Differential rates; arguments of Baltimore Commercial Associations before the Trunk-line Advisory Commission, March 1882.

Mode of access: Internet.

Argument of the committee appointed to represent the Baltimore corn and flour exchange, on the subject of differential rates, before the "Advisory commission" of the trunk-line railroads ...

Mode of access: Internet.

Untersuchungen uber die moglichkeit algebraischer, differential...

Thesis (doctoral)--

A treatise on differential equations

Mode of access: Internet.

A treatise on differential equations,

Mode of access: Internet.

Elements of the differential and integral calculus, by a new method, founded on the true system of Sir Isaac Newton, without the use of infinitesimals or limits.

Mode of access: Internet.

Theory of differential equations.

pt. I. (Vol. I) Exact equations and Pfaff's problem. 1890.--pt. II. (Vol. II-III) Ordinary equations, not linear. 1900.--pt. III. (Vol. IV) Ordinary equations. 1902.--pt. IV (vol. V-VI) Partial differential equations. 1906.

Heredity and social fitness; a study of differential mating in a Pennsylvania family,

"Paper no. 32 of the Station for experimental evolution at Cold Spring Harbor, New York."

Proceedings of the Advisory commission appointed by the trunk lines to consider the question of differential rates between seaboard cities and common points in the west ...

Sessions in New York (p. 1-71) and in Baltimore (p. [73]-103) have special title-pages.

A treatise on infinitesimal calculus, containing differential and integral calculus, calculus of variations, applications to algebra and geometry, and analytical mechanics.

Vol. 3 and 4 form the author's Treatise on analytical mechanics.

The elementary differential geometry of plane curves,

Mode of access: Internet.

Adaptive stepsize based on control theory for stochastic differential equations

The numerical solution of stochastic differential equations (SDEs) has been focussed recently on the development of numerical methods with good stability and order properties. These numerical implementations have been made with fixed stepsize, but there are many situations when a fixed stepsize is not appropriate. In the numerical solution of ordinary differential equations, much work has been carried out on developing robust implementation techniques using variable stepsize. It has been necessary, in the deterministic case, to consider the best choice for an initial stepsize, as well as developing effective strategies for stepsize control-the same, of course, must be carried out in the stochastic case. In this paper, proportional integral (PI) control is applied to a variable stepsize implementation of an embedded pair of stochastic Runge-Kutta methods used to obtain numerical solutions of nonstiff SDEs. For stiff SDEs, the embedded pair of the balanced Milstein and balanced implicit method is implemented in variable stepsize mode using a predictive controller for the stepsize change. The extension of these stepsize controllers from a digital filter theory point of view via PI with derivative (PID) control will also be implemented. The implementations show the improvement in efficiency that can be attained when using these control theory approaches compared with the regular stepsize change strategy. (C) 2004 Elsevier B.V. All rights reserved.

Polarisation mode dispersion correlations with the coarse-step method

Having a fixed differential-group delay (DGD) term b′ in the coarse-step method results in a repetitive pattern in the autocorrelation function (ACF). We solve this problem by inserting a varying DGD term at each integration step. Furthermore we compute the range of values needed for b′ and simulate the phenomenon of polarisation mode dispersion for different statistical distributions of b′. We examine systematically the modified coarse-step method compared to the analytical model, through our simulation results. © 2006 Elsevier B.V. All rights reserved.

Intracavity dynamics in high-power mode-locked fiber lasers

A theoretical model is developed which characterizes the intracavity pulse evolutions in high-power fiber lasers. It is shown that experimentally observed dynamics of the key pulse parameters can be described by a reduced model of ordinary differential equations. Critical in driving the intracavity dynamics is the amplitude and phase modulations generated by the discrete elements in the laser. The theory gives a simple geometrical description of the intracavity dynamics and possible operation modes of the laser cavity. Furthermore, it provides a simple and efficient method for optimizing the performance of complex multiparametric laser systems.

Aniseikonia tests: The role of viewing mode, response bias, and size-color illusions.

PURPOSE To identify the factors responsible for the poor validity of the most common aniseikonia tests, which involve size comparisons of red-green stimuli presented haploscopically. METHODS Aniseikonia was induced by afocal size lenses placed before one eye. Observers compared the sizes of semicircles presented haploscopically via color filters. The main factor under study was viewing mode (free viewing versus short presentations under central fixation). To eliminate response bias, a three-response format allowed observers to respond if the left, the right, or neither semicircle appeared larger than the other. To control decisional (criterion) bias, measurements were taken with the lens-magnified stimulus placed on the left and on the right. To control for size-color illusions, measurements were made with color filters in both arrangements before the eyes and under binocular vision (without color filters). RESULTS Free viewing resulted in a systematic underestimation of lens-induced aniseikonia that was absent with short presentations. Significant size-color illusions and decisional biases were found that would be mistaken for aniseikonia unless appropriate action is taken. CONCLUSIONS To improve their validity, aniseikonia tests should use short presentations and include control conditions to prevent contamination from decisional/response biases. If anaglyphs are used, presence of size-color illusions must be checked for. TRANSLATIONAL RELEVANCE We identified optimal conditions for administration of aniseikonia tests and appropriate action for differential diagnosis of aniseikonia in the presence of response biases or size-color illusions. Our study has clinical implications for aniseikonia management.