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Exploring plane-symmetric solutions in f(R) gravity

JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS 2016年第2期122卷 331-337页

作者： Shamir, M. F. Natl Univ Comp & Emerging Sci Dept Sci & Humanities Lahore Campus Islamabad Pakistan

The modified theories of gravity, especially the f(R) gravity, have attracted much attention in the last decade. This paper is devoted to exploring plane-symmetric solutions in the context of metric f(R) gravity. We extend the work on static plane-symmetric vacuum solutions in f(R) gravity already available in the literature [1, 2]. The modified field equations are solved using the assumptions of both constant and nonconstant scalar curvature. Some well-known solutions are recovered with power-law and logarithmic forms of f(R) models.

关键词： SYMMETRIC functions GRAVITY VACUUM SCALAR field theory PHYSICAL constants logarithmic functions

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A new formula for normal tissue complication probability (NTCP) as a function of equivalent uniform dose (EUD)

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PHYSICS IN MEDICINE AND BIOLOGY 2008年第1期53卷 23-36页

作者： Luxton, Gary Keall, Paul J. King, Christopher R. Stanford Univ Dept Radiat Oncol Sch Med Stanford CA 94305 USA

To facilitate the use of biological outcome modeling for treatment planning, an exponential function is introduced as a simpler equivalent to the Lyman formula for calculating normal tissue complication probability (NTCP). The single parameter of the exponential function is chosen to reproduce the Lyman calculation to within similar to 0.3%, and thus enable easy conversion of data contained in empirical fits of Lyman parameters for organs at risk (OARs). Organ parameters for the new formula are given in terms of Lyman model m and TD50, and conversely m and TD50 are expressed in terms of the parameters of the new equation. The role of the Lyman volume-effect parameter n is unchanged from its role in the Lyman model. For a non-homogeneously irradiated OAR, an equation relates d(ref), n, v(eff) and the Niemierko equivalent uniform dose (EUD), where d(ref) and v(eff) are the reference dose and effective fractional volume of the Kutcher-Burman reduction algorithm (i.e. the LKB model). It follows in the LKB model that uniform EUD irradiation of an OAR results in the same NTCP as the original non-homogeneous distribution. The NTCP equation is therefore represented as a function of EUD. The inverse equation expresses EUD as a function of NTCP and is used to generate a table of EUD versus normal tissue complication probability for the Emami-Burman parameter fits as well as for OAR parameter sets from more recent data.

关键词： EXPONENTIAL functions logarithmic functions LOGARITHMS ALGEBRA

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Two-dimensional radiative transfer due to curved Dirac delta line sources

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WAVES IN RANDOM AND COMPLEX MEDIA 2013年第4期23卷 461-474页

作者： Liemert, Andre Kienle, Alwin Inst Lasertechnol Med & Messtech Ulm Germany

In this article, the two-dimensional radiative transport equation is considered for the curved Dirac delta line source. In order to account this source type, Green's function of the radiative transport equation for the half-plane is derived in parts of the ballistic and diffuse contribution as well as under consideration of the Fresnel reflection at the boundary. The final results are verified with the Monte Carlo method for different collimated beams and several curved sources such as the elliptic and logarithmic spiral line source.

关键词： RADIATIVE transfer TRANSPORT theory (Mathematics) MONTE Carlo method FRESNEL function logarithmic functions

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A novel technique of semi-aerobic aged refuse biofilter for leachate treatment

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WASTE MANAGEMENT 2011年第8期31卷 1827-1832页

作者： Han, Zhi-Yong Liu, Dan Li, Qi-Bin Li, Gui-Zhi Yin, Zhao-Yang Chen, Xin Chen, Jian-Nan SW Jiaotong Univ Fac Geosci & Environm Engn Chengdu 610031 Peoples R China

