Crystal structures of the pyrazinamide–p‐aminobenzoic acid (1/1) cocrystal and the transamidation reaction product 4‐(pyrazine‐2‐carboxamido)benzoic acid in the molten state

The synthesis of pharmaceutical cocrystals is a strategy to enhance the performance of active pharmaceutical ingredients (APIs) without affecting their therapeutic efficiency. The 1:1 pharmaceutical cocrystal of the antituberculosis drug pyrazinamide (PZA) and the cocrystal former p‐aminobenzoic acid (p‐ABA), C₇H₇NO₂·C₅H₅N₃O, (1), was synthesized successfully and characterized by relevant solid‐state characterization methods. The cocrystal crystallizes in the monoclinic space group P2₁/n containing one molecule of each component. Both molecules associate via intermolecular O—H...O and N—H...O hydrogen bonds [O...O = 2.6102 (15) Å and O—H...O = 168.3 (19)°; N...O = 2.9259 (18) Å and N—H...O = 167.7 (16)°] to generate a dimeric acid–amide synthon. Neighbouring dimers are linked centrosymmetrically through N—H...O interactions [N...O = 3.1201 (18) Å and N—H...O = 136.9 (14)°] to form a tetrameric assembly supplemented by C—H...N interactions [C...N = 3.5277 (19) Å and C—H...N = 147°]. Linking of these tetrameric assemblies through N—H...O [N...O = 3.3026 (19) Å and N—H...O = 143.1 (17)°], N—H...N [N...N = 3.221 (2) Å and N—H...N = 177.9 (17)°] and C—H...O [C...O = 3.5354 (18) Å and C—H...O = 152°] interactions creates the two‐dimensional packing. Recrystallization of the cocrystals from the molten state revealed the formation of 4‐(pyrazine‐2‐carboxamido)benzoic acid, C₁₂H₉N₃O₃, (2), through a transamidation reaction between PZA and p‐ABA. Carboxamide (2) crystallizes in the triclinic space group P with one molecule in the asymmetric unit. Molecules of (2) form a centrosymmetric dimeric homosynthon through an acid–acid O—H...O hydrogen bond [O...O = 2.666 (3) Å and O—H...O = 178 (4)°]. Neighbouring assemblies are connected centrosymmetrically via a C—H...N interaction [C...N = 3.365 (3) Å and C—H...N = 142°] engaging the pyrazine groups to generate a linear chain. Adjacent chains are connected loosely via C—H...O interactions [C...O = 3.212 (3) Å and C—H...O = 149°] to generate a two‐dimensional sheet structure. Closely associated two‐dimensional sheets in both compounds are stacked via aromatic π‐stacking interactions engaging the pyrazine and benzene rings to create a three‐dimensional multi‐stack structure.     

1‐(7‐Chloro‐1,4‐dihydroquinolin‐4‐ylidene)thiosemicarbazide and its hydrochloride: evidence for the existence of a stable imine tautomer in the solid state of 4‐aminoquinoline free bases,an anomalous case in nitrogen heterocycles

In the solid state, crystals of both 1‐(7‐chloro‐1,4‐dihydroquinolin‐4‐ylidene)thiosemicarbazide–methanol–water (2/1/1), 2C₁₀H₉ClN₄S·CH₃OH·H₂O, (I), and its hydrochloride salt {systematic name: [(7‐chloro‐1,4‐dihydroquinolin‐4‐ylidene)azaniumyl]thiourea chloride}, C₁₀H₁₀ClN₄S⁺·Cl⁻, (II), assume the imine tautomeric form, contrary to other 4‐amino‐7‐chloroquinolines. Of particular interest are the N—C bond lengths, which have appreciable double‐bond character, and the C—N—C aromatic ring bond angle. Both of these parameters have been studied extensively in 4‐amino‐substituted quinolines. The crystal structures of (I) and (II) in this study provide interesting examples of the amino–imino tautomerism which exists in this class of compound and is, to the best of our knowledge, hitherto unreported.     

