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Best Possible Bounds for Yang Mean Using Generalized logarithmic Mean

MATHEMATICAL PROBLEMS IN ENGINEERING 2016年第1期2016卷 1-7页

作者： Qian, Wei-Mao Chu, Yu-Ming Huzhou Broadcast & TV Univ Sch Distance Educ Huzhou 313000 Peoples R China Huzhou Teachers Coll Dept Math Huzhou 313000 Peoples R China

We prove that the double inequality L-p (a, b) 0 with a not equal b if and only if p = 2 and find several sharp inequalities involving the trigonometric, hyperbolic, and inverse trigonometric functions, where p(0) = ... 详细信息

We prove that the double inequality L-p (a, b) < U (a, b) < L-q (a,b) holds for all a, b > 0 with a not equal b if and only if p <= p(0) and q >= 2 and find several sharp inequalities involving the trigonometric, hyperbolic, and inverse trigonometric functions, where p(0) = 0.5451... is the unique solution of the equation (p + 1)(1/p) = root 2 pi/2 on the trival (0, infinity), U(a, b) = (a - b)/[root 2 arctan ((a-b)/root 2ab)], and L-p (a, b) = [a(p+1) - b(p+1))/((p+1)(a-b))](1/p) (p not equal -1, 0), L-1(a, b) = (a - b)/(log a - log b) and L-0(a, b) = (a(a)/b(b))(1/(a-b))/e are the Yang, and pth generalized logarithmic means of a and b, respectively.

关键词： BOUNDS (Mathematics) ARITHMETIC mean logarithmic functions EQUIVALENCE (Mathematics) HYPERBOLIC functions TRIGONOMETRIC functions

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TESTING FOR NUMERICAL COMPUTATIONS

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IEE PROCEEDINGS-E COMPUTERS AND DIGITAL TECHNIQUES 1980年第2期127卷 69-76页

作者： KARPOVSKY, M Computer Science Department School of Advanced Technology State University of New York at Binghamton Binghamton USA

We consider the problem of error detection in programs or specialised devices computing real functions f(x), where the argument x is represented in binary form. For error detection we use the linear check inequalities |∑τεTf(x⊕ τ) −C| ≤ ε, where ε ≥ 0 is some given small constant, ⊕denotes componentwise addition mod 2 of binary vectors, T is some set of binary vectors and C is a constant. A method for the construction of a minimal check set T and constant C for the given f(x) and ɛ is proposed. This method is based on the techniques of Walsh transforms and least-absolute-error polynomial approximation. Several important examples of optimal checks for programs computing exponential, logarithmic and trigonometric functions will be given.

关键词： numerical computations Diagnostic, testing, debugging and evaluating systems polynomial approximation program testing real functions exponential functions Walsh transforms check inequalities programs trigonometric functions minimal check set error detection logarithmic functions

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Exact solution of free vibration of a uniform tensioned beam combined with both lateral and rotational linear sub-systems

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JOURNAL OF SOUND AND VIBRATION 2015年 341卷 206-221页

作者： Chen, Y. McFarland, D. M. Spencer, B. F., Jr. Bergman, L. A. Zhejiang Univ Dept Civil Engn Hangzhou 310027 Zhejiang Peoples R China Univ Illinois Dept Aerosp Engn Urbana IL 61801 USA Univ Illinois Dept Civil & Environm Engn Urbana IL 61801 USA

A general exact solution of free vibration of a uniform tensioned beam with any number of both lateral and rotational sub-systems is addressed. This study is completed in complex domain, because of the presence of the non-proportional damping caused by the dampers utilized in sub-systems, The sub-systems constructed herein could degenerate to the conventional supports and sub-systems, and be arbitrarily placed. Accordingly, the solution is also suitable for multi-span beams. The argument principle method (APM), which does not need initial values and iteration, is employed to solve the characteristic equation in complex domain. Nevertheless, the presence of multi-valued square root functions due to the axial loading renders the function non-analytic in complex domain. A variable substitution method, in which the main branch of logarithmic function is chosen, is proposed to solve this problem. The results obtained are compared with those in literature. Furthermore, several typical case studies were completed, and the root loci of the frequency parameters attained are compared with those obtained by the finite element method (FEM). A good agreement is observed, which confirms the validity of the presented methodologies in this paper. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： FREE vibration COMBINATIONS (Mathematics) LINEAR systems COMPLEXES (Mathematics) logarithmic functions

