A generalized funk’s section theorem for measures

If L is a star body in R~n whose central(n-i)-slices have the same(n-i)-dimensional measure μ_(n-i)(with appropriate density)as the central(n-i)-slices of an origin-symmetric star body K,then the corresponding n-dimensional measures μ_n of K and L satisfy μ_n(K)≤μ_n(L).This extends a generalized Funk’s section theorem for volumes to that for measures.     

Lüroth Expansion Digits and Maclaurin's Inequality

It is well known that for almost all real number x, the geometric mean of the first n digits d_i(x) in the Lüroth expansion of x converges to a number K_0 as n→∞. On the other hand, for almost all x, the arithmetric mean of the first n Lüroth expansion digits d_i(x) approaches infinity as n→∞. There is a sequence of refinements of the AM-GM inequality, Maclaurin's inequalities, relating the 1/k-th powers of the k-th elementary symmetric means of n numbers for 1≤k≤n. In this paper, we investigate what happens to the means of Lüroth expansion digits in the limit as one moves f(n) steps away from either extreme. We prove sufficient conditions on f(n) to ensure divergence when one moves away from the arithmetic mean and convergence when one moves f(n) steps away from geometric mean.     

Properties of a class of groups on <Emphasis Type="Italic">Z</Emphasis><Subscript><Emphasis Type="Italic">m</Emphasis></Subscript>

In this paper, we obtain the factorization of direct production and order of group GL(n, Z _m ) in a simple method. Then we generalize some properties of GL(2, Z _p ) proposed by Huppert, and prove that the group \(GL\left( {2,{Z_{{z^\lambda }}}} \right)\) is solvable. We also prove that group GL(n, Z _p ) is solvable if and only if GL(n, Z _p ) is solvable, and list the generators of groups GL(n, Z _p ) and SL(n, Z _p ). At last, we prove that PSL(2, Z _p )(p > 3) and PSL(n, Z _p )(n > 3) are simple.     

Vertex disjoint cycles in intersection graphs of bases of matroids

The intersection graph of bases of a matroid M=(E, B) is a graph G=G~I(M) with vertex set V(G) and edge set E(G) such that V(G)=B(M) and E(G)={BB′:|B∩B′|≠0, B, B′∈B(M), where the same notation is used for the vertices of G and the bases of M. Suppose that|V(G~I(M))| =n and k_1+k_2+…+k_p=n, where k_i is an integer, i=1, 2,…, p. In this paper, we prove that there is a partition of V(G~I(M)) into p parts V_1 , V_2,…, V_p such that |V_i| =k_i and the subgraph H_i induced by V_i contains a k_i-cycle when k_i ≥3, H_i is isomorphic to K_2 when k_i =2 and H_i is a single point when k_i =1.     

Gracefulness of several unconnected graphs with wheel

In the paper, we study the gracefulness of several unconnected graphs related to wheel. For natural number p ≥1,t ≥1, let n =2t +3, 2t +4, which proved W_n∪K_(p,t)~(1)∪K_(p,t)~(2) is graceful; for p ≥1, t ≥1,let n=2t+3,2t+4, then W_(n,2n+1)∪K_(p,t)~(1)∪K_(p,t)~(2) is graceful and for m≥1,r ≥1, let n =2m +5, W_(n,2n+1) ∪( C_3∨K m) U St( r)is graceful.     

Binding number,minimum degree and bipancyclism in bipartite graphs

Let G =(V_1,V_2,E) be a balanced bipartite graph with2 n vertices.The bipartite binding number of G,denoted by B(G),is defined to be n if G =K_n and min i∈{1,2}|N(S)|n min |N(S)|/|S|otherwise.We call G bipancyclic if it contains a cycle of every even length m for 4 ≤ m ≤ 2n.A theorem showed that if G is a balanced bipartite graph with 2n vertices,B(G) 3 / 2 and n 139,then G is bipancyclic.This paper generalizes the conclusion as follows:Let 0 c 3 / 2 and G be a 2-colmected balanced bipartite graph with 2n(n is large enough) vertices such that B(G) c and δ(G)(2-c)n/(3-c)+2/3.Then G is bipancyclic.     

