Search results for "degree"
showing 10 items of 875 documents
Elementary Integration of Superelliptic Integrals
2021
Consider a superelliptic integral $I=\int P/(Q S^{1/k}) dx$ with $\mathbb{K}=\mathbb{Q}(\xi)$, $\xi$ a primitive $k$th root of unity, $P,Q,S\in\mathbb{K}[x]$ and $S$ has simple roots and degree coprime with $k$. Note $d$ the maximum of the degree of $P,Q,S$, $h$ the logarithmic height of the coefficients and $g$ the genus of $y^k-S(x)$. We present an algorithm which solves the elementary integration problem of $I$ generically in $O((kd)^{\omega+2g+1} h^{g+1})$ operations.
Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model a…
2019
Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a compr…
Non-linear dynamics of alpha and theta rhythm: correlation dimensions and Lyapunov exponents from healthy subject's spontaneous EEG.
1997
The aim of the present paper was to analyze some non-linear dynamic properties of the resting EEG from healthy subjects under eyes closed conditions. For this purpose we digitally filtered the spontaneous EEG in the theta (3-8 Hz) and alpha frequency range (8-13 Hz) and considered these independent rhythms as signals from a deterministic system. Under certain conditions non-linear dynamic systems are able to generate deterministic chaos, which means that similar causes do not produce similar effects. This phenomenon is called sensitive dependence on initial conditions. From different lead positions (F3, F4, Cz, P3, P4, O1 and O2) we calculated the so-called correlation dimension D2, which i…
Implementation of transition moments between excited states in the approximate coupled-cluster singles and doubles model
2008
An implementation of transition moments between excited states for the approximate coupled-cluster singles and doubles model (CC2) using the resolution of the identity (RI) approximation is reported. The accuracy of the RI approximation is analyzed for a testset of 7 molecules and 76 transitions. The RI error is found to be very small for both transition moments and oscillator strengths. Furthermore, the performance of the CC2 model in comparison with coupled-cluster singles and doubles (CCSD) is studied for 40 transitions of the same testset, yielding deviations of about 12% for the transition moments and 24% for the oscillator strengths. In addition, for 13 transitions of the testset the …
Force probe simulations using a hybrid scheme with virtual sites.
2017
Hybrid simulations, in which a part of the system is treated with atomistic resolution and the remainder is represented on a coarse-grained level, allow for fast sampling while using the accuracy of atomistic force fields. We apply a hybrid scheme to study the mechanical unfolding and refolding of a molecular complex using force probe molecular dynamics (FPMD) simulations. The degrees of freedom of the solvent molecules are treated in a coarse-grained manner while atomistic resolution is retained for the solute. The coupling between the solvent and the solute is provided using virtual sites. We test two different common coarse-graining procedures, the iterative Boltzmann inversion method an…
Röntgenklein winkeluntersuchungen zur struktur der fehlgeordneten bereiche in verstrecktem polyäathylen. Teil II: Messungen an kontrastierten proben
1968
Aus der relativen Anderung der Intensitat der Rontgenkleinwinkelstreuung von teilkristanllinen, verstreckten Hochpolymeren bei Einlagerung eines Kontrastmittels hoher Elektronendichte lassen sich Ruckschhusse auf die Struktur der fehlgeordneten Berechie sowie auf die Dichtefluktuation entlang der Faserachse ziehe. In der vorliegenden Arbeit wird uber Messungen der Anderung der Kleinwinkelintensiat von verstrecktem Polyathylen in Abhangigkeit vom Jodgehalt berichtet. Aus der Beobachtung, das die auf dem Meridian gemessene Intensitat mit steigendem Jodgehalt zuerst abnimmt, dann aber wieder anwaachst, kann man schliesen, das die Elektronendichtedifferenz zwischen kristallinen und fehlgeordnet…
Deduction of the oxidation degree of the group A15 elements at the phthalocyanines on the basis of the Q band
2017
Learning and representation: the construction of masculinity in football. An analysis of the situation in Spain
2008
This essay examines the construction of masculinity through football in Spanish society. The results are presented from a study whose main objective was to investigate to what degree the changes th...
Recovery of damaged skeletal muscle in mdx mice by low-intensity endurance exercise
2010
Impact des allocations en ressources sur l'efficacité des écoles primaires en Côte d'Ivoire
2011
The quality of primary education in Côte d'Ivoire has deteriorated sharply over the past three decades. This situation is the result of an approximate management of the education system, which is characterized by a lack of educational support, a misallocation of resources, a congestion of classrooms (42 students for a teacher in primary school) and a lack of skilled and well trained teachers. In addition, the military-political conflict in September 2002 did not allow to improve this situation; on the contrary, it has further deteriorated the situation. Thus, the aim of this thesis is first to analyze the influence of resource endowments on the effectiveness of primary schools in Cote d'Ivo…