934 research outputs found
Generalizing the autonomous Kepler-Ermakov system in a Riemannian space
No full textWe generalize the two-dimensional autonomous Hamiltonian-Kepler-Ermakov dynamical system to three dimensions using the sl(2, R) invariance of Noether symmetries and determine all three-dimensional autonomous Hamiltonian-Kepler- Ermakov dynamical systems which are Liouville integrable via Noether symmetries. Subsequently, we generalize the autonomous Kepler-Ermakov system in a Riemannian space which admits a gradient homothetic vector by the requirements (a) that it admits a first integral (the Riemannian Ermakov invariant) and (b) it has sl(2, R) invariance. We consider both the non-Hamiltonian and the Hamiltonian systems. In each case, we compute the Riemannian-Ermakov invariant and the equations defining the dynamical system. We apply the results in general relativity and determine the autonomous Hamiltonian-Riemannian-Kepler-Ermakov system in the spatially flat Friedman-Robertson-Walker spacetime. We consider a locally rotational symmetric spacetime of class A and discuss two cosmological models. The first cosmological model consists of a scalar field with an exponential potential and a perfect fluid with a stiff equation of state. The second cosmological model is the f(R)-modified gravity model of Λ bcCDM. It is shown that in both applications the gravitational field equations reduce to those of the generalized autonomous Riemannian-Kepler-Ermakov dynamical system which is Liouville integrable via Noether integrals. © 2012 IOP Publishing Ltd
A Physical Approach for the Observation of Oil Spills in SAR Images
No full textIn this paper, a physical approach to support oil spills observation over synthetic aperture radar (SAR) images is presented. Electromagnetic model is based on an enhanced damping model that takes into account oil viscoelastic properties and wind speed. As a matter of fact, a multisensor approach is considered and a constant false alarm rate (CFAR) filter is used to minimize speckle effect. A set of experiments is presented and discussed. They show that oil spill processing is effective over single-look SAR images using mean input data
Ermakov-Lewis invariants and Reid systems
Get PDF"Reid´s mth-order generalized Ermakov systems of nonlinear coupling constant ? are equivalent to an integrable Emden-Fowler equation. The standard Ermakov-Lewis invariant is discussed from this perspective, and a closed formula for the invariant is obtained for the higher-order Reid systems (m ? 3). We also discuss the parametric solutions of these systems of equations through the integration of the Emden-Fowler equation and present an example of a dynamical system for which the invariant is equivalent to the total energy.
Alexander Ermakov: a historian and a teacher (1957–2007)
No full textВ статье представлены основные этапы жизненного и творческого пути уральского историка, кандидата исторических наук, доцента Александра Владиславовича Ермакова. Вся трудовая деятельность А. В. Ермакова была связана с Нижнетагильским государственным педагогическим институтом. Человек энциклопедических знаний, широкой научной эрудиции, он был не только видным специалистом по отечественной истории XX века и истории советского Урала, но и обладал необычайной скромностью и доброжелательным отношением к студентам и коллегам.The article represents the main stages of the life, career and study of Alexander Vladislavovich Ermakov — a talented historian, docent, a man with encyclopaedic knowledge and a broad scientific erudition. Most of the work activity of A. V. Ermakov was associated with the Nizhny Tagil State Pedagogical Institute. A. V. Ermakov was not only a noted expert in the history of the Soviet Urals, but he was also a gifted pedagogue
Detecting Yersinia ruckeri on the death of carp (Cyprinus carpio) farmed in southern Russia
No full textYersinia ruckeri was first discharged from carp brood fishes (Cyprinus carpio) farmed in ponds in southern Russia. The death of fish was observed at a temperature of 15°C in March-April 2015. Ten fish with clinical signs of the disease were taken for research. Water samples were taken for hydrochemical analysis. The research results indicated a high level of permanganate index (2.4-2.8 MAC), nitrite nitrogen (1.5-2 MAC), nitrate nitrogen (1.4-1.5 MAC), and a low oxygen content in the bottom layers (2.0 mg/dm3). A parasitological study of fish revealed an invasion by monogenes (Dactylogyrus extensus) and mollusks (Unio pinctorum). As a result of bacteriological studies, 62 isolates were discharged, 30 from water and 32 from fish. The determination of bacteria was carried out according to morphological and enzymatic properties. The biochemical characteristics of the Yersinia ruckeri strains made it possible to classify them as serotype 1. All Yersinia ruckeri strains were sensitive to ciprofloxacin, tetracycline, chloramphenicol and resistant to furazolidone. MALDI TOF mass spectrometry and PCR were used for additional identification of bacteria. Serious pathological and histopathological changes in the fish tissues were not detected
