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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
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
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
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
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
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
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
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
6. A Cauchy-Pompeiu formula in super Dunkl-Clifford analysis
- Creator:
- Yuan, Hongfen
- Format:
- print, bez média, and svazek
- 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
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
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
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
8. A characterization of the Riemann extension in terms of harmonicity
- Creator:
- Bejan, Cornelia-Livia and Eken, Şemsi
- Format:
- print, bez média, and svazek
- 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
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
9. A compactness result for polyharmonic maps in the critical dimension
- Creator:
- Zheng, Shenzhou
- Format:
- print, bez média, and svazek
- 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
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
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
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public