Search

In this work, we revise the concept of foliation and related aspects that are crucial when formulating the Hamiltonian evolution for various theories beyond General Relativity. In particular, we show the relation between the kinematic characteristics of timelike congruences (observers) and the existence of foliations orthogonal to them. We then explore how local Lorentz transformations acting on observers affect the existence of transversal foliations, provide examples, and discuss the implications of these results for the 3 + 1 formulation of tetrad modified theories of gravity. [ABSTRACT FROM AUTHOR]

The method presented in this paper is developed to assess the parameters (the application moment and the magnitude of a velocity impulse) of a maneuver-like perturbation of motion of the center of mass of a spacecraft in a near-circular orbit. The assessment is based on the information on the spacecraft's trajectory before the maneuver and the optical observations of the spacecraft's angular position (right ascension and declination angles) after the maneuver. This study considers the cases of solely transversal (in-track) or transversal and radial components of the velocity increment vector. A single pair of the values of angles is used for the assessment of the single transversal maneuver parameters and two pairs are used in the other cases. The method also makes it possible to estimate the parameters of a continuous maneuver performed with low-thrust engines. For this case the property of its symmetry is used. The approach described in this article makes it possible to determine the spacecraft's orbit after the maneuver much faster and more accurately in comparison to traditional methods. [ABSTRACT FROM AUTHOR]

With the rapid growth in the penetration rate of mobile devices and the surge in demand for mobile data services, small cells and mobile backhaul networks have become the critical focus of next-generation mobile network development. Backhaul requirements within current wireless networks are almost asymmetrical, with most traffic flowing from the core to the handset, but 5G networks will require more symmetrical backhaul capability. The deployment of small cells and the placement of transceivers for cellular phones are crucial in trading off the symmetric backhaul capability and cost-effectiveness. The deployment of small cells is related to the placement of transceivers for cellular phones. Chang, Kloks, and Lee transformed the placement problem into the maximum-clique transversal problem on graphs. From the theoretical point of view, our paper considers the parameterized complexity of variations of the maximum-clique transversal problem for split graphs, doubly chordal graphs, planar graphs, and graphs of bounded treewidth. [ABSTRACT FROM AUTHOR]

We investigate the behavior of the solutions of the ray equation in isotropic media. We discuss local and global transversals and wavefronts and give examples of rays without wavefronts. [ABSTRACT FROM AUTHOR]

Originally conceived as a thought experiment, an apparatus consisting of two Stern–Gerlach apparatuses joined in an inverted manner touched on the fundamental question of the reversibility of evolution in quantum mechanics. Theoretical analysis showed that uniting the two partial beams requires an extreme level of experimental control, making the proposal in its original form unrealizable in practice. In this work, we revisit the above question in a numerical study concerning the possibility of partial-beam recombination in a spin-coherent manner. Using the Suzuki–Trotter numerical method of wave propagation and a configurable, approximation-free magnetic field, a simulation of a transversal Stern–Gerlach interferometer under ideal conditions is performed. The result confirms what has long been hinted at by theoretical analyses: the transversal Stern–Gerlach interferometer quantum dynamics is fundamentally irreversible even when perfect control of the associated magnetic fields and beams is assumed. [ABSTRACT FROM AUTHOR]

Locally strictly convex surfaces in four-dimensional affine space are studied from a perspective of the affine structure invented by Nuño-Ballesteros and Sánchez, which is especially suitable in convex geometry. The surfaces that are embedded in locally strictly convex hyperquadrics are classified under assumptions that the second fundamental form is parallel with respect to the induced connection and the normal connection is compatible with a metric on the transversal bundle. Both connections are induced by a canonical transversal plane bundle, which is defined by certain symmetry conditions. The obtained surfaces are always products of an ellipse and a conical planar curve. [ABSTRACT FROM AUTHOR]

The paradigm shift prompted by Zadeh's fuzzy sets in 1965 did not end with the fuzzy model and logic. Extensions in various lines have produced e.g., intuitionistic fuzzy sets in 1983, complex fuzzy sets in 2002, or hesitant fuzzy sets in 2010. The researcher can avail himself of graphs of various types in order to represent concepts like networks with imprecise information, whether it is fuzzy, intuitionistic, or has more general characteristics. When the relationships in the network are symmetrical, and each member can be linked with groups of members, the natural concept for a representation is a hypergraph. In this paper we develop novel generalized hypergraphs in a wide fuzzy context, namely, complex intuitionistic fuzzy hypergraphs, complex Pythagorean fuzzy hypergraphs, and complex q-rung orthopair fuzzy hypergraphs. Further, we consider the transversals and minimal transversals of complex q-rung orthopair fuzzy hypergraphs. We present some algorithms to construct the minimal transversals and certain related concepts. As an application, we describe a collaboration network model through a complex q-rung orthopair fuzzy hypergraph. We use it to find the author having the most outstanding collaboration skills using score and choice values. [ABSTRACT FROM AUTHOR]