稀土处理钢用中间包覆盖剂岩相分析

分析了现场覆盖剂和实验室自配覆盖剂岩相结构，探讨了稀土氧化物在覆盖剂中的赋存状态。结果表明：在本实验条件下的覆盖剂，原渣矿物组成主要是黄长石，另有少量镁橄榄石和含铁的硅酸盐；稀土氧化物在覆盖剂中主要以稀土硅酸盐形式存在；当稀土氧化物含量增加到一定数量时，覆盖剂开始出现固态未溶的稀土氧化物，说明其在覆盖剂中有一定的溶解度；稀土氧化物在覆盖剂中可以部分代替CaO，形成稀土硅酸盐，其形成物种类随覆盖剂碱度降低有增加的趋势。     

A linear time algorithm for Shortest Cyclic Cover of Strings

Merging words according to their overlap yields a superstring. This basic operation allows to infer long strings from a collection of short pieces, as in genome assembly. To capture a maximum of overlaps, the goal is to infer the shortest superstring of a set of input words. The Shortest Cyclic Cover of Strings (SCCS) problem asks, instead of a single linear superstring, for a set of cyclic strings that contain the words as substrings and whose sum of lengths is minimal. SCCS is used as a crucial step in polynomial time approximation algorithms for the notably hard Shortest Superstring problem, but it is solved in cubic time. The cyclic strings are then cut and merged to build a linear superstring. SCCS can also be solved by a greedy algorithm. Here, we propose a linear time algorithm for solving SCCS based on a Eulerian graph that captures all greedy solutions in linear space. Because the graph is Eulerian, this algorithm can also find a greedy solution of SCCS with the least number of cyclic strings. This has implications for solving certain instances of the Shortest linear or cyclic Superstring problems.     

$(m,d)$-内射盖与Gorenstein $(m,d)$-平坦模

研究了$(m,d)$-内射$R$-模作成的类是(预)盖类的条件,证明了$(m,d)$-凝聚环上的每一个左$R$-模都具有$(m,d)$-内射盖.在此基础上,又引入研究了Gorenstein $(m,d)$-平坦模和Gorenstein $(m,d)$-内射模,证明了$(m,d)$-凝聚环上的左$R$-模$M$是Gorenstein$(m,d)$-平坦模的充分必要条件是它的特征模$M^{+}$是Gorenstein $(m,d)$-内射模.推广了Goresntein平坦模和Goresntein $n$-平坦模上的一些结果.     

Ultra‐low modulus polyazomethines and enhanced adhesion strength with copper foils

Polyazomethines (PAzMs) were prepared from dialdehydes containing different lengths of alkylene groups (m = 2–12) and an ether‐containing common aromatic diamine. The main purpose of this work is to achieve an ultra‐low modulus and a considerably high adhesion strength with a smooth surface (S‐side) of electro‐deposited copper foils for applications as novel coating‐type protective layer materials of flexible printed circuit boards. The elongation at break of the PAzM films was drastically enhanced by increasing the annealing temperature (T_a). The results are probably attributed to a chain extension effect accompanied with solid‐state polymerization promoted at elevated temperatures. An increase in the alkylene chain length (m) led to a gradual decrease in the modulus of the PAzM films owing to an increase in the chain flexibility. It also drastically improved the adhesion strength (S‐side); 8.3 N cm^–1 at m = 12 in spite of the absence of anchoring effect. To further decrease the modulus, the PAzM (m = 12) was modified with another diamine comonomer containing a polybutylene oxide block. This approach was very effective for achieving the present target properties; the PAzM copolymer displayed ultra‐low tensile modulus (0.20 GPa) and a very high adhesion strength (9.8 N cm^–1) with the S‐side of copper foils. Copyright © 2015 John Wiley & Sons, Ltd.     

Minimizing a monotone concave function with laminar covering constraints

Let V be a finite set with |V|=n. A family F⊆2^V is called laminar if for all two sets X,Y∈F, X∩Y≠∅ implies X⊆Y or X⊇Y. Given a laminar family F, a demand function , and a monotone concave cost function , we consider the problem of finding a minimum-cost such that x(X)?d(X) for all X∈F. Here we do not assume that the cost function F is differentiable or even continuous. We show that the problem can be solved in O(n²q) time if F can be decomposed into monotone concave functions by the partition of V that is induced by the laminar family F, where q is the time required for the computation of F(x) for any . We also prove that if F is given by an oracle, then it takes Ω(n²q) time to solve the problem, which implies that our O(n²q) time algorithm is optimal in this case. Furthermore, we propose an algorithm if F is the sum of linear cost functions with fixed setup costs. These also make improvements in complexity results for source location and edge-connectivity augmentation problems in undirected networks. Finally, we show that in general our problem requires Ω(2^n/2q) time when F is given implicitly by an oracle, and that it is NP-hard if F is given explicitly in a functional form.     

Further properties of a function of Ogg and Ligozat

Certain identities of Ramanujan may be succinctly expressed in terms of the rational function on the modular curve X ₀(N), where and f _χ is a certain modular unit on the Nebentypus cover X _χ (N) introduced by Ogg and Ligozat for prime and w _N is the Fricke involution. These correspond to levels N=5,13, where the genus g _N of X ₀(N) is zero. In this paper we study slightly more general kind of relations for each such that X ₀(N) has genus g _N =1,2, and also for each such that the Atkin–Lehner quotient X ₀⁺(N) has genus g _N ⁺=1,2. Finally we study the normal closure of the field of definition of the zeros of the latter.      

Covers of Point-Hyperplane Graphs

A cover of the non-incident point-hyperplane graph of projective dimension 3 for fields of characteristic 2 is constructed. For fields of even order larger than 2, this leads to an elementary construction of the non-split extension of SL₄( )by ⁶.     

More on convexity numbers of closed sets in

The convexity number of a set is the least size of a family of convex sets with . is countably convex if its convexity number is countable. Otherwise is uncountably convex.

Uncountably convex closed sets in have been studied recently by Geschke, Kubis, Kojman and Schipperus. Their line of research is continued in the present article. We show that for all , it is consistent that there is an uncountably convex closed set whose convexity number is strictly smaller than all convexity numbers of uncountably convex subsets of .

Moreover, we construct a closed set whose convexity number is and that has no uncountable -clique for any 1$">. Here is a -clique if the convex hull of no -element subset of is included in . Our example shows that the main result of the above-named authors, a closed set either has a perfect -clique or the convexity number of is in some forcing extension of the universe, cannot be extended to higher dimensions.

     

Principles of Cost Minimisation in Wireless Networks

This paper considers variations of the minimum connected vertex cover problem to be found in the study of wireless network design. A simple, theoretic formulation is followed by a discussion of practical constraints. Two algorithms are given and results compared.