Solving Finite-Linear-Path CTL-Formulas Using the CEGAR Approach

For any set S and any entire function f letwhere each zero of f — a with multiplicity m is repeated m times in Ef(S) (cf. [1]). It is assumed that the reader is familiar with the notations of the Nevanlinna Theory (see, for example, [2]). It will be convenient to let E denote any set of finite linear measure on 0 < r < ∞, not necessarily the same at each occurrence. We denote by S(r, f) any quantity satisfying .

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A Solution Method for an Optimal Controlled Vibrating Circle Shell by Measure and Classical Trajectory

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.52-54.1855 ◽

2011 ◽

Vol 52-54 ◽

pp. 1855-1860

Author(s):

J.A. Fakharzadeh ◽

F.N. Jafarpoor

Keyword(s):

Wave Equations ◽

Classical Trajectory ◽

Polar Coordinates ◽

Approximation Schemes ◽

Solution Technique ◽

Underlying Space ◽

The Mean ◽

Positive Coefficients ◽

And Control ◽

Finite Linear

The mean idea of this paper is to present a new combinatorial solution technique for the controlled vibrating circle shell systems. Based on the classical results of the wave equations on circle domains, the trajectory is considered as a finite trigonometric series with unknown coefficients in polar coordinates. Then, the problem is transferred to one in which its unknowns are a positive Radon measure and some positive coefficients. Extending the underlying space helps us to prove the existence of the solution. By using the density properties and some approximation schemes, the problem is deformed into a finite linear programming and the nearly optimal trajectory and control are identified simultaneously. A numerical example is also given.

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On the p-norm of the truncated n-dimensional Hilbert transform

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700029002 ◽

1991 ◽

Vol 43 (2) ◽

pp. 241-250 ◽

Cited By ~ 1

Author(s):

J.N. Pandey ◽

O.P. Singh

Keyword(s):

Linear Operator ◽

Linear Combination ◽

Hilbert Transform ◽

Bounded Linear Operator ◽

Measurable Subset ◽

Bounded Linear ◽

Finite Linear Combination ◽

The Hilbert Transform ◽

Finite Linear ◽

Hilbert Type

It is shown that a bounded linear operator T from Lρ(Rn) to itself which commutes both with translations and dilatations is a finite linear combination of Hilbert-type transforms. Using this we show that the ρ-norm of the Hilbert transform is the same as the ρ-norm of its truncation to any Lebesgue measurable subset of Rn with non-zero measure.

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The polynomial hull of a set of finite linear measure in Cn

Journal d Analyse Mathématique ◽

10.1007/bf02792540 ◽

1986 ◽

Vol 47 (1) ◽

pp. 238-242 ◽

Cited By ~ 4

Author(s):

H. Alexander

Keyword(s):

Linear Measure ◽

Polynomial Hull ◽

Finite Linear

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Evenly Convex Polyhedra: Finite Linear Systems Containing Strict Inequalities

Even Convexity and Optimization - EURO Advanced Tutorials on Operational Research ◽

10.1007/978-3-030-53456-1_2 ◽

2020 ◽

pp. 61-99

Author(s):

María D. Fajardo ◽

Miguel A. Goberna ◽

Margarita M. L. Rodríguez ◽

José Vicente-Pérez

Keyword(s):

Linear Systems ◽

Convex Polyhedra ◽

Strict Inequalities ◽

Finite Linear

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On Growth Rates of Permutations, Set Partitions, Ordered Graphs and Other Objects

The Electronic Journal of Combinatorics ◽

10.37236/799 ◽

2008 ◽

Vol 15 (1) ◽

Cited By ~ 1

Author(s):

Martin Klazar

Keyword(s):

Growth Rates ◽

Fibonacci Numbers ◽

Complete Graphs ◽

Linear Orders ◽

Set Partitions ◽

Ordered Graphs ◽

Containment Order ◽

Hereditary Properties ◽

Finite Linear ◽

Lower Ideal

For classes ${\cal O}$ of structures on finite linear orders (permutations, ordered graphs etc.) endowed with containment order $\preceq$ (containment of permutations, subgraph relation etc.), we investigate restrictions on the function $f(n)$ counting objects with size $n$ in a lower ideal in $({\cal O},\preceq)$. We present a framework of edge $P$-colored complete graphs $({\cal C}(P),\preceq)$ which includes many of these situations, and we prove for it two such restrictions (jumps in growth): $f(n)$ is eventually constant or $f(n)\ge n$ for all $n\ge 1$; $f(n)\le n^c$ for all $n\ge 1$ for a constant $c>0$ or $f(n)\ge F_n$ for all $n\ge 1$, $F_n$ being the Fibonacci numbers. This generalizes a fragment of a more detailed theorem of Balogh, Bollobás and Morris on hereditary properties of ordered graphs.

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