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Showing 1 to 18 of 18 for “"Functional equation"”.
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Towards a Connection between Linear Embedding and the Poincaré Functional Equation.
<p>Several linear embeddings of the logistic equation, <em>x</em><sub><em>n</em>+1</sub>=<em>ax<sub>n</sub></em>(1-<em>x<sub>n</sub></em>) are considered, the goal being to establish a connection between linear embedding and the Poincaré Functional Equation. In particular, we consider linear …
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On the Average Order of the Divisor Function, Lattice Point Functions, and Other Arithmetical Functions
… by Dirichlet series satisfying a very general functional equation with gamma factors. We obtain one and two-sided (OMEGA)-theorems for the error terms associated with certain weighted averages of these arithmetical functions. For example, if {a(n)} is such an arithmetical function generated by …
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A characterization of the tail _-field for certain Markov chains
… measurable sets of 0 leads to the solution of a functional equation of the general form pf = f.
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Hecke Correspondence for Automorphic Integrals with Infinite Log-Polynomial Periods
… his correspondence between Dirichlet series with functional equations and automorphic forms, there have been a great number of generalizations. Of particular interest is a generalization due to Bochner that gives a correspondence between Dirichlet series with any finite number of poles that …
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p-adic Heights of Heegner points on Shimura curves
… L_p(f_E,-) and prove that when the sign of its functional equation is -1, its central derivative is given by the p-adic height of a Heegner point on the abelian variety A associated to f. This p-adic Gross-Zagier formula generalises the result obtained by Perrin-Riou when F=Q and N satisfies the …
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Applications of probability to partial differential equations and infinite dimensional analysis
… approach to the study of the Wright-Fisher equation, an equation which is used to model demographic evolution in the presence of diffusion. The fundamental solution to the Wright-Fisher equation is carefully analyzed by relating it to the fundamental solution to a model equation which has …
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Higher Dimensional Adeles, Mean-Periodicity and Zeta Functions of Arithmetic Surfaces
… amongst them - meromorphic continuation and functional equation. Our weapon of choice is the so-called “mean-periodicity correspondence”, which provides a passage between nicely behaved arithmetic schemes and mean-periodic functions in certain functional spaces. In what follows, there are two …
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Kernels of adjoints of composition operators on Hilbert spaces of analytic functions
… by Hammond, Moorhouse, and Robbins to give a functional equation that characterizes functions in the kernel of the adjoint of a composition operator with a rational symbol of degree two on the Hardy space. Chapters 5 and 6 use the adjoint formulas by Goshabulaghi and Vaezi to prove some …
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Microlocal regularity of an inverse problem for the multidimensional wave equation
… problems for the multidimensional acoustic wave equation with point energy sources. The inverse problem is to identify the coefficients from the knowledge of boundary measurements of the solution. In this research we formulate an inverse problem for the wave equation with constant wave speed as a …
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Asymptotic distribution of eigenvalues of random matrices and characterization of the Gaussian distribution by rotational invariance
The study falls in the area of random equations; in particular properties of random matrices have been studied. The dissertation makes precise some statistical theories of spectra developed in recent years by a number of physicists. Two basic results have been achieved. The first result is a …
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A Deep Study of Fuzzy Implications
… QL-implications we get a full solution of the functional equation $I(x,y)=I(x,I(x,y))$, for all $x$, $y\in[0,1]$. In Chapter 6 we study for the most important t-norms, t-conorms and S-implications their robustness against different perturbations in a fuzzy rule-based system. We define and …
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Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance
… for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either …
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Acoustic diffraction from a semi-infinite elastic plate under arbitrary fluid loading with application to scattering from Arctic ice leads
… plate are adequately described by the thin plate equation (kH ≲ 1). The diffraction problem relates to issues in long range sound propagation through partially ice-covered Arctic waters, where open leads or polynya on the surface represent features from which acoustic energy can be diffracted or …
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Two Studies of Constraints in High Dimensions: Entropy Inequalities and the Randomized Symmetric Binary Perceptron
… ≥ xᵏ⁻¹H(x), where 0 < αₖ < 1 is given by a functional equation. The k = 2 case was the key technical tool driving recent breakthroughs on the union-closed sets conjecture, and the k → ∞ case can be considered the "high dimensional limit". We express ((dᵏ⁺¹) / (dxᵏ⁺¹)) xᵏ⁻ʳH(xʳ) as a rational …
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Higher Derivatives of the Hurwitz Zeta Function
<p>The Riemann zeta function ζ(s) is one of the most fundamental functions in number theory. Euler demonstrated that ζ(s) is closely connected to the prime numbers and Riemann gave proofs of the basic analytic properties of the zeta function. Values of the zeta function and its derivatives have …
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Computing policy parameters for stochastic inventory control using stochastic dynamic programming approaches
… the (R,s,S) policy computation in the form of a functional equation. The second is a heuristic formed by a hybridisation of (R,S) and (s,S) policy parameters solvers. These heuristics can compute near-optimal parameters in a fraction of time compared to the exact methods. They can be used to …
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Ramanujan's identities, Voronoi summation formula, and zeros of partial sums of zeta and L-functions
Made available in DSpace on 2015-09-29T20:38:57Z (GMT). No. of bitstreams: 2 ROY-DISSERTATION-2015.pdf: 821854 bytes, checksum: 7abf6b7f9b1c512d8963ac66590c92b7 (MD5) LICENSE.txt: 4208 bytes, checksum: 502c6a39161a3e8620cd8507bf46885c (MD5) Previous issue date: 2015-08-03