两类多元函数条件极值的判定

对于用拉格朗日乘数法求出多元函数条件极值问题的可疑极值点,利用隐函数存在定理,给出了两类多元函数的条件极值问题的一些适用范围比较广的判定定理,并举例验证该判定定理的有效性.     

罗尔中值定理在高等数学竞赛题中的运用

结合江苏省高等数学竞赛题探讨中值问题中等式的证明,从罗尔中值定理的结构分析、求导法则的熟练使用以及辅助函数构造的对比分析三个角度出发,分析了罗尔中值定理在微分中介值问题证明中的运用.     

点的存在性的证明方法的分析

本文主要讨论了在给定不同的条件下．证明点的存在性的一般分析方法。大体上分成三种情况：1）连续条件,利用连续函数的性质及其定理进行证明：2）可导或者积分,利用费马定理和中值定理证明;3）无连续或者可导条件时,通常需要用实数理论进行分析。     

Social innovation and employment in the digital age: The case of the connect employment shuttles in Spain

The digital revolution has shaped the modern world in unprecedented ways. Moreover, the COVID-19 pandemic has highlighted the value of digital technologies. As the health crisis’ effect rippled through economic, political, and social structures worldwide, it also accelerated the adoption of digital tools to pool expertise, ideas, and capacities for generating solutions to the pandemic’s short- and long-term implications. One of the areas where major challenges have arisen is employment.In the whole panorama of digital social innovation in Spain, we find an experience that can be described as outstanding and that links employment and digitalization. However, despite being highly successful, there is hardly any academic literature on this experience. The Connect Employment Shuttles will be the subject of specific in-depth analysis in this article. This is a socially innovative program that has been developed since 2020 in collaboration with the Santa María la Real Foundation. The Connect Employment Shuttles are an existing model specialization, the Employment Shuttles, but applied in the field of digitalization. In this article, we present the origin of the Employment Shuttles and the differences between them and other labor market integration initiatives, their constituent elements, and the social impact they exert.The research question of our study is whether this innovative mechanism combining employment and digitalization is valid and reliable. The answer is particularly relevant for private and public entities interested in implementing effective measures against unemployment, especially in vulnerable groups. The main contribution of this study is the systematized presentation of the experience of the Connect Employment Shuttles and its results so far, being the major limitation is the scarcity and dispersion of information sources.     

哥德巴赫猜想证明中的误差问题

在前期笔者对哥德巴赫猜想的证明思路的基础上,针对该证明中的误差问题,进一步进行解释并给出更明确的补充证明,使证明更其严密与完善。     

HA—凸函数及其Jsensen不等式

针对凸性及其广义凸性问题,提出了HA—凸函数的概念,给出了HA—凸函数的判定定理及其运算性质,建立了HA—凸函数的Jensen型不等式,列举了HA—凸函数的应用实例.     

儒家思想视域下的图书馆社会包容性解读

图书馆的社会包容理念要求避免身份排斥、人格排斥、设施排斥和制度排斥。中国儒家学说中的“仁”、礼”、“德”、“爱人”等伦理规范与图书馆社会包容理念之间具有内在的契合性。其具体表现有：儒家的“仁政”思想中蕴涵有避免身份排斥的意义,“礼”思想中蕴涵有避免人格排斥的意义,“爱人”思想中蕴涵有避免设施排斥的意义,“德政”思想中蕴涵有避免制度排斥的意义。     

导数极限定理的推广

导数的极限定理是数学分析中较重要的一个定理,既是导数的性质之一,又是求函数导数的工具.将导数极限定理推广到了高阶导数、偏导数、方向导数,从而得到了求高阶导数、偏导数以及方向导数的一个重要工具.     

中国古代数学中的方程问题研究

在河谷文明与早期数学至中世纪近代数学形成之前,代数范畴中的方程问题就已经成为数学重要内容之一了.探寻了中国人在这个漫长时期内各个阶段标志性方程的形式和解法,以及古代人的智慧和数学思想的形成.     

关于质点系功能原理和机械能守恒定律相关问题的讨论

阐述了引入外势能质点系的"功能原理"和机械能守恒定律在一般情况下不成立,而且有悖常识,没有存在的必要;并进一步指出质点系的"功能原理"应改为质点系的机械能定理,质点系的机械能守恒定律是力学中的能量转化与守恒定律,是力学中一条独立定律,而不是"功能原理"的推论.