Global Existence and Decay of Solutions for a Class of a Pseudo-Parabolic Equation with Singular Potential and Logarithmic Nonlocal Source

This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.

Simple and Pseudo Quadratic Leibniz Superalgebras

Compactness of subspaces of a Z2-graded vector space is introduced and used to study simple Leibniz superalgebras. We introduce left and right super-invariance of bilinear forms over superalgebras. Pseudo-quadratic Leibniz superalgebras are Leibniz superalgebras endowed with a non degenerate, supersymmetric and super-invariant bilinear form. In this paper, we show that every nondegenerate, supersymmetric and super-invariant bilinear form over a Leibniz superalgebra induce a Lie superalgebra over the underlying vector space. Then by using double extension extended to Leibniz superalgebras, we study pseudo-quadratic Leibniz superalgebras and the induced Lie superalgebras. In particular, we generalize some results on Leibniz algebras to Leibniz superalgebras.

Analysis of the Orbitation and Rotation of Celestial Bodies

We have developed a structure of dynamic knowledge for non-inertial systems, the so-called Theory of Dynamic Interactions (TDI) as a part of non-inertial dynamic knowledge, which incorporates a causal demonstration of phenomena accelerated by rotation, which would complement Classical Mechanics. We believe that the TDI mathematical model that we propose is of great conceptual importance. In addition, we think that it is not only necessary to understand the dynamics of rotating bodies, but also to understand the dynamics of the cosmos, with bodies that orbit and with constantly recurring movements, which make possible systems that have been in dynamic equilibrium for centuries and are not in a process of unlimited expansion. We even believe that this new dynamic theory allows us a better understanding of our universe, and the matter from which it is made.

Numerical Methods for Solving Logarithmic Nonlinear Schrödinger’s Equation

In this study, we will construct numerical techniques for tackling the logarithmic Schrödinger’s nonlinear equation utilizing the explicit scheme and the Crank-Nicolson scheme of the finite difference method. These schemes will be subjected to accuracy and stability tests before being used. Efficacy and robustness of the techniques under consideration will be demonstrated using an exact solution, one-Gausson, as well as conserved quantities. Interaction of two-soliton will be conducted. The numerical findings revealed, the interplay behavior is flexible.

Legendre Polynomial Kernel: Application in SVM

In machines learning problems, Support Vector Machine is a method of classification. For non-linearly separable data, kernel functions are a basic ingredient in the SVM technic. In this paper, we briefly recall some useful results on decomposition of RKHS. Based on orthogonal polynomial theory and Mercer theorem, we construct the high power Legendre polynomial kernel on the cube [-1,1]d. Following presentation of the theoretical background of SVM, we evaluate the performance of this kernel on some illustrative examples in comparison with Rbf, linear and polynomial kernels.

The Family of Exponential Attractors and Inertial Manifolds for a Generalized Nonlinear Kirchhoff Equations

In this paper, we study the long-time behavior of a class of generalized nonlinear Kichhoff equation under the condition of n dimension. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup related to the initial-boundary value problem are proved, and then the existence of its exponential attractor is obtained. By extending the space E0 to Ek, a family of the exponential attractors of the initial-boundary value problem is obtained. In the second part, we consider the long-time behavior for a system of generalized Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of a family of the inertial manifolds while such equations satisfy the spectrum interval condition.

The Light Timing Calculations of the Interferometer in the Quest to Detect Light Speed Anisotropy and a Case Study of the Michelson-Morley and Miller Mt Wilson Experiments

This paper formulates the light timing calculations for each interferometer arm;one that is parallel to the direction of motion of the interferometer through space and the other that is perpendicular. The calculations are done for a vacuum-mode interferometer and then for a gas-mode interferometer. The calculations show that no light timing difference is detectable in a vacuum-mode interferometer, but once an optical medium is present in the light path down the arms of the interferometer, this is no longer the case and a timing difference is detectable. Further to this, the timing equations obtained from the analysis are used to model the historical experiments of Michelson-Morley and Miller (Mt Wilson) and predictions are made by the model that accurately match the actual recorded results from those experiments. Thus, this timing analysis confirms that there is a light speed anisotropy in a reference frame that is moving through space, indicating the presence of a preferred Aether reference frame through which the Earth is moving.

