Let SH denote the homothety class generated by a convex set S ⊂ R: SH = {a + λS | a ∈ R, λ > 0}. We determine conditions for the Minkowski sum BH + CH or the Minkowski difference BH ∼ CH of homothety classes BH and CH generated by closed convex sets B,C ⊂ R to lie in a homothety class generated by a closed convex set (more generally, in the union of countably many homothety classes generated by...

Fakhruddin has proved that for two lattice polygons P and Q any lattice point in their Minkowski sum can be written as a sum of a lattice point in P and one in Q, provided P is smooth and the normal fan of P is a subdivision of the normal fan of Q. We give a shorter combinatorial proof of this fact that does not need the smoothness assumption on P .

Under the extra assumption that the boundary is of class C this was proven by S. Nakajima (= A. Matsumura) in 1926 Theorem 1 solves this problem. For convex bodies with C boundaries and positive curvature Nakajima’s result was generalized by Chakerian [?] in 1967 to “relative geometry” where the width and brightness are measured with with respect to some convex body K0 symmetric about the origi...

Purpose: To determine the analgesic response to a low-dose radiation therapy (RT) in trochanteric bursitis in elderly patient’s refractory to conventional therapies. Methods: We evaluated sixty consecutive patients diagnosed with trochanteric bursitis receiving RT in our institution from July 2010 to August 2014. All patients were treated with a total dose of 10 Gy in 10 daily fractions. The me...

Introduction: Risk of Nonunion, residual shoulder disability and symptomatic malunion are higher in conservative treatment of displaced midshaft clavicle fractures which are reportedly decreased by operative method but plating these fractu profile anatomically precontoured plates may reduce the rates of plate prominence and hardware removal. Objective: To assess the rate of plate prominence, ra...

Three antituberculosis medications are investigated in this work consist of rifampicin, isoniazid and pyrazinamide. The ultra violet (UV) spectra of these compounds are overlapped, thus use of suitable chemometric methods are helpful for simultaneous spectrophotometric determination of them. A generalized version of net analyte signal standard addition method (GNASSAM) was used for determinatio...

This work describes a new method for the correction of signal drift of a MS-based sensor by standard gas addition (SGA). It consists of introducing a gaseous He-Xe mixture continuously and independently of the carrier gas into the mass spectrometer source. To mimic the disturbances generated by periodical tuning of the mass detector, three series of adjustments were made to the main acquisition...

If a matrix effect is detected during the validation stage of an analytical method, the standard addition methodology must be applied. To reach a good estimation of the uncertainty associated with the determination, an adequate identification and evaluation of each uncertainty source should be done. As an example to illustrate how to calculate the uncertainty in this case, the simultaneous dete...

In this study, we investigate whether there is a need for the h index and its variants in addition to standard bibliometric measures (SBMs). Results from our recent study (L. Bornmann, R. Mutz, & H.-D. Daniel, 2008) have indicated that there are two types of indices: One type of indices (e.g., h index) describes the most productive core of a scientist’s output and informs about the number of pa...

The use of H-point curve isolation (HPCIM) and H-point standard addition methods (HPSAM) for spectrophotometric studies of complex formation equilibria are proposed. One step complex formation, two successive stepwise and mononuclear complex formation systems, and competitive complexation systems are studied successfully by the proposed methods. HPCIM is used for extracting the spectrum of comp...