Soil Properties under Major Halophytic Vegetation Communities in Arid Regions

Soil physical, chemical, and biological properties of seven desert halophytes (Kalidium foliatum, Achnatherum splendens, Leymus secalinus, Phragmites australis, Karelinia caspia, Tamarix ramosissima, Atriplex tatarica) were investigated in saline-sodic badlands of the Hexi Corridor, Gansu Province, China. The results showed that sampled soils were generally infertile and characterized by low levels of organic matter, available nitrogen, phosphorus, copper, manganese, and zinc as well as microbial communities with dominant bacteria supporting native desert halophytes. Available potassium and iron were sufficient in the study sites. With increasing soil layer depth, the concentrations of organic matter, available nitrogen, potassium, manganese, copper, bacteria, and actinomyces in the soil decreased significantly (P<0.05), while the concentrations of moisture, available iron, and zinc in the soil increased significantly (P<0.05). The contents of moisture, total salt, organic matter, available nitrogen, potassium, iron, manganese, zinc, copper, bacteria, and actinomyces showed significant seasonal variations (P<0.05). All these variables except bacteria and actinomyces were the greatest in summer and the lowest in spring. The redundancy analysis revealed that total salt, organic matter, available potassium, and copper were positively correlated with vegetation coverage. K. foliatum community was the constructive or dominant species in the desert community for the biological control of soil salinization.     

Research on a Class of Equations over Finite Fields

Let F_q stand for the finite field of odd characteristic p with q elements(q=p~n,n∈N)and F_q~* denote the set of all the nonzero elements of F_q.In this paper,by using the augmented degree matrix and the result given by Cao,we obtain a formula for the number of rational points of the following equation over F_q:f(x _1,x _2,...,x _n)=(a_1 x_1 x_2~d+a_2 x_2 x_3~d...+a_(n-1)x_(n-1)x_n~d+a_n x_n x_1~d)~λ-bx_1~(d1)x_2~d2...x_n~(dn),with a_i,b∈F_q~*,n≥2,λ0 being positive integers,and d,d_i being nonnegative integers for 1≤i n.This technique can be applied to the polynomials of the form h_1~λ=h_2 with λ being positive integer and h_1,h_2∈F_q[x _1,x _2,...,x _n].It extends the results of the Markoff-Hurwitz-type equations.     

Generation of Linear and Parabolic Concentration Gradients by Using a Christmas Tree-Shaped Microfluidic Network

This paper describes a simple method of generating concentration gradients with linear and parabolic profiles by using a Christmas tree-shaped microfluidic network.The microfluidic gradient generator consists of two parts:a Christmas tree-shaped network for gradient generation and a broad microchannel for detection.A two-dimensional model was built to analyze the flow field and the mass transfer in the microfluidic network.The simulating results show that a series of linear and parabolic gradient profiles were generated via adjusting relative flow rate ratios of the two source solutions(R_L~2≥0.995 and _PR~2≥0.999),which could match well with the experimental results(R_L~2≥0.987 and _PR~2≥0.996).The proposed method is promising for the generation of linear and parabolic concentration gradient profiles,with the potential in chemical and biological applications such as combinatorial chemistry synthesis,stem cell differentiation or cytotoxicity assays.     

Analysis of diversity of CO I gene and system generation of nine species of chitons

Cytochrome c oxidase subunit Ⅰ(COⅠ) genes from 9 chiton species in China’s coast area were sequenced. A phylogeny tree about these gene sequences were reconstructed together with other 4 COⅠgene sequences of chitons from Genbank. The affinity genetic relationship and the taxonomic status of molecular evolution for these 13 chiton species were analyzed. The results show that Liolophura japonica and Onithochiton hirasei belong to Chitonidae, Acanthochiton rubrolineatus and Acanthochiton dissimilis belong to Acanthochitonidae, and Placiphorella japonica and Mopalia retifera belong to the same family Mopliidae. However, Lepidozona coreanica, Ischnochiton comptus, and Ischnochiton hakodadensis are not supposed to be referred to Ischnochi-tonidae according to the genetic distance analysis (L. coreanica, I. comptus, and I. hakodadensis are usually classed as Ischnochitonidae according to their morphological character). Furthermore, I. hakodadensis could not been classed as Ischnochiton, and it is more likely to be treated as a close relative of Lepidozona.     

