In this note we extend a 2018 result of Bardos and Titi \cite{BT} to a new class of functional spaces $C^{0,α}_λ(\barΩ)$. It is shown that weak solutions $\,u\,$ satisfy the energy equality provided that $u\in L^3((0,T);C^{0,α}_λ(\barΩ))$ with...
The Hayward metric is a spherically symmetric charged regular black holes, a modification of the Reisnner-Nordstr$\ddot{o}$m black holes of Einstein's equations coupled to nonlinear electrodynamics. We consider Einstein-Gauss-Bonnet gravity (EGB) cou...
We propose and solve exactly the Schrödinger equation of a bound quantum system consisting in four particles moving on a real line with both translationally invariant four particles interactions of Wolfes type \cite{Wolf74} and additional non transl...
We conjecture that (when the notion of Hadamard state is suitably adapted) there is no isometry-invariant Hadamard state for the massive or massless covariant Klein-Gordon equation defined on the region of the Kruskal spacetime to the left of a surfa...
The KIDS framework for the nuclear equation of state (EoS) and energy density functional (EDF) offers the possibility to explore systematically the effect of EoS parameters on predictions for a variety of observables. The EoS parameters can be varied...
This article provides a discussion on the construction of conformal Gaussian gauge systems to study the evolution of solutions to the Einstein field equations with positive Cosmological constant. This is done by means of a gauge based on the properti...
We study the propagation, observation and control properties of the 1-d wave equation on a bounded interval discretized in space using the quadratic classical finite element approximation. A careful Fourier analysis of the discrete wave dynamics reve...
We address semigroup well-posedness for a linear, compressible viscous fluid interacting at its boundary with an elastic plate. We derive the model by linearizing the compressible Navier-Stokes equations about an arbitrary flow state, so the fluid PD...
In this article, I propose a systematic method for the inverse ultra-discretization of cell automata using a functionally complete operation. We derive difference equations for the 256 kinds of elementary cellular automata(ECA) introduced Wolfram\cit...
We determine the Compton effect from the Volkov solution of the Dirac equation for a process in a medium with the index of refraction n. Volkov solution involves the mass shift, or, the mass renormalization of an electron mass. We determine the mod...
New numerical models of line-driven stellar winds of late O stars are presented. Statistical equilibrium (NLTE) equations of the most abundant elements are solved. Properly obtained occupation numbers are used to calculate consistent radiative forc...
This paper is concerned with problems in the context of the theoretical foundation of adaptive (wavelet) algorithms for the numerical treatment of operator equations. It is well-known that the analysis of such schemes naturally leads to function spac...
In this paper, we use SEIR equations to make predictions for the number of mortality due to COVID-19 in İstanbul. Using excess mortality method, we find the number of mortality for the previous three waves in 2020 and 2021. We show that the predicti...
Inspired by Ogawa-Shimizu [JEE 2022] and Chen-Liang-Tsai [IMRN 2025] on the second and first order derivative estimates of solution of heat equation in the upper half space with boundary data in homogeneous Besov spaces, we extend the estimates to an...
In this paper, we consider a class of discontinuous Galerkin (DG) methods for one-dimensional nonlocal diffusion (ND) problems. The nonlocal models, which are integral equations, are widely used in describing many physical phenomena with long-range i...
The generator $\mathbf{L}$ of the linearized evolution equation of adiabatic oscillations of a gaseous star, ELASO, is a second order integro-differential operator and is realized as a self-adjoint operator in the Hilbert space of square integrable u...
The equations given earlier include the dependence of friction on materials and the normal force. The direction of friction is always opposite that of motion, parallel to the surface between objects, and …
Feb 17, 2023 · Find out the meaning of friction in physics. Learn its types, laws, & equations, along with a few examples and diagrams. What are its advantages & disadvantages.
In high Reynolds number turbulent flows, energy dissipation refers to the process of energy transfer from kinetic energy to internal energy due to molecular viscosity. In large eddy simulation (LES) with one-equation turbulence models, the energy dis...
Wormholes are interesting space-time structures connecting two asymptotic regions found in a universe or multiverse and are solutions to Einstein's field equations. These objects have many interesting features as far as physics is concerned. Morris a...
As the digital economy grows increasingly intangible, traditional productivity measures struggle to capture the true economic impact of artificial intelligence (AI). AI systems capable of cognitive work significantly enhance productivity, yet their c...
The main aim of this paper is to study soliton surfaces immersed in Lie algebras associated with ordinary differential equations (ODE's) for elliptic functions. That is, given a linear spectral problem for such an ODE in matrix Lax representation, we...
The vorticity dynamics of the two-dimensional (2D) Taylor-Green vortex (TGV) problem is investigated in its multi-cellular configuration by solving the incompressible Navier-Stokes equation for long time intervals using a pseudo-spectral method. This...
Starting with the usual definitions of octonions and split octonions in terms of Zorn vector matrix realization, we have made an attempt to write the consistent form of generalized Maxwell's equations in presence of electric and magnetic charges (dyo...
We consider regularization methods of Kaczmarz type in connection with the expectation-maximization (EM) algorithm for solving ill-posed equations. For noisy data, our methods are stabilized extensions of the well established ordered-subsets expect...
We present a nonlinear hydrodynamical description of a conformal plasma within the framework of divergence-type theories (DTTs), which are not based on a gradient expansion. We compare the equations of the DTT and the second-order theory (based on...
ultrasensitive transcription factors, afterwards the parameters of the equations (rate constants, enzyme efficiency coefficients and Michaelis constants) must be fitted
This work proposes a first approach towards a neo-Gibbsian thermodynamic theory for social systems, grounded in quantifiable economic and cultural parameters, while deliberately avoiding direct analogies with classical thermodynamic equations of stat...
In this paper, we prove the local well-posedness for the Navier-Stokes equations describing the motion of isotropic barotoropic compressible viscous fluid flow with non-slip boundary conditions, where the fluid domain is the $N$ dimensional half-sapc...
Gopal and Trefethen recently introduced "lightning solvers" for the 2D Laplace and Helmholtz equations, based on rational functions with poles exponentially clustered near singular corners. Making use of the Goursat representation in terms of analyti...
In this study, we solved Schrödinger equation with Cornell potential (Coulomb-plus-linear potential) by using neural network approach. Four different types of Cornell potential were used without a physical relevance. Besides that charmonium and bott...
The flow of the relativistic imperfect fluid in two dimensions is discussed. We calculate the symmetry group of the energy-momentum tensor conservation equation in the ultrarelativistic limit. Group-invariant solutions for the incompressible fluid...
We prove several results for the Dirichlet, Neumann and Regularity problems for the Laplace equation in graph Lipschitz domains in the plane, considering $A_{\infty}$-measures on the boundary. More specifically, we study the $L^{p,1}$-solvability for...
A homology theory is developed for set-theoretic Yang-Baxter equations, and knot invariants are constructed by generalized colorings by biquandles and Yang-Baxter cocycles....
We present a method for the computation of the Generalized Alignment Index (GALI), a fast and effective chaos indicator, using a multi-particle approach that avoids variational equations. We show that this approach is robust and accurate by deriving...
An exact expression for the leading-order (LO) gluon distribution function $G(x,Q^2)=xg(x,Q^2)$ from the DGLAP evolution equation for the proton structure function $F_2^{γp}(x,Q^2)$ for deep inelastic $γ^* p$ scattering has recently been obtained...
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In this paper, we consider the global wellposedness of 2-D incompressible magneto-hydrodynamical system with small and smooth initial data. It is a coupled system between the Navier-Stokes equations and a free transport equation with an universal n...