M/O)DERATOR TLOiIs N. KATZ (Chicago, Ill.): Before I call upon my colleagues I wish to make a few introductory remarks. We as physicians must view heart disease in all its ramifications. Heart disease is primarily a chronic process. The problem is more than the immediate alleviation of acute exa(erbations of the disease, involving a temporary sojourn in the acute hospital, or its equivalent at ...

The pullback approach to global Finsler geometry is adopted. Three classes of recurrence in Finsler geometry are introduced and investigated: simple recurrence, Ricci recurrence and concircular recurrence. Each of these classes consists of four types of recurrence. The interrelationships between the different types of recurrence are studied. The generalized concircular recurrence, as a new conc...

Linear recurring sequences of order k are investigated using matrix techniques and some finite group theory. An identity, well-known when k = 2, is extended to general k and is used to study the restricted period of a linear recurring sequence over a finite field.

This note employs path counting techniques to extend recent results on bounds for odd order linear recurrences to higher dimensions. The results imply optimal zero-free polydisks for multivariable power series with 0, 1 coefficients. Among the applications is a result that states that the optimal zero-free polydisk has radius approximately 1/(v + 1), for large dimensions v.

In this paper we study mixed sums of primes and linear recurrences. We show that if m ≡ 2 (mod 4) and m+1 is a prime then (m2n−1−1)/(m−1) 6= m+p for any n = 3, 4, . . . and prime power p. We also prove that if a > 1 is an integer, u0 = 0, u1 = 1 and ui+1 = aui + ui−1 for i = 1, 2, 3, . . ., then all the sums um + aun (m, n = 1, 2, 3, . . .) are distinct. One of our conjectures states that any i...

Among the vast assemblage of technical analysis tools, the ones based on Fibonacci recurrences in asset prices are relatively more scientific. In this paper, we review some of the popular technical analysis methodologies based on Fibonacci sequences and also advance a theoretical rationale as to why security prices may be seen to follow such sequences. We also analyse market data for an indicat...

We pursue the problem of counting the imbeddings of a graph in each of the orientable surfaces. We demonstrate how to achieve this for an iterated amalgamation of arbitrarily many copies of any graph whose genus distribution is known and further analyzed into a partitioned genus distribution. We introduce the concept of recombinant strands of face-boundary walks, and we develop the use of multi...

This paper addresses the problem of unsupervised TV program structuring. Program structuring allows direct and non linear access to the desired parts of a program. Our work addresses the structuring of programs like news, entertainment, shows, magazines... It is based on the detection of audio and visual recurrences. It proposes an effective classification and selection system, based on decisio...

This paper continues the work begun by D. Shanks and myself in [1] where certain cubic recurrences were used to give a very strong primality test. A complete characterization of the pseudoprimes for this test is given in terms of the periods of the corresponding sequences. Then these results are used to produce various types of pseudoprimes. A discussion of open problems is included.

Symmetric standard elliptic integrals are considered when one of their parameters is larger than the others. Distributional approach is used for deriving five convergent expansions of these integrals in inverse powers of the respective five possible asymptotic parameters. Four of these expansions involve also a logarithmic term in the asymptotic variable. Coefficients of these expansions are ob...