A supersimple theory eliminates hyperimaginaries. In particular, in a supersimple theory Lascar strong type is the same as strong type, and every strong type has a canonical base in C . It follows that the Amalgamation Theorem (Independence Theorem) holds for types over algebraically closed sets.

An odd prime p is called a Wieferich prime if 2p−1 ≡ 1 (mod p); alternatively, a Wilson prime if (p− 1)! ≡ −1 (mod p). To date, the only known Wieferich primes are p = 1093 and 3511, while the only known Wilson primes are p = 5, 13, and 563. We report that there exist no new Wieferich primes p < 4×1012 , and no new Wilson primes p < 5×108. It is elementary that both defining congruences above h...

Let ψm be the smallest strong pseudoprime to the first m prime bases. This value is known for 1 ≤ m ≤ 11. We extend this by finding ψ12 and ψ13. We also present an algorithm to find all integers n ≤ B that are strong pseudoprimes to the first m prime bases; with a reasonable heuristic assumption we can show that it takes at most B2/3+o(1) time.

We prove a uniform functional law of the logarithm for the local empirical process. To accomplish this we combine techniques from classical and abstract empirical process theory, Gaussian distributional approximation and probability on Banach spaces. The body of techniques we develop should prove useful to the study of the strong consistency of d-variate kernel-type nonparametric function estim...

This study focuses on the synthesis and characterization of the inclusion complex of β-Cyclodextrin (β-CD) with dicationic ionic liquid, 3,3'-(1,4-Phenylenebis [methylene]) bis(1-methyl-1H-imidazol-3-ium) di(bromide) (PhenmimBr). The inclusion complex was prepared at room temperature utilizing conventional kneading technique. Proton ((1)H) NMR and 2D ((1)H-(1)H) COSY NMR were the primary charac...

psychodynamic clinicians have long stressed the role of defense mechanisms in diagnosis and treatment of their patients. however, until recently the defense mechanisms were not the focus of extensive empirical research due to methodological limitations. the inclusion of defensive functioning scale (dfs) in dsm-iv has renewed the interest in psychodynamic approaches to clinical diagnosis, partic...

usd7 is one of the steel products of isfahan steel company. it is cast in continuous casting moulds and rolled up to a rod of 5 mm diameter. finally, it is wire drawn up to 3 mm and used as welding electrodes. this steel contains 0.05 to 0.09 wt. % carbon. the acceptable limit of the aluminium in this class of steel is less than 0.003 wt%. therefore, it is categorized as rimmed steel. during fo...

in this paper, we use the concept of graph convergence of h(.,.)-co-accretive mapping introduced by [r. ahmad, m. akram, m. dilshad, graph convergence for the h(.,.)-co-accretive mapping with an application, bull. malays. math. sci. soc., doi: 10.1007/s40840-014-0103-z, 2014$] and define an over-relaxed proximal point method to obtain the solution of a generalized variational inclusion problem ...