相关论文: A generalization of Tur\'{a}n's theorem

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 an improved form of an expectation of Polya and discuss several related questions

We prove a new vanishing theorem generalizing that of Le Potier for Schur functors of a vector bundle.

We use Koll\'ar's gluing theory to prove the contraction theorem for generalized pairs. In particular, we show that we can run the MMP for any generalized log canonical pairs.

We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory,…

In this paper we prove a generalization of Montel's theorem for a class of first order elliptic equations with measurable coefficients involving Hodge-Dirac operators. We then apply this result to sequences of solutions of second order…

We start with a bijective proof of Schur's theorem due to Alladi and Gordon and describe how a particular iteration of it leads to some very general theorems on colored partitions. These theorems imply a number of important results,…

We prove a generalized version of Renault's theorem for Cartan subalgebras. We show that the original assumptions of second countability and separability are not needed. This weakens the assumption of topological principality of the…

We give an elementary proof of the group law for elliptic curves using explicit formulas.

We prove a conjecture of S. Gao-J. Kiers-G. Orelowitz-A. Yong which asserts the reducibility of certain generalized Dyck paths. This gives a strengthening, and new proof, for their Width Bound Theorem on the Hilbert basis of the Kostka…

In the present note a generalization of Borel-Cantelli Lemma is proposed.

Originally, Tur\'{a}n's inequality states that if $(P_n(x))_{n\in\mathbb{N}_0}$ is the sequence of Legendre polynomials, then $\Delta_n(x):=P_n^2(x)-P_{n+1}(x)P_{n-1}(x)\geq0$ for all $n\in\mathbb{N}$ and $x\in[-1,1]$. Gasper specified the…

We prove an analytic Bertini theorem, generalizing a previous result of Fujino and Matsumura.

I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.

In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case.

In their study of the Yamabe problem in the presence of isometry group, Hebey and Vaugon announced a conjecture. This conjecture generalizes Aubin's conjecture, which has already been proven and is sufficient to solve the Yamabe problem. In…

We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.

We prove a stronger version of Jarden's Theorem for recurrence of powers of recursive functions

We show that Thompson's $A\times B$-Lemma can be obtained as a consequence of the Brauer pair version of Brauer's Third Main Theorem.

We generalize Rado's extension theorem to complex spaces.