Conditioning of Random Conic Systems Under a General Family of Input Distributions

We consider the conic feasibility problem associated with the linear homogeneous system Ax≤0, x≠0. The complexity of iterative algorithms for solving this problem depends on a condition number C(A). When studying the typical behavior of algorithms under stochastic input, one is therefore naturally led to investigate the fatness of the tails of the distribution of C(A). Introducing the very general class of uniformly absolutely continuous probability models for the random matrix A, we show that the distribution tails of C(A) decrease at algebraic rates, both for the Goffin–Cheung–Cucker number C _G and the Renegar number C _R . The exponent that drives the decay arises naturally in the theory of uniform absolute continuity, which we also develop in this paper. In the case of C _G , we also discuss lower bounds on the tail probabilities and show that there exist absolutely continuous input models for which the tail decay is subalgebraic. R. Hauser was supported by a grant of the Nuffield Foundation under the “Newly Appointed Lecturers” grant scheme (project number NAL/00720/G) and through grant GR/S34472 from the Engineering and Physical Sciences Research Council of the UK. The research in this paper was conducted while T. Müller was a research student at the University of Oxford. He was partially supported by EPSRC, the Oxford University Department of Statistics, Bekker-la-Bastide fonds, Dr. Hendrik Muller’s Vaderlandsch fonds, and Prins Bernhard Cultuurfonds.     

Silicon-containing polyphilic bent-core molecules: the importance of nanosegregation for the development of chirality and polar order in liquid crystalline phases formed by achiral molecules

Polyphilic molecules composed of a bent aromatic core, oligo(siloxane) units, and alkyl segments were synthesized, and the self-organization of these molecules was investigated. Most materials organize into polar smectic liquid crystalline phases. The switching process of these mesophases changes from antiferroelectric for the nonsilylated compounds via superparaelectric to surface-stabilized ferroelectric with increasing segregation of the silylated segments. It is proposed that the siloxane sublayers stabilize a polar synclinic ferroelectric (SmC(s)P(F)) structure, and the escape from a macroscopic polar order as well as steric effects leads to a deformation of the layers with formation of disordered microdomains, giving rise to optical isotropy. Another striking feature is the spontaneous formation of chiral domains with opposite handedness. For two compounds, a temperature-dependent inversion of the optical rotation of these domains was found, and this is associated with an increase of the tilt angle of the molecules from < 45 degrees to > 50 degrees. This observation confirms the recently proposed concept of layer optical chirality (Hough, L. E.; Clark, N. A. Phys. Rev. Lett. 2005, 95, 107802), which is a new source of optical activity in supramolecular systems. With increasing length of the alkyl chains, segregation is lost and a transition from smectic to a columnar phase is found. In the columnar phase, the switching process is antiferroelectric and takes place by rotation of the molecules around the long axes, which reverses the layer chirality; that is, the racemic ground-state structure is switched into a homogeneous chiral structure upon application of an electric field.     

Determination of tobramycin in human serum by capillary electrophoresis with contactless conductivity detection

A study on the determination of the antibiotic tobramycin by CE with capacitively coupled contactless conductivity detection is presented. This method enabled the direct quantification of the non-UV-absorbing species without incurring the disadvantages of the indirect approaches which would be needed for optical detection. The separation of tobramycin from inorganic cations present in serum samples was achieved by optimizing the composition of the acetic acid buffer. Field-amplified sample stacking was employed to enhance the sensitivity of the method and a detection limit of 50 microg/L (S/N = 3) was reached. The RSDs obtained for migration time and peak area using kanamycin B as internal standard were typically 0.12 and 4%, respectively. The newly developed method was validated by measuring the concentration of tobramycin in serum standards containing typical therapeutic concentrations of 2 and 10 mg/L. The recoveries were 96 and 97% for the two concentrations, respectively.     

Heteroleptic FeII Complexes of 2,2′‐Biimidazole and Its Alkylated Derivatives: Spin‐Crossover and Photomagnetic Behavior

Three iron(II) complexes, [Fe(TPMA)(BIM)](ClO₄)₂?0.5H₂O ( 1 ), [Fe(TPMA)(XBIM)](ClO₄)₂ ( 2 ), and [Fe(TPMA)(XBBIM)](ClO₄)₂ ?0.75CH₃OH ( 3 ), were prepared by reactions of Fe^II perchlorate and the corresponding ligands (TPMA=tris(2‐pyridylmethyl)amine, BIM=2,2′‐biimidazole, XBIM=1,1′‐(α,α′‐o‐xylyl)‐2,2′‐biimidazole, XBBIM=1,1′‐(α,α′‐o‐xylyl)‐2,2′‐bibenzimidazole). The compounds were investigated by a combination of X‐ray crystallography, magnetic and photomagnetic measurements, and Mössbauer and optical absorption spectroscopy. Complex 1 exhibits a gradual spin crossover (SCO) with T_1/2=190 K, whereas 2 exhibits an abrupt SCO with approximately 7 K thermal hysteresis (T_1/2=196 K on cooling and 203 K on heating). Complex 3 is in the high‐spin state in the 2–300 K range. The difference in the magnetic behavior was traced to differences between the inter‐ and intramolecular interactions in 1 and 2 . The crystal packing of 2 features a hierarchy of intermolecular interactions that result in increased cooperativity and abruptness of the spin transition. In 3 , steric repulsion between H atoms of one of the pyridyl substituents of TPMA and one of the benzene rings of XBBIM results in a strong distortion of the Fe^II coordination environment, which stabilizes the high‐spin state of the complex. Both 1 and 2 exhibit a photoinduced low‐spin to high‐spin transition (LIESST effect) at 5 K. The difference in the character of intermolecular interactions of 1 and 2 also manifests in the kinetics of the decay of the photoinduced high‐spin state. For 1 , the decay rate constant follows the single‐exponential law, whereas for 2 it is a stretched exponential, reflecting the hierarchical nature of intermolecular contacts. The structural parameters of the photoinduced high‐spin state at 50 K are similar to those determined for the high‐spin state at 295 K. This study shows that N‐alkylation of BIM has a negligible effect on the ligand field strength. Therefore, the combination of TPMA and BIM offers a promising ligand platform for the design of functionalized SCO complexes.     