Using a New Auxiliary Equation to Construct Abundant Solutions for Nonlinear Evolution Equations

In this paper, a new auxiliary equation method is proposed. Combined with the mapping method, abundant periodic wave solutions for generalized Klein-Gordon equation and Benjamin equation are obtained. They are new types of periodic wave solutions which are rarely found in previous studies. As m → 0 and m → 1, some new types of trigonometric solutions and solitary solutions are also obtained correspondingly. This method is promising for constructing abundant periodic wave solutions and solitary solutions of nonlinear evolution equations (NLEEs) in mathematical physics.

Generation of Hyperchaos from the LüSystem with a Sinusoidal Perturbation

This paper introduces a hyperchaotic system from the Lü system with a sinusoïdal perturbation. This hyperchaotic system has more complex dynamical behaviors, and can generate 2-scroll hyperchaotic attractor and 2-scroll chaotic attractor under different control parameters. Theoretical analyses and simulation are conducted to investigate the dynamical behaviors of the proposed hyperchaotic system by means of Lyapunov exponents, analysis of the bifurcation diagram and phase portraits.

Quantum of Space of the Universe—Correction of Previous Mistakes

A large number of scientific works, from ancient times to the present, have been dedicated to the search for “bricks” that make up the foundations of the material world. Justification of quantum of space parameters of the Universe is a complicated scientific problem, as its reliable information is unknown. Therefore, errors may appear in it, which must be corrected in a timely manner. In the latest works from this sphere, the quanta of the space of the Universe are replaced by hexahedral prisms instead of balls, which solves the problem of their dense packing. However, the mistake was the deformation of these prisms. The purpose of this work is to eliminate this deficiency. Its scientific novelty is the substantiation of the specified of refined parameters of the quantum of the space of the Universe on the basis of strict scientific provisions and the physical laws of nature. The solution to this problem is an urgent and important scientific and applied task, since it develops knowledge about the quantum foundations of the material world and the Universe as a whole. Research methods which used in this work: The performed work is based on the methods of deduction and induction in the research of the material world based on the application of the well-known reliable laws of physics and the general principles of the development of the theory of knowledge. Other research methods are still unknown, since the work performed is associated with new scientific discoveries, the search for which is difficult to formalize by known technique methods. Results and their discussion: The work is based on the hypothesis that was put forward that at the quantum-mechanical level of the material world, a longitudinal quantum shift by the wavelength λG and a transverse quantum shift by λG of the quantum of the Universe space is carried out in the time interval TG, which can be found on the basis of the Heisenberg uncertainty principle. The parameters obtained made it possible to clarify the length and shape of quanta of the space of the Universe, as well as the conditions for its rotation. It was also taken into account that the hexagonal prism of the circular quantum of the space of the Universe is composed of 6 trihedral prisms of elementary quanta of space. So she can be formed by 3 elements of real quark with a common top in the center of the prism, with the formation of 3 elements of virtual quark between them. In this case, a transverse shift by λG and a rotation of quarks by an angle of 2π/6 radians is performed without energy loss, only due to transformations of their real and virtual states. The totality of all the above transformations of quanta of the space of the Universe does not contradict previously known physical laws and regularities, which serves as the basis for confirming the scientific hypothesis put forward.

Effects of Small Permanent Charge on PNP Models

In this paper, a stationary one-dimensional Poisson-Nernst-Planck model with permanent charge is studied under the assumption that n - 1 positively charged ion species have the same valence and the permanent charge is small. By expanding the singular solutions of Poisson-Nernst-Planck model with respect to small permanent charge, the explicit formulae for the zeroth order approximation and the first order approximation of individual flux can be obtained. Based on these explicit formulae, the effects of small permanent charges on individual flux are investigated.

