On norm of single layer potentials on segments

2016 ◽  
Vol 22 (1) ◽  
Author(s):  
Seyed M. Zoalroshd
Keyword(s):  
Upper Bound ◽  
Single Layer ◽  
Exact Expression ◽  
Operator Norm ◽  
Equal Length ◽  
Layer Potentials ◽  
Schmidt Norm ◽  
Special Case

AbstractWe show that, for a special case, equality of the spectra of single layer potentials defined on two segments implies that these segments must have equal length. We also provide an upper bound for the operator norm and exact expression for the Hilbert–Schmidt norm of single layer potentials on segments.

scholarly journals Inversions Within Restricted Fillings of Young Tableaux

10.37236/1030 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Sarah Iveson
Keyword(s):  
Upper Bound ◽  
Exact Expression ◽  
Flag Varieties ◽  
Young Tableaux ◽  
Geometric Properties ◽  
Number Of Components ◽  
Hessenberg Varieties ◽  
Special Cases

In this paper we study inversions within restricted fillings of Young tableaux. These restricted fillings are of interest because they describe geometric properties of certain subvarieties, called Hessenberg varieties, of flag varieties. We give answers and partial answers to some conjectures posed by Tymoczko. In particular, we find the number of components of these varieties, give an upper bound on the dimensions of the varieties, and give an exact expression for the dimension in some special cases. The proofs given are all combinatorial.

scholarly journals A Study on f Number of Points for Number of Points with Inter-Distance of Less Than, or for Number of Points with Inter-Distance of or More to Necessarily Exist on Plane

2018 ◽  
Author(s):  
Benjamin Smith
Keyword(s):  
Upper Bound ◽  
Ramsey Number ◽  
Minimum Value ◽  
Special Case

We defined number of points with an inter-distance of β or more to necessarily exist on a plane. Furthermore, we aimed to reduce the range of this minimum value. We first showed that the upper bound of this value could be scaled by , and further reduced the constant that was multiplied. We compared the upper bound of and the Ramsey number in a special case and confirmed that was a better upper bound than except when were both small or trivial.

Poisson approximation for (k1, k2)-events via the Stein-Chen method

2004 ◽  
Vol 41 (4) ◽  
pp. 1081-1092 ◽  
Author(s):  
P. Vellaisamy
Keyword(s):  
Limit Theorem ◽  
Rate Of Convergence ◽  
Upper Bound ◽  
Success Probability ◽  
Random Variable ◽  
Poisson Approximation ◽  
Bernoulli Trials ◽  
Poisson Random Variable ◽  
Markov Dependent Trials ◽  
Special Case

Consider a sequence of independent Bernoulli trials with success probability p. Let N(n; k1, k2) denote the number of times that k1 failures are followed by k2 successes among the first n Bernoulli trials. We employ the Stein-Chen method to obtain a total variation upper bound for the rate of convergence of N(n; k1, k2) to a suitable Poisson random variable. As a special case, the corresponding limit theorem is established. Similar results are obtained for Nk3(n; k1, k2), the number of times that k1 failures followed by k2 successes occur k3 times successively in n Bernoulli trials. The bounds obtained are generally sharper than, and improve upon, some of the already known results. Finally, the technique is adapted to obtain Poisson approximation results for the occurrences of the above-mentioned events under Markov-dependent trials.

scholarly journals Analysis of Ring Compression Test by Upper Bound Theorem as Special Case of Non-symmetric Part

2015 ◽  
Vol 132 ◽  
pp. 334-341 ◽  
Author(s):  
A. Moncada ◽  
F. Martín ◽  
L. Sevilla ◽  
A.M. Camacho ◽  
M.A. Sebastián
Keyword(s):  
Compression Test ◽  
Upper Bound ◽  
Symmetric Part ◽  
Ring Compression Test ◽  
Upper Bound Theorem ◽  
Ring Compression ◽  
Bound Theorem ◽  
Special Case

scholarly journals TESTING EMBEDDABILITY BETWEEN METRIC SPACES

2009 ◽  
Vol 20 (02) ◽  
pp. 313-329
Author(s):  
CHING-LUEH CHANG ◽  
YUH-DAUH LYUU ◽  
YEN-WU TI
Keyword(s):  
Metric Space ◽  
Upper Bound ◽  
Metric Spaces ◽  
Graph Isomorphism ◽  
Upper And Lower Bounds ◽  
Wrong Answer ◽  
Probability Of Error ◽  
Finite Metric Space ◽  
Finite Metric Spaces ◽  
Special Case

Let L ≥ 1, ε > 0 be real numbers, (M, d) be a finite metric space and (N, ρ) be a metric space. A query to a metric space consists of a pair of points and asks for the distance between these points. We study the number of queries to metric spaces (M, d) and (N, ρ) needed to decide whether (M, d) is L-bilipschitz embeddable into (N, ρ) or ∊-far from being L-bilipschitz embeddable into N, ρ). When (M, d) is ∊-far from being L-bilipschitz embeddable into (N, ρ), we allow an o(1) probability of error (i.e., returning the wrong answer "L-bilipschitz embeddable"). However, no error is allowed when (M, d) is L-bilipschitz embeddable into (N, ρ). That is, algorithms with only one-sided errors are studied in this paper. When |M| ≤ |N| are both finite, we give an upper bound of [Formula: see text] on the number of queries for determining with one-sided error whether (M, d) is L-bilipschitz embeddable into (N, ρ) or ∊-far from being L-bilipschitz embeddable into (N, ρ). For the special case of finite |M| = |N|, the above upper bound evaluates to [Formula: see text]. We also prove a lower bound of Ω(|N|3/2) for the special case when |M| = |N| are finite and L = 1, which coincides with testing isometry between finite metric spaces. For finite |M| = |N|, the upper and lower bounds thus match up to a multiplicative factor of at most [Formula: see text], which depends only sublogarithmically in |N|. We also investigate the case when (N, ρ) is not necessarily finite. Our results are based on techniques developed in an earlier work on testing graph isomorphism.

