Cold and ultracold polar molecules with nonzero electronic angular momenta are of great interest for studies in quantum chemistry and control, investigations of novel quantum systems, and precision measurement. However, in mixed electric and magnetic fields, these molecules are generically subject to a large set of avoided crossings among their Zeeman sublevels; in magnetic traps, these crossin...

We prove that every element of the polar cone to the closed convex cone of monotone transport maps can be represented as the divergence of a measure field taking values in the positive definite matrices.

[1] The transport of black carbon (BC) to polar regions is studied using the University of Michigan IMPACT aerosol model driven by two sets of meteorological fields from the NCAR CAM5 and GFDL AM3 models. The sensitivity of the transport of BC to wet deposition processes is tested by varying the wet deposition in large-scale precipitation. BC concentrations and deposition in polar regions are s...

This paper is dedicated to bounded error identification with complex valued non-linear models. Complex intervals are characterized by using polar forms and a new inclusion function is given for the addition of sectors. The latter is expressed as an optimization problem solved analytically. The new complex interval arithmetic is used with actual data and a complex valued non-linear model for the...

Let H : <m×<n → <n be a locally Lipschitz function in a neighborhood of (ȳ, x̄) and H(ȳ, x̄) = 0 for ȳ ∈ <m and x̄ ∈ <n. The implicit function theorem in the sense of Clarke [1, 2] says that if πx∂H(ȳ, x̄) is of maximal rank, then there exist a neighborhood Y of ȳ and a Lipschitz function G(·) : Y → <n such that G(ȳ) = x̄ and for every y in Y , H(y,G(y)) = 0. In this paper, we shall further show tha...

Let $(A)$ be a complex $(ntimes n)$ matrix and assume that the numerical range of $(A)$ lies in the set of a sector of half angle $(alpha)$ denoted by $(S_{alpha})$. We prove the numerical ranges of the conjugate, inverse and Schur complement of any order of $(A)$ are in the same $(S_{alpha})$.The eigenvalues of some kinds of matrix product and numerical ranges of hadmard product, star-congruen...

This paper addresses the estimation of a speaker GMM through the selection and merging of a set of neighbors models for that speaker. The selection of the neighbors models is based on the likelihood score for the training data on a set of potential neighbor GMM. Once the neighbors models are selected, they are merged to give a model of the speaker, which can also be used as an a priori model fo...