Solvability of singular second order m-point boundary value problems of Dirichlet type

Let f : [0, 1] x R2 -> R be a function satisfying the Caxatheodory conditions and t(1 - t)e(t) epsilon L-1 (0, 1). Let a(i) epsilon R and xi(i) (0, 1) for i = 1,..., m - 2 where 0 < xi(1) < xi(2) < (...) < xi(m-2) < 1 - In this paper we study the existence of C[0, 1] solutions for the m-point boundary value problem [GRAPHICS] The proof of our main result is based on the Leray-Schauder continuation theorem.

Optimization of chemical plant simulation using double collocation

A method has been constructed for the solution of a wide range of chemical plant simulation models including differential equations and optimization. Double orthogonal collocation on finite elements is applied to convert the model into an NLP problem that is solved either by the VF 13AD package based on successive quadratic programming, or by the GRG2 package, based on the generalized reduced gradient method. This approach is termed simultaneous optimization and solution strategy. The objective functional can contain integral terms. The state and control variables can have time delays. Equalities and inequalities containing state and control variables can be included into the model as well as algebraic equations and inequalities. The maximum number of independent variables is 2. Problems containing 3 independent variables can be transformed into problems having 2 independent variables using finite differencing. The maximum number of NLP variables and constraints is 1500. The method is also suitable for solving ordinary and partial differential equations. The state functions are approximated by a linear combination of Lagrange interpolation polynomials. The control function can either be approximated by a linear combination of Lagrange interpolation polynomials or by a piecewise constant function over finite elements. The number of internal collocation points can vary by finite elements. The residual error is evaluated at arbitrarily chosen equidistant grid-points, thus enabling the user to check the accuracy of the solution between collocation points, where the solution is exact. The solution functions can be tabulated. There is an option to use control vector parameterization to solve optimization problems containing initial value ordinary differential equations. When there are many differential equations or the upper integration limit should be selected optimally then this approach should be used. The portability of the package has been addressed converting the package from V AX FORTRAN 77 into IBM PC FORTRAN 77 and into SUN SPARC 2000 FORTRAN 77. Computer runs have shown that the method can reproduce optimization problems published in the literature. The GRG2 and the VF I 3AD packages, integrated into the optimization package, proved to be robust and reliable. The package contains an executive module, a module performing control vector parameterization and 2 nonlinear problem solver modules, GRG2 and VF I 3AD. There is a stand-alone module that converts the differential-algebraic optimization problem into a nonlinear programming problem.

Determining the temperature from incomplete boundary data

An iterative procedure for determining temperature fields from Cauchy data given on a part of the boundary is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. A convergence proof of this method in a weighted L2-space is included, as well as a stopping criteria for the case of noisy data. Moreover, a solvability result in a weighted Sobolev space for a parabolic initial boundary value problem of second order with mixed boundary conditions is presented. Regularity of the solution is proved. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Fractional Derivatives and Fractional Powers as Tools in Understanding Wentzell Boundary Value Problems for Pseudo-Differential Operators Generating Markov Processes

Mathematics Subject Classification: 26A33, 31C25, 35S99, 47D07.

Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions

Mathematics Subject Classification: 35J05, 35J25, 35C15, 47H50, 47G30

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.

Monte Carlo Study of Particle Transport Problem in Air Pollution

2002 Mathematics Subject Classification: 65C05.

Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations

MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05

Continuous property measurement techniques and physics based mathematical model for frost growth control

The development of a new set of frost property measurement techniques to be used in the control of frost growth and defrosting processes in refrigeration systems was investigated. Holographic interferometry and infrared thermometry were used to measure the temperature of the frost-air interface, while a beam element load sensor was used to obtain the weight of a deposited frost layer. The proposed measurement techniques were tested for the cases of natural and forced convection, and the characteristic charts were obtained for a set of operational conditions. ^ An improvement of existing frost growth mathematical models was also investigated. The early stage of frost nucleation was commonly not considered in these models and instead an initial value of layer thickness and porosity was regularly assumed. A nucleation model to obtain the droplet diameter and surface porosity at the end of the early frosting period was developed. The drop-wise early condensation in a cold flat plate under natural convection to a hot (room temperature) and humid air was modeled. A nucleation rate was found, and the relation of heat to mass transfer (Lewis number) was obtained. It was found that the Lewis number was much smaller than unity, which is the standard value usually assumed for most frosting numerical models. The nucleation model was validated against available experimental data for the early nucleation and full growth stages of the frosting process. ^ The combination of frost top temperature and weight variation signals can now be used to control the defrosting timing and the developed early nucleation model can now be used to simulate the entire process of frost growth in any surface material. ^

