2,761 results on '"Cubic function"'
Search Results
152. The Analysis of Singularities and Bifurcation of Heteroclinic Loops of Two-Dimensional Cubic Polynomial Systems
- Subjects
Physics ,Mathematical analysis ,General Materials Science ,Gravitational singularity ,Cubic function ,Bifurcation - Published
- 2019
- Full Text
- View/download PDF
153. Polynomial approximate solutions of an unconfined Forchheimer groundwater flow equation
- Author
-
Jeffrey S. Olsen, Jeff Mortensen, and Aleksey S. Telyakovskiy
- Subjects
Polynomial ,010504 meteorology & atmospheric sciences ,Turbulence ,0208 environmental biotechnology ,Groundwater flow equation ,02 engineering and technology ,01 natural sciences ,020801 environmental engineering ,Exponential function ,Physics::Fluid Dynamics ,Quadratic equation ,Applied mathematics ,Boundary value problem ,Scaling ,Cubic function ,0105 earth and related environmental sciences ,Water Science and Technology ,Mathematics - Abstract
We consider a one-dimensional, unconfined groundwater flow equation for the horizontal propagation of water. This equation was derived by using a particular form of the Forchheimer equation in place of Darcy’s Law. Such equations can model turbulent flows in coarse and fractured porous media. For power-law head, exponential head, power-law flux and exponential flux boundary conditions at the inlet, the problems can be reduced, using similarity transformations, to boundary-value problems for a nonlinear ordinary differential equation. We construct quadratic and cubic approximate solutions of these problems. We also numerically compute solutions using a new modification of a method of Shampine, which exploits scaling properties of the governing equation. The polynomial approximate solutions replicate well the numerical solutions and they are easy to use. Last, we compare the predicted wetting front positions from our quadratic and cubic polynomials to predictions based on Adomian polynomials of the same degrees. The work demonstrates the value of polynomial approximate solutions for validating numerical solutions and for obtaining good approximations for water profiles and the extent of water propagation. This work also presents a new application of Shampine’s method for this type of groundwater flow equation. We note that this paper introduces additional classes of approximate solutions for the Forchheimer equation. Up to this date, not many solutions are known, especially for the transient cases considered here.
- Published
- 2019
- Full Text
- View/download PDF
154. Mazur's conjecture and an unexpected rational curve on Kummer surfaces and their superelliptic generalisations
- Author
-
Damián Gvirtz
- Subjects
Pure mathematics ,Algebra and Number Theory ,Conjecture ,010102 general mathematics ,Kummer surface ,01 natural sciences ,Elliptic curve ,Algebraic equation ,Quartic function ,Projective line ,Direct proof ,0101 mathematics ,Cubic function ,Mathematics - Abstract
We prove the following special case of Mazur's conjecture on the topology of rational points. Let $E$ be an elliptic curve over $\mathbb{Q}$ with $j$-invariant $1728$. For a class of elliptic pencils which are quadratic twists of $E$ by quartic polynomials, the rational points on the projective line with positive rank fibres are dense in the real topology. This extends results obtained by Rohrlich and Kuwata-Wang for quadratic and cubic polynomials. For the proof, we investigate a highly singular rational curve on the Kummer surface $K$ associated to a product of two elliptic curves over $\mathbb{Q}$, which previously appeared in publications by Mestre, Kuwata-Wang and Satge. We produce this curve in a simpler manner by finding algebraic equations which give a direct proof of rationality. We find that the same equations give rise to rational curves on a class of more general surfaces extending the Kummer construction. This leads to further applications apart from Mazur's conjecture, for example the existence of rational points on simultaneous twists of superelliptic curves. Finally, we give a proof of Mazur's conjecture for the Kummer surface $K$ without any restrictions on the $j$-invariants of the two elliptic curves.
- Published
- 2019
- Full Text
- View/download PDF
155. Three blocks solvable lattice models and Birman–Murakami–Wenzl algebra
- Author
-
Vladimir Belavin and Doron Gepner
- Subjects
High Energy Physics - Theory ,Physics ,Nuclear and High Energy Physics ,Conformal field theory ,Block (permutation group theory) ,Structure (category theory) ,FOS: Physical sciences ,Mathematical Physics (math-ph) ,Computer Science::Digital Libraries ,Mathematics::Geometric Topology ,Transfer matrix ,Connection (mathematics) ,Knot theory ,Algebra ,Lattice (module) ,High Energy Physics - Theory (hep-th) ,Mathematics::Quantum Algebra ,lcsh:QC770-798 ,lcsh:Nuclear and particle physics. Atomic energy. Radioactivity ,Mathematics::Representation Theory ,Cubic function ,Mathematical Physics - Abstract
Birman--Murakami--Wenzl (BMW) algebra was introduced in connection with knot theory. We treat here interaction round the face solvable (IRF) lattice models. We assume that the face transfer matrix obeys a cubic polynomial equation, which is called the three block case. We prove that the three block theories all obey the BMW algebra. We exemplify this result by treating in detail the $SU(2)$ $2\times 2$ fused models, and showing explicitly the BMW structure. We use the connection between the construction of solvable lattice models and conformal field theory. This result is important to the solution of IRF lattice models and the development of new models, as well as to knot theory., Comment: 16 pages, no figure
- Published
- 2019
- Full Text
- View/download PDF
156. Consistently formulated eddy-viscosity coefficient for k-equation model
- Author
-
Timo Siikonen, Ville Vuorinen, Karri Keskinen, Martti Larmi, Mizanur Rahman, Department of Mechanical Engineering, Energy Conversion, Aalto-yliopisto, and Aalto University
- Subjects
ta222 ,k-equation model ,Computational Mechanics ,ARTIFICIAL COMPRESSIBILITY METHOD ,General Physics and Astronomy ,Reynolds stress ,cubic equation ,01 natural sciences ,turbulence anisotropy ,010305 fluids & plasmas ,Physics::Fluid Dynamics ,FLOWS ,Consistency (statistics) ,0103 physical sciences ,REYNOLDS-STRESS ,0101 mathematics ,Mathematics ,Turbulence ,HOT-WIRE ,Mathematical analysis ,EXPLICIT ,Turbulence modeling ,Condensed Matter Physics ,production-to-dissipation ratio ,010101 applied mathematics ,Mechanics of Materials ,EPSILON ,TURBULENCE ,coefficient of eddy-viscosity ,Cubic function - Abstract
An approach to devising a consistency formulation for Pk/ϵ(production-to-dissipation ratio) is proposed to obtain a non-singular Cμ(coefficient of eddy-viscosity) embedded in the one-equation model based on the turbulent kinetic energy k. The dissipation rate ε is evaluated with an algebraically prescribed length scale having only one adjustable coefficient, accompanied by an anisotropic function qϵ enhancing the dissipation in non-equilibrium flow regions. The model accounts for the distinct effects of low Reynolds number (LRN) and wall proximity. The stress-intensity ratio Rb = u1u2/k is formulated as a function of local variables without resorting to a constant √C* μ= 0.3. The parameters Rb and Pk/ϵ entering the turbulence production Pk prevents presumably the overestimation of Pk in flow regions where non-equilibrium effects could result in a misalignment between turbulent stress and mean strain rate with a linear eddy-viscosity model. A comparative assessment of the present model with the Spalart–Allmaras (SA) one-equation model and the shear stress transport (SST) k–ω model is provided for well-documented simple and non-equilibrium turbulent flows. Finally, the current model provides a proposal to compute free shear flows.
