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Semi-empirical ground-state potential of carbon monoxide with physical behavior in the limits of small and large inter-atomic separations

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JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER 2018年 217卷 262-273页

作者： Meshkov, Vladimir V. Stolyarov, Andrey, V Ermilov, Aleksander Yu Medvedev, Emile S. Ushakov, Vladimir G. Gordon, Iouli E. Moscow MV Lomonosov State Univ Dept Chem Leninskie Gory 1-3 Moscow 119991 Russia Russian Acad Sci Inst Problems Chem Phys Prospect Akad Semenova 1 Chernogolovka 142432 Russia Harvard Smithsonian Ctr Astrophys Atom & Mol Phys Div 60 Garden St Cambridge MA 02138 USA

Recently, several empirical models of the potential energy function (PEF) of the ground electronic state of CO have been developed by Coxon and Hajigeorgiou using the direct-potential-fit (DPF) analysis. These models reproduce more than twenty thousand of observed ro-vibrational line positions within their experimental accuracies and follow the theoretically predicted long-range asymptotic behavior of the potential beyond Le Roy's radius. However, the applicability of these models to calculations of the intensities of weak transitions is not obvious due to limitations discussed in this work. Here, we make the next step by imposing an additional requirement that the model has to display physical behavior outside the region to which the available spectroscopic data pertain. We perform ab initio calculations of the potential in the short-range region r = 0.3-0.8 angstrom where the potential increases well above the dissociation limit and include these data along with the estimated uncertainties in the DPF analysis. At smaller r, our PEF tends to the well-known united-atom limit. In the long-range region, it follows the ab initio data with their estimated accuracies available in the literature. On top of the above, the model is analytical, i.e. it has continuous derivatives of all orders. The model constructed is a linear function of twenty three adjustable parameters, and a non-linear function of additional five parameters. The properties of the new PEF are investigated in comparison with the previous empirical model due to Coxon and Hajigeorgiou (2004). Our PEF provides reproduction of all observed lines at the same level of accuracy. The new potential changes the intensities of high overtone transitions dramatically. In addition, we find that the anomalies in the purely rotational and ro-vibrational spectra change their intensities between the two PEFs even for the low-v bands. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Motor Activity ab initio calculations electron states linear function

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Computation of analytical sensitivity matrix for the frequency-domain EM data: MATLAB code

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COMPUTERS & GEOSCIENCES 2018年第Aug.期117卷 41-48页

作者： Ogunbo, Jide Nosakare Fed Univ Technol Akure Dept Appl Geophys PMB 704 Akure Ondo State Nigeria

Among many applications of the sensitivity matrix is its use for performing nonlinear least-squares inversion of geophysical data. The mainstream finite difference approach is approximate. Some previous works have discussed the accurate analytical computation approach for the sensitivity matrix of the 1D geophysical problems but the codes are not publicly accessible. Using the basic differentiation rules (product and quotient) and the logarithmic differentiation the MATLAB code for analytical computation of the 1D recursive transverse electric frequency-domain electromagnetic forward response is presented. Because only a single call to the sensitivity matrix subroutine is needed for analytical computation the computation time is a linear function of the number of parameters. However, the computation time for the sensitivity matrix computation via the approximate method is a quadratic function of the model parameters. Experimentation results show that the analytical method increasingly gain speed over its counterpart approximate method (for instance, the analytical route is a million times faster than approximate method when the number of parameters is a million) with no loss of accuracy.

关键词： matrices computational time Codes Quadratics MATLAB Quotient Approximation method arithmetic linear function

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Integrated Space Logistics Mission Planning and Spacecraft Design with Mixed-Integer Nonlinear Programming

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JOURNAL OF SPACECRAFT AND ROCKETS 2018年第2期55卷 365-381页

作者： Chen, Hao Ho, Koki Univ Illinois Dept Aerosp Engn 104 S Wright St Urbana IL 61820 USA

This paper develops a campaign-level space logistics optimization framework that simultaneously considers mission planning and spacecraft design using mixed-integer nonlinear programming. In the mission planning part of the framework, deployment and utilization of in-orbit infrastructures, such as in-orbit propellant depots or in situ resource utilization plants, are also taken into account. Two methods are proposed: First, the mixed-integer nonlinear programming problem is converted into a mixed-integer linear programming problem after approximating the nonlinear model with a piecewise linear function and linearizing quadratic terms. In addition, another optimization framework is provided, based on simulated annealing, which separates the spacecraft model from mission planning formulation. An example mission scenario based on multiple Apollo missions is considered, and the results show a significant improvement in the initial mass in low Earth orbit by campaign-level design as compared with the traditional mission-level design. It is also shown that the mixed-integer linear programming-based method gives better-quality solutions than the simulated annealing-based method, although the simulated annealing method is more flexible for extension to a higher-fidelity spacecraft model.

