A new upper bound of geometric constant D ( X ) $D(X)$

Abstract

A new constant is introduced into any real -dimensional symmetric normed space X. By virtue of this constant, an upper bound of the geometric constant , which is used to measure the difference between Birkhoff orthogonality and isosceles orthogonality, is obtained and further extended to an arbitrary m-dimensional symmetric normed linear space (). As an application, the result is used to prove a special case for the reverse Hölder inequality.

α‐Aminoxy Peptoids: A Unique Peptoid Backbone with a Preference for cis‐Amide Bonds

“…[26] However,w e and others showed that the secondary structure in a-aminoxy peptidesi sp rimarily stabilized by eight-membered ring hydrogen bonds between the C=O i and the NÀH i+ +2 moieties, which are not possible in the case of a-aminoxy peptoids. [19,20,26] Thus, in order to furtheri nvestigatet he cis-amide preference in a-aminoxy peptoids, we performed an atural bond orbital (NBO) analysiso na ll-methyl model a-aminoxy peptoidsi ncisand trans-amide configurations ( Figures 4A and B) as well as the cis-amide a-aminoxy tripeptoid 9 ( Figure 4C).…”

“…In 2002, Shin and Park reported the preparation of a-aminoxy peptoid pentamers,b ut the folding properties were not investigated. [18] The backbone-controlled secondary structures of a-aminoxy peptides [19,20] prompted us to analyze the conformational properties of a-aminoxy peptoids (or oxa-analogues of b-peptoids) in detail.I nt his work, we report the results of our study revealing au nique cis-amide bond preference of a-aminoxy peptoids in comparison to other peptoid backbones.…”

Advances in ginsenoside biosynthesis and metabolic regulation

“…Besides, our laboratory used JA and methyl dihydrojasmonate (MDJ) as elicitors, and the highest total content of saponins (71.94 mg/g) was achieved after treatment with 5 mg/L JA, which was 2.09-fold higher than native roots and 8.45-fold higher than the control group. Furthermore, we found that JA and MDJ significantly upregulated the expression of the GPS, FPS, SS, SE, DS, CYP716A47, and CYP716A53v2 [37].…”

Improved Capacity Retention of Metal Oxide Anodes in Li‐Ion Batteries: Increasing Intraparticle Electronic Conductivity through Na Inclusion in Mn3O4

“…In order to increase the capacity and reversibility of MnO, Mn 3 O 4 and MnO 2 , different strategies have been tried. Complex nanostructures have been synthetized that aim to decrease the metal oxide volumetric expansion during cycling and minimize the Li ion diffusion length, such as nanorods, [9] nanoflakes, [10] hollow spheres, [11] microspheres, [12] nanowires, [13] nanosheets. [14] Another popular strategy is to create manganese oxide/carbon composites, [15,16] mainly utilizing a very highly conductive matrix such as reduced graphene oxide [17,18] or carbon nanotubes, [19,20] which both contribute to increase the interparticle electronic conductivity of the anode electrode and act as a buffer for the volumetric expansion experienced during cycling.…”