- Published
- 2019
- Full Text
- View/download PDF
157. Prediction of N, P, and K Contents in Sugarcane Leaves by VIS-NIR Spectroscopy and Modeling of NPK Interaction Effects
- Author
-
Xiao Chen, Ce Yang, Ce Wang, Lijia Wang, Shaodui Ma, Minzan Li, and Li Xiuhua
- Subjects
010504 meteorology & atmospheric sciences ,Vis nir spectroscopy ,Biomedical Engineering ,Analytical chemistry ,Soil Science ,Sampling (statistics) ,Forestry ,Regression analysis ,04 agricultural and veterinary sciences ,Interaction ,01 natural sciences ,Spectral line ,Linear regression ,Correlation analysis ,040103 agronomy & agriculture ,0401 agriculture, forestry, and fisheries ,Agronomy and Crop Science ,Cubic function ,0105 earth and related environmental sciences ,Food Science ,Mathematics - Abstract
Methods were studied to predict the N, P, and K contents in sugarcane leaves quickly and accurately at the seedling, tillering, and elongation stages from leaf spectral reflectance. A total of 117 valid leaf samples were used to obtain leaf spectral reflectance with an indoor VIS-NIR spectrophotometer. Using the spectral data processed by CARS-PCA as an independent variable, a six-fold cross-validated PLS model for N, P, and K contents was established. The R2 values of the CARS-PCA-PLS models for N, P, and K prediction were 0.859, 0.677, and 0.932, respectively. Correlation analysis of the predicted N, P, and K contents was performed to explore the interaction effects between N, P, and K. To simulate the interaction effects among the three nutrients, 19 factors were assumed, including possible linear, quadratic, and cubic relationships between N, P, and K, and multi-factor cubic polynomial PLS and MLR regression models were established from those factors. In the modified MLR models, the determinants of N, P, and K were 0.891, 0.802, and 0.944, respectively, which improved the performance of the models by 3.7%, 18.5%, and 1.3%, respectively, compared with the CARS-PCA-PLS models, which were based on the spectral reflectance data. The results showed that application of VIS-NIR spectra combined with interaction effects between the nutrients could effectively predict the N, P, and K contents in the early and middle growth stages of sugarcane.HighlightsCompetitive adaptive reweighted sampling (CARS) was adopted to select wavebands for nutrient prediction.N, P, and K interaction effects were simulated with 19 factors, including linear, quadratic, and cubic relationships.The interaction factors were used in multiple linear regression models, and improved prediction was achieved. Keywords: CARS-PCA, Interaction effect, NPK, Sugarcane, VIS-NIR spectroscopy.
- Published
- 2019
- Full Text
- View/download PDF
158. Qualitative Analysis of a Class of Cubic Polynomial Systems
- Subjects
Class (set theory) ,Pure mathematics ,Qualitative analysis ,Cubic function ,Mathematics - Published
- 2019
- Full Text
- View/download PDF
159. Long-time solutions of scalar nonlinear hyperbolic reaction equations incorporating relaxation I. The reaction function is a bistable cubic polynomial
- Author
-
Andrew P. Bassom and J. A. Leach
- Subjects
Differential equation ,Applied Mathematics ,010102 general mathematics ,Scalar (mathematics) ,01 natural sciences ,Method of matched asymptotic expansions ,010101 applied mathematics ,Nonlinear system ,Step function ,Attractor ,0101 mathematics ,Cubic function ,Analysis ,Dimensionless quantity ,Mathematics ,Mathematical physics - Abstract
We consider an initial-value problem based on a class of scalar nonlinear hyperbolic reaction–diffusion equations of the general form u τ τ + u τ = u x x + e ( F ( u ) + F ( u ) τ ) , in which x and τ represent dimensionless distance and time respectively and e > 0 is a parameter related to the relaxation time. Furthermore the reaction function, F ( u ) , is given by the bistable cubic polynomial, F ( u ) = u ( 1 − u ) ( u − μ ) , in which 0 μ 1 / 2 is a parameter. The initial data is given by a simple step function with u ( x , 0 ) = 1 for x ≤ 0 and u ( x , 0 ) = 0 for x > 0 . It is established, via the method of matched asymptotic expansions, that the large-time structure of the solution to the initial-value problem involves the evolution of a propagating wave front which is either of reaction–diffusion or of reaction–relaxation type. The one exception to this occurs when μ = 1 2 in which case the large time attractor for the solution of the initial-value problem is a stationary state solution of kink type centred at the origin.
- Published
- 2019
- Full Text
- View/download PDF
160. Liquid balance - steam for methanol mixing - Benzen using the Peng Robinson and Van-Laar models
- Author
-
Natalia Prieto-Jiménez, Miguel Fernando Palencia Muñoz, and Germán González Silva
- Subjects
Activity coefficient ,Materials science ,020209 energy ,General Engineering ,Mixing (process engineering) ,Thermodynamics ,02 engineering and technology ,chemistry.chemical_compound ,Dew point ,020401 chemical engineering ,chemistry ,0202 electrical engineering, electronic engineering, information engineering ,Fugacity ,Methanol ,Binary system ,Bubble point ,0204 chemical engineering ,Cubic function - Abstract
This paper is related to the procedure for calculating curves dew point and bubble point of a binary system, consisting of the methanol and benzene mixture to 45°C, using the Peng-Robinson cubic equation to calculate the fugacity coefficient of gas i in the mixture, and Van Laar model to calculate the activity coefficient of component i in the liquid mixture. Then a comparison between the theoretical data with the experimental data and later with the commercial simulator Hysys-Aspen, which applies the model of Wilson. The simulation was validated with experimental data,in addition to comparing the results with a commercial simulator.
- Published
- 2019
- Full Text
- View/download PDF
161. Classification of cubic equations
- Author
-
Juozas Juvencijus Mačys and Jurgis Sušinskas
- Subjects
quartics ,rational solutions ,lcsh:Mathematics ,cubics ,Applied mathematics ,Fourth degree ,algebraic solutions ,trigonometric solutions ,lcsh:QA1-939 ,Cubic function ,Mathematics - Abstract
Rather unexpectably all real equations of the fourth degree are solvable by real means. So we canclassify all real equations of the third and fourth degree. In this article we classify real cubics. Thereal quartics will be classified in another article.
- Published
- 2018
- Full Text
- View/download PDF
162. Noninteger Root Transformations for Preprocessing Nanoelectrospray Ionization High-Resolution Mass Spectra for the Classification of Cannabis
- Author
-
Peter de B. Harrington and Yue Tang
- Subjects
Principal Component Analysis ,Spectrometry, Mass, Electrospray Ionization ,Support Vector Machine ,Plant Extracts ,Dynamic range ,Chemistry ,Discriminant Analysis ,Mass spectrometry ,Linear discriminant analysis ,Analytical Chemistry ,Support vector machine ,Square root ,Ionization ,Mass spectrum ,Least-Squares Analysis ,Biological system ,Cubic function ,Cannabis - Abstract
Typically, for measurements with a high dynamic range, the range is reduced by using the square root transform. By using noninteger roots coupled with systematic experimental design, improvements to the measurements may be obtained. The effect of using noninteger root transformation was evaluated using high-resolution mass spectrometry (HRMS) combined with nanoelectrospray ionization (Nano-ESI) to differentiate 23 samples of Cannabis. The mass spectra were evaluated and classified using different mass resolving powers and noninteger root transformations. Classification was achieved by super partial least-squares discriminant analysis (sPLS-DA), support vector machine (SVM), and SVM classification tree type entropy (SVMTreeH). The 2.5 root transformation gave the best overall performance at different resolving powers for chemical profiling from a multilevel factorial experimental design using 2 factors and more than 4 levels. Response surface modeling using a cubic polynomial model of the bootstrapped sPLS-DA average prediction accuracies yielded optima at 0.005 for resolving power and 2.3 for the root transformation. Root transformation is an important spectral preprocessing tool for decreasing the dynamic range so that the relative variance of smaller but more important features may be inflated. For the classification of Cannabis using Nano-ESI, the optimal ranges of root and resolution were broad. The chasing-the-optimum method has been introduced for refining the polynomial response surface model.
- Published
- 2018
- Full Text
- View/download PDF
163. Bifurcations of Traveling Wave Solutions for a Modified Novikov’s Cubic Equation
- Author
-
Minzhi Wei
- Subjects
Dynamical systems theory ,Applied Mathematics ,Mathematical analysis ,Breaking wave ,01 natural sciences ,010101 applied mathematics ,Bifurcation theory ,0103 physical sciences ,Traveling wave ,Discrete Mathematics and Combinatorics ,Novikov self-consistency principle ,0101 mathematics ,010301 acoustics ,Cubic function ,Bifurcation ,Mathematics - Abstract
Exact traveling solutions for a modified Novikov’s cubic equation is considered based on the bifurcation method of dynamical systems in this paper. The two-dimensional system of modified Novikov’s cubic equation exists singular curve $$\phi ^2+a^2y^2=R$$ when $$R>0$$ and then it is proved that the corresponding traveling wave system of the modified Novikov’s cubic equation exists smooth solitary wave solutions and breaking wave solutions.
