scholarly journals An upper bound for higher order eigenvalues of symmetric graphs

2021 ◽  
Vol -1 (-1) ◽  
Author(s):  
Shinichiro KOBAYASHI
Keyword(s):  
Upper Bound ◽  
Higher Order ◽  
Symmetric Graphs

On the Modal μ-Calculus Over Finite Symmetric Graphs

2015 ◽  
Vol 65 (4) ◽  
Author(s):  
Giovanna D’Agostino ◽  
Giacomo Lenzi
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Satisfiability Problem ◽  
Finite Model ◽  
Model Property ◽  
Finite Model Property ◽  
Symmetric Graphs ◽  
Trivial Consequence

AbstractIn this paper we consider the alternation hierarchy of the modal μ-calculus over finite symmetric graphs and show that in this class the hierarchy is infinite. The μ-calculus over the symmetric class does not enjoy the finite model property, hence this result is not a trivial consequence of the strictness of the hierarchy over symmetric graphs. We also find a lower bound and an upper bound for the satisfiability problem of the μ-calculus over finite symmetric graphs.

A Higher-Order Period Function and Its Application

2015 ◽  
Vol 25 (10) ◽  
pp. 1550140 ◽  
Author(s):  
Linping Peng ◽  
Lianghaolong Lu ◽  
Zhaosheng Feng
Keyword(s):  
Periodic Orbits ◽  
Upper Bound ◽  
Critical Period ◽  
Higher Order ◽  
Quadratic System ◽  
Critical Periods ◽  
Explicit Formulas ◽  
Period Function ◽  
Isochronous System ◽  
Isochronous Centers

This paper derives explicit formulas of the q th period bifurcation function for any perturbed isochronous system with a center, which improve and generalize the corresponding results in the literature. Based on these formulas to the perturbed quadratic and quintic rigidly isochronous centers, we prove that under any small homogeneous perturbations, for ε in any order, at most one critical period bifurcates from the periodic orbits of the unperturbed quadratic system. For ε in order of 1, 2, 3, 4 and 5, at most three critical periods bifurcate from the periodic orbits of the unperturbed quintic system. Moreover, in each case, the upper bound is sharp. Finally, a family of perturbed quintic rigidly isochronous centers is shown, which has three, for ε in any order, as the exact upper bound of the number of critical periods.

Higher-order bounds on the conductivity of composites from symmetry considerations

1993 ◽  
Vol 443 (1918) ◽  
pp. 451-455 ◽  
Keyword(s):  
Upper Bound ◽  
Substantial Improvement ◽  
Higher Order ◽  
Geometric Parameters ◽  
Third Order ◽  
Symmetry Properties ◽  
Two Component ◽  
Order Bounds ◽  
Parameter Dependent ◽  
Independent Pair

It is well known that symmetry considerations can lead to improved bounds on, or even determine, the conductivity of two-component symmetric materials. The present work exploits symmetry properties to derive explicit higher-order bounds for three-component symmetric materials. The bounds contain geometric parame­ters. But even without any knowledge of these geometric parameters, substantial improvement on previous bounds is made. This is discussed in the context of equiaxed polycrystals. Results include a parameter-independent pair of bounds that for some polycrystals becomes third-order, and a parameter-dependent third-order upper bound that can be partially attained.

scholarly journals Some consequences of theories with maximal acceleration in laser–plasma acceleration

2019 ◽  
Vol 34 (15) ◽  
pp. 1950118 ◽  
Author(s):  
Ricardo Gallego Torromé
Keyword(s):  
Laser Plasma ◽  
Upper Bound ◽  
Charged Particles ◽  
Higher Order ◽  
Classical Electrodynamic ◽  
Plasma Acceleration ◽  
Maximal Acceleration ◽  
Jet Theory ◽  
Laser Plasma Acceleration

In this paper, we consider classical electrodynamic theories with maximal acceleration and some of their phenomenological consequences for laser–plasma acceleration. It is shown that in a recently proposed higher-order jet theory of electrodynamics, the maximal effective acceleration reachable by a consistent bunch of point-charged particles being accelerated by the wakefield is damped for bunches containing large number of charged particles. We argue that such a prediction of the theory is falsifiable. In the case of Born–Infeld kinematics, laser–plasma acceleration phenomenology provides an upper bound for the Born–Infeld parameter b. Improvements in the beam qualities will imply stronger constraints on b.

scholarly journals Density Estimates of 1-Avoiding Sets via Higher Order Correlations

