School Mathematics Textbooks in China

Abstract

Let µ and ν be two probability measures on R d , where µ(dx) = e −V (x) dx R d e −V (x) dx for some V ∈ C 1 (R d ). Explicit sufficient conditions on V and ν are presented such that µ * ν satisfies the log-Sobolev, Poincaré and super Poincaré inequalities. In particular, if V (x) = λ|x| 2 for some λ > 0 and ν(e λθ|•| 2 ) < ∞ for some θ > 1, then µ * ν satisfies the log-Sobolev inequality. This improves and extends the recent results on the log-Sobolev inequality derived in [20] for convolutions of the Gaussian measure and compactly supported probability measures. On the other hand, it is well known that the log-Sobolev inequality for µ * ν implies ν(e ε|•| 2 ) < ∞ for some ε > 0. RésuméDes conditions explicites suffisantes sur V et ν sont présentées telles que µ * ν satisfait des inégalités de Sobolev logarithmique, de Poincaré et de super-Poincaré. En particulier, si V (x) = λ|x| 2 pour quelque λ > 0 et ν(e λθ|•| 2 ) < ∞ avec θ > 1, alors µ * ν satisfait l'inégalité de Sobolev logarithmique. Cela améliore et étend des résultats récents sur l'inégalité de Sobolev logarithmique obtenus dans [20] pour des convolutions de la mesure de Gauss et des mesures de probabilité à support compact. D'autre part, il est bien connu que l'inégalité de Sobolev logarithmique pour µ * ν implique ν(e ε|•| 2 ) < ∞ pour quelque ε > 0.

An Empirical Study on the Three-Ring Teaching Method

“…In order to support the theoretical research of the three-ring teaching method, the empirical method is used to study the use value of the three-ring teaching method in the subject teaching of vocational colleges, and the influence of the three-ring teaching method on students' learning subjectivity is verified [5].…”

Coaching college students in the development of positive learning dispositions: A randomized control trial embedded mixed‐methods study

“…In this section, we provided a brief review of the essential role that learning dispositions play in college students' learning process. Mindful agency is positively correlated with academic emotion (Q. Wang & Zhang, 2016), learning strategy regulation abilities (Q. Wang & Ar, 2016), and creativity on the dimension of fluency and originality (Q. Wang & Hu, 2016). Mindful agency predicted positively a deep approach to learning through the mediator of need for cognition (Q. Wang & Pan, 2018) and negatively academic procrastination (Q. Wang & Yu, 2016) and test anxiety (Q. Wang & Zhang, 2016).…”

“…Mindful agency is positively correlated with academic emotion (Q. Wang & Zhang, 2016), learning strategy regulation abilities (Q. Wang & Ar, 2016), and creativity on the dimension of fluency and originality (Q. Wang & Hu, 2016). Mindful agency predicted positively a deep approach to learning through the mediator of need for cognition (Q. Wang & Pan, 2018) and negatively academic procrastination (Q. Wang & Yu, 2016) and test anxiety (Q. Wang & Zhang, 2016). A recent intervention study reported that improvement in mindful agency mediates the changes in self‐efficacy, emotional intelligence, and meta‐cognition after coaching (Peng & Wang, 2020).…”

Design of communication protocol and data processing algorithm for wireless laser power counting system

“…Compared with the traditional CRC algorithm, the table look-up method CRC algorithm [6] used in this paper has more efficient calculation efficiency while taking into account the detection ability. Data encryption algorithms are divided into three categories: symmetric encryption, asymmetric encryption and hybrid encryption [7][8][9]. The confidential algorithm TEA used in this paper aims to achieve maximum encryption and decryption speed while occupying the minimum memory [10].…”