Digital Generative Multimedia Tool Theory (DGMTT): A Theoretical Postulation

The development of digital technology has brought about a substantial evolution in the multimedia field.The use of generative technologies to produce digital multimedia material is one of the newer developments in this field.The“Digital Generative Multimedia Tool Theory”(DGMTT)is therefore presented in this theoretical postulation by Timothy Ekeledirichukwu Onyejelem and Eric Msughter Aondover.It discusses and describes the principles behind the development and deployment of generative tools in multimedia creation.The DGMTT offers an all-encompassing structure for comprehending and evaluating the fundamentals and consequences of generative tools in the production of multimedia content.It provides information about the creation and use of these instruments,thereby promoting developments in the digital media industry.These tools create dynamic and interactive multimedia content by utilizing machine learning,artificial intelligence,and algorithms.This theory emphasizes how crucial it is to comprehend the fundamental ideas and principles of generative tools in order to use them efficiently when creating digital media content.A wide range of industries,including journalism,advertising,entertainment,education,and the arts,can benefit from the practical use of DGMTT.It gives artists the ability to use generative technologies to create unique and customized multimedia content for its viewers.

On the Vacuum Hydrodynamics of Moving Bodies—The Theory of General Singularity

The Theory of General Singularity is presented, unifying quantum field theory, general relativity, and the standard model. This theory posits phonons as fundamental excitations in a quantum vacuum, modeled as a Bose-Einstein condensate. Through key equations, the role of phonons as intermediaries between matter, energy, and spacetime geometry is demonstrated. The theory expands Einsteins field equations to differentiate between visible and dark matter, and revises the standard model by incorporating phonons. It addresses dark matter, dark energy, gravity, and phase transitions, while making testable predictions. The theory proposes that singularities, the essence of particles and black holes, are quantum entities ubiquitous in nature, constituting the very essence of elementary particles, seen as micro black holes or quantum fractal structures of spacetime. As the theory is refined with increasing mathematical rigor, it builds upon the foundation of initial physical intuition, connecting the spacetime continuum of general relativity with the hydrodynamics of the quantum vacuum. Inspired by the insights of Tesla and Majorana, who believed that physical intuition justifies the infringement of mathematical rigor in the early stages of theory development, this work aims to advance the understanding of the fundamental laws of the universe and the perception of reality.

Poisson theory of generalized Bikhoff equations

This paper presents a Poisson theory of the generalized Birkhoff equations, including the algebraic structure of the equations, the sufficient and necessary condition on the integral and the conditions under which a new integral can be deduced by a known integral as well as the form of the new integral.

Quantum Gravity Based on Generalized Thermodynamics

This paper proposes a novel approach and simplified model of Quantum Gravity based on the unification framework of Generalized Thermodynamics which suggests cross-related terms and modified equations of General Relativity and Quantum Mechanics. To address the “background problem”, a metric tensor is introduced into stationary Schrödinger equations via curved coordinates yielding quantum spacetime variation term. Then quantum Lagrangian is added to Einstein-Hilbert functional yielding quantum stress-energy tensor. Obtained from one variational principle, two theories are linked by a common quantum spacetime field. The theory offers some interpretations of the quantum vacuum spacetime fluctuations, zero-point-fields, quantum fields shifting towards high spacetime densities, the quantum nature of spacetime, and black hole singularity.

Semigroup of Weakly Continuous Operators Associated to a Generalized Schrödinger Equation

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.

Group of Weakly Continuous Operators Associated to a Generalized Schrödinger Type Homogeneous Model

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study.

Assignment of terahertz vibrational modes of L-glutamine using density functional theory within generalized-gradient approximation

The crystal structure of L-glutamine is stabilized by a three-dimensional network of intermolecular hydrogen bonds.We utilize plane-wave density functional theory lattice-dynamics calculations within the generalized-gradient approximation（GGA）, Perdew–Burke–Ernzerhof（PBE）, PBE for solids（PBEsol）, PBE with Wu–Cohen exchange（WC）, and dispersion-corrected PBE, to investigate the effect of these intermolecular contacts on the absorption spectra of glutamine in the terahertz frequency range. Among these calculations, the solid-state simulated results obtained using the WC method exhibit a good agreement with the measured absorption spectra, and the absorption features are assigned with the help of WC. This indicates that the vibrational modes of glutamine were related to the combination of intramolecular and intermolecular motions, the intramolecular modes were dominated by rocking or torsion involving functional groups; the intermolecular modes mainly result from the translational motions of individual molecules, and the rocking of the hydrogenbonded functional groups.