Multiple solutions and numerical analysis to the dynamic and stationary models coupling a delayed energy balance model involving latent heat and discontinuous albedo with a deep ocean

We study a climatologically important interaction of two of the main components of the geophysical system by adding an energy balance model for the averaged atmospheric temperature as dynamic boundary condition to a diagnostic ocean model having an additional spatial dimension. In this work, we give deeper insight than previous papers in the literature, mainly with respect to the 1990 pioneering model by Watts and Morantine. We are taking into consideration the latent heat for the two phase ocean as well as a possible delayed term. Non-uniqueness for the initial boundary value problem, uniqueness under a non-degeneracy condition and the existence of multiple stationary solutions are proved here. These multiplicity results suggest that an S-shaped bifurcation diagram should be expected to occur in this class of models generalizing previous energy balance models. The numerical method applied to the model is based on a finite volume scheme with nonlinear weighted essentially non-oscillatory reconstruction and Runge–Kutta total variation diminishing for time integration.

Aplicação do método POLD® na redução da sintomatologia álgica da lombociatalgia

Projeto de Graduação apresentado à Universidade Fernando Pessoa como parte dos requisitos para obtenção do grau de Licenciado em Fisioterapia

Efeito da ingestão de cafeina sobre o deficit acumulado de oxigenio, sinal eletromiografico dos musculos superficiais do quadriceps e desempenho fisico de ciclistas

Universidade Estadual de Campinas . Faculdade de Educação Física

The UV/H2O2 - photodegradation of poly(ethyleneglycol) and model compounds

The general mechanism for the photodegradation of polyethyleneglycol (PEG) by H2O2/UV was determined studying the photooxidation of small model molecules, like low molecular weight ethyleneglycols (tetra-, tri-, di-, and ethyleneglycol). After 30 min of irradiation the average molar mass (Mw) of the degradated PEG, analysed by GPC, fall to half of its initial value, with a concomitant increase in polydispersitivity and number of average chain scission (S), characterizing a random chain scission process yielding oligomers and smaller size ethyleneglycols. HPLC analysis of the photodegradation of the model ethyleneglycols proved that the oxidation mechanism involved consecutive reactions, where the larger ethyleneglycols gave rise, successively, to smaller ones. The photodegradation of ethyleneglycol lead to the formation of low molecular weight carboxylic acids, like glycolic, oxalic and formic acids.

A simple procedure for reliability assessment of thin composite plates against buckling

In some circumstances ice floes may be modeled as beams. In general this modeling supposes constant thickness, which contradicts field observations. Action of currents, wind and the sequence of contacts, causes thickness to vary. Here this effect is taken into consideration on the modeling of the behavior of ice hitting inclined walls of offshore platforms. For this purpose, the boundary value problem is first equated. The set of equations so obtained is then transformed into a system of equations, that is then solved numerically. For this sake an implicit solution is developed, using a shooting method, with the accompanying Jacobian. In-plane coupling and the dependency of the boundary terms on deformation, make the problem non-linear and the development particular. Deformation and internal resultants are then computed for harmonic forms of beam profile. Forms of giving some additional generality to the problem are discussed.

Two-dimensional supersonic nonlinear Schrodinger flow past an extended obstacle

Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional (2D) defocusing nonlinear Schroumldinger (NLS) equation. This problem is of fundamental importance as a dispersive analog of the corresponding classical gas-dynamics problem. Assuming the oncoming flow speed is sufficiently high, we asymptotically reduce the original boundary-value problem for a steady flow past a slender body to the one-dimensional dispersive piston problem described by the nonstationary NLS equation, in which the role of time is played by the stretched x coordinate and the piston motion curve is defined by the spatial body profile. Two steady oblique spatial dispersive shock waves (DSWs) spreading from the pointed ends of the body are generated in both half planes. These are described analytically by constructing appropriate exact solutions of the Whitham modulation equations for the front DSW and by using a generalized Bohr-Sommerfeld quantization rule for the oblique dark soliton fan in the rear DSW. We propose an extension of the traditional modulation description of DSWs to include the linear ""ship-wave"" pattern forming outside the nonlinear modulation region of the front DSW. Our analytic results are supported by direct 2D unsteady numerical simulations and are relevant to recent experiments on Bose-Einstein condensates freely expanding past obstacles.