Fermat’s principle and the effect of jerk on light motion near the Sun

In classical mechanics, in the case of gravitational and electromagnetic interactions, the force on a particle is usually proportional to its acceleration: The force acts locally on the particle. However, there are situations possible-if the particle moves through a suitable medium, for example, in which the force depends also on the first-time derivative of its acceleration, the jerk, and on its second-time derivative, the snap, and possibly also on higher-time derivatives. Such forces are called nonlocal, and this work investigates such nonlocal forces, mainly those depending on the jerk. In particular, we implement jerk and acceleration in geodesics by means of the nonlocal-in-time kinetic energy approach to spacetime physics. We describe a framework that can be used to estimate the quantum nonlocal time parameter by studying the deflection of light around the Sun. Comparing our results with long baseline interferometry (VLBI) observations, we concluded that the nonlocal time parameter [Formula: see text] s.

Throughput Performance of A Delay Constraint Transmission For Half-Duplex And Full-Duplex Cognitive Relay Networks

The performance of a relay based Half-Duplex (HD) and Full-Duplex (FD) cooperative cognitive radio (CR) network with a RF energy harvesting (EH) is studied in this paper. Co-operative environment includes a network with multiple primary users (PUs), and CRs. The relay node is considered as an EH node which harvests energy (HE) from RF signal (RFS) of source and loop-back interference. The network performance is studied for instantaneous transmission and delay constraint transmission for decode and forward (DF) relaying protocol. The performance is investigated under a relay energy outage constraint and the expression of throughput is redesigned. Expressions of energy outage, data outage and throughput for HD and FD are developed. The impact of several parameters such as transmitting SNR, fractional harvesting time parameter, fractional transmission time parameter, and loop-back interference on the system throughput has been investigated.

Substantiating the pulse method for determining the time parameter of fire detectors with a thermoresistive sensing element

This paper substantiates the pulse method for determining the time parameter for fire detectors with a thermoresistive sensing element ‒ the time constant. The method is based on using the Joule-Lenz effect, which manifests itself when an electric current pulse passes through the thermoresistive sensing element of fire detectors. Thermal processes in such a sensing element are described by a mathematical model that belongs to the class of equations of mathematical physics. The solution to the differential equation of this class was derived using the Hankel integral transformation and is represented as a series relative to the Bessel functions. The resulting solution is used to construct a mathematical model of a thermoresistive sensing element in the form of a transfer function, which takes the form of the transfer function of the inertial link. To trigger the thermoresistive sensing element of fire detectors, a single pulse of electric current in the shape of a rectangular triangle is used. The integral Laplace transformation was applied to mathematically describe the response of a thermoresistive sensing element to the thermal effect of such a test influence. To obtain information about the time parameter of fire detectors with a thermoresistive sensing element, the ratio of its output signals is used, which are measured in the a priori defined moments. A two-parametric expression was built to determine the time parameter of fire detectors; a verbal interpretation of the pulse method to determine it was provided. The implementation of this method ensures the invariance of the time parameter of fire detectors with a thermoresistive sensing element relative to the amplitude of a single pulse of an electric current, as well as relative to the parameter that is included in its transfer coefficient.

Structure as an innovation

The purpose of the chapter is to present basic theoretical fundaments in the field of structurally significant formations that companies apply in the process of their business operations, market projections and innovative changes. Organizational forms and structures are presented in the evolutionary context of the time parameter, applying a chronological historical landmark. Knowledge of the variety of possibilities for structural dimensions of the functional manifestations of business activity provides an expanded range of possible solutions. Basic definition formulations are considered. The emphasis is on the organization and organizational structural forms, changes in their practical dimensions in accordance with the changes in purely managerial knowledge and the needs of business practice for innovative changes in various functions in the scope of company’s activity. With the help of various creative and purely managerial approaches, through cognitive brainstorming activities, a set of analytical, inductive-deductive, case and simulation methods, students gain new knowledge, practical skills and visionary views on the presented issues—by combining theoretical statements, empirical factology and analytical assignments based on the principle of learning by doing. The topic draws students’ attention to the study, selection and construction of internal units and structures, including innovative ones, as part of the necessary business projections for the construction of sustainable processes to generate new value and positive impacts for the environment and stakeholders.

