Simulation study on the influence of electrostatic adsorption grid on the pressure and particle concentration of flow field

Electrostatic adsorption dust removal can effectively improve the dust removal effect of inhalable particles. The grid layout in the flue gas affects the dust removal efficiency and channel pressure drop, and increases the power loss of the fan. In this paper, according to the velocity of flue gas and the concentration of particulate matter in flue gas, combined with the principle of electrostatic adsorption, a three-dimensional module including the main components of adsorption and dust removal was established. The distribution of pressure drop in the flue gas channel caused by the adsorption components with grid layout was simulated and analyzed, which provided a reference for the reasonable layout of dust adsorption components. The simulation results show that the smaller the component diameter, the smaller the pressure difference caused by the same number of components, and the smaller the longitudinal spacing of components.

Simple Finite-Dimensional Modules and Monomial Bases from the Gelfand-Testlin Patterns

One of the most important classes of Lie algebras is sl_n, which are the n×n matrices with trace 0. The representation theory for sl_n has been an interesting research area for the past hundred years and in it, the simple finite-dimensional modules have become very important. They were classified and Gelfand and Tsetlin actually gave an explicit construction of a basis for every simple finite-dimensional module. This paper extends their work by providing theorems and proofs and constructs monomial bases of the simple module.

The stabilizer of two-dimensional vector space of 27-dimensional module of type E6 over a field of characteristic two

The purpose of this paper is to use the notion of [Formula: see text]-sets (cocliques) introduced by the second author in [S. Aldhafeeri and M. Bani-Ata, On the construction of Lie-algebras of type [Formula: see text] for fields of characteristic two, Beitrag Zur Algebra und Geometry 58 (2017) 529–534.] and using Levi components and unipotent radical subgroups of [Formula: see text] to give an elementary and self-contained construction of the stabilizer of two dimensional vector space of 27-dimensional module of type [Formula: see text] over a field of characteristic two. This stabilizer is in fact the maximal parabolic subgroup [Formula: see text] of [Formula: see text] or a Borel subgroup. This construction is elementary on the account that we use not more than little naive linear algebra notions. For more information one can see [M. E. Aschbacher, The 27-dimensional module for [Formula: see text], 1, Invent. Math. 89 (1987) 159–195; M. E. Aschbacher, The 27-dimensional module for [Formula: see text], II, J. London Math. Soc. 37 (1988) 275–293; M. Bani-Ata, On Lie algebras of type [Formula: see text] and [Formula: see text] over finite fields of characteristic two, Preprint; B. Cooperstein, Subgroups of the group [Formula: see text] which are generated by root-subgroups, J. Algebra 46 (1977) 355–388.].

Minimal-dimensional representations of reduced enveloping algebras for

Let $\mathfrak{g}=\mathfrak{g}\mathfrak{l}_{N}(\Bbbk )$ , where $\Bbbk$ is an algebraically closed field of characteristic $p>0$ , and $N\in \mathbb{Z}_{{\geqslant}1}$ . Let $\unicode[STIX]{x1D712}\in \mathfrak{g}^{\ast }$ and denote by $U_{\unicode[STIX]{x1D712}}(\mathfrak{g})$ the corresponding reduced enveloping algebra. The Kac–Weisfeiler conjecture, which was proved by Premet, asserts that any finite-dimensional $U_{\unicode[STIX]{x1D712}}(\mathfrak{g})$ -module has dimension divisible by $p^{d_{\unicode[STIX]{x1D712}}}$ , where $d_{\unicode[STIX]{x1D712}}$ is half the dimension of the coadjoint orbit of $\unicode[STIX]{x1D712}$ . Our main theorem gives a classification of $U_{\unicode[STIX]{x1D712}}(\mathfrak{g})$ -modules of dimension $p^{d_{\unicode[STIX]{x1D712}}}$ . As a consequence, we deduce that they are all parabolically induced from a one-dimensional module for $U_{0}(\mathfrak{h})$ for a certain Levi subalgebra $\mathfrak{h}$ of $\mathfrak{g}$ ; we view this as a modular analogue of Mœglin’s theorem on completely primitive ideals in $U(\mathfrak{g}\mathfrak{l}_{N}(\mathbb{C}))$ . To obtain these results, we reduce to the case where $\unicode[STIX]{x1D712}$ is nilpotent, and then classify the one-dimensional modules for the corresponding restricted $W$ -algebra.

