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[Image: see text] Accurately determining the acid dissociation constants (K(a) or their logarithmic form, pK(a)) of small molecules and large biomolecules has proven to be pivotal for the study different biological processes and developing new drugs. This Viewpoint summarizes some of the most common methodologies and recent advances described for pK(a) prediction using computational techniques when experimental values are not easily accessible such as in proteins and/or for the screening of large libraries of new compounds.

This paper contributes to the environmental literature by (i) demonstrating that the estimated coefficients and the statistical significance of the non-leading terms in quadratic, cubic, and quartic logarithmic environmental Kuznets curve (EKC) specifications are arbitrary and should therefore not be used to choose the preferred specification and (ii) detailing a proposed general-to-specific type methodology for choosing the appropriate specifications when attempting to estimate higher-order polynomials such as cubic and quartic logarithmic EKC relationships. Testing for the existence and shape of the well-known EKC phenomenon is a hot topic in the environmental economics literature. The conventional approach widely employs quadratic and cubic specifications and more recently also the quartic specification, where the variables are in logarithmic form. However, it is important that researchers understand whether the estimated EKC coefficients, turning points, and elasticities are statistically acceptable, economically interpretable, and comparable. In addition, it is vital that researchers have a clear structured non-arbitrary methodology for determining the preferred specification and hence shape of the estimated EKC. We therefore show mathematically and empirically the arbitrary nature of estimated non-leading coefficients in quadratic, cubic, and quartic logarithmic EKC specifications, being dependent upon the units of measurement chosen for the independent variables (e.g. dependent upon a rescaling of the variables such as moving from $m to $bn). Consequently, the practice followed in many previously papers, whereby the estimates of the non-leading terms are used in the decision to choose the preferred specification of an estimated EKC relationship, is incorrect and should not be followed since it potentially could lead to misleading conclusions. Instead, it should be based upon the sign and statistical significance of the estimated coefficients of the leading terms, the location of turning point(s), and the sign and statistical significance of the estimated elasticities. Furthermore, we suggest that researchers should follow a proposed general-to-specific type methodology for choosing the appropriate order of polynomials when attempting to estimate higher-order polynomial logarithmic EKCs. Supplementary Information The online version contains supplementary material available at 10.1007/s11356-021-13463-y.

As we know, the inflation models have been considered by researchers in various fields of physics such as cosmology and particle physics for explaining early Universe. According to different conditions and conjectures, there are several types of inflation models. In this article, we want to examine a new condition for the inflation models which is known as the swampland criterion. Therefore, we consider f(R) model that includes a polynomial plus a logarithmic term as $$R+\alpha R^{2}+\beta R^{n}+\gamma R^{2}\log \gamma R$$ . So, by considering the corresponding modified f(R) gravity on the brane, we obtain the modified cosmological parameters such as spectral index, tensor-to-scalar ratio and a number of e-folds. These modified parameters give us the opportunity to test the compatibility of f(R) gravity model with swampland criteria. Finally, by using some figures as well as observable data, we specify the range of modified cosmological parameters.

Focusing on the weight function ω (x,t)=xαe-{1}{3}x{3}+tx, x∈[0,∞), α >-1, t>0, we state its asymptotic orthogonal polynomials. Through Toda evolution, differential equations of αn(t) and βn(t) have been worked. Consequently, we also talk about the approximate value of αn(t). Basing on the asymptotic value of αn(t), the asymptotic of second order differential equation of Pn(z) and expansion of the logarithmic form of Hankel determinant are confirmed.

A collaboration network model with improved triad formation (ITF) step is proposed and denominated as one-mode collaboration network with tunable clustering. We systematically study its structural features and find this network model can much more accurately reflect cooperative relationship in real society. We acquire expression of nodes degree distribution P(k) that possesses a power-law form with exponent γ whose range is (1,3]. Expression of clustering coefficient C(k) for nodes with degree k is also obtained and composes of a power-law section and a constant section. We verify clustering coefficient of individual nodes increases monotonically with the increase of parameter p that is the probability of ITF step occurring. When specific forms of P(k) and C(k) are given, the model’s average clustering coefficient C can be derived approximately. Finally, we analytically testify average path length L(N) increases with network size N in accordance with logarithmic form. When N is fixed, average path length of entire network decreases with the increase of p. All theoretically predicted results are consistent with simulative experimental results.