关键词： simulated annealing Apollo Missions spacecraft design close-orbit satellite Power grids initial mass mission planning linear function Mixed integer linear programming Logistics Nonlinear Programming spacecraft models Earth orbit

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functional Equations Characterizing Derivations: A Synthesis

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RESULTS IN MATHEMATICS 2018年第3期73卷 1-13页

作者： Ebanks, Bruce Univ Louisville Dept Math Louisville KY 40292 USA

Many articles have been written about functional equations characterizing derivations on integral domains (or sometimes commutative rings) of characteristic 0. Here we synthesize several recent results by various authors and extend them by showing that they hold more generally on commutative rings of sufficiently large finite characteristic.

关键词： Derivation of any order linear function integral domain commutative ring homogeneity

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Review of Roundabout Capacity Based on Gap Acceptance

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JOURNAL OF ADVANCED TRANSPORTATION 2019年第Pt.1期000卷 331-341页

作者： Guo, Ruijun Liu, Leilei Wang, Wanxiang Dalian Jiaotong Univ Sch Traff & Transportat Dalian 116028 Peoples R China

Circulating vehicles have priority at modern roundabouts. Entrance vehicles can enter the roundabout when there is a time gap larger than the critical gap;otherwise, the vehicles need to wait until there is a large enough gap. The gap acceptance theory was used to analyze the entrance capacity of roundabouts, which can be derived by queuing theory involving two vehicle streams. The paper introduces the main styles of headway distribution, which are named as bunched exponential distribution or M3 distribution. The calculation model of free stream ratio is also introduced. The entrance capacity models can be classified by different entrance vehicle types, which are piecewise function or linear function, or by different critical gap types, which are constant or stochastic function. For each form, the typical capacity expressions are given. The calculation values show a very small difference between these kinds of models. The capacity value based on the critical gap of stochastic function is more realistic and more complex in function style. Some conclusions were derived that drivers' nonhomogeneous and inconsistent character is more realistic than the fixed critical gap and following gap. The calculation results of capacity are similar to the field capacity under the assumption of homogeneity and continuance, with only a minor percent deviation. Finally, the paper points out additional problems and the suggested research in capacity of roundabouts.

关键词： Critical Gap Computational modeling vehicle value of calculation Gap acceptance queueing theory Roundabout Field Capacity Piecewise function linear function capacity value entry

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On functional Equations Characterizing Derivations: Methods and Examples

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RESULTS IN MATHEMATICS 2018年第2期73卷 1-27页

作者： Gselmann, Eszter Kiss, Gergely Vincze, Csaba Univ Debrecen Inst Math POB 400 H-4002 Debrecen Hungary Univ Luxembourg Fac Sci Technol & Commun Maison Nombre 6 Ave Fonte L-4364 Esch Sur Alzette Luxembourg

functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and automorphisms are additive functions satisfying some further functional equations as well. It is an important question that how these morphisms can be characterized among additive mappings in general. The paper contains some multivariate characterizations of higher order derivations. The univariate characterizations are given as consequences by the diagonalization of the multivariate formulas. This method allows us to refine the process of computing the solutions of univariate functional equations of the form Sigma(n)(k=1) x(pk) f(k)(x(qk)) = 0, where p(k) and q(k) (k = 1,..., n) are given nonnegative integers and the unknown functions are supposed to be additive on the ring R. It is illustrated by some explicit examples too. As another application of the multivariate setting we use spectral analysis and spectral synthesis in the space of the additive solutions to prove that it is spanned by differential operators. The results are uniformly based on the investigation of the multivariate version of the functional equations.

