## Recursos de colección

1. #### A new characterization of the generalized Hermite linear form

Ghressi, A.; Khériji, L.
We show that the Generalized Hermite linear form $\mathcal{H}(\mu)$, which is symmetric $D$-semiclassical of class one, is the unique $\mathcal{D}_{\theta}$-Appell classical where $\mathcal{D}_{\theta}$ is the Dunkl operator.

2. #### Continuous convexity and canonical partial metrics in normed spaces

Romaguera, S.; Oltra, S.; Sánchez Pérez, E.A.
The aim of this paper is to study the canonical partial metric associated to the norm of a normed space, whose related non-translation-invariant topology can be used to characterize the convexity properties of the original space. In order to do this, we define and characterize a new intermediate geometric property that we call continuous convexity, which appears in a natural way in the context of the canonical partial metric topology.

3. #### Systems of Submodules and an Isomorphism Problem for Auslander-Reiten Quivers

Schmidmeier, Markus
Fix a poset $\mathcal P$ and a natural number $n$. For various commutative local rings $\Lambda$, each of Loewy length $n$, consider the category $\textrm{sub}_\Lambda\mathcal P$ of $\Lambda$-linear submodule representations of $\mathcal P$. We give a criterion for when the underlying translation quiver of a connected component of the Auslander-Reiten quiver of $\sub_\Lambda\mathcal P$ is independent of the choice of the base ring $\Lambda$. If $\mathcal P$ is the one-point poset and $\Lambda=\mathbb Z/p^n$, then $\textrm{sub}_\Lambda\mathcal P$ consists of all pairs $(B;A)$ where $B$ is a finite abelian $p^n$-bounded group and $A\subset B$ a subgroup. We can respond to a remark by M.~C.~R. Butler concerning the first occurence of parametrized families of such subgroup embeddings.

4. #### Isometry Games in Banach Spaces

Baratella, Stefano; Ng, Siu-Ah
We study a property of extension of partial isometries in a Banach space. This property is formulated in game-theoretic language. It is weaker than transitivity, self-dual for reflexive spaces and it is related to a well-known open problem in functional analysis and to model-theoretic notions from mathematical logic.

5. #### Blow-up for solution of a system of quasilinear hyperbolic equations involving the $p-$laplacian

We study the blow-up for the solution of a system of quasilinear hyperbolic equations involving the $p$-laplacian. We derive a differential inequality for a function involving some norms of the solution which yields the finite time blow-up.

6. #### Quelques résultats de stabilisation indirecte des systèmes couplés non dissipatifs

Guesmia, Aïssa
La stabilisation des systèmes couplés soumis à un seul feedback (stabilisation indirecte) a suscité l'intérêt de nombreux auteurs ces dernières années. Les résultats les plus récents dans cette direction sont ceux obtenus par F. Alabau-Boussouira [1] et F. Alabau-Boussouira, P. Cannarsa et V. Komornik [2] où des estimations polynomiales (dépendant de la régularité des solutions) ont été démontrées pour quelques systèmes hyperboliques linéaires faiblement couplés. L'objectif de ce papier est d'étendre ces résultats au cas de systèmes {\it non linéaires} ou {\it non dissipatifs} et de donner des applications à la stabilisation indirecte de certains systèmes couplés non dissipatifs.

7. #### Rotundity, smoothness and drops in Banach spaces

García-Pacheco, Francisco J.; Seoane-Sepúlveda, Juan B.
In this note we study the geometry of drops in Banach spaces, and we use it to characterize two well known geometrical properties: rotundity and smoothness.

8. #### Complementability of spaces of affine continuous functions on simplices

Bačák, Miroslav; Spurný, Jiří
We construct metrizable simplices $X_1$ and $X_2$ and a homeomorphism $\varphi:\overline{ext X_1}\to\overline{ext X_2}$ such that $\varphi(ext X_1)=ext X_2$, the space $\mathfrak{A}(X_1)$ of all affine continuous functions on $X_1$ is complemented in $\mathcal C(X_1)$ and $\mathfrak{A}(X_2)$ is not complemented in any $\mathcal C(K)$ space. This shows that complementability of the space $\mathfrak{A}(X)$ cannot be determined by topological properties of the couple $(ext X,\overline{ext X})$.

9. #### Topological Homotopy Groups

Ghane, H.; Hamed, Z.; Mashayekhy, B.; Mirebrahimi, H.
D. K. Biss (Topology and its Applications 124 (2002) 355-371) introduced the topological fundamental group and presented some interesting basic properties of the notion. In this article we intend to extend the above notion to homotopy groups and try to prove some similar basic properties of the topological homotopy groups. We also study more on the topology of the topological homotopy groups in order to find necessary and sufficient conditions for which the topology is discrete. Moreover, we show that studying topological homotopy groups may be more useful than topological fundamental groups.

10. #### Constructions of subgeometry partitions

Johnson, Norman L.
New constructions of Sperner spaces using generalized extended André spreads' are used to construct a wide variety of new subgeometry partitions of finite projective spaces.