- Published
- 2018
- Full Text
- View/download PDF
164. Optimal Families of Perfect Polyphase Sequences from Cubic Polynomials
- Author
-
Hong Yeop Song and Min Kyu Song
- Subjects
Combinatorics ,Applied Mathematics ,Signal Processing ,Polyphase system ,Electrical and Electronic Engineering ,Computer Graphics and Computer-Aided Design ,Cubic function ,Mathematics - Published
- 2018
- Full Text
- View/download PDF
165. Predicting Nonlinear Wave Trough Distributions Utilizing A Transformed Linear Simulation Method
- Author
-
Ying-guang Wang
- Subjects
Hermite polynomials ,Renewable Energy, Sustainability and the Environment ,Mechanical Engineering ,020101 civil engineering ,Ocean Engineering ,Monotonic function ,02 engineering and technology ,Sea state ,Oceanography ,Trough (economics) ,01 natural sciences ,010305 fluids & plasmas ,0201 civil engineering ,Nonlinear system ,Distribution (mathematics) ,Transformation (function) ,0103 physical sciences ,Applied mathematics ,Cubic function ,Mathematics - Abstract
This paper first proposes a new approach for predicting the nonlinear wave trough distributions by utilizing a transformed linear simulation method. The linear simulation method is transformed based on a Hermite transformation model where the transformation is chosen to be a monotonic cubic polynomial and calibrated such that the first four moments of the transformed model match the moments of the true process. The proposed new approach is applied for calculating the wave trough distributions of a nonlinear sea state with the surface elevation data measured at the coast of Yura in the Japan Sea, and its accuracy and efficiency are convincingly validated by comparisons with the results from two theoretical distribution models, from a linear simulation model and a second-order nonlinear simulation model. Finally, it is further demonstrated in this paper that the new approach can be applied to all the situations characterized by similar nondimensional spectrum.
- Published
- 2018
- Full Text
- View/download PDF
166. Simple correlation for critical isotherm of pure compounds
- Author
-
Sparsh Ganju, Sunil S. Bhagwat, Prafullachandra P. Vora, and Ashwin Kane
- Subjects
Physics ,Imagination ,Chemical substance ,010304 chemical physics ,Applied Mathematics ,General Chemical Engineering ,Simple equation ,media_common.quotation_subject ,General Chemistry ,010402 general chemistry ,01 natural sciences ,Industrial and Manufacturing Engineering ,Ideal gas ,0104 chemical sciences ,Critical point (thermodynamics) ,0103 physical sciences ,Statistical physics ,Simple correlation ,Cubic function ,media_common - Abstract
A volumetric equation of state (PVT behavior of a fluid) is often based on a critical isotherm. Soave-Redlich-Kwong and Peng-Robinson are by far the most popular cubic equations of state. These equations use the first and second differential conditions at the critical point to obtain the parameters but fail to reproduce the P-V-T behavior near the critical point. A new simple equation is proposed for the critical isotherm which matches experimental data for a variety of molecules in the entire range from critical point to ideal gas condition as well as the liquid region. The new proposed critical isotherm equation matches experimental data of a wide variety of compounds much better than these cubic equations of state employed commonly.
- Published
- 2018
- Full Text
- View/download PDF
167. The dynamic stability of physically nonlinear plate systems under biaxial compression
- Author
-
Sergey Pavlovich Ivanov, Oleg Gennadevich Ivanov, and A S Ivanova
- Subjects
Differential equation ,Mathematical analysis ,пластинчатая система ,энергетический метод ,Displacement (vector) ,Numerical integration ,динамическая устойчивость ,symbols.namesake ,Nonlinear system ,lcsh:Architectural engineering. Structural engineering of buildings ,Buckling ,Deflection (engineering) ,lcsh:TH845-895 ,Euler's formula ,symbols ,пластина ,сжимающая нагрузка ,физическая нелинейность ,Cubic function ,вариационный метод Власова ,Mathematics - Abstract
The article presents the method of dynamic stability analysis of plate systems with nonshifting ribs. A plate system under the biaxial dynamic compression loads is considered. The Kirchhoff - Love hypotheses, the nonlinear-elastic body hypothesis are considered the basis of the calculations. The material of the plate system is assumed to be physically nonlinear, stress-deformation diagram is approximated in the form of a cubic polynomial. The displacement of points in normal direction to middle plane of plates is presented in the form of Vlasov expansion. To derive the basic differential equations of stability, the strainenergy method and Vlasov's variation method are used. The extreme value of total energy of the system is defined using Euler - Lagrange equation, after solving of which the set of basic nonlinear differential equations of buckling of the plate system with non-shifting ribs under dynamic compression loads is given. As an example, the stability calculation of physically nonlinear T-shaped plate system hinge-supported along the contour is carried out. Buckling of the plate system occurs longitudinally on one half-wave of sinusoid. At the solution of a task in the first approximation, a nonlinear differential equation is derived, the numerical integration of which was carried out by the Runge - Kutta method. Based on the results of the calculations, graphs of the relative magnitude of deflection against the dynamic coefficient are plotted. The influence of the degree of physical nonlinearity of the material, the rate of change of the dynamic compressive load on the dynamic criterion of buckling of the plate system was studied.
- Published
- 2018
168. On the temperature dependence of the α function in the cubic equation of state
- Author
-
Fufang Yang, Qiang Liu, Yuanyuan Duan, and Zhen Yang
- Subjects
Physics ,Applied Mathematics ,General Chemical Engineering ,Extrapolation ,Thermodynamics ,Monotonic function ,02 engineering and technology ,General Chemistry ,021001 nanoscience & nanotechnology ,Heat capacity ,Industrial and Manufacturing Engineering ,Supercritical fluid ,symbols.namesake ,020401 chemical engineering ,Virial coefficient ,symbols ,Isobar ,0204 chemical engineering ,van der Waals force ,0210 nano-technology ,Cubic function - Abstract
The cubic equation of state (EoS) is widely applied for modeling fluid thermodynamic properties in chemical processes. However, in the absence of a distinguishable reference property, the supercritical extrapolation of its only temperature-dependent parameter, the α function, resulted in nonphysical prediction of supercritical virial coefficients and heat capacities. From a theoretical perspective, we here rigorously derive the universal temperature-dependent behavior of the α function, using the generalized van der Waals theory without specifying the interaction potential. To isolate the behavior of the α function from the EoS structure, we examine the thermodynamic functions of realistic fluids at low densities. Our study reveals that the α function is finite, positive, and monotonically decreases with increasing temperature. We present a set of thermodynamic requirements and accordingly revise the predictive Soave and Twu α functions for the Redlich-Kwong and Peng-Robinson EoSs. Our study shows that the revised α functions avoid the divergent virial coefficients at infinite temperature, and the nonphysical bump on the heat capacity isobars immediately above the critical temperature, demonstrating the imperative need for thermodynamic requirements for the temperature dependence of the α function. Joule-Thomson inversion curve and vapor-liquid equilibria are also investigated.
- Published
- 2018
- Full Text
- View/download PDF
169. Oil spill modeling in deep waters: Estimation of pseudo-component properties for cubic equations of state from distillation data
- Author
-
Anusha L. Dissanayake, Meghan M. Daniels, Christopher H. Barker, Scott A. Socolofsky, Jonas Gros, and William Lehr
- Subjects
Databases, Factual ,010504 meteorology & atmospheric sciences ,010501 environmental sciences ,Aquatic Science ,Oceanography ,01 natural sciences ,law.invention ,chemistry.chemical_compound ,Viscosity ,law ,Component (UML) ,Water Pollution, Chemical ,Surface Tension ,Computer Simulation ,Petroleum Pollution ,Seawater ,Distillation ,Ecosystem ,0105 earth and related environmental sciences ,Petroleum engineering ,Pollution ,Hydrocarbons ,Petroleum ,chemistry ,Oil spill ,Cubic function ,Water Pollutants, Chemical - Abstract
Highlights • Pseudo-components for high-pressure deep-water oil spill models • Estimation of Peng-Robinson EOS parameters for distillation-cut pseudo-components • Modeling of the non-ideal chemistry of hydrocarbons in deep waters • New correlations to calculate chemical properties of petroleum fractions • Validated with 614 oils from the ADIOS oil library Abstract Deep-water oil spills represent a major, localized threat to marine ecosystems. Multi-purpose computer models have been developed to predict the fate of spilled oil. These models include databases of pseudo-components from distillation cut analysis for hundreds of oils, and have been used for guiding response action, damage assessment, and contingency planning for marine oil spills. However, these models are unable to simulate the details of deep-water, high-pressure chemistry. We present a new procedure to calculate the chemical properties necessary for such simulations that we validate with 614 oils from the ADIOS oil library. The calculated properties agree within 20.4% with average values obtained from data for measured compounds, for 90% of the chemical properties. This enables equation-of-state calculations of dead oil density, viscosity, and interfacial tension. This procedure enables development of comprehensive oil spill models to predict the behavior of petroleum fluids in the deep sea.