Element and mineral associations are fundamental parameters for palaeoceanographical reconstructions but laboratory methodologies are expensive, time-consuming and need a lot of material. Here, we investigate the quality and reliability of XRF measurements of major elements (Fe, Ti and Ca) using BTX II Benchtop, by comparing them with previous ICP-OES elemental analysis for a set of Late Pleistocene marine sediments from Campos Basin. Although the numerical values of the logarithmic form of the elementary ratios were different, the lnTi/Ca and lnFe/Ca ratios measured by both techniques (XRF and ICP-OES) presented similar downcore results. To correct the XRF intensity data, a linear regression model was calculated and, based on the linear equation generated, the logarithmic values of the elementary XRF ratios were corrected. After the correction, One-Sample t-test and Bland–Altman plot show that both techniques obtained similar results. In addition, a brief paleoceanographic interpretation, during the MIS 5 and MIS 4 periods, was conducted by comparing mineralogical and elementary analysis aiming to reconstruct the variations of the terrigenous input to the studied area. As a conclusion, the results from XRF measurements (BTX II) presented to confirm the viability of such a technique, showing that analysis using BTX II is a reliable, cheap, rapid and non-destructive option for obtaining elementary ratios and mineralogical downcore results at high resolution, allowing stratigraphic and paleoceanographic interpretations.

Models for postseismic transient displacements can be formulated using logarithmic and exponential decay formulas with single or multiple timescales. The logarithmic form is associated with rate and state friction theory and afterslip, while the exponential form is associated with bulk viscoelastic relaxation of coseismic stresses. It is now quite widely understood that one can model GPS/GNSS time series manifesting postseismic transient displacements almost equally well using trajectory models constructed using logarithmic or exponential transients. This is consistent with the consensus established by the late 1970s that it is difficult to use geodetic observations to distinguish between deep aseismic afterslip and more diffuse viscoelastic relaxation as the primary mechanism of postseismic deformation. In this paper, we assess the relative explanatory value of both logarithmic and exponential forms by focusing on GNSS time series measured with better than typical signal-to-noise ratios. We find that the double logarithmic transient typically provides much better fits than double exponential transient, when both models are given equal degrees of freedom. We also discuss the relative utility of the hybrid transient formulas in which the logarithmic component is assigned shorter decay timescale parameters than the exponential component. These models fit observed postseismic displacements almost as well as double logarithmic transients.

In this paper, a piecewise-defined function is proposed to estimate traffic noise in urban areas. The proposed approach allows the use of the model even in the case of very low or zero flows for which the classical logarithmic form is not suitable. A model based on the proposed approach is calibrated for a real case and compared with the results obtained with a model based only on the logarithmic form. The results obtained show how the proposed piecewise-defined function, linear for low traffic flows and logarithmic for medium-high volumes, is able to better represent real noise pollution levels in all conditions. The proposed approach is particularly useful when comparing two plan scenarios from the point of view of noise effects.

Anisotropic interparticle correlations in the simple cubic lattice of single-domain ferroparticles (SCLF) are studied using both theory and computer simulation. The theory is based on the Helmholtz free energy expansion like classical virial series up to the second virial coefficient. The analytical formula for the Helmholtz free energy is incorporated in a logarithmic form to minimize the effects of series truncation. The new theoretical approach, including discrete summation over lattice nodes coordinates, is compared critically against the classical virial expansion of the Helmholtz free energy for the dipolar hard sphere fluid; the main differences between the Helmholtz free energy of SCLF and dipolar hard sphere fluid are discussed. The theoretical results for the Helmholtz free energy, the magnetization, and the initial magnetic susceptibility of the SCLF are compared against Molecular Dynamic simulation data. In all cases, theoretical predictions using logarithmic form of the Helmholtz free energy are seen to be superior, but they only have an applicability range of the effective dipolar coupling constant $\lambda_e < 1.5$. For highest values of $\lambda_e$, the structural transition of the magnetic dipoles in SCLF is observed in Molecular Dynamic simulation. It has been shown that for $\lambda_e \gtrsim 2$, an antiferromagnetic order appears in the system., Comment: 13 pages, 8 figures, published in Physica A

All the previous authors discussed the quadratic equation only with continuous kernels by different methods. In this paper, we introduce a mixed nonlinear quadratic integral equation (MQNLIE) with singular kernel in a logarithmic form and Carleman type. An existence and uniqueness of MQNLIE are discussed. A quadrature method is applied to obtain a system of nonlinear integral equation (NLIE), and then the Toeplitz matrix method (TMM) and Nystrom method are used to have a nonlinear algebraic system (NLAS). The Newton–Raphson method is applied to solve the obtained NLAS. Some numerical examples are considered, and its estimated errors are computed, in each method, by using Maple 18 software.

