Resistance in blood vessels is directly related to the inner (luminal) diameter (ID). However, ID can be difficult to measure during physiological experiments because of poor transillumination of thick-walled or tightly constricted vessels. We investigated whether the wall cross-sectional area (WCSA) in cannulated arteries is nearly constant, allowing IDs to be calculated from outer diameters (...

CARL FAITH All rings considered are commutative with unit. A ring R is SISI (in Vámos' terminology) if every subdirectly irreducible factor ring R/I is self-injective . SISI rings include Noetherian rings, Morita rings, and almost maximal valuation rings ([Vil) . In [F3] we raised the question of whether a polynomial ring R[-1 over a SISI ring R is again SISI . In this paper we show this is not...

Let K be a complete field with a discrete valuation v, ring of integers OK , and maximal ideal (πK). Let k := OK/(πK) be the residue field, assumed to be separably closed of characteristic p ≥ 0. LetX/K be a smooth proper geometrically irreducible curve of genus g ≥ 1. Let X /OK denote a regular model of X/K. Let Xk = ∑v i=1 riCi be its special fiber, where Ci/k is an irreducible component of X...

A henselian valued field K is called a tame field if its algebraic closure K̃ is a tame extension, that is, the ramification field of the normal extension K̃|K is algebraically closed. Every algebraically maximal Kaplansky field is a tame field, but not conversely. We develop the algebraic theory of tame fields and then prove Ax–Kochen– Ershov Principles for tame fields. This leads to model compl...

Let M be an arbitrary Riemannian manifold diffeomorphic to S2. Let x, y be two arbitrary points of M. We prove that for every k = 1, 2, 3, . . . there exist k distinct geodesics between x and y of length less than or equal to (4k2 − 2k − 1)d, where d denotes the diameter of M. To prove this result we demonstrate that for every Riemannian metric on S2 there are two (not mutually exclusive) possi...

We continue a study initiated by Kraj́ıček of a Resolutionlike proof system working with clauses of linear inequalities, R(CP). For all proof systems of this kind Kraj́ıček proved in [1] an exponential lower bound of the form: exp(n) MO(W log2 n) , where M is the maximal absolute value of coefficients in a given proof and W is the maximal clause width. In this paper we improve this lower bound. F...

Let (α, β) ⊆ R denote the maximal interval of existence of solutions for the initial-value problem { dx dt = f(t, x), x(t0) = x0, where E is an open subset of Rm+1, f is continuous in E and (t0, x0) ∈ E. We show that, under the natural definition of computability from the point of view of applications, there exist initial-value problems with computable f and (t0, x0) whose maximal interval of e...

In this note we present new proofs of three basic theorems in calculus. Although these theorems are well-known, in each proof we obtain something which seems to be unknown. We start with the Heine-Cantor theorem about uniform continuity and obtain explicitly the optimal delta for the given epsilon. We then proceed with the Weierstrass extreme value theorem and present two proofs of it: the “env...

Jan proposed a mechanism that fulfils the requirement of a single key-lock (SKL for short) information protection system. Using Jan’s SKL method, each user is given a key, each file a sequence number, and an operating on the key of a user with the sequence number of a file yields the user’s corresponding access privilege on the file. In Jan’s literature, a formula to compute each user’s key for...

T paper proposes an extreme value approach to estimating interest-rate volatility, and shows that during the extreme movements of the U.S. Treasury market the volatility of interest-rate changes is underestimated by the standard approach that uses the thin-tailed normal distribution. The empirical results indicate that (1) the volatility of maximal and minimal changes in interest rates declines...