Historical incidents leading to the evolution of good manufacturing practice

The concept of good manufacturing practice (GMP) is not new; its roots are very old. The incidents that gave birth to the concept of GMP are summarized in this article. The journey from the FDA toward GMP is highlighted in chronological order. These regulations are mandatory for pharmaceutical industries in order to manufacture quality products.     

Lie group analysis of the axisymmetric flow

The non-linear equations of motion describing the incompressible axisymmetric flow in a flexible and extensible circular cylindrical tube is considered. By employing Lie theory, the full one-parameter infinitesimal transformation group leaving the equations of motion invariant is derived along with its associated Lie algebra. Subgroups of the full group are then used to obtain a reduction by one in the number of independent variable in the system. These reductions are continued until a system of ordinary differential equations is reached. A series type approximate solution of these ordinary differential equations is obtained which leads to a series type approximate solutions in R²{0} to momentum equations.     

Coincidence and fixed points for hybrid strict contractions

We define the property (E.A) for single-valued and multivalued mappings and introduce the notion of T-weak commutativity for a hybrid pair (f,T) of single-valued and multivalued maps. We obtain some coincidence and fixed point theorems for this class of maps and derive, as application, an approximation theorem.     

Template Syntheses of Copper(II) Complexes from Arylhydrazones of Malononitrile and their Catalytic Activity towards Alcohol Oxidations and the Nitroaldol Reaction: Hydrogen Bond‐Assisted Ligand Liberation and E/Z Isomerisation

A one‐pot template condensation of 2‐(2‐(dicyanomethylene)hydrazinyl)benzenesulfonic acid (H₂L¹, 1 ) or 2‐(2‐(dicyanomethylene)hydrazinyl)benzoic acid (H₂L², 2 ) with methanol (a), ethylenediamine (b), ethanol (c) or water (d) on copper(II), led to a variety of metal complexes, that is, mononuclear [Cu(H₂O)₂(κO¹,κN² L^1a] ( 3 ) and [Cu(H₂O)(κO¹,κN³ L^1b)] ( 4 ), tetranuclear [Cu₄(1 κO¹,κN²:2 κO¹ L^2a)₃‐(1 κO¹, κN²:2 κO² L^2a)] ( 5 ), [Cu₂(H₂O)(1 κO¹, κN²:2 κO¹ L^2c)‐(1 κO¹,1 κN²:2 κO¹,2 κN¹‐ L^2c)]₂ ( 6 ) and [Cu₂(H₂O)₂(κO¹,κN²‐ L^1dd)‐(1 κO¹,κN²:2 κO¹ L^1dd)(μ‐H₂O)]₂ ? 2 H₂O ( 7? 2 H₂O), as well as polymer‐ ic [Cu(H₂O)(κO¹,1 κN²:2 κN¹ L^1c)]_n ( 8 ) and [Cu(NH₂C₂H₅)(κO¹,1 κN²:2 κN¹L^2a)]_n ( 9 ). The ligands 2‐SO₃H‐C₆H₄‐(NH)N?C{(CN)[C(NH₂)‐(?NCH₂CH₂NH₂)]} (H₂L^1b, 10 ), 2‐CO₂H‐C₆H₄‐(NH)N?{C(CN)[C(OCH₃)‐(?NH)]} (H₂L^2a, 11 ) and 2‐SO₃H‐C₆H₄‐(NH)N?C{C(?O)‐(NH₂)}₂ (H₂L^1dd, 12 ) were easily liberated upon respective treatment of 4 , 5 and 7 with HCl, whereas the formation of cyclic zwitterionic amidine 2‐(SO₃^?)? C₆H₄? N?NC(? C?(NH⁺)CH₂CH₂NH)(?CNHCH₂CH₂NH) ( 13 ) was observed when 1 was treated with ethylenediamine. The hydrogen bond‐induced E/Z isomerization of the (HL^1d)^? ligand occurs upon conversion of [{Na(H₂O)₂(μ‐H₂O)₂}(HL^1d)]_n ( 14 ) to [Cu(H₂O)₆][HL^1d]₂ ? 2 H₂O ( 15 ) and [{CuNa(H₂O)‐(κN¹,1 κO²:2 κO¹ L^1d)₂}K_0.5(μ‐O)₂]n ? H₂O ( 16 ). The synthesized complexes 3 – 9 are catalyst precursors for both the selective oxidation of primary and secondary alcohols (to the corresponding carbonyl compounds) and the following diastereoselective nitroaldol (Henry) reaction, with typical yields of 80–99 %.     

