Theory and application of [integral sign]z̳ ex̳² dx and [integral sign]z̳ ep̳²y̳² dy [integral sign]y̳ ex̳² dx

On t.p. in the single integral, z̳ and x̳² are superscript; in the double integral, z̳, p̳²y̳², y̳, and x̳² are superscript.

The elements of arithmetic ... in which decimal and integral arithmetic are combined, and taught inductively, on the system of Pestalozzi. Part 1st [2d].

Mode of access: Internet.

Fast reconstruction of harmonic functions from Cauchy data using the Dirichlet-to-Neumann map and integral equations

We propose and investigate a method for the stable determination of a harmonic function from knowledge of its value and its normal derivative on a part of the boundary of the (bounded) solution domain (Cauchy problem). We reformulate the Cauchy problem as an operator equation on the boundary using the Dirichlet-to-Neumann map. To discretize the obtained operator, we modify and employ a method denoted as Classic II given in [J. Helsing, Faster convergence and higher accuracy for the Dirichlet–Neumann map, J. Comput. Phys. 228 (2009), pp. 2578–2576, Section 3], which is based on Fredholm integral equations and Nyström discretization schemes. Then, for stability reasons, to solve the discretized integral equation we use the method of smoothing projection introduced in [J. Helsing and B.T. Johansson, Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques, Inverse Probl. Sci. Eng. 18 (2010), pp. 381–399, Section 7], which makes it possible to solve the discretized operator equation in a stable way with minor computational cost and high accuracy. With this approach, for sufficiently smooth Cauchy data, the normal derivative can also be accurately computed on the part of the boundary where no data is initially given.

Thermal processing of miscanthus, sugarcane bagasse, sugarcane trash and their acid hydrolysis residues

The research presented in this thesis was developed as part of DIBANET, an EC funded project aiming to develop an energetically self-sustainable process for the production of diesel miscible biofuels (i.e. ethyl levulinate) via acid hydrolysis of selected biomass feedstocks. Three thermal conversion technologies, pyrolysis, gasification and combustion, were evaluated in the present work with the aim of recovering the energy stored in the acid hydrolysis solid residue (AHR). Mainly consisting of lignin and humins, the AHR can contain up to 80% of the energy in the original feedstock. Pyrolysis of AHR proved unsatisfactory, so attention focussed on gasification and combustion with the aim of producing heat and/or power to supply the energy demanded by the ethyl levulinate production process. A thermal processing rig consisting on a Laminar Entrained Flow Reactor (LEFR) equipped with solid and liquid collection and online gas analysis systems was designed and built to explore pyrolysis, gasification and air-blown combustion of AHR. Maximum liquid yield for pyrolysis of AHR was 30wt% with volatile conversion of 80%. Gas yield for AHR gasification was 78wt%, with 8wt% tar yields and conversion of volatiles close to 100%. 90wt% of the AHR was transformed into gas by combustion, with volatile conversions above 90%. 5volO2%-95vol%N2 gasification resulted in a nitrogen diluted, low heating value gas (2MJ/m3). Steam and oxygen-blown gasification of AHR were additionally investigated in a batch gasifier at KTH in Sweden. Steam promoted the formation of hydrogen (25vol%) and methane (14vol%) improving the gas heating value to 10MJ/m3, below the typical for steam gasification due to equipment limitations. Arrhenius kinetic parameters were calculated using data collected with the LEFR to provide reaction rate information for process design and optimisation. Activation energy (EA) and pre-exponential factor (ko in s-1) for pyrolysis (EA=80kJ/mol, lnko=14), gasification (EA=69kJ/mol, lnko=13) and combustion (EA=42kJ/mol, lnko=8) were calculated after linearly fitting the data using the random pore model. Kinetic parameters for pyrolysis and combustion were also determined by dynamic thermogravimetric analysis (TGA), including studies of the original biomass feedstocks for comparison. Results obtained by differential and integral isoconversional methods for activation energy determination were compared. Activation energy calculated by the Vyazovkin method was 103-204kJ/mol for pyrolysis of untreated feedstocks and 185-387kJ/mol for AHRs. Combustion activation energy was 138-163kJ/mol for biomass and 119-158 for AHRs. The non-linear least squares method was used to determine reaction model and pre-exponential factor. Pyrolysis and combustion of biomass were best modelled by a combination of third order reaction and 3 dimensional diffusion models, while AHR decomposed following the third order reaction for pyrolysis and the 3 dimensional diffusion for combustion.

