## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (198.174 recursos)

Bulletin of the Belgian Mathematical Society-Simon Stevin

1. #### 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...

2. #### 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.

3. #### 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.

4. #### 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|

5. #### 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 $p > 2$.

6. #### 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 $f$.

7. #### Compact perturbations resulting in hereditarily polaroid operators

Duggal, B.P.
A Banach space operator $A\in B({\cal X})$ is polaroid, $A\in(\cal P)$, if the isolated points of the spectrum $\sigma(A)$ are poles of the operator; $A$ is hereditarily polaroid, $A\in(\cal {HP})$, if every restriction of $A$ to a closed invariant subspace is polaroid. It is seen that operators $A\in(\cal {HP})$ have SVEP - the single-valued extension property - on $\Phi_{sf}(A)=\{\lambda: A-\lambda$ is semi Fredholm $\}$. Hence $\Phi^+_{sf}(A)=\{\lambda\in\Phi_{sf}(A), \ind(A-\lambda)>0\}=\emptyset$ for operators $A\in(\cal {HP})$, and a necessary and sufficient condition for the perturbation $A+K$ of an operator $A\in B({\cal X})$ by a compact operator $K\inB({\cal X})$ to be hereditarily polaroid is that $\Phi_{sf}^+(A)=\emptyset$. A sufficient condition for $A\in B({\cal X})$ to have...

8. #### A discrete-time approach in the qualitative theory of skew-product three-parameter semiflows

We obtain a characterization of the uniform exponential stability for the continuous-time skew-product three-parameter semiflows in Banach spaces, using a discrete-time approach. Our technique is based on the classical "test-function" method of O. Perron and Ta Li.

9. #### Generalized derivatives and approximation in weighted Lorentz spaces

Akgün, Ramazan; Yildirir, Yunus Emre
In the present article we prove direct, simultaneous and converse approximation theorems by trigonometric polynomials for functions $f$ and $\left( \psi ,\beta \right)$-derivatives of $f$ in weighted Lorentz spaces.

10. #### Numerical treatment of nonlocal boundary value problem with layer behaviour

Cimen, Erkan; Cakir, Musa
This paper deals with the singularly perturbed nonlocal boundary value problem for a linear first order differential equation. For the numerical solution of this problem, we use a fitted difference scheme on a piecewise uniform Shishkin mesh. An error analysis shows that the method is almost first order convergent, in the discrete maximum norm, independently of the perturbation parameter. Numerical results are presented which illustrate the theoretical results.

11. #### An explicit formula for the cup-length of the rotation group

Korbaš, Július
This paper gives an explicit formula for the $\mathbb Z_2$-cup-length of the rotation group $\mathrm{SO}(n)$.

12. #### Best approximative properties of exposed faces of $l_1$

Kalaiarasi, S.

13. #### A new analytical technique for solving Lane - Emden type equations arising in astrophysics

Deniz, Sinan; Bildik, Necdet
Lane - Emden type equations are nonlinear differential equations which represent many scientific phenomena in astrophysics and mathematical physics. In this study, a new analytic approximate technique for addressing nonlinear problems, namely the optimal perturbation iteration method, is introduced and implemented to singular initial value Lane-Emden type problems to test the effectiveness and performance of the method. This technique provides us to adjust the convergence regions when necessary.Comparing different methods reveals that the proposed method is highly accurate and has great potential to be a new kind of powerful analytical tool for Lane-Emden type equations.

14. #### A new analytical technique for solving Lane - Emden type equations arising in astrophysics

Deniz, Sinan; Bildik, Necdet
Lane - Emden type equations are nonlinear differential equations which represent many scientific phenomena in astrophysics and mathematical physics. In this study, a new analytic approximate technique for addressing nonlinear problems, namely the optimal perturbation iteration method, is introduced and implemented to singular initial value Lane-Emden type problems to test the effectiveness and performance of the method. This technique provides us to adjust the convergence regions when necessary.Comparing different methods reveals that the proposed method is highly accurate and has great potential to be a new kind of powerful analytical tool for Lane-Emden type equations.

15. #### Some remarks on the structure of Lipschitz-free spaces

Aizpuru, Petr; Hájek, M.; Novotný, Matěj
We give several structural results concerning the Lipschitz-free spaces $\mathcal F(M)$, where $M$ is a metric space. We show that $\mathcal F(M)$ contains a complemented copy of $\ell_1(\Gamma)$, where $\Gamma=\text{dens}(M)$. If $\mathcal N$ is a net in a finite dimensional Banach space $X$, we show that $\mathcal F(\mathcal N)$ is isomorphic to its square. If $X$ contains a complemented copy of $\ell_p, c_0$ then $\f(\mathcal N)$ is isomorphic to its\linebreak $\ell_1$-sum. Finally, we prove that for all $X\cong C(K)$ spaces, where $K$ is a metrizable compact, $\f(\mathcal N)$ are mutually isomorphic spaces with a Schauder basis.

16. #### Some remarks on the structure of Lipschitz-free spaces

Hájek, Peter; Novotný, Matěj
We give several structural results concerning the Lipschitz-free spaces $\mathcal F(M)$, where $M$ is a metric space. We show that $\mathcal F(M)$ contains a complemented copy of $\ell_1(\Gamma)$, where $\Gamma=\text{dens}(M)$. If $\mathcal N$ is a net in a finite dimensional Banach space $X$, we show that $\mathcal F(\mathcal N)$ is isomorphic to its square. If $X$ contains a complemented copy of $\ell_p, c_0$ then $\f(\mathcal N)$ is isomorphic to its$\ell_1$-sum. Finally, we prove that for all $X\cong C(K)$ spaces, where $K$ is a metrizable compact, $\f(\mathcal N)$ are mutually isomorphic spaces with a Schauder basis.

17. #### Stability constants for weighted composition operators on $L^p(\Sigma)$

Jabbarzadeh, M. R.; Bakhshkandi, M. Jafari
In this note we give an explicit formula for the Moore-Penrose inverse $W^{\dag}$ of a weighted composition operator $W$ on $L^2(\Sigma)$ and then we obtain the stability constant $K_W$ of $W$ on $L^p(\Sigma)$, where $1\leq p\leq \infty$. Moreover, we determine, under certain conditions, the essential norm of $W$ acting on $L^\infty(\Sigma)$.

18. #### Stability constants for weighted composition operators on $L^p(\Sigma)$

Jabbarzadeh, M. R.; Bakhshkandi, M. Jafari
In this note we give an explicit formula for the Moore-Penrose inverse $W^{\dag}$ of a weighted composition operator $W$ on $L^2(\Sigma)$ and then we obtain the stability constant $K_W$ of $W$ on $L^p(\Sigma)$, where $1\leq p\leq \infty$. Moreover, we determine, under certain conditions, the essential norm of $W$ acting on $L^\infty(\Sigma)$.

19. #### Homogeneous Geodesics in Generalized Wallach Spaces

Arvanitoyeorgos, Andreas; Wang, Yu
We classify generalized Wallach spaces which are g.o. spaces. We also investigate homogeneous geodesics in generalized Wallach spaces for any given invariant Riemannian metric and we give some examples.

20. #### Homogeneous Geodesics in Generalized Wallach Spaces

Arvanitoyeorgos, Andreas; Wang, Yu
We classify generalized Wallach spaces which are g.o. spaces. We also investigate homogeneous geodesics in generalized Wallach spaces for any given invariant Riemannian metric and we give some examples.

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