On a new geometric constant related to the modulus of smoothness of a Banach space

We shall introduce a new geometric constant A(X) of a Banach space X,which is closely related to the modulus of smoothness ρX(τ),and investigate it in relation with the constant A2(X) by Baronti et al.,the von Neumann–Jordan constant CNJ(X) and the James constant J(X).A sequence of recent results on these constants as well as some other geometric constants will be strengthened and improved.     

Notes on von Neumann–Jordan and James Constants for Absolute Norms on {\mathbb{R}^2}

Let ${\|\cdot\|_{\psi}}$ be the absolute norm on ${\mathbb{R}^2}$ corresponding to a convex function ${\psi}$ on [0, 1] and ${C_{\text{NJ}}(\|\cdot\|_{\psi})}$ its von Neumann–Jordan constant. It is known that ${\max \{M_1^2, M_2^2\} \leq C_{\text{NJ}}(\| \cdot \|_{\psi}) \leq M_1^2 M_2^2}$ , where ${M_1 = \max_{0 \leq t \leq 1} \psi(t)/ \psi_2(t)}$ , ${M_2 = \max_{0\leq t \leq 1} \psi_2(t)/ \psi(t)}$ and ${\psi_2}$ is the corresponding function to the ? ₂-norm. In this paper, we shall present a necessary and sufficient condition for the above right side inequality to attain equality. A corollary, which is valid for the complex case, will cover a couple of previous results. Similar results for the James constant will be presented.     

Novel des-fatty acyl-polymyxin B derivatives with Pseudomonas aeruginosa-specific antimicrobial activity

Polymyxin B (PMB) is a cationic cyclic decapeptide antibiotic with a fatty acyl (FA) modification at the α-amino group of Dab1 (Dab: L-α,γ-diaminobutyric acid). In this study, which is part of a series of PMB structure-activity relationship investigations focused on identifying clinically useful peptide antibiotics, we synthesized ten des-FA PMB derivatives whose N-terminal moieties were changed to basic or hydrophilic amino acids. The antimicrobial and lipopolysaccharide (LPS) binding activities of these synthetic analogs were tested. The analogs showed more potent antimicrobial activity against Pseudomonas aeruginosa (P. aeruginosa) compared with the PMB nonapeptide. In particular, [Ser2-Dap3]-PMB(2-10), Guanyl-[Thr2-Dab3]-PMB(2-10), Guanyl-[Dab1-Thr2-Dab3]-PMB(1-10), and N(α,γ)-diguanyl-[Dap3]-PMB(3-10) had antimicrobial activity equivalent to PMB. In LPS binding assays, the displacement curves shifted in a manner proportional to the number of positive charges available to bind to Escherichia coli (E. coli) and P. aeruginosa. Furthermore, peptides with basic side chains were comparable to PMB in binding activity assays against E. coli and P. aeruginosa. The acute toxicities of the peptides were evaluated by intravenously administering the peptides to mice through the tail vein. The toxicities of [Ser2-Dap3]-PMB(2-10), [Dap3]-PMB(3-10), and [Ser3]-PMB(3-10) were lower that of PMB (LD??, 4.8 μmol/kg).     

The effect of pressure on the phase transition behavior of tridecane, pentadecane, and heptadecane: a Fourier transform infrared spectroscopy study

The effect of pressure on the phase transition behavior of tridecane (C(13)), pentadecane (C(15)), and heptadecane (C(17)) has been investigated up to 489, 220, and 387 MPa, respectively, using Fourier transform infrared spectroscopy at 25 °C. The transition between the high pressure ordered (HPO) and high pressure rotator (HPR) phases has been observed in the pressure ranges of 270-220, 106-95, and 152-181 MPa for C(13), C(15), and C(17), respectively, and the transition between the HPR and liquid phases was observed in the pressure ranges of 171-112, 73-47, and 43-70 MPa for C(13), C(15), and C(17), respectively. The P(1)+P(3) band of the methylene rocking mode exhibits factor group splitting caused by intermolecular vibrational coupling. This was observed in both the HPO and HPR phases, while the P(1)+P(3) band did not split in the liquid phase. The separation of the peaks in the P(1)+P(3) band changed discontinuously at the HPO-HPR and HPR-liquid phase transitions, even though the separation is known to change continuously in the transition from the liquid to the high temperature rotator (HTR) phase. In the HPR phase, the ratio of the intensities of the higher and lower frequency components in the P(1)+P(3) doublet is roughly unity independent of pressure, while it is known to be much less than unity in the HTR phase. The separation of the P(1)+P(3) doublet in the HPR phase is found to be larger for longer alkanes. From the intensity ratio, a large proportion of alkane molecules is believed to participate in intermolecular vibrational coupling and possess herringbone-type short-range positional order in the HPR phase. Conversely, in the HTR phase only small proportion of alkane molecules participate in intermolecular vibrational coupling. From the pressure dependence of the separation of the doublet, intermolecular vibrational coupling and herringbone-type short-range positional order is considered to change discontinuously at the HPR-liquid phase transition, while they are reported to change continuously at the HTR-liquid phase transition. The HPR-liquid phase transition is governed by the effect of molecular packing while the HTR-liquid phase transition is predominantly governed by the difference in entropy between the herringbone-type and parallel-type packing.     

A Facile and Practical Procedure for the Synthesis of 8-Hydroxy-4-oxochroman Derivatives

Abstract: Novel 8-hydroxy-4-oxochroman derivatives were prepared from appropriate 4-chromanones via the Baeyer-Villiger oxidation followed by an intramolecular Fries rearrangement.     

Synthesis of phenylalkyl-substituted polyhydroxypiperidines as potent inhibitors for α-l-fucosidase

Synthesis and inhibitory activities against α-l-fucosidase of phenylalkyl-substituted polyhydroxypiperidines have been described. Among the newly synthesized compounds, 2,4,6-trichloro derivative (16q) showed very high inhibitory activity against α-l-fucosidase with IC₅₀ value of 0.005 μM, and K_i values of 0.0011 μM, respectively.     

Synthesis of Dibenzocyclooctadienes by Anodic Oxidation

the use of electrochemical oxidation was applied to the synthesis of dibenzocyclooctadiene lactones related to steganacin skeleton. This reaction, performed with compounds 1 and 2, led to results comparable with the oxidation with RuTFA, TTFA and VOF₃.     

Statistical fluctuation in zeta potential distribution of nanoliposomes measured by on‐chip microcapillary electrophoresis

The zeta potential of nanoliposomes with a diameter below 100 nm has been studied by the combined use of on‐chip microcapillary electrophoresis (μCE) and sensitive fluorescence imaging. Tracking the electrophoretic migration of individual nanoliposomes has enabled the accurate evaluation of the zeta potential distribution of nanoliposomes and the first observation of its abnormal broadening due to a statistical fluctuation phenomenon specific to the “nanoscale world.” The materials used for liposome preparation were phosphocholine as the neutral lipid, phosphatidylserine as the anionic lipid, and cholesterol. The size of the liposomes encapsulating calcein, a fluorescent dye used for imaging convenience, was tailored by extrusion through polycarbonate membrane filters of different pore sizes ranging from 50 to 1000 nm. The on‐chip μCE system comprised a μCE chip, a laser source, an inverted microscope, and an electron‐multiplying charge‐coupled device camera. The electrophoresis experiment using this system revealed that the relative standard deviation of the zeta potential distribution of nanoliposomes is inversely proportional to their diameter and apparently increases below 100 nm. This abnormal broadening of zeta potential distribution of nanoliposomes is explained by prominent discreteness effect of the number of anionic lipid molecules in nanoliposomes.