Inclusion Of Nonlinear Terms Research Articles

A SOCIAL WELFARE ESTIMATION OF RIDE-SHARING IN CHINA: EVIDENCE FROM TRANSACTION DATA ANALYSIS OF A LARGE ONLINE PLATFORM

This paper estimates the social welfare effect of China’s largest online ride-sharing platform. Under the plausible assumption that consumers would change from traditional transportation to online ride-sharing when the marginal benefit of saved time outgrows the additional cost, we calculate the distribution of implied wage rate of passengers. We then use the passenger wage rate to calculate the social welfare generated by the decrease in waiting time and the reduction of waiting uncertainty brought about by the ride-sharing platform. Our estimate suggests that the ride-sharing platform created a total of 130.5 billion Yuan of social welfare in the three years between 2016 and 2018, and the consumer surplus and producer surplus created by an average transaction are 5.4 Yuan and 2.5 Yuan, respectively. The robustness test finds that our results were insensitive to the assumed risk aversion coefficient in the model, the subsample number used for each city, and the inclusion of nonlinear terms in the model. Alternative hypotheses, such as learning effect, seem unable to explain our result.

Dynamics of stocks prices based in the Black & Scholes equation and nonlinear stochastic differentials equations

The effect of non-linear terms on Itô–Langevin diffusion model with aim to analyze the change generated on long-tail distribution of the probability density of the returns and volatilities and long range memory is investigated. In particular, whether the model still obeys to stylized facts obeyed by the financial markets that is, the behavior of the long-tail distribution of the returns and volatilities and the correspondent scale law. More specifically, whether after inclusion of nonlinear terms in the model, it still satisfies to the inverse cubic law obeyed for quasi all markets and therefore, if the model still obey to the aspects or statistical regularities obeyed by the financial markets.

Simulation of 2D Nonlinear Manifestations in a Layered-Block Medium with Hierarchical Inclusions

The geological environment is an open system that can be influenced by external and internal factors. They can lead it to an unstable state, which, as a rule, manifests itself locally in the form of zones called dynamically active elements, by which it is possible to identify, on the one hand, potential catastrophic sources that disrupt the technological process when mining the rock massif; оn the other hand, when producing oil from wells, this process can contribute to improving the movement of oil inclusions in the plastic environment of the reservoir. These objects, both in the rock massif and in the oil reservoir, differ from the host geological environment in their structural forms, which are often hierarchical forms. The process of their nonlinear activation can be observed using borehole monitoring of acoustic longitudinal and transversal waves, for the mathematical support of which new 2D modeling algorithms have been developed in that paper using the method of integral and integro-differential equations with the inclusion of nonlinear terms in the dependence of the wave parameter on frequency. When interpreting the results of acoustic monitoring, it is necessary to use the data of such observation systems that are configured to study the hierarchical structure of the environment.

A Comparative simulation on the grounding grid system of a wind turbine with FEA software

The mathematical models proposed in the literature are used to determine the grounding resistance value for electrical installations. These models are mathematical expressions that change according to grounding type and the mechanical properties of the grounding system elements. Besides, the inclusion of nonlinear terms is another important issue in the modeling studies. For the modeling of nonlinear systems and the analysis of the faults that may occur, the finite element analysis (FEA) approach provides realistic results. In the present study, the simulation of a grid fault that may occur in the grounding system of a sample wind turbine (WT) is modeled by 2D electrostatic solver in FEA software. The simulation results prove that the findings are similar to the realistic faults in the grounding system.

Ab initio studies of electron correlation effects in magnetic dipolar hyperfine interaction of Cs

The hyperfine-structure constant A of the S, P, and D states in Cs atom with the principal quantum number are calculated using the Dirac–Fock approximation, the low-order many-body perturbation theory, and relativistic coupled-cluster method in single and double approximations with and without the inclusion of nonlinear terms. The importance of electron correlation effects, especially the nonlinear corrections of the cluster operators, is demonstrated by comparing the results of various approximations with available experimental values. Moreover, the correlation trends for individual electron correlation effects involving direct, core-polarization, and pair-correlation ones in members of Rydberg series are also investigated in the framework of the coupled-cluster theory. Some interesting features are observed.