Maximal regularity and a singular limit problem for the Patlak–Keller–Segel system in the scaling critical space involving BMO

We consider a singular limit problem of the Cauchy problem for the Patlak–Keller–Segel equation in a scaling critical function space. It is shown that a solution to the Patlak–Keller–Segel system in a scaling critical function space involving the class of bounded mean oscillations converges to a solution to the drift-diffusion system of parabolic-elliptic type (simplified Keller–Segel model) strongly as the relaxation time parameter $$\tau \rightarrow \infty $$ τ → ∞ . For the proof, we show generalized maximal regularity for the heat equation in the homogeneous Besov spaces and the class of bounded mean oscillations and we utilize them systematically as well as the continuous embeddings between the interpolation spaces $$\dot{B}^s_{q,\sigma }({\mathbb {R}}^n)$$ B ˙ q , σ s ( R n ) and $$\dot{F}^s_{q,\sigma }({\mathbb {R}}^n)$$ F ˙ q , σ s ( R n ) for the proof of the singular limit. In particular, end-point maximal regularity in BMO and space time modified class introduced by Koch–Tataru is utilized in our proof.

Non-linear creep of polypropylene utilizing multiple integral

<p>Multiple integral representation (MIR) has been used to represent studying the effect of temperature on the amount of nonlinear creep on the semi- crystalline polypropylene (PP) under the influence of axial elastic stress. To complete this research, the Kernel functions were selected, for the purpose of performing an analogy, and for arranging the conditions for the occurrence of the first, second and third expansion in a temperature range between 20 °C-60 °C, i.e., between the glass transition and softening temperatures, within the framework of the energy law. It was observed that the independent strain time increased non-linearly with increasing stress, and non-linearly decreased with increase in temperature, although the time parameter increased non-linearly with stress and temperature directly. In general, a very satisfactory agreement between theoretical and practical results on the MIR material was observed.</p>

TEMPERATURE ERROR WHEN DETERMINING THE TIME PARAMETER OF A FIRE DETECTOR WITH A THERMORESISTIVE SENSITIVE ELEMENT

For fire detectors with a thermoresistive sensing element, a mathematical description of the reaction to the thermal action of an electric current pulse flowing through such a sensing element and having the shape of a right triangle is obtained. The mathematical description is constructed using the Laplace integral transformation and is shown to be a superposition of two Heaviside functions. The parameters of these functions are determined by the transmission coefficient and time constant of the thermoresistive sensitive element of the fire detector and the amplitude and duration of the electric current pulse. It is shown that the ratio of the output signals of the thermoresistive sensitive element of the fire detector at two a priori given moments of time can be used to determine the time parameter of the fire detector. The values ​​of a priori set moments of time, in which the temperature of the thermoresistive sensitive element of the fire detector is determined, are selected under the condition of simplicity of technical implementation. If there is a change in ambient temperature, it leads to a temperature error as a function of the time parameter of the fire detector. For such an error, a mathematical description is obtained in the general case, as well as for the case when the thermal influence on the thermoresistive sensitive element of the fire detector is due to the flow of an electric current pulse in the form of a right triangle. It is shown that the value of the temperature error has a minimum at the values ​​of the ratio of the output signals of the thermoresistive sensitive element of the fire detector at two a priori time points belonging to the range The value of this error does not exceed 4.9% with variations in ambient temperature, the value of which does not exceed 2.0%.

The coupled gravity of straight space-time and uncertainty principle

This article points out that when the boundary condition $\frac{T}{T_{c}}=z$ (when z is a complex number) is preset, bosons can produce Bose condensation without an energy layer. Under Bose condensation, incident waves may condense in various black holes in the theory of loop quantum gravity. This paper shows that under the gravitational subsystem composed of two bosons, the extreme value of the measurement uncertainty principle can be smaller because the probability flow density is related to the time parameter. This is a model to verify the existence of gravitons.