A family of conforming mixed finite elements with mass lumping on triangular grids are presented for linear elasticity. The stress field is approximated by symmetric $H({\rm div})-P_k (k\geq 3)$ polynomial tensors enriched higher order bubbles so as to allow lumping, which can be viewed the Hu-Zhang interior bubble functions. displacement $C^{-1}-P_{k-1}$ vectors terms ensure stability conditio...

We present what to our knowledge is a new method of optimized torsion-angle normal-mode analysis, in which the normal modes move along curved paths in Cartesian space. We show that optimized torsion-angle normal modes reproduce protein conformational changes more accurately than Cartesian normal modes. We also show that orthogonalizing the displacement vectors from torsion-angle normal-mode ana...

It is proved that equations between arrows assumed for cartesian categories are maximal in the sense that extending them with any new equation in the language of free cartesian categories collapses a cartesian category into a preorder. An analogous result holds for categories with binary products, which may lack a terminal object. The proof is based on a coherence result for cartesian categorie...

The Cartesian product of graphs was introduced more than 50 years ago and many fundamental results were obtained since then. Nevertheless, in the last years several basic problems on the Cartesian product were solved and interesting theorems proved on topics of contemporary interest in graph theory. Here we survey recent developments on the structure of the Cartesian product with emphasis on th...

In this paper, the Hyper - Zagreb index of the Cartesian product, composition and corona product of graphs are computed. These corrects some errors in G. H. Shirdel et al.[11].

The neural basis of pattern recognition is a central problem in visual neuroscience. Responses of single cells were recorded in area V4 of macaque monkey to three classes of periodic stimuli that are based on spatial derivative operators: polar (concentric and radial), hyperbolic, and conventional sinusoidal (Cartesian) gratings. Of 118 cells tested, 16 percent responded significantly more to p...