Topics in Lagrangian and Hamiltonian fluid dynamics : relabeling symmetry and ion-acoustic wave stability

Relabeling symmetries of the Lagrangian action are found for the ideal, compressible fluid and magnetohydrodynamics (MHD). These give rise to conservation laws of potential vorticity (Ertel's theorem) and helicity in the ideal fluid, cross helicity in MHD, and a conservation law for an ideal fluid with three thermodynamic variables. The symmetry that gives rise to Ertel's theorem is generated by an infinite parameter group, and leads to a generalized Bianchi identity. The existence of a more general symmetry is also shown, with dependence on time and space derivatives of the fields, and corresponds to a family of conservation laws associated with the potential vorticity. In the Hamiltonian formalism, Casimir invariants of the noncanonical formulation are directly constructed from the symmetries of the reduction map from Lagrangian to Eulerian variables. Casimir invariants of MHD include a gauge-dependent family of invariants that incorporates magnetic helicity as a special case. Novel examples of finite dimensional, noncanonical Hamiltonian dynamics are also presented: the equations for a magnetic field line flow with a symmetry direction, and Frenet formulas that describe a curve in 3-space. In the study of Lyapunov stability of ion-acoustic waves, existence of negative energy perturbations is found at short wavelengths. The effect of adiabatic, ionic pressure on ion-acoustic waves is investigated, leading to explicit solitary and nonlinear periodic wave solutions for the adiabatic exponent r = 3. In particular, solitary waves are found to exist at any wave speed above Mach number one, without an upper cutoff speed. Negative energy perturbations are found to exist despite the addition of pressure, which prevents the establishment of Lyapunov stability; however the stability of ion-acoustic waves is established in the KdV limit, in a manner far simpler than the proof of KdV soliton stability. It is also shown that the KdV free energy (Benjamin, 1972) is recovered upon evaluating (the negative of) the ion-acoustic free energy at the critical point, in the KdV approximation. Numerical study of an ion-acoustic solitary wave with a negative energy perturbation shows transients with increased perturbation amplitude. The localized perturbation moves to the left in the wave-frame, leaving the solitary wave peak intact, thus indicating that the wave may be stable.Physic

Targeting Estrogen Receptor Sites in Human Breast Cancer Cell Line T47D With Copper Conjugates of Nonsteriodal Anti-inflammatory Drug Derivatives: Antiproliferative Activity of Ketoprofen Derivative and its Copper Complex

A square planar copper complex of derivatized NSAID drug (Ketoprofen thiosemicarbazone [3-benzoyl-α-methyl benzene acetic acid thiosemicarbazone]), is characterized by elemental analysis, spectroscopy, electrochemistry and magnetic susceptibility studies which exhibits dose-dependent and enhanced antiproliferative effects on human breast cancer cell line T47D rich in progesterone receptors

Emerging role of Garcinol, the antioxidant chalcone from Garcinia indica Choisy and its synthetic analogs

Garcinol, harvested from Garcinia indica, has traditionally been used in tropical regions and appreciated for centuries; however its biological properties are only beginning to be elucidated. There is ample data to suggest potent antioxidant properties of this compound which have been used to explain most of its observed biological activities. However, emerging evidence suggests that garcinol could be useful as an anti-cancer agent, and it is increasingly being realized that garcinol is a pleiotropic agent capable of modulating key regulatory cell signaling pathways. Here we have summarized the progress of our current research knowledge on garcinol and its observed biological activities. We have also provided an explanation of observed properties based on its chemical structure and provided an insight into the structure and properties of chalcones, the precursors of garcinol. The available data is promising but more detailed investigations into the various properties of this compound, particularly its anti-cancer activity are urgently needed, and it is our hope that this review will stimulate further research for elucidating and appreciating the value of this nature's wonder agent

Enhanced Antioxidant Activities of Metal Conjugates of Curcumin Derivatives

Antioxidant properties of three Curcumin derivatives in which the 1,3-diketone system is appended with nitrogen and sulfur donors and their copper conjugates are examined for the first time. Metal conjugation seems to offer distinct advantages in radical scavenging activities of curcumin compounds

