There are very strong parallels between the properties of Mal’tsev and Jónsson-Tarski algebras, for example in the good behaviour of centrality and in the factorization of direct products. Moreover, the two classes between them include the majority of algebras that actually arise “in nature”. As a contribution to the research programme building a unified theory capable of covering the two class...

Certain observations have been reported according to which complications in association with gold therapy in rheumatoid arthritis would seem to be inversely proportional to the erythrocyte sedimentation rate (Goldie, 1939; Ellman and others, 1940; Lawrence, 1953). This has been explained on the basis that a high E.S.R. is generally seen in the active exudative stage of the disease, and that the...

We develop sharp large deviation asymptotics for the probability of ruin in a Markov-dependent stochastic economic environment and study the extremes for some related Markovian processes which arise in financial and insurance mathematics, related to perpetuities and the ARCH(1) and GARCH(1,1) time series models. Our results build upon work of Goldie [Ann. Appl. Probab. 1 (1991) 126–166], who ha...

This paper investigates fundamental theorems of regular variation (Uniform Convergence, Representation, and Characterization Theorems) some of which, in the classical setting of regular variation in R, rely in an essential way on the additive semi-group of natural numbers N (e.g. de Bruijn’s Representation Theorem for regularly varying functions). Other such results include Goldie’s direct proo...

Since 1935 several reports have dealt with the antistreptolysin-O (ASO) titre in rheumatoid arthritis (RA). The mean and the upper ASO values were first established in a group of normal subjects and in patients with no history of recent streptococcal illness, and subsequently the distribution of the ASO titres was recorded in patients suffering from RA. Table I summarizes the results of Blair a...

was established by Hahn [1; p. 217] in 1927, and independently by Banach [2; p. 212] in 1929, who also generalized Theorem 0 for real spaces, to the situation in which the functional q :E^>R is an arbitrary subadditive, positive homogeneous functional [2; p. 226]. Theorem 0 was not established for complex spaces until 1938, when it was deduced from the real theorem by Bohnenblust and Sobczyk [3...

A ring $R$ is called a left Ikeda-Nakayama (left IN-ring) if the right annihilator of intersection any two ideals sum annihilators. As generalization IN-rings, SA-ring annihilators an ideal $R$. It natural to ask IN and SA property can be extended from $R[x; \alpha, \delta]$. In this note, results concerning conditions will allow these properties transfer skew polynomials $R[x;\alpha,\delta]$ a...

Juberg R C, Hayward J R. A new familial syndrome of oral, cranial, and digital anomalies. J Pediatr 1969; 74: 755-62. 2 Nevin N C, Henry P, Thomas P T S. A case of the orocraniodigital (Juberg-Hayward) syndrome. J Med Genet 1981; 18: 478-80. 3 Savage D C L, Swift P G F, Johnston P G B, Goldie D J, Murphy D. Combined test of anterior pituitary function in children. Arch Dis Child 1978; 53: 301-4...

We consider the stochastic recursion Xn+1 = Mn+1Xn +Qn+1 on R , where (Mn, Qn) are i.i.d. random variables such that Qn are translations, Mn are similarities of the Euclidean space R. Under some standard assumptions the sequence Xn converges to a random variable R and the law ν of R is the unique stationary measure of the process. Moreover, the weak limit of properly dilated measure ν exists, d...

For an arbitrary ring R, the largest strong left quotient ring Ql (R) of R and the strong left localization radical lR are introduced and their properties are studied in detail. In particular, it is proved that Ql (Q s l (R)) ≃ Q s l (R), l s R/ls R = 0 and a criterion is given for the ring Ql (R) to be a semisimple ring. There is a canonical homomorphism from the classical left quotient ring Q...