Some results on best approximation in spaces with convex structure

Some generalizations of the result proved by S.P Singh[J.Approx.Theory 25(1979),89-90]are presented in convex metric spaces.The results proved contain several known results on the subject.     

1,2,4-triazolium-cation-based energetic salts

3,4,5-Triamino-1,2,4-triazole (guanazine, 1) can be readily methylated with methyl iodide yielding methylguanazinium iodide (2). Salts containing the novel methylguanazinium cation with energetic anions were synthesised by metathesis reactions with silver azide (3), silver nitrate (4), silver perchlorate (5), sodium 5,5'-azotetrazolate (6), silver 5-nitrotetrazolate (7) and silver dinitramide (8), yielding a new family of heterocycle-based salts, which were fully characterised by analytical (mass spectrometry and elemental analysis) and spectroscopic methods (IR, Raman and NMR). In addition, the molecular structures of all compounds were confirmed by X-ray analysis, revealing extensive hydrogen-bonding in the solid state and densities between 1.399 (3) and 1.669 g cm(-3) (5). The hydrogen-bonded ring motifs are discussed in the formalism of graph-set analysis for hydrogen-bond patterns and compared to each other. Preliminary sensitivity testing of the crystalline compounds indicate surprisingly low sensitivities to both friction and impact, the highest friction and shock sensitivity being found for the perchlorate (5, 220 N) and the dinitramide (8, 20 J) salts, respectively. In addition, DSC analysis was used to assess the thermal stabilities of the compounds: 3-6 melt above 200 degrees C with concomitant decomposition, whereas 7 and 8 have clearly defined melting points at 162 and 129 degrees C, respectively, and with decomposition occurring about 30 degrees C above the melting point. Lastly all compounds have positive calculated heats of formation between 336 (4) and 4070 kJ kg(-1) (6) and calculated detonation velocities in the range between 8330 (7) and 8922 m s(-1) (6) making them of interest as new highly energetic materials with low sensitivity.     

More efficient estimators for marginal additive hazards model in case-cohort studies with multiple outcomes

Case-cohort study designs are widely used to reduce the cost of large cohort studies. When several diseases are of interest, we can use the same subcohort. In this paper, we will study the casecohort design of marginal additive hazards model for multiple outcomes by a more efficient version. Instead of analyzing each disease separately, ignoring the additional exposure measurements collected on subjects with other diseases, we propose a new weighted estimating equation approach to improve the efficiency by utilizing as much information collected as possible. The consistency and asymptotic normality of the resulting estimator are established. Simulation studies are conducted to examine the finite sample performance of the proposed estimator, which confirm the efficiency gains.     

Partial Geometric Difference Families

We introduce the notion of a partial geometric difference family as a variation on the classical difference family and a generalization of partial geometric difference sets. We study the relationship between partial geometric difference families and both partial geometric designs and difference families, and show that partial geometric difference families give rise to partial geometric designs. We construct several infinite families of partial geometric difference families using Galois rings and the cyclotomy of Galois fields. From these partial geometric difference families, we generate a list of infinite families of partial geometric designs and directed strongly regular graphs.     

An Enumeration of Certain Projective Ternary Two‐Weight Codes

We detail the enumeration of all two‐intersection sets of the five‐dimensional projective space over the field of order 3 that are invariant under an element of order 7, which include the examples of Hill (1973) and Gulliver (1996). Up to projective equivalence, there are 6,635 such two‐intersection sets.     

(s,l)-叠加码的构作及其性质

一个二元叠加(s,l)-码在许多领域有着极为广泛的应用.利用有限集[n]的子集构作了一个(0,1)-矩阵C,并证明了它是一个(s,l)-码,给出了(s,l)-码的性质.