Exo conformers of N‐(pyridin‐2‐yl)‐ and N‐(pyridin‐3‐yl)norbornene‐5,6‐dicarboximide crystals

Two isomeric pyridine‐substituted norbornenedicarboximide derivatives, namely N‐(pyridin‐2‐yl)‐exo‐norbornene‐5,6‐dicarboximide, (I), and N‐(pyridin‐3‐yl)‐exo‐norbornene‐5,6‐dicarboximide, (II), both C₁₄H₁₂N₂O₄, have been crystallized and their structures unequivocally determined by single‐crystal X‐ray diffraction. The molecules consist of norbornene moieties fused to a dicarboximide ring substituted at the N atom by either pyridin‐2‐yl or pyridin‐3‐yl in an anti configuration with respect to the double bond, thus affording exo isomers. In both compounds, the asymmetric unit consists of two independent molecules (Z′ = 2). In compound (I), the pyridine rings of the two independent molecules adopt different conformations, i.e. syn and anti, with respect to the methylene bridge. The intermolecular contacts of (I) are dominated by C—H...O interactions. In contrast, in compound (II), the pyridine rings of both molecules have an anti conformation and the two independent molecules are linked by carbonyl–carbonyl interactions, as well as by C—H...O and C—H...N contacts.     

Ground state solutions and geometrically distinct solutions for generalized quasilinear Schrödinger equation

In this paper, we study the following generalized quasilinear Schrödinger equation where N≥3, is a C¹ even function, g(0) = 1 and g^′(s) > 0 for all s > 0. Under some suitable conditions, we prove that the equation has a ground state solution and infinitely many pairs ±u of geometrically distinct solutions. Copyright © 2016 John Wiley & Sons, Ltd.     

Global dynamics of an age‐structured virus model with saturation effects

An infection‐age virus dynamics model for human immunodeficiency virus (or hepatitis B virus) infections with saturation effects of infection rate and immune response is investigated in this paper. It is shown that the global dynamics of the model is completely determined by two critical values R ₀, the basic reproductive number for viral infection, and R ₁, the viral reproductive number at the immune‐free infection steady state (R ₁<R ₀). If R ₀<1, the uninfected steady state E ⁰ is globally asymptotically stable; if R ₀>1 > R ₁, the immune‐free infected steady state E ^? is globally asymptotically stable; while if R ₁>1, the antibody immune infected steady state is globally asymptotically stable. Moreover, our results show that ignoring the saturation effects of antibody immune response or infection rate will result in an overestimate of the antibody immune reproductive number. Copyright © 2016 John Wiley & Sons, Ltd.     

3‐(Pyridin‐4‐yl)acetylacetone: CdII and HgII compete for nitrogen coordination

3‐(Pyridin‐4‐yl)acetylacetone (HacacPy) acts as a pyridine‐type ligand towards Cd^II and Hg^II halides. With CdBr₂, the one‐dimensional polymer [Cd(μ‐Br)₂(HacacPy)Cd(μ‐Br)₂(HacacPy)₂]_∞ is obtained in which five‐ and six‐coordinated Cd^II cations alternate in the chain direction. Reaction of HacacPy with HgBr₂ results in [Hg(μ‐Br)Br(HacacPy)]_∞, a polymer in which each Hg^II centre is tetracoordinated. In both compounds, each metal(II) cation is N‐coordinated by at least one HacacPy ligand. Equimolar reaction between these Cd^II and Hg^II derivatives, either conducted in ethanol as solvent or via grinding in the solid state, leads to ligand redistribution and the formation of the well‐ordered bimetallic polymer catena‐poly[[bromidomercury(II)]‐μ‐bromido‐[aquabis[4‐hydroxy‐3‐(pyridin‐4‐yl)pent‐3‐en‐2‐one]cadmium(II)]‐di‐μ‐bromido], [CdHgBr₄(C₁₀H₁₁NO₂)₂(H₂O)]_n or [{HgBr}(μ‐Br){(HacacPy)₂Cd(H₂O)}(μ‐Br)₂]_∞. Hg^II and Cd^II cations alternate in the [100] direction. The HacacPy ligands do not bind to the Hg^II cations, which are tetracoordinated by three bridging and one terminal bromide ligand. The Cd^II centres adopt an only slightly distorted octahedral coordination. Three bromide ligands link them in a (2 + 1) pattern to neighbouring Hg^II atoms; two HacacPy ligands in a cis configuration, acting as N‐atom donors, and a terminal aqua ligand complete the coordination sphere. Classical O—H…Br hydrogen bonds stabilize the polymeric chain. O—H…O hydrogen bonds between aqua H atoms and the uncoordinated carbonyl group of an HacacPy ligand in a neighbouring strand in the c direction link the chains into layers in the (010) plane.     

