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2. $(m,r)$-central Riordan arrays and their applications

Creator:
Yang, Sheng-Liang, Xu, Yan-Xue, and He, Tian-Xiao
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
mathematics, Riordan array, central coefficient, central Riordan array, generating function, Fuss-Catalan number, Pascal matrix, Catalan matrix, 13, and 51
Language:
English
Description:
For integers $m > r \geq0$, Brietzke (2008) defined the $(m,r)$-central coefficients of an infinite lower triangular matrix $G=(d, h)=(d_{n,k})_{n,k \in\mathbb{N}}$ as $ d_{mn+r,(m-1)n+r}$, with $n=0,1,2,\cdots$, and the $(m,r)$-central coefficient triangle of $G$ as $G^{(m,r)} = (d_{mn+r,(m-1)n+k+r})_{n,k \in\mathbb{N}}. $ It is known that the $(m,r)$-central coefficient triangles of any Riordan array are also Riordan arrays. In this paper, for a Riordan array $G=(d,h)$ with $h(0)=0$ and $d(0), h'(0)\not= 0$, we obtain the generating function of its $(m,r)$-central coefficients and give an explicit representation for the $(m,r)$-central Riordan array $G^{(m,r)}$ in terms of the Riordan array $G$. Meanwhile, the algebraic structures of the $(m,r)$-central Riordan arrays are also investigated, such as their decompositions, their inverses, and their recessive expressions in terms of $m$ and $r$. As applications, we determine the $(m,r)$-central Riordan arrays of the Pascal matrix and other Riordan arrays, from which numerous identities are constructed by a uniform approach., Sheng-Liang Yang, Yan-Xue Xu, Tian-Xiao He., and Obsahuje bibliografii
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3. (Strongly) Gorenstein injective modules over upper triangular matrix Artin algebras

Creator:
Wang, Chao and Yang, Xiaoyan
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, (strongly) Gorenstein injective module, upper triangular matrix Artin algebra, triangulated category, recollement, 13, and 51
Language:
English
Description:
Let $\Lambda=\left(\begin{smallmatrix} A&M 0&B \end{smallmatrix}\right)$ be an Artin algebra. In view of the characterization of finitely generated Gorenstein injective $\Lambda$-modules under the condition that $M$ is a cocompatible $(A,B)$-bimodule, we establish a recollement of the stable category $\overline{\rm Ginj(\Lambda)}$. We also determine all strongly complete injective resolutions and all strongly Gorenstein injective modules over $\Lambda$., Chao Wang, Xiaoyan Yang., and Obsahuje bibliografii
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4. 1-Cocycles on the group of contactomorphisms on the supercircle S1|3 generalizing the Schwarzian derivative

Creator:
Agrebaoui, Boujemaa and Hattab, Raja
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, vektorová pole, derivace funkce, mathematics, vector fields, derivatives (mathematics), contact vector field, cohomology of groups, group of contactomorphisms, super-Schwarzian derivative, invariant differential operator, 13, and 51
Language:
English
Description:
The relative cohomology Hdiff1(K(1|3), osp(2, 3);Dγ,µ(S1|3)) of the contact Lie superalgebra K(1|3) with coefficients in the space of differential operators Dγ,µ(S1|3) acting on tensor densities on S1|3, is calculated in N.Ben Fraj, I. Laraied, S. Omri (2013) and the generating 1-cocycles are expressed in terms of the infinitesimal super-Schwarzian derivative 1-cocycle s(Xf) = D1D2D3(f)α31/2, Xf \in K(1|3) which is invariant with respect to the conformal subsuperalgebra osp(2, 3) of K(1|3). In this work we study the supergroup case. We give an explicit construction of 1-cocycles of the group of contactomorphisms K(1|3) on the supercircle S1|3 generating the relative cohomology Hdiff1(K(1|3), PC(2, 3); Dγ,µ(S1|3) with coefficients in Dγ,µ(S1|3). We show that they possess properties similar to those of the super-Schwarzian derivative 1-cocycle S3(Φ) = EΦ-1 (D1(D2),D3)α31/2, Φ ∈ K(1|3) introduced by Radul which is invariant with respect to the conformal group PC(2, 3) of K(1|3). These cocycles are expressed in terms of S3(Φ) and possess its properties., Boujemaa Agrebaoui, Raja Hattab., and Obsahuje seznam literatury
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5. 4-cycle properties for characterizing rectagraphs and hypercubes

Creator:
Bouanane, Khadra and Berrachedi, Abdelhafid
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, charakterizace, hypercube, (0, 2)-graph, rectagraph, 4-cycle, characterization, 13, and 51
Language:
English
Description:
A (0, 2)-graph is a connected graph, where each pair of vertices has either 0 or 2 common neighbours. These graphs constitute a subclass of (0, λ)-graphs introduced by Mulder in 1979. A rectagraph, well known in diagram geometry, is a triangle-free (0, 2)-graph. (0, 2)-graphs include hypercubes, folded cube graphs and some particular graphs such as icosahedral graph, Shrikhande graph, Klein graph, Gewirtz graph, etc. In this paper, we give some local properties of 4-cycles in (0, λ)-graphs and more specifically in (0, 2)-graphs, leading to new characterizations of rectagraphs and hypercubes., Khadra Bouanane, Abdelhafid Berrachedi., and Obsahuje bibliografii
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6. A Cauchy-Pompeiu formula in super Dunkl-Clifford analysis

