Search results for "Rotation formalisms in three dimensions"
showing 10 items of 17 documents
QuBiLS-MAS, open source multi-platform software for atom- and bond-based topological (2D) and chiral (2.5D) algebraic molecular descriptors computati…
2017
Background In previous reports, Marrero-Ponce et al. proposed algebraic formalisms for characterizing topological (2D) and chiral (2.5D) molecular features through atom- and bond-based ToMoCoMD-CARDD (acronym for Topological Molecular Computational Design-Computer Aided Rational Drug Design) molecular descriptors. These MDs codify molecular information based on the bilinear, quadratic and linear algebraic forms and the graph-theoretical electronic-density and edge-adjacency matrices in order to consider atom- and bond-based relations, respectively. These MDs have been successfully applied in the screening of chemical compounds of different therapeutic applications ranging from antimalarials…
Calculations of Starting Currents and Frequencies in Frequency-Tunable Gyrotrons
2012
Cold cavity and self-consistent formalisms for starting current and frequency calculations in frequency-tunable gyrotrons are summarized. Numerical solution schemes of the corresponding equations are discussed. A specific case is analyzed in detail.
A simple proof of the polylog counting ability of first-order logic
2007
The counting ability of weak formalisms (e.g., determining the number of 1's in a string of length N ) is of interest as a measure of their expressive power, and also resorts to complexity-theoretic motivations: the more we can count the closer we get to real computing power. The question was investigated in several papers in complexity theory and in weak arithmetic around 1985. In each case, the considered formalism (AC 0 -circuits, first-order logic, Δ 0 ) was shown to be able to count up to a polylogarithmic number. An essential part of the proofs is the construction of a 1-1 mapping from a small subset of {0, ..., N - 1} into a small initial segment. In each case the expressibility of …
Lagrangians, Hamiltonians and Noether’s Theorem
2015
This chapter is intended to remind the basic notions of the Lagrangian and Hamiltonian formalisms as well as Noether’s theorem. We shall first start with a discrete system with N degrees of freedom, state and prove Noether’s theorem. Afterwards we shall generalize all the previously introduced notions to continuous systems and prove the generic formulation of Noether’s Theorem. Finally we will reproduce a few well known results in Quantum Field Theory.
ComPWA: A common amplitude analysis framework for PANDA
2014
A large part of the physics program of the PANDA experiment at FAIR deals with the search for new conventional and exotic hadronic states like e.g. hybrids and glueballs. For many analyses PANDA will need an amplitude analysis, e.g. a partial wave analysis (PWA), to identify possible candidates and for the classification of known states. Therefore, a new, agile and efficient amplitude analysis framework ComPWA is under development. It is modularized to provide easy extension with models and formalisms as well as fitting of multiple datasets, even from different experiments. Experience from existing PWA programs was used to fix the requirements of the framework and to prevent it from restric…
Equilibrium and nonequilibrium many-body perturbation theory: a unified framework based on the Martin-Schwinger hierarchy
2013
We present a unified framework for equilibrium and nonequilibrium many-body perturbation theory. The most general nonequilibrium many-body theory valid for general initial states is based on a time-contour originally introduced by Konstantinov and Perel'. The various other well-known formalisms of Keldysh, Matsubara and the zero-temperature formalism are then derived as special cases that arise under different assumptions. We further present a single simple proof of Wick's theorem that is at the same time valid in all these flavors of many-body theory. It arises simply as a solution of the equations of the Martin-Schwinger hierarchy for the noninteracting many-particle Green's function with…
A Detailed Account of The Inconsistent Labelling Problem of Stutter-Preserving Partial-Order Reduction
2021
One of the most popular state-space reduction techniques for model checking is partial-order reduction (POR). Of the many different POR implementations, stubborn sets are a very versatile variant and have thus seen many different applications over the past 32 years. One of the early stubborn sets works shows how the basic conditions for reduction can be augmented to preserve stutter-trace equivalence, making stubborn sets suitable for model checking of linear-time properties. In this paper, we identify a flaw in the reasoning and show with a counter-example that stutter-trace equivalence is not necessarily preserved. We propose a stronger reduction condition and provide extensive new correc…
Statistical analysis when dealing with astigmatism: assessment of different spherocylindrical notations.
2001
Ophthalmic epidemiological studies frequently deal with ocular refractive errors, which are commonly expressed in the form sphere/cylinder x axis. However, this representation has been shown not to be the most suitable one for performing statistical analysis. Although alternative analytical and graphic methods to represent this kind of data have been developed, these formalisms have often gone unnoticed by researchers, despite their usefulness and versatility. Besides, there has been no discussion of how each of them fits in with a particular type of study. In this paper, several mathematical representations of dioptric power are revisited in a comprehensive way. The aim is to encourage res…
Post-Newtonian constraints onf(R)cosmologies in metric and Palatini formalism
2005
We compute the complete post-Newtonian limit of both the metric and Palatini formulations of $f(R)$ gravities using a scalar-tensor representation. By comparing the predictions of these theories with laboratory and solar system experiments, we find a set of inequalities that any lagrangian $f(R)$ must satisfy. The constraints imposed by those inequalities allow us to find explicit bounds to the possible nonlinear terms of the lagrangian. We conclude that in both formalisms the lagrangian $f(R)$ must be almost linear in $R$ and that corrections that grow at low curvatures are incompatible with observations. This result shows that modifications of gravity at very low cosmic densities cannot b…
Yang-Mills two-point functions in linear covariant gauges
2015
In this work we use two different but complementary approaches in order to study the ghost propagator of a pure SU(3) Yang-Mills theory quantized in the linear covariant gauges, focusing on its dependence on the gauge-fixing parameter $\xi$ in the deep infrared. In particular, we first solve the Schwinger-Dyson equation that governs the dynamics of the ghost propagator, using a set of simplifying approximations, and under the crucial assumption that the gluon propagators for $\xi>0$ are infrared finite, as is the case in the Landau gauge $(\xi=0)$. Then we appeal to the Nielsen identities, and express the derivative of the ghost propagator with respect to $\xi$ in terms of certain auxiliary…