Additivity of Substituent Effects. Core-Ionization Energies and Substituent Effects in Fluoromethylbenzenes

Carbon 1s ionization energies have been measured for all of the carbon atoms in eight fluoromethylbenzenes. Enthalpies of protonation have been calculated for protonation at all of the ring carbons in the same molecules. These data together with previously reported data on fluorobenzenes and methylbenzenes provide the basis for studying the additivity of substituent effects and the correlation between enthalpies of protonation with core-ionization energies. Although a linear additivity model accounts reasonably well for both the ionization energies and the enthalpies of protonation, a better description, especially for the enthalpies, is obtained by inclusion of nonlinear terms that account for interactions between two substituents on the same molecule. There are families of nearly parallel correlation lines between enthalpies of protonation and core-ionization energies. The existence of several families can be primarily understood in terms of the linear additivity picture and more completely understood when the nonlinear terms are taken into account. The role of the methyl group as a polarizible pi-electron donor is contrasted with the role of fluorine, which is a substituent of low polarizibility that acts to withdraw electrons from the adjacent carbon and to donate electrons through resonance to the ring. The role of the hydrogen atoms as pi-electron acceptors in the protonated species is illustrated.

Initial energy density and gluon distribution from the glasma in heavy-ion collisions

We estimate the energy density and the gluon distribution associated with the classical fields describing the early-time dynamics of heavy-ion collisions. In the McLerran-Venugopalan model, we first decompose the energy density into the momentum components exactly, with the use of the Wilson line correlators. Then we evolve the energy density with the free-field equation, which is justified by the dominance of the ultraviolet modes near the collision point. We also discuss the improvement that occurs with the inclusion of nonlinear terms into the time evolution. Our numerical results at RHIC energy are fairly consistent with the empirical values.

Quantitative structure–activity relations based on quantum theory and wavelet transformations

We describe the use of wavelet-transformed quantum-chemical property fields for three-dimensional quantitative structure–activity relations (3D-QSARs) and compare this new ansatz with standard approaches like comparative molecular field approach (CoMFA) or comparative molecular similarity approach (CoMSIA) for datasets from the literature. The gain in CPU-time and memory through using the wavelet transformation permits evaluation of many QSAR models to find the optimum one, the inclusion of nonlinear terms in the PLS is trivial. The limiting factor is still the quantum-chemical calculation of property fields on dense grids, preferentially by density functional theory, for the set of molecules.

A Simplified physical model of pressure wave dynamics and acoustic wave generation induced by laser absorption in the retina

Shock waves have been proposed in the literature as a mechanism for retinal damage induced by ultra-short laser pulses. For a spherical absorber, we derive a set of linear equations describing the propagation of pressure waves. We show that the formation of shock fronts is due to the form of the absorber rather than the inclusion of nonlinear terms in the equations. The analytical technique used avoids the need for a Laplace transform approach and is easily applied to other absorber profiles. Our analysis suggests that the ‘soft’ nature of the membrane surrounding retinal melanosomes precludes shock waves as a mechanism for the retinal damage induced by ultra-short pulse lasers. The quantitative estimates of the pressure gradients induced by laser absorption which are made possible by this work, together with detailed meso-scale or molecular modelling, will allow alternative damage mechanisms to be identified.

Quasiparticle random phase approximation with a nonlinear phonon operator

We present model calculations of the quasiparticle random phase approximation (QRPA) with a new form of the phonon operator. This modification of the QRPA is applied to the proton-neutron Lipkin model and we shall review it briefly. The present calculations show that the inclusion of nonlinear terms in the phonon operator leads to a much better agreement with the exact results obtained by the diagonalization of the nuclear Hamiltonian. It is further found that if all relevant nonlinear terms of the phonon operator are taken into account, all odd excited states are also exactly reproduced.

