We introduce a unifying approach for invariants of finite matroids that count mappings to set. The aim this paper is show if the cardinalities with fixed values on restricted set satisfy contraction–deletion rules, then there relation among them can be expressed in terms linear algebra. In way, we study regular chain groups, nowhere-zero flows and tensions graphs, acyclic totally cyclic orienta...

tungsten trioxide (wo3) films have been coated on indium thin oxide (ito) conductive glass substrate, using aqueous solution of peroxotungstic acid (pta) by the sol-gel dip coating method. x-ray diffractometery (xrd) analysis confirmed monoclinic and triclinic structure for the film and powdered wo3 respectively. fourier transforms infrared spectroscopy (ft-ir) exhibited the structure of peroxo...

The precise regulatory mechanisms of cyclic oviductal contraction in the cow are unclear. The purpose of this study was to evaluate the effect of luteinizing hormone (LH), steroids, prostaglandins (PGs) and peptides on the oviductal contraction and secretion of PGs and endothelin (ET-1). In addition, the cyclic expression of mRNA for ET-1 and its receptors (ET-R) was evaluated by reverse transc...

We establish the existence and uniqueness of finite free resolutions and their attendant Betti numbers for graded commuting d-tuples of Hilbert space operators. Our approach is based on the notion of free cover of a (perhaps noncommutative) row contraction. Free covers provide a flexible replacement for minimal dilations that is better suited for higher-dimensional operator theory. For example,...

The contraction and relaxation of the beating heart are mediated by highly coordinated processes that allow rapid activation and deactivation of the myofilaments. The sarcomere is the fundamental contractile element, and its shortening is the result of the myosin-containing thick filament sliding past the actin-containing thin filament. Fueled by ATP hydrolysis, myosin is the molecular motor th...