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...