Uncertain switched linear systems are known as an important class of control systems. Performance of these systems is affected by uncertainties and its stabilization is a main concern of recent studies. Existing work on stabilization of these systems only provides asymptotical stabilization via designing switching strategy and state-feedback controller. In this paper, a new switching strate...

Levinson's theorem for Dirac particles constraints the sum of the phase shifts at threshold by the total number of bound states of the Dirac equation. Recently , a stronger version of Levinson's theorem has been proven in which the value of the positive-and negative-energy phase shifts are separately constrained by the number of bound states of an appropriate set of Schrödinger-like equations. ...

Quantum query complexity is known to be characterized by the so-called quantum adversary bound. While this result has been proved in the standard discretetime model of quantum computation, it also holds for continuous-time (or Hamiltonianbased) quantum computation, due to a known equivalence between these two query complexity models. In this work, we revisit this result by providing a direct pr...

Deformation of the material during cyclic expansion extrusion (CEE) is investigated using upper-bound theorem. The analytical approximation of forming loads agrees very well with the FEM results for different amounts of chamber diameter, friction factor and also for lower die angles. However, the difference between analytical and numerical solution increases at higher die angles which are expla...

Rice’s Theorem states that all nontrivial language properties of recursively enumerable sets are undecidable. Borchert and Stephan [BS00] started the search for complexity-theoretic analogs of Rice’s Theorem, and proved that every nontrivial counting property of boolean circuits is UP-hard. Hemaspaandra and Rothe [HR00] improved the UP-hardness lower bound to UPO(1)-hardness. The present paper ...

This paper contributes to the solution of the Poincaré problem, which is to bound the degree of a (generalized algebraic) leaf of a (singular algebraic) foliation of the complex projective plane. The first theorem gives a new sort of bound, which involves the Castelnuovo–Mumford regularity of the singular locus of the leaf. The second theorem gives a bound in terms of two singularity numbers of...

In contrast to the nondegeneracy theorem, we present various scenarios in one-dimensional quantum mechanics that demonstrate how Wronskian of two bound-state eigenfunctions with same energy eigenvalue can be zero without implying are linearly dependent. It is shown theorem fails only when potential makes different solutions corresponding vanish at singular point or region singularity.

For a non-autonomous dynamics with discrete time defined by tempered sequence of upper-triangular matrices, we obtain lower and upper bounds for the Grobman regularity coefficients. We also give two applications these results: an bound coefficients exterior powers sequence, simple proof Oseledets' multiplicative ergodic theorem cocycles over measure-preserving transformation without using Kingm...

The Gilbert-Varshamov (GV) lower bound on the maximum cardinality of a q-ary code of length n with minimum Hamming distance at least d can be obtained by application of Turán’s theorem to the graph with vertex set {0, 1, . . . , q − 1}n in which two vertices are joined if and only if their Hamming distance is at least d. We generalize the GV bound by applying Turán’s theorem to the graph with v...

In this paper, we obtain an explicit Berry-Esseen bound in the central limit theorem for nonlinear statistics with bounded differences. Some examples are provided as well.