We construct projections from HΛk(Ω), the space of differential k forms on Ω which belong to L2(Ω) and whose exterior derivative also belongs to L2(Ω), to finite dimensional subspaces of HΛk(Ω) consisting of piecewise polynomial differential forms defined on a simplicial mesh of Ω. Thus, their definition requires less smoothness than assumed for the definition of the canonical interpolants base...

A novel crosslinking agent, suberoyl chloride, was used to crosslink N-phthaloyl acylated chitosan and improves the properties of chitosan membranes. Membranes with different crosslinking degrees were synthesized. The derivatives were characterized by Fourier transform infrared spectroscopy and ¹³C solid state nuclear magnetic resonance spectroscopy, which indicated that the crosslinking degree...

To preserve and strengthen the health of young people, one tasks state in field healthy nutrition is development production functional food products enriched with necessary macro- microelements; supplements biologically active substances orientation higher education to increase level valeology students, introduction relevant topics subjects into educational process institutions. The article dev...

This study aimed to analyze the composition of fatty acids, with particular emphasis on content cis9trans11 C18:2 (CLA) acid, minerals, and lipid quality indices in raw milk, pasteurized yogurts produced selected starter cultures enriched Bifidobacterium bifidum. The GC-FID method was used determine acid those dairy products. To contents microelements (copper, manganese, iron, zinc) macroelemen...

Metabolic syndrome (MetS) is characterized as a group of cardiometabolic risk factors that raise the risk for heart disease and other health problems, such as diabetes mellitus and stroke. Treatment strategies include pharmacologic interventions and supplementary (or "alternative") treatments. Nutraceuticals are derived from food sources (isolated nutrients, dietary supplements and herbal produ...

Geronimo, Hardin, et al have previously been able construct orthogonal and biorthogonal scaling vectors by extending a spline scaling vector with functions supported on [0, 1]. Many of these constructions occurred before the concept of balanced scaling vectors was introduced. This paper will show that adding functions on [0, 1] is insufficient for extending spline scaling vectors to scaling vec...

The purpose of this paper is to discuss the construction of a linear operator, referred to as the bubble transform, which maps scalar functions defined on Ω ⊂ Rn into a collection of functions with local support. In fact, for a given simplicial triangulation T of Ω, the associated bubble transform BT produces a decomposition of functions on Ω into a sum of functions with support on the correspo...

The purpose of this note is to discuss a generalization of the bubble transform to differential forms. This transform was dicussed for ordinary functions, or zero-forms, in [4]. The present note represents the beginnig of a similar study for differential forms, where we build a transformation which decomposes any function in HΛk(Ω) into a sum of local bubbles supported on appropriate macroeleme...