Analytic theory for the determination of velocity and stability of bubbles in a Hele-Shaw cell

An asymptotic theory is presented for the determination of velocity and linear stability of a steady symmetric bubble in a Hele-Shaw cell for small surface tension. In the first part, the bubble velocity U relative to the fluid velocity at infinity is determined for small surface tension T by determining a transcendentally small correction to the asymptotic series solution. It is found that for any relative bubble velocity U in the interval (U _c , 2), solutions exist at a countably infinite set of values of T (which has zero as its limit point) corresponding to the different branches of bubble solutions. The value of U _c decreases monotonically from 2 to 1 as the bubble area increases from 0 to . However, for a bubble of an arbitrarily given size, as T 0, a solution exists on any given branch with the relative bubble velocity U satisfying the relation 2–U=cT ^2/3, where c depends on the branch but is independent of the bubble area. The analytical evidence further suggests that there are no solutions for U>2. These results are in agreement with earlier analytical results for a finger.In Part II an analytic theory is presented for the determination of the linear stability of the bubble in the limit of zero surface tension. Only the solution branch corresponding to the largest possible U for given surface tension is found to be stable, while all the others are unstable, in accordance with earlier numerical results.This research has been supported by National Science Foundation Grant DMS-8713246. Partial support was also provided by the NASA Langley Research Center (NAS1-18605) while the author was in residence at the Institute of Computer Applications in Science and Engineering.     

Three New Acrylic Acid Derivatives from Achillea mellifolium as Potential Inhibitors of Urease from Jack Bean and α-Glucosidase from Saccharomyces cerevisiae

(1) Background: Achillea mellifolium belongs to a highly reputed family of medicinal plants, with plant extract being used as medicine in indigenous system. However, limited data is available regarding the exploitation of the medicinal potential of isolated pure compounds from this family; (2) Methods: A whole plant extract was partitioned into fractions and on the basis of biological activity, an ethyl acetate fraction was selected for isolation of pure compounds. Isolated compounds were characterized using different spectroscopic techniques. The compounds isolated from this study were tested for their medicinal potential using in-vitro enzyme assay, coupled with in-silico studies; (3) Results: Three new acrylic acid derivatives (1–3) have been isolated from the ethyl acetate fraction of Achillea mellifolium. The characterization of these compounds (1–3) was carried out using UV/Vis, FT-IR, 1D and 2D-NMR spectroscopy (¹H-NMR, ¹³C-NMR, HMBC, NOESY) and mass spectrometry. These acrylic acid derivatives were further evaluated for their enzyme inhibition potential against urease from jack bean and α glucosidase from Saccharomyces cerevisiae, using both in-silico and in-vitro approaches. In-vitro studies showed that compound 3 has the highest inhibition against urease enzyme (IC₅₀ =10.46 ± 0.03 μΜ), followed by compound 1 and compound 2 with percent inhibition and IC₅₀ value of 16.87 ± 0.02 c and 13.71 ± 0.07 μΜ, respectively, compared to the standard (thiourea-IC₅₀ = 21.5 ± 0.01 μΜ). The investigated IC₅₀ value of compound 3 against the urease enzyme is two times lower compared to thiourea, suggesting that this compound is twice as active compared to the standard drug. On the other hand, all three compounds (1–3) revealed mild inhibition potential against α-glucosidase. In-silico molecular docking studies, in combination with MD simulations and free energy, calculations were also performed to rationalize their time evolved mode of interaction inside the active pocket. Binding energies were computed using a MMPBSA approach, and the role of individual residues to overall binding of the inhibitors inside the active pockets were also computed; (4) Conclusions: Together, these studies confirm the inhibitory potential of isolated acrylic acid derivatives against both urease and α-glucosidase enzymes; however, their inhibition potential is better for urease enzyme even when compared to the standard.     