- Published
- 2018
- Full Text
- View/download PDF
170. Vehicle Path Prediction Using Yaw Acceleration for Adaptive Cruise Control
- Author
-
Wonhee Kim, Chang Mook Kang, Seung-Hi Lee, Young Seop Son, and Chung Choo Chung
- Subjects
Computer science ,Mechanical Engineering ,020208 electrical & electronic engineering ,Yaw ,020302 automobile design & engineering ,02 engineering and technology ,Curvature ,Computer Science Applications ,Computer Science::Robotics ,Acceleration ,0203 mechanical engineering ,Control theory ,Automotive Engineering ,Headway ,0202 electrical engineering, electronic engineering, information engineering ,Physics::Accelerator Physics ,Image sensor ,Cubic function ,Cruise control - Abstract
In this paper, we propose a vehicle path prediction employing yaw acceleration for adaptive cruise control (ACC). First, a path prediction method employing yaw acceleration is proposed to improve the path prediction performance of ego vehicles. In the proposed method, the vehicle path is predicted by using a clothoidal cubic polynomial curve model, and for this purpose, the curvature rate, yaw rate, and longitudinal velocity are required. The curvature rate can be mathematically obtained by differentiating the yaw rate without a camera sensor. To obtain the yaw acceleration from the noisy measured yaw rate, we derive the state-space model from the steer wheel angle for the yaw rate. Then, the KF is designed by using the state-space model to estimate the yaw acceleration. Second, a multirate longitudinal control method is proposed to improve the longitudinal control performance. The multirate KF employs the constant acceleration model in order to estimate the relative distance and velocity of the target vehicle at a faster sampling rate. Then, the desired acceleration is achieved to maintain a safe headway distance or velocity by means of the longitudinal controller. Consequently, the whole ACC system operates with a faster sampling rate so that multirate control scheme reduces ripples in both the relative longitudinal distance and the desired acceleration. The performance of the proposed method was evaluated via simulations and experiments.
- Published
- 2018
- Full Text
- View/download PDF
171. Atomic-Number Similarity of the K and L X-Ray Terms in Multielectron Atoms
- Author
-
G. V. Shpatakovskaya
- Subjects
Physics ,Physics and Astronomy (miscellaneous) ,Similarity (network science) ,Solid-state physics ,0103 physical sciences ,X-ray ,Atomic number ,Atomic physics ,010306 general physics ,010303 astronomy & astrophysics ,01 natural sciences ,Cubic function - Abstract
Dependences of experimental K, LI, LII, and LIII X-ray levels on the atomic number different from Moseley’s law have been revealed. The simplest cubic polynomial approximations of the found dependences make it possible not only to describe experimental data with an accuracy better than one percent but also to control their reliability.
- Published
- 2018
- Full Text
- View/download PDF
172. Three recipes for quasi-interpolation with cubic Powell–Sabin splines
- Author
-
Jan Grošelj and Hendrik Speleers
- Subjects
Local super-smoothness ,Cubic precision ,Aerospace Engineering ,Cubic B-spline basis ,010103 numerical & computational mathematics ,Bivariate analysis ,Quasi-interpolation ,Type (model theory) ,01 natural sciences ,Settore MAT/08 - Analisi Numerica ,symbols.namesake ,Cubic Powell-Sabin splines ,Applied mathematics ,0101 mathematics ,Mathematics ,Smoothness ,Hermite polynomials ,Lagrange polynomial ,Computer Graphics and Computer-Aided Design ,010101 applied mathematics ,Large set (Ramsey theory) ,Modeling and Simulation ,Automotive Engineering ,symbols ,Cubic function ,Interpolation - Abstract
We investigate the construction of bivariate quasi-interpolation methods based on C 1 cubic Powell–Sabin B-spline representations. Rather than using a large set of functional data to specify all the parameters in such representations, we study how to reduce them by imposing different super-smoothness properties while retaining cubic precision. This results in three recipes, which are completely general in the sense that they can be implemented with any local cubic polynomial approximation scheme (or a mixture of them). More precisely, they embed C 2 super-smoothness at the vertices and across the edges, C 2 super-smoothness inside the macro-triangles, and smoothness of Clough–Tocher type, respectively. To demonstrate their usefulness, we derive four specific methods based on local Hermite and Lagrange interpolation. We conclude with a selection of numerical experiments.
- Published
- 2018
- Full Text
- View/download PDF
173. Parameter estimation for cubic equations of state models subject to sufficient criteria for thermodynamic stability
- Author
-
Hatim Djelassi, Moll Helene Glass, and Alexander Mitsos
- Subjects
021103 operations research ,Estimation theory ,Applied Mathematics ,General Chemical Engineering ,0211 other engineering and technologies ,Structure (category theory) ,02 engineering and technology ,General Chemistry ,State (functional analysis) ,Industrial and Manufacturing Engineering ,Constraint (information theory) ,020401 chemical engineering ,Subject (grammar) ,Applied mathematics ,Chemical stability ,0204 chemical engineering ,Process simulation ,Cubic function ,Mathematics - Abstract
A formulation for parameter estimation in cubic equations of state (CEOS) models for phase equilibrium thermodynamics is proposed. This formulation guarantees for the regressed parameters that the predicted mole fractions correspond to stable equilibria, when standard methods fail and demonstrably entail erroneous process simulation results. The present formulation overcomes these deficiencies, which is predicated on a bilevel structure extending Mitsos et al. (2009a). That is, an upper-level (parameter fitting) problem is minimized, subject to multiple lower-level problems, which encode thermodynamic stability. The CEOS constitutes an equality constraint on the lower level, which adds to the difficulty of the bilevel program. For the VLE of C5H12/H2S, it is demonstrated that the method permits an acceptable fit with physically sensible CEOS root values. Thus, the regressed parameter values may be applied to, e.g., process simulation.
- Published
- 2018
- Full Text
- View/download PDF
174. Centrifugal Compressor Polytropic Performance—Improved Rapid Calculation Results—Cubic Polynomial Methods
- Author
-
Fred Evans and Matt Taher
- Subjects
Real gas ,compressor performance test ,polytropic path ,Energy Engineering and Power Technology ,Aerospace Engineering ,02 engineering and technology ,01 natural sciences ,010305 fluids & plasmas ,0203 mechanical engineering ,0103 physical sciences ,TJ1-1570 ,Range (statistics) ,Applied mathematics ,Mechanical engineering and machinery ,temperature-entropy ,Mathematics ,Mechanical Engineering ,Centrifugal compressor ,Polytropic process ,020303 mechanical engineering & transports ,real gas ,Path (graph theory) ,polytropic process ,piecewise cubic polynomial approximation ,Constant (mathematics) ,Cubic function ,Gas compressor ,ASME PTC-10 - Abstract
This paper presents a new improved approach to calculation of polytropic performance of centrifugal compressors. This rapid solution technique is based upon a constant efficiency, temperature-entropy polytropic path represented by cubic polynomials. New thermodynamic path slope constraints have been developed that yield highly accurate results while requiring fewer computing resources and reducing computing elapsed time. Applying this thermodynamically sound cubic polynomial model would improve accuracy and shorten compressor performance test duration at a vendor’s shop. A broad range of example case results verify the accuracy and ease of use of the method. The example cases confirm the cubic polynomial methods result in lower calculation uncertainty than other methods.
- Published
- 2021
- Full Text
- View/download PDF
175. Complex-valued Joint Eigenvalue Decomposition Based on LU Decomposition and Successive Rotations
- Author
-
Xiao-Feng Gong, Luming Wang, Fei Xiang, and Yawen Deng
- Subjects
MathematicsofComputing_NUMERICALANALYSIS ,020206 networking & telecommunications ,02 engineering and technology ,Rotation matrix ,LU decomposition ,Matrix decomposition ,law.invention ,Matrix (mathematics) ,law ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,020201 artificial intelligence & image processing ,Rotation (mathematics) ,Cubic function ,Eigenvalues and eigenvectors ,Eigendecomposition of a matrix ,Mathematics - Abstract
In this paper, we propose a complex-valued joint eigenvalue decomposition(C-JEVD) algorithm based on LU de-composition and successive rotations. The proposed algorithm factorizes the matrix of eigenvectors into a lower-triangular matrix and an upper-triangular matrix, and update these two matrices using successive rotations. In each rotation, the elementary rotation matrix contains only one complex-valued parameter, which could be easily obtained via solving a cubic equation. Therefore, the proposed algorithm has low complexity. The proposed algorithm is compared with other C-JEVD methods through simulations.