Analysis of an elasto-piezoelectric system of hemivariational inequalities with thermal effects

In this paper we prove the existence and uniqueness of a weak solution for a dynamic electo-viscoelastic problem that describes a contact between a body and a foundation. We assume the body is made from thermoviscoelastic material and consider nonmonotone boundary conditions for the contact. We use recent results from the theory of hemivariational inequalities and the fixed point theory.     

Low rank matrix recovery from rank one measurements

We study the recovery of Hermitian low rank matrices $X\in {\mathbb{C}}^{n\times n}$ from undersampled measurements via nuclear norm minimization. We consider the particular scenario where the measurements are Frobenius inner products with random rank-one matrices of the form $a_j{a}_j^{?}$ for some measurement vectors $a_1,\dots ,a_m$, i.e., the measurements are given by $b_j=\mathrm{tr}(X{a}_j{a}_j^{?})$. The case where the matrix $X=x{x}^{?}$ to be recovered is of rank one reduces to the problem of phaseless estimation (from measurements $b_j=|〈x,a_j〉{|}^2$) via the PhaseLift approach, which has been introduced recently. We derive bounds for the number m of measurements that guarantee successful uniform recovery of Hermitian rank r matrices, either for the vectors $a_j$, $j=1,\dots ,m$, being chosen independently at random according to a standard Gaussian distribution, or $a_j$ being sampled independently from an (approximate) complex projective t-design with $t=4$. In the Gaussian case, we require $m\ge Crn$ measurements, while in the case of 4-designs we need $m\ge \mathit{Cr}n\log ?(n)$. Our results are uniform in the sense that one random choice of the measurement vectors $a_j$ guarantees recovery of all rank r-matrices simultaneously with high probability. Moreover, we prove robustness of recovery under perturbation of the measurements by noise. The result for approximate 4-designs generalizes and improves a recent bound on phase retrieval due to Gross, Krahmer and Kueng. In addition, it has applications in quantum state tomography. Our proofs employ the so-called bowling scheme which is based on recent ideas by Mendelson and Koltchinskii.     

Maximum likelihood estimation for stochastic volatility in mean models with heavy‐tailed distributions

In this article, we introduce a likelihood‐based estimation method for the stochastic volatility in mean (SVM) model with scale mixtures of normal (SMN) distributions. Our estimation method is based on the fact that the powerful hidden Markov model (HMM) machinery can be applied in order to evaluate an arbitrarily accurate approximation of the likelihood of an SVM model with SMN distributions. Likelihood‐based estimation of the parameters of stochastic volatility models, in general, and SVM models with SMN distributions, in particular, is usually regarded as challenging as the likelihood is a high‐dimensional multiple integral. However, the HMM approximation, which is very easy to implement, makes numerical maximum of the likelihood feasible and leads to simple formulae for forecast distributions, for computing appropriately defined residuals, and for decoding, that is, estimating the volatility of the process. Copyright © 2017 John Wiley & Sons, Ltd.