The works of Lord Byron : in six volumes.

Vols. 1-4 are reissues of the four volumes of the edition of 1830.

Odes, and fugitive poetry.

Includes: The Mississippi--an ode; A night in the woods of Louisiana; A crevasse in the levee of the Mississipi [!]

Des Freyherrn von Canitz Gedichte, mehrentheils aus seinen eigenhändigen Schrifften verbessert und vermehret, mit Kupfern und anmerckungen nebst dessen Leben, und einer Untersuchung von dem Guten Geschmack in der Dicht- und Rede-Kunst,

"Ehren-Mahl der Frau von Canitz. Trost aus anderer Unglück. Trauer-ode des Herrn von Besser p. 125-138.

Théâtre de M. J. Chénier,

Vol. 3 has title: Théâtre posthume de M. J. Chénier, précédé de Considerations sur la liberté du théâtre en France.

Elkin Mathews' Garland of new poetry.

v. 1. First book of London visions / Laurence Binyon -- Purcell commemoration ode, and other poems / Robert Bridges -- Christ in Hades, and other poems / Stephen Phillips -- Aeromancy, and other poems / Margaret L. Woods -- Songs and odes / Richard Watson Dixon -- v. 2. The praise of life / Laurence Binyon -- Fancy's guerdon / Anodos -- Admirals all, and other verses / Henry Newbolt -- Songs and elegies / Manmohan Ghose -- Second book of London visions / Laurence Binyon.

Somnambulism and cramp,

"The following treatise, first published in the San Franciso Home journal, and here given as a distinct book, was written ... as portion of a ... work ... entitled: Der sensitive mensch und sein verhalten zum ode." - Translator's introd., p. [xiii]

August Wilhelm von Schlegel's sammtliche Werke.

Each volume has also special t.-p. Music ("Festgesang" and "Ode", both with text) 4 pages in v. 2, between p. 342 and [343]

Analysis of trigonometric implicit Runge-Kutta methods

Using generalized collocation techniques based on fitting functions that are trigonometric (rather than algebraic as in classical integrators), we develop a new class of multistage, one-step, variable stepsize, and variable coefficients implicit Runge-Kutta methods to solve oscillatory ODE problems. The coefficients of the methods are functions of the frequency and the stepsize. We refer to this class as trigonometric implicit Runge-Kutta (TIRK) methods. They integrate an equation exactly if its solution is a trigonometric polynomial with a known frequency. We characterize the order and A-stability of the methods and establish results similar to that of classical algebraic collocation RK methods. (c) 2006 Elsevier B.V. All rights reserved.

Mathematical modelling and control of agitated extraction columns

Liquid-liquid extraction has long been known as a unit operation that plays an important role in industry. This process is well known for its complexity and sensitivity to operation conditions. This thesis presents an attempt to explore the dynamics and control of this process using a systematic approach and state of the art control system design techniques. The process was studied first experimentally under carefully selected. operation conditions, which resembles the ranges employed practically under stable and efficient conditions. Data were collected at steady state conditions using adequate sampling techniques for the dispersed and continuous phases as well as during the transients of the column with the aid of a computer-based online data logging system and online concentration analysis. A stagewise single stage backflow model was improved to mimic the dynamic operation of the column. The developed model accounts for the variation in hydrodynamics, mass transfer, and physical properties throughout the length of the column. End effects were treated by addition of stages at the column entrances. Two parameters were incorporated in the model namely; mass transfer weight factor to correct for the assumption of no mass transfer in the. settling zones at each stage and the backmixing coefficients to handle the axial dispersion phenomena encountered in the course of column operation. The parameters were estimated by minimizing the differences between the experimental and the model predicted concentration profiles at steady state conditions using non-linear optimisation technique. The estimated values were then correlated as functions of operating parameters and were incorporated in·the model equations. The model equations comprise a stiff differential~algebraic system. This system was solved using the GEAR ODE solver. The calculated concentration profiles were compared to those experimentally measured. A very good agreement of the two profiles was achieved within a percent relative error of ±2.S%. The developed rigorous dynamic model of the extraction column was used to derive linear time-invariant reduced-order models that relate the input variables (agitator speed, solvent feed flowrate and concentration, feed concentration and flowrate) to the output variables (raffinate concentration and extract concentration) using the asymptotic method of system identification. The reduced-order models were shown to be accurate in capturing the dynamic behaviour of the process with a maximum modelling prediction error of I %. The simplicity and accuracy of the derived reduced-order models allow for control system design and analysis of such complicated processes. The extraction column is a typical multivariable process with agitator speed and solvent feed flowrate considered as manipulative variables; raffinate concentration and extract concentration as controlled variables and the feeds concentration and feed flowrate as disturbance variables. The control system design of the extraction process was tackled as multi-loop decentralised SISO (Single Input Single Output) as well as centralised MIMO (Multi-Input Multi-Output) system using both conventional and model-based control techniques such as IMC (Internal Model Control) and MPC (Model Predictive Control). Control performance of each control scheme was. studied in terms of stability, speed of response, sensitivity to modelling errors (robustness), setpoint tracking capabilities and load rejection. For decentralised control, multiple loops were assigned to pair.each manipulated variable with each controlled variable according to the interaction analysis and other pairing criteria such as relative gain array (RGA), singular value analysis (SVD). Loops namely Rotor speed-Raffinate concentration and Solvent flowrate Extract concentration showed weak interaction. Multivariable MPC has shown more effective performance compared to other conventional techniques since it accounts for loops interaction, time delays, and input-output variables constraints.