Functional Military Textile: Plasma-Induced Graft Polymerization of DADMAC for Antimicrobial Treatment on Nylon-Cotton Blend Fabric

In this study, diallyldimethylammonium chloride (DADMAC), a quaternary ammonium salt monomer, is graft polymerized on 50?C50 Nylon-Cotton (NyCo) standard military fabric using atmospheric pressure glow discharge plasma to impart self-detoxification capability. Atmospheric pressure plasma?is used to induce free radical chain polymerization of the DADMAC monomer to introduce a graft polymerized network on the fabric with durable antimicrobial properties. Pentaerythritol tetraacrylate (PETA) is used as a cross-linking agent to obtain a highly cross-linked, durable polymer network. The presence of polyDADMAC on the fabric surface is confirmed using acid dye staining, SEM, and TOF?CSIMS. Antibacterial performance is investigated using standard AATCC Test Method 100 for both gram positive and gram negative bacteria. Results show 99.9?% reduction in the bacterial activities of Klebsiella pneumoniae and Staphylococcus aureus.     

Determination of creatine and phosphocreatine in muscle biopsy samples by capillary electrophoresis with contactless conductivity detection

A capillary electrophoresis method with contactless conductivity detection was evaluated as a new approach for quantification of creatine and phosphocreatine in human quadriceps femoris biopsy samples. The running buffers employed consisted of 1 M acetic acid at a pH of 2.3 for the determination of creatine and 50 mM 3-(N-morpholino)propanesulfonic acid/30 mM histidine at a pH of 6.4 for the determination of phosphocreatine in the centrifuged muscle extracts. The limits of detection for creatine and phosphocreatine were found to be 2.5 and 1.0 μM, respectively. Creatine and phosphocreatine were determined in six human muscle biopsy samples and the results were found comparable to those of a standard enzymatic assay. The procedures developed for creatine and phosphocreatine also allow the determination of creatinine as well as adenosine diphosphate and adenosine triphosphate.     

Enantiomeric separation of some common controlled stimulants by capillary electrophoresis with contactless conductivity detection

CE methods with capacitively coupled contactless conductivity detection (C⁴D) were developed for the enantiomeric separation of the following stimulants: amphetamine (AP), methamphetamine (MA), ephedrine (EP), pseudoephedrine (PE), norephedrine (NE) and norpseudoephedrine (NPE). Acetic acid (pH 2.5 and 2.8) was found to be the optimal background electrolyte for the CE‐C⁴D system. The chiral selectors, carboxymethyl‐β‐cyclodextrin (CMBCD), heptakis(2,6‐di‐O‐methyl)‐β‐cyclodextrin (DMBCD) and chiral crown ether (+)‐(18‐crown‐6)‐2,3,11,12‐tetracarboxylic acid (18C6H₄), were investigated for their enantioseparation properties in the BGE. The use of either a single or a combination of two chiral selectors was chosen to obtain optimal condition of enantiomeric selectivity. Enantiomeric separation of AP and MA was achieved using the single chiral selector CMBCD and (hydroxypropyl)methyl cellulose (HPMC) as the modifier. A combination of the two chiral selectors, CMBCD and DMBCD and HPMC as the modifier, was required for enantiomeric separation of EP and PE. In addition, a combination of DMBCD and 18C6H₄ was successfully applied for the enantiomeric separation of NE and NPE. The detection limits of the enantiomers were found to be in the range of 2.3–5.7 μmol/L. Good precisions of migration time and peak area were obtained. The developed CE‐C⁴D method was successfully applied to urine samples of athletes for the identification of enantiomers of the detected stimulants.     

Inclusion Complex between Local Anesthetic/2-hydroxypropyl-β-cyclodextrin in Stealth Liposome

The drugs delivery system in the treatment of diseases has advantages such as reduced toxicity, increased availability of the drug, etc. Therefore, studies of the supramolecular interactions between local anesthetics (LAs) butamben (BTB) or ropivacaine (RVC) complexed with 2-hydroxypropyl-β-cyclodextrin (HP-βCD) and carried in Stealth liposomal (SL) are performed. ¹H-NMR nuclear magnetic resonance (DOSY and STD) were used as the main tools. The displacements observed in the ¹H-NMR presented the complexion between LAs and HP-βCD. The diffusion coefficients of free BTB and RVC were 7.70 × 10⁻¹⁰ m² s⁻¹ and 4.07 × 10⁻¹⁰ m² s⁻¹, and in the complex with HP-βCD were 1.90 × 10⁻¹⁰ m² s⁻¹ and 3.64 × 10⁻¹⁰ m² s⁻¹, respectively, which indicate a strong interaction between the BTB molecule and HP-βCD (98.3% molar fraction and Ka = 72.279 L/mol). With STD-NMR, the encapsulation of the BTB/HP-βCD and RVC/HP-βCD in SL vesicles was proven. Beyond the saturation transfer to the LAs, there is the magnetization transfer to the hydrogens of HP-βCD. BTB and RVC have already been studied in normal liposome systems; however, little is known of their behavior in SL.     

The neutrino as a tachyon

We investigate the hypothesis that at least one of the known neutrinos travels faster than light. The current experimental situation is examined within this purview.