In this note we announce an extension of these theorems to the setting of Stiefel manifolds and matrix space. Our work makes it possible to construct holomorphic discrete series representations for the real symplectic group by decomposing a tensor product of certain projective representations introduced earlier by Shale and Weil. (See Weil [11] and also Shalika [10].) Proofs of the results anno...

In this paper, we give a fourth-order compact finite difference scheme for the general forms of two point boundary value problems and two dimensional elliptic partial differential equations (PDE’s). By decomposing the coefficient matrix into a sum of several matrixes after we discretize the original problem, we can obtain a lower bound for the smallest eigenvalue of the coefficient matrix. Thus...

We experimentally and theoretically analyze the radiation emitted from subwavelength-sized apertures in near-field optical probes. By decomposing the experimentally obtained radiation patterns into vector spherical waves, we describe the fields in terms of a series of multipole sources. We fit polarization-resolved angular intensity distributions, measured as far as 150 degrees from the normal,...

Abstract Based on the ERA5 reanalysis datasets during 1980–2019, a total of eleven zonal shear lines (ZSLs) that caused heavy precipitation and lasted more than 60 hours over Tibetan Plateau in summer are selected for composite analysis. By decomposing kinetic energy ( K ) near ZSL into divergent rotational energies D R interaction between wind RD ), influence winds evolution intensity is inves...

Abstract. We propose several models to segment images corrupted by additive or multiplicative noise, and by a smooth field (as global intensity inhomogeneity) in a variational curve evolution approach. The proposed energies can be seen as particular K −functionals or J −functionals that arise in the theory of interpolation between spaces. In the additive case, we decompose a data function u0 in...

How complex signaling networks shape highly coordinated, multistep cellular responses is poorly understood. Here, we made use of a network-perturbation approach to investigate causal influences, or "crosstalk," among signaling modules involved in the cytoskeletal response of neutrophils to chemoattractant. We quantified the intensity and polarity of cytoskeletal marker proteins over time to cha...

Research was conducted to determine suitable chemical parameters as indicators of odor from decomposing food wastes. Prepared food scraps were stored in 18 l plastic buckets (2 kg wet weight each) at 20 °C and 8 °C to reproduce high and low temperature conditions. After 1, 3, 7, 10 and 14 days of storage, the odor from the buckets were marked to an intensity scale of 0 (no odor) to 5 (intense) ...