关键词： linear function derivation multiadditive function spectral analysis and synthesis

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Modelling and the representational imagination

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ZDM-MATHEMATICS EDUCATION 2018年第1-2期50卷 45-59页

作者： Brady, Corey Vanderbilt Univ 221 Kirkland Hall Nashville TN 37235 USA

This article examines the work of 30 in-service teachers engaged with modelling activities during a course within an Ecuadorian master's degree program in mathematics teaching. These teachers experienced a sequence of activities designed to explore imaginative aspects of mathematical modelling and problem solving, inviting perspectives from life outside of school. They built rich connections between real-world phenomena and a range of ideas about functions and representations of them. An analysis of the teachers' work identifies a modelling resource-the representational imagination-describing its nature and the implications for models of classroom modelling aiming to support this resource.

关键词： Modelling cycle Perception linear function Representational imagination

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Building Detail-Sensitive Semantic Segmentation Networks with Polynomial Pooling

Building Detail-Sensitive Semantic Segmentation Networks wit...

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IEEE/CVF Conference on Computer Vision and Pattern Recognition

作者： Zhen Wei Jingyi Zhang Li Liu Fan Zhu Fumin Shen Yi Zhou Si Liu Yao Sun Ling Shao Institute of Information Engineering Chinese Academy of Sciences Center for Future Media and School of Computer Science and Engineering University of Electronic Science and Technology of China Inception Institute of Artificial Intelligence Beijing Key Laboratory of Digital Media School of Computer Science and Engineering Beihang University

ISBN: (纸本)9781728132945

Semantic segmentation is an important computer vision task, which aims to allocate a semantic label to each pixel in an image. When training a segmentation model, it is common to fine-tune a classification network pre-trained on a large-scale dataset. However, as an intrinsic property of the classification model, invariance to spatial perturbation resulting from the lose of detail-sensitivity prevents segmentation networks from achieving high performance. The use of standard poolings is one of the key factors for this invariance. The most common standard poolings are max and average pooling. Max pooling can increase both the invariance to spatial perturbations and the non-linearity of the networks. Average pooling, on the other hand, is sensitive to spatial perturbations, but is a linear function. For semantic segmentation, we prefer both the preservation of detailed cues within a local feature region and non-linearity that increases a network's functional complexity. In this work, we propose a polynomial pooling (P-pooling) function that finds an intermediate form between max and average pooling to provide an optimally balanced and self-adjusted pooling strategy for semantic segmentation. The P-pooling is differentiable andcan be applied into a variety of pre-trained networks. Extensive studies on the PASCAL VOC, Cityscapes and ADE20k datasets demonstrate the superiority of P-pooling over other poolings. Experiments on various network architectures and state-of-the-art training strategies also show that models with P-pooling layers consistently outperform those directly.

关键词： pooling NETWORK STRUCTURE nonlinearity Semantics images invariance local image feature computer vision linear function

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Approximation of Neural Networks for Verification

Approximation of Neural Networks for Verification

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MBMV 2019;22nd Workshop - Methods and Description Languages for Modelling and Verification of Circuits and Systems

作者： Fin Hendrik Bahnsen Goerschwin Fey Institute of Embedded Systems Hamburg University of Technology

ISBN: (纸本)9783800749454

Statistical learning methods enable the adaptation of artificial neural networks (ANN) to complex problems. Meanwhile, formal properties can be verified on small ANNs under simplified assumptions. First we show a simple algorithm to convert neural networks into a system of equations with boundary conditions. In particular, we discuss how non-linear functions may be approximated. In experiments we study the impact of this approximation on the validity on the proof of formal guarantees.

关键词： Neural network approximation Artificial neural networks Verification System of equations Proof Learning methods Statistical learning linear function

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On Models Of Economic Development, Taking Into Account Lending

On Models Of Economic Development, Taking Into Account Lendi...

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International Asian School-Seminar Optimization Problems of Complex Systems

作者： Sergey M. Antsyz Sobolev Institute of Mathematics Novosibirsk State University

ISBN: (纸本)9781728129877

A new approach to the construction of mathematical models of complex socio-economic systems is described. The period of economic growth consisting of intervals equal in duration is considered. It is assumed that per capita consumption at each interval is limited from below. The choice of restrictions, providing growth of welfare of individuals, is supported by the process of taking and repayment loans. In contrast to the classical Ramsey-Solow model, it is proposed to minimize the total income for the period. The neoclassical function of economic growth is approximated at each interval by a linear function. It is shown that the development of the economy strategy, obtained with the help of a new approach, allows reducing damage to the environment.

关键词： Economic growth Investment Consumption Wealth growth Lending Pollution environmental Economic Growth Investments degradation of the environment Consumer Behavior Tuberculosis Economic Development linear function

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