Related papers: A short proof of Cramer's theorem in R
We revisit a classic proof of the Blaschke-Lebesgue theorem. It is based on the support function of a convex curve and the approximation of constant width curves by Reuleaux polygons.
In this note, we give short inductive proofs of two known results on $k$-extendible graphs based on a property proved in [Qinglin Yu, A note on $n$-extendable graphs. Journal of Graph Theory, 16:349-353, 1992].
We prove a variation of Gronwall's lemma.
Theorem 1 of [14], a minimax result for functions $f:X\times Y\to {\bf R}$, where $Y$ is a real interval, was partially extended to the case where $Y$ is a convex set in a Hausdorff topological vector space ([15], Theorem 3.2). In doing…
We present a proof of Moessner's theorem by double induction, using only basic rules of arithmetic. No prerequisite knowledge is assumed. Familiarity with summation is advised.
We have found a possibility to streamline the proof of the Treves' theorem (Duke Math. J., 108, 251-295, 2001) on an algebraic characterization of the KdV hierarchy which makes it significantly shorter, following essentially the logic of…
We prove a vanishing theorem for the twisted de Rham cohomology of a compact manifold.
A new concise proof is given of a duality theorem connecting completely monotone relaxation functions with Bernstein class creep functions. The proof makes use of the theory of complete Bernstein functions and Stieltjes functions and is…
We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.
In this paper, we obtain some new inequalities for ({\alpha},m)-convex functions. The analysis used in the proofs is fairly elementary and based on the use of Power-mean inequality.
We present a short proof, relaying on the divergence theorem, verifying that minimal sets in the plane are trivial.
In this paper we consider Erd\"os-Mordell inequality and its extension in the plane of triangle to the Erd\"os-Mordell curve. Algebraic equation of this curve is derived, and using modern computer tools in mathematics, we verified one…
We give a new proof of the existence of designs, which is much shorter and gives better bounds.
We give a short proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis. The part of the proof which is my own (not Pin's) is a complete replacement of the same part in an earlier version of this paper.
Gives a short proof of Dehornoy's latest result. The same simple argument (and more) was discovered by Laver's student Larue.
A key idea in convex optimization theory is to use well-structured affine functions to approximate general functions, leading to impactful developments in conjugate functions and convex duality theory. This raises the question: what are the…
We give a proof of the Greene-Krantz conjecture on convex domains in $\CC^2$. Curiously, the proof technique depends on subelliptic estimates for the $\bar{\partial}$ problem.
It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.
We prove analogues of the Craig interpolation theorem for the continuous model theory of metric structures.
We present a simple method based on the stability and duality of the properties of sampling and interpolation, which allows one to substantially simplify the proofs of some classical results.