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Because of its small average droplet size, low carrier gas flow rate and the droplets not easy to splash etc, the ultrasonic atomizing spray technology is particularly suitable for making photoresist films. In order to get a reasonable spray scan interval, the parabolic deposition model was used to study the relationship between the spray overlap width and the photoresist film thickness and uniformity, and it can be concluded that the thickness of the film increases and the thickness variance of the film decreases oscillatorily along with the increasing of the spray overlap width.To obtain good uniformity of the photoresist film, the dimensionless overlap width should be at least greater than 0.15.

The precision of growing stock were assessed. Industrial & fuel wood volumes of beech trees in Shanderman District was surveyed. For this purpose, 10% of the annual marked trees for loggings were randomly selected in five parcel from this District. After measuring the diameter at breast height (DBH) to estimate the volume of trees by Tariff table, the trees were cut; the volumes of the industrial woods of trees were computed by using Huber's formula. The volume of fuel woods with diameter above 12 cm also were calculated by Huber's method and the diameter below 12 cm were estimated as ester. The results indicated that there were significant differences between estimation of total tree volumes by Tariff table and the total volumes of cut trees at 0.01 confidence levels. The suitable model for relationship between DBH and total volumes was a parabolic model. Industrial and fuel wood volumes of beech trees were 68.9% and 31.1% in the study area, respectively (at 95% confidential). The mean industrial volume of beech trees to total volume was between 61.1%&76.7% and fuel wood volume was between 26.49%&35.71%.

We prove global existence and qualitative behavior of classical solutions for a hyperbolic-parabolic system describing chemotaxis on bounded domains. It is shown that classical solutions to the initial-boundary value problem of the one-dimensional model exist globally in time for large initial data, and the solutions converge to constant equilibrium states exponentially in time, which rigorously demonstrates the collapsing of cell populations in chemotaxis. Moreover, similar results are established for the multidimensional model when the initial data are small.

A quasilinear parabolic problem is investigated. It models the evolution of a single population species with a nonlinear diffusion and a logistic reaction function. We present a new treatment combining standard theory of monotone operators in L 2 (Ω) with some order- preserving properties of the evolutionary equation. The advantage of our approach is that we are able to obtain the existence and long-time asymptotic behavior of a weak solution almost simultaneously. We do not employ any uniqueness results; we rely on the uniqueness of the minimal and maximal solutions instead. At last, we answer the question of (long-time) survival of the population in terms of a critical value of a spectral parameter.

The thin-layer drying behavior of tiger nut seeds dried using hot air, solar drier and open sun drying was investigated. The drying took place in the falling rate period. Six thin-layer drying equations were used to fit the drying data. For oven drying, the parabolic model had the highest correlation coefficients, R2 of 0.972 to 0.990 and the lowest Chi-square value (χ2) of 0.000941 to 0.001463 and root mean square error (RMSE) of 0.028213 to 0.034594. The logarithmic model had the highest R2 (0.995 and 0.994) and the lowest χ2 (0.000446 and 0.000417) and RMSE (0.019869 and 0.019051) for sun and solar drying of tiger nut. The effective moisture diffusivity coefficient varied from 2.39 × 10−10 to 7.23 × 10−9 m2/s while the activation energy was 28.14 kJ/mol for oven drying of tiger nuts. This indicates that the diffusion process requires lower energy hence ease of drying of the tiger nut. PRACTICAL APPLICATION Tiger nut can be categorized as one of the lesser known and underutilized crops, which are potentially valuable as human and animal foods. Its proper processing will produce products that can be used to maintain a balance between population growth and agricultural productivity. Drying is a fundamental unit operation in the processing of this seed, which influences the physicochemical and quality characteristic of the product. An increase in the utilization of the crop and the formulation of a wide range of possible products from tiger nut will require that the traditional open-air sun-drying method be replaced with efficient drying systems. Therefore, an evaluation of the drying characteristics as a function of different drying conditions could help in predicting suitable drying conditions for good quality products.

