Monoidal Hom-Hopf algebras

Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a symmetric monoidal category such that Hom-algebras coincide with algebras in this monoidal category, and similar properties for coalgebras, Hopf algebras and Lie algebras.Comment: 25 pages; extended version: compared to the version that appeared in Comm. Algebra, the Section Preliminary Results and Remarks 5.1 and 6.1 have been adde

A multiple exp-function method for nonlinear differential equations and its application

A multiple exp-function method to exact multiple wave solutions of nonlinear partial differential equations is proposed. The method is oriented towards ease of use and capability of computer algebra systems, and provides a direct and systematical solution procedure which generalizes Hirota's perturbation scheme. With help of Maple, an application of the approach to the $3+1$ dimensional potential-Yu-Toda-Sasa-Fukuyama equation yields exact explicit 1-wave and 2-wave and 3-wave solutions, which include 1-soliton, 2-soliton and 3-soliton type solutions. Two cases with specific values of the involved parameters are plotted for each of 2-wave and 3-wave solutions.Comment: 12 pages, 16 figure

Support vector machine classifier via L0/1 soft-margin loss

Support vector machines (SVM) have drawn wide attention for the last two decades due to its extensive applications, so a vast body of work has developed optimization algorithms to solve SVM with various soft-margin losses. To distinguish all, in this paper, we aim at solving an ideal soft-margin loss SVM: L0/1 soft-margin loss SVM (dubbed as L0/1 -SVM). Many of the existing (non)convex soft-margin losses can be viewed as one of the surrogates of the L0/1 soft-margin loss. Despite its discrete nature, we manage to establish the optimality theory for the L0/1 -SVM including the existence of the optimal solutions, the relationship between them and P-stationary points. These not only enable us to deliver a rigorous definition of L0/1 support vectors but also allow us to define a working set. Integrating such a working set, a fast alternating direction method of multipliers is then proposed with its limit point being a locally optimal solution to the L0/1 -SVM. Finally, numerical experiments demonstrate that our proposed method outperforms some leading classification solvers from SVM communities, in terms of faster computational speed and a fewer number of support vectors. The bigger the data size is, the more evident its advantage appears

Minimization of the environmental impact in the chrome tanning process by a closed-loop recycling technology

Content: It is acknowledged that conventional chrome tanning in leather processing discharges significant amounts of chromium, dissolved solids and chlorides. The recycling technology is one of the effective solutions to reduce the environmental impact of chrome tanning waste water at source. In this work, a novel closed recycling technology of chrome tanning wastewater was applied in the tanning process of the goat skins at a pilot scale level. The properties of chrome tanning liquors obtained by the recycling technology and the resultant crust were analyzed. The results show that this close recycling process works well. The contents of Cr2O3, total organic carbon, ammonia nitrogen and chloride ion in the waste water tend to accumulate with the increase of recycling times, and finally reach a balance after 5 times of recycling. The obtained leather sample is full, soft and having a shrinkage temperature comparable to that of conventional chrome tanned leather. SEM images indicate that the resulting leather samples by this recycling technology show fine and clean grain and well-dispersed fibrils. TG and DSC results show that the thermal stability of wet blue leathers tanned by the circular process are similar to those tanned by conventional chrome tanning process. Compared with conventional chrome tanning technology, water, salt and chrome tanning agent are saved in this process, and the zero emission of chrome tanning wastewater is realized. The cleaner production technology exhibits promising application prospect for its economic and environmental benefits. Take-Away: 1. A novel closed recycling technology of chrome tanning wastewater was applied in the tanning process of the goat skins at a pilot scale level. 2. The chrome tanning liquors obtained by the recycling technology and the resultant crust were analyzed. 3. Water, Sodium chloride and chrome tanning agent are saved by the closed recycling technology, and the zero emission of chrome tanning wastewater is realized

Strong and auxiliary forms of the semi-Lagrangian method for incompressible flows