This paper is concerned with the Cauchy problem for the one-dimensional compressible Euler equations with critical time-dependent overdamping. In this critical case, the damped Euler system is proved to admit a unique global solution that converges time-asymptotically to the corresponding nonlinear diffusion wave. Particularly, the optimal convergence rate in logarithmic form is first derived by the technical time-weighted method.

Studies on allometric models are essential for quantifying the potential of a stand, especially when the objective is to know the wood stock through estimates. This study aimed to select height, volume and artificial form factor equations for a teak stand with data from a sample with 81 trees at 96 months in different diameter classes. The correlation analysis was performed between the variables total height, diameter with and without bark at 1.30 m soil height (dbhcc and dbhsc), total volume with and without bark (VTcc and VTsc) and artificial form factor with and without bark (ffcc and ffsc), using the Pearson coefficient. Six models were evaluated for each category: height, volume and artificial form factor, which were selected by the following criteria: analysis of variance, adjusted coefficient of determination, standard error of estimate, Akaike information criterion and graphical analysis of residues. The selected equations were validated by applying the L & O test. The variables dbhcc, dbhsc, HT, VTcc and VTsc presented significant correlations, ranging from moderate to very strong, the others presented weak correlation. The model that presented the best relation of total height to diameter was the model of Azevedo and contributors. For the total volume with and without bark, Schumacher and Hall model in its logarithmic form was the one that presented the best results. The adjusted models for artificial form factor did not present satisfactory results and, therefore, the use of average form factor is recommended. The mean form factor values by diameter class ranged from 0.4498 to 0.7139 and 0.4480 to 0.7075 for diameter with and without bark, respectively.

In this paper, we establish regularity conditions of weak solutions for the 3D incompressible viscous magnetohydrodynamics (MHD) equations, and show that weak solutions to this system are actually regular if the pressure or the gradient of velocity and magnetic fields satisfies some integrable conditions with the logarithmic form in the critical Besov space B ∞ , ∞ − 1 .

Based on the factorization in perturbative QCD, a jet cross sections in heavy-ion collisions can be expressed as a convolution of the jet cross section in $p+p$ collisions and a jet energy loss distribution. Using this simple expression and the Markov Chain Monte Carlo method, we carry out Bayesian analyses of experimental data on jet spectra to extract energy loss distributions for both single inclusive and $\gamma$-triggered jets in $Pb+Pb$ collisions with different centralities at two colliding energies at the Large Hadron Collider. The average jet energy loss has a dependence on the initial jet energy that is slightly stronger than a logarithmic form and decreases from central to peripheral collisions. The extracted jet energy loss distributions with a scaling behavior in $x=\Delta p_T /\langle \Delta p_T\rangle$ have a large width. These are consistent with the linear Boltzmann transport model simulations, in which the observed jet quenching is caused on the average by only a few out-of-cone scatterings., Comment: 5 pages in RevTex, 3 figures, final version to appear in Phys. Rev. Letters

The purpose of this paper is to study singular holomorphic foliations of arbitrary codimension defined by logarithmic forms on projective spaces., 45 pages

Many crystalline materials are known to exhibit creep at low temperatures (T

In this paper, we deal with the growth and the oscillation of solutions of the linear difference equation an (z) f (z + n) + an-1 (z) f (z + n - 1) + ··· + a1 (z) f (z + 1) + a0 (z) f (z) = 0; where an(z),···, a0(z) are meromorphic functions of finite logarithmic order such that an(z)a0(z) 6≢ 0.

The prediction of delayed deformations of concrete at very long term is particularly important for prestressed structures such as nuclear power plant containments. The basic creep, which corresponds to the deformation of the concrete under load, without exchange of water with the environment, is a major component of the delayed strains. The analysis of several experimental results indicates that this component can be expressed in a logarithmic form. However, Brooks very long term tests (more than 30 years) seem to indicate a deviation from this trend and an acceleration of creep after 3 years of testing. This could be due to a non-linear behavior but these deviations can also be explained by experimental artefacts. In the case of Brooks tests, because the sample were stored in renewed water, calcium leaching could explain the evolution of the behavior on the very long term. Assuming a simple model for leaching and that the leached part of the sample does not sustain stress, it is possible to estimate the evolution of the stress within the core of the sample. Using the creep model fitted on the first part of the tests (before 1000 days) and in the framework of the superposition principle, it is possible to show that leaching indeed could explain the very long term behavior.