The special case of unity dispersive Mach number of the hyperbolic axial dispersion model is investigated as the more realistic and simpler alternative to the parabolic model with zero Mach number. Simple corrections to the mean temperature difference or to the heat transfer coefficients are derived as functions of the dispersive Peclet numbers. As an example the model is applied to a cascade of stirred tanks in overall counterflow arrangement.

The concept of the first and the second singularity point was introduced in the paper. The singularity points would lead to the iteration divergence in the solution of rolling by rigid plasticity finite element method. Double velocity model and parabolic model of relative slip velocity were proposed for solution of the first and the second singularity point respectively. The influence of the models to improve the effects of singularity point on calculating time and iteration step was discussed according to the practical strip rolling condition. The results showed that for the element numbers from 200 to 2000, the iteration step and total calculating time was reduced about 8~67% by the double velocity model in the same condition compared to normal model for the solution of first singularity point. The iteration step and calculating time was reduced about 15~61% with the parabolic model of relative slip velocity. The double velocity model and parabolic model of relative slip velocity could be used to improve the convergence and increase efficiency of the solution in strip rolling by rigid plasticity finite element method.

This paper presents MEPBAY and SMC software tools that allow comprehending and solving problems in headland-bay beach through a parabolic model. These tools can be employed as coastal engineering design tools (including nourishment designs) and also for academic purposes. They are oriented to different end-users, including coastal technicians, scientists and undergraduates and as coastal engineering design tools, they can be applied to different operational levels (pre-design and design). The aim of the paper is to present design guidelines, the capabilities of the tools, their potential use and applications. Both tools were applied to analyze San Lorenzo Beach and demonstrate their ability at different project levels.

This paper focuses on the effects of heat source profiles during thermal analysis of grinding. Three different models of heat source, namely triangular model, parabolic model and elliptic model, have been suggested and their numeric formulas are provided. These models take into account of the variation of heat flux along the contact zone, so as to improve the accuracy of numeric results. Finite Element Analysis (FEA) is utilized to investigate the temperature distributions under different thermal models and the effects of two profile parameters (η and ξ). The result is a) peak temperature decreases as η increases and the location of peak value moves backwards simultaneously; b) peak temperature decreases as ξ increases and the location of peak value moves forwards simultaneously.

We extend the concept of the well-known hyperbolic two-step model for micro heat transfer to the case of energy exchanges in a generalized N-carrier system. The model satisfies an energy estimate and hence is well-posed. Based on this result, a finite difference scheme is developed for solving the hyperbolic microscopic model. The scheme is shown to satisfy a discrete analogue of the energy estimate, implying that it is unconditionally stable. Finally, the scheme is tested by an example. The difference between the hyperbolic model and the corresponding parabolic model for a multi-carrier system is also compared.

A smoothing spline-based method and a hyperbolic heat conduction model is applied to regularize the recovery of the initial profile from a parabolic heat conduction model in two-dimensions. An ill-posed inverse problem involving recovery of the initial temperature distribution from measurements of the final temperature distribution is investigated. A hyperbolic heat conduction model is considered instead of a parabolic model and smoothing splines are applied to regularize the recovered initial profile. The comparison of the proposed procedure and parabolic model is presented graphically by examples.

In this paper we present a numerical study of the hyperbolic model for convection-diffusion transport problems that has been recently proposed by the authors [16]. This model avoids the infinite speed paradox, inherent to the standard parabolic model and introduces a new parameter t called relaxation time. This parameter plays the role of an ?inertia? for the movement of the pollutant. The analysis presented herein is twofold: first, we perform an accurate study of the 1D steady-state equations and its numerical solution. We compare the solution of the hyperbolic model with that of the parabolic model and we analyze the influence of the relaxation time on the solution. On the other hand, we explore the possibilities of the proposed model for real-world applications. With this aim we solve an example concerning the evolution of a pollutant being spilled in the harbor of A Corunaa (northwest of Spain, EU).

