We investigate the Mott transition in innnite dimensions in the orbitally degenerate Hubbard model. We nd that the qualitative features of the Mott transition found in the one band model are also present in the orbitally degenerate case. Surprisingly, the quantitative aspects of the transition around density one are not very sensitive to orbital degeneracy, justifying the quantitative success o...

Let I⊂(0,∞) be an interval that is closed with respect to the multiplication. The operations Cf,g:I2→I of formCf,g(x,y)=(f∘g)−1(f(x)⋅g(y)),where f,g are bijections I considered. Their connections generalized weighted quasi-geometric means presented. It shown invariance question within class these leads iterative type and a problem on composite functional equation. An application identity determ...

We investigate the Mott transition in infinite dimensions in the orbitally degenerate Hubbard model. The qualitative features of the Mott transition found in the one-band model are also present in the orbitally degenerate case. We show that the quantitative aspects of the low-energy behavior near the Mott insulating state with one electron per site are not very sensitive to orbital degeneracy, ...

In this paper we study the question of the existence of a continuous inverse to the multiplication mapping (/, g) -» (fg, g) defined on pairs of C°° functions on a manifold M. Obviously, restrictions must be imposed on the domain of such an inverse. This leads us to the study of a modified problem: Find an appropriate domain for the inverse of (/, G) -» (/(/> ° G), G), where G is a C°° mapping ...

We consider the Schrödinger equation with a nondispersive logarithmic nonlinearity and repulsive harmonic potential. For suitable range of coefficients, there exist two positive stationary solutions, each one generating continuous family solitary waves. These solutions are Gaussian, turn out to be orbitally unstable. also discuss notion ground state in this setting: for any natural definition, ...

We prove the existence of solutions for third-order nonconvex state-dependent sweeping process with unbounded perturbations of the form: −A x 3 t ∈ N K t, ẋ t ; A ẍ t F t, x t , ẋ t , ẍ t G x t , ẋ t , ẍ t a.e. 0, T , A ẍ t ∈ K t, ẋ t , a.e. t ∈ 0, T , x 0 x0, ẋ 0 u0, ẍ 0 υ0, where T > 0, K is a nonconvex Lipschitz set-valued mapping, F is an unbounded scalarly upper semicontinuous convex set-v...

In this paper, characterizations of the degree to which a mapping $mathcal{T} : L^{X}longrightarrow M$ is an $(L, M)$-fuzzy topology are studied in detail.What is more, the degree to which an $L$-subset is an $L$-open set with respect to $mathcal{T}$ is introduced.Based on that, the degrees to which a mapping $f: Xlongrightarrow Y$ is continuous,open, closed or a quotient mapping with respect t...

Suppose that $f$ is a $K$-quasiconformal self-mapping of the unit disk $\mathbb{D}$, which satisfies following: $(1)$ biharmonic equation $\Delta(\Delta f)=g$ $(g\in \mathcal{C}(\overline{\mathbb{D}}))$, (2) boundary condition $\Delta f=\varphi$ ($\varphi\in\mathcal{C}(\mathbb{T})$ and $\mathbb{T}$ denotes circle), $(3)$ $f(0)=0$. The purpose this paper to prove Lipschitz continuos, and, furthe...