A renorming in some Banach spaces with applications to fixed point theory

We consider a Banach space X endowed with a linear topology τ and a family of seminorms {Rk(⋅)} which satisfy some special conditions. We define an equivalent norm ?⋅? on X such that if C is a convex bounded closed subset of (X,?⋅?) which is τ-relatively sequentially compact, then every nonexpansive mapping T:C→C has a fixed point. As a consequence, we prove that, if G is a separable compact group, its Fourier-Stieltjes algebra B(G) can be renormed to satisfy the FPP. In case that G=T, we recover P.K. Lin's renorming in the sequence space ?₁. Moreover, we give new norms in ?₁ with the FPP, we find new classes of nonreflexive Banach spaces with the FPP and we give a sufficient condition so that a nonreflexive subspace of L₁(μ) can be renormed to have the FPP.     

B-allenyl- and B-(gamma-trimethylsilylpropargyl)-10-phenyl-9-borabicyclo[3.3.2]decanes: asymmetric synthesis of propargyl and alpha-allenyl 3-degree-carbinols from ketones

Simple and efficient Grignard procedures are reported for the syntheses of B-allenyl-10-(phenyl)-9-borabicyclo[3.3.2]decane (1) and its B-(gamma-trimethylsilylpropargyl) counterpart (2) in both enantiomeric forms. Both add selectively to ketones, providing propargyl- and alpha-silylallenyl 3-degree-carbinols, respectively (i.e., 6 (61-93% ee) and 9 (64-98% ee)). The air-stable boron byproduct is efficiently recovered and recycled back to either 1 or 2. The ozonolysis and bromination of 9 provide nonracemic alpha-hydroxy acids and gamma-bromopropynyl carbinols, respectively.     

Tuning the In Vivo Transport of Anticancer Drugs Using Renal‐Clearable Gold Nanoparticles

Precise control of in vivo transport of anticancer drugs in normal and cancerous tissues with engineered nanoparticles is key to the future success of cancer nanomedicines in clinics. This requires a fundamental understanding of how engineered nanoparticles impact the targeting‐clearance and permeation‐retention paradoxes in the anticancer‐drug delivery. Herein, we systematically investigated how renal‐clearable gold nanoparticles (AuNPs) affect the permeation, distribution, and retention of the anticancer drug doxorubicin in both cancerous and normal tissues. Renal‐clearable AuNPs retain the advantages of the free drug, including rapid tumor targeting and high tumor vascular permeability. The renal‐clearable AuNPs also accelerated body clearance of off‐target drug via renal elimination. These results clearly indicate that diverse in vivo transport behaviors of engineered nanoparticles can be used to reconcile long‐standing paradoxes in the anticancer drug delivery.     

Direct Visualization of Live Zebrafish Glycans via Single‐Step Metabolic Labeling with Fluorophore‐Tagged Nucleotide Sugars

Dynamic turnover of cell‐surface glycans is involved in a myriad of biological events, making this process an attractive target for in vivo molecular imaging. Metabolic glycan labeling coupled with bioorthogonal chemistry has paved the way for visualizing glycans in living organisms. However, a two‐step labeling sequence is required, which suffers from the tissue‐penetration difficulties of the imaging probes. Here, by exploring the substrate promiscuity of endogenous glycosyltransferases, we developed a single‐step fluorescent glycan labeling strategy by using fluorophore‐tagged analogues of the nucleotide sugars. Injecting fluorophore‐tagged sialic acid and fucose into the yolk of zebrafish embryos at the one‐cell stage enables systematic imaging of sialylation and fucosylation in live zebrafish embryos at distinct developmental stages. From these studies, we obtained insights into the role of sialylated and fucosylated glycans in zebrafish hematopoiesis.     

Zero‐valent Iron Nanoparticles Modified Screen‐printed Electrode for FIA or HPLC Amperometric Detection of Metronidazole in Pharmaceutical Formulations

A zero‐valent iron nanoparticles modified electrode was employed as an amperometric detector in flow conditions to determine metronidazole and 2‐methyl‐5‐nitroimidazole in pharmaceutical formulations. Flow injection analysis at ?0.6 V (vs. Ag) achieved limits of detection of 2 and 6 μM for metronidazole and 2‐methyl‐5‐nitroimidazole, respectively, but the analysis was not discriminative between the two compounds. When reverse phase high performance liquid chromatography was applied previous to the electrochemical detection both analytes could be analysed simultaneously. However, the limits of detection slightly increased (10 μM) as a consequence of the use of an organic solvent and a lower sample volume. The relative standard deviation of analytical repeatability was <4.0 % in both techniques. The methods were validated by comparing the results obtained from the analysis of commercial samples with those provided by HPLC‐DAD and no significant differences were detected. Results probed that the modified electrode was a successful tool in the FIA and HPLC analysis of nitro compounds.     

Evaluation of the Performance of a Mediatorless Microbial Fuel Cell by Electrochemical Impedance Spectroscopy

A mediatorless microbial fuel cell was developed using Escherichia coli bacteria and platinised titanium mesh as electrodes, producing a maximum power density of 627 mW m^?2. The performance characteristics of the fuel cell were evaluated using both electrochemical and optical techniques. Cyclic Voltammetry showed that an anaerobically grown cell suspension of E. coli was electrochemically active, and is consistent with a role for E. coli‐secreted mediators in the functioning of the cell, after the formation of a biofilm on the surface of the electrode. Electrochemical impedance spectroscopy (EIS) data show a variation in the internal resistance during bacterial growth. EIS analysis based on an equivalent circuit revealed that the initial internal resistance of the cell (5.6 MΩ) initially reduces by around 50 % over an 8 hour period; more or less the same time where the fuel cell reaches its maximum potential of 860 mV, whereupon the resistance begins to increase resulting in the corresponding fall in potential; this trend was reversible upon the introduction of further nutrients into the cell.     