The Radar Cross Section Analysis of Radome Based on Conjugate Gradient Fast Fourier Transform

This paper presents an algorithm for analysis of the dielectric radomes. In this method, the radome is discretized by a regular grid with rooftop basic functions. The Volume Integral Equation (VIE) for 3D dielectric object is transformed to linear system by Galerkin’s testing formulation. Furthermore, the linear system is presented by Toeplitz matrix which can be solved by the Conjugate Gradient algorithm combined with Fast Fourier Transform (CG-FFT) iteratively. Also, the algorithm requires less computational complexity and memory. This paper simulates the mono-static Radar Cross Section of dielectric radome by the CG-FFT, which was validated against commercial software FEKO.

A Series Solution Approach to the Circular Restricted Gravitational Three-Body Dynamical Problem

The present manuscript examines the circular restricted gravitational three-body problem (CRGTBP) by the introduction of a new approach through the power series method. In addition, certain computational algorithms with the aid of Mathematica software are specifically designed for the problem. The algorithms or rather mathematical modules are established to determine the velocity and position of the third body’s motion. In fact, the modules led to accurate results and thus proved the new approach to be efficient.

Revisiting the Computation of Cohomology Classes of the Witt Algebra Using Conformal Field Theory and Aspects of Conformal Algebra

In this article, we revisit some aspects of the computation of the cohomology class of H2 (Witt, C)?using some methods in two-dimensional conformal field theory and conformal algebra to obtain the one-dimensional central extension of the Witt algebra to the Virasoro algebra. Even though this is well-known in the context of standard mathematical physics literature, the operator product expansion of the energy-momentum tensor in two-dimensional conformal field theory is presented almost axiomatically. In this paper, we attempt to reformulate it with the help of a suitable modification of conformal algebra (as developed by V. Kac), and apply it to compute the representative element of the cohomology class which gives the desired central extension. This paper was written in the scope of an undergraduate’s exploration of conformal field theory and to gain insight on the subject from a mathematical perspective.

Four Algorithms for Boundary Control with Breaking in Space and Time

Typically, active control systems either have a priori complete information about the boundary-value problem and damped waves before switching on, or get it during the measurement process or accumulate and update information online (identification process in adaptive systems). In this case, the boundary problem is completely imprinted in the information arrays of the control system. However, very often complete information about a boundary-value problem is not available in principle or this info is changing in time faster than the process of its accumulation. The article considers examples of boundary control algorithms based almost without any information. The algorithms presented in the article cannot be obtained within the framework of the harmonic representation of the problem by complex amplitudes. And these algorithms carry out fast control in microstructured boundary problems. It is shown that in some cases it is possible to find simple solutions if we remove restrictions: 1) on the spatio-temporal resolution of controlling elements of a boundary-value problem;2) on the high-frequency radiation of the controlled boundary.

Fundamental Fields as Eigenvectors of the Metric Tensor in a 16-Dimensional Space-Time

An alternative approach to the usual Kaluza-Klein way to field unification is presented which seems conceptually more satisfactory and elegant. The main idea is that of associating each fundamental interaction and matter field with a vector potential which is an eigenvector of the metric tensor of a multidimensional space-time manifold ?(n-dimensional “vierbein”). We deduce a system of field equations involving both Einstein and Maxwell-like equations for the fundamental fields. Confinement of the fields within the observable 4-dimensional space-time and non-vanishing particles’ rest mass problem are shown to be related to the choice of a scalar boson field (Higgs boson) appearing in the theory as a gauge function. Physical interpretation of the results, in order that all the known fundamental interactions may be included within the metric and connection, requires that the extended space-time is 16-dimensional. Fermions are shown to be included within the additional components of the vector potentials arising because of the increased dimensionality of space-time. A cosmological solution is also presented providing a possible explanation both to space-time flatness and to dark matter and dark energy as arising from the field components hidden within the extra space dimensions. Suggestions for gravity quantization are also examined.