Representations of E7, equivalent combinatorics and algebraic varieties

In our earlier work on a new functor from [Formula: see text]-Mod to [Formula: see text]-Mod, we found a one-parameter ([Formula: see text]) family of inhomogeneous first-order differential operator representations of the simple Lie algebra of type [Formula: see text] in [Formula: see text] variables. Letting these operators act on the space of exponential-polynomial functions that depend on a parametric vector [Formula: see text], we prove that the space forms an irreducible [Formula: see text]-module for any [Formula: see text] if [Formula: see text] is not on an explicitly given projective algebraic variety. Certain equivalent combinatorial properties of the basic oscillator representation of [Formula: see text] over its 27-dimensional module play key roles in our proof. Our result can also be used to study free bosonic field irreducible representations of the corresponding affine Kac–Moody algebra.

DEVELOPMENT OF THE DIMENSIONAL MODULE (GIS-PROJECT) OF THE ECOLOGICAL FRAMEWORK FOR THE BOGRADSKY DISTRICT, THE REPUBLIC OF KHAKASSIA

<p>The current paper describes the basics of the ecological framework theory as a tool aimed at improving functional target characteristics of the regional network in protected areas. It introduces a brief analysis of the experience in the environmental framework development in various subjects of theRussian Federation. The research used ARC GIS 10.1. software to create a spatial ecological framework module for the Bogradsky district (theRepublicofKhakassia). The article offers brief geographical and environmental characteristics of the area as the basis of the content of the information model. The novelty of the research is in its comprehensive and systematically structured approach to the development of the ecological framework, which encompasses the elements of the network of protected areas together with objects of protected natural areas associated with different species of wildlife. The article contains a list of elements included in the spatial GIS module within the project «The Ecological Framework of the Bogradsky District, theRepublicofKhakassia». The project can be a useful tool for inventory, monitoring and development of protected areas</p>

The hyperplanes of DW(5,F) arising from the Grassmann embedding

The hyperplanes of the symplectic dual polar space DW(5; F) that arise from the Grassmann embedding have been classied in [B.N. Cooperstein and B. De Bruyn. Points and hyperplanes of the universal embedding space of the dual polar space DW(5; q), q odd. Michigan Math. J., 58:195{212, 2009.] in case F is a finite field of odd characteristic, and in [B. De Bruyn. Hyperplanes of DW(5;K) with K a perfect eld of characteristic 2. J. Algebraic Combin., 30:567{584, 2009.] in case F is a perfect eld of characteristic 2. In the present paper, these classifications are extended to arbitrary fields. In the case of characteristic 2 however, it was not possible to provide a complete classification. The main tool in the proof is the classification of the quasi-Sp(V; f)-equivalence classes of trivectors of a 6-dimensional symplectic vector space (V; f) obtained in [B. De Bruyn and M. Kwiatkowski. A 14-dimensional module for the symplectic group: orbits on vectors. Comm. Algebra,43:4553{4569, 2015.

On projective coordinate spaces

In the present study, an (n+1)-dimensional module over the local ringK = Mmm(R) is constructed. Further, an n-dimensional projective coordinate space over this module is constructed with the help of equivalence classes. The points and lines of this space are determined and the points are classified. Finally, for a 3-dimensional projective coordinate space, the incidence matrix for a line that goes through the given points and also all points of a line given with the incidence matrix are found by the use of Maple commands.

Strongly 0-dimensional Modules

In a multiplication module, prime submodules have the following property: if a prime submodule contains a finite intersection of submodules, then one of the submodules is contained in the prime submodule. In this paper, we generalize this property to infinite intersection of submodules and call such prime submodules strongly prime submodules. A multiplication module in which every prime submodule is strongly prime will be called a strongly 0-dimensional module. It is also an extension of strongly 0-dimensional rings. After this we investigate properties of strongly 0-dimensional modules and give relations of von Neumann regular modules, Q-modules and strongly 0-dimensional modules