Noria: A Highly Xe‐Selective Nanoporous Organic Solid

Separation of xenon and krypton is of industrial and environmental concern; the existing technologies use cryogenic distillation. Thus, a cost‐effective, alternative technology for the separation of Xe and Kr and their capture from air is of significant importance. Herein, we report the selective Xe uptake in a crystalline porous organic oligomeric molecule, noria, and its structural analogue, PgC‐noria, under ambient conditions. The selectivity of noria towards Xe arises from its tailored pore size and small cavities, which allows a directed non‐bonding interaction of Xe atoms with a large number of carbon atoms of the noria molecular wheel in a confined space.     

Observation of Slow Relaxation and Single‐Molecule Toroidal Behavior in a Family of Butterfly‐Shaped Ln4 Complexes

A family of five isostructural butterfly complexes with a tetranuclear [Ln₄] core of the general formula [Ln₄(LH)₂(μ₂‐η¹η¹Piv)(η²‐Piv)(μ₃‐OH)₂]?x H₂O?y MeOH?z CHCl₃ ( 1 : Ln=Dy^III, x=2, y=2, z=0; 2 : Ln=Tb^III, x=0, y=0, z=6; 3 : Ln=Er^III, x=2, y=2, z=0; 4 : Ln=Ho^III, x=2, y=2, z=0; 5 : Ln=Yb^III, x=2, y=2, z=0; LH₄=6‐{[bis(2‐hydroxyethyl)amino]methyl}‐N′‐(2‐hydroxy‐3‐methoxybenzylidene)picolinohydrazide; PivH=pivalic acid) was isolated and characterized both structurally and magnetically. Complexes 1 – 5 were probed by direct and alternating current (dc and ac) magnetic susceptibility measurements and, except for 1 , they did not display single‐molecule magnetism (SMM) behavior. The ac magnetic susceptibility measurements show frequency‐dependent out‐of‐phase signals with one relaxation process for complex 1 and the estimated effective energy barrier for the relaxation process was found to be 49 K. We have carried out extensive ab initio (CASSCF+RASSI‐SO+SINGLE_ANISO+POLY_ANISO) calculations on all the five complexes to gain deeper insights into the nature of magnetic anisotropy and the presence and absence of slow relaxation in these complexes. Our calculations yield three different exchange coupling for these Ln₄ complexes and all the extracted J values are found to be weakly ferro/antiferromagentic in nature (J₁=+2.35, J₂=?0.58, and J₃=?0.29 cm^?1 for 1 ; J₁=+0.45, J₂=?0.68, and J₃=?0.29 cm^?1 for 2 ; J₁=+0.03, J₂=?0.98, and J₃=?0.19 cm^?1 for 3 ; J₁=+4.15, J₂=?0.23, and J₃=?0.54 cm^?1 for 4 and J₁=+0.15, J₂=?0.28, and J₃=?1.18 cm^?1 for 5 ). Our calculations reveal the presence of very large mixed toroidal moment in complex 1 and this is essentially due to the specific exchange topology present in this cluster. Our calculations also suggest presence of single‐molecule toroics (SMTs) in complex 2 . For complexes 3 – 5 on the other hand, the transverse anisotropy was computed to be large, leading to the absence of slow relaxation of magnetization. As the magnetic field produced by SMTs decays faster than the normal spin moments, the concept of SMTs can be exploited to build qubits in which less interference and dense packing are possible. Our systematic study on these series of Ln₄ complexes suggest how the ligand design can help to bring forth such SMT characteristics in lanthanide complexes.     

