scholarly journals Matrix Representations of a Special Polynomial Sequence in Arbitrary Dimension

2012 ◽  
Vol 12 (2) ◽  
pp. 371-391 ◽  
Author(s):  
Isabel Cação ◽  
Maria Irene Falcão ◽  
Helmuth R. Malonek
Keyword(s):  
Arbitrary Dimension ◽  
Matrix Representations ◽  
Polynomial Sequence ◽  
Special Polynomial

Combinatorial Property of a Special Polynomial Sequence

1977 ◽  
Vol 20 (2) ◽  
pp. 183-188 ◽  
Author(s):  
L. Carlitz
Keyword(s):  
Combinatorial Property ◽  
Polynomial Sequence ◽  
Special Polynomial ◽  
Image Position

Leeming [4] has defined a sequence of polynomials {Q4n(x)} and a sequence of integers {Q4n} by means of1and2Thus3Leeming showed that the Q4n are all odd and that4It is proved in [3] that5

scholarly journals Multiplicative Chow–Künneth decompositions and varieties of cohomological K3 type

2021 ◽  
Author(s):  
Lie Fu ◽  
Robert Laterveer ◽  
Charles Vial
Keyword(s):  
Projective Variety ◽  
Arbitrary Dimension ◽  
Smooth Projective Variety ◽  
The Other ◽  
Fano Variety ◽  
Fano Varieties ◽  
Intersection Product ◽  
Canonical Class ◽  
Main Input

AbstractGiven a smooth projective variety, a Chow–Künneth decomposition is called multiplicative if it is compatible with the intersection product. Following works of Beauville and Voisin, Shen and Vial conjectured that hyper-Kähler varieties admit a multiplicative Chow–Künneth decomposition. In this paper, based on the mysterious link between Fano varieties with cohomology of K3 type and hyper-Kähler varieties, we ask whether Fano varieties with cohomology of K3 type also admit a multiplicative Chow–Künneth decomposition, and provide evidence by establishing their existence for cubic fourfolds and Küchle fourfolds of type c7. The main input in the cubic hypersurface case is the Franchetta property for the square of the Fano variety of lines; this was established in our earlier work in the fourfold case and is generalized here to arbitrary dimension. On the other end of the spectrum, we also give evidence that varieties with ample canonical class and with cohomology of K3 type might admit a multiplicative Chow–Künneth decomposition, by establishing this for two families of Todorov surfaces.

scholarly journals Modelling with star-shaped distributions

2020 ◽  
Vol 8 (1) ◽  
pp. 45-69
Author(s):  
Eckhard Liebscher ◽  
Wolf-Dieter Richter
Keyword(s):  
Probabilistic Models ◽  
Arbitrary Dimension ◽  
Probability Density Functions ◽  
Density Functions ◽  
Wide Range ◽  
Gaussian Density ◽  
Spherical Distributions ◽  
Data Points ◽  
Non Gaussian ◽  
General Method

AbstractWe prove and describe in great detail a general method for constructing a wide range of multivariate probability density functions. We introduce probabilistic models for a large variety of clouds of multivariate data points. In the present paper, the focus is on star-shaped distributions of an arbitrary dimension, where in case of spherical distributions dependence is modeled by a non-Gaussian density generating function.

scholarly journals Electron liquid state in the symmetric Anderson lattice

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Igor N. Karnaukhov
Keyword(s):  
Low Temperatures ◽  
Arbitrary Dimension ◽  
Mean Field ◽  
Coulomb Repulsion ◽  
Anomalous Behavior ◽  
Effective Field ◽  
Kondo Lattice ◽  
Field Approach ◽  
Cubic Lattices ◽  
Half Filling

AbstractUsing mean field approach, we provide analytical and numerical solution of the symmetric Anderson lattice for arbitrary dimension at half filling. The symmetric Anderson lattice is equivalent to the Kondo lattice, which makes it possible to study the behavior of an electron liquid in the Kondo lattice. We have shown that, due to hybridization (through an effective field due to localized electrons) of electrons with different spins and momenta $$\mathbf{k} $$ k and $$\mathbf{k} +\overrightarrow{\pi }$$ k + π → , the gap in the electron spectrum opens at half filling. Such hybridization breaks the conservation of the total magnetic momentum of electrons, the spontaneous symmetry is broken. The state of electron liquid is characterized by a large Fermi surface. A gap in the spectrum is calculated depending on the magnitude of the on-site Coulomb repulsion and value of s–d hybridization for the chain, as well as for square and cubic lattices. Anomalous behavior of the heat capacity at low temperatures in the gapped state, which is realized in the symmetric Anderson lattice, was also found.

scholarly journals Collapses and Watersheds in Pseudomanifolds of Arbitrary Dimension

2014 ◽  
Vol 50 (3) ◽  
pp. 261-285 ◽  
Author(s):  
Jean Cousty ◽  
Gilles Bertrand ◽  
Michel Couprie ◽  
Laurent Najman
Keyword(s):  
Arbitrary Dimension

General matrix representations for B-splines

2000 ◽  
Vol 16 (3-4) ◽  
pp. 177-186 ◽  
Author(s):  
Kaihuai Qin
Keyword(s):  
Matrix Representations ◽  
General Matrix ◽  
B Splines
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