The empirical Colebrook equation from 1939 is still accepted as an informal standard way to calculate the friction factor of turbulent flows (4000 8) through pipes with roughness between negligible relative roughness (ε/D ⟶ 0) to very rough (up to ε/D = 0.05). The Colebrook equation includes the flow friction factor λ in an implicit logarithmic form, λ being a function of the Reynolds number Re and the relative roughness of inner pipe surface ε/D: λ = f(λ, Re, ε/D). To evaluate the error introduced by the many available explicit approximations to the Colebrook equation, λ ≈ f(Re, ε/D), it is necessary to determinate the value of the friction factor λ from the Colebrook equation as accurately as possible. The most accurate way to achieve that is by using some kind of the iterative method. The most used iterative approach is the simple fixed-point method, which requires up to 10 iterations to achieve a good level of accuracy. The simple fixed-point method does not require derivatives of the Colebrook function, while the most of the other presented methods in this paper do require. The methods based on the accelerated Householder’s approach (3rd order, 2nd order: Halley’s and Schröder’s method, and 1st order: Newton–Raphson) require few iterations less, while the three-point iterative methods require only 1 to 3 iterations to achieve the same level of accuracy. The paper also discusses strategies for finding the derivatives of the Colebrook function in symbolic form, for avoiding the use of the derivatives (secant method), and for choosing an optimal starting point for the iterative procedure. The Householder approach to the Colebrook’ equations expressed through the Lambert W-function is also analyzed. Finally, it is presented one approximation to the Colebrook equation with an error of no more than 0.0617%.

International audience; The structural properties of model two-dimensional (2D) ionic liquids are examined, with a particular focus on the charge ordering process, with the use of computer simulation and integral equation theories. The influence of the logarithmic form of the Coulomb interaction, versus that of a 3D screened interaction form, is analysed. Charge order is found to hold and to be analogous for both interaction models, despite their very different form. The influence of charge ordering in the low density regime is discussed in relation to well known properties of 2D Coulomb fluids, such as the Kosterlitz-Thouless transition and criticality. The present study suggests the existence of a stable thermodynamic labile cluster phase, implying the existence of a liquid-liquid " transition " above the liquid-gas binodal. The liquid-gas and Kosterlitz-Thouless transitions would then take place inside the predicted cluster phase.

We consider a heteroclinic connection in a planar system, between two symmetric hyperbolic saddles of which the eigenvalues are resonant. Starting with a C-infinity normal form, defined globally near the connection, we normally linearize the vector field by using finitely smooth tags of logarithmic form. We furthermore define an asymptotic entry-exit relation, and we discuss on two examples how to deal with counting limit cycles near a limit periodic set involving such a connection. (C) 2017 Elsevier Inc. All rights reserved.

In this note we consider M-theory compactified on a warped Calabi-Yau fourfold including the eight-derivative terms in the eleven-dimensional action known in the literature. We dimensionally reduce this theory on geometries with one Kahler modulus and determine the resulting three-dimensional Kahler potential and complex coordinate. The logarithmic form of the corrections suggests that they might admit a physical interpretation in terms of one-loop corrections to the effective action. Including only the known terms the no-scale condition in three dimensions is broken, but we discuss caveats to this conclusion. In particular, we consider additional new eight-derivative terms in eleven dimensions and show that they are strongly constrained by compatibility with the Calabi-Yau threefold reduction. We examine their impact on the Calabi-Yau fourfold reduction and the restoration of the no-scale property., 24 pages

This article deals with the irreducible components of the space of codi- mension one foliations in a projective space defined by logarithmic forms of a certain degree. We study the geometry of the natural parametrization of the logarithmic com- ponents and we give a new proof of the stability of logarithmic foliations, obtaining also that these irreducible components are reduced. Fil: Cukierman, Fernando Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina Fil: Gargiulo Acea, Javier Nicolás. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina Fil: Massri, Cesar Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina

The concept of logarithmic order in the unit disc forms a bridge between meromorphic functions of unbounded Nevanlinna characteristic and meromorphic functions of (usual) zero order of growth. A collection of fundamental results for meromorphic functions of finite logarithmic order is given. Some of these results are reminiscent from the finite order case. Part I of this paper culminates in solving the inverse problem related to the famous defect relation in the case of finite logarithmic order. Part II deals with the analytic case.