A Review in Ermakov Systems and Their Symmetries
No full textA review of the mathematical and physical aspects of the Ermakov systems is presented. The main properties of Lie algebra invariants are extensively used. The two and tridimensional Ermakov systems are fully analyzed and the correspondent invariants found. Then, we go over quantization with special emphasis in the two dimensional case. An application to Nonlinear Optics is hereby developed. We also treat the so-called “one dimensional” case, which is easily solved in the classical case but offers special interest in the quantum realm, where one can find exactly the Feynman propagator. We finish with the stationary phase approximation which contains also some interesting features when compared with the exact solution. Some prospects for future research are also discussed
Ermakov-Lewis Symmetry In Photonic Lattices
No full textWe present a class of waveguide arrays that is the classical analog of a quantum harmonic oscillator, where the mass and frequency depend on the propagation distance. In these photonic lattices, refractive indices and secondneighbor couplings define the mass and frequency of the analog quantum oscillator, while first-neighbor couplings are a free parameter to adjust the model. The quantum model conserves the Ermakov-Lewis invariant, thus the photonic crystal also possesses this symmetry. © 2014 Optical Society of America
Two discretisations of the Ermakov-Pinney equation
No full textWe propose two candidates for discrete analogues to the nonlinear Ermakov-Pinney equation. The first one based on an association with a two-dimensional conformal mapping defines a second-degree difference scheme. It possesses the same features as in the continuum: a nonlinear superposition principle relating its general solution to a second-order linear difference equation and by direct linearisation a relationship with a third-order difference equation. The second form, which is new, is obtained from a slight improvement of the superposition principle. It has the advantage of leading to a first degree difference scheme and preserves all the nice properties of its linearisation. (C) 1997 Elsevier Science B.V
A new perspective on the Ermakov-Pinney and scalar wave equations
No full textThe first part of the paper proves that a subset of the general set of Ermakov-Pinney equations can be
obtained by differentiation of a first-order non-linear differential equation. The second part of the paper
proves that, similarly, the equation for the amplitude function for the parametrix of the scalar wave
equation can be obtained by covariant differentiation of a first-order non-linear equation. The construction
of such a first-order non-linear equation relies upon a pair of auxiliary 1-forms (psi, rho). The 1-form psi
satisfies the divergenceless condition div(psi) = 0, whereas the 1-form rho fulfills the non-linear equation
div(rho) + rho**2 = 0. The auxiliary 1-forms (psi, rho) are evaluated explicitly in Kasner space-time, hence, amplitude
and phase function in the parametrix are obtained. Thus, the novel method developed in this paper
can be used with profit in physical applications
New data on wild grey mullet (mugil cephalus linnaeus, 1758) myxosporean (myxobolus episquamalis egusa et al., 1990) in the black sea
Get PDFFlathead grey mullet, Mugil cephalus, with mass whitish cystlike plasmodia on their scales were collected at Kerchensky preglass of the Black Sea in 2015. The prevalence of infected fish varied from 15% in spring, reached 100% in summer, and declined to 2.5% in autumn. No fish mortality was detected. The spores were oval in frontal view, tapering to a blunt apex. Two unequal polar capsules were pyriform and extended over the anterior half of spore. Spores were 8.2±0.03 μm (7.9-8.4) long, 5.9±0.23 μm (5.2-7.3) wide, and 4.4±0.17 μm (4.0-4.7) thick. Two pyriform and unequal polar capsules were observed (4.0±0.07 μm (3.3-4.5) long, and 1.5±0.24 μm (1.1-1.8) wide). The investigation of nucleotide sequences of the 18S rDNA gene of the myxosporean spores from scales with universal primer A (5′-ACCTGGTTGATCCTGCCAGT-3′) and B (5′-TGATCCTTCTGCAGGTTCACCTAC-3′) showed 100% identity with episquamalis, and 99 % with M. bizerti, M. ichkeulensis, M. spinacurvata and Myxobolus sp. previously detected in mullets. The results obtained from the present study reveal that M. episquamalis, found on the scales of M. cephalus from Kerchensky preglass of the Black Sea, is new record for Russian waters
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