A smoothing splines method and a hyperbolic heat conduction model is applied to regularize the recovery of the initial profile from a parabolic heat conduction model. The recovery of initial profile with parabolic model is extremely ill-posed and it is desirable to develop a method to recover some useful information about the initial profile. It is demonstrated in this article that the recovery of the initial profile by a parabolic model is impossible in case of corrupted data, however, it is possible to recover the initial profile in a stable way by reformulating the problem by a hyperbolic model together with a smoothing splines method. One example is used for comparison of parabolic model and the proposed model for different modes and time displacements. A graphical comparison is given between the proposed model and the parabolic model.

To facilitate picoscopic modeling of traffic flow, an engine model is needed to determine the available power and further torque under varying speeds, which serves as an integral part of the vehicle model, which, in turn, determines a vehicle’s acceleration capability. This chapter presents and formulates three candidate engine models (models I, II, and III), among which model I is an existing one and the other two models are new. Their performances are evaluated on the basis of a system of metrics including accuracy, accessibility, computational efficiency, formulation, and the need for calibration. Overall, model II outperforms the other two models and appears promising to fit the need of the particular application.

We consider the dynamics of forward rate process which is modeled by the parabolic type infinite-dimensional factor model. The parameters included in this parabolic model are estimated by using the yield curve as the observation data. In this paper, we propose the filtering and identification method for the parabolic type factor model by using the particle filter algorithm.

We consider a fully parabolic model for chemotaxis with volume-filling effect and a nonlinear diffusion that degenerates in a two-sided fashion. We address the questions of existence of weak solutions and of their regularity by using, respectively, a regularization method and the technique of intrinsic scaling. Outstanding Young Investigators Award from the Research Council of Norway; (J. M. Urbano) CMUC/FCT, Project POCI/MAT/57546/2004

InAs/GaAs quantum dot electron spectra obtained from the capacitance–voltage measurements by B.T. Miller et al. [B.T. Miller, W. Hansen, S. Manus, R.J. Luyken, A. Lorke, J.P. Kotthaus, S. Huant, G. Medeiros-Ribeiro, P.M. Petroff, Phys. Rev. B 56 (1997) 6764] are quantitatively interpreted by applying a three-dimensional model of a semiconductor quantum dot with energy-dependent electron effective mass and finite confinement potential. The Coulomb interaction between tunnelled electrons is taken into account by perturbation theory. The observed significant increase in the electron effective mass of the quantum dot in respect to its bulk value is explained by the non-parabolic effect.

Investigations on the synthesis of bauxite-based β-Sialon-bonded SiC composites by in situ nitridation-reaction sintering process have been carried out. The phase composition and microstructure have been determined by XRD and SEM. Oxidation behaviors of bauxite-based β-Sialon-bonded SiC are also studied, the composites exhibit satisfactory resistance to oxidation, the oxidation kinetics of the composites in dry air over 1200–1300 °C are fitted to the parabolic model.

In this paper we show the advantages of using Mathematica software in engineering mathematics classes through the study of an example problem concerning heat conduction in a slab. Firstly the problem is solved from the point of view of a parabolic model of heat conduction, and secondly from the viewpoint of a hyperbolic model.

A characteristic-Galerkin approximation of a new two-dimensional Shallow Water viscous parabolic model is presented and a semi-implicit-Lagrangian finite element scheme is used. A convergence result is proved and numerical experiments on academic tests are shown.

The validity of the use of the microscopic parabolic heat conduction model under the effect of a moving heating source is investigated. Two configurations are considered which are the finite and the semi-infinite domains. For each configuration, two types of thermal boundary conditions are considered which are the isothermal and the insulated types. Four dimensionless parameters are found to control the thermal behavior of the considered problem which are the dimensionless heating source speed U, heat capacity ratio C R, dimensionless amplitude of the heating source S 0, and dimensionless plate thickness ξ0 for the finite domain configuration. It is found that the use of the microscopic parabolic heat conduction model instead of the parabolic macroscopic model is essential when the dimensionless speed of the source U > 0.1 The heat capacity ratio C R is found to have insignificant effect on the domain thermal behavior. However, the deviation between the microscopic and macroscopic models increases as ξ0 decreases. The deviation between the two models is significant within the very early stages of time.