scholarly journals On Partitioning and Packing Products with Rectangles

1994 ◽  
Vol 3 (4) ◽  
pp. 429-434 ◽  
Author(s):  
Rudolf Ahlswede ◽  
Ning Cai
Keyword(s):  
Upper Bound ◽  
Complete Graphs ◽  
Minimal Size ◽  
Uniform Hypergraphs ◽  
Image Position ◽  
Special Case

In [1] we introduced and studied for product hypergraphs where ℋi = (i,ℰi), the minimal size π(ℋn) of a partition of into sets that are elements of . The main result was thatif the ℋis are graphs with all loops included. A key step in the proof concerns the special case of complete graphs. Here we show that (1) also holds when the ℋi are complete d-uniform hypergraphs with all loops included, subject to a condition on the sizes of the i. We also present an upper bound on packing numbers.

scholarly journals A NOTE ON AXISYMMETRIC SUPERCRITICAL CONING IN A POROUS MEDIUM

2014 ◽  
Vol 55 (4) ◽  
pp. 327-335 ◽  
Author(s):  
G. C. HOCKING ◽  
H. ZHANG
Keyword(s):  
Porous Medium ◽  
Spectral Method ◽  
Flow Rate ◽  
Upper Bound ◽  
Single Layer ◽  
Withdrawal Rate ◽  
Entry Angle ◽  
Single Entry ◽  
Layer Flow

AbstractThe steady response of a fluid with two layers of different density in a porous medium is considered during extraction through a point sink. Supercritical withdrawal in which both layers are being withdrawn is investigated using a spectral method. We show that for each withdrawal rate, there is a single entry angle of the interface into the point sink. As the flow rate decreases the angle of entry steepens until it becomes almost vertical, at which point the method fails. This limit is shown to correspond to the upper bound on sub-critical (single-layer) flow.

scholarly journals Collision-avoidance and flocking in the Cucker–Smale-type model with a discontinuous controller

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jianfei Cheng ◽  
Xiao Wang ◽  
Yicheng Liu
Keyword(s):  
Weight Function ◽  
Collision Avoidance ◽  
Upper Bound ◽  
Finite Time ◽  
Relative Velocity ◽  
Sufficient Conditions ◽  
Repulsive Force ◽  
Type Model ◽  
Movement Tendency ◽  
Special Case

<p style='text-indent:20px;'>The collision-avoidance and flocking of the Cucker–Smale-type model with a discontinuous controller are studied. The controller considered in this paper provides a force between agents that switches between the attractive force and the repulsive force according to the movement tendency between agents. The results of collision-avoidance are closely related to the weight function <inline-formula><tex-math id="M1">\begin{document}$ f(r) = (r-d_0)^{-\theta } $\end{document}</tex-math></inline-formula>. For <inline-formula><tex-math id="M2">\begin{document}$ \theta \ge 1 $\end{document}</tex-math></inline-formula>, collision will not appear in the system if agents' initial positions are different. For the case <inline-formula><tex-math id="M3">\begin{document}$ \theta \in [0,1) $\end{document}</tex-math></inline-formula> that not considered in previous work, the limits of initial configurations to guarantee collision-avoidance are given. Moreover, on the basis of collision-avoidance, we point out the impacts of <inline-formula><tex-math id="M4">\begin{document}$ \psi (r) = (1+r^2)^{-\beta } $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M5">\begin{document}$ f(r) $\end{document}</tex-math></inline-formula> on the flocking behaviour and give the decay rate of relative velocity. We also estimate the lower and upper bound of distance between agents. Finally, for the special case that agents moving on the 1-D space, we give sufficient conditions for the finite-time flocking.</p>

scholarly journals Extremal eigenvalues of local Hamiltonians

Quantum ◽  
2017 ◽  
Vol 1 ◽  
pp. 6 ◽  
Author(s):  
Aram W. Harrow ◽  
Ashley Montanaro
Keyword(s):  
Ground State Energy ◽  
Constraint Satisfaction ◽  
Upper Bound ◽  
Ground State ◽  
State Energy ◽  
Constraint Satisfaction Problems ◽  
Operator Norm ◽  
Product State ◽  
Classical Algorithm ◽  
Spin Hamiltonians

We apply classical algorithms for approximately solving constraint satisfaction problems to find bounds on extremal eigenvalues of local Hamiltonians. We consider spin Hamiltonians for which we have an upper bound on the number of terms in which each spin participates, and find extensive bounds for the operator norm and ground-state energy of such Hamiltonians under this constraint. In each case the bound is achieved by a product state which can be found efficiently using a classical algorithm.

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