Optical properties of LiNbO3:Cr crystals co-doped with germanium oxide

Lithium niobate (LiNbO₃) crystals doped with chromium ions show a clear green colouring reflecting the absorption profile of the dominating [Cr]_Li defect centres. A significant change in its colouration takes place when it is co-doped with other valency impurities such as Mg²⁺, Sc³⁺ and W⁶⁺, above a certain threshold concentration. This concentration singularity has been attributed to the formation of [Cr]_Nb centres coexisting with the [Cr]_Li centres.In this work, we extended the investigation on the effect of co-dopant ions in Cr:LiNbO₃ to tetravalent cation such as GeO₂. A singularity in the relative intensity of the ⁴A₂→⁴T₁ and ⁴A₂→⁴T₂ absorption band was observed for a concentration of ～1.5 mol%, compared with 4.5 mol% for Mg²⁺. The photoluminescence emission spectra also reveal a new emission band, at a lower energy than the [Cr]_Li centre, corresponding to this threshold concentration. A charge compensation model is proposed to explain the role of cation impurities and results are compared with those of other valence impurities.     

Non-Commutative Harmonic and Subharmonic Polynomials

The paper introduces a notion of the Laplace operator of a polynomial p in noncommutative variables x = (x ₁,…, x _g ). The Laplacian Lap[p, h] of p is a polynomial in x and in a noncommuting variable h. When all variables commute we have Lap[p, h] = h ²Δ _x p where Δ _x p is the usual Laplacian. A symmetric polynomial in symmetric variables will be called harmonic if Lap[p, h] = 0 and subharmonic if the polynomial q(x, h) :=  Lap[p, h] takes positive semidefinite matrix values whenever matrices X ₁,…, X _g , H are substituted for the variables x ₁,…, x _g , h. In this paper we classify all homogeneous symmetric harmonic and subharmonic polynomials in two symmetric variables. We find there are not many of them: for example, the span of all such subharmonics of any degree higher than 4 has dimension 2 (if odd degree) and 3 (if even degree). Hopefully, the approach here will suggest ways of defining and analyzing other partial differential equations and inequalities. Dedicated to Israel Gohberg on the occasion of his 80^th birthday. All authors were partially supported by J.W. Helton’s grants from the NSF and the Ford Motor Co. and J. A. Hernandez was supported by a McNair Fellowship.     

Vibrational analysis of amino acids and short peptides in hydrated media. 3. Successive KL repeats induce highly stable beta-strands capable of forming non-H-bonded aggregates

Circular dichroism (CD) and Raman scattering were applied to the aqueous solution of minimalist LK peptides constructed with successive KL repeats leading to the following generic primary sequence: (KL)nK. Three peptides of this family, a 3-mer (n=1), a 9-mer (n=4), and a 15-mer (n=7), are analyzed in this report. Raman spectra of the 3-mer (KLK, a random chain) and its labile-hydrogen deuterated species yield a set of interesting information for analyzing longer peptides of this series. Although the CD spectrum of the 9-mer (KLKLKLKLK) reveals a signal traditionally assigned to a random structure, the corresponding Raman spectrum allows finding a mixture of conformations in solution, adopting predominantly beta-type structures. This fact proves the utility of Raman spectroscopy to eliminate eventual ambiguity concerning conformational assignments in peptides based only on the use of CD technique. Finally, the 15-mer (KLKLKLKLKLKLKLK) gives rise to CD and Raman spectra clearly assignable to a beta-type structure. On the basis of all the observed results on the 15-mer, we can confirm that this peptide may exist as isolated beta-strands at low concentration (sub-micromolar), flat-oriented at the air/water interface, whereas at high concentrations (millimolar), non-H-bonded immersible aggregates might be formed. A hypothetical model for these beta-strand aggregates could be proposed as stabilized by an interior hydrophobic core and a hydrophilic external face, formed by leucine and lysine side chains, respectively.     

On the benefits of acquiring peptide fragment ions at high measured mass accuracy

The advantages and disadvantages of acquiring tandem mass spectra by collision-induced dissociation (CID) of peptides in linear ion trap Fourier-transform hybrid instruments are described. These instruments offer the possibility to transfer fragment ions from the linear ion trap to the FT-based analyzer for analysis with both high resolution and high mass accuracy. In addition, performing CID during the transfer of ions from the linear ion trap (LTQ) to the FT analyzer is also possible in instruments containing an additional collision cell (i.e., the "C-trap" in the LTQ-Orbitrap), resulting in tandem mass spectra over the full m/z range and not limited by the ejection q value of the LTQ. Our results show that these scan modes have lower duty cycles than tandem mass spectra acquired in the LTQ with nominal mass resolution, and typically result in fewer peptide identifications during data-dependent analysis of complex samples. However, the higher measured mass accuracy and resolution provides more specificity and hence provides a lower false positive ratio for the same number of true positives during database search of peptide tandem mass spectra. In addition, the search for modified and unexpected peptides is greatly facilitated with this data acquisition mode. It is therefore concluded that acquisition of tandem mass spectral data with high measured mass accuracy and resolution is a competitive alternative to "classical" data acquisition strategies, especially in situations of complex searches from large databases, searches for modified peptides, or for peptides resulting from unspecific cleavages.