Related papers: Analytic integrability of two lopsided systems
In this work we study the integrability of a family of nonlinear oscillators. Dynamical systems from this family appear in different applications from mechanics to chemistry. We propose an approach for finding first integrals and…
An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…
Performing a stability analysis during the design of any electronic circuit is critical to guarantee its correct operation. A closed-loop stability analysis can be performed by analysing the impedance presented by the circuit at a…
The phase transition to mirrorless oscillation in resonantly enhanced four-wave mixing in double-$\Lambda$ systems are studied analytically for the ideal case of infinite lifetimes of ground-state coherences. The stationary susceptibilities…
We study a class of functional problems reducible to computing $f^{(n)}(x)$ for inputs $n$ and $x$, where $f$ is a polynomial-time bijection. As we prove, the definition is robust against variations in the type of reduction used in its…
We describe a procedure to solve an up to $2N$ problem where the particles are separated topologically in $N$ groups with at most two particles in each. Arbitrary interactions are allowed between the (two) particles within one group. All…
We calculate the Landauer conductance through chaotic ballistic devices in the semiclassical limit, to all orders in the inverse number of scattering channels without and with a magnetic field. Families of pairs of entrance-to-exit…
We introduce the notion of topological electronic states on random lattices in non-integer dimensions. By considering a class $D$ model on critical percolation clusters embedded in two dimensions, we demonstrate that these topological…
We introduce two numerical conjugacy invariants for dynamical systems -- the complexity and weak complexity indices -- which are well-suited for the study of "completely integrable" Hamiltonian systems. These invariants can be seen as "slow…
Wave fields obeying the 2D Helmholtz equation on branched surfaces (Sommerfeld surfaces) are studied. Such surfaces appear naturally as a result of applying the reflection method to diffraction problems with straight scatterers bearing…
We describe methods to evaluate elementary logarithmic integrals. The integrand is the product of a rational function and a linear polynomial in ln x.
The notion of integrability is discussed for classical nonautonomous systems with one degree of freedom. The analysis is focused on models which are linearly spanned by finite Lie algebras. By constructing the autonomous extension of the…
The problem of scattering of particles on the line with repulsive interactions, gives rise to some well-known integrable Hamiltonian systems, for example, the nonperiodic Toda lattice or Calogero's system. The aim of this note is to outline…
Under-approximations of reachable sets and tubes have been receiving growing research attention due to their important roles in control synthesis and verification. Available under-approximation methods applicable to continuous-time linear…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
The goal of this thesis is the search for integrable and superintegrable systems with magnetic field. We formulate the quantum mechanical determining equations for second order integrals of motion in the cylindrical coordinates and we find…
Reversible logic circuit is a necessary construction for achieving ultra low power dissipation as well as for prominent post-CMOS computing technologies such as Quantum computing. Consequently automatic synthesis of a Boolean function using…
Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply-rates are employed here for…
Scientists form hypotheses and experimentally test them. If a hypothesis fails (is refuted), scientists try to explain the failure to eliminate other hypotheses. The more precise the failure analysis the more hypotheses can be eliminated.…
This paper addresses the resilience of large-scale closed-loop structured systems in the sense of arbitrary pole placement when subject to failure of feedback links. Given a structured system with input, output, and feedback matrices, we…