A Characterisation of a Class of Semigroups with Locally Commuting Idempotents

McAlister proved that a necessary and sufficient condition for a regular semigroup S to be locally inverse is that it can be embedded as a quasi-ideal in a semigroup T which satisfies the following two conditions: (1) T = TeT, for some idempotent e; and (2) eTe is inverse. We generalise this result to the class of semigroups with local units in which all local submonoids have commuting idempotents.     

A review on <Superscript>90</Superscript>Y-labeled compounds and biomolecules

The field of therapeutic nuclear medicine is emerging rapidly as choice of treatment in oncology and other cellular malignancies. The growth of this branch of nuclear medicine is greatly facilitated by the introduction of a number of new radiopharmaceuticals and radionuclides. ⁹⁰Y-radiopharmaceuticals have confirmed their worth in medical and clinical areas in a very short span of time. The ⁹⁰Y is a radioisotope widely used for therapeutic purposes and considerable perfection has been made to understand the chemistry of ⁹⁰Y-labeled radiopharmaceuticals. The development of these radiopharmaceuticals can be made favorable by using appropriate buffer, incubation period, optimal pH, specific activity and reaction temperature. In this review, we have discussed the preparation of range of ⁹⁰Y transporting biological molecules such as antibodies radiolabeled peptides, antigens and microsphere with their clinical applications.     

Vibrational dynamics of the organometallic compound triarylorganoantimony (V) SbPh<Subscript>3</Subscript>[O<Subscript>2</Subscript>CC(OH)Ph<Subscript>2</Subscript>]<Subscript>2</Subscript>

A complete normal coordinate analysis was performed for five-coordinate non-rigid triarylantimony diester SbPh₃(O₂CR)₂, known to be a bioactive molecule, using Wilson G-F matrix method and Urey Bradley force field. The study of vibrational dynamics was performed using the concept of group frequencies and band intensities.      

Armatans A and B,New Antimicrobial Isoflavans from Colutea armata

Chemistry of Natural Compounds - Armatans A (1) and B (2), new isoflavans, have been isolated from the EtOAc-soluble fraction of the MeOH extract of Colutea armata Hemsl. &amp; Lace, along with...     

Copper-Catalyzed Regioselective [3+3] Annulations of Alkynyl Ketimines with α-Cyano Ketones: the Synthesis of Polysubstituted 4H-Pyran Derivatives with a CF3-Containing Quaternary Center

Regioselective [3+3] annulation of alkynyl ketimines with α-cyano ketones for the synthesis of polysubstituted 4H-pyran derivatives with a quaternary CF₃-containing center has been realized by using Cu(OAc)₂ as the catalyst. The novel strategy tolerates a wide range of α-CF₃ alkynyl ketimines and α-cyano ketones with both aryl and alkyl substitutents. A preliminary asymmetric synthesis of chiral product 3 has been attempted by using copper and chiral thiourea as the cocatalyst with excellent yields (86-99 %) and good enantioselectivities (71–78 % ee). Furthermore, product 3 aa could be obtained on a gram-scale reaction with 75 % yield and 99 % ee after recrystallization. Several products were also transformed readily. Control experiments indicate that the reaction involves a process with a base-catalyzed or chiral thiourea-catalyzed Mannich-type reaction followed by a highly regioselective copper-catalyzed ring-closing reaction on the alkynyl moiety in a 6-endo-dig fashion.     

A Novel Synthesis and Characterization of Titanium Superoxide and its Application in Organic Oxidative Processes

A novel, exceptionally stable titanium superoxide radical ion was prepared and its structure determined by FTIR, ESR, Raman spectroscopy, X-ray diffraction, thermogravimetric/differential thermal analysis and elemental analysis. This heterogeneous catalyst has been found to be effective for the selective oxidation of aromatic amines and phenols to the corresponding nitro aromatics and p-quinones, respectively. In addition, this non-toxic, inexpensive and reusable catalyst has also been used in aminobromination of olefins, which proceed to give the 1, 2-bromoaminated anti-Markovnikov product. A brief account of these results is summarized in this review.