有向循环图的连通度

本文给出了有向循环图连通度达到其最小度的一个充要条件.     

The spectrum for large sets of pure directed triple systems

An LPDTS(ν) is a collection of 3(ν-2) disjoint pure directed triple systems on the same set ofνelements. It is showed in Tian's doctoral thesis that there exists an LPDTS(ν) forν=0,4 (mod 6),ν≥4. In this paper, we establish the existence of an LPDTS(ν) forν= 1,3 (mod 6),ν> 3. Thus the spectrum for LPDTS(ν) is completely determined to be the set {ν:ν= 0, 1 (mod 3),ν≥4}.     

On coverings in the lattice of all group topologies of arbitrary Abelian groups

The remainder of the completion of a topological abelian group (G, τ₀) contains a nonzero element of prime order if and only if G admits a Hausdorff group topology τ₁ that precedes the given topology and is such that (G, τ₀) has no base of closed zero neighborhoods in (G, τ₁).     

Anisotropic photocorrosion of n-type MoS2 MoSe2, and WSe2 single crystal surfaces: the role 0f cleavage steps,line and screw dislocations

The photocorrosive behavior of the semiconducting transition metal dichalcogenides in contact with aqueous electrolytes is extremely anisotropic. Enhanced reactivity was observed at cleavage steps and on either line or screw dislocation cores emerging at the surface exposing mainly (101̄1) faces lying in 〈112̄0〉 directions. Corrosion patterns, however, could never be observed on smooth (0001) faces. The corrosion products of the molybdenum compounds are soluble, whereas WSe₂ formed WO₃ precipitates on the surface.     

Photoreactions of nitroso compounds in solution—XXVIII: Applications of non-oxidative and oxidative photoreactions of nitrosamides

Two model nitrosamides were used to illustrate the application of oxidative and non-oxidative nitrosamide photorearrangements. N-nitroso-N-acetyldehydroabietylamine photolytically rearranges to give stable 6α-nitroso and 6α-nitrato derivatives respectively. Similar photorearrangement of N-nitroso-N-methyl-o-toluamide gave good yields of the corresponding oximino and nitrate esters; they, however underwent facile photolytic and thermal reactions to give various products.     

A problem of rights arbitration from the Talmud

A man dies leaving certain amounts of his estate to each of his sons, but the amounts sum to more than the total available. Various solutions are discussed, some based in the theory of games. The method endorsed here regards the problem as one of rights arbitration in which the division is based on interpreting the applicable rules, rather than on weighing the parties' powers and possible benefits.     

Optical emission spectroscopy with a microwave-induced plasma in a sealed microtube

A microwave system is used to induce a plasma inside a sealed microtube containing a sample or standard, and the emission from the analyte is measured. The detection limits are about 4 ng for S, Cl and Br, and 100 ng for Cd and Sn, in approximately 30-mul samples. Both gaseous and liquid samples can be analysed.     

Distinguished Completion of a Direct Product of Lattice Ordered Groups

The distinguished completion E(G) of a lattice ordered group G was investigated by Ball [1], [2], [3]. An analogous notion for MV-algebras was dealt with by the author [7]. In the present paper we prove that if a lattice ordered group G is a direct product of lattice ordered groups G _i (i I), then E(G) is a direct product of the lattice ordered groups E(G _i). From this we obtain a generalization of a result of Ball [3].