Some inequalities related to two expansions of ( 1 + 1 / x ) x $(1+1/x)^{x}$

Ren, Bijun; Xiao, Li

doi:10.1186/s13660-015-0928-5

Cited by 3 publications

(3 citation statements)

References 9 publications

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“…12 + x) k . Then Ren and Li [36] proved that (i) if m ≥ 6 is even, we have S m (x) > σ m (x) for all x > 0 and (ii) if m ≥ 7 is odd, we have S m (x) > σ m (x) for all x > 1. This provides an intuitive explanation for the main result in Mortici and Hu [32].…”

Section: Summary Of Previous Resultsmentioning

confidence: 99%

Approximation formulas for the constant e and an improvement to a Carleman-type inequality

Chen

Paris

2018

Journal of Mathematical Analysis and Applications

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Section: Summary Of Previous Resultsmentioning

confidence: 99%

Approximation formulas for the constant e and an improvement to a Carleman-type inequality

Chen

Paris

2018

Journal of Mathematical Analysis and Applications

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“…Nano-barium sulfate particles have good interfacial bonding with the PVC matrix after the grafting modification. 12–16…”

Section: Characterizationmentioning

confidence: 99%

A study on the modification of nano-barium sulfate using a grafting method

Liu,

Li,

2023

Journal of Chemical Research

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In this paper, the wet modification method is compared with the grafting method to modify nano-barium sulfate. The effects of the modification method, the modification time, the modifier dosage, the modification temperature, and other factors on the degree of activation of modified nano-barium sulfate are investigated to solve the nano-barium sulfate agglomeration problems and to make it a suitable process for industrial production. Thermogravimetric analysis, infrared spectroscopy, and scanning electron microscopy are used to characterize the morphology and encapsulation of modified nano-barium sulfate. The grafting method is used to modify nano-barium sulfate with a modification time of 120 min, a modifier dosage of 27%, and a modification temperature of 80 °C. From the experimental results, a hydrophobic nano-barium sulfate in powder form with 76.86% activation degree and 77.41% oil absorption value is obtained.

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“…Except for the above typical sensing methods, researchers have also developed some other MIPs‐based sensing techniques with diverse novel mechanisms, such as combination with surface‐enhanced Raman scattering (SERS) technology and Surface plasmon resonance (SPR) technology. [ 262 , 263 ] These neoteric sensing techniques enriched the existing MIPs‐based sensing systems and advanced MIPs sensors for wider chemical and biological applications.…”

Section: Biomedical Applicationsmentioning

confidence: 99%

Bio‐Inspired Imprinting Materials for Biomedical Applications

et al. 2022

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Inspired by the recognition mechanism of biological molecules, molecular imprinting techniques (MITs) are imparted with numerous merits like excellent stability, recognition specificity, adsorption properties, and easy synthesis processes, and thus broaden the avenues for convenient fabrication protocol of bio-inspired molecularly imprinted polymers (MIPs) with desirable functions to satisfy the extensive demands of biomedical applications. Herein, the recent research progress made with respect to bio-inspired imprinting materials is discussed in this review. First, the underlying mechanism and basic components of a typical molecular imprinting procedure are briefly explored. Then, emphasis is put on the introduction of diverse MITs and novel bio-inspired imprinting materials. Following these two sections, practical applications of MIPs in the field of biomedical science are focused on. Last but not least, perspectives on the remaining challenges and future development of bio-inspired imprinting materials are presented.

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Some inequalities related to two expansions of ( 1 + 1 / x ) x $(1+1/x)^{x}$

Abstract: We prove the following theorem: Let MSC: 42B25; 42B35

Cited by 3 publications

References 9 publications

Approximation formulas for the constant e and an improvement to a Carleman-type inequality

Approximation formulas for the constant e and an improvement to a Carleman-type inequality

A study on the modification of nano-barium sulfate using a grafting method

Bio‐Inspired Imprinting Materials for Biomedical Applications

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