Chain Conditions on Essetial Subacts

Let S be a semigroup with zero and an S-act be a centered left S-act. This paper is devoted to the study of chain conditions on PS-acts. We prove that a PS-act having finite decomposition has ACC （DCC） on all subacts if it has ACC （DCC） on essential subacts. Moreover, a PS-act with ACC （DCC） on essential subacts has ACC （DCC） on all subacts if and only if it has finite decomposition. We characterize the structure of a PS-act and generalize some results of the Goldie dimension and semisimple S-acts.

Generalised Chain Conditions,Prime Ideals,and Classes of Locally Finite Lie Algebras

A Noetherian(Artinian)Lie algebra satisfies the maximal(minimal)condition for ideals.Generalisations include quasi-Noetherian and quasi-Artinian Lie algebras.We study conditions on prime ideals relating these properties.We prove that the radical of any ideal of a quasi-Artinian Lie algebra is the intersection of finitely many prime ideals,and an ideally finite Lie algebra is quasi-Noetherian if and only if it is quasi-Artinian.Both properties are equivalent to soluble-by-finite.We also prove a structure theorem for serially finite Artinian Lie algebras.

Matching Boundary Conditions for a Heterogeneous Atomic Chain

We propose accurate boundary treatments for a heterogeneous atomic chain, in terms of matching boundary conditions （MBCs）. The main challenge lies in reproducing the physical reflection across the boundary to a correct amount. With reflection coefficients we demonstrate that the accuracy is improved when more atoms are used under the boundary condition. The inclusion of an atom in the embedded sublattice B may considerably enhance the performance. Numerical testing illustrates the effectiveness of the proposed MBCs.

On Left A-Injective Rings

The main results of this paper are following theorems: (1)A left A-injective ring satisfying the ascending chain condition on right annihilator is QF ring. (2)A left A-injective ring satisfying the ascending hain condition on left annihilator is QF ring. (3)If R satisfies the following conditions: (ⅰ) r(A∩B)=r(A)+r(B), for each pair of left ils A,B;(ⅱ) rl(I)=I, for every right ideal I. Then R is semiperfect ring and has essential left s. In particular, any right CF left A-injective (or E(_RR) is projective left R-module) is QF ring

Case History of the Disastrous Debris Flows of Tianmo Watershed in Bomi County, Tibet, China: Some Mitigation Suggestions

Debris flows and landslides, extensively developing and frequently occurring along Parlung Zangbo, seriously damage the Highway from Sichuan to Tiebt(G318) at Bomi County. The disastrous debris flows of the Tianmo Watershed on Sept. 4, 2007, July 25, 2010 and Sept. 4, 2010, blocked Parlung Zangbo River and produced dammed lakes, whose outburst flow made 50 m high terrace collapse at the opposite bank due to intense scouring on the foot of the terrace. As a result, the traffic was interrupted for 16 days in 2010 because that 900 m highway base was destructed and 430 m ruined. These debris flows were initiated by the glacial melting which was induced by continuous higher temperature and the following intensive rainfall, and expanded by moraines along channels and then blocked Parlung Zangbo. At the outlet of watershed,the density, velocity and peak discharge of debris flow was 2.06 t/m3, 12.7 m/s and 3334 m3/s, respectively. When the discharge at the outlet and the deposition volume into river exceeds 2125 m3/s and 126×103 m3, respectively, debris flow will completely blocked Parlung Zangbo. Moreover,if the shear stress of river flow on the foot of terrace and the inclination angel of terrace overruns 0. 377 N/m2 and 26°, respectively, the unconsolidated terrace will be eroded by outburst flow and collapse. It was strongly recommended for mitigation that identify and evade disastrous debris flows, reduce the junction angel of channels between river and watershed, build protecting wall for highway base and keep appropriate distance between highway and the edge of unconsolidated terrace.

Weight hierarchies of linear codes satisfying the almost chain condition

The weight hierarchy of a linear [n, k;q] code C over GF(q) is the sequence (d1,d2,..., dk) where dr is the size of the smallest support of an r-dimensional subcode of C. An [n,k;q] code satisfies the chain condition if there exists subcodes D1 D2 … Dk = C of C such that Dr has dimension r and support of size dr for all r. Further, C satisfies the almost chain condition if it does not satisfy the chain condition, but there exist subcodes Dr of dimension r and support of size dr for all r such that D2 D3 Dk = C and D1 D3. A simple necessary condition for a sequence to be the weight hierarchy of a code satisfying the almost chain condition is given. Further, explicit constructions of such codes are given, showing that in almost all cases, the necessary conditions are also sufficient.

Chain Condition on Annihilators and Strongly Hopfian Property in Hurwitz Series Ring

In this paper we study some properties of the Hurwitz series ring HA over a commutative ring A, such as the nilradical of HA and the chain condition on its an- nihilators. We provide an example showing that the last property does not pass from A to HA. A strongly Hopfian ring is a ring satisfying the chain condition on some type of annihilators. We give a large class of strongly Hopfian rings A such that HA are not strongly Hopfian.

A Simple Proof of ACC for Minimal Log Discrepancies for Surfaces

Following Shokurov's idea,we give a simple proof of the ACC conjecture for minimal log discrepancies for surfaces.

The Radicals of Lattice-Ordered Rings

We discuss the nilpotency of nil single-sided l-ideals of lattice-ordered rings.It is shown that for many rings satisfying specific lattice-ordered ring identities all theradicals coincide.

ON A CLASS OF WEIGHT HIERARCHIES OF TERNARY LINEAR CODES OF DIMENSION 4

The possible weight hierarchies of ternary codes of dimension 4 satisfying thealmost chain condition are completely determined in this paper.

Finite Projective Geometries and Classification of the Weight Hierarchies of Codes(Ⅰ)

The weight hierarchy of a binary linear [n, k] code C is the sequence (d 1, d 2, . . . , d k ), where d r is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes and the possible weight hierarchies in each class is determined by finite projective geometries. The possible weight hierarchies in class A, B, C, D are determined in Part (I). The possible weight hierarchies in class E, F, G, H, I are determined in Part (II).

Geodesic metrics on fractals and applications to heat kernel estimates

It is well known that for a Brownian motion, if we change the medium to be inhomogeneous by a measure μ, then the new motion(the time-changed process) will diffuse according to a different metric D(·, ·).In 2009, Kigami initiated a general scheme to construct such metrics through some self-similar weight functions g on the symbolic space. In order to provide concrete models to Kigami’s theoretical construction, in this paper,we give a thorough study of his metric on two classes of fractals of primary importance: the nested fractals and the generalized Sierpinski carpets;we further assume that the weight functions g := ga are generated by“symmetric” weights a. Let M be the domain of a such that Dgadefines a metric, and let S be the boundary of M. One of our main results is that the metrics from ga satisfy the metric chain condition if and only if a ∈ S.To determine M and S, we provide a recursive weight transfer construction on the nested fractals, and a basic symmetric argument on the Sierpinski carpet. As an application, we use the metric chain condition to obtain the lower estimate of the sub-Gaussian heat kernel. This together with the upper estimate obtained by Kigami allows us to have a concrete class of metrics for the time change, and the two-sided sub-Gaussian heat kernel estimate on the fundamental fractals.