Evans functions for integral neural field equations with Heaviside firing rate function

In this paper we show how to construct the Evans function for traveling wave solutions of integral neural field equations when the firing rate function is a Heaviside. This allows a discussion of wave stability and bifurcation as a function of system parameters, including the speed and strength of synaptic coupling and the speed of axonal signals. The theory is illustrated with the construction and stability analysis of front solutions to a scalar neural field model and a limiting case is shown to recover recent results of L. Zhang [On stability of traveling wave solutions in synaptically coupled neuronal networks, Differential and Integral Equations, 16, (2003), pp.513-536.]. Traveling fronts and pulses are considered in more general models possessing either a linear or piecewise constant recovery variable. We establish the stability of coexisting traveling fronts beyond a front bifurcation and consider parameter regimes that support two stable traveling fronts of different speed. Such fronts may be connected and depending on their relative speed the resulting region of activity can widen or contract. The conditions for the contracting case to lead to a pulse solution are established. The stability of pulses is obtained for a variety of examples, in each case confirming a previously conjectured stability result. Finally we show how this theory may be used to describe the dynamic instability of a standing pulse that arises in a model with slow recovery. Numerical simulations show that such an instability can lead to the shedding of a pair of traveling pulses.

A small area 8 bits 50 MHz CMOS DAC for Bluetooth transmitter

This paper presents a small-area CMOS current-steering segmented digital-to-analog converter (DAC) design intended for RF transmitters in 2.45 GHz Bluetooth applications. The current-source design strategy is based on an iterative scheme whose variables are adjusted in a simple way, minimizing the area and the power consumption, and meeting the design specifications. A theoretical analysis of static-dynamic requirements and a new layout strategy to attain a small-area current-steering DAC are included. The DAC was designed and implemented in 0.35 mu m CMOS technology, requiring an active area of just 200 mu m x 200 mu m. Experimental results, with a full-scale output current of 700 mu A and a 3.3 V power supply, showed a spurious-free dynamic range of 58 dB for a 1 MHz output sine wave and sampling frequency of 50 MHz, with differential and integral nonlinearity of 0.3 and 0.37 LSB, respectively.

Speed sensorless vector control of induction machines

A novel rotor velocity estimation scheme applicable to vector controlled induction motors has been described. The proposed method will evaluate rotor velocity, ωr, on-line, does not require any extra transducers or injection of any signals, nor does it employ complicated algorithms such as MRAS or Kalman filters. Furthermore, the new scheme will operate at all velocities including zero with very little error. The procedure employs motor model equations, however all differential and integral terms have been eliminated giving a very fast, low-cost, effective and practical alternative to the current available methods. Simulation results verify the operation of the scheme under ideal and PWM conditions.

INDEFINITE QUASILINEAR ELLIPTIC EQUATIONS IN EXTERIOR DOMAINS WITH EXPONENTIAL CRITICAL GROWTH

This paper is concerned with the existence of solutions for the quasilinear problem {-div(vertical bar del u vertical bar(N-2) del u) + vertical bar u vertical bar(N-2) u = a(x)g(u) in Omega u = 0 on partial derivative Omega, where Omega subset of R(N) (N >= 2) is an exterior domain; that is, Omega = R(N)\omega, where omega subset of R(N) is a bounded domain, the nonlinearity g(u) has an exponential critical growth at infinity and a(x) is a continuous function and changes sign in Omega. A variational method is applied to establish the existence of a nontrivial solution for the above problem.

Uma trajetória da disciplina de análise e um estado do conhecimento sobre seu ensino

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A irracionalidade e transcendência do número π

Pós-graduação em Matemática em Rede Nacional - IBILCE

Influence of alternative drying aids on water sorption of spray dried mango mix powders: a thermodynamic approach

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Suspended matter on the meridional section in the Laptev Sea in August-September 1991

Suspended matter concentration along a meridian section from the Lena River delta to 78°N (~500 km) at ten stations from the surface to the bottom was studied with weight and optical (light attenuation index) techniques. At seven stations average residence time of suspended matter in surface waters was determined by the disequilibrium 234Th method. Average residence time of suspended matter in other depth intervals was calculated by regression dependence between the 234Th/238U ratio and suspended matter concentration. Differential and integral fluxes of suspended matter in the water column were also calculated. Nepheloid matter dominates in suspended matter composition in surface waters. Calculations indicate that, before being buried on the bottom, solid river run-off is resuspended 2.3 times (aver.). Redistribution of nepheloid suspended matter in the near-bottom layer results in formation of a strongly pronounced depocentre - an area of maximal discharge of solid river run-off within the Laptev Sea.

Integral Manifolds and Bounded Solutions of Singularly Perturbed Systems of Impulsive Differential Equations

Sufficient conditions for the existence of bounded solutions of singularly perturbed impulsive differential equations are obtained. For this purpose integral manifolds are used.

Integral Manifolds and Perturbations of the Nonlinear Part of Systems of Autonomous Differential Equations with Impulses at Fixed Moments

* This investigation was supported by the Bulgarian Ministry of Science and Education under Grant MM-7.

Higher mathematics for students of chemistry and physics, with special reference to practical work,

The differential calculus.--Coordinate or analytical geometry.--Functions with singular properties.--The integral calculus.--Infinite series and their uses.--How to solve numerical equations.--How to solve differential equations.--Fourier's theorum.--Probability and the theory of errors.--The calculus of variations.--Determinants.--Collection of formulae for references.--Reference tables.