Peptide‐poly(ε‐caprolactone) biohybrids by grafting‐from ring‐opening polymerization: Synthesis,aggregation, and crystalline properties

Well‐defined peptide‐poly(ε‐caprolactone) (Pep‐PCL) biohybrids were successfully synthesized by grafting‐from ring‐opening polymerization (ROP) of ε‐caprolactone (CL) using designed amine‐terminated sequence‐defined peptides as macroinitiators. MALDI‐TOF‐MS and ¹H NMR analyses confirmed the successful attachment of peptide to the PCL chain. The gel permeation chromatography (GPC) measurement showed that the Pep‐PCL biohybrids with controllable molecular weights and low polydispersities (PDI <1.5) were obtained by this approach. The aggregation of Pep‐PCL hybrid molecules in THF solution resulted in the formation of micro/nanospheres as confirmed through FESEM, TEM, and DLS analyses. The circular dichroism study revealed that the secondary structure of peptide moiety was changed in the peptide‐PCL biohybrids. The crystallization and melting behavior of Pep‐PCL hybrids were somewhat changed compared with that of neat PCL of comparable molecular weight as revealed by DSC and XRD measurements. In Pep‐PCL biohybrids, extinction rings were observed in the PCL spherulites, in contrast with the normal spherulite morphology of the neat PCL. There was a substantial decrease (4–5 folds) in the spherulitic growth rate after the incorporation of peptide moiety at the end of PCL chain as measured by polarizing optical microscopy. Pseudomonas lipase catalyzed enzymatic degradation was studied for Pep‐PCL hybrids and neat PCL. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Addendum to “Spatiotemporal evolution in a (2+1) -dimensional chemotaxis model” [Physica A 391 (2012) 107–112]

After our article, Physica A 391 (2012) 107–112, had been published online, T. Hillen told us about a theorem by Osaki, relevant for our numerical simulations.     

Towards a queueing-based framework for in-network function computation

We seek to develop network algorithms for function computation in sensor networks. Specifically, we want dynamic joint aggregation, routing, and scheduling algorithms that have analytically provable performance benefits due to in-network computation as compared to simple data forwarding. To this end, we define a class of functions, the Fully-Multiplexible functions, which includes several functions such as parity, MAX, and kth-order statistics. For such functions we characterize the maximum achievable refresh rate of the network in terms of an underlying graph primitive, the min-mincut. In acyclic wireline networks we show that the maximum refresh rate is achievable by a simple algorithm that is dynamic, distributed, and only dependent on local information. In the case of wireless networks we provide a MaxWeight-like algorithm with dynamic flow-splitting, which is shown to be throughput-optimal.     

Enhanced magnetic anisotropy of nickel nanosheet prepared in Na-4 mica

Nanosheets of nickel with thickness equal to 0.6 nm have been grown within the interlayer spaces of Na-4 mica. The sheets are made up of percolative clusters of nanodisks. Magnetization characteristics indicate a superparamagnetic behavior with a blocking temperature of 428 K. The magnetic anisotropy constant as extracted from the coercivity data has been found to be higher than that of bulk nickel by two orders of magnitude. This is ascribed to a large aspect ratio of the nickel nanophase. The Bloch exponent is also found to be considerably different from that of bulk nickel because of a size effect. The Bloch equation is still found to be valid for the two dimensional structures.     

Structure-Based Design,Synthesis, and Biological Evaluation of Hsp90β-Selective Inhibitors

The 90 kDa heat shock proteins (Hsp90) are molecular chaperones that are responsible for the folding and/or trafficking of ∼400 client proteins, many of which are directly associated with cancer progression. Consequently, inhibition of Hsp90 can exhibit similar activity as combination therapy as multiple signaling nodes can be targeted simultaneously. In fact, seventeen small-molecule inhibitors that bind the Hsp90 N-terminus entered clinical trials for the treatment of cancer, all of which exhibited pan-inhibitory activity against all four Hsp90 isoforms. Unfortunately, most demonstrated undesired effects alongside induction of the pro-survival heat shock response. As a result, isoform-selective inhibitors have been sought to overcome these detriments. Described herein is a structure-based approach to design Hsp90β-selective inhibitors along with preliminary SAR. In the end, compound 5 was shown to manifest ∼370-fold selectivity for Hsp90β versus Hsp90α, and induced the degradation of select Hsp90β-dependent clients. These data support the development of Hsp90β-selective inhibitors as a new paradigm to overcome the detriments associated with pan-inhibition of Hsp90.     

On some aspects of pedagogy in applied mathematics

This paper, after analysing the meaning of ‘applied mathematics’, seeks to explore and set forth some broad outlines of the pedagogical implications of studies in the application of mathematics.