. However, the weighting factors of the criteria groups in the international L.1023 circularity scoring standard need to be determined beforehand. No comprehensive analysis of the connection between carbon footprint based life cycle assessment (LCA) results – of the product to be evaluated and redesigned – and these weighting factors has been published. Here a method, based on lifetime reduction and Analytical Hierarchy Process (AHP), for establishing weighting factors in the L.1023 standard for circularity scoring of electronic goods (EEE), is presented. The scope of the present investigation is the life cycle of a generic EEE evaluated with the L.1023 standard, AHP and carbon emissions. Statistical hypothesis testing at the single circularity score level shows that for the EEE example, the chance of mistakenly favoring the redesigned alternative over the status quo when they are in reality indistinguishable can be as low as 0.6%.

This work is an in-depth study of the class of norm-attainable operators in a general Banach space setting. We give characterizations of norm-attainable operators on involutive stereotype tubes with algebraically connected component of the identity. In particular, we prove reflexivity, boundedness and compactness properties when the set of these operators contains unit balls with involution for the tubes when they are of stereotype category.

In this article we study the existence of periodic and strong solutions of Navier-Stokes equations, in two dimensions, with non-local viscosity.

In this paper we consider the following abstract class of weakly dissipative second-order systems with infinite memory, \(u”(t)+Au(t)-\displaystyle\int_{0}^{\infty} g(s)A^\alpha u(t-s)ds=0,~t>0,\) and establish a general stability result with a very general assumption on the behavior of \(g\) at infinity; that is \(g'(t) \leq – \xi(t) G \left(g(t)\right),~~t \geq 0.\) where \(\xi\) and \(G\) are two functions satisfying some specific conditions. Our result generalizes and improves many earlier results in the literature. Moreover, we obtain our result with imposing a weaker restrictive assumption on the boundedness of initial data used in many earlier papers in the literature such as the one in [1-5]. The proof is based on the energy method together with convexity arguments.

In this paper, we study the initial boundary value problem for a p-biharmonic parabolic equation with logarithmic nonlinearity. By using the potential wells method and logarithmic Sobolev inequality, we obtain the existence of the unique global weak solution. In addition, we also obtain decay polynomially of solutions.

In this paper, we investigate some properties of the \(AP\)-Henstock integral on a compact set and prove that the product of an \(AP\)-Henstock integrable function and a function of bounded variation is \(AP\)-Henstock integrable. Furthermore, we prove that the product of an \(AP\)-Henstock integrable function and a regulated function is also \(AP\)-Henstock integrable. We also define the \(AP\)-Henstock integral on an unbounded interval, investigate some properties, and show similar multiplier properties.

This paper consists of the results about \(\omega\)-order preserving partial contraction mapping using perturbation theory to generate a one-parameter semigroup. We show that adding a bounded linear operator \(B\) to an infinitesimal generator \(A\) of a semigroup of the linear operator does not destroy A’s property. Furthermore, \(A\) is the generator of a one-parameter semigroup, and \(B\) is a small perturbation so that \(A+B\) is also the generator of a one-parameter semigroup.