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- Calderon-Zygmund theory (3)
- Bilinear operators (2)
- Singular integrals (2)
- Anisotropic elementary symbols (1)
- Anisotropic inhomogeneous symbols (1)
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- Bessel potential (1)
- Bilinear Hormander classes (1)
- Bilinear pseudodifferential operators (1)
- Calderón–Zygmund operators (1)
- Ceva theorem (1)
- Commutators (1)
- Commutators. (1)
- Eavesdroppers (1)
- Geometric models for secrecy in wireless networks (1)
- HELP inequality (1)
- Indefinite Sturm-Liouville problem (1)
- LU factorization (1)
- Maximal function (1)
- Menelaus theorem (1)
- Poisson point processes (1)
- Regular critical point (1)
- Riesz basis (1)
- Riesz potential (1)
- Routh's triangle theorem (1)
- Secrecy graph (1)
- Separable nonlinear equations (1)
- Sobolev inequality (1)
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Articles 1 - 13 of 13
Full-Text Articles in Physical Sciences and Mathematics
Compact Bilinear Operators And Commutators, Árpád Bényi, Rodolfo H. (Rodolfo Humberto) Torres
Compact Bilinear Operators And Commutators, Árpád Bényi, Rodolfo H. (Rodolfo Humberto) Torres
Mathematics Faculty Publications
A notion of compactness in the bilinear setting is explored. Moreover, commutators of bilinear Calderon-Zygmund operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be compact.
Percolation In The Secrecy Graph, Amites Sarkar, Martin Haenggi
Percolation In The Secrecy Graph, Amites Sarkar, Martin Haenggi
Mathematics Faculty Publications
The secrecy graph is a random geometric graph which is intended to model the connectivity of wireless networks under secrecy constraints. Directed edges in the graph are present whenever a node can talk to another node securely in the presence of eavesdroppers, which, in the model, is determined solely by the locations of the nodes and eavesdroppers. In the case of infinite networks, a critical parameter is the maximum density of eavesdroppers that can be accommodated while still guaranteeing an infinite component in the network, i.e., the percolation threshold. We focus on the case where the locations of the …
Comprehensive Analysis Of Escape-Cone Losses From Luminescent Waveguides, Stephen R. Mcdowall, Tristan Butler, Edward Bain, Kelsey Scharnhorst, David L. Patrick
Comprehensive Analysis Of Escape-Cone Losses From Luminescent Waveguides, Stephen R. Mcdowall, Tristan Butler, Edward Bain, Kelsey Scharnhorst, David L. Patrick
Mathematics Faculty Publications
Luminescent waveguides (LWs) occur in a wide range of applications, from solar concentrators to doped fiber amplifiers. Here we report a comprehensive analysis of escape-cone losses in LWs, which are losses associated with internal rays making an angle less than the critical angle with a waveguide surface. For applications such as luminescent solar concentrators, escape-cone losses often dominate all others. A statistical treatment of escape-cone losses is given accounting for photoselection, photon polarization, and the Fresnel relations, and the model is used to analyze light absorption and propagation in waveguides with isotropic and orientationally aligned luminophores. The results are then …
A Generalization Of Routh's Triangle Theorem, Árpád Bényi, Branko Ćurgus
A Generalization Of Routh's Triangle Theorem, Árpád Bényi, Branko Ćurgus
Árpád Bényi
No abstract provided.
On A Class Of Bilinear Pseudodifferential Operators, Árpád Bényi, Tadahiro Oh
On A Class Of Bilinear Pseudodifferential Operators, Árpád Bényi, Tadahiro Oh
Mathematics Faculty Publications
We provide a direct proof for the boundedness of pseudodifferential operators with symbols in the bilinear Hörmander class BS10,ƍ, 0 ≤ ƍ
On The Hörmander Classes Of Bilinear Pseudodifferential Operators, Ii, Árpád Bényi, Frederic Bernicot, Diego Maldonado, Rodolfo H. (Rodolfo Humberto) Torres, Virginia Naibo
On The Hörmander Classes Of Bilinear Pseudodifferential Operators, Ii, Árpád Bényi, Frederic Bernicot, Diego Maldonado, Rodolfo H. (Rodolfo Humberto) Torres, Virginia Naibo
Mathematics Faculty Publications
Boundedness properties for pseudodifferential operators with symbols in the bilinear Hörmander classes of sufficiently negative order are proved. The results are obtained in the scale of Lebesgue spaces, and in some cases, end-point estimates involving weak-type spaces and BMO are provided as well. From the Lebesgue space estimates, Sobolev ones are then easily obtained using functional calculus and interpolation. In addition, it is shown that, in contrast with the linear case, operators associated with symbols of order zero may fail to be bounded on products of Lebesgue spaces.
