Supported by the National Natural Science Foundation of China(Grant No.12371334);the Natural Science Foundation of Jiangsu Province(Grant No.BK20221383)。
Recently,Andrews and Paule established the generating functions for the k-elongated plane partition function d_(k)(n)and proved a large number of results on d_(k)(n)with k=2,3.In particular,they posed some conjectures...
In this paper, we prove Legendre’s conjecture: There is a prime number between n2 and (n +1)2 for every positive integer n. We also prove three related conjectures. The method that we use is to ...
J. S. Bell’s well-known proofs of inequalities (and related work) are shown to be invalidated by two counter-arguments (-examples) that are based on Einstein-local propositions: Bell-type inequalities of Einstein-Pod...
The first proof (Sections 2 - 4), applies Doppler shifts to the Fourier time sine series. It shows if K = f'/f (frequency ratio of the shift, f' the shifted frequency), then the value of the serie...
supported by National Natural Science Foundation of China(Grant No.11801451).supported by National Natural Science Foundation of China(Grant No.11371184);the Natural Science Foundation of Henan Province(Grant Nos.162300410086,2016B259 and 172102410069)。
Applying an addition formula of Liu(2007),we deduce certain Jacobi theta function identities.From these results we confirm several q-trigonometric identities con.jectured by Gosper(2001).Another conjectured identity o...
the National Natural Science Foundation of China under projects 61772150 and 61862012;the Guangxi Key R&D Program under project AB17195025;the Guangxi Natural Science Foundation under grants 2018GXNSFDA281054 and 2018GXNSFAA281232;the National Cryptography Development Fund of China under project MMJJ20170217;the Guangxi Young Teachers’ Basic Ability Improvement Program under Grant 2018KY0194;and the open program of Guangxi Key Laboratory of Cryptography and Information Security under projects GCIS201621 and GCIS201702.
The remote data integrity auditing technology can guarantee the integrity of outsourced data in clouds. Users can periodically run an integrity auditing protocol by interacting with cloud server, to verify the latest ...
Consider the Cauchy problem for the n-dimensional incompressible NavierStokes equations:??tu-α△u+(u·?)u+?p = f(x, t), with the initial condition u(x, 0) = u_0(x) and with the incompressible conditions ? · u = 0, ?...
This work is supported,in part,by the National Natural Science Foundation of China under grant No.61872069;in part,by the Fundamental Research Funds for the Central Universities(N171704005);in part,by the Shenyang Science and Technology Plan Projects(18-013-0-01).
With the development of cloud storage,the problem of efficiently checking and proving data integrity needs more consideration.Therefore,much of growing interest has been pursed in the context of the integrity verifica...
This work discovers and proves that all the photons/quantum particles have a “Nucleus of mass and charge.” The nucleus is located off-center in the particles. The constructive, destructive and intermediate Interfere...
Verifiable computation (VC) paradigm has got the captivation that in real term is highlighted by the concept of third party computation. In more explicate terms, VC allows resource constrained clients/organizations ...