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Prediction of Infinite-Dilution Activity Coefficients Using UNIFAC and COSMO-SAC Variants

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INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 2010年第16期49卷 7488-7496页

作者： Gerber, Renan P. Soares, Rafael de P. Univ Fed Rio Grande do Sul Escola Engn Dept Engn Quim BR-90040040 Porto Alegre RS Brazil

Infinite-dilution activity coefficients (IDAC) can be used to predict, for example, the behavior of liquid-liquid equilibrium or to determine parameters for excess Gibbs free energy expressions like NRTL, Wilson, or UNIQUAC. For systems where limited (or no) experimental data are available, predictive tools as the well-known UNIFAC variations can be very helpful. An alternative approach is to use methods based on conductor-like screening model (COSMO). In this work, we have tested a modified UNIFAC model with a recent parameter set and three variations of the COSMO-SAC model. To compare the models, a database with a total of 748 IDAC experimental points was assembled with data from the literature and is available as Supporting Information. For nonaqueous solutions, the IDAC logarithm absolute average deviation for UNIFAC was 0.28, while it was 0.48 for a COSMO-SAC with parameters adjusted in this work. On the other hand, for aqueous systems, a COSMO-SAC with optimized parameters led to a deviation of 0.81 against 1.47 for the UNIFAC model tested.

关键词： INFINITY (Mathematics) DILUTION LIQUID-liquid equilibrium GIBBS' free energy logarithmic functions MATHEMATICAL models EMPIRICAL research

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Parity detection achieves the Heisenberg limit in interferometry with coherent mixed with squeezed vacuum light

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NEW JOURNAL OF PHYSICS 2011年第8期13卷 1-13页

作者： Seshadreesan, Kaushik P. Anisimov, Petr M. Lee, Hwang Dowling, Jonathan P. Louisiana State Univ Hearne Inst Theoret Phys Baton Rouge LA 70803 USA Louisiana State Univ Dept Phys & Astron Baton Rouge LA 70803 USA

The interference between coherent and squeezed vacuum light effectively produces path entangled N00N states with very high fidelities. We show that the phase sensitivity of the above interferometric scheme with parity detection saturates the quantum Cramer-Rao bound, which reaches the Heisenberg limit when the coherent and squeezed vacuum light are mixed in roughly equal proportions. For the same interferometric scheme, we draw a detailed comparison between parity detection and a symmetric-logarithmic-derivative-based detection scheme suggested by Ono and Hofmann.

关键词： PARITY (Physics) HEISENBERG model QUANTUM theory INTERFEROMETRY logarithmic functions

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Decomposition of China's Carbon Emissions Intensity from 1995 to 2010: An Extended Kaya Identity

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MATHEMATICAL PROBLEMS IN ENGINEERING 2013年第1期2013卷 1-7页

作者： Li, Wei Ou, Qing-Xiang North China Elect Power Univ Dept Econ Management Baoding 071003 Peoples R China

This paper employs an extended Kaya identity as the scheme and utilizes the logarithmic Mean Divisia Index (LMDI II) as the decomposition technique based on analyzing CO2 emissions trends in China. Change in CO2 emissions intensity is decomposed from 1995 to 2010 and includes measures of the effect of Industrial structure, energy intensity, energy structure, and carbon emission factors. Results illustrate that changes in energy intensity act to decrease carbon emissions intensity significantly and changes in industrial structure and energy structure do not act to reduce carbon emissions intensity effectively. Policy will need to significantly optimize energy structure and adjust industrial structure if China's emission reduction targets in 2020 are to be reached. This requires a change in China's economic development path and energy consumption path for optimal outcomes.

