MAXIMAL L^(1)-REGULARITY OF GENERATORS FOR BOUNDED ANALYTIC SEMIGROUPS IN BANACH SPACES

In this paper,we prove that the generator of any bounded analytic semigroup in(θ,1)-type real interpolation of its domain and underlying Banach space has maximal L^(1)-regularity,using a duality argument combined with the result of maximal continuous regularity.As an application,we consider maximal L^(1)-regularity of the Dirichlet-Laplacian and the Stokes operator in inhomogeneous B_(q),^(s),1-type Besov spaces on domains of R^(n),n≥2.

The Cordiality on the Union of 3-regular Connected Graph and Cycle

Diab proved the following graphs are Cordial;Pm K1,n if and only if(m,n) =(1,2);Cm K1,n;Pm Kn;Cm Kn for all m and n except m ≡ 2(mod 4).In this paper,we proved the Cordiality on the union of 3-regular connected graph K3 and cycle Cm.First we have the Lemma 2,if uv ∈ E(G),G is Cordial,we add 4 vertices x,y,z,w in sequence to the edge uv,obtain a new graph denoted by G*,then G* is still Cordial,by this lemma,we consider four cases on the union of 3-regular connected graph R3,and for every case we distinguish four subcases on the cycle Cm.

A POLYNOMIAL ALGORITHM FOR FINDING THEMINIMUM FEEDBACK VERTEX SET OF A3-REGULAR SIMPLE GRAPH

A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vertex set of a 3-regular simple graph is provided.

COUNTING ROOTED NEAR-4-REGULAR EULERIAN MAPSON SOME SURFACES

In this article the rooted planar near-4-regular Eulerian trails are enum erated and an explicit form ula for such m aps is presented. Further, the rooted near-4-regular Eulerian m aps on the torus are counted in an exact w ay.

Counting Rooted Nearly 2-regular Planar Maps

The number of rooted nearly 2-regular maps with the valency of root-vertex, the number of non-rooted vertices and the valency of root-face as three parameters is obtained. Furthermore, the explicit expressions of the special cases including loopless nearly 2-regular maps and simple nearly 2-regular maps in terms of the above three parameters are derived.

Cover a 3-regular Claw-free Graph by Induced Matchings

The induced matching cover number of a graph G without isolated vertices, denoted by imc(G),is the minimum integer k such that G has k induced matchings {M1,M2,···,Mk}such that,V(M1)∪V(M2)∪···∪V(Mk)covers V(G).This paper shows that,if G is a 3-regular claw-free graph,then imc(G)∈{2,3}.

I-semi-π-regular Rings

Let R be a ring and I an ideal of R. A ring R is called I-semi-π--regular if R/I is π-regular and idempotents of R can be strongly lifted modulo I. Characterizations of I-semi-π-regular rings are given and relations between semi-π-regular rings and semiregular rings are explored.

REGULARITY FOR CERTAIN QUASILINEAR ELLIPTIC SYSTEMS OF DIVERGENCE STRUCTURE

The regularity of the gradient of Holder continuous solutions of quasi-linear elliptic systems of the form -Dj(aij(x,u,Du)Diuk)=-Difki=gk is investigated. Partial regularity and ε-regularity are shown to hold under the structural assumption -Dj(aij(x,u,Du))=hi∈L∞

Notes on Noncommutative VNL-rings and GVNL-rings

In this note, a counterexample is given to show that a noncommutative VNL-ring need not be an SVNL-ring, answering an open question of Chen and Tong （Glasgow Math. J., 48（1）（2006）） negatively. Moreover, some new results about VNL-rings and GVNL-ringsare also given.

ε_0-Regularity for Mean Curvature Flow from Surface to Flat Riemannian Manifold

In this paper we prove an so-regularity theorem for mean curvature flow from surface to a flat Riemannian manifold. More precisely, we prove that if the initial energy ∫∑0 ｜A｜^2 ≤ ε0 and the initial area u0（∑0） is not large, then along the mean curvature flow, we have ∫∑t ｜A｜^2 ≤ ε0. As an application, we obtain the long time existence and convergence result of the mean curvature flow.

A Fixed Point Method for Convex Systems

We present a new fixed point technique to solve a system of convex equations in several variables. Our approach is based on two powerful algorithmic ideas: operator-splitting and steepest descent direction. The quadratic convergence of the proposed approach is established under some reasonable conditions. Preliminary numerical results are also reported.

替换环什么时候是冯诺依曼正则环（英文）

We study when exchange rings are von Neumann regular. An exchange ring R with primitive factors Artinian is von Neumann regular, if the Jacobson radical of any indecomposable homomorphic image of R is T-nilpotent, and if any indecomposable homomorphic image of R is semiprime. Every indecomposable semiprimitive factor ring of R is regular, if R is an exchange ring such that every left primitive factor ring of R is a ring of index at most n and if R has nil-property.

