A control problem for delay partial differential equations is considered. The Fourier method and special functions, called the delayed sine and delayed cosine functions, are used for solving. AMS Subject Classifications: 35Q93, 34K35, 35L20.

By taking sets of utility functions as primitive, we define an ordering over assumptions on utility functions that gauges their measurement requirements. Cardinal and ordinal assumptions constitute two levels of measurability, but other assumptions lie between these extremes. We apply the ordering to explanations of why preferences should be convex. The assumption that utility is concave qualif...

K Arrow’s work on social welfare proposed a set of conditions that a function to aggregate ordinal preferences of the members of a group should satisfy, proving that it was not possible to satisfy all these assumptions simultaneously. Later, Ralph Keeney adapted these conditions and proposed a cardinal utility axiomatization for the problem of aggregating the utility functions. This note discus...

In this paper, an effective direct method to determine the numerical solution of linear and nonlinear Fredholm and Volterra integral and integro-differential equations is proposed. The method is based on expanding the required approximate solution as the elements of Chebyshev cardinal functions. The operational matrices for the integration and product of the Chebyshev cardinal functions are des...

A numerical technique is presented for the solution of Falkner-Skan equation. The nonlinear ordinary differential equation is solved using Chebyshev cardinal functions. The method have been derived by first truncating the semi-infinite physical domain of the problem to a finite domain and expanding the required approximate solution as the elements of Chebyshev cardinal functions. Using the oper...

t AbstractLeast-squares' sine-fit algorithms are used extensively in signal-processing applications. The parameter estimates produced by such algorithms are subject to both random and systematic errors when the record of input samples consists of a fundamental sine wave corrupted by harmonic distortion or noise. The errors occur because, in general, such sine-fits will incorporate a portion of ...

In this paper, we investigate the dynamics of a completely inelastic ball on a vertically vibrated plate. We construct a computational model using various forcing waveforms for the plate and generate associated bifurcation diagrams. The forcing functions used are a superposition of two sine waves with an integer ratio of frequencies. We then observe experimentally some of the predictions made b...

We study the properties of the double-frequency sine–Gordon model in the vicinity of the Ising quantum phase transition displayed by this model. Using a mapping onto a generalised lattice quantum Ashkin-Teller model, we obtain critical and nearly-off-critical correlation functions of various operators. We discuss applications of the double-sine-Gordon model to one-dimensional physical systems, ...