2020 ◽  
Author(s):  
Gergely Ambrus ◽  
Máté Matolcsi
Keyword(s):  
Linear Programming ◽  
Autocorrelation Function ◽  
Upper Bound ◽  
Linear Constraints ◽  
Higher Order ◽  
Density Estimates ◽  
Unit Distance ◽  
Measurable Set ◽  
Linear Programming Methods

AbstractWe improve the best known upper bound on the density of a planar measurable set A containing no two points at unit distance to 0.25442. We use a combination of Fourier analytic and linear programming methods to obtain the result. The estimate is achieved by means of obtaining new linear constraints on the autocorrelation function of A utilizing triple-order correlations in A, a concept that has not been previously studied.

An Upper Bound on the Minimum Number of Monomials Required to Separate Dichotomies of {−1, 1}n

2006 ◽  
Vol 18 (12) ◽  
pp. 3119-3138 ◽  
Author(s):  
Erhan Oztop
Keyword(s):  
Upper Bound ◽  
Polynomial Function ◽  
Binary Classification ◽  
Classification Problem ◽  
Deterministic Algorithm ◽  
Higher Order ◽  
Function Solution ◽  
Order Neuron ◽  
Minimum Number ◽  
First Time

It is known that any dichotomy of {−1, 1}n can be learned (separated) with a higher-order neuron (polynomial function) with 2n inputs (monomials). In general, less than 2n monomials are sufficient to solve a given dichotomy. In spite of the efforts to develop algorithms for finding solutions with fewer monomials, there have been relatively fewer studies investigating maximum density (II(n)), the minimum number of monomials that would suffice to separate an arbitrary dichotomy of {−1, 1}n . This article derives a theoretical (upper) bound for this quantity, superseding previously known bounds. The main theorem here states that for any binary classification problem in {−1, 1}n (n > 1), one can always find a polynomial function solution with 2n −2n/4 or fewer monomials. In particular, any dichotomy of {−1, 1}n can be learned by a higher-order neuron with a fan-in of 2n −2n/4 or less. With this result, for the first time, a deterministic ratio bound independent of n is established as II (n)/2n ≤ 0 75. The main theorem is constructive, so it provides a deterministic algorithm for achieving the theoretical result. The study presented provides the basic mathematical tools and forms the basis for further analyses that may have implications for neural computation mechanisms employed in the cerebral cortex.

scholarly journals On the Upper Bounds of Eigenvalues for a Class of Systems of Ordinary Differential Equations with Higher Order

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Gao Jia ◽  
Li-Na Huang ◽  
Wei Liu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Upper Bound ◽  
Upper Bounds ◽  
Higher Order ◽  
Geometric Measure ◽  
Systems Of Differential Equations

The estimate of the upper bounds of eigenvalues for a class of systems of ordinary differential equations with higher order is considered by using the calculus theory. Several results about the upper bound inequalities of the ()th eigenvalue are obtained by the first eigenvalues. The estimate coefficients do not have any relation to the geometric measure of the domain. This kind of problem is interesting and significant both in theory of systems of differential equations and in applications to mechanics and physics.

scholarly journals Growth of a polynomial not vanishing in a disk

2019 ◽  
Vol 73 (1) ◽  
pp. 41
Author(s):  
Abdullah Mir
Keyword(s):  
Upper Bound ◽  
Maximum Modulus ◽  
Higher Order ◽  
Complex Polynomial ◽  
Derivatives Of

This paper deals with the problem of finding some upper bound estimates for the maximum modulus of the derivative and higher order derivatives of a complex polynomial on a disk under the assumption that the polynomial has no zeros in another disk. The estimates obtained strengthen the well-known inequality of Ankeny and Rivlin about polynomials.

scholarly journals Estimates of Upper Bound for Differentiable Functions Associated with k-Fractional Integrals and Higher Order Strongly s-Convex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-9 ◽  
Author(s):  
Shanhe Wu ◽  
Muhammad Uzair Awan ◽  
Zakria Javed
Keyword(s):  
Upper Bound ◽  
Convex Functions ◽  
Higher Order ◽  
Fractional Integrals ◽  
Differentiable Functions ◽  
Second Derivatives ◽  
Integral Identities

In this paper, we establish two integral identities associated with differentiable functions and the k-Riemann-Liouville fractional integrals. The results are then used to derive the estimates of upper bound for functions whose first or second derivatives absolute values are higher order strongly s-convex functions.

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