Cone complementarity problems with finite solution sets

We introduce the notion of a complementary cone and a nondegenerate linear transformation and characterize the finiteness of the solution set of a linear complementarity problem over a closed convex cone in a finite dimensional real inner product space. In addition to the above, other geometrical properties of complementary cones have been explored.     

Comparative molecular field analysis and comparative molecular similarity indices analysis of hydroxyethylamine derivatives as selective human BACE-1 inhibitor

Three-dimensional quantitative structure–activity relationship (3D-QSAR) models were developed based on comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA), on a series of 43 hydroxyethylamine derivatives, acting as potent inhibitors of β-site amyloid precursor protein (APP) cleavage enzyme (BACE-1). The crystal structure of the BACE-1 enzyme (PDB ID: 2HM1) with one of the most active compound 28 was available, and we assumed it to be the bioactive conformation of the studied series, for 3D-QSAR analysis. Statistically significant 3D-QSAR model was established on a training set of 34 compounds, which were validated by a test set of 9 compounds. For the best CoMFA model, the statistics are, r ² =  0.998, r²_cv = 0.810{r^{2}_{\rm cv} = 0.810} , n =  34 for the training set and r²_pred = 0.934{r^{2}_{\rm pred} = 0.934} , n = 9 for the test set. For the best CoMSIA model (combined steric, electrostatic, hydrophobic, and hydrogen bond donor fields), the statistics are r ² =  0.978, r²_cv = 0.754{r^{2}_{\rm cv} = 0.754} , n =  34 for the training set and r²_pred = 0.750{r^{2}_{\rm pred} = 0.750} , n =  9 for the test set. The resulting contour maps, produced by the best CoMFA and CoMSIA models, were used to identify the structural features relevant to the biological activity in this series of analogs. The data generated from the present study will further help to design novel, potent, and selective BACE-1 inhibitors.     

Linearization relations for the generalized Bedient polynomials of the first and second kinds via their integral representations

The main object of this paper is to investigate several general families of hyper-geometric polynomials and their associated multiple integral representations. By suitably specializing our main results, the corresponding integral representations are deduced for such familiar classes of hypergeometric polynomials as (for example) the generalized Bedient polynomials of the first and second kinds. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials.     

Comparative Study of Natural Terpenoid Precursors in Reactive Plasmas for Thin Film Deposition

If plasma polymer thin films are to be synthesised from sustainable and natural precursors of chemically heterogeneous composition, it is important to understand the extent to which this composition influences the mechanism of polymerisation. To this end, a well-studied monoterpene alcohol, terpinen-4-ol, has been targeted for a comparative study with the naturally occurring mix of terpenes (viz. Melaleuca alternifolia oil) from which it is commonly distilled. Positive ion mode mass spectra of both terpinen-4-ol and M. alternifolia oil showed a decrease in disparities between the type and abundance of cationic species formed in their respective plasma environments as applied plasma power was increased. Supplementary biological assay revealed the antibacterial action of both terpinen-4-ol and M. alternifolia derived coatings with respect to S. aureus bacteria, whilst cytocompatibility was demonstrated by comparable eukaryotic cell adhesion to both coatings. Elucidating the processes occurring within the reactive plasmas can enhance the economics of plasma polymer deposition by permitting use of the minimum power, time and precursor pre-processing required to control the extent of monomer fragmentation and fabricate a film of the desired thickness and functionality.     

A New Ecological RP-HPLC Method for the Determination of Pitavastatin,Fenofibrate and Their Impurities in a Novel Fixed Dose Combination

Chromatographia - We developed a simple, rapid, ecological RP-HPLC method for the estimation of Pitavastatin (PIT), Fenofibrate (FEN), and their impurities in a novel fixed dose combination. We...     

Nano Gd2O3 catalyzed synthesis and anti-oxidant activity of new α-aminophosphonates

A one pot three-component nano Gd₂O₃ catalyzed neat reaction of 2-morpholinoethanamine and dimethylphosphite with various salicylaldehydes under microwave irradiation afforded a series of new α-aminophosphonates in high yields. The synthesized compounds were characterized by FT-IR, (¹H, ¹³C, ³¹P)-NMR, and mass spectral methods. The antioxidant activity of these compounds was evaluated against DPPH, NO, and H₂O₂ methods and found that the compound Dimethyl (2-hydroxy-5-nitrophenyl) (2-morpholinoethylamino) methylphosphonate (4h) has higher antioxidant activity than the corresponding standards.     

