The boundary value problems of the previous chapter are distinguished by the fact that it is possible to derive more or less explicit solutions for the cases considered. A partial exception to this is the problem of the wave equation with an elastic constraint, for which the solution breaks the...
Further, we provide necessary and sufficient optimality conditions, and we show that our duality principle can be reformulated as a min–max result which is quite useful for numerical implementations. As an example, we illustrate the application of our method to a celebrated free boundary problem....
where p¯(nΔ) is a number between the maximum and the minimum value of p(x),x∈(nΔ−Δ,nΔ] (such a number exists by the mean value theorem of calculus). Then we can write (2.155)H(xΔ)=−∑n=−∞+∞Δp¯(nΔ)log(Δp¯(nΔ)), and since ∑n=−∞+∞...
The latter problem was connected to the question of expressing the sum of a series using an integral. The outcome of this research was Euler's derivation of what would later become known as the Euler–Maclaurin formula. Euler subsequently returned to interpolation and formulated the theory of ...
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Keywords Boundary value problem Distribution Fourier transform Functional Analysis PDE Sobolev space Systems and Control convolution harmonic analysis Search within this book Search Table of contents (6 chapters) Front Matter Pages i-xxxv Download chapter PDF Notation and Conventions ...
If that doesn't work, please contact support so we can address the problem. Abstract We start from Marra–Spada duality between semisimple MV-algebras and Tychonoff spaces, and we consider the particular cases when the ω-skeleta of the MV-algebras are restricted in some way. In particular ...
calculus formal verification logic programming verification algorithm analysis and problem complexity Table of contents (26 papers) Front Matter Download chapterPDF Combining Petri Nets and other formal methods W. Reisig Pages 24-44 A polynomial-time graph algorithm to decide liveness of some basic clas...
Such an equation is often referred to as the thin-film equation, and although it is much simpler than the full hydrodynamic problem, it still captures its basic features. Detailed descriptions of the long-wave approximation can be found in Refs. [44, 54, 57]....
In the problem of variable selection we are given a set (ψγ)γ∈Γ of functions from the input space X into the output space Y and we aim at selecting those functions which are needed to represent the regression function, where the representation is typically given by a linear combination...