A Schur complement approach to preconditioning sparse linear least-squares problems with some dense rows

The effectiveness of sparse matrix techniques for directly solving large-scale linear least-squares problems is severely limited if the system matrix A has one or more nearly dense rows. In this paper, we partition the rows of A into sparse rows and dense rows (A s and A d ) and apply the Schur complement approach. A potential difficulty is that the reduced normal matrix AsTA s is often rank-deficient, even if A is of full rank. To overcome this, we propose explicitly removing null columns of A s and then employing a regularization parameter and using the resulting Cholesky factors as a preconditioner for an iterative solver applied to the symmetric indefinite reduced augmented system. We consider complete factorizations as well as incomplete Cholesky factorizations of the shifted reduced normal matrix. Numerical experiments are performed on a range of large least-squares problems arising from practical applications. These demonstrate the effectiveness of the proposed approach when combined with either a sparse parallel direct solver or a robust incomplete Cholesky factorization algorithm

Stability and rheological properties of beverage emulsions with additive of ghatti gum

W pracy badano wpływ stężenia gumy ghatti (2 -10%) na stabilność i cechy reologiczne emulsji napojowych. Stabilność emulsji oznaczono metodą turbidymetryczną (indeks wielkości cząstek fazy zdyspergowanej i zmętnienie) oraz metodą dyfrakcji laserowej. Test przechowalniczy emulsji napojowych oraz napojów prowadzono przez 12 tygodni. Oznaczano lepkość względną emulsji. Stwierdzono, że guma ghatti tworzy stabilne, co najmniej przez trzy miesiące, emulsje napojowe. Emulsje zawierające mniejsze krople olejowe charakteryzowały się większą względną lepkością i stabilnością. Bardziej stabilne emulsje otrzymano stosując dodatek gumy ghatti w ilości 2-4% niż dodatek 6-10%.The influence of ghatti concentration (2 — 10 wt%) on the stability and rheology of beverage emulsions was studied. The stability of emulsions was determined by turbidimetric method (the droplet size index of dispersed phase and opacity) and laser scattering method. Storage test of emulsions and beverages was carried out for 12 weeks. The relative viscosity of the emulsions was determined. It was found that ghatti gum forms beverage emulsions which are stable for three mouths or more. The emulsions containing smaller droplets demonstrated larger relative viscosity and stability. More stable emulsions were obtained by using ghatti gum in amount 2 - 4 % in comparison to those obtainedfor 6-10%

Production of soft drinks with apply beverage emulsions

W artykule przedstawiono aktualny stan wiedzy na temat otrzymywania napojów bezalkoholowych z emulsji aromatów, składników recepturowych tych emulsji i problemów związanych z ich trwalościąprzechowalniczą. Znajomość poruszanych w artykule zagadnień może pomóc w pracach nad poprawą jakości produkowanych napojów bezalkoholowych, jak również w postępie techniczno-technologicznym w zakresie wprowadzania nowych produktów, takich jak napoje o nowych oryginalnych smakach i kolorach, napoje z coraz większym udziałem soków owocowych oraz wzbogacane w składniki prozdrowotne.Beverages with fruit test and typical cloudiness to natural juices are obtaining from flavour emulsions. Beverage emulsions are first prepared as an emulsion concentrate which is later diluted in sugar solution in order to produce the finished beverage. Stability of beverage emulsion in both the concentrated and diluted forms is the technological problem in soft drinks industry. In soft drinks, the beverage emulsion may provide flavour, colour and cloudy appearance for the beverage. A typical beverage emulsion composition includes flavour oils and weighing agents in the oil phase, and water, emulsifier, acids, and preservatives in the water phase

Effect of homogenisation pressure on the stability of beverage emulsions with addition of modified starch

Celem pracy było określenie wpływu parametrów homogenizacji na stabilność emulsji napojowych. Jako emulgator i zarazem stabilizator emulsji zastosowano skrobię modyfikowaną hydrofobowo. Stabilność emulsji określano na podstawie charakterystyki wielkości cząstek fazy zdyspergowanej, wyników pomiaru czasu załamania emulsji jak również metodą światła wstecznie rozproszonego. Uzyskane wyniki mają ogromne znaczenie techniczno-praktyczne.The aim of this study was to evaluate the effect of homogenization parameters on the stability of beverage emulsions. Hydrophobically modified starch was applied to emulsify and stabilize the emulsion. The stability was determined on the basis of the characteristics of particle size of dispersed phase and the results of time to breakage of emulsion and by measuring changes in the intensity of backscattered light from the emulsion with height. The results obtained have great technological weight

Effect of microencapsulation on concentration of isoflavones during simulated in vitro digestion of isotonic drink

Isotonic drinks, fortified with microencapsulated maltodextrin and inulin isoflavone extract, were evaluated by organoleptic assessment and color measurement on the CIE L*a*b scale, then they were subjected to in vitro digestion. Changes of concentrations of isoflavones released during digestion of drinks and their ability to neutralize free radicals (ABTS) were determined. The effect of microencapsulation and storage on isoflavone content in isotonic drinks was also evaluated. In the organoleptic evaluation, beverages without additives and beverages fortified with microencapsulated extract were evaluated as better than a beverage with pure extract. Microencapsulation largely eliminated the unpleasant taste and odor of isoflavones and masked their color. Before digestion, isotonic drinks contained 29.07–43.17 μg of isoflavones in 1 ml. Microencapsulated isoflavones were released gradually during simulated digestion. The highest recovery of these compounds was observed for glycoside and malonylate derivatives of daidzein. Daidzin and genistin with encapsulation showed bioavailability of 0.02%–0.07%. The use of inulin as a carrier increased the stability of microcapsules during the storage of isotonic beverages. Microencapsulated of isoflavones from soybeans can increase the health benefits of conventional beverages available on the market