Effects of Rotation on Turbulence Production

Direct numerical simulations (DNS) of non-rotating and rotating turbulent channel flow were conducted. The data base obtained from these DNS simulations was used to investigate the prominent coherent structures involved in the turbulence generation cycle. Predictions from three theoretical models concerning the formation and evolution of sublayer streaks, three-dimensional hairpin vortices and propagating plane waves were validated using visualizations from the present DNS data. Quadrant analysis was used to determine a phase shift between the fluctuating streamwise and wall-normal velocities as a characteristic of turbulence production in the suction region at a low rotation number.

Simulated and Experimental Study of Single Particle Measurement Using Inductively Coupled Plasma Mass Spectrometry

A droplet carrying particle is desolvation, vaporization, ionization, and diffusion in an inductively coupled plasma (ICP) to form a cloud of ions. It then is detected as a mass-spectrum peak of individual particle. The diameter of the particle is derived from its mass, which is calibrated using the peak area. This is the basic principle of measuring single particles using inductively coupled plasma mass spectrometry (ICP-MS). In this paper, a mathematical model describing single particles in plasma is investigated. This makes it possible to investigate the process and contributing factors of single particles measurement by ICP-MS. A series of processes are investigated, which include increasing the droplet temperature to the boiling point, desolvation of the droplets, increasing the particle temperature to the melting point, the particles are melted from a solid to the liquid, increasing the particle temperature to the boiling point, and particle vaporization. The simulation shows that both the atomic (ion) diffusion in the plasma and the incomplete vaporization of the particles are two important factors that limit the signal intensity of the particle’s mass spectrum. The experiment reveals that ICP-MS is very linear for Ag nanoparticles below 100 nm and SiO2 particles below 1000 nm. Both the simulation and experiment reveal the measurement deviation for large particles and that an increase of sampling depth can extend the diffusion time and cause signal suppression. The model can be used to study the mechanisms of monodispersed droplet or single-particle mass spectrometry, analyze the contributing parameters for single particle measurements by ICP-MS and provide a theoretical base for the optimization of single particle measurements in the practical application, such as nanoparticle devices, magnetic materials, biomedical materials additives and consumer products.

Particles Actually Represent the Names of Types of Waves

It is accepted that quantum mechanics (QM) describes motion of waves and particles. Therefore, we must use wave-particle duality (WPD), which is usually considered as one of the foundations of QM;however, WPD is well known as a self-contradictory concept. These contradictions insensibly spoil our subconscious thinking about the micro-world (MW). This article shows that known trials to solve these contradictions are erroneous. Quantum jumps (QJs) are shown to be very lame arguments for the real existence of particles. I offer rejecting the concept of particles and using their names as labels for types of corresponding waves. Thus, we can discard contradictions created by WPD. This approach is validated in the article by careful analysis of real calculation methods of quantum electrodynamics (QED). For the first time, it is noticed that proper 4-coordinates of particles are not in use in real calculations in QED. This implies that particles do not take part in real calculations, which describe properties of atoms and molecules. It follows that particles do not exist as such. Therefore, we must acknowledge that we actually use the names of “particles” merely as names of types of given waves, but not as real, physical objects.

Controlled Fusion Strategy Using Ultra-Intense Laser Derived Positron Generation for Initiation

A controllable strategy for eliciting nuclear fusion is presented through ultra-intenselaser derived positron generation by a conceptual first physics perspective. The capability to generate positrons on demand in a controlled manner through an ultra-intense laser incident on a high atomic number target, such as gold, is the intrinsic core to the foundation of controllable nuclear fusion. Positron antimatter generated from the periphery of the fusion fuel pellet provides the basis for initiating the fusion reaction, which is regulated by controlling the operation of the ultra-intense laser. A dual pulsed Fast Ignition mechanism is selected to achieve the fusion reaction. Based on first physics performance analysis the controllable strategy for eliciting nuclear fusion through ultra-intenselaser derived positron generation offers a realizable means for achieving regulated nuclear fusion. A future perspective of the controllable fusion strategy addresses the opportunities and concerns of a pathway toward regulated nuclear fusion.