Enveloping algebras of generalized H-Hom-Lie algebras

Let H be a Hopf algebra and HYD the Yetter- Drinfeld category over H. First, the enveloping algebra of generalized H-Hom-Lie algebra L, i.e., Hom-Lie algebra L H in the category HYD, is constructed. Secondly, it is obtained that U（L） = T（ L）/L where I is the Hom-ideal of T（L） generated by {ll＇-l_（（-1））·l＇l_0-[l,l＇]｜l,l＇∈L}, and u： L,T（L）/I is the canonical map. Finally, as the applications of the result, the enveloping algebras of generalized H-Lie algebras, i.e., the Lie algebras in the category MyDn and the Hom-Lie algebras in the category of left H-comodules are presented, respectively.

Bursting oscillation in CO oxidation with small excitation and the enveloping slow-fast analysis method

Based on the traditional scheme for a nonlinear system with multiple time scales, the enveloping slow-fast analysis method is developed in the paper, which can be employed to investigate the dynamics of nonlinear fields with multiple time scales with periodic excitation. Upon using the method, the behaviors of the kinetic model of CO oxidation on the platinum group metals have been explored in detail. Two typicM bursting phenomena such as Fold/Fold/Hopf bursting and Fold/Fold bursting, are presented, the bifurcation mechanisms of which have been obtained. Furthermore, the dynamic difference between the two cases corresponding to relatively large and small perturbation frequencies, respectively, has been presented, which can be used to describe the influence of the frequencies involving in the evolution on the bursting behaviors in the system.

Temperature Field Simulation and Experimental Study of Anti‑backlash Single‑Roller Enveloping Hourglass Worm Gear

In gear transmission,temperature rise has a non-negligible impact on the accuracy,noise and transmission efficiency.However,there is no relevant research on the temperature rise of the anti-backlash single-roller enveloping hourglass worm(ASEHW)gear.To solve this problem,based on tribology principle and Hertz contact theory,the thermal power calculation method of the ASEHW gear was proposed for the first time and thermal analysis was carried out by Ansys software.The bulk temperature of the ASEHW gear under four different rotating speed(300 r/min,600 r/min,900 r/min,1200 r/min)is calculated.The main factors causing temperature rise of the ASEHW gear are analyzed theoretically.Meanwhile,an experimental study is performed to verify the simulation results and validate the theory methods.The theory presented in this paper provides a solution for the thermal power calculation of ASEHW gear.This research provides a theoretical basis for further optimization of ASEHW gear.

Extensions of quantum enveloping algebras

In this paper, we define a class of extended quantum enveloping algebras Uq （f（K, J）） and some new Hopf algebras, which are certain extensions of quantum enveloping algebras by a Hopf algebra H. This construction generalizes some well-known extensions of quantum enveloping algebras by a Hopf algebra and provides a large of new noncommutative and nonco- commutative Hopf algebras.

Experiment on low-frequency electromagnetic waves propagating in shock-tube-generated magnetized cylindrical enveloping plasma

We propose a method of applying a static magnetic field to reduce the attenuation of the magnetic field component(SH) of low-frequency electromagnetic(LF EM) waves in dense plasma. The principle of this method is to apply a static magnetic field to limit electron movement, thereby increasing the equivalent resistance and thus reducing the induced current and SH. We consider the static magnetic field acting on the plasma of the entire induced current loop rather than on the local plasma, where the induced current is excited by the magnetic field component of LF EM waves. Analytical expressions of SH suitable for magnetized cylindrical enveloping plasma are derived by adopting an equivalent circuit approach, by which SHis calculated with respect to various plasma parameter settings. The results show that SH can be reduced under a static magnetic field and the maximum magnetic field strength that mitigates blackout is less than 0.1 T. Experiments in which LF EM waves propagate in a shock-tubegenerated magnetized cylindrical enveloping plasma are also conducted. SH measured under the magnetic field(the magnetic field strength B0 acting on the magnetic field probe was about0.06 T) reduces at f=10 MHz and f=30 MHz when ne≈1.9×1013 cm-3, which is consistent with theoretical results. The verification of the theory thus suggests that applying a static magnetic field with a weak magnetic field has the potential to improve the transmission capacity of LF EM waves in dense plasma.

Enveloping Lie Algebras of Low Dimensional Leibniz Algebras

We calculate the enveloping Lie algebras of Leibniz algebras of dimensions two and three. We show how these Lie algebras could be used to distinguish non-isomorphic (nilpotent) Leibniz algebras of low dimension in some cases. These results could be used to associate geometric objects (loop spaces) to low dimensional Leibniz algebras.