Creator:
Yuan, Hongfen
Format:
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Type:
model:article and TEXT
Subject:
matematika, mathematics, super Dunkl-Dirac operator, Stokes formula, Cauchy-Pompeiu integral formula, Morera's theorem, Painlevé theorem, 13, and 51
Language:
English
Description:
Using a distributional approach to integration in superspace, we investigate a Cauchy-Pompeiu integral formula in super Dunkl-Clifford analysis and several related results, such as Stokes formula, Morera's theorem and Painlevé theorem for super Dunkl-monogenic functions. These results are nice generalizations of well-known facts in complex analysis., Hongfen Yuan., and Obsahuje bibliografické odkazy
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7. A characterization of a certain real hypersurface of type (A2) in a complex projective space

Creator:
Kim, Byung Hak, Kim, In-Bae, and Maeda, Sadahiro
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, ruled real hypersurface, nonflat complex space form, real hypersurfaces of type (A2) in a complex projective space, geodesics, structure torsion, Hopf manifold, 13, and 51
Language:
English
Description:
In the class of real hypersurfaces M²n−¹ isometrically immersed into a nonflat complex space form Mn(c) of constant holomorphic sectional curvature c (≠ 0) which is either a complex projective space ℂPn(c) or a complex hyperbolic space ℂHn(c) according as c > 0 or c < 0, there are two typical examples. One is the class of all real hypersurfaces of type (A) and the other is the class of all ruled real hypersurfaces. Note that the former example are Hopf manifolds and the latter are non-Hopf manifolds. In this paper, inspired by a simple characterization of all ruled real hypersurfaces in Mn(c), we consider a certain real hypersurface of type (A2) in ℂPn(c) and give a geometric characterization of this Hopf manifold., Byung Hak Kim, In-Bae Kim, Sadahiro Maeda., and Obsahuje bibliografii
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8. A characterization of the Riemann extension in terms of harmonicity

Creator:
Bejan, Cornelia-Livia and Eken, Şemsi
Format:
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Type:
model:article and TEXT
Subject:
matematika, mathematics, harmonické tenzorové pole, Semi-Riemannian manifold, cotangent bundle, natural Riemann extension, harmonic tensor field, 13, and 51
Language:
English
Description:
If (M,∇) is a manifold with a symmetric linear connection, then T*M can be endowed with the natural Riemann extension g¯ (O. Kowalski and M. Sekizawa (2011), M. Sekizawa (1987)). Here we continue to study the harmonicity with respect to g¯g¯ initiated by C. L.Bejan and O.Kowalski (2015). More precisely, we first construct a canonical almost para-complex structure PP on (T*M, g¯) and prove that P is harmonic (in the sense of E.Garciá-Río, L.Vanhecke and M. E.Vázquez-Abal (1997)) if and only if g¯ reduces to the classical Riemann extension introduced by E.M. Patterson and A.G. Walker (1952)., Cornelia-Livia Bejan, Şemsi Eken., and Obsahuje bibliografii
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9. A compactness result for polyharmonic maps in the critical dimension

Creator:
Zheng, Shenzhou
Format:
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Type:
model:article and TEXT
Subject:
singularity (matematika), mathematics, singularities (mathematics), polyharmonic map, compactness, Coulomb moving frame, Palais-Smale sequence, removable singularity, 13, and 51
Language:
English
Description:
For n=2m\geqslant 4, let \Omega\in \mathbb{R}^{n} be a bounded smooth domain and N\subset \mathbb{R}^{L} a compact smooth Riemannian manifold without boundary. Suppose that \left \{ uk \right \}\in W^{m,2}\left ( \Omega ,N \right ) is a sequence of weak solutions in the critical dimension to the perturbed m-polyharmonic maps \frac{{\text{d}}}{{{\text{dt}}}}\left| {_{t = 0}{E_m}({\text{II}}(u + t\xi )) = 0} \right with Ωk → 0 in W^{m,2}\left( \Omega ,N \right )* and {u_k} \rightharpoonup u weakly in W^{m,2}\left( \Omega ,N \right ). Then u is an m-polyharmonic map. In particular, the space of m-polyharmonic maps is sequentially compact for the weak- W^{m,2} topology., Shenzhou Zheng., and Obsahuje seznam literatury
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10. A curvature identity on a 6-dimensional Riemannian manifold and its applications

Creator:
Euh, Yunhee, Park, Jeong Hyeong, and Sekigawa, Kouei
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, Chern-Gauss-Bonnet theorem, curvature identity, locally harmonic manifold, 13, and 51
Language:
English
Description:
We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. Moreover, some applications of the curvature identity are given. We also define a generalization of harmonic manifolds to study the Lichnerowicz conjecture for a harmonic manifold "a harmonic manifold is locally symmetric" and provide another proof of the Lichnerowicz conjecture refined by Ledger for the 4-dimensional case under a slightly more general setting., Yunhee Euh, Jeong Hyeong Park, Kouei Sekigawa., and Obsahuje bibliografii
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