PURPOSE Dual-energy CT (DECT) is arguably the most accurate energy mapping technique in CT-based attenuation correction (CTAC) implemented on hybrid PET/CT systems. However, this approach is not attractive for clinical use owing to increased patient dose. The authors propose a novel energy mapping approach referred to as virtual DECT (VDECT) taking advantage of the DECT formulation but using CT...

Filter-bank outputs are extended into tensors to yield precise acoustic features for speech recognition using deep neural networks (DNNs). The filter-bank outputs with temporal contexts form a time-frequency pattern of speech and have been shown to be effective as a feature parameter for DNN-based acoustic models. We attempt to project the filter-bank outputs onto a tensor product space using d...

We prove approximate controllability of the bilinear Schrödinger equation in the case in which the uncontrolled Hamiltonian has discrete nonresonant spectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the Galerkin approximations and...

Let $X$ be a Banach space of $dim X > 2$ and $B(X)$ be the space of bounded linear operators on X. If $L : B(X)to B(X)$ be a Lie higher derivation on $B(X)$, then there exists an additive higher derivation $D$ and a linear map $tau : B(X)to FI$ vanishing at commutators $[A, B]$ for all $A, Bin B(X)$ such that $L = D + tau$.

Abstract Let G be a locally compact unimodular group, and let $\phi $ some function of n variables on . To such , one can associate multilinear Fourier multiplier, which acts -fold product the noncommutative $L_p$ -spaces group von Neumann algebra. One may also define an associated Schur Schatten classes $S_p(L_2(G))$ We generalize well-known transference results from linear case to case. In pa...

There are many good references for this material including [EKM], [L], [Pf] and [S]. 1 Quadratic forms Let k be a field with char k = 2. Definition 1.1. A quadratic form q : V → k on a finite-dimensional vector space V over k is a map satisfying: 1. q(λv) = λ 2 q(v) for v ∈ V , λ ∈ k. 2. The map b q : V × V → k, defined by b q (v, w) = 1 2 [q(v + w) − q(v) − q(w)] is bilinear. We denote a quadr...

The classical result that r-fold vector cross products exist only for d-dimensional vector spaces with r = 1 and d even; r = 2 and d = 3 or 7; r = 3 and d = 8; and r = d − 1 for arbitrary d will be explained. Vector cross products will then be used to construct exceptional Lie superalgebras. 1. Bilinear vector cross products We all are familiar with the usual vector cross product × in R3, which...

As an application of Hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. We have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear Backlund transformations and construction of ...