## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (204.174 recursos)

Bulletin of the Belgian Mathematical Society-Simon Stevin

1. #### Nielsen periodic point theory on infra-nilmanifolds

Dugardein, Gert-Jan
In this paper, we expand certain aspects of Nielsen periodic point theory from tori and nilmanifolds to infra-nilmanifolds. We show that infra-nilmanifolds are essentially reducible to the GCD and essentially toral. With these structural properties in mind, we develop a method to compute the full Nielsen-Jiang number $NF_n(f)$. We also determine for which maps it holds that $NF_n(f)=N(f^n)$, for all $n$.

2. #### Nielsen periodic point theory on infra-nilmanifolds

Dugardein, Gert-Jan
In this paper, we expand certain aspects of Nielsen periodic point theory from tori and nilmanifolds to infra-nilmanifolds. We show that infra-nilmanifolds are essentially reducible to the GCD and essentially toral. With these structural properties in mind, we develop a method to compute the full Nielsen-Jiang number $NF_n(f)$. We also determine for which maps it holds that $NF_n(f)=N(f^n)$, for all $n$.

3. #### Stabilizers of fixed point classes and Nielsen numbers of $n$-valued maps

Brown, Robert F.; Nan, Junzheng
The stabilizer of a fixed point class of a map is the fixed subgroup of the induced fundamental group homomorphism based at a point in the class. A theorem of Jiang, Wang and Zhang is used to prove that if a map of a graph satisfies a strong remnant condition, then the stabilizers of all its fixed point classes are trivial. Consequently, if $\phi_{p, f}$ is the $n$-valued lift to a covering space $p$ of a map $f$ with strong remnant of a graph, then the Nielsen numbers are related by the equation $N(\phi_{p, f}) = n \cdot N(f)$. Additional...

4. #### Stabilizers of fixed point classes and Nielsen numbers of $n$-valued maps

Brown, Robert F.; Nan, Junzheng
The stabilizer of a fixed point class of a map is the fixed subgroup of the induced fundamental group homomorphism based at a point in the class. A theorem of Jiang, Wang and Zhang is used to prove that if a map of a graph satisfies a strong remnant condition, then the stabilizers of all its fixed point classes are trivial. Consequently, if $\phi_{p, f}$ is the $n$-valued lift to a covering space $p$ of a map $f$ with strong remnant of a graph, then the Nielsen numbers are related by the equation $N(\phi_{p, f}) = n \cdot N(f)$. Additional...

5. #### Stabilizers of fixed point classes and Nielsen numbers of $n$-valued maps

Brown, Robert F.; Nan, Junzheng
The stabilizer of a fixed point class of a map is the fixed subgroup of the induced fundamental group homomorphism based at a point in the class. A theorem of Jiang, Wang and Zhang is used to prove that if a map of a graph satisfies a strong remnant condition, then the stabilizers of all its fixed point classes are trivial. Consequently, if $\phi_{p, f}$ is the $n$-valued lift to a covering space $p$ of a map $f$ with strong remnant of a graph, then the Nielsen numbers are related by the equation $N(\phi_{p, f}) = n \cdot N(f)$. Additional...

6. #### Stabilizers of fixed point classes and Nielsen numbers of $n$-valued maps

Brown, Robert F.; Nan, Junzheng
The stabilizer of a fixed point class of a map is the fixed subgroup of the induced fundamental group homomorphism based at a point in the class. A theorem of Jiang, Wang and Zhang is used to prove that if a map of a graph satisfies a strong remnant condition, then the stabilizers of all its fixed point classes are trivial. Consequently, if $\phi_{p, f}$ is the $n$-valued lift to a covering space $p$ of a map $f$ with strong remnant of a graph, then the Nielsen numbers are related by the equation $N(\phi_{p, f}) = n \cdot N(f)$. Additional...

7. #### Linear systems over $\mathbb Z[Q_{16}]$ and roots of maps of some 3-complexes into $M_{Q_{16}}$

Aniz, Claudemir
Let $\mathbb Z[Q_{16}]$ be the group ring where $Q_{16}=\langle x,y|x^4=y^2,\,xyx=y\rangle$ is the quaternion group of order 16 and $\varepsilon$ the augmentation map. We show that, if $PX=K(x-1)$ and $PX=K(-xy+1)$ has solution over $\mathbb Z[Q_{16}]$ and all $m\times m$ minors of $\varepsilon (P)$ are relatively prime, then the linear system $PX=K$ has a solution over $\mathbb Z[Q_{16}]$, where $P=[p_{ij}]$ is an $m\times n$ matrix with $m\leq n$. As a consequence of such results, we show that there is no map $f:W\to M_{Q_{16}}$ that is strongly surjective, i.e., such that $MR[f,a]=\min\{\#(g^{-1}(a))|g\in [f]\}\neq 0$. Here, $M_{Q_{16}}$ is the orbit space of the...

