# Recursively enumerable sets of polynomials over a finite field are Diophantine

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- Norms as products of linear polynomials. Schindler, Damaris; Skorobogatov, Alexei // Journal of the London Mathematical Society;Apr2014, Vol. 89 Issue 2, p559
Let $F$ be a number field, and let $F\subset K$ be a field extension of degree $n$. Suppose that we are given $2r$ sufficiently general linear polynomials in $r$ variables over $F$. Let $X$ be the variety over $F$ such that the $F$-points of $X$ bijectively correspond to the representations of...

- Algorithm to solve certain ternary quartic Diophantine equations. SZALAY, László // Turkish Journal of Mathematics;Sep2013, Vol. 37 Issue 5, p733
In this paper, we develop an algorithm to solve completely the Diophantine equation F(x; y) = zÂ², where the quartic inhomogeneous polynomial F(x; y) with integer coefficients satisfies certain technical conditions. The procedure is an extension of the version of Runge's method given by Poulakis.

- Two condensed macro-elements with full approximation power. Alfeld, Peter; Schumaker, Larry L.; Sorokina, Tatyana // Advances in Computational Mathematics;May2010, Vol. 32 Issue 4, p381
A variant of the classical C1 Powell-Sabin-12 macro-element is defined that has the same approximation power, but has fewer degrees of freedom and only requires vertex data. The same idea is then applied to a related C1 trivariate macro-element.

- Simplifying method for algebraic approximation of certain algebraic numbers. Xia, Jingbo; Chen, Jianhua; Zhang, Silan // Mathematical Notes;Sep2012, Vol. 92 Issue 3/4, p383
A new simple method for approximating certain algebraic numbers is developed. By applying this method, an effective upper bound is derived for the integral solutions of the quartic Thue equation with two parameters , where s > 32 t. As an application, Ljunggren's equation is solved in an...

- Improved Bound on Approximating Jug Measuring Problem. MIN-ZHENG SHIEH; SHI-CHUN TSAI // Journal of Information Science & Engineering;May2011, Vol. 27 Issue 3, p1159
No abstract available.

- THE SEMIADDICTION OF CONTINUOUS ANALYTIC CAPACITY AND THE INNER BOUNDARY CONJECTURE. Tolsa, Xavier // American Journal of Mathematics;Jun2004, Vol. 126 Issue 3, p523
Let Î±(E) be the continuous analytic capacity of a compact set E âŠ‚ C. In this paper we obtain a characterization of Î± in terms of curvature of measures with zero linear density, and we deduce that Î± is countably semiadditive. This result has important consequences for the theory of...

- Polynomials Satisfying Functional and Differential Equations and Diophantine Properties of Their Zeros. Calogero, Francesco; Yi, Ge // Letters in Mathematical Physics;Jun2013, Vol. 103 Issue 6, p629
By investigating the behavior of two solvable isochronous N-body problems in the immediate vicinity of their equilibria, functional equations satisfied by the para-Jacobi polynomial $${p_{N} \left(0, 1; \gamma; x \right)}$$ and by the Jacobi polynomial $${P_{N}^{\left(-N-1,-N-1 \right)} \left(x...

- Refinement of an inequality of P. L. Chebyshev. Dryanov, D.; Fournier, R. // Acta Mathematica Hungarica;Jan2009, Vol. 122 Issue 1/2, p59
Let P n denote the linear space of polynomials p( z:=Î£ a k( p) z k of degree â‰¦ n with complex coefficients and let | p|[âˆ’1,1]: = max xâˆˆ[âˆ’1,1]| p( x)| be the uniform norm of a polynomial p over the unit interval [âˆ’1, 1]. Let t n âˆˆ P n be the nth Chebyshev...

- SzegÃ¶ theorem, carathÃ©odory domains, and boundedness of calculating functionals. Abdullaev, F. G.; Dovgoshei, A. A. // Mathematical Notes;Jan/Feb2005, Vol. 77 Issue 1/2, p3
Suppose thatGis a bounded simply connected domain on the plane with boundary G,z0 ?G, ? is the harmonic measure with respect toz0 on G, Âµ is a finite Borel measure with support supp(Âµ)G, Âµa + Âµs is the decomposition of Âµ with respect to ?, andtis a positive real number. We solve...