Related papers: An Elementary Proof for the Basel Problem
We present here a simple and direct proof of the classic geometric version of Hahn-Banach Theorem from its analitic version, in the real case. The reciprocal implication, and the direct proofs of both versions, are already well kown, but…
We prove Union-Closed sets conjecture.
If the left multiplication group of a loop is simple, then the loop is simple. We use this observation to give examples of infinite simple Bol loops.
We provide a short proof of the 1-dimensional flat chain conjecture.
We present short elementary proofs of the well-known Ruffini-Abel-Galois theorems on insolvability of algebraic equations in radicals. These proofs are obtained from existing expositions by stripping away material not required for the…
After Abel Ruffini theorem and Galois Theory the search for a method or formula to solve quintic equation ends. This paper discuss about the radical solution of quintic equation using a method that could be proved in some simple steps. A…
This paper presents a new, significantly simpler proof of one of the main results of applied pi-calculus: the theorem that the concepts of observational and labeled equivalence of extended processes in applied pi-calculus coincide.
The article presents the proof of Casas-Alvero conjecture.
We present, discuss and generalize an elegant geometrical proof of the law of cosines, due to Al Cuoco.
We give a direct analytic proof of the classical Boundary Harnack inequality for solutions to linear uniformly elliptic equations in either divergence or non-divergence form.
We give a short, elementary and explicit proof of the existence of Hilbert schemes of points on affine schemes. As a direct consequence we obtain the existence of the Hilbert scheme of points on any projective scheme, not necessarily of…
Three comparison criteria for the Abel equation of 1es kind are proved. The results obtained are used to obtain global solvability criteria and some criteria of existence of closed solutions for the mentioned equation. The results obtained…
This paper is purely expository. We present short elementary proofs of * the Gauss Theorem on constructibility of regular polygons; * the existence of a cubic equation unsolvable in real radicals; * the existence of a quintic equation…
Collatz Conjecture is one of the most famous, for its simple form, proposed more than eighty years ago. This paper presents a full attempt to prove the affirmative answer to the question proposed by the conjecture. In the first section, we…
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.
Evidential reasoning is cast as the problem of simplifying the evidence-hypothesis relation and constructing combination formulas that possess certain testable properties. Important classes of evidence as identifiers, annihilators, and…
A diagrammatic logical calculus for the syllogistic reasoning is introduced and discussed. We prove that a syllogism is valid if and only if it is provable in the calculus.
Herbrand's theorem is often presented as a corollary of Gentzen's sharpened Hauptsatz for the classical sequent calculus. However, the midsequent gives Herbrand's theorem directly only for formulae in prenex normal form. In the Handbook of…
In this exposition-type note we present detailed proofs of certain assertions concerning several algebraic properties of the cone and cylinder algebras. These include a determination of the maximal ideals, the solution of the B\'ezout…
In this paper, we will study the simplest kind of beauty that can be found in a simple piece of music and can be appreciated universally. The proposed approach shows that aesthetically appealing patterns deliver higher amount of information…