- Published
- 2021
- Full Text
- View/download PDF
176. WITHDRAWN: An efficient method for determining DEM parameters of a loose cohesive soil modelled using Hysteretic Spring and Linear Cohesion contact models
- Author
-
Wuquan Wei, Qingkai Zhang, Yuxiang Huang, Zuoli Fu, Xuezhen Wang, and Jinpu He
- Subjects
Moisture ,Rolling resistance ,Forestry ,Aquatic Science ,Angle of repose ,Computer Science Applications ,Spring (device) ,Soil water ,Cohesion (geology) ,Animal Science and Zoology ,Geotechnical engineering ,Agronomy and Crop Science ,Water content ,Cubic function ,Mathematics - Abstract
Appropriate determination of discrete element modelling (DEM) parameters is essential for accurate predictions of soil properties and disturbance behaviours in agriculture. In this paper, DEM parameters of a loose cohesive soil modelled using Hysteretic Spring and Linear Cohesion contact models were determined by a combination of Plackett-Burman (PB) test, Steepest Ascent test and Central Composite test. The accuracies of DEM models developed under different soil moisture contents (ranging from 0.27 to 22 %) were evaluated using slumping angle of repose (SAOR) test and funnelling angle of repose (FAOR) test. The results showed that heap angles under different soil moisture contents decreased quadratically with time with determination coefficients ranging from 0.750 2 to 0.969. For the given soil, friction or rolling friction coefficient of soil-soil changed with a cubic function as moisture content increased. Similar coefficients of friction (from 0.23 to 0.25) and rolling friction (from 0.038 to 0.049) of soil-soil were found for soils with moisture contents from 12 to 22 %. Based on the analysis of variance (ANOVA) outputs, soil properties tested were significantly affected by soil moisture content at p
- Published
- 2021
- Full Text
- View/download PDF
177. An analysis about analytical calculation of volume roots from cubic equations of state
- Author
-
Vilmar Steffen and Edson Antonio da Silva
- Subjects
Physics ,Environmental Engineering ,Volume (thermodynamics) ,General Chemical Engineering ,Mathematical analysis ,State (functional analysis) ,Root-finding algorithm ,Cubic function ,Biotechnology - Published
- 2021
- Full Text
- View/download PDF
178. Lower bounds for the local cyclicity for families of centers
- Author
-
Jaume Giné, Luiz F.S. Gouveia, Joan Torregrosa, Univ Lleida, Univ Autonoma Barcelona, Universidade Estadual Paulista (Unesp), and Ctr Recerca Matemat
- Subjects
Pure mathematics ,Class (set theory) ,Lyapunov constants ,Applied Mathematics ,Small-amplitude limit cycle ,010102 general mathematics ,Holomorphic function ,Higher order developments and parallelization ,Higher-order developments and parallelization ,Center (group theory) ,01 natural sciences ,010101 applied mathematics ,Polynomial vector field ,Quartic function ,Center cyclicity ,Vector field ,Limit (mathematics) ,0101 mathematics ,Cubic function ,Analysis ,Bifurcation ,Mathematics - Abstract
Made available in DSpace on 2021-06-25T12:30:34Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-02-25 Catalan AGAUR Spanish Ministerio de Ciencia, Innovacion y Universidades -Agencia estatal de investigacion European Community Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) In this paper, we are interested in how the local cyclicity of a family of centers depends on the parameters. This fact was pointed out in [21], to prove that there exists a family of cubic centers, labeled by C D-31(12) in [25], with more local cyclicity than expected. In this family, there is a special center such that at least twelve limit cycles of small amplitude bifurcate from the origin when we perturb it in the cubic polynomial general class. The original proof has some crucial missing points in the arguments that we correct here. We take advantage of a better understanding of the bifurcation phenomenon in nongeneric cases to show two new cubic systems exhibiting 11 limit cycles and another exhibiting 12. Finally, using the same techniques, we study the local cyclicity of holomorphic quartic centers, proving that 21 limit cycles of small amplitude bifurcate from the origin, when we perturb in the class of quartic polynomial vector fields. (C) 2020 Elsevier Inc. All rights reserved. Univ Lleida, Dept Matemat, Avda Jaume II 69, Lleida 6925001, Catalonia, Spain Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Catalonia, Spain Univ Estadual Paulista, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, Brazil Ctr Recerca Matemat, Campus Bellaterra, Barcelona 08193, Catalonia, Spain Univ Estadual Paulista, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, Brazil Catalan AGAUR: 2017SGR1617 Catalan AGAUR: 2017SGR127 Spanish Ministerio de Ciencia, Innovacion y Universidades -Agencia estatal de investigacion: MTM2017-84383-P Spanish Ministerio de Ciencia, Innovacion y Universidades -Agencia estatal de investigacion: PID2019-104658GB-I00 European Community: H2020-MSCA-RISE-2017-777911 CNPq: 200484/2015-0 FAPESP: 2020/04717-0
- Published
- 2021
179. Recursion orders for weights of Boolean cubic rotation symmetric functions.
- Author
-
Cusick, Thomas W. and Johns, Bryan
- Subjects
- *
BOOLEAN functions , *SYMMETRIC functions , *RECURSION theory , *CRYPTOGRAPHY , *PROBLEM solving , *HAMMING distance - Abstract
Rotation symmetric (RS) Boolean functions have been extensively studied in recent years because of their applications in cryptography. In cryptographic applications, it is usually important to know the weight of the functions, so much research has been done on the problem of determining such weights. Recently it was proved that for cubic RS functions in n variables generated by a single monomial, the weights of the functions as n increases satisfy a linear recursion. Furthermore, explicit methods were found for generating these recursions and the initial values needed to use the recursions. It is important to be able to compute the order of these recursions without needing to determine all of the coefficients. This paper gives a technique for doing that in many cases, based on a new notion of towers of RS Boolean functions. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
180. Assessment of Cubic Equations of State: Machine Learning for Rich Carbon-Dioxide Systems
- Author
-
George Truc, Nejat Rahmanian, and Mahboubeh Pishnamazi
- Subjects
Equation of state ,Finite-state machine ,Artificial neural network ,Environmental effects of industries and plants ,Renewable Energy, Sustainability and the Environment ,Geography, Planning and Development ,Relative standard deviation ,Thermodynamics ,TJ807-830 ,02 engineering and technology ,Management, Monitoring, Policy and Law ,021001 nanoscience & nanotechnology ,equation of state (EoS) ,TD194-195 ,Renewable energy sources ,Environmental sciences ,machine learning ,020401 chemical engineering ,fluid package selection ,GE1-350 ,0204 chemical engineering ,carbon capture systems (CCS) ,0210 nano-technology ,Cubic function ,Mathematics - Abstract
Carbon capture and storage (CCS) has attracted renewed interest in the re-evaluation of the equations of state (EoS) for the prediction of thermodynamic properties. This study also evaluates EoS for Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK) and their capability to predict the thermodynamic properties of CO2-rich mixtures. The investigation was carried out using machine learning such as an artificial neural network (ANN) and a classified learner. A lower average absolute relative deviation (AARD) of 7.46% was obtained for the PR in comparison with SRK (AARD = 15.0%) for three components system of CO2 with N2 and CH4. Moreover, it was found to be 13.5% for PR and 19.50% for SRK in the five components’ (CO2 with N2, CH4, Ar, and O2) case. In addition, applying machine learning provided promise and valuable insight to deal with engineering problems. The implementation of machine learning in conjunction with EoS led to getting lower predictive AARD in contrast to EoS. An of AARD 2.81% was achieved for the three components and 12.2% for the respective five components mixture.
- Published
- 2021
181. First integrals and phase portraits of planar polynomial differential cubic systems with the maximum number of invariant straight lines
- Author
-
Cristina Bujac, Jaume Llibre, and Nicolae Vulpe
- Subjects
Phase portrait ,Invariant polynomial ,Applied Mathematics ,010102 general mathematics ,First integrals ,Multiplicity (mathematics) ,01 natural sciences ,010101 applied mathematics ,Combinatorics ,Planar ,Discrete Mathematics and Combinatorics ,Algebraic curve ,0101 mathematics ,Invariant (mathematics) ,Cubic function ,Mathematics - Abstract
In the article Llibre and Vulpe (Rocky Mt J Math 38:1301–1373, 2006) the family of cubic polynomial differential systems possessing invariant straight lines of total multiplicity 9 was considered and 23 such classes of systems were detected. We recall that 9 invariant straight lines taking into account their multiplicities is the maximum number of straight lines that a cubic polynomial differential systems can have if this number is finite. Here we complete the classification given in Llibre and Vulpe (Rocky Mt J Math 38:1301–1373, 2006) by adding a new class of such cubic systems and for each one of these 24 such classes we perform the corresponding first integral as well as its phase portrait. Moreover we present necessary and sufficient affine invariant conditions for the realization of each one of the detected classes of cubic systems with maximum number of invariant straight lines when this number is finite.
