scholarly journals Outlier eigenvalues for non-Hermitian polynomials in independent i.i.d. matrices and deterministic matrices

2021 ◽  
Vol 26 (none) ◽  
Author(s):  
Serban Belinschi ◽  
Charles Bordenave ◽  
Mireille Capitaine ◽  
Guillaume Cébron
Keyword(s):  
Hermitian Polynomials

scholarly journals On impulse excitation of the global poloidal modes in the magnetosphere

2006 ◽  
Vol 24 (10) ◽  
pp. 2429-2433 ◽  
Author(s):  
P. N. Mager ◽  
D. Yu. Klimushkin
Keyword(s):  
Second Harmonic ◽  
Temporal Structure ◽  
Background Field ◽  
Plasma Pressure ◽  
Radial Structure ◽  
Combined Action ◽  
Spatio Temporal ◽  
Field Lines ◽  
Hermitian Polynomials ◽  
Impulsive Source

Abstract. Through the combined action of the field line curvature and finite plasma pressure in some regions of the magnetosphere (plasmapause, ring current) there can exist global poloidal Alfvén modes standing both along field lines and across magnetic shells and propagating along azimuth. In this paper we investigate the spatio-temporal structure of such waves generated by an impulsive source. In general, the mode is the sum of radial harmonics whose structure is described by Hermitian polynomials. For the usually observed second harmonic structure along the background field, frequencies of these radial harmonics are very close to each other; therefore, the generated wave is almost a monochromatic oscillation. But mixing of the harmonics with different radial structure causes the evolution of the initially poloidal wave into the toroidal one. This casts some doubts upon the interpretation of observed high-m poloidal waves as global poloidal modes.

Zeros of the Hermitian Polynomials

1936 ◽  
Vol 43 (6) ◽  
pp. 354-358 ◽  
Author(s):  
E. R. Smith
Keyword(s):  
Hermitian Polynomials

Stress Analysis of Mitred Bends by Ring Elements

1984 ◽  
Vol 106 (1) ◽  
pp. 54-62 ◽  
Author(s):  
O. Watanabe ◽  
H. Ohtsubo
Keyword(s):  
Stress Analysis ◽  
Degrees Of Freedom ◽  
Shell Theory ◽  
Trigonometric Functions ◽  
Shape Functions ◽  
Straight Pipe ◽  
Shell Elements ◽  
Hermitian Polynomials ◽  
Ring Elements ◽  
Thin Shell Theory

This paper proposes a ring element for the stress analysis of mitred bends, which is an extension of ring elements for pipe bends proposed by the present authors. Since accurate treatments of continuity conditions on the connecting lines between straight pipe segments are employed and strain-displacement relations derived from the general thin shell theory with shear strains are considered, the present method can be applied to problems of mitred bends of complex configurations under general loading conditions. Shape functions are developed by trigonometric functions and Hermitian polynomials of second order in the circumferential and longitudinal directions, respectively. This finite element method requires fewer number of degrees of freedom for the same accuracy than the conventional shell elements.

scholarly journals SIGNATURE PAIRS FOR GROUP-INVARIANT HERMITIAN POLYNOMIALS

2011 ◽  
Vol 22 (03) ◽  
pp. 311-343 ◽  
Author(s):  
DUSTY GRUNDMEIER
Keyword(s):  
Cr Geometry ◽  
Cyclic Subgroups ◽  
Group Invariant ◽  
Positivity Ratio ◽  
Finite Subgroups ◽  
Hermitian Polynomials

We study the signature pair for certain group-invariant Hermitian polynomials arising in CR geometry. In particular, we determine the signature pair for the finite subgroups of SU(2). We introduce the asymptotic positivity ratio and compute it for cyclic subgroups of U(2). We calculate the signature pair for dihedral subgroups of U(2).

scholarly journals Dynamic analysis of prestressed Bernoulli beams resting on two-parameter foundation under moving harmonic load

2006 ◽  
Vol 28 (3) ◽  
pp. 176-188 ◽  
Author(s):  
Nguyen Dinh Kien ◽  
Bui Thanh Hai
Keyword(s):  
Dynamic Analysis ◽  
Moving Load ◽  
Excitation Frequency ◽  
Harmonic Load ◽  
Left Hand ◽  
Moving Harmonic Load ◽  
Load Vector ◽  
Hermitian Polynomials ◽  
Current Loading ◽  
Two Parameter

This paper describes the dynamic analysis of prestressed Bernoulli beams resting on a two-parameter elastic foundation under a moving harmonic load by the finite element method. Using the cubic Hermitian polynomials as interpolation functions for the deflection, the stiffness of the Bernoulli beam element augmented by that of the foundation support and prestress is formulated. The nodal load vector is derived using the polynomials with the abscissa measured from the left-hand node of the current loading element to the position of the moving load. Using the formulated element, the dynamic response of the beams is computed with the aid of the direct integration Newmark method. The effects of the foundation support, prestress as well as excitation frequency, velocity and acceleration on the dynamic characteristics of the beams are investigated in detail and highlighted.

Properties of functional Hermitian polynomials

1970 ◽  
Vol 21 (3) ◽  
pp. 320-324 ◽  
Author(s):  
A. N. Demenin
Keyword(s):  
Hermitian Polynomials

scholarly journals Nonuniversality of fluctuations of outliers for Hermitian polynomials in a complex Wigner matrix and a spiked diagonal matrix

2019 ◽  
Vol 09 (04) ◽  
pp. 2050013
Author(s):  
Mireille Capitaine
Keyword(s):  
Probability Theory ◽  
Free Probability ◽  
Diagonal Matrix ◽  
Free Probability Theory ◽  
Wigner Matrix ◽  
Wigner Matrices ◽  
Hermitian Polynomial ◽  
Hermitian Polynomials

We study the fluctuations associated to the a.s. convergence of the outliers established by Belinschi–Bercovici–Capitaine of an Hermitian polynomial in a complex Wigner matrix and a spiked deterministic real diagonal matrix. Thus, we extend the nonuniversality phenomenon established by Capitaine–Donati-Martin–Féral for additive deformations of complex Wigner matrices, to any Hermitian polynomial. The result is described using the operator-valued subordination functions of free probability theory.

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