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We investigate the resonant states for the parabolic potential barrier known also as inverted or reversed oscillator. They correspond to the poles of meromorphic continuation of the resolvent operator to the complex energy plane. As a…
The CR analogue of B.-Y. Chen's conjecture on pseudo biharmonic maps will be shown. Pseudo biharmonic, but not pseudo harmonic, isometric immersions with parallel pseudo mean curvature vector fields, will be characterized. Several examples…
A variety of models describing the interaction between flows and oscillating structures are discussed. The main aim is to analyze conditions under which structural instability (flutter) induced by a fluid flow can be suppressed or…
Symmetries and differential invariants of viscid flows with viscosity depending on temperature on a space curve are given. Their dependence on thermodynamic states of media is studied, and a classification of thermodynamic states is given.
A supersymmetric extension of the two-phase fluid flow system is formulated. A superalgebra of Lie symmetries of the supersymmetric extension of this system is computed. The classification of the one-dimensional subalgebras of this…
We develop a parabolic pluripotential theory on compact K{\"a}hler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge-Amp{\`e}re equations. We provide a parabolic analogue of the celebrated Bedford-Taylor…
To contrast different generators for flow equations for Hamiltonians and to discuss the dependence of physical quantities on unitarily equivalent, but effectively different initial Hamiltonians, a numerically solvable model is considered…
In this expository article we introduce a diagrammatic scheme to represent reverse classes of weights and some of their properties.
Incompressible fluids on curved surfaces are considered with respect to the interplay between topology, geometry and fluid properties using a surface vorticity-stream function formulation, which is solved using parametric finite elements.…
We consider the CY orbifolds connected with the products of N = (2, 2) supersymmetric minimal models. We use the spectral flow construction of states, as well as its mirror one, to explicitly show that these CY orbifolds are canonically…
An analysis of axisymmetric equilibria with arbitrary incompressible flow and finite resistivity is presented. It is shown that with large aspect ratio approximation or vanishing poloidal current, a uniform conductivity profile is…
We study a hierarchy of models based on kinetic equations for the descriptions of traffic flow in presence of autonomous and human--driven vehicles. The autonomous cars considered in this paper are thought of as vehicles endowed with some…
In the present thesis, we study the heat flow in mesoscopic one-dimensional transport systems. Using the analysis of full counting statistics, we calculate the cumulant generating function of the particle and heat flows and prove its…
We tackle the problem of estimating optical flow from a monocular camera in the context of autonomous driving. We build on the observation that the scene is typically composed of a static background, as well as a relatively small number of…
We apply the parabolic flow method to solving complex quotient equations on closed K\"ahler manifolds. We study the parabolic equation and prove the convergence. As a result, we solve the complex quotient equations.
Various aspects of Supersymmetry in 1-dimensional systems are analyzed.
We consider the junction of multiple one-dimensional systems and study how conserved currents transport at the junction. To characterize the transport process, we introduce reflection/transmission coefficients by applying boundary conformal…
We study out-of-equilibrium energy flow in a strongly coupled system by using the AdS/CFT correspondence. In particular, we describe the appearance of a steady state connecting two asymptotic equilibrium systems. We obtain results within…
In our previous paper an effective algorithm for inverting polynomial automorphisms was proposed. We extend its application to the case of formal power series over a field of arbitrary characteristic and illustrate the proposed approach…
We present a new fluid-dynamical model of traffic flow. This model generalizes the model of Aw and Rascle [SIAM J. Appl. Math. 60 916-938] and Greenberg [SIAM J. Appl. Math 62 729-745] by prescribing a more general source term to the…