- Published
- 2021
182. Fast Matrix Based Computation of Eigenvalues in PolSAR Data
- Author
-
Allan Aasbjerg Nielsen
- Subjects
Matrix (mathematics) ,Quadratic equation ,Computation ,Applied mathematics ,Solver ,Row and column spaces ,Cubic function ,Hermitian matrix ,Eigenvalues and eigenvectors ,Mathematics - Abstract
We describe calculation of eigenvalues of 2×2 and 3×3 Hermitian matrices as used in the analysis of multilook polarimetric SAR data.The eigenvalues are calculated as the roots of quadratic or cubic equations. The methods are well suited for fast matrix oriented computer implementation and we obtain speed-ups over calculations based on a built-in eigenproblem solver in for-loops over rows and columns in an image by a factor of 350 (for dual pol) and 175 (for full/quad pol).
- Published
- 2021
- Full Text
- View/download PDF
183. Limit cycles for continuous and discontinuous perturbations of uniform isochronous cubic centers
- Author
-
Jaume Llibre and Jackson Itikawa
- Subjects
Hopf bifurcation ,Phase portrait ,Applied Mathematics ,Mathematical analysis ,Averaging theory ,Order (ring theory) ,Center (group theory) ,Computational Mathematics ,symbols.namesake ,Limit cycles ,Periodic orbit ,Polynomial vector field ,Limit cycle ,Poincaré conjecture ,symbols ,Uniform isochronous center ,Limit (mathematics) ,Cubic function ,Computer Science::Databases ,Mathematics - Abstract
Agraïments: FEDER-UNAB10-4E-378. The second author is supported by a Ciência sem Fronteiras-CNPq grant number 201002/2012-4. Let p be a uniform isochronous cubic polynomial center. We study the maximum number of small or medium limit cycles that bifurcate from p or from the periodic solutions surrounding p respectively, when they are perturbed, either inside the class of all continuous cubic polynomial differential systems, or inside the class of all discontinuous differential systems formed by two cubic differential systems separated by the straight line y = 0. In the case of continuous perturbations using the averaging theory of order 6 we show that the maximum number of small limit cycles that can appear in a Hopf bifurcation at p is 3, and this number can be reached. For a subfamily of these systems using the averaging theory of first order we prove that at most 3 medium limit cycles can bifurcate from the periodic solutions surrounding p, and this number can be reached. In the case of discontinuous perturbations using the averaging theory of order 6 we prove that the maximum number of small limit cycles that can appear in a Hopf bifurcation at p is 5, and this number can be reached. For a subfamily of these systems using the averaging method of first order we show that the maximum number of medium limit cycles that can bifurcate from the periodic solutions surrounding p is 7, and this number can be reached. We also provide all the first integrals and the phase portraits in the Poincar'e disc for the uniform isochronous cubic centers.
- Published
- 2021
184. Limit cycles for a class of continuous and discontinuous cubic polynomial differential systems
- Author
-
Jaime R. de Moraes, Bruno D. Lopes, and Jaume Llibre
- Subjects
Class (set theory) ,Isochronous center ,Applied Mathematics ,Mathematical analysis ,Averaging theory ,First order ,Differential systems ,Combinatorics ,Discontinuity (linguistics) ,Limit cycles ,Periodic orbit ,Polynomial vector field ,Limit cycle ,Discrete Mathematics and Combinatorics ,Beta (velocity) ,Limit (mathematics) ,Cubic function ,Mathematics - Abstract
Agraïments: FEDER-UNAB10-4E-378. The first and second author are supported by CAPES-MECD grant PHB-2009-0025-PC. The third author is supported by FAPESP-2010/17956-1. We study the maximum number of limit cycles that bifurcate from the periodic solutions of the family of isochronous cubic polynomial centers x˙ = y(−1 + 2αx + 2βx2), y˙ = x + α(y2 − x2) + 2βxy2, α ∈ R, β < 0, when it is perturbed inside the classes of all continuous and discontinuous cubic polynomial differential systems. We obtain that the maximum number of limit cycles which can be obtained by the averaging method of first order is 3 for the perturbed continuous systems and for the perturbed discontinuous systems at least 12 limit cycles can appear.
- Published
- 2021
185. The Maximum Modulus Set of a Polynomial
- Author
-
David J. Sixsmith and Leticia Pardo-Simón
- Subjects
Polynomial ,Singleton ,Applied Mathematics ,010102 general mathematics ,Type (model theory) ,01 natural sciences ,Finite sequence ,Quintic function ,Combinatorics ,Set (abstract data type) ,Computational Theory and Mathematics ,0101 mathematics ,Positive real numbers ,Cubic function ,Analysis ,Mathematics - Abstract
We study the maximum modulus set, $${{\mathcal {M}}}(p)$$ M ( p ) , of a polynomial p. We are interested in constructing p so that $${{\mathcal {M}}}(p)$$ M ( p ) has certain exceptional features. Jassim and London gave a cubic polynomial p such that $${{\mathcal {M}}}(p)$$ M ( p ) has one discontinuity, and Tyler found a quintic polynomial $${\tilde{p}}$$ p ~ such that $${{\mathcal {M}}}({\tilde{p}})$$ M ( p ~ ) has one singleton component. These are the only results of this type, and we strengthen them considerably. In particular, given a finite sequence $$a_1, a_2, \ldots , a_n$$ a 1 , a 2 , … , a n of distinct positive real numbers, we construct polynomials p and $${\tilde{p}}$$ p ~ such that $${{\mathcal {M}}}(p)$$ M ( p ) has discontinuities of modulus $$a_1, a_2, \ldots , a_n$$ a 1 , a 2 , … , a n , and $${{\mathcal {M}}}({\tilde{p}})$$ M ( p ~ ) has singleton components at the points $$a_1, a_2, \ldots , a_n$$ a 1 , a 2 , … , a n . Finally we show that these results are strong, in the sense that it is not possible for a polynomial to have infinitely many discontinuities in its maximum modulus set.
- Published
- 2021
186. On the singularities of the planar cubic polynomial differential systems and the Euler Jacobi formula
- Author
-
Jaume Llibre and Claudia Valls
- Subjects
Pure mathematics ,Polynomial ,Applied Mathematics ,Differential systems ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,Planar ,Cubic polynomial differential systems ,0103 physical sciences ,Euler's formula ,symbols ,Discrete Mathematics and Combinatorics ,Gravitational singularity ,Vector field ,Singular points ,0101 mathematics ,Algebraic number ,Euler-Jacobi formula ,010301 acoustics ,Cubic function ,Topological index ,Mathematics - Abstract
Using the Euler-Jacobi formula we obtain an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the planar cubic polynomial differential systems when these systems have nine finite singular points.
- Published
- 2021
187. Uncalibrated Photometric Stereo Using Superquadrics with Cast Shadow
- Author
-
Norikazu Takahashi, Takumi Nasu, and Tsuyoshi Migita
- Subjects
Image formation ,Computer science ,business.industry ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,Inverse problem ,Computer graphics ,Set (abstract data type) ,Photometric stereo ,Computer Science::Computer Vision and Pattern Recognition ,Superquadrics ,Computer vision ,Artificial intelligence ,Graphics ,business ,Cubic function ,ComputingMethodologies_COMPUTERGRAPHICS - Abstract
Formulated as an inverse problem of computer graphics, inverse rendering (or photometric stereo) can estimate parameters, such as the shapes and configurations of objects and light sources in the scene, from a set of images. Such results can be useful for applications including recognition, inspection, and/or VR. In the present paper, we extend previous studies in such a way as to incorporate more complex image formation models, specifically superquadrics with cast shadows, that are implemented on a standard graphics API and verify the framework on synthetic and real-world data.
- Published
- 2021
- Full Text
- View/download PDF
188. A note on one-sided interval edge colorings of bipartite graphs
- Author
-
Carl Johan Casselgren
- Subjects
Discrete mathematics ,Vertex (graph theory) ,Polynomial ,Discrete Mathematics ,Edge (geometry) ,Diskret matematik ,Theoretical Computer Science ,Combinatorics ,One-sided interval edge coloring ,Interval edge coloring ,Bipartite graph ,Edge coloring ,One sided ,FOS: Mathematics ,Mathematics - Combinatorics ,Discrete Mathematics and Combinatorics ,Interval (graph theory) ,Combinatorics (math.CO) ,Cubic function ,Mathematics - Abstract
For a bipartite graph G with parts X and Y, an X-interval coloring is a proper edge coloring of G by integers such that the colors on the edges incident to any vertex in X form an interval. Denote by χ i n t ′ ( G , X ) the minimum k such that G has an X-interval coloring with k colors. Casselgren and Toft (2016) [12] asked whether there is a polynomial P ( Δ ) such that if G has maximum degree at most Δ, then χ i n t ′ ( G , X ) ≤ P ( Δ ) . In this short note, we answer this question in the affirmative; in fact, we prove that a cubic polynomial suffices. We also deduce some improved upper bounds on χ i n t ′ ( G , X ) for bipartite graphs with small maximum degree.
