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### 3D monolithic finite element approach for aero-thermics processes in industrial furnaces⋆

ESAIM: Proceedings

We consider in this paper a mathematical and numerical model to design an industrial software solution able to handle real complex furnaces configurations in terms of geometries, atmospheres, parts positioning, heat generators and physical thermal phenomena. A three dimensional algorithm based on stabilized finite element methods (SFEM) for solving the momentum, energy, turbulence and radiation equations is presented. An immersed volume method (IVM) for thermal coupling of fluids and solids is introduced...

### A Computational Procedure for the Approximation of Random Functions.

Numerische Mathematik

### A conjecture related to the approximation operators of binomial type.

General Mathematics

### A counterexample in comonotone approximation in ${L}^{p}$ space

Colloquium Mathematicae

Refining the idea used in [24] and employing very careful computation, the present paper shows that for 0 < p ≤ ∞ and k ≥ 1, there exists a function $f\in {C}_{\left[-1,1\right]}^{k}$, with ${f}^{\left(k\right)}\left(x\right)\ge 0$ for x ∈ [0,1] and ${f}^{\left(k\right)}\left(x\right)\le 0$ for x ∈ [-1,0], such that lim supn→∞ (en(k)(f)p) / (ωk+2+[1/p](f,n-1)p) = + ∞ where ${e}_{n}^{\left(k\right)}{\left(f\right)}_{p}$ is the best approximation of degree n to f in ${L}^{p}$ by polynomials which are comonotone with f, that is, polynomials P so that ${P}^{\left(k\right)}\left(x\right){f}^{\left(k\right)}\left(x\right)\ge 0$ for all x ∈ [-1,1]. This theorem, which is a particular case of a more general one, gives a complete solution...

### A Discrepancy Theorem Concerning Polynomials of Best Approximation in L...[-1, 1].

Monatshefte für Mathematik

### A general theorem on triangular finite ${C}^{\left(m\right)}$-elements

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

### A generalization of Hermite interpolation.

International Journal of Mathematics and Mathematical Sciences

### A Korovkin type approximation theorems via $ℐ$-convergence

Czechoslovak Mathematical Journal

Using the concept of $ℐ$-convergence we provide a Korovkin type approximation theorem by means of positive linear operators defined on an appropriate weighted space given with any interval of the real line. We also study rates of convergence by means of the modulus of continuity and the elements of the Lipschitz class.

### A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients.

Journal of Applied Mathematics

### A lower bound for the second moment of Schoenberg operator.

General Mathematics

### A method for summability of Lagrange interpolation.

International Journal of Mathematics and Mathematical Sciences

### A new exceptional polynomial for the integer transfinite diameter of $\left[0,1\right]$

Journal de théorie des nombres de Bordeaux

Using refinement of an algorithm given by Habsieger and Salvy to find integer polynomials with smallest sup norm on [0, 1] we extend their table of polynomials up to degree 100. For the degree 95 we find a new exceptionnal polynomial which has complex roots. Our method uses generalized Müntz-Legendre polynomials. We improve slightly the upper bound for the integer transfinite diameter of [0, 1] and give elementary proofs of lower bounds for the exponents of some critical polynomials.

### A new generating function of ($q$-) Bernstein-type polynomials and their interpolation function.

Abstract and Applied Analysis

### A new H(div)-conforming p-interpolation operator in two dimensions

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we construct a new H(div)-conforming projection-based p-interpolation operator that assumes only Hr(K) $\cap$$\stackrel{˜}{𝐇}$-1/2(div, K)-regularity (r &gt; 0) on the reference element (either triangle or square) K. We show that this operator is stable...

### A new H(div)-conforming p-interpolation operator in two dimensions

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we construct a new H(div)-conforming projection-based p-interpolation operator that assumes only Hr(K) $\cap$$\stackrel{˜}{𝐇}$-1/2(div, K)-regularity (r > 0) on the reference element (either triangle or square) K. We show that this operator is stable with...

### A Note on a Result of Zolotarev and Bernstein.

Manuscripta mathematica

### A note on Diophantine approximation.

International Journal of Mathematics and Mathematical Sciences

### A note on lacunary approximation on [-1,1]

Colloquium Mathematicae

### A note on polynomial approximation in Sobolev spaces

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

### A note on polynomial approximation in Sobolev spaces

ESAIM: Mathematical Modelling and Numerical Analysis

For domains which are star-shaped w.r.t. at least one point, we give new bounds on the constants in Jackson-inequalities in Sobolev spaces. For convex domains, these bounds do not depend on the eccentricity. For non-convex domains with a re-entrant corner, the bounds are uniform w.r.t. the exterior angle. The main tool is a new projection operator onto the space of polynomials.

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