The problem of guaranteed cost control for the networked control systems (NCSs) with time-varying delays, time-varying sampling intervals and signals quantization was investigated, wherein the physical plant was continuous-time one, and the control input was discrete-time one. By using an input delay approach and a sector bound method, the network induced delays, quantization parameter and sampling intervals were presented in one framework in the case of the state and the control input by quantized in a logarithmic form. A novel Lyapunov function with discontinuity, which took full advantages of the NCS characteristic information, was exploited. In addition, it was shown that Lyapunov function decreased at the jump instants. Furthermore, the Leibniz-Newton formula and free-weighting matrix methods were used to obtain the guaranteed cost controller design conditions which were dependent on the NCS characteristic information. A numerical example was used to illustrate the effectiveness of the proposed methods.

We describe mirror symmetry for weak Fano toric manifolds as an equivalence of filtered D \mathcal {D} -modules. We discuss in particular the logarithmic degeneration behavior at the large radius limit point and express the mirror correspondence as an isomorphism of Frobenius manifolds with logarithmic poles. The main tool is an identification of the Gauß-Manin system of the mirror Landau-Ginzburg model with a hypergeometric D \mathcal {D} -module, and a detailed study of a natural filtration defined on this differential system. We obtain a solution of the Birkhoff problem for lattices defined by this filtration and show the existence of a primitive form, which yields the construction of Frobenius structures with logarithmic poles associated to the mirror Laurent polynomial. As a final application, we show the existence of a pure polarized non-commutative Hodge structure on a Zariski open subset of the complexified Kähler moduli space of the variety.

A thermodynamic model for calculating the mass action concentrations of structural units in Fe-Al binary melts based on the atom-molecule coexistence theory, i.e., AMCT-N-i model, has been developed and verified through comparing with the reported activities of both Al and Fe in Fe-Al binary melts in a temperature from 1 573 K to 1 873 K by different researchers. The calculated mass action concentration N-Al of Al or N-Fe of Fe can be applied to ideally substitute the measured activity a(R, Al) of Al or a(R, Fe) of Fe relative to pure liquid AI(I) or Fe(I) as standard state in Fe-Al binary melts. The following equations were derived for the activity coefficient of Al in natural logarithmic form In gamma(Al) and the calculated activity coefficient of Fe in natural logarithmic form In gamma(Fe) in the temperature range from 1 573 K to 1 873 K. In gamma(Al)= -3.810+4.476x(Al) 0 < x(Al)

We define the compound logarithmic function on simple connected region. As an application of such function, we point out a slight mistake of Hayman in his proof for logarithmic derivative theorem (Lemma 2.3, Page 36), in his book Meromorphic Functions, published in 1964. We modify his proof.

The free vibration behaviors of functionally graded rings were investigated theoretically. The material graded in the thickness direction according to the power law rule and the rings were assumed to be in plane stress and plane strain states. Based on the first-order shear deformation theory and the kinetic relation of von Kárman type, the frequency equation for free vibration of functionally graded ring was derived. The derived results were verified by those in literatures which reveals that the present theory can be appropriate to predict the free vibration characteristics for quite thick rings with the radius-to-thickness ratio from 60 down to 2.09. Comparison between the plane stress case and the plane strain case indicates a slight difference. Meanwhile, the effects of the structural dimensional parameters and the material inhomogeneous parameter are examined. It is interesting that the value of the logarithmic form of vibration frequency is inversely proportional to the logarithmic form of the radius-to-thickness ratio or the mean radius.

In the probe limit, we investigate the nonlinear electrodynamical effects of the both exponential form and the logarithmic form on the holographic paramagnetism-ferromagnetism phase transition in the background of a Schwarzschild-AdS black hole spacetime. Moreover, by comparing the exponential form of nonlinear electrodynamics with the logarithmic form of nonlinear electrodynamics and the Born-Infeld nonlinear electrodynamics which has been presented in Ref.~\cite{Wu:2016uyj}, we find that the higher nonlinear electrodynamics correction makes the critical temperature smaller and the magnetic moment harder form in the case without external field. Furthermore, the increase of nonlinear parameter b will result in extending the period of the external magnetic field. Especially, the effect of the exponential form of nonlinear electrodynamics on the periodicity of hysteresis loop is more noticeable., arXiv admin note: text overlap with arXiv:1212.6693, arXiv:1208.5902 by other authors