- Published
- 2021
- Full Text
- View/download PDF
189. CHAPTER 10. Solvation Gibbs Energy: The Equation of State Approach
- Author
-
C. Panayiotou, E. Voutsas, and V. Hatzimanikatis
- Subjects
Physics ,Quantitative Biology::Biomolecules ,Range (particle radiation) ,Equation of state ,Physicochemical Phenomenon ,Solvation ,Thermodynamics ,Gibbs free energy ,Thermodynamic model ,symbols.namesake ,symbols ,Physics::Chemical Physics ,Cubic function ,UNIFAC - Abstract
The solvation Gibbs energy is a key thermodynamic quantity for understanding physicochemical phenomena and for designing physicochemical processes. It is a valuable quantitative measure of the solute–solvent affinity, of crucial importance in separation/partitioning processes. It is also the bridging quantity between the formation free energies of the solute in the (ideal) gas state and in solution. These features make the solvation Gibbs energy particularly important in numerous fields and applications, including life processes and metabolism under both ambient and remote external conditions. Systematic study of the solvation/hydration Gibbs energy over a broad range of external pressure and temperature conditions calls for an equation of state approach. This chapter focuses on two representative routes of the equation of state approach to solvation. In the first, the predictive UMR–PRU (Universal Mixing Rule – Peng–Robinson UNIFAC) cubic equation of state is explored for the estimation of solvation Gibbs energy over an extensive range of external conditions. Its predictions compare favorably with available experimental data from a recent large database with a mean absolute deviation of ca. 0.4 kcal mol−1 for all binary data (here 1 cal = 4.187 J). In the second, a versatile statistical thermodynamic model is explored that permits, in addition, the study of key components of solvation Gibbs energy such as components from cavitation, charging and solute conformations/solvent restructuring contributions. These latter components shed light on the mechanism of solvation and contribute to our understanding of solvation phenomena. The challenges and perspectives of the equation of state approach to solvation are critically discussed.
- Published
- 2021
- Full Text
- View/download PDF
190. Encounters with Cardano’s Method
- Author
-
Rina Zazkis and Boris Koichu
- Subjects
Literature ,business.industry ,School classroom ,History of mathematics ,Negative number ,Relation (history of concept) ,business ,Cubic function - Abstract
Many people, including ourselves, have been intrigued when first introduced to a story of inventing a formula for solving cubic equations. We invite the reader to recall a sixteenth-century story, in which characters possessing sonorous Italian names – del Ferro, Tartaglia, Cardano, and Bombelli – were on the stage. Different authors have depicted this story in relation to inventing complex numbers and legitimizing negative numbers (e.g., Guilbeaur 1930; Kenney 1989; Feldmann 1961). The story is an important milestone in the history of mathematics, and many teachers and mathematics educators like bringing it to a secondary school classroom or a course for mathematics teachers.
- Published
- 2021
- Full Text
- View/download PDF
191. Application of Cubic EOS for Shale Gas Adsorption Study
- Author
-
Zhengfu Ning, Qing Wang, Liang Huang, Fangtao Lyu, Wentong Zhang, and Xiaojun Wu
- Subjects
Materials science ,Adsorption ,Shale gas ,Thermodynamics ,Density functional theory ,Molecular simulation ,Cubic function ,Bulk density ,Grand canonical monte carlo - Abstract
Cubic equation of state (EOS) is vital to density calculation in shale gas experimental and theoretical adsorption studies. However, plenty of cubic EOSs have been given and their accuracies on density calculation were still uncertain. Therefore, it is necessary to analyze the applications of different types of cubic EOSs on shale gas adsorption study, according to the density calculation accuracy. Seven Peng-Robinson (PR) type EOSs and eight Soave-Redlich-Kwong (SRK) type EOSs were selected due to their application effect on shale gas. With grand canonical Monte Carlo (GCMC) density data and widely recognized Setzmann-Wagner (SW) EOS, these 15 cubic EOSs were compared and analyzed. Furthermore, cubic and SW EOSs were applied to simplified local density (SLD) model, and the effect of calculated density on adsorption simulation was investigated with GCMC adsorption data. Generally, the densities from PR type EOSs are larger than GCMC data. The SRK type EOS modified by Ghanbari and Check (SRKGC) is as accurate as SW EOS with a small error, 0.6%. The SRK type EOS modified by Morch et al. has the largest error, which is 7.99%, and is inappropriate to shale gas study. The effect of density accuracy on adsorption simulation could not be neglected. With larger bulk density, absolute adsorption value would get larger, while excess adsorption value would be smaller. This research could be a reference to experiment, molecular simulation, density functional theory and SLD methods for shale gas adsorption study, and the calculation accuracy could be improved effectively.
- Published
- 2021
- Full Text
- View/download PDF
192. Hamiltonian nilpotent center of linear plus cubic homogenous polynomial vector fields
- Author
-
Jaume Llibre, Ilker E. Colak, and Claudia Valls
- Subjects
Discrete mathematics ,Pure mathematics ,Nilpotent center ,General Mathematics ,Poincaré disk model ,Hamiltonian system ,Phase portrait ,symbols.namesake ,Nilpotent ,Homogeneous polynomial ,Cubic systems ,symbols ,Cubic form ,Vector field ,Hamiltonian (quantum mechanics) ,Cubic function ,Mathematics - Abstract
Agraïments: The first author has been supported by AGAUR FI-DGR 2010. The third author has been supported by AGAUR PIV-DGR-2010, and by the Portuguese National Funds through FCT-Fundaçâo para a Ciência e a Tecnologia within the project PTDC/MAT/117106/2010 and by CAMGSD. We provide normal forms and the global phase portraits in the Poincaré disk for all Hamiltonian nilpotent centers of linear plus cubic homogeneous planar polynomial vector fields.
- Published
- 2021
193. New family of cubic Hamiltonian centers
- Author
-
Jaume Llibre and Martín Eduardo Frías-Armenta
- Subjects
Isochronous center ,Phase portrait ,General Mathematics ,010102 general mathematics ,Differential systems ,01 natural sciences ,010101 applied mathematics ,Combinatorics ,symbols.namesake ,Poincaré conjecture ,symbols ,Hamiltonian system ,0101 mathematics ,Hamiltonian (quantum mechanics) ,Cubic function ,Mathematical physics ,Mathematics - Abstract
We characterize the 11 non-topological equivalent classes of phase portraits in the Poincare disc of the new family of cubic polynomial Hamiltonian differential systems with a center at the origin and Hamiltonian $$\begin{aligned} H= \frac{1}{2} ( (x + a x^2 + b x y + c y^2)^2+y^2 ), \end{aligned}$$ with $$a^2+b^2+c^2\ne 0$$ .
- Published
- 2021
194. The jump phenomenon associated with the dynamics of the duffing equation
- Author
-
M. P. Markakis
- Subjects
Physics ,Jump phenomenon ,Mathematical analysis ,Dynamics (mechanics) ,General Physics and Astronomy ,Duffing equation ,34C15 ,70K40 ,Classification of discontinuities ,34A34 ,lcsh:QC1-999 ,34C23 ,Amplitude ,Phenomenon ,Cubic function ,Bifurcation ,lcsh:Physics - Abstract
The mathematical nature of the jump phenomenon associated with the damped, harmonically forced Duffing equation is investigated, as regards the amplitude of the harmonic response of the system. The occurring discontinuities are treated as a bifurcation induced phenomenon, where the critical values of the respective control parameter are determined in relation to the solution of a cubic equation. Moreover, graphs illustrating the phenomenon, as well as bifurcation diagrams in the parameter planes of the system are presented. Finally, application of the presented analysis to phenomena of this kind as regards the behavior of living organisms is also discussed.
- Published
- 2020
195. Social Transfers Hardly Affected Growth.
- Author
-
Lindert, Peter H.
