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- Connectivity (2)
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Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Riesz Bases Of Root Vectors Of Indefinite Sturm-Liouville Problems With Eigenparameter Dependent Boundary Conditions. Ii, Paul Binding, Branko Ćurgus
Riesz Bases Of Root Vectors Of Indefinite Sturm-Liouville Problems With Eigenparameter Dependent Boundary Conditions. Ii, Paul Binding, Branko Ćurgus
Mathematics Faculty Publications
We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions affinely dependent on the eigenparameter. We give sufficient conditions under which the root vectors of this Sturm-Liouville problem can be selected to form a Riesz basis of a corresponding weighted Hilbert space.
Highly Connected Random Geometric Graphs, Paul Balister, Béla Bollobás, Amites Sarkar, Mark Walters
Highly Connected Random Geometric Graphs, Paul Balister, Béla Bollobás, Amites Sarkar, Mark Walters
Mathematics Faculty Publications
Let P be a Poisson process of intensity 1 in a square Sn of area n. We construct a random geometric graph Gn,k by joining each point of P to its k nearest neighbours. For many applications it is desirable that Gn,k is highly connected, that is, it remains connected even after the removal of a small number of its vertices. In this paper we relate the study of the s-connectivity of Gn,k to our previous work on the connectivity of Gn,k. Roughly speaking, we show that for s=o(logn), the threshold (in k) for …
Optical Tomography For Media With Variable Index Of Refraction, Stephen R. Mcdowall
Optical Tomography For Media With Variable Index Of Refraction, Stephen R. Mcdowall
Mathematics Faculty Publications
Optical tomography is the use of near-infrared light to determine the optical absorption and scattering properties of a medium M ⊂ Rn. If the refractive index is constant throughout the medium, the steady-state case is modeled by the stationary linear transport equation in terms of the Euclidean metric and photons which do not get absorbed or scatter travel along straight lines. In this expository article we consider the case of variable refractive index where the dynamics are modeled by writing the transport equation in terms of a Riemannian metric; in the absence of interaction, photons follow the geodesics …
Modulation Invariant Bilinear T(1) Theorem, Árpád Bényi, Ciprian Demeter, Andrea R. Nahmod, Christoph M. Thiele, Rodolfo H. (Rudolfo Humberto) Torres, Paco Villarroya
Modulation Invariant Bilinear T(1) Theorem, Árpád Bényi, Ciprian Demeter, Andrea R. Nahmod, Christoph M. Thiele, Rodolfo H. (Rudolfo Humberto) Torres, Paco Villarroya
Mathematics Faculty Publications
We prove a T(1) theorem for bilinear singular integral operators (trilinear forms) with a one-dimensional modulation symmetry.
Local Well-Posedness Of Nonlinear Dispersive Equations On Modulation Spaces, Árpád Bényi, Kasso A. Okoudjou
Local Well-Posedness Of Nonlinear Dispersive Equations On Modulation Spaces, Árpád Bényi, Kasso A. Okoudjou
Mathematics Faculty Publications
By using tools of time-frequency analysis, we obtain some improved local well-posedness results for the nonlinear Schrödinger, nonlinear wave and nonlinear Klein–Gordon equations with Cauchy data in modulation spaces ℳ0,sp,1.
A Critical Constant For The K Nearest-Neighbour Model, Paul Balister, Béla Bollobás, Amites Sarkar, Mark Walters
A Critical Constant For The K Nearest-Neighbour Model, Paul Balister, Béla Bollobás, Amites Sarkar, Mark Walters
Mathematics Faculty Publications
Let P be a Poisson process of intensity 1 in a square Sn of area n. For a fixed integer k, join every point of P to its k nearest neighbours, creating an undirected random geometric graph Gn,k. We prove that there exists a critical constant ccrit such that, for c‹ccrit, Gn,⌊clogn⌋ is disconnected with probability tending to 1 as n →∞ and, for c‹ccrit, Gn,⌊clogn⌋ is connected with probability tending to 1 as n →∞. This answers a question …
Numerical Bifurcation Of Separable Parameterized Equations, Yun-Qiu Shen, Tjalling Ypma
Numerical Bifurcation Of Separable Parameterized Equations, Yun-Qiu Shen, Tjalling Ypma
Mathematics Faculty Publications
Many applications give rise to separable parameterized equations, which have the form A(y, µ)z + b(y, µ) = 0, where z ∈ RN , y ∈ Rn, µ ∈ Rs, and the (N + n) × N matrix A(y, µ) and (N + n) vector b(y, µ) are C2 -Lipschitzian in (y, µ) ∈ Ω ⊂ Rn × Rs. We present a technique which reduces the original equation to the form …