Dissipation in perpendicularly magnetized ultrathin films studied using the complex AC susceptibility

Dissipation due to domain wall motion in perpendicularly magnetized ultrathin Fe/2ML Ni/W(1 1 0) films has been studied using measurements of the real (reversible) and imaginary (irreversible) components of the magnetic AC susceptibility, χ( T), as a function of frequency and the modulation field amplitude. The additional information afforded by Im χ(T) allows: extraction of the distribution of activation energies for motion of existing domain walls, revealing that it has the form of a narrow, truncated Lorentzian; demonstration of a separate dynamical freezing of the domain density as the temperature is lowered — possibly due to a barrier to domain wall creation; and the quantitative description of the crossover from a metastable, single domain hysteretic state to one with freely moving domains by inclusion of non-linear terms in the susceptibility. Together, these points permit a quantitative, self-consistent description of both components of the measured AC susceptibility.

Comparing linear and nonlinear forecasts for stock returns

We compare the out-of-sample performance of monthly returns forecasts for two indices, namely the Dow Jones (DJ) and the Financial Times (FT) indices. A linear and a nonlinear artificial neural network (ANN) model are used to generate the out-of-sample competing forecasts for monthly returns. Stationary transformations of dividends and trading volume are considered as fundamental explanatory variables in the linear model and the input variables in the ANN model. The comparison of out-of-sample forecasts is done on the basis of forecast accuracy, using the Diebold and Mariano test [J. Bus. Econ. Stat. 13 (1995) 253.], and forecast encompassing, using the Clements and Hendry approach [J. Forecast. 5 (1998) 559.]. The results suggest that the out-of-sample ANN forecasts are significantly more accurate than linear forecasts of both indices. Furthermore, the ANN forecasts can explain the forecast errors of the linear model for both indices, while the linear model cannot explain the forecast errors of the ANN in either of the two indices. Overall, the results indicate that the inclusion of nonlinear terms in the relation between stock returns and fundamentals is important in out-of-sample forecasting. This conclusion is consistent with the view that the relation between stock returns and fundamentals is nonlinear.

Neural network linear forecasts for stock returns

AbstractWe examine the out‐of‐sample performance of monthly returns forecasts for the Dow Jones and the FT, using a linear and an artificial neural network (ANN) model. The comparison of out‐of‐sample forecasts is done on the basis of directional accuracy, using the Pesaran and Timmermann (1992. A simple nonparametric test of predictive performance, Journal of Business and Economic Statistics 10: 461–465) test, and forecast encompassing, using the Clements and Hendry (1998. Forecasting Economic Time Series. Cambridge University Press: Cambridge, UK) approach. While both models perform badly in terms of predicting the directional change of the two indices, the ANN forecasts can explain the forecast errors of the linear model while the linear model cannot explain the forecast errors of the ANN for both indices. Thus, the ANN forecasts are preferable to linear forecasts, indicating that the inclusion of nonlinear terms in the relation between stock returns and fundamentals is important in out‐of‐sample forecasting. This conclusion is consistent with the view that the underlying relation between stock returns and fundamentals is nonlinear. Copyright © 2001 John Wiley & Sons, Ltd.

Nonlinear Interaction of Capillary-Gravity Waves with a Subsonic Gas in the Presence of Magnetic Field