The N—H and O—H bond dissociation energies in 4-hydroxydiphenylamine Ph—NH—C6H4—OH (D NH= 353.4, D OH=339.3 kJ mol–1) and its semiquinone radicals D NH(Ph—NH—C6H4—O·) = 273.6, D OH(Ph—N·—C6H4—OH) = 259.5 kJ mol–1 were first estimated using the parabolic model and experimental data (rate constants) on two elementary reactions with participation of N-phenyl-1,4-benzoquinonemonoimine (2). One of the reactions, namely, that of 2 with aromatic amines, was studied in this work using a specially developed method.

It is discovered that the distribution of density of dislocations in corrosion-resistant steels depends on the type of functional relationship between the yield strength and density of dislocations. For a linear model of hardening, this is a normal distribution. At the same time, for a parabolic model, this is a Weibull-type law with singularity in the region of low densities of dislocations. The distributions obtained for high values of density differ insignificantly.

In this paper we study finite time blow-up of solutions of a hyperbolic model for chemotaxis. Using appropriate scaling this hyperbolic model leads to a parabolic model as studied by Othmer and Stevens (1997) and Levine and Sleeman (1997). In the latter paper, explicit solutions which blow-up in finite time were constructed. Here, we adapt their method to construct a corresponding blow-up solution of the hyperbolic model. This construction enables us to compare the blow-up times of the corresponding models. We find that the hyperbolic blow-up is always later than the parabolic blow-up. Moreover, we show that solutions of the hyperbolic problem become negative near blow-up. We calculate the “zero-turning-rate” time explicitly and we show that this time can be either larger or smaller than the parabolic blow-up time.

This paper deals with interactions among three kinds of nonlinear mechanisms: nonlinear diffusion, nonlinear reaction and nonlinear boundary flux in a parabolic model with multiple nonlinearities. The necessary and sufficient blow-up conditions are established together with blow-up rate estimates for the positive solutions of the problem.

A multiscale finite element simulation is presented to solve a parabolic problem efficiently. This parabolic model has highly oscillatory coefficient, which make the conventional methods expensive costs or bad behaviors. The new multiscale finite element scheme, whose multiscale basis functions may reflect the local strong oscillation, can acquire good simulation on the macroscopical scale. The Euler backward difference time discretization is applied. Our method just computes on the coarse grids and saves plenty of computer resources, and it obtains convergent and controllable errors with the time iterations.

In this paper we present numerical methods for solving a non-linear time-fractional parabolic model. To cope with non-local in time nature of the problem, we exploit the idea of the two-grid method and develop fast numerical algorithms. Moreover, we show that suitable modifications of the standard two-grid technique lead to significant reduction of the computational time. Numerical results are also discussed.

Josef Stern's book “focuses on two elements in the Maimonidean revolution in the study of ta‘amei ha-miṣvot and their impact on Naḥmanides. The first is Maimonides' idea of the problematic commandment. The second is his idea that explanations of commandments—both individual laws and the . . . totality of commandments as a whole . . . should be modelled after the multileveled interpretation of parables” (p. 3). In Chapters Two, Three, and Six, Stern discusses Maimonides' well-known “historically sensitive, context-dependent . . . explanations for the legislation of the ḥuqqim ” (p. 4). While Stern briefly touches upon a number of problems that Maimonides grapples with in light of these explanations, he focuses on “specific arguments the Guide contains to counter the antinomianism implicit in its explanation of the ḥuqqim ” (p. 5). Stern's arguments and readings in these chapters are thoughtful and suggestive, if at times open to question, but space constraints prevent an analysis. hey also prevent my paying more than the barest attention to Stern's remarks about Naḥmanides. Rather, I will concentrate on the second focus of Stern's work, contained in Chapters One, Two, and Five; namely, his understanding of “Maimonides' theory of multileveled parabolic interpretation” (p. 68) and his claim that Maimonides extends this “parabolic model to the explanation of the commandments” (p. 11).

The published data on bimolecular processes of radical generation in chain degradation, polymerisation, oxidation and halogenation reactions of organic compounds are systematised and analysed within the framework of the parabolic model of homolytic bimolecular reactions. The specific features of these highly endothermic reactions are discussed with a special emphasis on their striking similarity to radical abstraction processes with identical reaction centres in the transition state. The feasibility of theoretical evaluation of the activation energies and the rate constants of bimolecular reactions in radical generation is demonstrated. The bibliography includes 86 references.