8. #### Linear systems over $\mathbb Z[Q_{16}]$ and roots of maps of some 3-complexes into $M_{Q_{16}}$

Aniz, Claudemir
Let $\mathbb Z[Q_{16}]$ be the group ring where $Q_{16}=\langle x,y|x^4=y^2,\,xyx=y\rangle$ is the quaternion group of order 16 and $\varepsilon$ the augmentation map. We show that, if $PX=K(x-1)$ and $PX=K(-xy+1)$ has solution over $\mathbb Z[Q_{16}]$ and all $m\times m$ minors of $\varepsilon (P)$ are relatively prime, then the linear system $PX=K$ has a solution over $\mathbb Z[Q_{16}]$, where $P=[p_{ij}]$ is an $m\times n$ matrix with $m\leq n$. As a consequence of such results, we show that there is no map $f:W\to M_{Q_{16}}$ that is strongly surjective, i.e., such that $MR[f,a]=\min\{\#(g^{-1}(a))|g\in [f]\}\neq 0$. Here, $M_{Q_{16}}$ is the orbit space of the...

9. #### Linear systems over $\mathbb Z[Q_{16}]$ and roots of maps of some 3-complexes into $M_{Q_{16}}$

Aniz, Claudemir
Let $\mathbb Z[Q_{16}]$ be the group ring where $Q_{16}=\langle x,y|x^4=y^2,\,xyx=y\rangle$ is the quaternion group of order 16 and $\varepsilon$ the augmentation map. We show that, if $PX=K(x-1)$ and $PX=K(-xy+1)$ has solution over $\mathbb Z[Q_{16}]$ and all $m\times m$ minors of $\varepsilon (P)$ are relatively prime, then the linear system $PX=K$ has a solution over $\mathbb Z[Q_{16}]$, where $P=[p_{ij}]$ is an $m\times n$ matrix with $m\leq n$. As a consequence of such results, we show that there is no map $f:W\to M_{Q_{16}}$ that is strongly surjective, i.e., such that $MR[f,a]=\min\{\#(g^{-1}(a))|g\in [f]\}\neq 0$. Here, $M_{Q_{16}}$ is the orbit space of the...

10. #### Linear systems over $\mathbb Z[Q_{16}]$ and roots of maps of some 3-complexes into $M_{Q_{16}}$

Aniz, Claudemir
Let $\mathbb Z[Q_{16}]$ be the group ring where $Q_{16}=\langle x,y|x^4=y^2,\,xyx=y\rangle$ is the quaternion group of order 16 and $\varepsilon$ the augmentation map. We show that, if $PX=K(x-1)$ and $PX=K(-xy+1)$ has solution over $\mathbb Z[Q_{16}]$ and all $m\times m$ minors of $\varepsilon (P)$ are relatively prime, then the linear system $PX=K$ has a solution over $\mathbb Z[Q_{16}]$, where $P=[p_{ij}]$ is an $m\times n$ matrix with $m\leq n$. As a consequence of such results, we show that there is no map $f:W\to M_{Q_{16}}$ that is strongly surjective, i.e., such that $MR[f,a]=\min\{\#(g^{-1}(a))|g\in [f]\}\neq 0$. Here, $M_{Q_{16}}$ is the orbit space of the...

11. #### Nielsen-Reidemeister indices for multivalued maps

Crabb, M.C.
A Nielsen-Reidemeister index is constructed for multivalued maps defined by fractions $f/p$ where $p: \tilde X \to X$ is a fibrewise manifold with closed fibres over a compact ENR and $f:\tilde X\to X$ is a continuous map. In the case that $p$ is a finite $n$-fold cover, this index is shown to agree with the index of the $n$-valued map $\tilde X\multimap \tilde X$ associated with $f/p$ by a construction of Brown [4].

12. #### Nielsen-Reidemeister indices for multivalued maps

Crabb, M.C.
A Nielsen-Reidemeister index is constructed for multivalued maps defined by fractions $f/p$ where $p: \tilde X \to X$ is a fibrewise manifold with closed fibres over a compact ENR and $f:\tilde X\to X$ is a continuous map. In the case that $p$ is a finite $n$-fold cover, this index is shown to agree with the index of the $n$-valued map $\tilde X\multimap \tilde X$ associated with $f/p$ by a construction of Brown [4].