GENERALIZED THEORY OF NONLINEAR AND UNSTEADY MECHANICS AND APPLICATIONS TO PARTICLE PHYSICS

In this paper we consider that the momentum of a free particle motion withhigh-level speed presenting nonlinear effects may be expanded by using Laurent seriesand then obtain the complete expression of nonlinear and unsteady momentum. These nonlinear and unsieady phenoniena of high-level speed may further expand to the theory of kinematics and it may be determined by Fredholm's integral equation of the first kind. In addition, according to the nonlinear and unsteady momentum obtained the relations of the nonlinear mechanics equations .work and energy, mass and energymay be derived.Finaly .this paper also calculates those experimental results which done in particle physics for mu-mesons u±and fast neutrons n, these results are in agreement with data perfectly.

Transient response of multilayered hollow cylinder using various theories of generalized thermoelasticity

The present paper deals with thermoelastic problems of finitely long hollow cylinder com-posed of two different materials with axial sym- metry. The medium is traction-free, with neglig-ible body forces and with internal and external heat generations. The governing equations for different theories of the generalized thermoe-lasticity are written in terms of displacement and temperature increment. The exact solution of the problem;using different theories of generalized thermoelasticity;has been deduced. The analytical expressions for displacements, temperature and stresses are found in final forms, and a numerical example has been taken to discuss the effect of the relaxation times. Finally, the results have been illustrated graphi- cally to find the responses of different theories.

Numerical verification of similar Cam-clay model based on generalized potential theory

From the mathematical principles, the generalized potential theory can be employed to create constitutive model of geomaterial directly. The similar Cam-clay model, which is created based on the generalized potential theory, has less assumptions,clearer mathematical basis, and better computational accuracy. Theoretically, it is more scientific than the traditional Cam-clay models. The particle flow code PFC3 D was used to make numerical tests to verify the rationality and practicality of the similar Cam-clay model. The verification process was as follows: 1) creating the soil sample for numerical test in PFC3 D, and then simulating the conventional triaxial compression test, isotropic compression test, and isotropic unloading test by PFC3D; 2)determining the parameters of the similar Cam-clay model from the results of above tests; 3) predicting the sample's behavior in triaxial tests under different stress paths by the similar Cam-clay model, and comparing the predicting results with predictions by the Cam-clay model and the modified Cam-clay model. The analysis results show that the similar Cam-clay model has relatively high prediction accuracy, as well as good practical value.

SOLUTION TO A PARAMETRIC EQUATION WITH GENERALIZED BOUNDARY CONDITION IN TRANSPORT THEORY

This paper deals with the solution of a parametric equation with generalized boundary condiiton in transport theory. It gives the distribution of parameter (so called delta-eigenvalue [1]) with which the equation has non-zero solution. A necessary and sufficient condition for the existence of; he control critical eigenvalue delta0 is established.

The Quantum Chromodynamics Gas Density Drop and the General Theory of Relativity Ether

β decay is one of the most fundamental and thoroughly studied nuclear decay. Surprisingly, the β decay rates were found to have a periodic time variability [1]. However, others argued that there is no evidence for such cyclic deviation from the exponential first order kinetics decay law [2]. Here we propose that the β decay is a pseudo-first order exchange reaction triggered by uddũexotic mesons and propose a QCD gas theory. In analogy to the atmospheric gas density, the proposed QCD gas density drops with elevation from the sun. Accordingly, we propose that the β decay rate periodic variability is due to the pseudo-first order exchange reaction kinetics and the QCD gas atmospheric density drop. The proposed QCD gas may be a possible candidate for Einstein’s general theory of relativity ether [3]. Our main results are the derived formulas for calculating the effective mass of the QCD gas and the cosmology perfect fluid equation of state dimensionless parameter, based on the measured ratio of the β decay rates at the earth trajectory aphelion and perihelion dates. .

