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182. SCAP-subalgebras of Lie algebras

Creator:
Chehrazi, Sara and Salemkar, Ali Reza
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Type:
model:article and TEXT
Subject:
matematika, algebra, mathematics, Lie algebra, SCAP-subalgebra, chief series, solvable, supersolvable, 13, and 51
Language:
English
Description:
A subalgebra H of a finite dimensional Lie algebra L is said to be a SCAP-subalgebra if there is a chief series 0 = L0 \subset L1 \subset...\subset Lt = L of L such that for every i = 1, 2,..., t, we have H + Li = H + Li-1 or H ∩ Li = H ∩ Li-1. This is analogous to the concept of SCAP-subgroup, which has been studied by a number of authors. In this article, we investigate the connection between the structure of a Lie algebra and its SCAP-subalgebras and give some sufficient conditions for a Lie algebra to be solvable or supersolvable., Sara Chehrazi, Ali Reza Salemkar., and Obsahuje seznam literatury
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183. Separately radial and radial Toeplitz operators on the projective space and representation theory

Creator:
Quiroga-Barranco, Raul and Sanchez-Nungaray, Armando
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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
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184. Shells of monotone curves

Creator:
Mikeš, Josef and Strambach, Karl
Format:
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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
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185. Singer-Thorpe bases for special Einstein curvature tensors in dimension 4

Creator:
Dušek, Zdeněk
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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
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186. Skew inverse power series rings over a ring with projective socle

Creator:
Paykan, Kamal
Format:
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Type:
model:article and TEXT
Subject:
mathematics, flat socle ring, skew inverse power series ring, skew polynomial ring, annihilator, projective socle ring, 13, and 51
Language:
English
Description:
A ring R is called a right PS-ring if its socle, Soc(RR), is projective. Nicholson and Watters have shown that if R is a right PS-ring, then so are the polynomial ring R[x] and power series ring R[[x]]. In this paper, it is proved that, under suitable conditions, if R has a (flat) projective socle, then so does the skew inverse power series ring R[[x−1; alfa, delta]] and the skew polynomial ring R[x; alfa, delta], where R is an associative ring equipped with an automorphism and an alfa-derivation delta. Our results extend and unify many existing results. Examples to illustrate and delimit the theory are provided., Kamal Paykan., and Seznam literatury
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187. Small discriminants of complex multiplication fields of elliptic curves over finite fields

Creator:
Shparlinski, Igor E
Format:
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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
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188. Some characterizations of harmonic Bloch and Besov spaces

Creator:
Fu, Xi and Lu, Bowen
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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
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189. Some dimensional results for a class of special homogeneous Moran sets

Creator:
Hu, Xiaomei
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Type:
model:article and TEXT
Subject:
fraktály, geometrie, mathematics, fractals, geometry, Hausdorffova dimenze, homogeneous Moran set, {mk}-Moran set, {mk}-quasi homogeneous Cantor set, Hausdorff dimension, 13, and 51
Language:
English
Description:
We construct a class of special homogeneous Moran sets, called {mk}-quasi homogeneous Cantor sets, and discuss their Hausdorff dimensions. By adjusting the value of {mk}k\geqslant 1, we constructively prove the intermediate value theorem for the homogeneous Moran set. Moreover, we obtain a sufficient condition for the Hausdorff dimension of ho- mogeneous Moran sets to assume the minimum value, which expands earlier works., Xiaomei Hu., and Obsahuje seznam literatury
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190. Some estimates for commutators of Riesz transform associated with Schrödinger type operators

Creator:
Liu, Yu, Zhang, Jing, Sheng, Jie-Lai, and Wang, Li-Juan
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
mathematics, Schrödinger equation, commutator, Hardy space, everse Hölder inequality, Riesz transform, Schrödinger operator, Schrödinger type operator, 13, and 51
Language:
English
Description:
Let L1 = −Δ + V be a Schrödinger operator and let L2 = (−Δ)2 + V2 be a Schrödinger type operator on \mathbb{R}^{n}\left ( n\geqslant 5 \right ) where V≠ 0 is a nonnegative potential belonging to certain reverse Hölder class Bs for s\geqslant n/2. The Hardy type space H_{L2}^{1} is defined in terms of the maximal function with respect to the semigroup \left\{ {{e^{ - t{L_2}}}} \right\} and it is identical to the Hardy space H_{L2}^{1} established by Dziubański and Zienkiewicz. In this article, we prove the Lp-boundedness of the commutator Rb = bRf - R(bf) generated by the Riesz transform R = {\nabla ^2}L_2^{ - 1/2} , where b \in BM{O_\theta }(\varrho ) , which is larger than the space BMO\left (\mathbb{R}^{n} \right ). Moreover, we prove that Rb is bounded from the Hardy space H_{L2}^{1} into weak L_{weak}^1 (\mathbb{R}^n )., Yu Liu, Jing Zhang, Jie-Lai Sheng, Li-Juan Wang., and Obsahuje seznam literatury
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