We developed a semi-aerobic aged refuse biofilter (SAARB) for leachate treatment and examined its advantages and disadvantages compared to previous aged refuse biofilters (ARBs). To assess its treatment capability, decontamination mechanisms and optimal performance parameters, a single-period experiment and L-9(3(4)) orthogonal array design experiments were conducted on artificial leachate. The SAARB markedly enhanced the treatment capability and removal efficiency of organic matter and nitrogen pollutants due to the alternating aerobic-anoxic-anaerobic zones in situ. The reduction in chemical oxygen demand (COD), ammonia nitrogen (NH4+-N) and total nitrogen (TN) exceeded 98%, 94%, and 80%, respectively. After the leachate was distributed onto the SAARB surface, the effluent velocity decreased as a logarithmic function, and there was a concomitant reduction in leachate effluent volume. Based on the capacity for removal of COD. NH4+-N, and TN, the effective height of aged refuse in a SAARB was enough to be 900 mm. An excellent treatment efficiency could be achieved at 20-35 degrees C, with a leachate distribution time of 1 h once every period of 2-3 days, hydraulic loading of 11-30 L/(m(3) day), and COD loading of 550-1200 g/(m(3) day). This new SAARB system demonstrates superior efficacy for biofilter compared to other ARB systems, especially for nitrogen removal from leachate. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： WASTE management BIOFILTRATION LEACHATE FILTERS & filtration ORGANIC compounds CHEMICAL oxygen demand POLLUTANTS logarithmic functions DENITRIFICATION

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logarithmic KLEIN-GORDON EQUATION

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ACTA PHYSICA POLONICA B 2009年第1期40卷 59-66页

作者： Gorka, Przemyslaw Warsaw Univ Technol Dept Math & Informat Sci PL-00661 Warsaw Poland

We study weak solutions to the Klein-Gordon equation with the logarithmic nonlinearity on interval. Such kinds of nonlinearities appear in inflation cosmology and in supersymmetric field theories. Moreover, this framework is applied in nuclear physics, optics, and geophysics. We obtained the existence of weak solutions. For this purpose the Galerkin method, logarithmic Sobolev inequality and compactness theorem are applied.

关键词： logarithmic functions NONLINEAR theories INFLATIONARY universe NUCLEAR physics OPTICS GEOPHYSICS GALERKIN methods

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On stochastic optimality for a linear controller with attenuating disturbances

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AUTOMATION AND REMOTE CONTROL 2013年第4期74卷 628-641页

作者： Belkina, T. A. Palamarchuk, E. S. Russian Acad Sci Cent Econ & Math Inst Moscow Russia

For a linear stochastic control system with quadratic objective functional, we introduce various generalizations of the notions of optimality on average and stochastic optimality on an infinite time interval that take into account possible degeneration of the parameter of the disturbing process with time (attenuation of the disturbances) or the presence of a discount function in the objective functional. This lets us improve upon the quality estimate for a well known optimal control in this problem from the point of view of both asymptotic behavior of the functional's expectation and its asymptotic probabilistic properties. In particular, in the considered case we have found an improvement for the well known logarithmic upper bound on the optimal control for a family of defect processes.

关键词： STOCHASTIC control theory LINEAR control systems OPTIMAL control theory logarithmic functions ASYMPTOTES

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An analysis method for the vibration signal with amplitude modulation in a bearing system

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JOURNAL OF SOUND AND VIBRATION 2007年第3-5期303卷 538-552页

作者： Sheen, Yuh-Tay So Taiwan Univ Technol Dept Mech Engn Yung Kang 710 Taiwan

In this paper, an envelope detection method for the vibration signal with amplitude modulation is proposed. The method is to filter the vibration signal through a designated band-pass filter. According to the resonance of the vibration signal in the passband, the filtered signal would be decomposed into a sinusoidal function basis at the resonant frequency. Under the assumption of a stepwise function for the envelope signal, the envelope signal could be derived by the linear least-squares analysis. In addition, the filtered signal could be easily reconstructed from the envelope signal. Furthermore, the logarithmic transformation is applied in this envelope signal, the defect frequencies due to bearing defects could be more enhanced by suppressing the corresponding sidebands. However, the logarithmic transformation would have little effect in the spectrum for a normal bearing. Accordingly, logarithmic transformation would be helpful to apply the signal processing method in enhancing the defect frequencies for the bearing defect diagnosis. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： MECHANICAL vibration research AMPLITUDE modulation AMPLITUDE modulation detectors RADIO filters LEAST squares logarithmic functions