About the Conflicts between the Unitary Quantum Theory and the Special and General Relativity Theories

The authors discuss contradictions between the principal branches of the modern physical picture of the universe. Space and time have been shown in the Unitary Quantum Theory (UQT) not to be connected one with the other, unlike in the Special Theory of Relativity. In UQT, time becomes Newtonian again, and the growth of the particle’s mass with growing speed proceeds from other considerations of physics. Unlike the quantum theory, the modern gravitation theory (the general theory of relativity) is not confirmed by experiments and needs to be considerably revised.

From Control Theory to Gravitational Waves

When D:ξ→η is a linear ordinary differential (OD) or partial differential (PD) operator, a “direct problem” is to find the generating compatibility conditions (CC) in the form of an operator D1:η→ξ such that Dξ = η implies D1η = 0. When D is involutive, the procedure provides successive first-order involutive operators D1,...,Dn when the ground manifold has dimension n. Conversely, when D1 is given, a much more difficult “inverse problem” is to look for an operator D:ξ→η having the generating CC D1η = 0. If this is possible, that is when the differential module defined by D1 is “torsion-free”, that is when there does not exist any observable quantity which is a sum of derivatives of η that could be a solution of an autonomous OD or PD equation for itself, one shall say that the operator D1 is parametrized by D. The parametrization is said to be “minimum” if the differential module defined by D does not contain a free differential submodule. The systematic use of the adjoint of a differential operator provides a constructive test with five steps using double differential duality. We prove and illustrate through many explicit examples the fact that a control system is controllable if and only if it can be parametrized. Accordingly, the controllability of any OD or PD control system is a “built in” property not depending on the choice of the input and output variables among the system variables. In the OD case and when D1 is formally surjective, controllability just amounts to the formal injectivity of ad(D1), even in the variable coefficients case, a result still not acknowledged by the control community. Among other applications, the parametrization of the Cauchy stress operator in arbitrary dimension n has attracted many famous scientists (G. B. Airy in 1863 for n = 2, J. C. Maxwell in 1870, E. Beltrami in 1892 for n = 3, and A. Einstein in 1915 for n = 4). We prove that all these works are already explicitly using the self-adjoint Einstein operator, which cannot be parametrized and the comparison needs no comment. As a byproduct, they are all based on a confusion between the so-called div operator D2 induced from the Bianchi operator and the Cauchy operator, adjoint of the Killing operator D which is parametrizing the Riemann operator D1 for an arbitrary n. This purely mathematical result deeply questions the origin and existence of gravitational waves, both with the mathematical foundations of general relativity. As a matter of fact, this new framework provides a totally open domain of applications for computer algebra as the quoted test can be studied by means of Pommaret bases and related recent packages.

Between Quantum Mechanics and General Relativity

The origin of elementary particle mass is considered as a function of n-valued graviton quanta. To develop this concept we begin in a cold region of “empty space” comprised of only microscopic gravitons oscillating at angular frequency ω. From opposite directions enters a pair of stray protons. Upon colliding, heat and energy are released. Customarily, this phase and what follows afterward would be described by Quantum Chromodynamics (QCD). Instead, we argue for an intermediary step. One in which neighboring gravitons absorb discrete amounts of plane-wave energy. Captured by the graviton, the planewave becomes a standing wave, whereupon its electromagnetic energy densities are converted into gravitational quanta. Immediately thereafter an elementary particle is formed and emitted, having both mass and spin. From absorption to conversion to emission occurs in less than 3.7 × 10−16 s. During this basic unit of hybrid time, general relativity and quantum physics unite into a common set of physical laws. As additional stray protons collide the process continues. Over eons, vast regions of spacetime become populated with low-mass particles. These we recognize to be dark matter by its effects on large scale structures in the universe. Its counterpart, dark energy, arises when the conversion of gravitational quanta to particle emission is interrupted. This causes the gravitational quanta to be ejected. It is recognized by its large scale effects on the universe.