A Note on the Prime Spectrums of Character Rings of Finite Groups

Let G be a finite group with order g and S be a subring of the algebraic number field which contains the integral extension over Z generated by a g-th primitive root co of unity, and R（G） be the character ring of G. The prime spectrum of the commutative ring S×Z R（G） iv denoted by Spec（S×Z R（G）） and set π={p｜p is a rational prime number such that p^-1 S}. We prove that when G is a regroup, a π＇-group, or a finite Abelian group, the number of the connetted components of Spec（ S×Z R （G） ） coincides with the number of the π-regular classes in G,

关于3-正则哈密尔顿图的围长的一个注记

It is well-known that the Petersen graph is nonhamiltonian.A very short proof for this result was presented in[2]due to D.B.West.In this note,by extending the proof technique in[2],we briefly show that the girth of every 3-regular hamiltonian graph on n≥10 vertices is at most(n+4)/3.

Quantile Regression Based on Laplacian Manifold Regularizer with the Data Sparsity in <i>l</i>1 Spaces

In this paper, we consider the regularized learning schemes based on l1-regularizer and pinball loss in a data dependent hypothesis space. The target is the error analysis for the quantile regression learning. There is no regularized condition with the kernel function, excepting continuity and boundness. The graph-based semi-supervised algorithm leads to an extra error term called manifold error. Part of new error bounds and convergence rates are exactly derived with the techniques consisting of l1-empirical covering number and boundness decomposition.

On Green’s Relations, 2~0-regularity and Quasi-ideals in Γ-semigroups

In this paper, we introduce the definition of （m, n）0-regularity in Г-semigroups. we in- vestigate and characterize the 20-regular class of F-semigroups using Green＇s relations. Extending and generalizing the Croisot＇s Theory of Decomposition for F-semigroups, we introduce and study the absorbent and regular absorbent Г-semigroups. We approach this problem by examining quasi-ideals using Green＇s relations.

Some Mixed Soft Operations and Extremally Soft Disconnectedness via Two Soft Topologies

In this paper, we study the concept of soft sets which is introduced by Molodtsov [5]. We give the definition of (τ1,τ2)-semi open soft (resp. (τ1,τ2)-pre open soft, (τ1,τ2)-α-open soft, (τ1,τ2)-β-open soft, (τ1,τ2)'-semi open soft, (τ1,τ2)'-pre open soft, (τ1,τ2)'-α-open soft, (τ1,τ2)'-βopen soft) set via two soft topologies. Also we introduce (τ1,τ2)-regular open soft and ESDC on two soft topologies. The aim of this paper is to investigate properties of some mixed soft operations and characterizations of ESDC. Finally, we study τ2-ESDC soft topologies τ1.

Generalized Inverses and Units in a Unitary Ring

Let R be a unitary ring and a,b∈R with ab=0.We find the 2/3 property of Drazin invertibility:if any two of a,b and a+b are Drazin invertible,then so is the third one.Then,we combine the 2/3 property of Drazin invertibility to characterize the existence of generalized inverses by means of units.As applications,the need for two invertible morphisms used by You and Chen to characterize the group invertibility of a sum of morphisms is reduced to that for one invertible morphism,and the existence and expression of the inverse along a product of two regular elements are obtained,which generalizes the main result of Mary and Patricio(2016)about the group inverse of a product.

GTB-PPI:Predict Protein-protein Interactions Based on L1-regularized Logistic Regression and Gradient Tree Boosting

Protein-protein interactions(PPIs)are of great importance to understand genetic mechanisms,delineate disease pathogenesis,and guide drug design.With the increase of PPI data and development of machine learning technologies,prediction and identification of PPIs have become a research hotspot in proteomics.In this study,we propose a new prediction pipeline for PPIs based on gradient tree boosting(GTB).First,the initial feature vector is extracted by fusing pseudo amino acid composition(Pse AAC),pseudo position-specific scoring matrix(Pse PSSM),reduced sequence and index-vectors(RSIV),and autocorrelation descriptor(AD).Second,to remove redundancy and noise,we employ L1-regularized logistic regression(L1-RLR)to select an optimal feature subset.Finally,GTB-PPI model is constructed.Five-fold cross-validation showed that GTB-PPI achieved the accuracies of 95.15% and 90.47% on Saccharomyces cerevisiae and Helicobacter pylori datasets,respectively.In addition,GTB-PPI could be applied to predict the independent test datasets for Caenorhabditis elegans,Escherichia coli,Homo sapiens,and Mus musculus,the one-core PPI network for CD9,and the crossover PPI network for the Wnt-related signaling pathways.The results show that GTB-PPI can significantly improve accuracy of PPI prediction.The code and datasets of GTB-PPI can be downloaded from https://github.com/QUST-AIBBDRC/GTB-PPI/.

On Product-Cordial Index Sets and Friendly Index Sets of 2-Regular Graphs and Generalized Wheels

A vertex labeling f ： V →Z2 of a simple graph G = （V, E） induces two edge labelings The friendly index set and the product-cordial index set of G are defined as the setsf is friendly}. In this paper we study and determine the connection between the friendly index sets and product-cordial index sets of 2-regular graphs and generalized wheel graphs.