Search results for "Theorem"
showing 10 items of 1250 documents
Global properties of codimension two spacelike submanifolds in Minkowski space
2009
Abstract We consider codimension two spacelike submanifolds with a parallel normal field (i.e. vanishing normal curvature) in Minkowski space. We use the analysis of their contacts with hyperplanes and hyperquadrics in order to get some global information on them. As a consequence we obtain new versions of Carathéodory's and Loewner's conjectures on spacelike surfaces in 4-dimensional Minkowski space and 4-flattenings theorems for closed spacelike curves in 3-dimensional Minkowski space.
Eigenvalues of non-hermitian matrices: a dynamical and an iterative approach. Application to a truncated Swanson model
2020
We propose two different strategies to find eigenvalues and eigenvectors of a given, not necessarily Hermitian, matrix (Formula presented.). Our methods apply also to the case of complex eigenvalues, making the strategies interesting for applications to physics and to pseudo-Hermitian quantum mechanics in particular. We first consider a dynamical approach, based on a pair of ordinary differential equations defined in terms of the matrix (Formula presented.) and of its adjoint (Formula presented.). Then, we consider an extension of the so-called power method, for which we prove a fixed point theorem for (Formula presented.) useful in the determination of the eigenvalues of (Formula presented…
On the Directly and Subdirectly Irreducible Many-Sorted Algebras
2015
AbstractA theorem of single-sorted universal algebra asserts that every finite algebra can be represented as a product of a finite family of finite directly irreducible algebras. In this article, we show that the many-sorted counterpart of the above theorem is also true, but under the condition of requiring, in the definition of directly reducible many-sorted algebra, that the supports of the factors should be included in the support of the many-sorted algebra. Moreover, we show that the theorem of Birkhoff, according to which every single-sorted algebra is isomorphic to a subdirect product of subdirectly irreducible algebras, is also true in the field of many-sorted algebras.
Cyclic (noncyclic) phi-condensing operator and its application to a system of differential equations
2019
We establish a best proximity pair theorem for noncyclic φ-condensing operators in strictly convex Banach spaces by using a measure of noncompactness. We also obtain a counterpart result for cyclic φ-condensing operators in Banach spaces to guarantee the existence of best proximity points, and so, an extension of Darbo’s fixed point theorem will be concluded. As an application of our results, we study the existence of a global optimal solution for a system of ordinary differential equations.
Existence of a unique solution for a third-order boundary value problem with nonlocal conditions of integral type
2021
The existence of a unique solution for a third-order boundary value problem with integral condition is proved in several ways. The main tools in the proofs are the Banach fixed point theorem and the Rus’s fixed point theorem. To compare the applicability of the obtained results, some examples are considered.
Contextuality is About Identity of Random Variables
2014
Contextual situations are those in which seemingly "the same" random variable changes its identity depending on the conditions under which it is recorded. Such a change of identity is observed whenever the assumption that the variable is one and the same under different conditions leads to contradictions when one considers its joint distribution with other random variables (this is the essence of all Bell-type theorems). In our Contextuality-by-Default approach, instead of asking why or how the conditions force "one and the same" random variable to change "its" identity, any two random variables recorded under different conditions are considered different "automatically". They are never the…
Necessary and Sufficient Conditions for an Extended Noncontextuality in a Broad Class of Quantum Mechanical Systems
2015
The notion of (non)contextuality pertains to sets of properties measured one subset (context) at a time. We extend this notion to include so-called inconsistently connected systems, in which the measurements of a given property in different contexts may have different distributions, due to contextual biases in experimental design or physical interactions (signaling): a system of measurements has a maximally noncontextual description if they can be imposed a joint distribution on in which the measurements of any one property in different contexts are equal to each other with the maximal probability allowed by their different distributions. We derive necessary and sufficient conditions for th…
Fluctuation theorems for non-Markovian quantum processes
2013
Exploiting previous results on Markovian dynamics and fluctuation theorems, we study the consequences of memory effects on single realizations of nonequilibrium processes within an open system approach. The entropy production along single trajectories for forward and backward processes is obtained with the help of a recently proposed classical-like non-Markovian stochastic unravelling, which is demonstrated to lead to a correction of the standard entropic fluctuation theorem. This correction is interpreted as resulting from the interplay between the information extracted from the system through measurements and the flow of information from the environment to the open system: Due to memory e…
Quantum Computation in a radio single mode cavity: the dissipative Jaynes and Cummings Model
2008
In this paper we have considered the interaction of a Jaynes and Cummings system with the electromagnetic field in its vacuum state and, solving the dynamical problem, we have analyzed the amount of entanglement induced in the bipartite system (atom + cavity mode) by the common electromagnetic reservoir. This has allowed us to quantitatively characterize the regime under which field-induced cooperative effects are not vanished by dissipation. Once the Decoherence Free Regime is reached, transient entanglement tends to become stationary and, therefore, usable for quantum gate implementation.
Evolution of the $B$-Meson Light-Cone Distribution Amplitude in Laplace Space
2020
The $B$-meson light-cone distribution amplitude is a central quantity governing non-perturbative hadronic dynamics in exclusive $B$ decays. We show that the information needed to describe such processes at leading power in $\Lambda_{\rm QCD}/m_b$ is most directly contained in its Laplace transform $\tilde\phi_+(\eta)$. We derive the renormalization-group (RG) equation satisfied by this function and present its exact solution. We express the RG-improved QCD factorization theorem for the decay $B^-\to\gamma\ell^-\bar\nu$ in terms of $\tilde\phi_+(\eta)$ and show that it is explicitly independent of the factorization scale. We propose an unbiased parameterization of $\tilde\phi_+(\eta)$ in ter…