Representation of the Fibonacci and Lucas Numbers in Terms of Floor and Ceiling

In the paper we show how to express the Fibonacci numbers and Lucas numbers using the floor and ceiling operations.Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok, PolandGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek and Piotr Rudnicki. Two programs for SCM. Part I - preliminaries. Formalized Mathematics, 4(1):69-72, 1993.Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.Yoshinori Fujisawa, Yasushi Fuwa, and Hidetaka Shimizu. Public-key cryptography and Pepin's test for the primality of Fermat numbers. Formalized Mathematics, 7(2):317-321, 1998.Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.Konrad Raczkowski and Andrzej Nędzusiak. Real exponents and logarithms. Formalized Mathematics, 2(2):213-216, 1991.Piotr Rudnicki and Andrzej Trybulec. Abian's fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997.Robert M. Solovay. Fibonacci numbers. Formalized Mathematics, 10(2):81-83, 2002.Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Piotr Wojtecki and Adam Grabowski. Lucas numbers and generalized Fibonacci numbers. Formalized Mathematics, 12(3):329-333, 2004

Commander\u27s Call and the Air Force Now Film: Meeting the needs of Air Force Internal Communcation?

The U.S. Air Force is a diversified organization of nearly half a million people based worldwide. Because of its nature and complex mission, the organization has unique internal communication needs. One program established to satisfy those needs is Commander’s Call, and a mandatory component of each Commander\u27s Call is the latest edition of the Air Force Now film. Because Commander\u27s Call is held monthly at the unit 1evai and attendance Is mandatory for all personnel, and because a fifteen to thirty minute color sound-on film is produced monthly .for it, the program represents a substantial investment of resources and a strong commitment to internal communication. This study aska whether Commander\u27s Call and the Air Force Now --------------------------- are in fact meeting the needs of Air Force internal communication. A . .. ■ ■hi..., ; ■ - . field research method employing che survey technique was used to collect data from an independent sample drawn from the military population at Grand Forks Air Force Base, North Dakota, a basA whose mission is to maintain long range missiles and bomber aircraft or. strategic alert. The study asks whether position in the military rank structure, degree of job satisfaction, or command position affect attitudes toward Commander’s Call. It also asks whether attitudes toward Commander*s Call influence attitudes toward Air Force Now, and whether .Air Force Now enhances or detracts from Commander\u27s Call. Finally, it asks whether attitudes toward Air Force Now and Commander\u27s Call warrant their continued use. The findings indicate that job satisfaction and command position variables significantly affect attitudes toward Commander\u27s Call. They also indicate that the film and the program are probably evaluated independently, aid the film is regarded with significantly more favor than Commander’s Call, finally they indicate that valuation of both programs are generally favorable, and no evidence exists that they should be discontinued. There Is strong evidence, however, to support the overall conclusion that certain changes in the programs would enhance their communication effectiveness, Those changes include more solicitation by commanders of the topics considered salient by their subordinates, more commander flexibility as to where, when and how to conduct the program, and an Air ?orce wide program to collect, analyze and respond to feed-back by participants

Beyond Emotions: Oscillations of the Amygdala and Their Implications for Electrical Neuromodulation

The amygdala is a structure involved in emotions, fear, learning and memory and is highly interconnected with other brain regions, for example the motor cortex and the basal ganglia that are often targets of treatments involving electrical stimulation. Deep brain stimulation of the basal ganglia is successfully used to treat movement disorders, but can carry along non-motor side effects. The origin of these non-motor side effects is not fully understood yet, but might be altered oscillatory communication between specific motor areas and the amygdala. Oscillations in various frequency bands have been detected in the amygdala during cognitive and emotional tasks, which can couple with oscillations in cortical regions or the hippocampus. However, data on oscillatory coupling between the amygdala and motor areas are still lacking. This review provides a summary of oscillation frequencies measured in the amygdala and their possible functional relevance in different species, followed by evidence for connectivity between the amygdala and motor areas, such as the basal ganglia and the motor cortex. We hypothesize that the amygdala could communicate with motor areas through coherence of low frequency bands in the theta-alpha range. Furthermore, we discuss a potential role of the amygdala in therapeutic approaches based on electrical stimulation

