Abstract A mathematical model is developed to determine the steady-state electric current flow through in non-homogeneous isotropic conductor whose shape has a three-dimensional hollow body. The equations of Maxwell's theory solid body are used formulate corresponding boundary value problem. determination steady motion charges based on concept electrical conductance. derivation upper and lower ...

We demonstrate the generation of high-quality narrowband biphotons from a Doppler-broadened hot rubidium atomic vapor cell. Choosing a double-K atomic energy level scheme for optimizing both spontaneous four-wave mixing nonlinear parametric interaction and electromagnetically induced transparency (EIT), we achieve a biphoton spectral brightness as high as 14 000 s MHz . Meanwhile, we apply a sp...

This paper follows the recent discussion on the sparse solution recovery with quasi-norms lq, q ∈ (0, 1) when the sensing matrix possesses a Restricted Isometry Constant δ2k (RIC). Our key tool is an improvement on a version of “the converse of a generalized Cauchy-Schwarz inequality” extended to the setting of quasi-norm. We show that, if δ2k ≤ 1/2, any minimizer of the lq minimization, at lea...

We present optimal order preconditioners for certain discontinuous Galerkin (DG) finite element discretizations of elliptic boundary value problems. A specific assembling process is proposed which allows us to use the hierarchy of geometrically nested meshes. We consider two variants of hierarchical splittings and study the angle between the resulting subspaces. Applying the corresponding two-l...

Single photons are generated from an ensemble of cold Cs atoms via the protocol of Duan et al. [Nature (London), ()]]. Conditioned upon an initial detection from field 1 at 852 nm, a photon in field 2 at 894 nm is produced in a controlled fashion from excitation stored within the atomic ensemble. The single-quantum character of field 2 is demonstrated by the violation of a Cauchy-Schwarz inequa...

1. INTRODUCTION. Hypergraphs. Information Theory. Cauchy-Schwarz. It seems reasonable to assume that most mathematicians would be puzzled to find these three terms as, say, key words for the same mathematical paper. (Just in case this puzzlement is a result of being unfamiliar with the term " hypergraph " : a hypergraph is nothing other than a family of sets, and will be defined formally later....

We prove one-sided universal bounds on coarsening rates for two kinds of mean field models of phase transitions, one with a coarsening rate l ∼ t and the other with l ∼ t. Here l is a characteristic length scale. These bounds are both proved by following a strategy developed by Kohn and Otto (Comm. Math. Phys. 229 (2002), 375-395). The l ∼ t rate is proved using a new dissipation relation which...