Fault-tolerant cycles embedding in folded hypercubes

The generalized conditional fault-tolerant embedding is investigated, in which the n-dimensional folded hypercube networks(denoted by FQ_n) acts as the host graph, and the longest fault-free cycle represents the guest graph. Under the conditions looser than that of previous works, it is shown that FQ_n has a cycle with length at least 2~n-2︱F_v︱ when the number of faulty vertices and non-critical edges is at most 2n-4; where ︱F_v︱ is the number of faulty vertices. It provides further theoretical evidence for the fact that FQ_n has excellent node-fault-tolerance and edge-fault-tolerance when used as a topology of large scale computer networks.     

Further results on generalized LCM matrices

Let S={x_1,x_2,...,x_n } be a set of n distinct positive integers and f be an arithmetic function.By(f[S])(resp.( f[S])),we denote the n*n matrix whose i,j entry is Σ[x_i,x_j]|l l∈S f(l) (resp.Σx∈Sf(x)-Σ x_i,|l l∈S f(l)-Σ x_j,|l l∈S f(l)+Σ[x_i,x_j]|l l∈S f(l)).In this paper,we first investigate the structures of the matrices ( f[S]) and( f[S]),then we give the formulae for the determinants of these matrices.These extend the results obtained by Bege in 2011.Finally,we give two examples to demonstrate the validity of our main results.     

A novel hydrothermal method for zinc extraction and separation from zinc ferrite and electric arc furnace dust

A novel hydrothermal process was developed to extract zinc from pure zinc ferrite (ZnFe₂O₄) nanopowder and zinc-containing electric arc furnace (EAF) dust using hexahydrated ferric chloride (FeCl₃·6H₂O) as a decomposing agent. The effects of solid FeCl₃·6H₂O to ZnFe₂O₄ ratio by mass (R_F/Z), hydrothermal reaction temperature, and time on zinc extraction were systematically investigated. In the results, when the hydrothermal reaction is conducted at 150℃ for 2 h with R_F/Z of 15:20, the efficiency of zinc extraction from ZnFe₂O₄ reaches 97.2%, and the concentration of ferric ions (Fe3+) in the leaching solution is nearly zero, indicating a high selectivity for zinc. In addition, the zinc extraction efficiency from the EAF dust reaches 94.5% in the case of the hydrothermal reaction performed at 200℃ for 10 h with the solid FeCl₃·6H₂O to EAF dust ratio by mass (R_{F/EAF dust}) of 15:10. Zinc and iron separation is achieved by adjusting the pH value of the leaching solution according to the different precipitation pH values of metal hydroxides.     

Threshold Dynamics of an SIR Epidemic Model with Nonlinear Incidence Rate and Non-Local Delay Effect

In this paper, we are concerned with a reaction- diffusion SIR epidemic model with nonlinear incidence rate and non-local delay effect in a continuous bounded spatial domain. We introduce the basic reproduction number R₀ of the model by the idea of next generation operator. By means of the theory of dynamical systems and uniform persistence, we investigate the global dynamics of the model in terms of R₀. Finally, we implement numerical simulations to show the feasibility of our results and explore some epidemiological insights.     

Activity coefficients of NiO and CoO in CaO-Al2O3-SiO2 slag and their application to the recycling of Ni-Co-Fe-based end-of-life superalloys via remelting

To design optimal pyrometallurgical processes for nickel and cobalt recycling, and more particularly for the end-of-life process of Ni-Co-Fe-based end-of-life (EoL) superalloys, knowledge of their activity coefficients in slags is essential. In this study, the activity coefficients of NiO and CoO in CaO-Al₂O₃-SiO₂ slag, a candidate slag used for the EoL superalloy remelting process, were measured using gas/slag/metal equilibrium experiments. These activity coefficients were then used to consider the recycling efficiency of nickel and cobalt by remelting EoL superalloys using CaO-Al₂O₃-SiO₂ slag. The activity coefficients of NiO and CoO in CaO-Al₂O₃-SiO₂ slag both show a positive deviation from Raoult's law, with values that vary from 1 to 5 depending on the change in basicity. The activity coefficients of NiO and CoO peak in the slag with a composition near B=(%CaO)/(%SiO₂)=1, where B is the basicity. We observed that controlling the slag composition at approximately B=1 effectively reduces the cobalt and nickel oxidation losses and promotes the oxidation removal of iron during the remelting process of EoL superalloys.     

