FIBONACCI RATIO IN A THERMODYNAMICAL CASE 239 the three results occurring at the end of Section 3, it is possible to deduce the coefficient of x k ~ 1 when k is even. The coefficient is k L 3(k-2) 3* 5(fe-2)(k-4) k-1\ 2(k-3) 2 • 4(fc-3)(&-5) 3-5-liX-2)(k-4)(fe-6)) 2 • 4 • 6(fc-3)(fc-5)(k-7) + " J ' the expression within the brackets terminating, since k is even. Consider the thermodynamics of a...

In this paper, we present a measure associated with detection and inference of statistically anomalous clusters of a graph based on the likelihood test of observed and expected edges in a subgraph. This measure is adapted from spatial scan statistics for point sets and provides quantitative assessment for clusters. We discuss some important properties of this statistic and its relation to modul...

We consider second order parabolic and elliptic systems with leading coefficients having the property of vanishing mean oscillation (VMO) in the spatial variables. An Lq −Lp theory is established for systems both in divergence and non-divergence form. Higher order parabolic and elliptic systems are also discussed briefly.

tin(ii)-ion-selective electrode consisting of dibenzo-18-crown-6 (db18c6) as an ionophore inpvc matrix was developed. the influences of membrane composition, selectivity, response time,reversibility and temperature on the electrode performance were investigated. the electrodeshowed a near nernstian response for sn2+ ions over a concentration range from 1.0× 10-6 – 1.0× 10-2 m with a slope of 27...

Abstract When the ordering of variables is fixed, e.g., x1 ≥ x2 ≥ · · · ≥ xn, the monomial X α = x α1 1 · · ·xn n majorizing the monomial X β = x1 1 · · ·xn n (|α| = |β|) means that ∑k i=1 αi ≥ ∑k i=1 βi (k = 1, · · · , n − 1). In this paper, a necessary condition of positively terminating of a general successive difference substitution algorithm (KSDS) for an input f is obtained by using a maj...

Contrast-enhanced liver MR image sequences acquired at multiple times before and after contrast administration have been shown to be critically important for the diagnosis and monitoring of liver tumors and may be used for the quantification of liver inflammation and fibrosis. However, over multiple acquisitions, the liver moves and deforms due to patient and respiratory motion. In order to ana...

This paper will study Fourier Series with random coefficients. We begin with an introduction to Fourier series on the torus and give some of the most important results. We then give some important results from probability theory, and build on these to prove a variety of theorems that deal with the convergence or divergence of general random series. In the final section, the focus is placed on r...