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Mathematical Rotordynamic Model Regarding Excitation Due to Elliptical Shaft Journals in Electrical Motors Considering the Gyroscopic Effect  [PDF]
Ulrich Werner
Applied Mathematics (AM) , 2013, DOI: 10.4236/am.2013.48A009

The paper presents a mathematical rotordynamic model regarding excitation due to elliptical shaft journals in sleeve bearings of electrical motors also considering the gyroscopic effect. For this kind of excitation, a mathematical rotordynamic model was developed considering the influence of the oil film stiffness and damping of the sleeve bearings, the stiffness of the end-shields and bearing housings, the stiffness of the rotor, the electromagnetic stiffness in the air gap of the electrical motor and the mass moment of inertia of the rotor and therefore also considering the gyroscopic effect. The solution of the linear differential equation system leads to the mathematical description of the absolute orbits of the shaft centre, the shaft journals and the bearing housings and to the relative orbits between the shaft journals and the bearing housings. Additionally, the bearing housing velocities can also be derived with this mathematical rotordynamic model.

Dependence of Gravity Induced Absorption Changes on the Earth’s Magnetic Field as Measured during Parabolic Flight Campaigns  [PDF]
Werner Schmidt
Journal of Modern Physics (JMP) , 2013, DOI: 10.4236/jmp.2013.411190

Various spectroscopic experiments performed on the AIRBUS ZERO G—located in Bordeaux, France—in the years 2002 to 2012 exhibit minute optical reflection/absorption changes (GIACs) as a result of gravitational changes between 0 and 1.8 g in various biological species such as maize, oats, Arabidopsis and particularly Phycomyces sporangiophores. During a flight day, the AIRBUS ZERO G conducts 31 parabolas, each of which lasts about three minutes including a period of 22 s of weightlessness. So far, we participated in 11 parabolic flight campaigns including more than 1000 parabolas performing various kinds of experiments. During our campaigns, we observed an unexplainable variability of the measuring signals (GIACs). Using GPS-positioning systems and three dimensional magnetic field sensors, these finally were traced back to the changing earth’s magnetic field associated with the various flight directions. This is the first time that the interaction of

Gravireception in Phycomyces: Threshold Determination on the Sounding Rocket TEXUS 50  [PDF]
Werner Schmidt
Journal of Modern Physics (JMP) , 2015, DOI: 10.4236/jmp.2015.610143
Abstract: Under parabolic flight conditions microgravity is not lower than 3 to 5 times 10-2 g. In contrast to parabolic flights, sounding rocket flights are virtually vibrational-free allowing microgravity as low as 10-5 g. Thus, a rotating platform serving as centrifuge allows the precise generation of gravitational forces ranging from 5 to 100 mg (not possible during parabolic flights). On this basis we determined the threshold1 for optical reflection/absorption changes in Phycomyces to be lower than 25 × 10-3 g. This compares well with the threshold determination of gravitropism in Phycomyces on a clinostat centrifuge. Kinetics of gravity-induced absorption changes and gravity as generated by the on-board centrifuge do not coincide but show a distinctive hysteresis with a latency of 4 s (75 mg-ramp, pull-up).
An Extension of the Black-Scholes and Margrabe Formulas to a Multiple Risk Economy  [PDF]
Werner Hürlimann
Applied Mathematics (AM) , 2011, DOI: 10.4236/am.2011.24053
Abstract: We consider an economic model with a deterministic money market account and a finite set of basic economic risks. The real-world prices of the risks are represented by continuous time stochastic processes satisfying a stochastic differential equation of diffusion type. For the simple class of log-normally distributed instantaneous rates of return, we construct an explicit state-price deflator. Since this includes the Black-Scholes and the Vasicek (Ornstein-Uhlenbeck) return models, the considered deflator is called Black-Scholes- Vasicek deflator. Besides a new elementary proof of the Black-Scholes and Margrabe option pricing formulas a validation of these in a multiple risk economy is achieved.
Did Major Impacts Affect Sedimentologic/Sequence-Analytical Pattern of the Early Palaeozoic Sedimentary Systems of Jordan, Arabian Plate?  [PDF]
Werner Schneider, Elias Salameh
Open Journal of Geology (OJG) , 2012, DOI: 10.4236/ojg.2012.24024
Abstract: Based on profound sequence-analytical data of the early Palaeozoic sedimentary systems of Jordan, Arabian Plate, a correlation attempt is proposed with regard to possible major impact events after Price [10]. His methodological concept tells that abrupt 441 Ma. Referring to the fact that major impacts may trigger, respectively influence, exogenic and endogenic processes on an over-regional, even global, extent, this paper put the “sensitive” geological setting of Jordan at the Arabian Platform’s margin into focus. That mainly concerns the early Palaeozoic coastlines as to sea level change as well as the Jordan Valley Rift as being possibly to susceptible for tectonic re-activation changes of both direction and speed of plate motions would indicate such convulsive processes as occurred on: 550 Ma, 526.5 Ma, 514 Ma, 502 Ma, 456/455.4 Ma, and following triggering of magmatism at the Precambrian/Cambrian boundary. The following phenomena are taken into account: Faulting and magmatism triggered along the Jordan Valley Rift (Wadi Araba) in connection with the Pan-African Orogeny, anoxic sediments, temporary high detrital input onto the adjoining stable platform from Gondwana hinterlands, and significant chemical weathering in the Gondwana source areas by intensive acid (nitric) rain directing mineral content variation in the “Nubian Sandstones” (e.g. feldspar, kaolinite/dickite, tourmaline).
Uncommon and Impact-Suspicious Geologic Phenomena across Jordan and Adjacent Areas, Arabian Plate  [PDF]
Werner Schneider, Elias Salameh
Open Journal of Geology (OJG) , 2014, DOI: 10.4236/ojg.2014.412051
Abstract: For the discovery and analysis of Jebel Waqf as Suwwan (JWS) Impact Crater, Jordan pushed the authors to consequently focusing on other unusual geologic phenomena such as circular/oval structures (some of “crypto-volcanic” origin), disharmonic folding, horizontal stylolites, and a broad stripe of Sanidine-Hornfels-Facies, all of them hosted in Upper Cretaceous/Paleogene carbonate rocks exposed across Jordan and adjacent areas. Shatter cones are the most useful tools during field work in the realm of circular structures. In addition to the impact-geologic data of JWS Impact Structure hitherto available, the cooling process of melted Lower Cretaceous Kurnub-Sandstone could be verified by microscopically identified SiO2-modifications between the melting point (1714°C) and low temperatures. In comparison with the Suffield 500 tons explosion tests [20] and with the Ries Impact Crater, Germany, excavation and vaporization processes of target rocks demand drilling between Central Uplift and Inner Ring of the JWS Impact Structure (“Chert-Carbonate-Impact-Chess Game”). In a scenario: “Impacting meets Plate Tectonics”, phenomena like disharmonic folding, horizontal stylolites, and an abundance of circular/oval structures of high diameter variation through northwest Jordan are discussed under aspects of gravitational gliding, effects of seismic surface waves (Love-), transpressional structures related to Jordan Rift-Tectonics, and possible impact processes of unknown number occurred on the Arabian Plate in southeastern direction with northwest-directed impulse. The so-called “Mottled Zone” of Jordan and Palestine owning a high number (~100) of mineral neoformations with formation temperatures up to ~1120°C(pseudo-wollastonite = β
Bell’s Ternary Quadratic Forms and Tunnel’s Congruent Number Criterion Revisited  [PDF]
Werner Hürlimann
Advances in Pure Mathematics (APM) , 2015, DOI: 10.4236/apm.2015.55027