There are few conventional dating methods that can be used to estimate the geological age of siliceous sediments on the order of 104–105 yr. In contrast, methods such as δ18O are available for dating carbonate-containing sediments in this geological age range. We focused on amino acid chronology as an alternative dating method for siliceous sediments. We analyzed the enantiomeric ratio ( D -isomer/ L -isomer) of aspartic acid (Asp) in bulk diatom assemblages in two siliceous sediment cores collected at Station (St.) 3 (approx. lat. 50°N, long. 165°E) and St. 5 (approx. lat. 40°N, long. 165°E) in the northwestern North Pacific. Radiocarbon and paleomagnetic ages were also obtained from both cores to use as reference ages. Two models, a reversible first-order kinetic model and a parabolic model, were used to determine the relationship between the D / L ratios of Asp and reference ages from the core at St. 5. By using these models, Asp ages were then estimated for the core at St. 3, and these ages were compared to paleomagnetic ages from that core. There was a large difference between Asp ages estimated by the first-order kinetic model and the reference ages. On the other hand, Asp ages estimated by the parabolic model were consistent with the reference ages. Therefore, an Asp dating method using the parabolic model is suitable for dating siliceous sediments. However, although generally the D / L ratio of Asp increased with increasing depth in the core at St. 5, the ratio did not continue to increase below about 10 m depth. The D / L ratio of Asp and the paleomagnetic age at that depth were 0.37 and 350 kyr BP, respectively. Therefore, the Asp racemization reaction apparently does not continue to progress in diatom frustules older than this age. This finding implies that Asp chronology can be used to determine ages up to about 350 kyr BP in sediments composed of diatom ooze. Although the Asp dating method using the parabolic model has a limitation of 350 kyr BP for siliceous sediments, it is available for the estimation of ages on the order of 104–105 yr BP, which is beyond the time range (up to 50 kyr BP) datable by the 14C method.

Retrodisproportionation reactions R"C=NR"" + HY → R"\({\text{C}}^ \cdot\)NHR"" + \({\text{Y}}^ \cdot\), RC≡N + HY → R\({\text{C}}^ \cdot\)=NH + \({\text{Y}}^ \cdot\), RN=NR + HY → R\({\text{N}}^ \cdot\)NHR + \({\text{Y}}^ \cdot\), RNO + HY → R\({\text{N}}^ \cdot\)OH + \({\text{Y}}^ \cdot\), and RNO2 + HY → RN(\({\text{O}}^ \cdot\))OH + \({\text{Y}}^ \cdot\) (where HY represents hydrocarbons, alcohols, phenols, amines, thiophenols, etc.) are considered as sources of radical generation. The enthalpies of these reactions are calculated. The parabolic model is used to calculate the rate constants for 254 such reactions. Various HY compounds acting as hydrogen-atom donors are compared with nitrogen-containing compounds acting as hydrogen-atom acceptors. The PhN(O) and PhNO2 compounds exhibit the highest activity among the studied acceptors.

We consider the term structure modeling by using a appropriate stochastic parabolic system with boundary noises. After finding a sufficient condition for the no arbitrage opportunity, we solve the mean-variance optimal control problem in the incomplete market.

Numerous experimental data for the cyclization of free radicals C·H2(CH2)nCH=CH2 → cyclo-[(CH2)n+1CH(C·H2)], and C·H2(CH2)nCH=CHR → cyclo-[(CH2)n+1C·HCHR] were analyzed in the framework of the parabolic model. The activation energy of thermoneutral (ΔH e = 0) cyclization E e0 decreases linearly with an increase in the energy of cycle strain E rsc: E e0(n) (kJ mol–1) = 85.5 – 0.44E rsc(n) (n is the number of atoms in the cycle). The activation entropy of cyclization ΔS # also depends on the cycle size: the larger the cycle, the lower ΔS #. A linear dependence of ΔS # on the difference between the entropies of formation S° of cyclic hydrocarbon and the corresponding paraffin was found: ΔS # = 1.00[S°(cycle) – S°(CnH2n+2)]. The E e0 values coincide for cyclization reactions with the formation of the six-membered cycle and the bimolecular addition of alkyl radicals to olefins.

