Mixed-integer quadratic programming is in NP

Mixed-integer quadratic programming is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of mixed-integer quadratic programming is in NP, thereby showing that it is NP-complete. This is established by showing that if the decision version of mixed-integer quadratic programming is feasible, then there exists a solution of polynomial size. This result generalizes and unifies classical results that quadratic programming is in NP (Vavasis in Inf Process Lett 36(2):73–77 [17]) and integer linear programming is in NP (Borosh and Treybig in Proc Am Math Soc 55:299–304 [1], von zur Gathen and Sieveking in Proc Am Math Soc 72:155–158 [18], Kannan and Monma in Lecture Notes in Economics and Mathematical Systems, vol. 157, pp. 161–172. Springer [9], Papadimitriou in J Assoc Comput Mach 28:765–768 [15]).     

Understanding and tuning of polymer surfaces for dialysis applications

Tailoring membrane properties for biomedical applications, e.g., hemodialysis, have been a challenge which material scientists have been addressing for last few decades. The fundamental challenge lies in identifying and controlling the parameters which are responsible for yielding cytocompatibility and hemocompatibility to the material. The present article is an attempt to understand the physical parameters which are responsible for the biological manifestations of a polymer membrane. Two types of dialysis membranes, viz., high performance membrane and high cutoff, have been synthesized. Membrane surfaces were modified via dry and wet annealing, and conditions of annealing were optimized. Subsequently, physical and surface properties of the membranes after annealing were investigated. In‐depth investigation of biological and blood response has been undertaken on the basis of fundamental parameters like polarizability and surface rigidity. Cell adhesion, proliferation, protein adsorption, hemolysis, platelet adhesion, thrombus formation, and complement activation tests were performed on the membranes. It was observed that dry heating increases surface smoothness but in the process develops cracks on membrane surface as well as increases work of adhesion for blood contact. On the other hand, wet heating of membrane surface not only improves biological performance but it is also easy to retrofit with existing spinning technologies for spinning dialysis membranes. In‐house spinning technology was used to synthesize hemodialysis membranes which were annealed at the optimized conditions, and their surfaces were compared with commercial fibers to ascertain the rationale of annealing as a facile method to lend desired surface properties to membranes. Copyright © 2016 John Wiley & Sons, Ltd.     

Naphthalene-cholesterol conjugate as simple gelator for selective sensing of CN– ion

Cholesterol-based Schiff base 1 has been designed and synthesised. The Schiff base 1 forms yellow coloured gel in DMF:H₂O (2:1, v/v) and the gel is anion responsive. Among different anions, the gel phase of 1 is selectively transformed into sol in the presence of CN^– ions and validates its visual sensing. ¹H NMR, FTIR and HRMS spectroscopic techniques were adopted to study the gelation of 1 and its responsive behaviour towards anions.     

Naphthalene and pyrrole substituted guanidine in selective sensing of Cu2+, Hg2+, Pb2+ and CN− ions under different conditions

Naphthalene and pyrrole substituted guanidine 1 has been designed and synthesised. Compound 1 efficiently distinguishes Cu²⁺, Hg²⁺ and Pb²⁺ ions by exhibiting different responses in fluorescence. While compound 1 exhibited turn-on emission selectively in the presence of Hg²⁺ and Pb²⁺ ions in CH₃CN and CH₃CN–H₂O (1:1, v/v), respectively, it showed decrease in emission upon interaction with Cu²⁺ ion in CH₃CN. Furthermore, the Cu-1 ensemble has been established as a potential probe for selective detection of CN^? ion over a series of other anions involving colour change (in ordinary light: colourless to light yellow and under UV light: colourless to sky blue). Theoretical insight has been invoked to understand the mode of metal–ligand interaction.     

Exclusive Detection of Sub‐Nanomolar Levels of Palladium(II) in Water: An Excellent Probe for Multiple Applications

A new colorimetric probe has been developed for the detection and estimation of Pd^II at sub‐nanomolar concentrations. The probe consisted of rhodamine (signaling unit), which was linked with a bis‐picolyl moiety (binding site) through a phenyl ring. Pd^II induced opening of the spirolactam ring of the probe with the generation of a prominent pink color. The excellent selectivity of the probe towards Pd^II over Pd⁰ or Rh^II ensured its potential utility for the detection of residual palladium contamination in pharmaceutical drugs and in Pd‐catalyzed reactions. The probe showed a “turn‐on” (bright yellow) fluorescence upon the addition of Pd^II, which made it suitable for the detection of Pd contaminants in mammalian cells.     