关键词： CARBON & the environment BIODEGRADATION of carbon compounds logarithmic functions EMISSIONS (Air pollution) ENERGY intensity (Economics) ECONOMIC development ENERGY consumption CHINA

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Increasing perfluoroalkyl contaminants in east Greenland polar bears (Ursus maritimus):: A new toxic threat to the Arctic bears

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ENVIRONMENTAL SCIENCE & TECHNOLOGY 2008年第7期42卷 2701-2707页

作者： Dietz, R. Bossi, R. Riget, F. F. Sonne, C. Born, E. W. Univ Aarhus Natl Environm Res Inst Dept Arctic Environm DK-4000 Roskilde Denmark Univ Aarhus Natl Environm Res Inst Dept Atmospher Environm DK-4000 Roskilde Denmark Greenland Inst Nat Resources DK-3900 Nuuk Greenland

A well-defined subsample of 128 subadult (3-5 years) polar bears (Ursus maritimus) from 19 sampling years within the period 1984-2006 was investigated for perfluoroalkyl contaminants (PFCs), Linear regression analysis of logarithmic-transformed median concentrations showed significant annual increases for PFOS (4.7%), PFNA (6.1%), PFUnA (5.9%), PFDA (4.3%), PFTrA (8.5%), PFOA (2.3%), and PFDoA (5.2%). For four of the PFCs, a LOESS smoother model provided significantly better descriptions, revealing steeper linear annual increases for PFOSA of 9.2% after 1990 and between 18.6 and 27.4% for PFOS, PFDA, and PFTrA after 2000. Concentrations of Sigma PFCs, by 2006, exceeded the concentrations of all conventional OHCs (organohalogen compounds), of which several have been documented to correlate with a number of negative health effects. If the PFC concentrations in polar bears continue to increase with the steepest observed trends, then the lowest no-adverse-effect level (NOAEL) and lowest-adverse-effect level (LOAEL) detected for rats and monkeys will be exceeded in 2014-2024. In addition, the rapidly increasing concentrations of PFCs are likely to cause cumulative and combined effects on the polar bear, compounding the already detected threats from OHCs.

关键词： Regression analysis Pollution Polar bear Organic compounds Organohalogen compounds logarithmic functions Perfluorocarbons Log-linear models

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Why W?

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AMERICAN SCIENTIST 2005年第2期93卷 104-108页

作者： Hayes, B 211 Dacian Ave Durham NC 27701 USA

No, not that W. I won't be drawn into presidential politics here. The W Iwant to discuss is something else entirely: the Lambert W function, a mathematical contrivance thathas been getting a fair amount of attention lately. The buzz began in the world of computer-algebrasystems such as Macsyma, Maple and Mathematica, but word of W has also been spreading throughjournal articles, preprints, conference presentations and Internet news groups. The W function evenhas its own poster (see http://***/LambertW). The concept at the root of W can be tracedback through more than two centuries of the mathematical literature, but the function itself hashad a name only for the past 10 years or so. (A few years longer if you count a name used within theMaple software but otherwise unpublished.) When it comes to mathematical objects, it turns out thatnames are more important than you might guess.

关键词： MATHEMATICAL formulas INVERSE functions logarithmic functions EXPONENTIAL functions MATHEMATICAL analysis

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Comment on "Annular inhomogeneities with eigenstrain and interphase modeling" [2014, J. Mech. Phys. Solids 64, 468-482]

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2014年 73卷 1-2页

作者： Shodja, H. M. Khorshidi, A. Sharif Univ Technol Dept Civil Engn Tehran Iran Sharif Univ Technol Inst Nanosci & Nanotechnol Tehran Iran Brown Univ Sch Engn Providence RI 02912 USA

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Evaluation of the olefinic proton signals in the H-1-NMR spectra of allylic hydroxy groups in long-chain compounds

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CHEMISTRY AND PHYSICS OF LIPIDS 1996年第1期82卷 33-37页

作者： Knothe, G Bagby, MO Weisleder, D [a] Oil Chemical Research USDA/ARS/NCAUR 1815 N. University St. Peoria IL 61604 USA [b] Analytical Chemistry Support USDA/NCAUR Peoria IL 61604 USA

The positional isomers of monounsaturated long-chain fatty compounds containing allylic hydroxy groups (shown for trans double bonds) are distinguished by H-1-NMR spectroscopy through the chemical shift differences of the olefinic protons. These differences are expressed as rational functions (the differences being proportional to the negative third power of the position of the unsaturation), or logarithmic functions (the differences being proportional to the position of the unsaturation raised as power). The present results on more sensitive H-1-NMR spectra complement previous work on the C-13-NMR spectra of these compounds. Theoretical models for explaining shifts in C-13-NMR therefore also apply to H-1-NMR.

关键词： H-1-NMR spectroscopy rational functions logarithmic functions allylic hydroxy groups fatty acids fatty esters

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