Bell’s theorem determines the number of representations of a positive integer in terms of the ternary quadratic forms x2+by2+cz2 with b,c \"\"{1,2,4,8}. This number depends only on the number of representations of an integer as a sum of three squares. We present a modern elementary proof of Bell’s theorem that is based on three standard Ramanujan theta function identities and a set of five so-called three-square identities by Hurwitz. We use Bell’s theorem and a slight extension of it to find explicit and finite computable expressions for Tunnel’s congruent number criterion. It is known that this criterion settles the congruent number problem under the weak Birch-Swinnerton-Dyer conjecture. Moreover, we present for the first time an unconditional proof that a square-free number n\"\" 3(mod 8) is not congruent.

Optimal Bounds for the Largest Eigenvalue of a 3 × 3 Correlation Matrix  [PDF]
Werner Hürlimann
Advances in Pure Mathematics (APM) , 2015, DOI: 10.4236/apm.2015.57039
Abstract: A new approach that bounds the largest eigenvalue of 3 × 3 correlation matrices is presented. Optimal bounds by given determinant and trace of the squared correlation matrix are derived and shown to be more stringent than the optimal bounds by Wolkowicz and Styan in specific cases.
Historical Course Follows Climate Change: Patterns of the Northern Hemisphere — From Peoples’ Migration until the Industrial Revolution (3rd-18th Century)  [PDF]
Werner Schneider, Elias Salameh
Open Journal of Geology (OJG) , 2018, DOI: 10.4236/ojg.2018.813071
Abstract: This paper relates to the statement that the so-called “Little Ice Age” (RCC 6: 1.350-1.800 A.D.) represents—besides the 8k-Event (8.200-8.000 yr cal. B.P.)—the fastest and strongest onset in Holocene History [1]. Its intention focuses on the correlation of interplaying natural processes (i.e. solar energy variation, aerosols, oceanic currents, volcanism as part of plate tectonics, heat flow) with social/political evidence through the time-span of Peoples’ Migration until Industrial Revolution (3rd-18th Century). The time-span comprises the cool/wet/respectively dry climate phase of the P.M. (260-550), a Climate Optimum (600-1.100 A.D.) owning a final Thermal Maximum (1.100-1.260 A.D.) and the “little Ice Age” (1.350-1.800 A.D.), the latter intercalated by the Spörer Minimum (1.460-1.550 A.D.) and the Maunder Minimum (1.650-1.720 A.D.). Thereby, an average temperature difference of 1.0°C - 2.0°C seems sufficient for incising climatic/cultural consequences [2]. It has become obvious that a Climate Optimum primarily provides constructive life conditions; however with a problematic final as the following “Effect-Chain” tells: balanced agricultural/cultural population growth rich harvests satisfying nourishment health, encouragement overpopulation under favorable materialistic conditions
Some Applications of Optimal Control in Sustainable Fishing in the Baltic Sea  [PDF]
Dmitriy Stukalin, Werner H. Schmidt
Applied Mathematics (AM) , 2011, DOI: 10.4236/am.2011.27115
Abstract: Issues related to the implementation of dynamic programming for optimal control of a three-dimensional dynamic model (the fish populations management problem) are presented. They belong to a class of models called Lotka-Volterra models. The existence of bionomic equilibria will be considered. The problem of optimal harvest policy is then solved for the control of various classes of its behaviour. Therefore the focus will be the optimality conditions by using the Bellman principle. Moreover, we consider a different form for the optimal value of the control vector, namely the feedback or closed-loop form of the control. Academic examples are studied in order to demonstrate the proposed methods.
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