Nuclear magnetic resonance (NMR) structure modeling usually produces a sparse set of inter-atomic distances in protein. In order to calculate the three-dimensional structure of protein, current approaches need to estimate all other “missing” distances to build a full set of distances. However, the estimation step is costly and prone to introducing errors. In this report, we describe a geometric...

Here we demonstrate the emergence of Grassmann variables in matrix models based on the exceptional Jordan algebra. The Grassmann algebras are built naturally using the octonion algebra. We argue the appearance of Grassmann variables solidifies the relationship between supersymmetry and triality.

A monic quadratic Hermitian matrix polynomial L(λ) can be factorized into a product of two linear matrix polynomials, say L(λ) = (Iλ−S)(Iλ−A). For the inverse problem of finding a quadratic matrix polynomial with prescribed spectral data (eigenvalues and eigenvectors) it is natural to prescribe a right solvent A and then determine compatible left solvents S. This problem is explored in the pres...

the purpose of this research was to prepare a floating matrix tablet containing domperidone as a model drug. polyethylene oxide (peo) and hydroxypropyl methylcellulose (hpmc) were evaluated for matrix-forming properties. a simplex lattice design was applied to systemically optimize the drug release profile. the amounts of peo wsr 303, hpmc k15m and sodium bicarbonate were selected as independen...

This paper concerns the geometry of noncommutative domains and analytic free maps. These maps are free analogs of classical analytic functions in several complex variables, and are defined in terms of noncommuting variables amongst which there are no relations they are free variables. Analytic free maps include vector-valued polynomials in free (noncommuting) variables and form a canonical clas...

We analyze low rank tensor completion (TC) using noisy measurements of a subset of the tensor. Assuming a rank-$r$, order-$d$, $N \times N \times \cdots \times N$ tensor where $r=O(1)$, the best sampling complexity that was achieved is $O(N^{\frac{d}{2}})$, which is obtained by solving a tensor nuclear-norm minimization problem. However, this bound is significantly larger than the number of fre...

this paper presents a rational haar wavelet operational method for solving the inverse laplace transform problemand improves inherent errors from irrational haar wavelet. the approach is thus straightforward, rather simple andsuitable for computer programming. we define that $p$ is the operational matrix for integration of the orthogonalhaar wavelet. simultaneously, simplify the formulaes of li...