Dubrovin Type Equations for Completely Integrable Systems Associated with a Polynomial Pencil

Dubrovin type equations for the N -gap solution of a completely integrable system associated with a polynomial pencil is constructed and then integrated to a system of functional equations. The approach used to derive those results is a generalization of the familiar process of finding the 1-soliton (1-gap) solution by integrating the ODE obtained from the soliton equation via the substitution u = u(x + λt).

Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

Asymptotic Expansion of Solution for Almost Regular and Weakly Perturbed Systems of Ordinary Differential Equations

Л. И. Каранджулов, Н. Д. Сиракова - В работата се прилага методът на Поанкаре за решаване на почти регулярни нелинейни гранични задачи при общи гранични условия. Предполага се, че диференциалната система съдържа сингулярна функция по отношение на малкия параметър. При определени условия се доказва асимптотичност на решението на поставената задача.

Lie-szimmetriák egy közgazdasági alkalmazása (An economic application of the Lie symmetries)

Ebben a tanulmányban ismertetjük a Nöther-tétel lényegi vonatkozásait, és kitérünk a Lie-szimmetriák értelmezésére abból a célból, hogy közgazdasági folyamatokra is alkalmazzuk a Lagrange-formalizmuson nyugvó elméletet. A Lie-szimmetriák dinamikai rendszerekre történő feltárása és viselkedésük jellemzése a legújabb kutatások eredményei e területen. Például Sen és Tabor (1990), Edward Lorenz (1963), a komplex kaotikus dinamika vizsgálatában jelent®s szerepet betöltő 3D modelljét, Baumann és Freyberger (1992) a két-dimenziós Lotka-Volterra dinamikai rendszert, és végül Almeida és Moreira (1992) a három-hullám interakciós problémáját vizsgálták a megfelelő Lie-szimmetriák segítségével. Mi most empirikus elemzésre egy közgazdasági dinamikai rendszert választottunk, nevezetesen Goodwin (1967) ciklusmodelljét. Ennek vizsgálatát tűztük ki célul a leírandó rendszer Lie-szimmetriáinak meghatározásán keresztül. / === / The dynamic behavior of a physical system can be frequently described very concisely by the least action principle. In the centre of its mathematical presentation is a specic function of coordinates and velocities, i.e., the Lagrangian. If the integral of the Lagrangian is stationary, then the system is moving along an extremal path through the phase space, and vice versa. It can be seen, that each Lie symmetry of a Lagrangian in general corresponds to a conserved quantity, and the conservation principle is explained by a variational symmetry related to a dynamic or geometrical symmetry. Briey, that is the meaning of Noether's theorem. This paper scrutinizes the substantial characteristics of Noether's theorem, interprets the Lie symmetries by PDE system and calculates the generators (symmetry vectors) on R. H. Goodwin's cyclical economic growth model. At first it will be shown that the Goodwin model also has a Lagrangian structure, therefore Noether's theorem can also be applied here. Then it is proved that the cyclical moving in his model derives from its Lie symmetries, i.e., its dynamic symmetry. All these proofs are based on the investigations of the less complicated Lotka Volterra model and those are extended to Goodwin model, since both models are one-to-one maps of each other. The main achievement of this paper is the following: Noether's theorem is also playing a crucial role in the mechanics of Goodwin model. It also means, that its cyclical moving is optimal. Generalizing this result, we can assert, that all dynamic systems' solutions described by first order nonlinear ODE system are optimal by the least action principle, if they have a Lagrangian.

