Search results for "equation"

showing 10 items of 4219 documents

Fields of values of odd-degree irreducible characters

2019

Abstract In this paper we clarify the quadratic irrationalities that can be admitted by an odd-degree complex irreducible character χ of an arbitrary finite group. Write Q ( χ ) to denote the field generated over the rational numbers by the values of χ, and let d > 1 be a square-free integer. We prove that if Q ( χ ) = Q ( d ) then d ≡ 1 (mod 4) and if Q ( χ ) = Q ( − d ) , then d ≡ 3 (mod 4). This follows from the main result of this paper: either i ∈ Q ( χ ) or Q ( χ ) ⊆ Q ( exp ⁡ ( 2 π i / m ) ) for some odd integer m ≥ 1 .

Rational numberFinite groupCharacter valuesScience & TechnologyDegree (graph theory)General Mathematics010102 general mathematicsField (mathematics)Rationality01 natural sciencesREPRESENTATIONS0101 Pure MathematicsCombinatoricsQuadratic equationCharacter (mathematics)Integer0103 physical sciencesPhysical Sciences010307 mathematical physics0101 mathematicsMathematicsMathematics
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A combined experimental and theoretical study of the unimolecular elimination kinetics of 2-alkoxypropionic acids in the gas phase

1999

Abstract The reaction mechanism associated with the decomposition of three 2-alkoxypropionic acids (2-methoxy-, 2-ethoxy- and 2-isopropoxypropionic acid) in gas phase to form acetaldehyde, carbon monoxide, and the corresponding alcohol has been analyzed by a combination of experimental and theoretical studies. The kinetics of these systems were determined in a static system over the temperature and pressure range of 301.2–370.7°C and 61–190 Torr, respectively, in seasoned vessel, with the free-radical inhibitor cyclohexene. The experimental data show that these decompositions are homogeneous, unimolecular and follow a first-order rate law. A detailed characterization, at MP2/6-31G** computa…

Reaction mechanismCyclohexeneSubstituentGeneral Physics and AstronomyRate equationPhotochemistryRate-determining stepchemistry.chemical_compoundchemistryYield (chemistry)Alkoxy groupPhysical chemistryPhysical and Theoretical ChemistryCarbon monoxide
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Oxygenation of Alkane C−H Bonds with Methyl(trifluoromethyl)dioxirane:  Effect of the Substituents and the Solvent on the Reaction Rate

2005

[Chemical reaction: See text] The mechanism of the oxygenation of alkane C-H bonds with methyl(trifluoromethyl)dioxirane (1a) is studied through the effect of the substituent and solvent on the rate of oxygenation of 2-substituted adamantanes (2). The results suggest a remarkable electron deficiency at the reacting carbon atom in the transition state leading to the regular oxygenation products. The linearity of the Hammett plot reveals that the reaction mechanism does not change within a range of 0.15-0.67 units of sigma(I). A change in the solvent does not affect the distribution of the products, indicating a through-bond transmission of the substituent effect as the origin of the deactiva…

Reaction mechanismTrifluoromethylOrganic ChemistrySubstituentGeneral MedicineElectron deficiencyPhotochemistryMedicinal chemistryChemical reactionReaction ratechemistry.chemical_compoundHammett equationchemistryDioxiraneSolvent effectsThe Journal of Organic Chemistry
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Calculation of the rate constants for hydrogen abstraction reactions by Hydroperoxyl radical from Methanol, and the investigation of stability of CH3…

2020

Abstract Master equation (ME) with Lennard-Jones potential utilized to simulate the collision between CH3OH and HO2 radical in the presence of bath gas. The reaction mechanism explored through the lowest doublet potential energy surface at CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level of theory that is barrierless and forms shallow energized intermediate at the entrance channel. The investigation of the fractional population showed that lifetime of CH3OH.HO2 intermediate (INT*) is fairly short due to its shallow depth, and at the low temperature, most reaction takes place by re-dissociation back to reactants and also when the pressure is high enough, the INT* is thermalized and comes into eq…

Reaction mechanismeducation.field_of_study010304 chemical physicsChemistryPopulationThermodynamics010402 general chemistryCondensed Matter PhysicsHydrogen atom abstraction01 natural sciencesBiochemistry0104 chemical scienceschemistry.chemical_compoundReaction rate constantHydroperoxyl0103 physical sciencesPotential energy surfaceMaster equationPhysical and Theoretical ChemistryeducationEquilibrium constantComputational and Theoretical Chemistry
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Equilibrium real gas computations using Marquina's scheme