We present a review of the semi-Lagrangian method for advection-diusion and incompressible Navier-Stokes equations discretized with high-order methods. In particular, we compare the strong form where the departure points are computed directly via backwards integration with the auxiliary form where an auxiliary advection equation is solved instead; the latter is also referred to as Operator Integration Factor Splitting (OIFS) scheme. For intermediate size of time steps the auxiliary form is preferrable but for large time steps only the strong form is stable

Structural evolution of GeMn/Ge superlattices grown by molecular beam epitaxy under different growth conditions

GeMn/Ge epitaxial 'superlattices' grown by molecular beam epitaxy with different growth conditions have been systematically investigated by transmission electron microscopy. It is revealed that periodic arrays of GeMn nanodots can be formed on Ge and GaAs substrates at low temperature (approximately 70°C) due to the matched lattice constants of Ge (5.656 Å) and GaAs (5.653 Å), while a periodic Ge/GeMn superlattice grown on Si showed disordered GeMn nanodots with a large amount of stacking faults, which can be explained by the fact that Ge and Si have a large lattice mismatch. Moreover, by varying growth conditions, the GeMn/Ge superlattices can be manipulated from having disordered GeMn nanodots to ordered coherent nanodots and then to ordered nanocolumns

Uncertainty quantification for kinetic models in socio-economic and life sciences

Kinetic equations play a major rule in modeling large systems of interacting particles. Recently the legacy of classical kinetic theory found novel applications in socio-economic and life sciences, where processes characterized by large groups of agents exhibit spontaneous emergence of social structures. Well-known examples are the formation of clusters in opinion dynamics, the appearance of inequalities in wealth distributions, flocking and milling behaviors in swarming models, synchronization phenomena in biological systems and lane formation in pedestrian traffic. The construction of kinetic models describing the above processes, however, has to face the difficulty of the lack of fundamental principles since physical forces are replaced by empirical social forces. These empirical forces are typically constructed with the aim to reproduce qualitatively the observed system behaviors, like the emergence of social structures, and are at best known in terms of statistical information of the modeling parameters. For this reason the presence of random inputs characterizing the parameters uncertainty should be considered as an essential feature in the modeling process. In this survey we introduce several examples of such kinetic models, that are mathematically described by nonlinear Vlasov and Fokker--Planck equations, and present different numerical approaches for uncertainty quantification which preserve the main features of the kinetic solution.Comment: To appear in "Uncertainty Quantification for Hyperbolic and Kinetic Equations

Experimental investigation on liquefaction and post-liquefaction deformation of stratified saturated sand under cyclic loading

The soils are often distributed in a stratified structure. When an earthquake occurs, there are always risks of liquefaction for stratified soils which can cause serious consequences. The research aims to investigate the liquefaction and post-liquefaction deformation of saturated sand with stratified structure. The influences of liquefaction and post-liquefaction deformation were analyzed by varying the thickness, position, and layers of powdery sands. The findings showed that the correlations between the times taken to reach liquefaction for cyclic loading and the thicknesses of the powdery sandy interlayer are non-linear. With the optimal thickness, the powdery sand interlayer can effectively prevent the transfer of power water pressure. And two-layer powdery interlayer in the sample was more favorable to resist pore water pressure than that with single layer. The strength of post-liquefaction deformation and failure patterns are closely related to the distribution of powdery layer. The work provides new research evidence on the liquefaction and failure mechanism of saturated sands with stratified structure under cyclic loading which often happen during earthquakes

A Class of Coupled KdV systems and Their Bi-Hamiltonian Formulations

A Hamiltonian pair with arbitrary constants is proposed and thus a sort of hereditary operators is resulted. All the corresponding systems of evolution equations possess local bi-Hamiltonian formulation and a special choice of the systems leads to the KdV hierarchy. Illustrative examples are given.Comment: 8 pages, late

Extension of Hereditary Symmetry Operators

Two models of candidates for hereditary symmetry operators are proposed and thus many nonlinear systems of evolution equations possessing infinitely many commutative symmetries may be generated. Some concrete structures of hereditary symmetry operators are carefully analyzed on the base of the resulting general conditions and several corresponding nonlinear systems are explicitly given out as illustrative examples.Comment: 13 pages, LaTe