The Reverse Hoelder Classes in Martingale Setting

In martingale setting, it has been shown that Ap weights can be factorized in terms of A1 weights. This factorization benefits many problems very much. ]n this paper, the new class of RH~ plays the same role for RHs, which makes the reverse HOlder inequalities hold with exponent s＞1, that the class A1 does for Ap class. Therefore, the Jones‘ factorization theorem for Ap weights was extended to include some information about the reverse HOlder classes. And it is the most convenient obiect in weight theory indeed.     

Generalized Intersection Bodies with Parameter

AIn 2005, the classical intersection bodies and L_p intersection bodies were extended. Afterwards, the concept of general L_p intersection bodies and the generalized intersection bodies was introduced. In this paper, we define the generalized bodies with parameter. Besides, we establish the extremal values for volume, Brunn-Minkowski type inequality for radial combination and L_p harmonic Blaschke combination of this notion.     

On the Dual <Emphasis Type="Italic">p</Emphasis>-Measures of Asymmetry for Star Bodies

Recently, the connection between p-measures of asymmetry and the L_p -mixed volumes for convex bodies was found soon after the p-measure of asymmetry was proposed, and the Orlicz-measures of asymmetry was proposed inspired by such a kind of connection. In this paper, by a similar way the dual p -measures of asymmetry for star bodies (naturally for convex bodies) is introduced first. Then the connection between dual p -measures of asymmetry and L_p -dual mixed volumes is established. Finally, the best lower and upper bounds of dual p-measures and the corresponding extremal bodies are discussed.     

Influences of the shape of magnetic material on the magnetoelectric properties of the PZT/Metglas composite

In this paper, the influences of the shape of magnetic material on the magnetoelectric(ME) properties of PZT/Metglas magnetoelectric(ME) composites have been investigated. The results indicate that, with the decrease of the waist length(L_w) of the dumbbell-shaped Metglas, the magnetic flux density in the center region and ME coefficients(α_(ME)) of the composites increase, while the optimal bias magnetic field Hdc decreases on the contrary. In an AC magnetic field of 1 kHz, the maximum αME(α_(Max)) of the composite with L_w= 20 mm exhibits 1.3 times larger than that of the one with L_w=50 mm, and the optimal Hdc deceases by 15%. At the resonant frequencies of each composites, α_(Max) is enhanced by 1.3 times as L_w decreases from 50 to 20 mm. The simulation made by Comsol Multiphysics and the theoretical analysis based on an equivalent magnetic circuit confirm the experimental results.     

Microstructure and electrolysis behavior of self-healing Cu-Ni-Fe composite inert anodes for aluminum electrowinning

The microstructure evolution and electrolysis behavior of (Cu₅₂Ni₃₀Fe₁₈)-xNiFe₂O₄ (x=40wt%, 50wt%, 60wt%, and 70wt%) composite inert anodes for aluminum electrowinning were studied. NiFe₂O₄ was synthesized by solid-state reaction at 950℃. The dense anode blocks were prepared by ball-milling followed by sintering under a N₂ atmosphere. The phase evolution of the anodes after sintering was determined by scanning electron microscopy and energy-dispersive X-ray spectroscopy. The results indicate that a substitution reaction between Fe in the alloy phase and Ni in the oxide phase occurs during the sintering process. The samples were also examined as inert anodes for aluminum electrowinning in the low-temperature KF-NaF-AlF₃ molten electrolyte for 24 h. The cell voltage during electrolysis and the corrosion scale on the anodes were analyzed. The results confirm that the scale has a self-repairing function because of the synergistic reaction between the alloy phase with Fe added and the oxide phase. The estimated wear rate of the (Cu₅₂Ni₃₀Fe₁₈)-50NiFe₂O₄ composite anode is 2.02 cm·a-1.