The Carroll and Chang conjecture of equal Indscal components when Candecomp/Parafac gives perfect fit

The Candecomp/Parafac algorithm approximates a set of matrices ${\mathbf{X}}_1\text{,}\dots \text{,}{\mathbf{X}}_I$ by products of the form ${\mathbf{AC}}_i{\mathbf{B}}^{\prime }$, with ${\mathbf{C}}_i$ diagonal, $i=1\text{,}\dots \text{,}I$. Carroll and Chang have conjectured that, when the matrices are symmetric, the resulting $\mathbf{A}$ and $\mathbf{B}$ will be column wise proportional. For cases of perfect fit, Ten Berge et al. have shown that the conjecture holds true in a variety of cases, but may fail when there is no unique solution. In such cases, obtaining proportionality by changing (part of) the solution seems possible. The present paper extends and further clarifies their results. In particular, where Ten Berge et al. solved all $I\times 2\times 2$ cases, now all $I\times 3\times 3$ cases, and also the $I\times 4\times 4$ cases for $I=2\text{,}8$, and 9 are clarified. In a number of cases, $\mathbf{A}$ and $\mathbf{B}$ necessarily have column wise proportionality when Candecomp/Parafac is run to convergence. In other cases, proportionality can be obtained by using specific methods. No cases were found that seem to resist proportionality.     

3-Methyl-3a,4-Dihydro-3H-Thiochromeno[4,3-c]isoxazol

Abstract  The crystal structure of the title compound, C₁₁H₁₁NOS, was determined by an X-ray diffraction analysis. The compound crystallizes in the monoclinic space group P2₁/c with cell parameters a = 10.533(2) ?, b = 12.7826(19) ?, c = 7.6491(17) ?, β = 107.997(17)^°, V = 979.5(3) ?³ and Z = 4. The S containing heterocycle adopts a sofa conformation, whereas the 5-membered ring adopts an envelope conformation. The crystal packing is characterized by weak C–H···N contacts and π-stacking interactions. Graphical Abstract  The title compound, 3-methyl-3a,4-dihydro-3H-thiochromeno[4,3-c]isoxazol was synthesized by an 1,3 dipolar cycloaddition reaction and its crystal structure determined. Single crystal X-ray diffraction analysis reveals that the aromatic 6-membered ring is planar, whereas the ring containing the S atom adopts a sofa conformation and the 5-membered ring an envelope conformation. The methyl group is in an equatorial position.      

Analyzing multiset data by the Power STATIS-ACT method

The STATIS-ACT method is a generalization of principal component analysis used to study simultaneously several data tables measured on the same observation units or variables. The goal of this method is to analyze the relationship between these data tables and to combine them into a compromise matrix corresponding to an optimal agreement between the data. In this paper, we propose a new approach to this method, referred to as the Power STATIS-ACT method, where the compromise matrix is derived from a general s-power based criterion ${(s\geqslant 1)}$ and investigate some of its theoretical and practical properties. Special attention is devoted to the 1-power case which makes the introduction of low rank versions of the compromise possible. We also examine the effect of varying the power parameter s on the compromise solutions. All results are illustrated with a number of real data tables.     

Constitutive model for a semi-crystalline polymer under dynamic loading

This paper deals with a viscoelastic–viscoplastic model for semi-crystalline polymers in crash applications. A polymer behaviour model is implemented in the commercial PAM CRASH© code thanks to a user material card. Global variables (load, displacement) and local variables (strain) are validated on flat and notched tensile specimens by comparing the numerical responses with data obtained by digital image correlation.     

First detection of Shiga toxin-producing Escherichia coli in shellfish and coastal environments of Morocco

Shiga toxin Escherichia coli (STEC), also called verotoxin-producing E. coli, is a major cause of food-borne illness, capable of causing hemorrhagic colitis and hemolytic–uremic syndrome (HUS). This study was carried out to evaluate the presence of (STEC) and E. coli O157:H7 in shellfish and Mediterranean coastal environments of Morocco. The contamination of shellfish and marine environment with Shiga toxin-producing E. coli (STEC) and E. coli O157:H7, was investigated during 2007 and 2008. A total of 619 samples were analyzed and 151 strains of E. coli were isolated. The presence of the stx1, stx2, and eae genes was tested in E. coli isolates strains using a triplex polymerase chain reaction. STEC was detected in three positives samples (1.9%), corresponding to the serotype O157:H7, the others Shiga toxin-producing E. coli non-O157 were also detected.