Related papers: Note on the Chen-Lin result with Li-Zhang method
By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.
By extending the author's prior work to the family case, this paper presents a new proof of the gluing formula for the analytic torsion forms, considerably simplifying the proof given by Puchol-Zhang-Zhu.
In this note, we derive a Leibniz rule for difference quotient.
We give a new proof of Carlitz-Wan's conjecture, previously proved by Lenstra (1995).Our proofs are natural and intuitive, and shed new insights into the study of exceptional polynomials.
We can give a slight improvement for a result related to the distribution of squares in Piatetski-Shapiro sequences of Liu-Shparlinski-Zhang \cite{lsz} by involving three different ideas.
Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.
We derive new matrix representation for higher-order changhee numbers and polynomials. This helps us to obtain simple and short proofs of many previous results on higher-order changhee numbers and polynomials. Moreover, we obtain recurrence…
We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.
We give a stack-theoretic proof for some results on families of hyperelliptic curves.
A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector,…
The purpose of the paper is to present an short proof of the Chuang's inequality.
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
This article describes a new proof of the equality condition for the Brunn-Minkowski inequality.
We propose a proof of the Lagrange Interpolation Formula based on the Chinese Remainder Theorem for arbitrary rings. Even such relationships are known, we think that our viewpoint is worth being published.
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.
We extend the classical Landesman-Lazer results to the setting of second order Hamilton-Jacobi-Bellman equations. A number of new phenomena appear.
In this paper, we give a first negative answer to a question proposed by Li and Lin (Arch Ration Mech Anal 203(3): 943-968, 2012). Meanwhile we also give a second positive answer to the Li-Lin's open problem. The first positive answer was…
We give a new proof of the Mordell-Lang conjecture in positive characteristic for finitely generated subgroups. We also make some progress towards the full Mordell-Lang conjecture in positive characteristic.
We use the Taylor-Wiles-Kisin patching method to prove some new cases of the Breuil-Schneider conjecture.