ENVELOPING THEORY BASED METHOD FOR THE DETERMINATION OF PATH INTERVAL AND TOOL PATH OPTIMIZATION FOR SURFACE MACHINING

An enveloping theory based method for the determination of path interval in three axis NC machining of free form surface is presented, and a practical algorithm and the measures for improving the calculating efficiency of the algorithm are given. Not only the given algorithm can be used for ball end cutter, flat end cutter, torus cutter and drum cutter, but also the proposed method can be extended to arbitrary milling cutters. Thus, the problem how to strictly calculate path interval in the occasion of three axis NC machining of free form surfaces with non ball end cutters has been resolved effectively. On this basis, the factors that affect path interval are analyzed, and the methods for optimizing tool path are explored.

EXPERIMENTAL STUDY ON LUBRICATION BEHAVIOR OF DOUBLE ENVELOPING HOUK GLASSWOKM GEARING

The lubrication behavior of double enveloping hourglass worm gearing is studied experimently. The effects of rotational speed of the worm and load on the formation of the fluid film between engagement tooth surfaces are investigated in detail. and working angle of this worm gearing is also analyzed. Some beneficial results are obtained。

Realization of Poisson enveloping algebra

For a Poisson algebra, the category of Poisson modules is equivalent to the module category of its Poisson enveloping algebra, where the Poisson enveloping algebra is an associative one. In this article, for a Poisson structure on a polynomial algebra S, we first construct a Poisson algebra R, then prove that the Poisson enveloping algebra of S is isomorphic to the specialization of the quantized universal enveloping algebra of R, and therefore, is a deformation quantization of R.

Discovery of “Enveloping Surface of Oil and Gas Overpressure Migration” in the Songliao Basin and its bearings on hydrocarbon migration and accumulation mechanisms

The Fuyang oil layer of the Songliao Basin is a tight and low-permeability sandstone pay zone formed in the fluvial-shallow water delta environment.In the formation are mainly lithologic reservoir and tight reservoir.The lacustrine-mudstone of K2qn1 is a good source rock and also acts as a good regional cap rock.The Fuyang oil layer is a typical upper-source and lower-reservoir pattern distributed in a large area.Based on a large number of exploration and development data, a macroscopic enveloping surface is found developed in the Fuyang oil layer, which is below K2qn1.The effective reservoirs within the enveloping surface are commonly saturated with oil, and below the enveloping surface are mainly water layers.The distance from the enveloping surface to the bottom of the source rock is usually 100-350 m and at most 550 m.Through the research of the distribution patterns and the physical properties of the sandbodies above or beneath the source rock, it is concluded that: 1) the enveloping surface is the boundary of the overpressure hydrocarbon migration; 2) the spacial distribution of the pressure release beds controls the direction and the distance of the overpressure hydrocarbon migration; 3) tight oil reservoirs and lenticular oil reservoirs are mainly formed inside the envelope surface, whereas, conventional reservoirs are formed outside the envelope surface as a result of the buoyancy hydrocarbon migration.The discovery of the "overpressure hydrocarbon migration enveloping surface" and the concepts of overpressure hydrocarbon migration and buoyancy hydrocarbon migration not only challenge the old notion that "hydrocarbon migrates along the faults and is distributed along fault belts" in the Fuyang oil layer of the Songliao Basin, give a new explanation to the long-distance-oil-downwards migration (hundreds of meters) and expand the exploration potential of the Fuyang oil layer, and provide a rational guidance to the exploration of syncline plays, but also better categorize tight oil/gas and conventional reservoirs in all of the key elements related to hydrocarbon migration, accumulation, reservoir characteristics and oil and gas spatial distribution.

Realizing Enveloping Algebras via Varieties of Modules

By using the Ringel-Hall algebra approach, we investigate the structure of the Lie algebra L（A） generated by indecomposable constructible sets in the varieties of modules for any finite- dimensional C-algebra A. We obtain a geometric realization of the universal enveloping algebra R（A） of L（A）, this generalizes the main result of Riedtmann. We also obtain Green＇s formula in a geometric form for any finite-dimensional C-algebra A and use it to give the comultiplication formula in R（A）.

(Quasi-)Poisson Enveloping Algebras

We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative Poisson algebra, the category of quasi-Poisson modules is equivalent to the category of left modules over its quasi-Poisson enveloping algebra, and the category of Poisson modules is equivalent to the category of left modules over its Poisson enveloping algebra.

DG Poisson algebra and its universal enveloping algebra

We introduce the notions of differential graded(DG) Poisson algebra and DG Poisson module. Let A be any DG Poisson algebra. We construct the universal enveloping algebra of A explicitly, which is denoted by A^(ue). We show that A^(ue) has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over A is isomorphic to the category of DG modules over A^(ue). Furthermore, we prove that the notion of universal enveloping algebra A^(ue) is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra.