Dynamic Behavior and Fatigue Life of Highway Bridges Due to Doubling Heavy Vehicles

An increase in the demand for the freight shipping in the United States has been predicted for the near future and Longer Combination Vehicles (LCVs), which can carry more loads in each trip, seem like a good solution for the problem. Currently, utilizing LCVs is not permitted in most states of the US and little research has been conducted on the effects of these heavy vehicles on the roads and bridges. In this research, efforts are made to study these effects by comparing the dynamic and fatigue effects of LCVs with more common trucks. Ten Steel and prestressed concrete bridges with span lengths ranging from 30’ to 140’ are designed and modeled using the grid system in MATLAB. Additionally, three more real bridges including two single span simply supported steel bridges and a three span continuous steel bridge are modeled using the same MATLAB code. The equations of motion of three LCVs as well as eight other trucks are derived and these vehicles are subjected to different road surface conditions and bumps on the roads and the designed and real bridges. By forming the bridge equations of motion using the mass, stiffness and damping matrices and considering the interaction between the truck and the bridge, the differential equations are solved using the ODE solver in MATLAB and the results of the forces in tires as well as the deflections and moments in the bridge members are obtained. The results of this study show that for most of the bridges, LCVs result in the smallest values of Dynamic Amplification Factor (DAF) whereas the Single Unit Trucks cause the highest values of DAF when traveling on the bridges. Also in most cases, the values of DAF are observed to be smaller than the 33% threshold suggested by the design code. Additionally, fatigue analysis of the bridges in this study confirms that by replacing the current truck traffic with higher capacity LCVs, in most cases, the remaining fatigue life of the bridge is only slightly decreased which means that taking advantage of these larger vehicles can be a viable option for decision makers.

Incrustação em poço produtor de petróleo e gás natural: um estudo de caso

Water and gas is a common by - product of the oil production process. Production may be compromised by the precipitation of inorganic salts in both the reservoir and producing well, through scale formation. This precipitation is likely the cause of the formation damage. High temperatures and h igh pressures (HTHP) may favor the precipitation of insoluble salts. The most common types of scale in oil fields are calcium carbonate and calcium sulphate, strontium and barium sulphate. New types of scale formation have attracted special attention such as zinc sulphide and lead. This precipitation may occur in the pores of reservoir rocks, in the production string and in equipment, causing obstructions and consequent production losses. In this study, the influence of well depth on incrustation compositio n was investigated to design removal treatments and assess the behavior of these deposits along the string, through the analysis of pressure and temperature. Scale residues were recovered from the inside of the production string of an oil and gas well duri ng the string removal operation. A total of 10 samples from different depths (15.4 m to 4061.5 m) were obtained. Initially a dissolution test was conducted in weak acid, similar to that used in removal operations with this type of scale formation. Majority composition was defined and confirmed by dissolution tests using X - Ray Fluorescence Spectroscopy (XRF), X - Ray Diffraction (XRD) and Scanning Electron Microscope (SEM) techniques. Residues with distinct characteristics were observed in different proportion s, showing a tendency toward increased and/or decreased mass with depth. In the samples closest to the surface, typical sandstone residues were found, with calcium (45% Ca) as the metal of highest concentration. The obtained results indicate correlations o f the scale types studied with the depth and, consequently, with the thermodynamic conditions of pressure and temperature.