In this paper, time-dependent nonlinear numerical and analytical computational models suitable for rheological analysis of prestressed cable nets subjected to creep effects are presented. The principal aim of this contribution is to describe a developed design computational tool for a theoretical simulation of the time-dependent behavior of cable nets and predict their rheological characteristics. For this purpose, a modified finite-element method for the time-dependent analysis of materially linear and geometrically nonlinear cable nets is proposed. Creep constitutive equations in the logarithmic form are incorporated into the finite-element model to express the current lengths of cables as the functions of creep strain increments. As an extension of the Irvine approach, a geometrically nonlinear time-dependent analytical static solution of taut flat cable nets over an orthogonal square plan is presented. The cable net is replaced by an equivalent membrane. Creep strain is incorporated into the c...

International audience; Starting from the general expression for the ground state correlation energy in the adiabatic connection fluctuation dissipation theorem (ACFDT) framework, it is shown that the dielectric matrix formulation, which is usually applied to calculate the direct random phase approximation (dRPA) correlation energy, can be used for alternative RPA expressions including exchange effects. Within this famework, the ACFDT analog of the second order screened exchange (SOSEX) approximation leads to a logarithmic formula for the correlation energy similar to the direct RPA expression. Alternatively, the contribution of the exchange can be included in the kernel used to evaluate the response functions. In this case the use of an approximate kernel is crucial to simplify the formalism and to obtain a correlation energy in logarithmic form. Technical details of the implementation of these methods are discussed and it is shown that one can take advantage of density fitting or Cholesky decomposition techniques to improve the computational efficiency; a discussion on the numerical quadrature made on the frequency variable is also provided. A series of test calculations on atomic correlation energies and molecular reaction energies shows that exchange effects are instrumental to improve over direct RPA results.

We study an element of the ring of algebraic integers having the special form 1 − zλ. We obtain a formula for calculating its logarithmic functions. Thus, we verify the conjecture that logarithmic functions of the element 1 − zλ are polynomials in z such that z appears only in powers that are divisors of the number of the logarithmic function.

SUMMARY The discrete optimal orientation design of the composite laminate can be treated as a material selection problem dealt with by using the concept of continuous topology optimization method. In this work, a new bi-value coding parameterization (BCP) scheme of closed form is proposed to this aim. The basic idea of the BCP scheme is to ‘code’ each material phase using integer values of +1 and –1 so that each available material phase has one unique ‘code’ consisting of +1 and/or –1 assigned to design variables. Theoretical and numerical comparisons between the proposed BCP scheme and existing schemes show that the BCP has the advantage of an evident reduction of the number of design variables in logarithmic form. The benefit is particularly remarkable when the number of candidate materials becomes important in large-scale problems. Numerical tests with up to 36 candidate material orientations are illustrated for the first time to indicate the reliability and efficiency of the BCP scheme in solving this kind of problem. It proves that the BCP is an interesting and valuable scheme to achieve the optimal orientations for large-scale design problems. Besides, a four-layer laminate example is tested to demonstrate that the proposed BCP scheme can easily be extended to multilayer problems. Copyright © 2012 John Wiley & Sons, Ltd.

Combustion kinetic parameters (i.e., activation energy and frequency factor) of coal have been proven to relate closely to coal properties; however, the quantitative relationship between them still requires further study. This paper adopts a support vector regression machine (SVR) to generate the models of the non-linear relationship between combustion kinetic parameters and coal quality. Kinetic analyses on the thermo-gravimetry (TG) data of 80 coal samples were performed to prepare training data and testing data for the SVR. The models developed were used in the estimation of the combustion kinetic parameters of ten testing samples. The predicted results showed that the root mean square errors (RMSEs) were 2.571 for the activation energy and 0.565 for the frequency factor in logarithmic form, respectively. TG curves defined by predicted kinetic parameters were fitted to the experimental data with a high degree of precision.

Existing analytical models for mean wind profiles within canopies are applicable only in dense canopy scenarios, where all momentum is absorbed by canopy elements and, hence, the effect of the ground on turbulent mixing is not important. Here, we propose a new analytical model that can simulate mean wind profiles within sparse canopies under neutral conditions. The model adopts a linearized canopy-drag parametrization and a first-order turbulence closure scheme taking into account the effects of both the ground and canopy elements on turbulent mixing. The resulting wind profile within a sparser canopy appears to be more like a logarithmic form, with the no-slip condition at the ground being satisfied. The analytical solution converges exactly to the standard surface-layer logarithmic wind profile in the case of zero canopy density (i.e., no-canopy scenario) and tends to be an exponential wind profile for a dense canopy; this feature is unique compared with existing analytical models for canopy wind profiles. Results from the new model are in good agreement with those from laboratory experiments and numerical simulations.