The method of multiple scales is used to analyse the nonlinear propagation of waves on the interface between a liquid and a subsonic gas in the presence of magnetic field taking into account surface tension. The evolution of the amplitude is governed by a nonlinear Schr6dinger equation which gives the criterion for modulational instability. Numerical results are given in the graphical form. considerable attention during the last decade. We consider in this paper, the weakly nonlinear physical system, the interaction of capillary gravity waves with a subsonic flow moving uni- formly parallel to the undisturbed liquid surface in the presence of magnetic field. The same problem without magnetic field when the liquid is of finite depth has been investigated earlier by Nayfeh and Hassan (1). The inclusion of nonlinear terms results in amplitude modulation. In various problems of interest, it has been shown that the long-time slow modulation of wave amplitude is governed by the nonlinear Schr0dinger equation. In recent years, evolution of wave packets on the surface of an electrically conducting fluid has been investigated by a number of workers. El Shehawey (2) discussed the nonlinear condi- tions of stability and instability of electro-hydrodynamic Kelvin-Helmholtz mechanisms in the presence of a normal field in the absence of surface charges on the interface. Pusri and Malik (3) investigated the propagation of wave packets on the surface of an electrically conducting fluid of uniform depth in the presence of a tangential magnetic field in three dimensions by extending the analyses of Djordjevic and Redekopp (4) and Ablowitz and Segur (5) to incorporate magne- tohydrodynamic effects. The method of multiple scales was very successfully used by Hasimoto and Ono (6) to derive a single equation describing the long-time evolution of the envelope of a packet of plane finite amplitude gravity waves. In this presentation, by the multiple scale method, we plan to develop the nonlinear Schrodinger equation describing the evolution of the finite amplitude wave packet on the liquid surface in the presence of normal magnetic field with

Theory of fermion liquids.

We develop a general theory of fermion liquids in spatial dimensions greater than one. The principal method, bosonization, is applied to the cases of short and long range longitudinal interactions, and to transverse gauge interactions. All the correlation functions of the system may be obtained with the use of a generating functional. Short-range and Coulomb interactions do not destroy the Landau Fermi fixed point. Novel fixed points are found, however, in the cases of a super-long range longitudinal interaction in two dimensions and transverse gauge interactions in two and three spatial dimensions. We consider in some detail the 2+1-dimensional problem of a Chern-Simons gauge action combined with a longitudinal two-body interaction $V({\bf q}) \propto |{\bf q}|^{y-1}$ which controls the density, and hence gauge, fluctuations. For $y < 0$ we find that the gauge interaction is irrelevant and the Landau fixed point is stable, while for $y > 0$ the interaction is relevant and the fixed point cannot be accessed by bosonization. Of special importance is the case $y = 0$ (Coulomb interaction) which describes the Halperin-Lee-Read theory of the half-filled Landau level. We obtain the full quasiparticle propagator which is of a marginal Fermi liquid form. Using Ward Identities, we show that neither the inclusion of nonlinear terms in the fermion dispersion, nor vertex corrections, alters our results: the fixed point is accessible by bosonization. As the two-point fermion Green's function is not gauge invariant, we also investigate the gauge-invariant density response function. Near momentum $Q = 2 k_F$, in addition to the Kohn anomaly we find singular behavior. In Appendices we present a numerical calculation of the spectral function for a Fermi liquid with Landau parameter $f_0 \neq 0$. We also show how Kohn's theorem is

Stress Distribution in Granular Media and Nonlinear Wave Equation

We propose phenomenological equations to describe how forces propagate within a granular nledium. Trie linear part of these equations is a wave equation, where the vertical coordinate plays trie rote of time, and trie horizontal coordinates trie raie of space. This means that (in two dimensions) trie stress propagates along light-cones; trie angle of these canes is related (but not equal to) trie angle of repose. Dispersive corrections to trie picture, and various types of nonlinearity are discussed. Inclusion of nonlinear terms may be able to describe trie arching phenomenon, which has been proposed to explain trie nonintuitive hor- izontal distribution of vertical pressure (with a local minimum or dip under the apex of trie pile) observed experimentally. However, for physically motivated parameter choices, a hump, rather than a dip, is predicted. This is aise true of a perturbative solution of the continuum stress equations for nearly-flot piles. The nature of trie force fluctuations is aise briefly discussed.

