The Lp dual Minkowski problem for p > 1 and q > 0

General $L_p$ dual curvature measures have recently been introduced by Lutwak, Yang and Zhang [24]. These new measures unify several other geometric measures of the Brunn–Minkowski theory and the dual Brunn–Minkowski theory. $L_p$ dual curvature measures arise from qth dual intrinsic volumes by means of Alexandrov-type variational formulas. Lutwak, Yang and Zhang [24] formulated the $L_p$ dual Minkowski problem, which concerns the characterization of $L_p$ dual curvature measures. In this paper, we solve the existence part of the $L_p$ dual Minkowski problem for $p>1$ and $q>0$, and we also discuss the regularity of the solution.     

Synthesis,characterization, thermal properties and biological activity of diazine-ring containing hydrazones and their metal complexes

Journal of Thermal Analysis and Calorimetry - New coordination compounds have been synthesized by reacting Zn(II) and Co(II) nitrate or acetate in the presence of triethylamine with Schiff-base...     

Antimicrobial loading into and release from poly(ethylene glycol)/poly(acrylic acid) semi‐interpenetrating hydrogels

Electrostatic interactions within a semi‐interpenetrating network (semi‐IPN) gel can control the postsynthesis loading, long‐term retention, and subsequent release of small‐molecule cationic antibiotics. Here, electrostatic charge is introduced into an otherwise neutral gel [poly(ethylene glycol) (PEG)] by physically entrapping high‐molecular‐weight poly(acrylic acid) (PAA). The network structure is characterized by small‐angle neutron scattering. PEG/PAA semi‐IPN gels absorb over 40 times more antibiotic than PAA‐free PEG gels. Subsequent soaking in physiological buffer (pH 7.4; 0.15 M NaCl) releases the loaded antibiotics for periods as long as 30 days. The loaded gels elute antibiotics with diffusivities of 4.46 × 10^?8 cm²/s (amikacin) and 2.08 × 10^?8 cm²/s (colistin), which are two orders of magnitude less than those in pure PEG gels where diffusion is controlled purely by gel tortuosity. The release and hindered diffusion can be understood based on the partial shielding of the charged groups within the loaded gel, and they have a significant effect on the antimicrobial properties of these gels. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 64–72     

Expanding the Ligand Classes Used for Mn(II) Complexation: Oxa-aza Macrocycles Make the Difference

We report two macrocyclic ligands based on a 1,7-diaza-12-crown-4 platform functionalized with acetate (tO2DO2A²⁻) or piperidineacetamide (tO2DO2AM^Pip) pendant arms and a detailed characterization of the corresponding Mn(II) complexes. The X−ray structure of [Mn(tO2DO2A)(H₂O)]·2H₂O shows that the metal ion is coordinated by six donor atoms of the macrocyclic ligand and one water molecule, to result in seven-coordination. The Cu(II) analogue presents a distorted octahedral coordination environment. The protonation constants of the ligands and the stability constants of the complexes formed with Mn(II) and other biologically relevant metal ions (Mg(II), Ca(II), Cu(II) and Zn(II)) were determined using potentiometric titrations (I = 0.15 M NaCl, T = 25 °C). The conditional stabilities of Mn(II) complexes at pH 7.4 are comparable to those reported for the cyclen-based tDO2A²⁻ ligand. The dissociation of the Mn(II) chelates were investigated by evaluating the rate constants of metal exchange reactions with Cu(II) under acidic conditions (I = 0.15 M NaCl, T = 25 °C). Dissociation of the [Mn(tO2DO2A)(H₂O)] complex occurs through both proton− and metal−assisted pathways, while the [Mn(tO2DO2AM^Pip)(H₂O)] analogue dissociates through spontaneous and proton-assisted mechanisms. The Mn(II) complex of tO2DO2A²⁻ is remarkably inert with respect to its dissociation, while the amide analogue is significantly more labile. The presence of a water molecule coordinated to Mn(II) imparts relatively high relaxivities to the complexes. The parameters determining this key property were investigated using ¹⁷O NMR (Nuclear Magnetic Resonance) transverse relaxation rates and ¹H nuclear magnetic relaxation dispersion (NMRD) profiles.     