The Sobolev Inequality On The Torus Revisited, Árpád Bényi, Tadahiro Oh
The Sobolev Inequality On The Torus Revisited, Árpád Bényi, Tadahiro Oh
Mathematics Faculty Publications
We revisit the Sobolev inequality for periodic functions on the d-dimensional torus. We provide an elementary Fourier analytic proof of this inequality which highlights both the similarities and differences between the periodic setting and the classical d-dimensional Euclidean one.
Compact Bilinear Operators And Commutators, Árpád Bényi, Rodolfo H. (Rodolfo Humberto) Torres
Compact Bilinear Operators And Commutators, Árpád Bényi, Rodolfo H. (Rodolfo Humberto) Torres
Mathematics Faculty Publications
A notion of compactness in the bilinear setting is explored. Moreover, commutators of bilinear Caldeŕon-Zygmund operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be compact.
Anisotropic Classes Of Inhomogeneous Pseudodifferential Symbols, Árpád Bényi, Marcin Bownik
Anisotropic Classes Of Inhomogeneous Pseudodifferential Symbols, Árpád Bényi, Marcin Bownik
Mathematics Faculty Publications
We introduce a class of pseudodifferential operators in the anisotropic setting induced by an expansive dilation A which generalizes the classical isotropic class Smγ,δ of inhomogeneous symbols. We extend a well-known L 2-boundedness result to the anisotropic class S0δ,δ(A), 0 ≤ δ < 1. As a consequence, we deduce that operators with symbols in the anisotropic class S01,0(A) are bounded on L p spaces, 1 < p < ∞.
The Riesz Basis Property Of An Indefinite Sturm-Liouville Problem With Non-Separated Boundary Conditions, Branko Ćurgus, Andreas Fleige, Aleksey Kostenko
The Riesz Basis Property Of An Indefinite Sturm-Liouville Problem With Non-Separated Boundary Conditions, Branko Ćurgus, Andreas Fleige, Aleksey Kostenko
Mathematics Faculty Publications
We consider a regular indefinite Sturm–Liouville eigenvalue problem −f′′ + q f = λ r f on [a, b] subject to general self-adjoint boundary conditions and with a weight function r which changes its sign at finitely many, so-called turning points. We give sufficient and in some cases necessary and sufficient conditions for the Riesz basis property of this eigenvalue problem. In the case of separated boundary conditions we extend the class of weight functions r for which the Riesz basis property can be completely characterized in terms of the local behavior of r in …
Solving Separable Nonlinear Equations Using Lu Factorization, Yun-Qiu Shen, Tjalling Ypma
Solving Separable Nonlinear Equations Using Lu Factorization, Yun-Qiu Shen, Tjalling Ypma
Mathematics Faculty Publications
Separable nonlinear equations have the form F(y,z) ≡ A (y)z + b(y) = 0, where the matrix A(y)∈ R m × N and the vector b(y) ∈ Rmare continuously differentiable functions of y ∈ Rn and z ∈ RN. We assume that m ≥ N + n, and F'(y,z) has full rank. We present a numerical method to compute the solution (y∗, z∗) for fully determined systems (m = N+ n) and compatible overdetermined systems (m …
Secrecy Coverage, Amites Sarkar, Martin Haenggi
Secrecy Coverage, Amites Sarkar, Martin Haenggi
Mathematics Faculty Publications
Motivated by information-theoretic secrecy, geometric models for secrecy in wireless networks have begun to receive increased attention. The general question is how the presence of eavesdroppers affects the properties and performance of the network. Previously, the focus has been mostly on connectivity. Here we study the impact of eavesdroppers on the coverage of a network of base stations. The problem we address is the following. Let base stations and eavesdroppers be distributed as stationary Poisson point processes in a disk of area n. If the coverage of each base station is limited by the distance to the nearest eavesdropper, …
M-Addition, Tim Mesikepp
M-Addition, Tim Mesikepp
WWU Graduate School Collection
This study builds upon the work of Gardner, Hug and Weil [1, Section 6] by further exploring the properties of M-addition. It is shown that several well-known theorems on Minkowski addition have M-addition parallels, including results involving intersections, the valuation property and the convex hull. The last of these enables us to detail su cient conditions for when the M-sum of convex polytopes is a convex polytope. Nested operations of M-addition are also examined and an M-addition generalization of the Shapley-Folkman Lemma and a related bound are offered.