数学类通识教育课程的"金课"建设是大学数学课程教学改革中的重要课题.在新文科建设背景下,地方财经院校的数学类通识教育课程的建设,在传授数学知识与技能之外,对人文精神和思维能力的培养也提出了更高要求.本研究针对当前教学范式过于专业化的问题,提出在数学类通识教育课程中结合数学学科特点和育人定位,潜移默化地将思政元素和美育元素融入该课程教学中,使学生从专业知识学习走向思维能力构建,实现科学精神与人文素养的融会贯通.

提升人才培养质量是高等学校的核心工作.院系作为基层教学单位,具体落实立德树人根本任务,处在高校教学、科研和学生管理工作一线,其工作成效直接影响人才培养的质量.基于院系视角和多年的教学科研管理工作实践,从学科专业、课程教材、师资队伍、基层教学组织建设、教研和学生管理等方面统筹开展高校人才培养提质创新研究,寻找有效的高校人才培养提质创新途径,以期为高校提高人才培养质量和开展教育教学管理改革提供参考.

本文研究素变数方程a1p21+a2p22+a3p23+a4p34+a5p35+ a6p36=b的可解性,其中a1,a2,…,a6是非零整数,b是整数.本文利用圆法证明了,当a1,a2,…,a6和b满足给定条件时,(i)如果a1,a2,…,a6都是正数,那么当b≥max{｜aj｜}33+ε时方程有素数解;(ii)如果a1,a2,…,a6不都是正数,那么方程的素数解满足max{p21,p22,p23,p34,p35,p36｝《|b｜+max{｜aj｜}32+ε.

Let λf (n) be the n-th Fourier coefficient of a holomorphic Hecke eigenform f of weight k for the full modular group F,∧(n) is the Mangoldt function.In this paper,we proved the following result:∑x＜n＜≤2x∧(n)λf(n)e(√nα)(<<)f,α X5/6 (log X)13/2,(α＞0),which improved Zhao's result.

In order to improve the thermal conductivity of paraffin which is regarded as cool storage of phase change material,six kinds of paraffin-carbon nanotubes composite phase change materials are prepared by adding different mass fractions of carbon nanotube into paraffin (0％,1％,2％,3％,4％ and 5％),and their thermo-physical properties and stability are tested.The results show that,with the increasing of carbon nanotubes,the phase transition temperature of composite phase change materials remains the same,phase change latent heat dwindles and thermal conductivity gradually increases.Compared with the pure paraffin,when the mass fraction of carbon nanotube is 5％,the melting and solidifying of phase change latent heat of composite phase change materials are 128.2 J/g and 134.4 J/g which reduce by 15.5％ and 13.8％,respectively;the thermal conductivity of the solid and liquid are 0.487 W/(m.K) and 0.516 W/(m.K) which increase 39.5％ and 40.3％,respectively;Furthermore,it has good cycling stability.

研究了敞开式冷藏陈列柜底板长度对柜内食品包温度的影响.结果表明:添加挡风板使下侧食品包温度减小0.16 ～0.65K;随着底板长度的增加,搁架内外侧食品包平均温差逐渐减小;底板长度每增加100mm,底板最外侧食品包温度升高约0.35K;底板长度增加0～ 200mm,可以有效地减少风幕冷量的外溢.

考虑了一个混合幂次为2,3,4,5的素变量非线性型的整数部分表示无穷多素数的问题.运用Davenport-Heilbronn方法证明了:如果λ1,λ2,λ3,λ4是正实数,至少有一个λi/λj(1≤i＜j≤4)是无理数,那么存在无穷多素数p1,p2,p3,p4,p,使得[λ1p21+λ2p32+λ3p43+λ4p54]=p.

证明了整系数素变数方程a1p1+a2p22+a3p23+a4p24=b当整数a1,…,a4,b满足一定条件时有素数解,并给出了此方程有素数解时小素数解的上界.

In order to improve the performance of refrigerated display cabinet, decrease the food temperature and restrain the temperature fluctuation during defrosting, a kind of composite shelf is proposed in the food refrigerated display cabinet (RDC) based on the high-thermal conductivity of heat pipe and cool storage of phase change materials. The influence of three phase change materials of RT3, RT4, RT5 on the temperature of food packages, the characteristic of heat transfer and cool storage of composite shelf were investigated. Compared with the ordinary shelf, the food temperature on composite shelf of RT3 reduces by 13.7%-80%, temperature fluctuation decreases 53.3%-70%; the food temperature on composite shelf of RT4 reduces by 20%-83.3%, temperature fluctuation decreases 83.3%-87.5%; the food temperature fluctuation on composite shelf of RT5 decreases 66.7%-75%. Compared with the other two composite shelves, the average food temperature of each floor and each row on composite shelf of RT4 is the lowest and within 5℃, thus the cool storage performance of phase change material of RT4 is the best.

