Duality of Anderson tt-motives having N≠0N\ne0

This paper extends the main result of the paper "Duality of Anderson $t$-motives", that the lattice of the dual of a t-motive $M$ is the dual lattice of $M$, to the case when the nilpotent operator $N$ of $M$ is non-zero.Comment: 21 pages; minor correction

Lattice map for Anderson t-motives : first approach

There exists a lattice map from the set of pure uniformizable Anderson t-motives to the set of lattices. It is not known what is the image and the fibers of this map. We prove a local result that sheds the first light to this problem and suggests that maybe this map is close to 1 -- 1. Namely, let $M(0)$ be a t-motive of dimension $n$ and rank $r=2n$ \ --- \ the $n$-th power of the Carlitz module of rank 2, and let $M$ be a t-motive which is in some sense "close" to $M(0)$. We consider the lattice map $M \mapsto L(M)$, where $L(M)$ is a lattice in $C^n$. We show that the lattice map is an isomorphism in a "neighborhood" of $M(0)$. Namely, we compare the action of monodromy groups: (a) from the set of equations defining t-motives to the set of t-motives themselves, and (b) from the set of Siegel matrices to the set of lattices. The result of the present paper gives that the size of a neighborhood, where we have an isomorphism, depends on an element of the monodromy group. We do not know whether there exists a universal neighborhood. Method of the proof: explicit solution of an equation describing an isomorphism between two t-motives by a method of successive approximations using a version of the Hensel lemma.Comment: 26 pages. Minor improvement

The aerodynamics of a jet of particles in a channel

The main cause for dust discharge is ejection, i.e. formation of directional air flows in a stream of a bulk material due to the dynamic interaction of bombarding particles with air. Discovery of induced air flow occurrence regularities enables both forecasting the level of air pollutions with aerosol emission and choosing the optimum engineering solutions of air containment and dedusting. So far we have studied solid particles flowing in a chute and a jet of loose matter. Both situations represent extreme cases of the more general problem of material flowing through a duct with different distances between flow boundaries and duct walls. Without detriment to generality of the problem we shall consider a flat flow limited by vertical walls

Ejection of air by the stream of bulk materials in a vertical perforated channel

Were obtained and solved the hydrodynamic equations for estimating intercomponent communication in a vertical perforated chute when moving there gravitational flows of granular materials and ejected air. Identified parameters that provide the greatest decrease in volumes of ejection through recycling air. The research is being supported by the Council for Grants of the President of the Russian Federation (projects NSH-588.2012.8), RFBR (project number 12-08-97500-p_center_a), and Strategic Development Plan of BSTU named after. V. G. Shukhov

Basic regularities of ejection air by flow of freely falling particles

Entrained air (ejection process) by flow of freely falling particles of the bulk material is considered by us from the position of the classical laws of dynamics of twocomponent streams "particulate matter - the air." The nature of this process is determined by the volumetric intercomponent interaction, detected as a result of excessive speed over the speed of the incident particles of ejected air. The research is being supported by the Council for Grants of the President of the Russian Federation (projects NSH-588.2012.8), RFBR (project number 12-08-97500-p_center_a), and Strategic Development Plan of BSTU named after. V. G. Shukhov

Introduction to Anderson t-motives: a survey

This is a survey on Anderson t-motives -- the functional field analogs of abelian varieties with multiplication by an imaginary quadratic field. We define their lattices, the group $H^1$, their tensor products and the duality functor. Some examples of explicit calculations are given, some elementary research problems are stated.Comment: 30 page

Aerodynamic properties of particles in the gravitational flow of a chuted bulk material

Chutes are a linking element of transportation lines used for transfers of reprocessed materials from one transporting group or equipment to another. The mode of the chuted material motion and the nature of the associated aerodynamic processes are determined by the aggregate physical and mechanical properties of the material being transferred and structural design of chutes. Structurally chutes are subdivided into prismatic, cylindrical and pyramid-shaped (bin) chutes by shape and into vertical, tip and kinked chutes by the bottom slope angle. The most common in practice are tip chutes of a prismatic or a pyramid shape. The purpose of this work was the study of particle movement of granular materials in the sloping chute. In the result of the research, we revealed the following