Let A = (aij)n×n be a nonnegative, symmetric, irreducible and invertible matrix. We prove the existence and uniqueness of radial solutions to the following Liouville system with singularity:  ∆ui + ∑n j=1 aij |x| βj ej = 0, R2, i = 1, ..., n ∫ R2 |x| βieui(x)dx <∞, i = 1, ..., n where β1, ..., βn are constants greater than −2. If all βis are negative we prove that all solutions are radial and...

Newly reported normalized cumulant moments of charged particles in ee collisions by the SLD collaboration are analyzed by the truncated modified negative binomial distribution (MNBD) and the negative binomial distribution (NBD). Calculated result by the MNBD describes the oscillatory behavior of the data much better than that by the NBD. PACS number(s): 13.65.+i, 34.10.+x Normalized cumulant mo...

Abstract This thesis is concerned with the synthesis of -sultams and the development of new routes for the synthesis of bicyclic versions of these molecules as potential anti-bacterials. The synthesis of 1-azetines, 1,2-thiazetin-1,1-dioxides and isothiazol-1,1-dioxides as precursors of bicyclic heterocycles is described. 1-Azetines were synthesised from azetidin-2-ones prepared via the [2+2] c...

Proof: Let R1 and R2 denote the instances of a region R in I1 and I2. In order to detect the entire region R, at least one descriptor d1 ∈ R1 has to randomly sample its correct match d2 ∈ R2 (following which the entire region will be ‘grown’ due to the propagation phase of the Region Growing Algorithm described in Section 4). So, the probability of detecting a region is equal to the probability...

This paper studies the behavior under iteration of the maps Tab(x, y) = (Fab(x)−y, x) of the plane R2, in which Fab(x) = ax if x ≥ 0 and bx if x < 0. The orbits under iteration correspond to solutions of the nonlinear difference equation xn+2 = 1/2(a− b)|xn+1|+1/2(a+ b)xn+1−xn. This family of piecewise-linear maps has the parameter space (a, b) ∈ R2. These maps are area-preserving homeomorphism...

Metabolic impairment is the common cause for mortality in acromegalic patients. In this study, long-term improvements of metabolic parameters were evaluated according to 2 different remission criteria.This was an observational cohort study before and up to 1 year after transsphenoidal adenomectomy (TSA). Participants were 187 patients with acromegaly. At 6 months after TSA, remitted patients wi...