- Abstract
In his presidential address to the American Economic Association, Nobel Laureate Robert Lucas offered two findings about the huge costs of taxation and, by implication, of the social transfers that are the excuse for most taxes: “[S]tudies found that reducing capital income taxation from its current U.S. level to zero (using other taxes to [replace it]) would … imply an increase of consumption along a balanced growth path of 7.5 to 15 percent.” “Edward C. Prescott … shows that … [t]he steady-state welfare gain to French households of adopting American tax rates would be the equivalent of a consumption increase of about 20 percent … with no increase in work effort! … in the neoclassical growth model.” Such findings have two distinctive features. First, they show big numbers. Second they are not really findings. Contrary to the words offered so traditionally and casually by economists, none of these authors actually “found” or “showed” their results. Rather, they chose to imagine the results they announced. In every study Lucas cited here the crucial ingredient was a theoretical model laden with assumptions. It is educated, intelligent, plausible fiction – but fiction nonetheless, just like the blackboard diagrams, parables, and simulations we questioned in Chapter 10. Theory and fiction cannot be dismissed out of hand, of course. Every theoretical model, like every good novel, is inspired by observation of the real world. [ABSTRACT FROM AUTHOR]
- Published
- 2004
- Full Text
- View/download PDF
196. Reconciling Unemployment and Growth in the OECD.
- Author
-
Lindert, Peter H.
- Abstract
It is time for a showdown between the findings of two separate strands of empirical literature. On one side, studies of jobs and unemployment find that giving more to the unemployed cuts the number of jobs and raises unemployment. On the other, as we have seen, studies of the effects of total social transfers on the growth or level of GDP find no reliable statistical effect. The conflict stares at us directly in the raw data and is not just a subtlety revealed by the buildup of statistical studies. Just looking at the postwar record, we can see that unemployment rose dramatically in many countries after the 1960s, yet their GDP did not visibly drop relative to countries with less unemployment. How can these two strands be tied together? How can GDP not be cut if jobs are cut? Is it just that transfers to the unemployed cut jobs and output, while other transfers actually raise output? If the story of no clear GDP cost is correct, did more generous unemployment compensation really not destroy any jobs, contrary to past findings? If subsidizing the unemployed makes fewer people have jobs, is the GDP literature overlooking true costs? The reconciliation cannot simply hinge on differences between the GDP effects of the dole and the GDP effects of total social transfers, since Chapter 18 found that even the dole itself did not have a significant GDP cost. Alternatively, could more unemployment compensation remove only completely unproductive workers, whose marginal product is zero? [ABSTRACT FROM AUTHOR]
- Published
- 2004
- Full Text
- View/download PDF
197. Affine equivalence for cubic rotation symmetric Boolean functions with variables.
- Author
-
Cusick, Thomas W. and Cheon, Younhwan
- Subjects
- *
AFFINE algebraic groups , *BOOLEAN functions , *MATHEMATICAL variables , *EQUIVALENCE relations (Set theory) , *PERMUTATION groups , *MATHEMATICAL proofs - Abstract
Abstract: Rotation symmetric Boolean functions have been extensively studied in the last fifteen years or so because of their importance in cryptography and coding theory. Until recently, very little was known about the basic question of when two such functions are affine equivalent. The simplest case of quadratic rotation symmetric functions which are generated by cyclic permutations of the variables in a single monomial was only settled in a 2009 paper of Kim, Park and Hahn. The much more complicated analogous problem for cubic functions was solved for permutations using a new concept of patterns in a 2011 paper of Cusick, and it is conjectured that, as in the quadratic case, this solution actually applies for all affine transformations. The patterns method enables a detailed analysis of the affine equivalence classes for various special classes of cubic rotation symmetric functions in variables. Here the case of functions generated by a single monomial and having variables, where and are primes, is examined in detail, and in particular, a formula for the number of classes is proved. This is significant because it is the first time that a complete enumeration of the number of classes has been found when the number of variables is divisible by two distinct primes. [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
- View/download PDF
198. Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter
- Author
-
Faiza Qayyum, Tahir Nazir, Yushalify Misro, Muhammad Abbas, Kenjiro T. Miura, and Abdul Majeed
- Subjects
General Mathematics ,Basis function ,010103 numerical & computational mathematics ,02 engineering and technology ,01 natural sciences ,Shape parameter ,geometric modeling ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics ,Basis (linear algebra) ,B-spline ,lcsh:Mathematics ,Mathematical analysis ,lcsh:QA1-939 ,C3 and C5 continuity ,cubic curves and its properties ,Geometric design ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Computer Science::Graphics ,cubic trigonometric b-spline functions ,Computer Science::Programming Languages ,020201 artificial intelligence & image processing ,Trigonometry ,Geometric modeling ,Cubic function - Abstract
Trigonometric B-spline curves with shape parameters are equally important and useful for modeling in Computer-Aided Geometric Design (CAGD) like classical B-spline curves. This paper introduces the cubic polynomial and rational cubic B-spline curves using new cubic basis functions with shape parameter &xi, &isin, [0,4]. All geometric characteristics of the proposed Trigonometric B-spline curves are similar to the classical B-spline, but the shape-adjustable is additional quality that the classical B-spline curves does not hold. The properties of these bases are similar to classical B-spline basis and have been delineated. Furthermore, uniform and non-uniform rational B-spline basis are also presented. C3 and C5 continuities for trigonometric B-spline basis and C3 continuities for rational basis are derived. In order to legitimize our proposed scheme for both basis, floating and periodic curves are constructed. 2D and 3D models are also constructed using proposed curves.
- Published
- 2020
- Full Text
- View/download PDF
199. Experimental density data of three carbon dioxide and oxygen binary mixtures at temperatures from 276 to 416 K and at pressures up to 20 MPa
- Author
-
Salaheddine Chabab, Alain Valtz, Laura Blanco-Martín, Christophe Coquelet, Snaide Ahamada, Centre Thermodynamique des Procédés (CTP), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), and Centre de Géosciences (GEOSCIENCES)
- Subjects
General Chemical Engineering ,chemistry.chemical_element ,Thermodynamics ,Context (language use) ,02 engineering and technology ,Mole fraction ,7. Clean energy ,Oxygen ,chemistry.chemical_compound ,[CHIM.GENI]Chemical Sciences/Chemical engineering ,020401 chemical engineering ,Calibration ,[SPI.GPROC]Engineering Sciences [physics]/Chemical and Process Engineering ,Densitometer ,0204 chemical engineering ,Chromatography ,Fluids ,Liquids ,General Chemistry ,021001 nanoscience & nanotechnology ,Supercritical fluid ,[CHIM.THEO]Chemical Sciences/Theoretical and/or physical chemistry ,chemistry ,13. Climate action ,Mixtures ,Carbon dioxide ,0210 nano-technology ,Cubic function - Abstract
International audience; In the context of power-to-gas systems, including power-to-gas–oxyfuel, possible storage of a mixture of CO2 and O2 requires density data information and evaluation of equations of state. Densities of three CO2–O2 binary systems were measured using a vibrating tube densitometer, and the forced path mechanical calibration method in the gas, liquid, and supercritical regions between 276 and 416 K and at pressures up to 20 MPa (maximum expanded uncertainties U(p) = 0.0005 MPa, U(T) = 0.3 K, and U(ρ) = 15 kg·m–3). The mole fractions of the prepared CO2–O2 mixtures are 0.726:0.274, 0.517:0.483, and 0.872:0.128. The Peng–Robinson cubic equation of state (PR EoS) and the EoS-CG, based on GERG-2008 (and implemented in Refprop v10.0), were considered for the analysis of the data. Comparisons were carried out with literature data. It appears that the data are overall better predicted by the EoS-CG than the PR EoS
- Published
- 2020
- Full Text
- View/download PDF
200. Proposal for a New Method to Improve the Trajectory Generation of a Robotic Arm Using a Distribution Function
- Author
-
Oscar Zatarain, Jezreel Mejia, Carmen Lizarraga, and Yadira Quiñonez
- Subjects
Acceleration ,Distribution function ,Control theory ,Computer science ,Process (computing) ,Trajectory ,Motion control ,Robotic arm ,Cubic function ,Compile time - Abstract
Robotic control is one of the most important problems and is considered the central part of trajectory planning and motion control, and several methods can be found to generate the trajectory of a robotic arm. However, those methods imply a lot of calculation process and operations or other problems that cause decreasing the accuracy of the results and much compile time. For these reasons, a novel method is proposed to calculate the trajectory and get really accurate results with an insignificant compile time. Also, it is easy to implement, and it can make different velocities and acceleration shapes to obtain a smooth trajectory, opening new ways of control applications. the values for different initial and final positions using the distribution function proposed, LSPB, and cubic polynomial have been compared with a trajectory of 1 and 0.5 s. The paper ends with a critical discussion of experimental results.
- Published
- 2020
- Full Text
- View/download PDF
Catalog
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.