Hydroxynaphthoquinone Metal Complexes as Antitumor Agents X: Synthesis, Structure, Spectroscopy and In Vitro Antitumor Activity of 3-Methyl-Phenylazo Lawsone Derivatives and Their Metal Complexes Against Human Breast Cancer Cell Line MCF-7

The C-3 substituted phenylazo derivatives of lawsone (2-hydroxy-l,4 p-naphthoquinone, III) were synthesized and characterized. The X-ray crystal structure was determined for the ligand 3-(3′-methyl phenylazo) lawsone. The copper complexes of these derivatives were found to possess 1:2 metal stoichiometry and square planar geometries with intermolecular stackings, resulting in antiferromagnetic exchange interactions. The in vitro activity of all the synthesized compounds was examined against human breast cancer cell-line, MCF-7, which revealed enhanced activities for the metal complexes, the highest activity being observed for the copper compound of 3-(3′-methyl phenylazo) lawsone

Synthesis and Characterization of Coordinatively Unsaturated Copper (II) Complexes of 1,3-Bis(2'-Pyridyl)-1,2-Diaza-2-Butene and Their Antityrosinase Activity

The coordinatively unsaturated copper (II) complexes of 1,3-bis(2'-pyridyl)-1,2-diaza-2- butene with different ancillary anions were synthesized which can bind to copper centers of tyrosinase enzyme. The compounds were found to exhibit inhibitory activities against mushroom tyrosinase and the nature and extent of inhibition is modulated according to the type of ancillary anions

Hormone Anchored Metal Complexes. 1. Synthesis, Structure, Spectroscopy and In Vitro Antitumor Activity of Testosterone Acetate Thiosemicarbazone and its Metal Complexes

Testosterone acetate thiosemicarbazone (TATSC, 17-β-hydroxyandrost-4-one acetate thiosemicarbazone) was synthesized and characterized by single crystal X-ray structure determination. The copper and platinum complexes of this steroid derivative were synthesized and characterized by spectroscopy and electrochemiatry. The in vitro activity of these compounds against human breast cancer cell line MCF-7 was tested. The highest activity was found for the [Pt(TATSC)Cl1] followed by [Cu(TATSC)Cl2] and the ligand in compariosn with cisplatin

Molecular docking and inhibition of matrix metalloproteinase-2 by novel difluorinatedbenzylidene curcumin analog

We recently described the synthesis and characterization of a novel difluorinatedbenzylidene analog of curcumin, commonly referred as CDF, which demonstrated significantly enhanced bioavailability and in vivo anticancer activity. CDF targets many factors similar to curcumin, albeit with more potency, as reported previously. To further highlight this differential behavior of CDF, we chose matrix metalloproteinase protein MMP-2 which is involved in the processes of invasion and metastasis of human tumors. Both curcumin and CDF were characterized for their binding characteristics using in silico docking studies; they were also evaluated via biological assays involving gelatin zymography, miRNA analysis, invasion assays and ELISA. CDF was found to inhibit MMP-2 expression and activity in A549 and H1299 NSCLC cells much more effectively than curcumin, validating molecular modeling results. miR-874, an MMP-2-targeting miRNA, was up-regulated by CDF. Thus, it appears that CDF can inhibit MMP-2 through multiple mechanisms. Our results are suggestive of a more potent inhibition of invasion and metastasis by CDF, compared to curcumin, thus warranting its further evaluation as an effective anticancer agent

PAMAM Dendrimers as Promising Nanocarriers for RNAi Therapeutics

Therapeutics based on RNA interference mechanisms are highly promising for the management of several diseases including multi-drug resistant cancers. However, effective delivery of siRNAs and oligonucleotides still remains challenging. In this regard, hyper-branched, PAMAM dendrimers having unique three-dimensional architecture and nanoscale size, with cationic surface charge can potentially serve as siRNA condensing agents as well as robust nano-vectors for targeted delivery. In addition, their surface functionality permits conjugation of drugs and genes or development of hybrid systems for combination therapy. Thus far, in vitro cellular testing of dendrimer-mediated siRNA delivery has revealed great potential, with reports on their in vivo effectiveness starting to appear. These favorable outcomes portend a promising future for dendrimer mediated RNAi therapeutics