Nonlinear time series analysis aims at understanding the dynamics of stochastic or chaotic processes. In recent years, quite a few methods have been proposed to transform a single time series to a complex network so that the dynamics of the process can be understood by investigating the topological properties of the network. We study the topological properties of horizontal visibility graphs constructed from fractional Brownian motions with different Hurst index $H\in(0,1)$. Special attention has been paid to the impact of Hurst index on the topological properties. It is found that the clustering coefficient $C$ decreases when $H$ increases. We also found that the mean length $L$ of the shortest paths increases exponentially with $H$ for fixed length $N$ of the original time series. In addition, $L$ increases linearly with respect to $N$ when $H$ is close to 1 and in a logarithmic form when $H$ is close to 0. Although the occurrence of different motifs changes with $H$, the motif rank pattern remains unchanged for different $H$. Adopting the node-covering box-counting method, the horizontal visibility graphs are found to be fractals and the fractal dimension $d_B$ decreases with $H$. Furthermore, the Pearson coefficients of the networks are positive and the degree-degree correlations increase with the degree, which indicate that the horizontal visibility graphs are assortative. With the increase of $H$, the Pearson coefficient decreases first and then increases, in which the turning point is around $H=0.6$. The presence of both fractality and assortativity in the horizontal visibility graphs converted from fractional Brownian motions is different from many cases where fractal networks are usually disassortative., 12 pages, 8 figures

In this paper, we study quantum corrections to the temperature and entropy of a regular Ay\'{o}n-Beato-Garc\'{\i}a-Bronnikov black hole solution by using tunneling approach beyond semiclassical approximation. We use the first law of black hole thermodynamics as a differential of entropy with two parameters, mass and charge. It is found that the leading order correction to the entropy is of logarithmic form. In the absence of the charge, i.e., $e=0$, these corrections approximate the corresponding corrections for the Schwarzschild black hole., Comment: 15 pages, accepted for publication in Astrophysics and Space Science

In this article, a theoretical procedure has been developed for the kinetic study of the glass-crystal transformations under continuous heating regime in materials involving formation and growth of nuclei, obtaining the corresponding parameters: kinetic exponent, activation energy, and pre-exponential frequency. It is an integral procedure, which is based on a transformation rate independent of the thermal history of the material and assumes that the quoted rate depends only on the transformed fraction, x, across the f(x) function, and temperature, considering that these variables are independent ones. Therefore, the transformation rate is expressed as the product of two separable functions of absolute temperature and the transformed fraction. The quoted f(x) function corresponds to a theoretical method that we have developed and recently published, whose details are given in the Sect. “Basic theory” of this study. The above-mentioned integral procedure considers the same pair of temperatures for the different heating rates and obtains a constant value for temperature integral and, therefore, a plot of a function of the transformed fraction versus the reciprocal of the heating rate leads to a straight line with an intercept of zero, if the value of kinetic exponent is correctly chosen. The process may be repeated for other pairs of temperatures and, consequently, other straight lines will be obtained. By using different values of kinetic exponent for each of the quoted lines, it is taken the best correlation coefficient to choose the quoted exponent more suitable. On the other hand, by using the first mean value theorem to approach the temperature integral, one obtains a relationship between a function of the temperature and other function of the transformed fraction. The logarithmic form of the quoted relationship leads to a straight line, whose slope and intercept allow the obtaining of the activation energy and of the pre-exponential frequency. In addition, this study applies the quoted procedure to the analysis of the crystallization kinetics of the Ge0.08Sb0.15Se0.77 glassy alloy resulting in ranges of variation both of the kinetic exponent, n, with the temperature and of the activation energy, E, with the crystallized fraction, which contain the values of n and E, obtained according to the already quoted theoretical method, that we have developed and recently published. This fact shows the reliability of the theoretical procedure described in this article to analyze the glass-crystal transformation kinetics of glassy alloy.

