scholarly journals On graphs with an eigenvalue of maximal multiplicity

2013 ◽  
Vol 313 (11) ◽  
pp. 1162-1166 ◽  
Author(s):  
Peter Rowlinson
Keyword(s):  
Maximal Multiplicity

Bib Designs with Blocks of Maximal Multiplicity.

1982 ◽  
Author(s):  
G. M. Constantine ◽  
A. S. Hedaya
Keyword(s):  
Maximal Multiplicity

scholarly journals On the maximal multiplicity of block sizes in a random set partition

2020 ◽  
Vol 56 (3) ◽  
pp. 867-891
Author(s):  
Ljuben R. Mutafchiev ◽  
Mladen Savov
Keyword(s):  
Random Set ◽  
Set Partition ◽  
Maximal Multiplicity ◽  
Block Sizes

Hausdorff Dimension of Sets of Escaping Points and Escaping Parameters for Elliptic Functions

2015 ◽  
Vol 59 (3) ◽  
pp. 671-690
Author(s):  
Piotr Gałązka ◽  
Janina Kotus
Keyword(s):  
Hausdorff Dimension ◽  
Elliptic Function ◽  
Meromorphic Functions ◽  
Elliptic Functions ◽  
Critical Value ◽  
Parameter Plane ◽  
Dynamical Plane ◽  
The Family ◽  
Maximal Multiplicity ◽  
Additional Assumptions

AbstractLetbe a non-constant elliptic function. We prove that the Hausdorff dimension of the escaping set offequals 2q/(q+1), whereqis the maximal multiplicity of poles off. We also consider theescaping parametersin the familyfβ=βf, i.e. the parametersβfor which the orbit of one critical value offβescapes to infinity. Under additional assumptions onfwe prove that the Hausdorff dimension of the set of escaping parametersεin the familyfβis greater than or equal to the Hausdorff dimension of the escaping set in the dynamical space. This demonstrates an analogy between the dynamical plane and the parameter plane in the class of transcendental meromorphic functions.

Bounds for the multiplicities of the roots of a complex polynomial

2011 ◽  
Vol 54 (3) ◽  
pp. 587-598
Author(s):  
A. I. Bonciocat ◽  
N. C. Bonciocat ◽  
A. Zaharescu
Keyword(s):  
Complex Polynomial ◽  
Complex Polynomials ◽  
Integer Coefficients ◽  
Separability Criteria ◽  
Maximal Multiplicity

AbstractWe refine a result of Dubickas on the maximal multiplicity of the roots of a complex polynomial, and obtain several separability criteria for complex polynomials with large leading coefficient. We also give p-adic analogous results for polynomials with integer coefficients.

scholarly journals Multiplicity-induced-dominancy in parametric second-order delay differential equations: Analysis and application in control design

2020 ◽  
Vol 26 ◽  
pp. 57 ◽  
Author(s):  
Islam Boussaada ◽  
Silviu-Iulian Niculescu ◽  
Ali El-Ati ◽  
Redamy Pérez-Ramos ◽  
Karim Trabelsi
Keyword(s):  
Differential Equations ◽  
Output Feedback ◽  
Control Design ◽  
Second Order ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Argument Principle ◽  
Reduced Order ◽  
Maximal Multiplicity ◽  
Delay Differential

This work revisits recent results on maximal multiplicity induced-dominancy for spectral values in reduced-order time-delay systems and extends it to the general class of second-order retarded differential equations. A parametric multiplicity-induced-dominancy property is characterized, allowing to a delayed stabilizing design with reduced complexity. As a matter of fact, the approach is merely a delayed-output-feedback where the candidates’ delays and gains result from the manifold defining the maximal multiplicity of a real spectral value, then, the dominancy is shown using the argument principle. Sensitivity of the control design with respect to the parameters uncertainties/variation is discussed. Various reduced order examples illustrate the applicative perspectives of the approach.

scholarly journals Minimizing Key Materials: The Even–Mansour Cipher Revisited and Its Application to Lightweight Authenticated Encryption

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Ping Zhang ◽  
Qian Yuan
Keyword(s):  
Open Problem ◽  
Provable Security ◽  
Simple Structure ◽  
Block Ciphers ◽  
Authenticated Encryption ◽  
Maximal Multiplicity ◽  
Symmetric Key ◽  
Security Bound

The Even–Mansour cipher has been widely used in block ciphers and lightweight symmetric-key ciphers because of its simple structure and strict provable security. Its research has been a hot topic in cryptography. This paper focuses on the problem to minimize the key material of the Even–Mansour cipher while its security bound remains essentially the same. We introduce four structures of the Even–Mansour cipher with a short key and derive their security by Patarin’s H-coefficients technique. These four structures are proven secure up to O˜2k/μ adversarial queries, where k is the bit length of the key material and μ is the maximal multiplicity. Then, we apply them to lightweight authenticated encryption modes and prove their security up to about minb/2,c,k−log μ-bit adversarial queries, where b is the size of the permutation and c is the capacity of the permutation. Finally, we leave it as an open problem to settle the security of the t-round iterated Even–Mansour cipher with short keys.

Complete designs with blocks of maximal multiplicity

1983 ◽  
Vol 7 (4) ◽  
pp. 417 ◽  
Author(s):  
G.M. Constantine ◽  
A.S. Hedayat
Keyword(s):  
Maximal Multiplicity

Maximally Flat Filter Functions With the Maximum Number of Transmission Zeros Having Maximal Multiplicity

2014 ◽  
Vol 61 (10) ◽  
pp. 778-782 ◽  
Author(s):  
Miona V. Andrejevic Stosovic ◽  
Jaroslav M. Zivanic ◽  
Vanco B. Litovski
Keyword(s):  
Transmission Zeros ◽  
Maximal Multiplicity
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