Interface Amorphization of Two-Dimensional Black Phosphorus upon Treatment with Diazonium Salts

Two-dimensional (2D) black phosphorus (BP) represents one of the most appealing 2D materials due to its electronic, optical, and chemical properties. Many strategies have been pursued to face its environmental instability, covalent functionalization being one of the most promising. However, the extremely low functionalization degrees and the limitations in proving the nature of the covalent functionalization still represent challenges in many of these sheet architectures reported to date. Here we shine light on the structural evolution of 2D-BP upon the addition of electrophilic diazonium salts. We demonstrated the absence of covalent functionalization in both the neutral and the reductive routes, observing in the latter case an unexpected interface conversion of BP to red phosphorus (RP), as characterized by Raman, ³¹P-MAS NMR, and X-ray photoelectron spectroscopies (XPS). Furthermore, thermogravimetric analysis coupled to gas chromatography and mass spectrometry (TG-GC-MS), as well as electron paramagnetic resonance (EPR) gave insights into the potential underlying radical mechanism, suggesting a Sandmeyer-like reaction.     

Synthesis of activated carbon foams with high specific surface area using polyurethane elastomer templates for effective removal of methylene blue

Carbon foams have gained significant attention due to their tuneable properties that enable a wide range of applications including catalysis, energy storage and wastewater treatment. Novel synthesis pathways enable novel applications via yielding complex, hierarchical material structure. In this work, activated carbon foams (ACFs) were produced from waste polyurethane elastomer templates using different synthesis pathways, including a novel one-step method. Uniquely, the produced foams exhibited complex structure and contained carbon microspheres. The ACFs were synthesized by impregnating the elastomers in an acidified sucrose solution followed by direct activation using CO₂ at 1000 ℃. Different pyrolysis and activation conditions were investigated. The ACFs were characterized by a high specific surface area (S_BET) of 2172 m²/g and an enhanced pore volume of 1.08 cm³/g. Computer tomography and morphological studies revealed an inhomogeneous porous structure and the presence of numerous carbon spheres of varying sizes embedded in the porous network of the three-dimensional carbon foam. X-ray diffraction (XRD) and Raman spectroscopy indicated that the obtained carbon foam was amorphous and of turbostratic structure. Moreover, the activation process enhanced the surface of the carbon foam, making it more hydrophilic via altering pore size distribution and introducing oxygen functional groups. In equilibrium, the adsorption of methylene blue on ACF followed the Langmuir isotherm model with a maximum adsorption capacity of 592 mg/g. Based on these results, the produced ACFs have potential applications as adsorbents, catalyst support and electrode material in energy storage systems.     

Delayed nonlinear cournot and bertrand dynamics with product differentiation

Dynamic duopolies will be examined with product differentiation and isoelastic price functions. We will first prove that under realistic conditions the equilibrium is always locally asymptotically stable. The stability can however be lost if the firms use delayed information in forming their best responses. Stability conditions are derived in special cases, and simulation results illustrate the complexity of the dynamism of the systems. Both price and quantity adjusting models are discussed.     

Strong Asymptotics of the Orthogonal Polynomials with Respect to a Measure Supported on the Plane

We consider the orthogonal polynomials with respect to the measure over the whole complex plane. We obtain the strong asymptotic of the orthogonal polynomials in the complex plane and the location of their zeros in a scaling limit where n grows to infinity with N . The asymptotics are described in terms of three (probability) measures associated with the problem. The first measure is the limit of the counting measure of zeros of the polynomials, which is captured by the g‐function much in the spirit of ordinary orthogonal polynomials on the real line. The second measure is the equilibrium measure that minimizes a certain logarithmic potential energy, supported on a region K of the complex plane. The third measure is the harmonic measure of K ^c with a pole at ∞ . This appears as the limit of the probability measure given (up to the normalization constant) by the squared modulus of the n^th orthogonal polynomial times the orthogonality measure, i.e., The compact region K that is the support of the second measure undergoes a topological transition under the variation of the parameter in a double scaling limit near the critical point given by we observe the Hastings‐McLeod solution to Painlevé II in the asymptotics of the orthogonal polynomials. © 2014 Wiley Periodicals, Inc.