A linear time algorithm for the Koopmans–Beckmann QAP linearization and related problems

An instance of the quadratic assignment problem (QAP) with cost matrix $Q$ is said to be linearizable if there exists an instance of the linear assignment problem (LAP) with cost matrix $C$ such that for each assignment, the QAP and LAP objective function values are identical. The QAP linearization problem can be solved in $O\left(n^4\right)$ time. However, for the special cases of Koopmans–Beckmann QAP and the multiplicative assignment problem the input size is of $\Omega \left(n^2\right)$. We show that the QAP linearization problem for these special cases can be solved in $O\left(n^2\right)$ time. For symmetric Koopmans–Beckmann QAP, Bookhold [I. Bookhold, A contribution to quadratic assignment problems, Optimization 21 (1990) 933–943.] gave a sufficient condition for linearizability and raised the question if the condition is necessary. We show that Bookhold’s condition is also necessary for linearizability of symmetric Koopmans–Beckmann QAP.     

New insights into silica-based NMR "chromatography"

Silica is used as an important component for NMR “chromatography”. In this study the effect of the binding strength to silica of a variety of compounds on their diffusion rate is measured for the first time. Over two orders of magnitude of diffusion difference enhancement was obtained in the presence of silica for some compounds. An explanation of the enhancement is given that also allows one to predict the “chromatographic” behavior of new compounds or mixtures. The binding strength is divided into categories of weakly bound, singly bound and multiply bound. Carboxylates, sulfonates, and diols are found to be particularly strongly bound and to diffuse up to 2½ orders of magnitude more slowly in the presence of silica.     

Cytotoxicity and fluorescence studies of silica-coated CdSe quantum dots for bioimaging applications

The toxicological effects of silica-coated CdSe quantum dots (QDs) were investigated systematically on human cervical cancer cell line. Trioctylphosphine oxide capped CdSe QDs were synthesized and rendered water soluble by overcoating with silica, using aminopropyl silane as silica precursor. The cytotoxicity studies were conducted by exposing cells to freshly synthesized QDs as a function of time (0–72 h) and concentration up to micromolar level by Lactate dehydrogenase assay, MTT [3-(4,5-Dimethylthiazol-2-yl)-2,5-Diphenyltetrazolium Bromide] assay, Neutral red cell viability assay, Trypan blue dye exclusion method and morphological examination of cells using phase contrast microscope. The in vitro analysis results showed that the silica-coated CdSe QDs were nontoxic even at higher loadings. Subsequently the in vivo fluorescence was also demonstrated by intravenous administration of the QDs in Swiss albino mice. The fluorescence images in the cryosections of tissues depicted strong luminescence property of silica-coated QDs under biological conditions. These results confirmed the role of these luminescent materials in biological labeling and imaging applications.     

A characterization of bounded symmetric domains of type IV

Let ?? be a bounded symmetric domain of type IV and dimension bigger than four. We show that a Stein manifold of the same dimension as ?? and with the same automorphism group is biholomorphic to ??.     

Hydrogen-Bonded Crystalline Molecular Machines with Ultrafast Rotation and Displacive Phase Transitions

Two new crystalline rotors 1 and 2 assembled through N−H⋅⋅⋅N hydrogen bonds by using halogenated carbazole as stators and 1,4-diaza[2.2.2]bicyclooctane (DABCO) as the rotator, are described. The dynamic characterization through ¹H T₁ relaxometry experiments indicate very low rotational activation barriers (E_a) of 0.67 kcal mol⁻¹ for 1 and 0.26 kcal mol⁻¹ for 2 , indicating that DABCO can reach a THz frequency at room temperature in the latter. These E_a values are supported by solid-state density functional theory computations. Interestingly, both supramolecular rotors show a phase transition between 298 and 250 K, revealed by differential scanning calorimetry and single-crystal X-ray diffraction. The subtle changes in the crystalline environment of these rotors that can alter the motion of an almost barrierless DABCO are discussed here.     

A nondestructive and noninvasive method to determine water content in lyophilized proteins using low-field time-domain NMR

Determining the moisture content in lyophilized solids is a fundamental step towards predicting the quality and stability of lyophilized products, but conventional methods are time-consuming, invasive, and destructive. High levels of residual moisture in a lyophilized product can lead to cake collapse, product degradation, and reduced shelf life. The aim of this study was to develop a fast, noninvasive, nondestructive, and inexpensive method for determining the moisture content in a lyophilized monoclonal antibody (mAb) formulation using benchtop low-field time-domain nuclear magnetic resonance spectroscopy.     

Bose–Einstein condensation transition studies for atoms confined in Laguerre–Gaussian laser modes

Multiply-connected traps for cold, neutral atoms fix vortex cores of quantum gases. Laguerre–Gaussian laser modes are ideal for such traps due to their phase stability. We report theoretical calculations of the Bose–Einstein condensation transition properties and thermal characteristics of neutral atoms trapped in multiply connected geometries formed by Laguerre–Gaussian (LG_p^l) beams. Specifically, we consider atoms confined to the anti-node of a LG₀¹ laser mode detuned to the red of an atomic resonance frequency, and those confined in the node of a blue-detuned LG₁¹ beam. We compare the results of using the full potential to those approximating the potential minimum with a simple harmonic oscillator potential. We find that deviations between calculations of the full potential and the simple harmonic oscillator can be up to 3%–8% for trap parameters consistent with typical experiments.     

DP-3-coloring of some planar graphs

In this article, we use a unified approach to prove several classes of planar graphs are DP-3-colorable, which extend the corresponding results on 3-choosability.     

Paclitaxel loaded poly (DL lactic acid co castor oil) 60:40 with poloxamer‐F68 rod shape cylindrical nanoparticle preparation and in vitro cytotoxicity studies

This research presents a thin‐film hydration‐solvent evaporation method to formulate the paclitaxel loaded poly (DL lactic acid co castor oil) 4:6 with poloxamer‐F68 cylindrical shape nanoparticles. The particles were less than 250 nanometers (nm) in size, with an average width of 60 nm and an average length of 100 nm. The percent yield, encapsulation efficiency (EE), and percent drug loading (DL) were detected. This approach produces drug loading values between 5% and 20% w/w. X‐ray powder diffraction (XRD) identified the physicochemical properties of nanoparticles differential scanning calorimetry (DSC) and Fourier‐transform infrared spectroscopy (FTIR). The investigation shows that the drug is molecularly dispersed in polymers or given in an amorphous or semicrystalline state. Horizontal water bath shaker technology considered the in vitro release of PTX loaded nanoparticles under sink conditions. Poly (DL lactic acid co castor oil) 4:6 nanoparticles exhibited a sustained release analysis. At the end of 30 hours, the percent cumulative drug release from the formulations was between 74.52% and 92.87% for F1 and F4. In vitro cytotoxicity assays indicate that PTX having p (DLLA:CO60:40) nanoparticles have a higher cytotoxic effect on MCF‐7/ADR.