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We consider the minimization problem for an average distance functional in the plane, among all compact connected sets of prescribed length. For a minimizing set, the blow-up sequence in the neighborhood of any point is investigated. We show existence of the blow up limits and we characterize them, using the results to get some partial regularity statements. [ABSTRACT FROM AUTHOR]

We study the asymptotic behavior of the eigenvalues of Hermitian n × n block Toeplitz matrices Tn, with k × k blocks, as n tends to infinity. No hypothesis is made concerning the structure of the blocks. Such matrices {Tn} are generated by the Fourier coefficients of a Hermitian matrix-valued function f ∈ L², and we study the distribution of their eigenvalues for large n, relating their behavior to some properties of f as a function; in particular, we show that the distribution of the eigenvalues converges to a limit μf, and we explicitly compute μf in terms of f, showing that F dμf = 1/k TrF(f). Some consequences of this distribution and some localization results for the eigenvalues of Tn are discussed. We also study the eigenvalues of the preconditioned matrices {Pn-1Tn}, where the sequence {Pn} is generated by a positive definite matrix-valued function p. We show that the spectrum of any Pn-1Tn is contained in the interval [r,R], where r is the smallest and R the largest eigenvalue of p-1f. We also prove that the first m eigenvalues of Pn-1Tn tend to r and the last m tend to R, for any fixed m. Finally, the exact limit value of the condition number of the preconditioned matrices is computed. [ABSTRACT FROM AUTHOR]

Kidney haemodynamics appear to change after the early phases of diabetic nephropathy: increases in glomerular filtration rate and in renal plasma flow have been widely reported, while kidney size is increased. As the renal kallikrein-kinin system has been demonstrated to regulate kidney blood circulation, we have evaluated the excretion of urinary kallikrein in 87 Type 1 (insulin-dependent) diabetic patients with and without hyperfiltration. Urinary kallikrein excretion was measured in 24-h urine collections. The esterolytic activity was determined by fluorimetric assay. The excretion of urinary kallikreins was significantly higher in hyperfiltering patients (472±125 esterase units/24 h) than in normofiltering (168±77 esterase units/24 h) and control subjects (151±39 esterase units/24 h), p<0.001. Furthermore, we observed a positive correlation between urinary kallikrein excretion and glomerular filtration rate ( r=0.785). These data suggest that variations of kallikrein and kinin concentrations may play a role in the alteration of renal haemodynamics in Type 1 diabetes. It is possible that the kinin-kallikrein system, the renin-angiotensin system and the prostaglandins may interact to determine the haemodynamic alterations which are present in the diabetic disease. [ABSTRACT FROM AUTHOR]

We study the asymptotic behaviour of the eigenvalues of Hermitian n× n block Topelitz matrices T , with k×k blocks, as n tends to infinity. No hypothesis is made concerning the structure of the blocks. Such matrices {T } are generated by the Fourier coefficients of a Hermitian matrix valued function f∈ L , and we study the distribution of their eigenvalues for large n, relating their behaviour to some properties of the function f. We also study the eigenvalues of the preconditioned matrices {P T}, where the sequence {P } is generated by a positive definite matrix valued function p. We show that the spectrum of any P T is contained in the interval [ r, R], where r is the smallest and R the largest eigenvalue of p f. We also prove that the first m eigenvalues of P T tend to r and the last m tend to R, for any m fixed. Finally, exact limit values for both the condition number and the conjugate gradient convergence factor for the preconditioned matrices P T are computed. [ABSTRACT FROM AUTHOR]

In this paper we deal with the problem of locating all the zeros of a given polynomial p( x) and approximating them to any degree of precision: by combining classical iterative methods with homotopy path tracking techniques, we introduce a new algorithm for polynomial root finding, prove its convergence and estimate its computational cost. [ABSTRACT FROM AUTHOR]