A new four-dimensional hyperchaotic Chen system and its generalized synchronization

Based on the Chen chaotic system, a new four-dimensional hyperchaotic Chen system is constructed, and the basic dynamic behaviours of the system were studied, and the generalized synchronization has been observed in the coupled four-dimensional hyperchaotic Chen system with unknown parameters. The Routh Hurwitz theorem is used to derive the conditions of stability of this system. Furthermore based on Lyapunov stability theory, the control laws and adaptive laws of parameters are obtained to make generalized synchronization of the coupled new four-dimensional hyperchaotic Chen systems. Numerical simulation results are presented to illustrate the effectiveness of this method.

Adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions

The adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions is investigated in this paper. Based on Lyapunov stability theory and Barbalat＇s lemma, generalized matrix projective lag synchronization criteria are derived by using the adaptive control method. Furthermore, each network can be undirected or directed, connected or disconnected, and nodes in either network may have identical or different dynamics. The proposed strategy is applicable to almost all kinds of complex networks. In addition, numerical simulation results are presented to illustrate the effectiveness of this method, showing that the synchronization speed is sensitively influenced by the adaptive law strength, the network size, and the network topological structure.

Generalized Odd-Even Mode Theory and Mode Synthesis Antenna Design Approach

In this article,studies on the multimode excitation problem of waveguides and antennas,the balance/unbalance mech-anism and the balanced feeding techniques in dipole antenna systems are first briefly historically reviewed.In this context,general-ized odd-even mode theory is advanced to quantitatively and approximately describe the mutual coupling effect between a feed line and an antenna.As is mathematically deduced and demonstrated,the modal parity mismatch between the feed line and the antenna should ultimately dominate the unbalance phenomenon in antenna systems.Thus,an elegant,closed-form formula is derived to ap-proximately calculate the“unbalance degree”of a straight dipole off-center fed by a symmetric twin-wire line.Design approaches for the simplest,linear,1-D multimode resonant antennas are introduced.Moreover,the“falling tone excitation”law gauged based on prototype dipoles is revealed and used to develop a mode synthesis design approach for microstrip patch antennas(MPAs)and 2-D sectorial electric dipole antennas.Design examples with distinctive radiation performance are presented and discussed.Finally,possible development trends of multimode resonant antennas are prospected.

Generalized thermoelastic functionally graded spherically isotropic solid containing a spherical cavity under thermal shock

This paper is concerned with the determination of thermoelastic displacement, stress and temperature in a functionally graded spherically isotropic infinite elastic medium having a spherical cavity, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters （Green and Lindsay theory）. The surface of cavity is stress-free and is subjected to a time-dependent thermal shock. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. Numerical inversion of the transforms is carried out using the Bellman method. Displacement, stress and temperature are computed and presented graphically. It is found that variation in the thermo-physical properties of a material strongly influences the response to loading. A comparative study with a corresponding homogeneous material is also made.

Free vibration and critical speed of moderately thick rotating laminated composite conical shell using generalized differential quadrature method

The generalized differential quadrature method （GDQM） is employed to con- sider the free vibration and critical speed of moderately thick rotating laminated compos- ite conical shells with different boundary conditions developed from the first-order shear deformation theory （FSDT）. The equations of motion are obtained applying Hamilton＇s concept, which contain the influence of the centrifugal force, the Coriolis acceleration, and the preliminary hoop stress. In addition, the axial load is applied to the conical shell as a ratio of the global critical buckling load. The governing partial differential equations are given in the expressions of five components of displacement related to the points ly- ing on the reference surface of the shell. Afterward, the governing differential equations are converted into a group of algebraic equations by using the GDQM. The outcomes are achieved considering the effects of stacking sequences, thickness of the shell, rotating velocities, half-vertex cone angle, and boundary conditions. Furthermore, the outcomes indicate that the rate of the convergence of frequencies is swift, and the numerical tech- nique is superior stable. Three comparisons between the selected outcomes and those of other research are accomplished, and excellent agreement is achieved.