Related papers: A short proof of Isserlis' theorem
We prove a categorical version of the Torelli theorem for cubic threefolds. More precisely, we show that the non-trivial part of a semi-orthogonal decomposition of the derived category of a cubic threefold characterizes its isomorphism…
We provide a simple and short proof of the Karush-Kuhn-Tucker theorem with finite number of equality and inequality constraints. The proof relies on an elementary linear algebra lemma and the local inverse theorem.
We prove Sklar's theorem in infinite dimensions via a topological argument and the notion of inverse systems.
In this short paper we review and extract some features of the Fredholm Alternative problem .
We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.
A stability version of the reverse isoperimetric inequality, and the corresponding inequality for isotropic measures are established.
We suggest an alternative proof of a theorem due to Lambek and Moser using a perceptible model.
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…
In this expository note we give proof of the Weierstrass gap theorem in Cohomology terminology. We analyze gap sequence for finding possible gaps and non-gaps on X.
We give a q-analogue of Gauss' divisibility theorem
Generalizing recent work on isotropic tensor fields in isotropic and achiral condensed matter systems from two to arbitrary dimensions we address both mathematical aspects assuming perfectly isotropic systems and applications focusing on…
We prove that the Lalescu sequence is monotonically decreasing.
In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.
We prove a second main theorem for elliptic projective planes.
This is a new version of our previous work. In this version, we fill a gap included in the original proof of Theorem 1.1 in our previous paper entitled "An iterative method for Kirchhoff type equations and its applications".
We present an alternative proof of Perron's theorem, which is probabilistic in nature. It rests on the representation of the Perron eigenvector as a functional of the trajectory of an auxiliary Markov chain.
We study \L o\'s's theorem in a choiceless context. We introduce some variants of \L o\'s's theorem. These variants seem weaker than \L o\'s's theorem, but we prove that these are equivalent to \L o\'s's theorem.
We prove a stronger version of a termination theorem appeared in the paper "On existence of log minimal models II". We essentially just get rid of the redundant assumptions so the proof is almost the same as in there. However, we give a…
For the generalized oscillator, we prove a Rellich type theorem, or characterize the order of growth of eigenfunctions. The proofs are given by an extensive use of commutator arguments invented recently by Ito and Skibsted. These arguments…
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.