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Start Over Subject matematika Harvested from CDK

183. Separately radial and radial Toeplitz operators on the projective space and representation theory

Creator:
Quiroga-Barranco, Raul and Sanchez-Nungaray, Armando
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, Toeplitz operator, projective space, 13, and 51
Language:
English
Description:
We consider separately radial (with corresponding group ${\mathbb{T}}^n$) and radial (with corresponding group ${\rm U}(n))$ symbols on the projective space ${\mathbb{P}^n({\mathbb{C}})}$, as well as the associated Toeplitz operators on the weighted Bergman spaces. It is known that the $C^*$-algebras generated by each family of such Toeplitz operators are commutative (see R. Quiroga-Barranco and A. Sanchez-Nungaray (2011)). We present a new representation theoretic proof of such commutativity. Our method is easier and more enlightening as it shows that the commutativity of the $C^*$-algebras is a consequence of the existence of multiplicity-free representations. Furthermore, our method shows how to extend the current formulas for the spectra of the corresponding Toeplitz operators to any closed group lying between ${\mathbb{T}}^n$ and ${\rm U}(n)$., Raul Quiroga-Barranco, Armando Sanchez-Nungaray., and Obsahuje bibliografii
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

184. Shells of monotone curves

Creator:
Mikeš, Josef and Strambach, Karl
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
Matematika, matematika, mathematics, geodesic, shell of a curve, affine connection, (pseudo-)Riemannian metric, projective equivalence, 13, and 51
Language:
English
Description:
We determine in \mathbb{R}^{n} the form of curves C corresponding to strictly monotone functions as well as the components of affine connections \Delta for which any image of C under a compact-free group Ω of affinities containing the translation group is a geodesic with respect to \Delta . Special attention is paid to the case that Ω contains many dilatations or that C is a curve in \mathbb{R}^{3}. If C is a curve in \mathbb{R}^{3} and Ω is the translation group then we calculate not only the components of the curvature and the Weyl tensor but we also decide when \Delta yields a flat or metrizable space and compute the corresponding metric tensor., Josef Mikeš, Karl Strambach., and Obsahuje seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

185. Singer-Thorpe bases for special Einstein curvature tensors in dimension 4

Creator:
Dušek, Zdeněk
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, Einstein manifold, 2-stein manifold, Singer-Thorpe basis, 13, and 51
Language:
English
Description:
Let (M, g) be a 4-dimensional Einstein Riemannian manifold. At each point p of M, the tangent space admits a so-called Singer-Thorpe basis (ST basis) with respect to the curvature tensor R at p. In this basis, up to standard symmetries and antisymmetries, just 5 components of the curvature tensor R are nonzero. For the space of constant curvature, the group O(4) acts as a transformation group between ST bases at TpM and for the so-called 2-stein curvature tensors, the group Sp(1) ⊂ SO(4) acts as a transformation group between ST bases. In the present work, the complete list of Lie subgroups of SO(4) which act as transformation groups between ST bases for certain classes of Einstein curvature tensors is presented. Special representations of groups SO(2), T2, Sp(1) or U(2) are obtained and the classes of curvature tensors whose transformation group into new ST bases is one of the mentioned groups are determined., Zdeněk Dušek, Hradec Králové., and Obsahuje seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

186. Small discriminants of complex multiplication fields of elliptic curves over finite fields

Creator:
Shparlinski, Igor E
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, elliptic curve, complex multiplication field, Frobenius discriminant, 13, and 51
Language:
English
Description:
We obtain a conditional, under the Generalized Riemann Hypothesis, lower bound on the number of distinct elliptic curves E over a prime finite field F_{p} of p elements, such that the discriminant D(E) of the quadratic number field containing the endomorphism ring of E over F_{p} is small. For almost all primes we also obtain a similar unconditional bound. These lower bounds complement an upper bound of F. Luca and I.E. Shparlinski (2007)., Igor E. Shparlinski., and Obsahuje seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

187. Some characterizations of harmonic Bloch and Besov spaces

Creator:
Fu, Xi and Lu, Bowen
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, funkce, mathematics, functions, harmonic function, Bloch space, Besov space, majorant, 13, and 51
Language:
English
Description:
The relationship between weighted Lipschitz functions and analytic Bloch spaces has attracted much attention. In this paper, we define harmonic ω-α-Bloch space and characterize it in terms of \omega \left( {{{\left( {1 - {{\left| x \right|}^2}} \right)}^\beta }{{\left( {1 - {{\left| y \right|}^2}} \right)}^{\alpha - \beta }}} \right)\left| {\frac{{f\left( x \right) - f\left( y \right)}}{{x - y}}} \right| and \omega \left( {{{\left( {1 - {{\left| x \right|}^2}} \right)}^\beta }{{\left( {1 - {{\left| y \right|}^2}} \right)}^{\alpha - \beta }}} \right)\left| {\frac{{f\left( x \right) - f\left( y \right)}}{{\left| x \right|y - x'}}} \right| where ω is a majorant. Similar results are extended to harmonic little ω-α-Bloch and Besov spaces. Our results are generalizations of the corresponding ones in G.Ren, U.Kähler (2005)., Xi Fu, Bowen Lu., and Obsahuje seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

188. Some finite generalizations of Euler's pentagonal number theorem

Creator:
Liu, Ji-Cai
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, q-binomial coefficient, q-binomial theorem, pentagonal number theorem, 13, and 51
Language:
English
Description:
Euler's pentagonal number theorem was a spectacular achievement at the time of its discovery, and is still considered to be a beautiful result in number theory and combinatorics. In this paper, we obtain three new finite generalizations of Euler's pentagonal number theorem., Ji-Cai Liu., and Seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

189. Some inequalities for radial Blaschke-Minkowski homomorphisms

Creator:
Ji, Lewen and Zeng, Zhenbing
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, radial Blaschke-Minkowski homomorphism, Orlicz radial sum, 13, and 51
Language:
English
Description:
We establish some Brunn-Minkowski type inequalities for radial Blaschke-Minkowski homomorphisms with respect to Orlicz radial sums and differences of dual quermassintegrals., Lewen Ji, Zhenbing Zeng., and Obsahuje bibliografické odkazy
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

190. Some results on the annihilator graph of a commutative ring

Creator:
Afkhami, Mojgan, Khashyarmanesh, Kazem, and Rajabi, Zohreh
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, kruhový graf, číslo kliky, chromatická čísla, annihilator graph, zero-divisor graph, outerplanar, ring-graph, cut-vertex, clique number, weakly perfect, chromatic numbers, polynomial ring, ring of fractions, 13, and 51
Language:
English
Description:
Let R be a commutative ring. The annihilator graph of R, denoted by AG(R), is the undirected graph with all nonzero zero-divisors of R as vertex set, and two distinct vertices x and y are adjacent if and only if ann(xy) \neqann R(x)\cup annR(y), where for z \in R, annR(z) = {r \in R: rz = 0}. In this paper, we characterize all finite commutative rings R with planar or outerplanar or ring-graph annihilator graphs. We characterize all finite commutative rings R whose annihilator graphs have clique number 1, 2 or 3. Also, we investigate some properties of the annihilator graph under the extension of R to polynomial rings and rings of fractions. For instance, we show that the graphs AG(R) and AG(T(R)) are isomorphic, where T(R) is the total quotient ring of R. Moreover, we investigate some properties of the annihilator graph of the ring of integers modulo n, where n>1., Mojgan Afkhami, Kazem Khashyarmanesh, Zohreh Rajabi., and Obsahuje bibliografii
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

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