Case Studies of Seismic Energy Release Ahead of Underground Coal Mining Before Strong Tremors

We would like to test the concept that induced seismicity prior to relatively large mining tremor (ML[2.5, E[106J) can be inferred from the cumulative Benioff strain release (BSR) as power law time-to-failure before the strong event. This study presents the application of accelerating BSR prior to a large earthquake, widely used in natural seismicity, for analysis of this phenomenon in induced seismicity. The Benioff strain release is quantified as accelerated releases of cumulative (square root sum) of seismic energy in the time series. During the study, five sequences were extracted from the seismic catalogues from two Polish hard coal mines: exhausted Bobrek Mine (data form the ISEPOS Platform) and from a mine belonging to the Polish Mining Group. Next, a search radius was used to select precursory events and to indicate the type of processes occurring in the coal seam and its vicinity. The fitted power law of cumulative Benioff strain release showed changes of m-parameter. If the value of m was lower than 1.0, the process was regarded as an accelerating-like and if m was higher than 1.0—as a quiescence-like. The investigation of m-parameter vs. the search radius showed the general behaviour of the rock mass in the studied areas and allowed to evaluate the relationship between the critical radius and magnitude of the target event. The obtained scaling relation log(Rc) * 0.35 ML is similar to these reported by other authors who analysed natural seismicity which might suggest that the scaling relation works in a wide range of magnitudes

Zarys problematyki wojny w religii i mitologii mieszkańców Pomorza na przełomie epok brązu i żelaza

The author of this article attempts to depict the possibilities of reconstructing the role of war in religion and mythology of Pomerania region in the late Bronze and early Iron Age. Knowing that in prehistory every human activity had sacral significance leads to the conclusion that almost all military conflicts had it too. Lack of historical sources describing religion of that region and period forces us to look for another way to reconstruct it. However, we know multiple Indo-European sources from different times and places thatcan be extrapolated on societies being our object of interest. Archaeological sources such as weaponry, iconography known from urns but also arms, and evidence of violence held huge non-utility significance. Compared with some schemes gained from known mythological systems, they can lead us to conclusions about the role of war and war related violence in past societies’ religious systems.Artykuł jest próbą nakreślenia możliwości odtworzenia znaczenia konfliktów zbrojnych dla systemów wierzeniowych ludów zamieszkujących Pomorze w czasach tzw. kultur pól popielnicowych. Podstawą do owych rozważań jest analiza mitologii ludów indoeuropejskich i próba odnalezienia uniwersalnych schematów, możliwych do zastosowania dla omawianych społeczeństw a także analiza przedmiotów związanych z wojowniczością i śmiercią oraz śladów konfliktów pod kątem ich sakralnego znaczenia

Determination of Destress Blasting Effectiveness Using Seismic Source Parameters

Underground mining of coal seams in the Upper Silesian Coal Basin is currently performed under difficult geological and mining conditions. The mining depth, dislocations (faults and folds) and mining remnants are responsible for rockburst hazard in the highest degree. This hazard can be minimized by using active rockburst prevention, where destress blastings play an important role. Destress blastings in coal seams aim to destress the local stress concentrations. These blastings are usually performed from the longwall face to decrease the stress level ahead of the longwall. An accurate estimation of active rockburst prevention effectiveness is important during mining under disadvantageous geological and mining conditions, which affect the risk of rockburst. Seismic source parameters characterize the focus of tremor, which may be useful in estimating the destress blasting effects. Investigated destress blastings were performed in coal seam no. 507 during its longwall mining in one of the coal mines in the Upper Silesian Coal Basin under difficult geological and mining conditions. The seismic source parameters of the provoked tremors were calculated. The presented preliminary investigations enable a rapid estimation of the destress blasting effectiveness using seismic source parameters, but further analysis in other geological and mining conditions with other blasting parameters is required