Projective resolution of irreducible modules over tiled order

We indicate the method for computing the kernels of projective resolution of irreducible module over tiled order. On the base of this method we construct projective resolution of irreducible module and calculate the global dimension of tiled order. The evident view of kernels of projective resolution allows to check easily the regularity of tiled order

Tiled orders of width 3

We consider projective cover over tiled order and calculate the kernel of epimorphism from direct sum of submodules of distributive module to their sum

DEVELOPMENT OF MATHEMATICAL MODEL OF PROCESS OF BLACK CURRANT BERRIES DRYING IN VACUUMDEVICE WITH THE MICROWAVE POWER SUPPLY

Summary. The mathematical model allowed to reproduce and study at qualitative level the change of berries form and the structure of the berries layer in the course of drying. The separate berry in the course of drying loses gradually its elasticity, decreases in volume, the peel gathers in folds, there appear internal emptiness. In the course of drying the berries layer decreases in thickness, contacting berries stick strongly with each other due to the coordinated folds of peel appearing, the layer is condensed due to penetration of the berries which have lost elasticity into emptiness between them. The model with high specification describes black currant drying process and therefore has a large number of the parameters available to change. Among them three most important technological parameters, influencing productivity and the drying quality are chosen: the power of microwave radiation P, thickness of the berries layer h, environmental pressure p. From output indicators of the model the most important are three functions from time: dependence of average humidity of the layer on time Wcp (t), dependence of the speed of change of average humidity on time dWcp (t)/dt, dependence of the layer average temperature on time Tср (t). On the standard models classification the offered model is algorithmic, but not analytical. It means that output characteristics of model are calculated with the entrance ones, not by analytical transformations (it is impossible principally for the modeled process), but by means of spatial and temporary sampling and the corresponding calculation algorithm. Detailed research of the microwave drying process by means of the model allows to allocate the following stages: fast heating, the fast dehydration, the slowed-down dehydration, consolidation of a layer of a product, final drying, heating after dehydration

DEVELOPMENT OF MATHEMATICAL MODEL OF BLACK CURRANT BERRIES DRYING PROCESS IN VACUUM DEVICE WITH THE MICROWAVE POWER SUPPLY

Summary. The mathematical model of black currant berries drying process in vacuum device with the microwave power supply, differing in high space and temporary specification is developed, the structure of separate berries and a layer of berries is considered, heat- and physical parameters depend on coordinate and time as well as in the accounting of berries form change and a berries layer structure in the dehydration process. We used the particles dynamics method for modeling of mechanical behavior of berries which is increasingly being used now in different branches of science and technology. To give the model the high space specification the modeled berries layer consists of 20–50 separate berries, each berry depending on diameter being broken into approximately 100 separate elements. Berries elements are divided into 3 types depending on the physical properties (peel, pulp, seeds). Therefore, in general, from the point of space detail, a layer of berries consists of 2000- 5000 elements. Modeling is carried out in two-dimensional Cartesian space X–Z. The condition of each element of circle is set by four variables: Cartesian coordinates of its center and two components of speed. Mechanical interaction of elements among themselves is accepted to be viscous and elastic that allows to consider the main mechanical properties of berries – the elasticity module, internal friction index. Within the developed model it is considered that between the neighbor elements there can be pushing away forces (at the introduction of elements into each other), or attractions (at a distance of the linked elements from each other). The description of the processes of warm and moisture exchange between the elements as well as between the elements and environment is based upon the standard equations of drying. In model it is considered that the microwave power brought is redistributed in the heated volume in proportion to elements moisture