Multichromophoric Organic Molecules Encapsulated in Polymer Nanoparticles for Artificial Light Harvesting

We designed a self‐assembled multichromophoric organic molecular arrangement inside polymer nanoparticles for light‐harvesting antenna materials. The self‐assembled molecular arrangement of quaterthiophene molecules was found to be an efficient light‐absorbing antenna material, followed by energy transfer to Nile red (NR) dye molecules, which was confined in polymer nanoparticles. The efficiency of the antenna effect was found to be 3.2 and the effective molar extinction coefficient of acceptor dye molecules was found to be enhanced, which indicates an efficient light‐harvesting system. Based on this energy‐transfer process, tunable photo emission and white light emission has been generated with 14 % quantum yield. Such self‐assembled oligothiophene–NR systems encapsulated in polymer nanoparticles may open up new possibilities for fabrication of artificial light harvesting system.     

SH-type waves dispersion in an isotropic medium sandwiched between an initially stressed orthotropic and heterogeneous semi-infinite media

The present paper studies the propagation of shear waves (SH-type waves) in an homogeneous isotropic medium sandwiched between two semi infinite media. The upper half-space is considered as orthotropic medium under initial stress and lower half-space considered as heterogeneous medium. We have obtained the dispersion equation of phase velocity for SH-type waves. The propagation of SH-type waves are influenced by inhomogeneity parameters and initial stress parameter. The velocity of SH-type wave has been computed for different cases. We have also obtained the dispersion equation of phase velocity in homogeneous media in the absence of initial stress. The velocities of SH-type waves are calculated numerically as a function of kH (non-dimensional wave number) and presented in a number of graphs. To study the effect of inhomogeneity parameters and initial stress parameter we have plotted the velocity of SH-type wave in several figure. We have observed that the velocity of wave increases with the increase inhomogeneity parameters. We found that in both homogeneous and inhomogeneous media the velocity of SH-type wave increases with the increase of initial stress parameter. The results may be useful for the study of seismic waves propagation during any earthquake and artificial explosions.     

Ethyl 2‐[N‐(tert‐butyl­oxy­carbonyl)‐l‐alanyl­amino]‐4‐methyl‐1,3‐thia­zole‐5‐carboxyl­ate reveals a trans orientation of the preceding amide N—H with respect to the thia­zole‐ring sulfur

The title mol­ecule, C₁₅H₂₃N₃O₅S, was prepared as a synthetic precursor to 4‐methyl­thia­zole‐based DNA minor groove binders which would bear chiral amino acids in the sequence. The crystallographic evidence presented herein shows that the aromatic amide NH group preceding the thia­zole ring points away from the direction of sulfur. The mol­ecule is biplanar, with the dihedral angle between the N‐terminus peptide moiety and the thia­zole‐containing plane being 49.7 (5)°, with a bend at the Cα carbon.     

Magnetic responses in 1D mesoscopic rings and cylinders

I investigated a detailed study of persistent current and low-field magnetic susceptibility in one-dimensional mesoscopic rings and cylinders threaded by slowly varying magnetic flux φ in the tight-binding model. In perfect rings described by constant number of electrons N_e, current shows only saw-tooth variation with φ, while for those rings described by constant chemical potential μ, current varies saw-tooth like for some special choices of μ, but in all other cases it shows kink-like structures. On the other hand, in perfect cylinders I get both saw-tooth and kink-like structures in persistent current whether these cylinders are described by constant N_e or μ. In presence of impurity, current gets a continuous variation with φ only for the rings described by constant N_e, while in all other cases it depends on the choice of μ. My exact calculation predicts that the diamagnetic and paramagnetic sign of the low-field currents can be determined exactly for the rings described by constant N_e. In perfect rings, I get only diamagnetic currents both for odd and even N_e, while in presence of impurity current always shows diamagnetic sign for the rings with odd N_e and paramagnetic sign for the rings with even N_e. Both for the perfect and disordered rings described by constant μ the sign of the current cannot be mentioned exactly since it depends on the choice of μ and disordered configurations. Similar arguments are also true for the cylinders those are described either by constant N_e or by constant μ since the sign of the current in these systems depends on N_e, μ and disordered configurations.