A simple closure approximation for slow dynamics of a multiscale system: nonlinear and multiplicative coupling

Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical simulations of such systems often require relatively small time discretization step to resolve fast dynamics, which, in turn, increases computational expense. As a result, it became a popular approach in applications to develop a closed approximate model for slow variables alone, which both effectively reduces the dimension of the phase space of dynamics, as well as allows for a longer time discretization step. In this work we develop a new method for approximate reduced model, based on the linear fluctuation-dissipation theorem applied to statistical states of the fast variables. The method is suitable for situations with quadratically nonlinear and multiplicative coupling. We show that, with complex quadratically nonlinear and multiplicative coupling in both slow and fast variables, this method produces comparable statistics to what is exhibited by an original multiscale model. In contrast, it is observed that the results from the simplified closed model with a constant coupling term parameterization are consistently less precise

The Hopf algebra structure of the Z3_3-graded quantum supergroup GLq,j(1∣1)_{q,j}(1|1)

In this work, we give some features of the Z$_3$-graded quantum supergroup

Express method for assessing proteolysis in cheese and aromatic addi- tives with cheese flavor

The method based on the determination of the amount of active amino groups using o-Phthaldialdehyde (OPA method) can be applied in practice to assess accurately the degree of proteolysis in cheeses. The work establishes that the OPA method gives results that strictly correlate (R2 > 0.80, p < 0.01) with the results of assessing the degree of proteolysis by the Kjeldahl method. The results of the OPA method, expressed in the absorption intensity of the colored sample at a wavelength of 340 nm (OD340), can be converted to the content of soluble nitrogenous substances in cheese (WSN), using the calibration relationship between these indicators.The accuracy of the calibration relationship between WSN and OD340 can be increased (R2 > 0.91, p< 0.01) when using the OPA method in relation to a homogeneous group of cheeses produced by the same technology using the same type of milk clotting enzyme and lactic acid starter culture and having a similar shape of the molecular mass distribution of proteolysis products.The OPA method can be used to assess the content of proteolysis products, which form cheese flavor, in EMС. The results of assessing the degree of proteolysis by the OPA method (OD340) are proportional to both the total content of soluble nitrogen and the proportion of nitrogenous substances in it with a mass of less than 0.5 kDa, which make the greatest contribution to the formation of cheese flavor.The advantage of using the OPA method for assessing proteolysis in cheeses and EMC instead of the Kjeldahl method is a simpler measurement procedure and the possibility of studying more samples in less time

THE INFLUENCE OF MILK-CLOTTING ENZYMES ON THE FUNCTIONAL PROPERTIES OF PIZZA-CHEESES

The effect of the type and dose of milk-clotting enzymes (Chy-max® M based on recombinant camel chymosin, Fromase® TL based on Rhizomucor miehei protease) on the physicochemical, functional properties and shelf life of pizza-cheeses was studied. When using a low dose of milk-clotting enzymes (MCE) for milk coagulation (250–1100 IMCU per 100 kg of milk), cheeses were obtained with an increased moisture content (55–57%), excessive acidity (pH 4.8–4.9) and texture defects (incoherent, crumbly, with separation of free moisture). This is due to the formation of a weak curd, which releases moisture poorly during processing. The use of an increased dose of MCE makes it possible to obtain a denser curd, better releasing moisture. Cheese produced with a high dose of milk-clotting enzymes (2000–2800 IMCU per 100 kg of milk) had a lower moisture content (52–53%) and lower acidity (pH 5.0–5.1). The protein matrix is more hydrated in these cheeses, which ensures its better water holding capacity and a more homogeneous and cohesive texture. The use of an increased dose of MCE with a high total proteolytic activity (Fromase) gives undesirable consequences in the form of accelerated proteolysis of cheese mass proteins, rapid loss of functional properties of the cheese, and a decrease in the shelf life of cheese (less than 60 days). Cheese production using an increased dose of MCE with a low level of total proteolytic activity (Chy-max M) allows achieving a low level of proteolysis during cheese ripening and increasing its shelf life