International audience; Lane marking detection provides key information for scene understanding in structured environments. Such information has been widely exploited in Advanced Driving Assistance Systems and Autonomous Vehicle applications. This paper presents an enhanced lane marking detection approach intended for low-level perception. It relies on a multi-kernel detection framework with hierarchical weights. First, the de- tection strategy performs in Bird's Eye View (BEV) space and starts with an image filtering using a cell-based blob method. Then, lane marking parameters are optimized following a parabolic model. Finally, a self-assessment process provides an integrity indicator to improve the output performance of detection results. An evaluation using images from a public dataset confirms the effectiveness of the method.

The effect of pretreatment and drying temperature on the drying kinetics and quality of cocoyam was investigated in this study. The best model to predict the drying kinetics was also determined. Cocoyam slices were pretreated by water blanching (WB) and soaking in sodium metabisulphite (SM) and dried in a hot air oven at temperatures of 50, 60 and 70 °C while untreated samples were sun dried. Seventhin layer drying models (Exponential, Generalized Exponential, Page, Logarithmic, Parabolic, Wang and Singh and Two-term) were fitted to the experimental data and selection was done basedon model with highest correlationcoefficient (R2), and lowest reduced chi-square (χ 2), sum square error (SSE) and root mean square error (RMSE) respectively. The Logarithmic and Parabolic model was found to best describe the oven and sun drying of cocoyam respectively. The vitamin C and beta-carotene value of the dried cocoyam slices, which varied from 0.0038 to 0.0075 and 4.1 to 5.888 mg/100 g respectivelygenerally decreased with an increase in drying temperature.

General interpolating expressions, valid for near- and arbitrary overcritical sizes of clusters, are proposed for the nucleation fluxes and distributions. Results are expressed in terms of the deterministic growth rates, and are characterized by a non-Gaussian dependence on the size of nuclei. In a sense, the proposed approximations combine the positive aspects of the parabolic model by Trinkaus and Yoo [Philos. Mag. A 55, 269 (1987)] and of the boundary layer (“matched asymptotic”) solution earlier described by the author [Sov. Phys. Tech. Phys. 32, 76 (1987); 33, 1338 (1988)]. Specifications of the general results are made for several mainstream nucleation models via selection of appropriate growth rates. Examples include surface- and diffusion-limited nucleation in the continuous (Zeldovich–Frenkel) and discrete (Becker–Doring, Turnbull–Fisher) versions of the nucleation equation.

The assumptions of the parabolic model are questioned. These assumptions pertain to an expectation of universal T c optima for cuprates at an “experimental” hole concentration of p = 0.16n, where n is the number of CuO2 planes. This model was developed based on the T c maximum for La2 − x Sr x CuO4 at x = 0.16. However, a variety of cases are presented for higher optimal hole concentrations, including La2CuO4.16, where it is twice as high. Also, the success of a charge order model in universally predicting optimal T c at formal stoichiometric holes, h = 0.5n, suggests a need for expansion of the parabolic model. By quantitatively taking into account the deleterious effect of the blocking layer, optimal T c can be absolutely calibrated at a uniform optimal charge order with alternate holes.

The effect of storage temperature and soluble solids concentration (Brix) on non-enzymatic browning of peach juice concentrate was studied by measuring absorbance at a 420-nm wavelength. The light absorbance of 70°Brix concentrate stored at 3 and 37°C was measured. Comparing the results with literature data for other fruit juices stored at 37°C, it was found that PJC browning rate is noticeably higher. Samples stored at 3, 15 and 30°C in the range of 12°Brix to 89°Brix followed a browning kinetics that can be satisfactorily fitted by means of a parabolic model. The maximum browning rates were found at high solids concentration. Lowering the storage temperature provoked those maximum to shift towards lower concentrations, probably due to the viscosity effect on reacting ions mobility. The browning rate followed an Arrhenius type of dependence upon temperature. It was found that PJC stored at 3°C underwent almost no colour changes, which suggests that it is a good storage option instead of the −20°C adopted by some manufacturers.

