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2. (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

3. 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:
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4. 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

5. 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

6. 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:
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7. 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

8. 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

9. A Fiedler-like theory for the perturbed Laplacian

Creator:
Rocha, Israel and Trevisan, Vilmar
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, perturbed Laplacian matrix, Fiedler vector, algebraic connectivity, graph partitioning, 13, and 51
Language:
English
Description:
The perturbed Laplacian matrix of a graph G is defined as DL = D−A, where D is any diagonal matrix and A is a weighted adjacency matrix of G. We develop a Fiedler-like theory for this matrix, leading to results that are of the same type as those obtained with the algebraic connectivity of a graph. We show a monotonicity theorem for the harmonic eigenfunction corresponding to the second smallest eigenvalue of the perturbed Laplacian matrix over the points of articulation of a graph. Furthermore, we use the notion of Perron component for the perturbed Laplacian matrix of a graph and show how its second smallest eigenvalue can be characterized using this definition., Israel Rocha, Vilmar Trevisan., and Obsahuje seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

10. A new algorithm for approximating the least concave majorant

Creator:
Franců, Martin, Kerman, Ron, and Sinnamon, Gord
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, algoritmy, mathematics, algorithms, least concave majorant, level function, spline approximation, 13, and 51
Language:
English
Description:
The least concave majorant, $\hat F$, of a continuous function $F$ on a closed interval, $I$, is defined by $ \hat F (x) = \inf\{ G(x) G \geq F, G \text{ concave}\},\quad x \in I. $ We present an algorithm, in the spirit of the Jarvis March, to approximate the least concave majorant of a differentiable piecewise polynomial function of degree at most three on $I$. Given any function $F \in\mathcal{C}^4(I)$, it can be well-approximated on $I$ by a clamped cubic spline $S$. We show that $\hat S$ is then a good approximation to $\hat F$. We give two examples, one to illustrate, the other to apply our algorithm., Martin Franců, Ron Kerman, Gord Sinnamon., and Obsahuje bibliografii
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

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