Isosceles Orthogonal Triples in Linear 2-Normed Spaces

A triple (x, y, z) in a linear 2-normed space (X, ‖.,.‖) is called an isosceles orthogonal triple, denoted |(x, y, z), if |(.,.,.) is said to be homogeneous if |(x, y, z) implies |(ax, y, z) for all real a and it is additive if |(x₁, y, z) and |(x₂, y, z) imply that |(x₁ + x₂, y, z). In addition to developing some basic properties of |(.,.,.), this paper shows that under the assumption of strict convexity, every subspace of X of dimension ≤ 3 contains an isosceles orthogonal triple. Further, if (X, ‖.,.‖) is strictly convex and |(…,.) is either homogeneous or additive, then (X, ‖.,.‖) is a 2-inner product space.     

Viscoelastic properties of single poly(ethylene glycol) molecules.

The viscoelastic properties of single poly(ethylene glycol) (PEG) molecules were measured by analysis of thermally and magnetically driven oscillations of an atomic force microscope (AFM) cantilever/molecule system. The molecular and monomer stiffness and friction of the PEG polymer were derived using a simple harmonic oscillator (SHO) model. Excellent agreement between the values of these two parameters obtained by the two approaches indicates the validity of the SHO model under the experimental regimes and the excellent reproducibility of the techniques. A sharp minimum in the monomeric friction is seen at around 180 pN applied force which we propose is due to a force induced change in the shape of the energy landscape describing the conformational transition of PEG from a helical to a planar state, which in turn affects the timescale of the transition and therefore modifies the measured internal friction. A knowledge of the viscoelastic response of PEG monomers is particularly important since PEG is widely used as a linker molecule for tethering groups of interest to the AFM tip in force spectroscopy experiments, and we show here that care must be exercised because of the force-dependent viscoelastic properties of these linkers.     

Substitution-Inert Metal Complex Mobile Phases in Non-Suppressed Cation Chromatography

Substitution-inert metal complexes, [Co(edda)(H₂O)₂]⁺, (Co(edda)(en)]⁺, [Co(edda)(dmen)]⁺, [Co(en)₂-(gly)]²⁺, [Co(en)₂(acac)]²⁺, and [Co(trien)(gly)]²⁺ in their nitrate salt solutions are used as eluents in nonsuppressed cation chromatography (where edda = ethylenediamine-N,N′-diacetic acid, en = ethylenediamine, dmen = N,N′-dime-thylethylenediamine, gly = glycine, acac = acetylacetone, and trien = triethylenetetraamine). It is found that all the mono- and di-valent charged complexes can be used to separate alkali and alkaline earth metal cations, respectively. The separations for monovalent cations are sometimes comparable to those using ultrapure HNO₃ solutions. However, the divalent Ca²⁺ and Sr²⁺ ions cannot be resolved using the metal complex eluents. On the other hand, a selected, direct non-suppressed IC separation of zinc(II) and cadmium(II) ions is demonstrated for the first time using a substitution-inert metal complex eluent and a conductivity detector. Comparisons of these eluents with those reported previously, i. e. HNO₃ and ethylenediammonium salt solution are made and explanations are proposed to account for the different selectivities observed where possible. The future development of this technique is also briefly discussed.     

Congruence modularity implies the Arguesian identity

It is shown that if is any variety of algebras all of whose congruence lattices are modular, then the congruence lattice of every algebra in satisfies the Arguesian law.     

Nitro-oxidized carboxycellulose nanofibers from moringa plant: effective bioadsorbent for mercury removal

Cellulose - Mercury contamination in drinking water is a worldwide problem due to its severely harming effects on the human body. A nanostructured natural bioadsorbent, carboxycellulose nanofiber...     

Synthesis and Biological Evaluation of Novobiocin Core Analogues as Hsp90 Inhibitors

Development of heat shock protein 90 (Hsp90) C‐terminal inhibitors has emerged as an exciting strategy for the treatment of cancer. Previous efforts have focused on modifications to the natural products novobiocin and coumermycin. Moreover, variations in both the sugar and amide moieties have been extensively studied, whereas replacements for the coumarin core have received less attention. Herein, 24 cores were synthesized with varying distances and angles between the sugar and amide moieties. Compounds that exhibited good anti‐proliferative activity against multiple cancer cell lines and Hsp90 inhibitory activity, were those that placed the sugar and amide moieties between 7.7 and 12.1 Å apart along with angles of 180°.     

The Effect of Auxiliary Nitrogenated Linkers on the Design of New Cadmium-Based Coordination Polymers as Sensors for the Detection of Explosive Materials

Three new cadmium-based coordination polymers, denoted [Cd(hfipbb)(4,4’-bipy)] ( CdPF-1 ), [Cd(hfipbb)(2,2’-bipy)] ( CdPF-2 ), and [Cd(hfipbb)(1,10-phen)] ( CdPF-3 ), have been hydrothermally synthesized by using the well-known V-shaped organic linker 4,4’-(hexafluoroisopropylidene)bis(benzoic acid) (H₂hfipbb), together with different nitrogenated auxiliary linkers. Considering the d¹⁰ configuration of the transition metal selected, the luminescent properties for these CdPF-n materials were explored, finding that materials CdPF-2 and CdPF-3 act as excellent sensors in the detection of explosive nitro aromatic compounds. The photoluminescence properties of CdPF-2 and CdPF-3 revealed that significant and sensitive fluorescence quenching was observed toward NP (nitrophenol) for CdPF-2 and PA (picric acid) for CdPF-3 in MeOH suspensions.     

Window on Washington

Abstract

Causality: Models, Reasoning, and Inference by Judea Pearl, Cambridge, U.K.: Cambridge University Press, 2000. Reviewed by Roderick P. McDonald