The rheology of solutions of randomly methylated (1.8) β-cyclodextrin (β-CD) in 1-ethyl-3-methyl imidazolium acetate ([EMIM][Ac]) was studied in detail by rotational and oscillatory shear measurements. It was found that a gel structure was formed even at a relatively low β-CD concentration, which induced intriguing results in oscillation experiments. The solutions showed abrupt changes of the structurally dependent rheological moduli and reproducible transitions from gel to sol state at specific shear stress. For all β-CD solutions, a non-Newtonian flow behavior including shear thinning was obtained. The influence of temperature and β-CD concentration on the flow behavior was studied for all solutions, and the flow activation energies were calculated from the logarithmic form of the Arrhenius equation for nonassociating electrolytes.

We propose some nonlinear Schrodinger equations by adding some higher order terms to the Lagrangian density of Schrodinger field, and obtain the Gross-Pitaevskii (GP) equation and the logarithmic form equation naturally. In addition, we prove the coefficient of nonlinear term is very small, i.e., the nonlinearity of Schrodinger equation is weak.

We empirically study the genealogical trees of ten families for about five centuries in Korea. Although each family tree contains only the paternal part, the family names of women married to the family have been recorded, which allows us to estimate roughly the family name distributions for the past five hundred years. Revealed is the fact that the unique Korean family name distribution, characterized by a logarithmic form of the cumulative distribution and an exponentially decaying rank-size plot often called the Zipf plot, has remained unchanged for a long time. We discuss the implications of our results within a recently suggested theoretical model and compare them with observations in other countries in which power-law forms are abundantly found., Comment: 5 pages, 3 figures

In 1981 J. Noguchi proved that in a logarithmic algebraic manifold, having logarithmic irregularity strictly bigger than its dimension, any entire curve is algebraically degenerate. In the present paper we are interested in the case of manifolds having logarithmic irregularity equal to its dimension. We restrict our attention to Brody curves, for which we resolve the problem completely in dimension 2: in a logarithmic surface with logarithmic irregularity 2 and logarithmic Kodaira dimension 2, any Brody curve is algebraically degenerate. In the case of logarithmic Kodaira dimension 1, we still get the same result under a very mild condition on the Stein factorization map of the quasi-Albanese map of the log surface, but we show by giving a counter-example that the result is not true any more in general. Finally we prove that a logarithmic surface having logarithmic irregularity 2 admits certain types of algebraically non degenerate entire curves if and only if its logarithmic Kodaira dimension is zero, and we also give a characterization of this case in terms of the quasi-Albanese map.

By using a slow growth scale, the logarithmic order, with which to measure the growth of functions, we obtain basic results on the value distribution of a class of meromorphic functions of zero order.

Let $f:\Cal C\to S$ be a flat family of curves over a smooth curve $S$ such that $f$ is smooth over $S_0=S\ssm\{s_0\}$ and $f^{-1}(s_0)=\Cal C_0$ is irreducible with one node. We have an associated family $\Cal M_{S_0}\to S_0$ of moduli spaces of semistable vector bundles and the relative theta line bundle $\Theta_{S_0}$. We are interested in the problem: to find suitable degeneration $\Cal M_S$ of moduli spaces and extension $\Theta_S$ of theta line bundles such that the direct image of $\Theta_S$ is a vector bundle on $S$ with a logarithmic projective connection. In this paper, we figured out the conditions of existence of the connection and solved the problem for rank one., Comment: 26 pages, amstex

The adsorption of copper(II) to Shirasu, a pyroclastic flow deposit, was examined by a batch-and-column method. The effect of the grain size was investigated in the range

The Generalized Minimal Massive Gravity (GMMG) theory is realized by adding the CS deformation term, the higher derivative deformation term, and an extra term to pure Einstein gravity with a negative cosmological constant. In the present paper we obtain exact solutions to the GMMG field equations in the non-linear regime of the model. GMMG model about $AdS_3$ space is conjectured to be dual to a 2-dimensional CFT. We study the theory in critical points corresponding to the central charges $c_-=0$ or $c_+=0$, in the non-linear regime. We show that $AdS_3$ wave solutions are present, and have logarithmic form in critical points. Then we study the $AdS_3$ non-linear deformation solution. Furthermore we obtain logarithmic deformation of extremal BTZ black hole. After that using Abbott-Deser-Tekin method we calculate the energy and angular momentum of these types of black hole solutions., Comment: 16 pages, no figure, some Refs added, minor changes, as published in Gen Relativ Gravit

We develop the Newton-Kantorovich method to solve the system of2×2nonlinear Volterra integral equations where the unknown function is in logarithmic form. A new majorant function is introduced which leads to the increment of the convergence interval. The existence and uniqueness of approximate solution are proved and a numerical example is provided to show the validation of the method.