Green’s Function for the Hodge Laplacian on Some Classes of Riemannian and Lorentzian Symmetric Spaces

We compute the Green’s function for the wave equation on forms on the symmetric spaces M × Σ, where M is a simply connected n-dimensional Riemannian or Lorentzian manifold of constant curvature and Σ is a simply connected Riemannian surface of constant curvature. Our approach is based on a generalization to the case of differential forms of the method of spherical means and on the use of Riesz distributions on manifolds. The radial part of the Green’s function is governed by a fourth order analogue of the Heun equation.     

Experimental and computational study on the aqueous acidity constants of some new aminobenzoic acid compounds

The acidity constants of three new aminobenzoic acid derivatives were determined using potentiometric and spectrophotometric methods in 0.10 M aqueous potassium nitrate solution as supporting electrolyte. The potentiometric data and UV–Vis absorption spectra of solutions were recorded in the course of their pH-metric titration with a standard base solution. The protolytic equilibrium constants, concentration distribution diagrams and number of components involved have been calculated. The relative pK_a values for three acids were also calculated using ab initio quantum mechanical method at the HF/6-31G** level of theory in combination with CPCM continuum solvation method. The influence of substituents on the ionization constants of the studied molecular structures was investigated. The satisfactory agreement between the experimentally derived and theoretically calculated pK_a values provides solid support for the acid–base reactions proposed in this work.     

Two characterizations of pure injective modules

Let be a commutative ring with identity and an -module. It is shown that if is pure injective, then is isomorphic to a direct summand of the direct product of a family of finitely embedded modules. As a result, it follows that if is Noetherian, then is pure injective if and only if is isomorphic to a direct summand of the direct product of a family of Artinian modules. Moreover, it is proved that is pure injective if and only if there is a family of -algebras which are finitely presented as -modules, such that is isomorphic to a direct summand of a module of the form , where for each , is an injective -module.

     

Hydrogen and halogen bonding in the haloetherification products in chalcone

Cooperative action of hydrogen and halogen bonding in the reaction of 3‐(3,5‐di‐tert‐butyl‐4‐hydroxyphenyl)‐1‐phenylprop‐2‐en‐1‐one with HCl or HBr in alcohol medium under microwave irradiation (20 W, 80 °C, 10 min) allows the isolation of the haloetherification products (2S,3S)‐3‐(3‐tert‐butyl‐5‐chloro‐4‐hydroxyphenyl)‐2‐chloro‐3‐ethoxy‐1‐phenylpropan‐1‐one, C₂₁H₂₄Cl₂O₃, (2S,3S)‐2‐bromo‐3‐(3‐tert‐butyl‐5‐bromo‐4‐hydroxyphenyl)‐3‐methoxy‐1‐phenylpropan‐1‐one, C₂₀H₂₂Br₂O₃, and (2S,3S)‐2‐bromo‐3‐(3‐tert‐butyl‐5‐bromo‐4‐hydroxyphenyl)‐3‐ethoxy‐1‐phenylpropan‐1‐one, C₂₁H₂₄Br₂O₃, in good yields. Both types of noncovalent interactions, e.g. hydrogen and halogen bonds, are formed to stabilize the obtained products in the solid state.     

Associated primes of local cohomology modules

Let be an ideal of a commutative Noetherian ring and a finitely generated -module. Let be a natural integer. It is shown that there is a finite subset of , such that is contained in union with the union of the sets , where and . As an immediate consequence, we deduce that the first non- -cofinite local cohomology module of with respect to has only finitely many associated prime ideals.