Extension of a quantized enveloping algebra by a Hopf algebra

Suppose that H is a Hopf algebra,and g is a generalized Kac-Moody algebra with Cartan matrix A =(aij)I×I,where I is an index set and is equal to either {1,2,...,n} or the natural number set N.Let f,g be two mappings from I to G(H),the set of group-like elements of H,such that the multiplication of elements in the set {f(i),g(i)|i ∈I} is commutative.Then we define a Hopf algebra Hgf Uq(g),where Uq(g) is the quantized enveloping algebra of g.

q-DEFORMED BOSON REPRESENTATIONS OF UNIVERSAL ENVELOPING ALGEBRAS IN THE CASE WHERE q IS A ROOT OF UNITY

By further improving the method of q-deformed boson realization, the standard basis is built for the typical subalgebra chains. When q is a root of unity, the irreducible and indecomposable representations of quantum universal enveloping algebras (A_(l-1))q and (C_l)q are constructed and their reduction structure and decompositions are analyzed.

Universal Enveloping Algebras of Simple Symplectic Anti-Jordan Triple Systems

In this work we axe concerned with the universal associative envelope of a finite-dimensional simple symplectic anti-Jordan triple system （AJTS）. We prove that if T is a triple system as above, then there exists an associative algebra U（T） and an injective homomorphism ε ： T→ U（T）, where U（T） is an AJTS under the triple product defined by （a, b, c） = abc- cba. Moreover, U（T） is a universal object with respect to such homomorphisms. We explicitly determine the PBW-basis of U（T）, the center Z（U（T）） and the Gelfand-Kirillov dimension of U（T）.

The CCAAT/Enhancer Binding Protein Beta(cebpb)is essential for the development of enveloping layer(EVL)in zebrafish

Epiboly,the coordinated spreading of the enveloping layer(EVL),the yolk syncytial layer(YSL)and the deep cells(DCs)toward the vegetal pole,is required for gastrulation.Interference with the EVL leads to early developmental failure.However,the genetic factors underlying EVL differentiation are so far unknown.By in-depth analyzing of single-cell sequencing data from 4 h post fertilization zebrafish embryos,we identified 105 genes(FDR<0.05)which showed highly specific EVL expression,among which the transcription factor cebpb and genes(krt18,cldne,cldnb,krt4,krt5)involved in cell-cell junction formation were exclusively expressed in EVL.To explore the role of cebpb in EVL differentiation,we knocked down its expression by morpholino-labeled antisense RNA.The morphant embryos showed disrupted EVL and developmental termination prior to epiboly.In accordance,expression of the EVL specific cell-adhesion molecule genes were significantly reduced.Thus,cebpb is the earliest EVL marker and essential for EVL differentiation in zebrafish.The elucidation of the specific EVL gene set provides us new insights into the molecular mechanisms underlying EVL differentiation.

A Parameterization of the Canonical Bases of Affine Modified Quantized Enveloping Algebras

For a symmetrizable Kac-Moody Lie algebra g, Lusztig introduced the corresponding modified quantized enveloping algebra˙U and its canonical basis˙B given by Lusztig in 1992. In this paper, in the case that g is a symmetric Kac-Moody Lie algebra of finite or affine type, the authors define a set M which depends only on the root category R and prove that there is a bijection between M and ˙B, where R is the T^2-orbit category of the bounded derived category of the corresponding Dynkin or tame quiver. The method in this paper is based on a result of Lin, Xiao and Zhang in 2011, which gives a PBW-type basis of U^+.

Three-Dimensional Sound Source Location Algorithm for Subsea Leakage Using Hydrophone

Leakages from subsea oil and gas equipment cause substantial economic losses and damage to marine ecosystem,so it is essential to locate the source of the leak.However,due to the complexity and variability of the marine environment,the signals collected by hydrophone contain a variety of noises,which makes it challenging to extract useful signals for localization.To solve this problem,a hydrophone denoising algorithm is proposed based on variational modal decomposition(VMD)with grey wolf optimization.First,the average envelope entropy is used as the fitness function of the grey wolf optimizer to find the optimal solution for the parameters K andα.Afterward,the VMD algorithm decomposes the original signal parameters to obtain the intrinsic mode functions(IMFs).Subsequently,the number of interrelationships between each IMF and the original signal was calculated,the threshold value was set,and the noise signal was removed to calculate the time difference using the valid signal obtained by reconstruction.Finally,the arrival time difference is used to locate the origin of the leak.The localization accuracy of the method in finding leaks is investigated experimentally by constructing a simulated leak test rig,and the effectiveness and feasibility of the method are verified.

Global Solutions to Nonconvex Problems by Evolution of Hamilton-Jacobi PDEs

Computing tasks may often be posed as optimization problems.The objective functions for real-world scenarios are often nonconvex and/or nondifferentiable.State-of-the-art methods for solving these problems typically only guarantee convergence to local minima.This work presents Hamilton-Jacobi-based Moreau adaptive descent(HJ-MAD),a zero-order algorithm with guaranteed convergence to global minima,assuming continuity of the objective function.The core idea is to compute gradients of the Moreau envelope of the objective(which is"piece-wise convex")with adaptive smoothing parameters.Gradients of the Moreau envelope(i.e.,proximal operators)are approximated via the Hopf-Lax formula for the viscous Hamilton-Jacobi equation.Our numerical examples illustrate global convergence.