Wall imperfections as a triggering mechanism for Stokes-layer transition

The boundary layer generated by the harmonic oscillations of a wavy wall in a fluid otherwise at rest is studied. First the wall waviness is assumed to be of small amplitude and large values of the Reynolds number are considered. The results obtained by means of a linear analysis, where the time variable appears only as a parameter, show that resonance may occur. Indeed it is found that when the Reynolds number is larger than a critical value, an instant within the decelerating part of the cycle exists such that a waviness of infinitesimal amplitude induces unbounded perturbations of the flow in the Stokes layer. The passage through resonance is then studied by means of a multiple-timescale approach, taking into account the damping effect of local acceleration within a small time range around resonance. The asymptotic approach fails beyond a threshold value of the Reynolds number, because the damping effect of the local acceleration terms spreads over the whole cycle. The problem is then tackled by means of an approach that takes into account the above damping effect throughout the whole cycle. Finally, a numerical procedure is used that also allows the inclusion of nonlinear terms and the study of the interactions among forced and free modes. The numerical approach reveals that, even for relatively large values of the amplitude of the wall waviness, nonlinear effects are negligible and the damping of resonance is mainly due to local acceleration effects. The relevance of the results to the understanding of transition to turbulence in Stokes layers is discussed.

Reference values for respiratory function tests in males: prediction formulas with tobacco smoking parameters

Prediction equations for respiratory function tests were obtained by multiple regression of data from 263 healthy males. The material was evenly distributed in the ages 20-70 years, about one third each of non-smokers, smokers and ex-smokers. Measurements were done of lung volumes (with body plethysmograph), airways resistance, ventilatory capacity including flow-volume registration, gas distribution and closing volume, transfer factor and static elastic recoil pressures of the lung with calculation of static compliance. The parameters age, height, weight, years of tobacco smoking and grams of tobacco smoked each day showed significant correlation with the outcome of the test in most of the respiratory function tests. Therefore a set of basic regression equations including these parameters were calculated. In addition an 'extended' set of equations was calculated for prediction of some tests with inclusion of nonlinear terms and the parameter 'years of abstinence from smoking.' The reduction in variance which followed inclusion of tested parameters was moderate (20-69%). There were significant differences between results of the present study and several previously published regression formulas.

Frequency spectrum of the flicker phenomenon in erythrocytes

Red blood cells show a remarkable flicker phenomenon under physiological conditions. We have studied experimentally the correlations functions G(R12, ω) for the flicker intensities measured at two different points r 1 r2 on the cell surface, at various filtering frequencies ω. We find that the shape of G is universal and involves only one characteristic length λ(ω) varying like ω-n, where 0.12 < n < 0.19. Measurements of G(0, ω) (i.e. at a single point) show an ω-m dependence, where 1.30 < m < 1.45. These results are then interpreted theoretically in term of thermal fluctuations of the cell thickness. In physiological conditions the membrane surface tension vanishes exactly and the resistance to deformation is mainly due to curvature energy. In this approximation : a) the fluctuations are of very large amplitude (a fraction of a micron) as required by the observations ; b) the detailed shape of the correlations is in rather good agreement with the theory ; c) the scaling length λ(ω) is expected to vary like ω-1/6; d) the single point spectrum G(0, ω) should go like ω-4/3. The approximation involves the neglect of some non linear effects related to surface tension and to the Evans elastic energy. We show that the inclusion of non linear terms leads to a problem related to the critical point of a (special) two dimensional magnetic system. Our approximation (equivalent to a mean field theory) essentially ignores the exponent correction η introduced by Fisher for phase transitions. Thus, the experimental evidence favours a rather small η. We conclude that a purely physical interpretation of the flicker effect is sufficient, but that rather stringent physiological conditions are required to maintain the zero surface tension which is crucial to the effect.

Strength of Very Slender Beams

Response to lateral loads and twisting couples is affected by presence of bending moments in plane of major stiffness; resulting nonlinear theory discussed; inclusion of nonlinear terms in strain displacement relations corresponds generally to stiffening of structure as compared with familiar linear theory; theory presented is corroborated experimentally with fair degree of accuracy.