11. #### A TVD-MUSTA scheme for hyperbolic conservation laws

Zahran, Yousef Hashem
The aim of this paper is to develop an improved version of the Multi-Stage (MUSTA) approach to the construction of upwind fluxes that avoid the solution of the Riemann Problem (RP) in the conventional manner. We propose to use the second order TVD flux as a building block in the MUSTA scheme instead of the first order flux used in the original MUSTA. The numerical solution is advanced by TVD Runge-Kutta method. The new MUSTA scheme improves upon the original MUSTA and TVD schemes in terms of better convergence, higher overall accuracy, better resolution of discontinuities and find its justification when solving very complex systems for...

12. #### Composition methods and homotopy types of the gauge groups of $Sp(2)$ and $SU(3)$

Choi, Younggi; Hirato, Yoshihiro; Mimura, Mamoru
We estimate the number of homotopy types of the gauge groups of $Sp(2)$ and $SU(3)$.

13. #### Higher order functions and Walsh coefficients revisited

Iglesias, M.; Vidal, T.C.; Verschoren, A.
The main purpose of this note is to present an alternative, more transparent treatment of the results obtained in [4], which link the epistasis of a function to its Walsh coefficients and its order.

14. #### On the Stability of Cauchy Additive Mappings

Jun, Kil-Woung; Roh, Jaiok
It is well-known that the concept of Hyers-Ulam-Rassias stability originated by Th. M. Rassias (Proc. Amer. Math. Soc. 72(1978), 297-300) and the concept of Ulam-Gavruta-Rassias stability by J. M. Rassias (J. Funct. Anal. U.S.A. 46(1982), 126-130; Bull. Sc. Math. 108 (1984), 445-446; J. Approx. Th. 57 (1989), 268-273) and P. Gavruta (`An answer to a question of John M. Rassias concerning the stability of Cauchy equation", in: Advances in Equations and Inequalities, in: Hadronic Math. Ser. (1999), 67-71). In this paper we give results concerning these two stabilities.

15. #### A Subordination Result with Generalized Sakaguchi Univalent Functions Related to Complex Order

Güney, H. Özlem; Owa, Shigeyoshi
In the present paper, we obtain an interesting subordination relation for a family of analytic functions of complex order by using subordination theorem.

16. #### Fredholm Theory in Hilbert Space - A Concise Introductory Exposition

Kubrusly, Carlos S.
This is a brief introduction to Fredholm theory for Hilbert space operators organized into ten sections. The classical partition of the spectrum into point, residual, and continuous spectra is reviewed in Section 1. Fredholm operators are introduced in Section 2, and Fredholm index in Section 3. The essential spectrum is considered in Section 4, the spectral picture is presented in Section 5, and Riesz points are discussed in Section 6. Weyl spectrum is the subject of Section 7 and, after bringing some basic results on ascent and descent in Section 8, Browder spectrum is investigated in Section 9. Finally, Weyl and Browder theorems close this expository paper in Section...

17. #### On the stability of the quadratic equation on groups

Faĭziev, Valeriĭ A.; Sahoo, Prasanna K.
In this paper the stability of the quadratic equation is considered on arbitrary groups. Since the quadratic equation is stable on Abelian groups, this paper examines the stability of the quadratic equation on noncommutative groups. It is shown that the quadratic equation is stable on $n$-Abelian groups when $n$ is a positive integer. The stability of the quadratic equation is also established on the noncommutative group $T(2, K)$, where $K$ is an arbitrary commutative field. It is proved that every group can be embedded into a group in which the quadratic equation is stable.

18. #### A mechanical interpretation of least squares fitting in 3D

Penne, Rudi
We address the computation of the line that minimizes the sum of the least squared distances with respect to a given set of $n$ points in 3-space. This problem has a well known satisfying solution by means of PCA. We offer an alternative interpretation for this optimal line as the center of the screw motion that minimizes the sum of squared velocities in the given points. The numerical translation of this viewpoint is a generalized eigenproblem, where the total residue of the optimal line appears as the smallest generalized eigenvalue.

19. #### Multiple bifurcation in the solution set of the von Kármán equations with $S^{1}$-symmetries

Janczewska, Joanna
In this work we study bifurcation of forms of equilibrium of a thin circular elastic plate lying on an elastic base under the action of a compressive force. The forms of equilibrium may be found as solutions of the von Kármán equations with two real positive parameters defined on the unit disk in $\mathbb R^2$ centered at the origin. These equations are equivalent to an operator equation $F(x,p)=0$ in the real Hölder spaces with a nonlinear $S^{1}$-equivariant Fredholm map of index $0$. For the existence of bifurcation at a point $(0,p)$ it is necessary that $\dim\operatorname{Ker}F_{x}^{\prime}(0,p)>0$. The space $\operatorname{Ker}F_{x}^{\prime}(0,p)$ can be at most four-dimensional. We apply the Crandall-Rabinowitz theorem to...

20. #### Hermitian Clifford-Hermite wavelets: an alternative approach

Brackx, F.; De Schepper, H.; De Schepper, N.; Sommen, F.
Clifford analysis is a higher dimensional function theory offering a refinement of classical harmonic analysis, which has proven to be an appropriate framework for developing a higher dimensional continuous wavelet transform theory. In this setting a very specific construction of the wavelets has been established, encompassing all dimensions at once as opposed to the usual tensorial approaches, and being based on generalizations to higher dimension of classical orthogonal polynomials on the real line, such as the radial Clifford--Hermite polynomials, leading to Clifford--Hermite wavelets. More recently, Hermitian Clifford analysis has emerged as a new and successful branch of Clifford analysis, offering yet a refinement of the orthogonal...

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