Abstract:
In this paper we study the set of ℊ-valued functions which can be approximated by ℊ-valued continuous functions in the norm Lℊ∞(I,w), where I⊂ℝ is a compact interval, ℊ is a separable real Hilbert space and w is a certain ℊ-valued weakly measurable weight. Thus, we obtain a new extension of the celebrated Weierstrass approximation theorem.

Abstract:
In this paper we study the set of ？-valued functions which can be approximated by ？-valued continuous functions in the norm L ？ ∞ ( I , w ) , where I ？ ？ is a compact interval, ？ is a separable real Hilbert space and w is a certain ？-valued weakly measurable weight. Thus, we obtain a new extension of the celebrated Weierstrass approximation theorem.

Abstract:
In this paper we study the set of functions $\GG$-valued which can be approximated by $\GG$-valued continuous functions in the norm $L^\infty_{\GG}(I,w)$, where $I$ is a compact interval, $\GG$ is a real and separable Hilbert space and $w$ is certain $\GG$-valued weakly measurable weight. Thus, we obtain a new extension of celebrated Weierstrass approximation theorem.

Abstract:
We prove the interior approximate controllability of the following broad class of reaction diffusion equation in the Hilbert spaces =2(Ω) given by =？

Abstract:
this paper we provides an alternative proof of hurewicz theorem when the topological space x is a cw-complex. indeed, we show that if x0 c x1 c ... xn-1 c xn = x is the cw decomposition of x, then the hurewicz homomorphism ∏n+1 (xn+1,xn) → hn+1 (xn+1,xn) is an isomorphism, and together with a result from homological algebra we prove that if x is (n-1)-connected, the hurewicz homomorphism ∏n (x) → hn (x) is an isomorphism.

Abstract:
This paper we provides an alternative proof of Hurewicz theorem when the topological space X is a CW-complex. Indeed, we show that if X0 C X1 C ... Xn-1 C Xn = X is the CW decomposition of X, then the Hurewicz homomorphism ∏n+1 (Xn+1,Xn) → Hn+1 (Xn+1,Xn) is an isomorphism, and together with a result from Homological Algebra we prove that if X is (n-1)-connected, the Hurewicz homomorphism ∏n (X) → Hn (X) is an isomorphism. En este artículo damos una demostración alternativa de el teorema de Hurewicz cuando el espacio topológico X es CW-complejo. En realidad probamos que si X0 C X1 C ... Xn-1 C Xn = X es una descomposición CW de X, el homomorfismo de Hurewicz ∏n+1 (Xn+1,Xn) → Hn+1 (Xn+1,Xn) es un isomorfismo y usando un resultado de álgebra Homológica demostramos que si X es conexo, el homomorfismo de Hurewicz ∏n (X) → Hn (X) es un isomorfismo.

Abstract:
The Multiple Intelligence Theory (MI) is one of the models that study and describe the cognitive abilities of an individual. In [7] is presented a referential system which allows to identify the Multiple Intelligences of the students of a course and to classify the level of development of such Intelligences. Following this tendency, the purpose of this paper is to describe the model of Multiple Intelligences as a quotient space, and also to study the Multiple Intelligences of an individual in terms of this new mathematical representation.

Abstract:
The celebrated and famous Weierstrass approximation theorem characterizes the set of continuous functions on a compact interval via uniform approximation by algebraic polynomials. This theorem is the first significant result in Approximation Theory of one real variable and plays a key role in the development of General Approximation Theory. Our aim is to investigate some new results relative to such theorem, to present a history of the subject, and to introduce some open problems.

Abstract:
In this paper we study the controllability of the controlled Laguerre equation and the controlled Jacobi equation. For each case, we found conditions which guarantee when such systems are approximately controllable on the interval $[0, t_1]$. Moreover, we show that these systems can never be exactly controllable

Abstract:
Let $\{Q^{(\alpha)}_{n,\lambda}\}_{n\geq 0}$ be the sequence of monic orthogonal polynomials with respect the Gegenbauer-Sobolev inner product $$\langle f,g\rangle_{S}:=\int_{-1}^{1}f(x)g(x)(1-x^{2})^{\alpha-\frac{1}{2}}dx+\lambda \int_{-1}^{1}f'(x)g'(x)(1-x^{2})^{\alpha-\frac{1}{2}} dx,$$ where $\alpha>-\frac{1}{2}$ and $\lambda\geq 0$. In this paper we use a recent result due to B.D. Bojanov and N. Naidenov \cite{BN2010}, in order to study the maximization of a local extremum of the $k$th derivative $\frac{d^k}{dx^k}Q^{(\alpha)}_{n,\lambda}$ in $[-M_{n,\lambda}, M_{n,\lambda}]$, where $M_{n,\lambda}$ is a suitable value such that all zeros of the polynomial $Q^{(\alpha)}_{n,\lambda}$ are contained in $[-M_{n,\lambda}, M_{n,\lambda}]$ and the function $\left|Q^{(\alpha)}_{n,\lambda}\right|$ attains its maximal value at the end-points of such interval. Also, some illustrative numerical examples are presented.