A combinatorial proof of a result on generalized Lucas polynomials

We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2. The initial values are 〈0〉 = 2; 〈1〉= s, respectively

Some properties of Fibonacci dumbers, deneralized Fibonacci numbers and generalized Fibonacci polynomial sequences

In this paper we study the Fibonacci numbers and derive some interesting properties and recurrence relations. We prove some charecterizations for Fp, where p is a prime of a certain type. We also define period of a Fibonacci sequence modulo an integer, m and derive certain interesting properties related to them. Afterwards, we derive some new properties of a class of generalized Fibonacci numbers. In the last part of the paper we introduce some generalized Fibonacci polynomial sequences and we derive some results related to them

Some results on generalized multiplicative perfect numbers

In this article, based on ideas and results by Sándor (J Inequal Pure Appl Math 2:Art. 3, 2001; J Inequal Pure Appl Math 5, 2004), we define k-multiplicatively e-perfect numbers and k-multiplicatively e-superperfect numbers and prove some results on them. We also characterize the k-T0T∗-perfect numbers defined by Das and Saikia (Notes Number Theory Discrete Math 19:37–42, 2013) in details

PULSED LASER AND ELECTRON BEAM INDUCED DIFFUSION OF ANTIMONY IN SILICON

The aim of this work is to compare the diffusion into silicon of a thin film (~ 100 Å) of deposited antimony induced either by a pulsed laser irradiation or electron beam and to interpret the different experimental behaviours as observed by Rutherford backscattering spectrometry, by using the calculated temperature distributions obtained by solving the heat flow equation for the two different annealing processes

DESIGN AND FIRST IMPLEMENTATION OF A VACUUM DATABASE FOR LHC MAIN RING AND TRANSFER LINES

Abstract During the construction of LHC, much information about vacuum equipment is scattered at different levels and activities have to be shared and not duplicated. To gather this data, a completely new database is designed, in relation with other existing databases and personal data storage. An inventory and analysis of the data required by the users has been done. Disparate types like history of existing equipment, coming from an existing Oracle Database, test results, drawings and studies need to be stored. Different groups of people are involved and a user interface will provide access to an overview of LHC activities for the vacuum group. This paper presents the results of the analysis of the user requirements and some ideas how to implement them

Effect of articular cartilage proteoglycan depletion on high frequency ultrasound backscatter

AbstractObjective To study the effect of variations of articular cartilage proteoglycans (PG) on high-frequency ultrasound backscatter.Design The study was performed on patellar cartilages of immature and mature rats (N=36). The variation of PG content was induced by enzyme digestion. Control and treated cartilages were explored in vitro using a 55MHz scanning acoustic microscopy, then assessed by histology for the fibrillar collagen organization analysis. The variations of proteoglycan and collagen content were evaluated. Thickness measurements performed on both B-scan images and histologic sections were compared. Ultrasonic radio-frequency signals reflected by the cartilage surface and backscattered from its internal matrix were processed to estimate the integrated reflection coefficient (IRC) and apparent integrated backscatter (AIB).Results Although hyaluronidase treatment of immature and mature cartilages removed approximately 50% of the proteoglycans, the echogenicity level of ultrasound images of degraded cartilages was similar to that of controls. IRC and AIB parameters did not significantly vary. Histologic sections of degraded cartilage displayed no change in collagen fiber organization. The thickness mean values measured by ultrasound in PG-depleted groups were significantly higher than in controls, whereas no significant difference in thickness was detected by histological measurement. The increase in cartilage thickness may potentially be explained by a decrease of speed of sound in PG-depleted cartilages that is more likely subsequent to an increase of water content.ConclusionCurrent results indicate that PG depletion has no significant effect on high frequency ultrasound backscattered from rat patellar cartilage. Ultrasound may provide information about variations of PG content via speed of sound measurement. Copyright 2002 OsteoArthritis Research Society International. Published by Elsevier Science Ltd. All rights reserved

PULSED ELECTRON BEAM ANNEALING OF As AND B IMPLANTED SILICON

p-type (100) silicon wafers have been implanted either by As or B ions at 20 and 200 keV energies and doses of 1016cm-2. Pulsed electron beam annealing has been performed with fluences of 1.1 and 1.4 J/cm2 using a mean electron energy of 15 keV. The pulse duration was 50 ns. The annealed layers have been investigated by Rutherford backscattering under random and channeling conditions and by S.I.M.S. profiling. Good crystal regrowth and high dopant activation occur in all cases except for the 200 keV Boron implant. Impurities redistribution is observed but no significant segregation effects appear. The experimental profiles are in good agreement with a diffusion model using a modified green function solution and taking into account dopant diffusion in liquid phase and the computed melt front location. The deduced diffusion coefficient are in the 5.10-5cm2/s range for boron and 2.10-4cm2/s range for arsenic

Inter-vehicle gap statistics on signal-controlled crossroads

We investigate a microscopical structure in a chain of cars waiting at a red signal on signal-controlled crossroads. Presented is an one-dimensional space-continuous thermodynamical model leading to an excellent agreement with the data measured.Moreover, we demonstrate that an inter-vehicle spacing distribution disclosed in relevant traffic data agrees with the thermal-balance distribution of particles in the thermodynamical traffic gas (discussed in [1]) with a high inverse temperature (corresponding to a strong traffic congestion). Therefore, as we affirm, such a system of stationary cars can be understood as a specific state of the traffic sample operating inside a congested traffic stream.Comment: 6 pages, 4 figures, accepted for publication in J. Phys. A: Math. Theo