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Stability and error analysis of the LED-logarithmic electrometer

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INTERNATIONAL JOURNAL OF ELECTRONICS 1999年第8期86卷 999-1011页

作者： Acharya, YB Vyavahare, PD Phys Res Lab Ahmedabad 380009 Gujarat India Shri GS Inst Technol & Sci Indore 452003 India

Theoretical analysis of the stability and error in the LED-logarithmic electrometer is presented. It has been shown that a resistance in series with the log element improves the response by a factor of 7 at 1 pA. Error analysis of the electrometer, involving mainly device parameter sensitivity, is also presented. It has been found that variation in temperature and change in value of the device constant are more important factors than other device parameters in influencing the variation in the output voltage. An eight-decade temperature compensated LED-logarithmic electrometer is designed for the measurement of low currents from 1 pA to 0.1 mA and has been tested for its performance in the temperature range of -20 to 70 degrees C.

关键词： ELECTROMETERS LIGHT emitting diodes ELECTRIC currents logarithmic functions

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Saint-Venant torsion of a circular bar with a bridged radial crack incorporating surface elasticity

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ACTA MECHANICA 2017年第2期228卷 651-672页

作者： Yang, Moxuan Wang, Xu East China Univ Sci & Technol Sch Mech & Power Engn 130 Meilong Rd Shanghai 200237 Peoples R China

We examine the contribution of crack bridging and surface elasticity to the Saint-Venant torsion problem of a circular cylinder containing a radial crack. The surface effect on the crack faces is incorporated by using the continuum-based surface/interface model of Gurtin and Murdoch. The bridging force is assumed proportional to the crack opening displacement, while the bridging stiffness is allowed to vary arbitrarily along the crack. Both an internal crack and an edge crack are studied. By using the Green's function method, the boundary value problem is reduced to a first-order Cauchy singular integro-differential equation. After the utilization of the Gauss-Chebyshev integration formula and the expansion of both the unknown dislocation density and the known variable bridging stiffness into Chebyshev polynomials, the singular integro-differential equation is solved numerically by using the collocation method. The stresses exhibit a weak logarithmic singularity rather than a strong square root singularity at the crack tips due to the surface effect. The strengths of the logarithmic singularity at the crack tips, the reduction in torsional rigidity and the jump in warping function across the crack faces are calculated. Our results also show that both surface elasticity and crack bridging will stiffen the cracked cylinder and that the stiffening effect of crack bridging is remarkable in the case when the crack is very long or is extremely close to the lateral surface of the cylinder.

关键词： TORSION ELASTICITY SHALLOW-water equations CHEBYSHEV polynomials logarithmic functions

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Global warming projections derived from an observation-based minimal model

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EARTH SYSTEM DYNAMICS 2016年第1期7卷 51-70页

作者： Rypdal, K. UiT Arctic Univ Norway Dept Math & Stat Tromso Norway

A simple conceptual model for the global mean surface temperature (GMST) response to CO2 emissions is presented and analysed. It consists of linear long-memory models for the GMST anomaly response Delta T to radiative forcing and the atmospheric CO2-concentration response Delta C to emission rate. The responses are connected by the standard logarithmic relation between CO2 concentration and its radiative forcing. The model depends on two sensitivity parameters, alpha(T) and alpha(C), and two "inertia parameters," the memory exponents beta(T) and beta(C). Based on observation data, and constrained by results from the Climate Model Intercomparison Project Phase 5 (CMIP5), the likely values and range of these parameters are estimated, and projections of future warming for the parameters in this range are computed for various idealised, but instructive, emission scenarios. It is concluded that delays in the initiation of an effective global emission reduction regime is the single most important factor that influences the magnitude of global warming over the next 2 centuries. The most important aspect of this study is the simplicity and transparency of the conceptual model, which makes it a useful tool for communicating the issue to non-climatologists, students, policy makers, and the general public.

关键词： CONCEPTUAL models SURFACE temperature GLOBAL warming RADIATIVE forcing logarithmic functions ATMOSPHERIC models

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