2003

Marquina's approximate Riemann solver for the compressible Euler equations for gas dynamics is generalized to an arbitrary equilibrium equation of state. Applications of this solver to some test problems in one and two space dimensions show the desired accuracy and robustness

Real gasApplied MathematicsMechanical EngineeringMathematical analysisMathematicsofComputing_NUMERICALANALYSISComputational MechanicsSolverSpace (mathematics)Compressible flowRiemann solverComputer Science ApplicationsEuler equationsRunge–Kutta methodssymbols.namesakeMechanics of MaterialsComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONCompressibilitysymbolsMathematicsInternational Journal for Numerical Methods in Fluids
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Comparison results for Monge - Ampère type equations with lower order terms

2003

In this paper we deal with Monge-Ampère type equations in two dimensions and, using the symmetrization with respect to the perimeter, we prove some comparison results for solutions of such equations involving the solutions of conveniently symmetrized problems.

RearrangementsMathematics::Complex VariablesIndependent equationApplied MathematicsMathematical analysisMathematics::Analysis of PDEsComparison resultsSymmetrizationLower orderType (model theory)Monge-Ampère equationsPerimeterSettore MAT/05 - Analisi MatematicaSimultaneous equationsFully nonlinear elliptic equationsSymmetrizationAmpereAnalysisMathematics
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Inequalities for Information Potentials and Entropies

2020

We consider a probability distribution p0(x),p1(x),&hellip

Recurrence relationprobability distributionGeneral MathematicsTsallis entropylcsh:Mathematics010102 general mathematicsLinear operatorsfunctional equationslcsh:QA1-93901 natural sciencesinformation potentialRényi entropyCombinatorics010104 statistics & probabilityRényi entropyinequalitiesComputer Science (miscellaneous)Order (group theory)Probability distribution0101 mathematicsTsallis entropyEngineering (miscellaneous)MathematicsMathematics
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The lift computation for an oscillating flat plate in incompressible potential flow

1994

The initial aim of this work was the estimation of the lift acting on a flat plate performing small oscillations in a plane uniform stream by means of a simplified model based on one or at the most two lumped vortices, and the assessment of its results by comparison to those that were exact. The model was found to work well up to a reduced frequency of about 1 or 2, above which the results diverged from those that were correct. In order to improve the model, its behaviour at very high frequencies was then investigated, discovering: (i) that if the number of lumped vortices is greater than one the possibility to impose all boundary conditions is subject to certain geometrical constraints; (i…

Reduced frequencyLift (data mining)Mechanical EngineeringMathematical analysisGeometryCondensed Matter PhysicsIntegral equationVortexSingularityMechanics of MaterialsIncompressible flowPotential flowBoundary value problemMathematicsMeccanica
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Multiple solutions for strongly resonant Robin problems

2018

We consider nonlinear (driven by the p†Laplacian) and semilinear Robin problems with indefinite potential and strong resonance with respect to the principal eigenvalue. Using variational methods and critical groups, we prove four multiplicity theorems producing up to four nontrivial smooth solutions.

Regularity theoryPure mathematicsSemilinear equationStrong resonanceGeneral Mathematics010102 general mathematicsp-LaplacianMultiplicity (mathematics)Mathematics::Spectral Theory01 natural sciences010101 applied mathematicsNonlinear systemCritical groupSettore MAT/05 - Analisi Matematicap-Laplacian0101 mathematicsLaplace operatorEigenvalues and eigenvectorsCritical groupMathematics
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A numerical meshless particle method in solving the magnetoencephalography forward problem

2012

In this paper, a numerical meshless particle method is presented in order to solve the magnetoencephalography forward problem for analyzing the complex activation patterns in the human brain. The forward problem is devoted to compute the scalp potential and magnetic field distribution generated by a set of current sources representing the neural activity, and in this paper, it has been approached by means of the smoothed particle hydrodynamics method suitably handled. The Poisson equation generated by the quasi-stationary Maxwell's curl equations, by assuming Neumann boundary conditions has been considered, and the current sources have been simulated by current dipoles. The adopted meshless…

Regularized meshless methodSingular boundary methodComputer Science ApplicationsSmoothed-particle hydrodynamicssymbols.namesakeClassical mechanicsMaxwell's equationsMesh generationModeling and SimulationNeumann boundary conditionsymbolsApplied mathematicsElectrical and Electronic EngineeringPoisson's equationBoundary element methodMathematicsInternational Journal of Numerical Modelling: Electronic Networks, Devices and Fields
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