相关论文: A truly elementary proof of Bertrand's theorem

In the present work, metrics which lead to projected closed orbits are found by comparing the relativistic differential equation of orbits with the corresponding classical differential equation. Physical and geometrical properties of these…

The relativistic precession can be quickly inferred from the nonlinear polar orbit equation without actually solving it.

It is generally accepted that Everett's theory of quantum mechanics cannot be experimentally tested as such experiment would involve operations on the observer which are beyond our current technology. We propose an alternative to test…

While it is widely agreed that Bell's theorem is an important result in the foundations of quantum physics, there is much disagreement about what exactly Bell's theorem shows. It is agreed that Bell derived a contradiction with experimental…

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…

Following the Perron-Frobenius theorem, the spectral radius of a primitive matrix is a simple eigenvalue. It is shown that for a primitive matrix $A$, there is a positive rank one matrix $X$ such that $B = A \circ X$, where $\circ$ denotes…

We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.

We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…

We argue that in the general relativistic calculation of planetary orbits, the choice of a reference frame which is an obligatory condition in the Newtonian approach is replaced by an appropriate boundary condition on the solution of…

We give an elementary proof of the Mazur-Tate-Teitelbaum conjecture for elliptic curves by using Kato's element.

We give a simple proof of Bourgain's theorem on the singularity of Ornstein's maps.

We give a geometric proof of the Routh's theorem for tetrahedra.

In his talk "Integral Apollonian disk Packings" Peter Sarnak asked if there is a "proof from the Book" of the Descartes theorem on circles. A candidate for such a proof is presented in this note

It is shown in our earlier paper that, using only tools of elementary geometry, the classical Routh's theorem for triangles can be fully extended to tetrahedra. In this article we first give another proof of Routh's theorem for tetrahedra…

This proof of Godel's first incompleteness theorem doesn't require omega-consistency, nor does it refer to codes of negated sentences as in Rosser's. It begins from where Godel's usual proof ends, and stalks it till it ends proving it.

Given a base point free linear system on an algebraic variety, many classes of singularities are stable under taking suitable members after enlarging the base field. We establish analogous results when the base ring is an excellent ring.

We argue that for the proof of Bell's theorem no assumptions about realism or free will are necessary. The key formula \[E(AB|a,b) = \int A(a,b,\lambda)B(a,b,\lambda)\rho(\lambda) d\lambda\] follows from the logic of plausible reasoning…

We present a notion of primitive which corresponds exactly with the Riemann integral. We obtain a characterization of the integrability in the sense of Riemann which produces a Fundamental Theorem of Calculus without special assumptions. We…

We give a proof for the fundamental theorem of algebra,using the Fredholm index phenomena