Insights into the Gelating Abilities of Ricinelaidic Acid and its Ammonium Salts: How do Stereochemistry,Charge, and Chain Lengths Control Gelation of a Long‐Chain Alkenoic Acid?

The gelating abilities of ricinelaidic acid (d ‐REA), the trans‐isomer of ricinoleic acid (d ‐RA), and a series of its alkylammonium and alkane‐α,ω‐diammonium salts have been examined in a wide range of organic liquids. The gelation efficiency of the trans acid is much better than that of the cis, although neither is as efficient as is the completely saturated molecular gelator analogue, (R)‐12‐hydroxystearic acid (d ‐12HSA). The formation of ammonium salts also improves the gelation ability of d ‐REA in high polarity liquids. The gelating properties are highly dependent upon the chain length of the alkyl group of the alkylammonium salts, but not very dependent on the chain length of the alkane‐α,ω‐diammonium salts. Structural insights from Fourier transform infrared spectroscopy and powder X‐ray diffraction indicate that the absence or presence of unsaturation, the incorporation of (charged) ammonium centers, and the different chain lengths of the alkylammonium salts lead to different packing arrangements and different strengths of H‐bonding interactions within the gel assemblies of the d ‐REA derivatives. Insights into the relationships among the various systematic structural changes to d ‐REA and the properties of their aggregated structures, including the gel states, are provided.     

(R)‐12‐Hydroxystearic Acid Hydrazides as Very Efficient Gelators: Diffusion,Partial Thixotropy,and Self‐Healing in Self‐Standing Gels

The gelation properties of derivatives of N‐alkylated (R)‐12‐hydroxystearic acid hydrazide (n‐HSAH, n=0, 2, 6, 10; n is the length of an n‐alkyl chain on the terminal nitrogen atom) in a wide variety of liquids is reported. The n‐HSAH compounds were derived from a naturally occurring alkanoic acid, (R)‐12‐hydroxystearic acid (R‐12HSA), and although they differ from the analogous N‐alkyl (R)‐12‐hydroxystearamides (n‐HSAA) only by the presence of one N?H group, their behavior as gelators is very different. For example, the parent molecule (0‐HSAH) is a supergelator in ethylene glycol, in which it forms self‐standing gels that are self‐healing, partially thixotropic, moldable, and load‐bearing; gels of 0‐HSAA are not self‐standing. 0‐HSAH is structurally the simplest molecular gelator of which we are aware that is capable of forming both self‐standing and partially thixotropic gels. Also, diffusion of the cationic dye erythrosine B and the anionic dye methylene blue in 0‐HSAH/ethylene glycol gel blocks is much slower than the self‐diffusion of ethylene glycol. Polarizing optical microscopy, X‐ray diffraction, and FTIR studies revealed that the self‐assembled fibrillar networks (SAFINs) of the gels are crystalline, and that 0‐HSAH molecules may be arranged in a triclinic subcell with bilayer stacking. The SAFINs are stabilized by strong hydrogen‐bonding interactions between the hydrazide groups of adjacent molecules and a perpendicular hydrogen‐bonding network between the pendent hydroxyl groups of 0‐HSAH. The other n‐HSAH (n=2, 6, 10) molecules appear to be arranged in orthorhombic subcells with monolayers and strong hydrogen‐bonding interactions between the hydrazide group of one gelator molecule and the hydroxyl group of a neighboring one. These results show how small structural modifications of structurally simple gelator molecules can be exploited to form gels with novel properties that can lead potentially to valuable applications, such as in drug delivery.     

Synthesis of a new class of bisheterocycles from phenacylsulfonylacetic acid methyl ester

Novel bisheterocycles, 1,2,3‐selenadiazoles, thiadiazoles and 2H‐diazaphospholes in combination with oxadiazoles, thiadiazoles and triazoles were prepared from phenacylsulfonylacetic acid methyl ester.