Up until the present time, there has been little research devoted to applying a time‐dependent parabolic model to describe wave breaking and wide‐angle wave incidence. The purpose of this paper is to extend the applicability range of the time‐dependent parabolic equation model for both improving the radiation boundary conditions, and including an energy dissipation term in the mild‐slope equation. The wave breaking and energy dissipation model was examined using experimental data. The comparison indicates that the proposed model can adequately predict the behavior of wave breaking and energy dissipation in the surf zone. The computational results also show that the proposed model may improve the conventional treatment of the radiation boundary conditions for wide‐angle wave incidence.

The relative performance and validity of the parabolic-equation model coupled with a modified FLARE procedure for analyzing three-dimensional buoyancy-assisted flow separation in a vertical duct are verified by the full elliptic Navier ? Stokes model. Numerical solutions for the flow and thermal fields are presented, and a comparison between the two models under various heating conditions and over wide ranges of values of Prandtl number (Pr), aspect ratio of the cross section of the duct (B), and buoyancy parameter (Gr/Re) has been made. Results show that the solutions yielded by the parabolic model agree closely with the elliptic-model solutions within the considered parameter ranges. Computation time required in the full elliptic model is approximately 15,000 CPU seconds on a CRAY XMP EA/116se computer to complete a case, whereas the parabolic-model analysis takes only about 2000 CPU seconds or less.

The difference-harmonic susceptibility due to in- tersubband transitions of electrons in quantized metallic films is calculated. The double-resonant contributions to suscepti- bility are analyzed based on the quasi-classical quantization of electron states. The roles of anisotropic and non-parabolic energy spectra are discussed. Numerical results are presented for the parabolic model of the dispersion laws and the bound- ary conditions of the third kind at interfaces.

It has been shown theoretically using a parabolic model of radical reactions that alkyl radicals formed from artemisinin are involved in the rapid intramolecular chain oxidation of artemisinin to a polyfunctional initiator with several hydroperoxy groups.

We present a new technique for long-term global motion estimation of image objects. The estimated motion parameters describe the continuous and time-consistent motion over the whole sequence relatively to a fixed reference coordinate system. The proposed method is suitable for the estimation of affine motion parameters as well as for higher order motion models like the parabolic model-combining the advantages of feature matching and optical flow techniques. A hierarchical strategy is applied for the estimation, first translation, affine motion, and finally higher order motion parameters, which is robust and computationally efficient. A closed-loop prediction scheme is applied to avoid the problem of error accumulation in long-term motion estimation. The presented results indicate that the proposed technique is a very accurate and robust approach for long-term global motion estimation, which can be used for applications such as MPEG-4 sprite coding or MPEG-7 motion description. We also show that the efficiency of global motion estimation can be significantly increased if a higher order motion model is applied, and we present a new sprite coding scheme for on-line applications. We further demonstrate that the proposed estimator serves as a powerful tool for segmentation of video sequences.

The effect of nonparabolicity of conduction band on the electron reflection spectrum of multiquantum barriers (MQB) has been examined. Drastic reduction in the effective barrier height is expected by adopting the nonparabolic model on the MQB which had been designed using the parabolic model for 1.5 μm semiconductor lasers (LDs). The predicted enhancement in barrier height by the MQB is over 600 meV under parabolic model. However, it decreases to 40 meV under nonparabolic model with the same structure. On the other hand, the experimental enhancement in barrier height by the MQB is estimated to be around 30 meV on 1.5 μm LDs, close to the value calculated by nonparabolic model. Those results suggest that a much higher effective barrier height can be realized by optimizing the MQB design taking the nonparabolicity into account. The conduction band nonparabolicity was incorporated by the k⋅p perturbation method.

Exact spherically symmetric solutions of the Einstein equations with quasi-vacuum source p = −e are found in the form of spatially inhomogeneous Tolman metrics describing the inflationary stage of the evolution of the universe.