The physical models from the supermarket scale,open vertical refrigerated display cabinet to the shelf scale were built based on the system multiscale method,and the fluid flow and heat transfer character of three different scales were analyzed. The computational results showed the temperature and velocity fields had very good agreement among three scales. The average deviations of temperature and air velocity for the second shelf were 1. 31 ℃ and 0. 2 m/ s,respectively. The multiscale method of the proposed system could correctly predict the temperature and velocity distribution from the supermarket space to inside of refrigerated display cabinet.

设计一种填充相变材料的热管型搁架改善冷藏陈列柜中温度分布的均匀性.实验表明:该类型的搁架降低了食品中心温度,减少了搁架前后排食品温差,改善了沿柜深及柜长方向温度分布均匀性;由于相变材料的蓄冷特性,也减少了融霜期间食品温度的回升.与未填充相变材料的搁架相比,食品包温度由3.5℃～5.5℃降低到0.5℃～5℃,温度降低10％以上.食品包温度波动约0.5℃～0.7℃,温度波动减小70％～ 75％.和文献中水和硼砂复合搁架左右侧食品包温差相比,该设计的搁架左右侧食品包温差比文献的温差降低了83.3％.

为了降低冷藏陈列柜在融霜过程中食品温度的上升和改善柜内温度场分布,设计了带有相变蓄冷材料的热管型搁架,研究其传热性能.结果发现:热管改善了蓄冷搁架前后方向的传热性能,但左右两侧温度分布不均匀.针对此问题提出了在蓄冷搁架内添加肋片进行强化传热,研究结果表明:在蓄冷搁架中添加肋片可以使搁架温度场均匀性得到改善,显著提高蓄冷搁架的蓄冷速率.

令n=e0+e12+…+ek2k,其中ej=0,1 (j=0,…,k)表示自然数n的二进制展开式, N0表示二进制展开式中项数为偶数的自然数的集合.分别给出了这个特殊集上素变数方程P1+P2+pk3=N和P1 +P22 +p23+p24+N解的个数的渐近公式.

假设λ1,λ2,λ3,λ4是正实数,λi/λj(1≤i＜j≤4)至少有一个是无理数.那么,对于正整数x1,x2,x3,x4,λ1x21+λ2x32+λ3x43+λ4x44的整数部分可表示无穷多素数.这个证明极大改进了以前的结果.

Using Davenport-Heilbronn method,this paper proved that under certain conditions the inequality |λ1 p1+λ2 p2+λ3 pk3+η|<ε has infinitely many primes solutions p1,p2,p3.And there exist infinitely many primes p and pairs of primes p1,p2 such that [λp1+μpk2]=mp.In particular,[λp1+μpk2] represents infinitely many primes.

运用Davenport-Heilbronn方法证明了:如果μ1,…,μr是不全为负的非零实数,至少一个μj(1≤j≤r)是无理数,k,m,r是正整数,k≥4,r≥2k-1 +1,则存在无穷多素数pi,…,pr,p,使得[μ1pk1+…+μrpkr]=mp.特别地,[μ1pk1+…+μrpkr]可表示无穷多素数.

In this note, using the Davenport-Heilbronn circle method, we proved that under certain conditions the integer parts of λ1x13+λ2x23+λ3x33+λ4x44+λ5x54+λ6x64 are prime in nitely often for natural numbers xj. This result deepens Brüdern's conclusion which is under general Riemann Hypothesis and same powers.

It is shown that ifλ,μ,νare non-zero real numbers,at least one of which isnon-negative,A is irrational,and k is a positive integer,then there exist infinite primesP_1,P_2,P_3,P,such that[λp_1~2 +μp_2~2 +υp_3~2]= kp.In particular.[λp_1~2 +μp_2~2 +υp_3~2]represents infinite primes.

证明了:假设λ,μ是不全为负的非零实数,λ是无理数,k是正整数,那么存在无穷多素数p,p1,p2,使得[λp1+μp22]=kp.特别地,[λp1+μp22]表示无穷多素数.

本文首先讨论了PBL教学法的优势、实施PBL教学法的必要性,然后举例说明在数学分析教学中如何应用PBL教学法,最后讨论实施PBL教学法过程中存在的问题及对策.