13. #### Nielsen-Reidemeister indices for multivalued maps

Crabb, M.C.
A Nielsen-Reidemeister index is constructed for multivalued maps defined by fractions $f/p$ where $p: \tilde X \to X$ is a fibrewise manifold with closed fibres over a compact ENR and $f:\tilde X\to X$ is a continuous map. In the case that $p$ is a finite $n$-fold cover, this index is shown to agree with the index of the $n$-valued map $\tilde X\multimap \tilde X$ associated with $f/p$ by a construction of Brown [4].

14. #### Nielsen-Reidemeister indices for multivalued maps

Crabb, M.C.
A Nielsen-Reidemeister index is constructed for multivalued maps defined by fractions $f/p$ where $p: \tilde X \to X$ is a fibrewise manifold with closed fibres over a compact ENR and $f:\tilde X\to X$ is a continuous map. In the case that $p$ is a finite $n$-fold cover, this index is shown to agree with the index of the $n$-valued map $\tilde X\multimap \tilde X$ associated with $f/p$ by a construction of Brown [4].

15. #### New Numerical Solution For Solving Nonlinear Singular Thomas-Fermi Differential Equation

Parand, Kourosh; Delkhosh, Mehdi
In this paper, the nonlinear singular Thomas-Fermi differential equation on a semi-infinite domain for neutral atoms is solved by using the generalized fractional order of the Chebyshev orthogonal functions (GFCFs) of the first kind. First, this collocation method reduces the solution of this problem to the solution of a system of nonlinear algebraic equations. Second, using solve a system of nonlinear equations, the initial value for the unknown parameter $L$ is calculated, and finally, the value of $L$ to increase the accuracy of the initial slope is improved and the value of $y'(0)=-1.588071022611375312718684509$ is calculated. The comparison with some numerical...

16. #### A remark on the Chow ring of some hyperkähler fourfolds

Laterveer, Robert
Let $X$ be a hyperkähler variety. Voisin has conjectured that the classes of Lagrangian constant cycle subvarieties in the Chow ring of $X$ should lie in a subring injecting into cohomology. We study this conjecture for the Fano variety of lines on a very general cubic fourfold.

17. #### Sums of asymptotically midpoint uniformly convex spaces

Dilworth, S. J.; Kutzarova, Denka; Randrianarivony, N. Lovasoa; Romney, Matthew
We study the property of asymptotic midpoint uniform convexity for infinite direct sums of Banach spaces, where the norm of the sum is defined by a Banach space $E$ with a 1-unconditional basis. We show that a sum $(\sum_{n=1}^\infty X_n)_E$ is asymptotically midpoint uniformly convex (AMUC) if and only if the spaces $X_n$ are uniformly AMUC and $E$ is uniformly monotone. We also show that $L_p(X)$ is AMUC if and only if $X$ is uniformly convex.

18. #### Criteria for univalence, Integral means and Dirichlet integral for Meromorphic functions

Let $\mathcal{A}(p)$ be the class consisting of functions $f$ that are holomorphic in $\mathbb D\setminus \{p\}$, $p\in (0,1)$ possessing a simple pole at the point $z=p$ with nonzero residue and normalized by the condition $f(0)=0=f'(0)-1$. In this article, we first prove a sufficient condition for univalency for functions in $\mathcal{A}(p)$. Thereafter, we consider the class denoted by $\Sigma(p)$ that consists of functions $f \in \mathcal{A}(p)$ that are univalent in $\mathbb D$. We obtain the exact value for $\displaystyle\max_ {f\in \Sigma(p)}\Delta(r,z/f)$, where the Dirichlet integral $\Delta(r,z/f)$ is given by  \Delta(r,z/f)=\displaystyle\iint_{|z|

19. #### Generalized CAT(0) spaces

Khamsi, M. A.; Shukri, S. A.
We extend the Gromov geometric definition of CAT(0) spaces to the case where the comparison triangles are not in the Euclidean plane but belong to a general Banach space. In particular, we study the case where the Banach space is $\ell_p$, for $p > 2$.

20. #### Density by moduli and Wijsman statistical convergence

Bhardwaj, Vinod K.; Dhawan, Shweta; Dovgoshey, Oleksiy A.
In this paper, we have generalized the Wijsman statistical convergence of closed sets in metric space by introducing the $f$-Wijsman statistical convergence of these sets, where $f$ is an unbounded modulus. It is shown that the Wijsman convergent sequences are precisely those sequences which are $f$-Wijsman statistically convergent for every unbounded modulus $f$. We have also introduced a new concept of Wijsman strong Cesàro summability with respect to a modulus $f$, and investigate the relationship between the $f$-Wijsman statistically convergent sequences and the Wijsman strongly Cesàro summable sequences with respect to $f$.

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