Related papers: An Example of Exact Solution in the LTB Model

We describe several new ways of specifying the behaviour of Lemaitre-Tolman (LT) models, in each case presenting the method for obtaining the LT arbitrary functions from the given data, and the conditions for existence of such solutions. In…

We define an integrable lattice model which, in the notation of Yang, in addition to the conventional 2-particle $R$-matrices also contains non-reducible 3-particle $R$-matrices. The corresponding modified Yang-Baxter equations are solved…

We discuss exact analytical solutions of a variety of statistical models recently obtained for finite systems by a novel powerful mathematical method, the Laplace-Fourier transform. Among them are a constrained version of the statistical…

The logarithmic triplet model W_2,3 at c=0 is studied. In particular, we determine the fusion rules of the irreducible representations from first principles, and show that there exists a finite set of representations, including all…

Parabolic integro-differential non degenerate Cauchy problem is considered in the scale of H\"older spaces of functions whose regularity is defined by a radially O-regularly varying L\'evy measure. Existence and uniqueness and the estimates…

We consider the Cauchy problem on a nonlinear conversation law with large initial data. By Green's function methods, energy methods, Fourier analysis, frequency decomposition, pseudo-differential operators, we obtain the global existence…

This paper considers the linear objective function optimization with respect to a novel system of fuzzy relation equations, where the fuzzy compositions are defined by the minimum t-norm. It is proved that the feasible solution set is…

In the paper we extend the Multiple-Relaxation-Time (MRT) Lattice Boltzmann (LB) model proposed in [Europhys. Lett. \textbf{90}, 54003 (2010)] so that it is suitable also for incompressible flows. To decrease the artificial oscillations,…

This work studies the Cauchy problem for the energy-critical inhomogeneous Hartree equation with inverse square potential $$i\partial_t u-\mathcal K_\lambda u=\pm |x|^{-\tau}|u|^{p-2}(I_\alpha *|\cdot|^{-\tau}|u|^p)u, \quad \mathcal…

Nonlinear dispersionless equations arise as the dispersionless limit of well know integrable hierarchies of equations or by construction, such as the system of hydrodynamic type. Some of these equations are integrable in the Hamiltonian…

We construct a finitely presented group with undecidable word problem and with Dehn function bounded by a quadratic function on an infinite set of positive integers.

We consider a linear non-autonomous evolutionary Cauchy problem \begin{equation} \dot{u} (t)+A(t)u(t)=f(t) \hbox{ for }\ \hbox{a.e. t}\in [0,T],\quad u(0)=u_0, \end{equation} where the operator $A(t)$ arises from a time depending…

Topological defects play a fundamental role in the investigation of symmetries in quantum field theories. For conformal field theories in two space-time dimensions, it is possible to construct these defects using lattice models allowing…

Latent feature models (LFM)s are widely employed for extracting latent structures of data. While offering high, parameter estimation is difficult with LFMs because of the combinational nature of latent features, and non-identifiability is a…

With a sufficiently fine discretisation, the Lattice Boltzmann Method (LBM) mimics a second order Crank-Nicolson scheme for certain types of balance laws (Farag et al. [2021]). This allows the explicit, highly parallelisable LBM to…

This paper deals with uncertain parabolic fluid flow problem where the uncertainty occurs due to the initial conditions and parameters involved in the system. Uncertain values are considered as fuzzy and these are handled through a recently…

We propose a fast method for high order approximations of the solution of the Cauchy problem for the linear non-stationary Stokes system in $R^3$ in the unknown velocity $\bf u$ and kinematic pressure $P$. The density ${\bf f}({\bf x},t)$…

Uncertainty estimation is critical for cost-sensitive deep-learning applications (i.e. disease diagnosis). It is very challenging partly due to the inaccessibility of uncertainty groundtruth in most datasets. Previous works proposed to…

In this paper, we are dealing with the solution of the functional equation $$ \varphi\Big(\frac{x+y}2\Big)(f(x)-f(y))=F(x)-F(y), $$ concerning the unknown functions $\varphi,f$ and $F$ defined on a same open subinterval of the reals.…

A fast convergence in a fixed-time of solutions of nonlinear dynamical systems, for which special requirements are satisfied on the derivative of a quadratic function calculated along the solutions of the system, is proposed. The conditions…