A Novel Curcumin Arginine Salt: A Solution for Poor Solubility and Potential Anticancer Activities

Curcumin is a natural polyphenolic compound with well-known anticancer properties. Poor solubility and permeability hamper its use as an anticancer pharmaceutical product. In this study, L-arginine, a basic amino acid and a small hydrophilic molecule, was utilized to form a salt with the weak acid curcumin to enhance its solubility and potentiate the anticancer activities of curcumin. Two methods were adopted for the preparation of curcumin: L-arginine salt, namely, physical mixing and coprecipitation. The ion pair or salt was characterized for docking, solubility, DSC, FTIR, XRD, in vitro dissolution, and anticancer activities using MCF7 cell lines. The molecular docking suggested a salt/ion-pair complex between curcumin and L-arginine. Curcumin solubility was increased 335- and 440-fold by curcumin in L-arginine, physical, and co-precipitated mixtures, respectively. Thermal and spectral analyses supported the molecular docking and formation of a salt/ion pair between curcumin and L-arginine. The cytotoxicity of curcumin L-arginine salt significantly improved (p < 0.05) by 1.4-fold, as evidenced by the calculated IC_50%, which was comparable to Taxol (the standard anticancer drug but with common side effects).     

Combinatorial Structure of Schulte’s Chiral Polyhedra

Schulte classified the discrete chiral polyhedra in Euclidean 3-space and showed that they belong to six families. The polyhedra in three of the families have finite faces and the other three families consist of polyhedra with (infinite) helical faces. We show that all the chiral polyhedra with finite faces are combinatorially chiral. However, the chiral polyhedra with helical faces are combinatorially regular. Moreover, any two such polyhedra with helical faces in the same family are isomorphic.     

Depth and Stanley Depth of Multigraded Modules

We study the behavior of depth and Stanley depth along short exact sequences of multigraded modules and under reduction modulo an element.     

Tunable nonlinear beam shaping by non‐collinear interactions

A method is proposed for nonlinear beam shaping, employing a non‐collinear quasi phase‐matched interaction in a crystal whose nonlinear coefficient is encoded by a computer generated hologram pattern. In this method the same axis is used for both satisfying the phase‐matching requirements and encoding the holographic information, the result is a single shaped beam in the generated frequency. This allows to shape beams in one‐dimension using a very simple method to fabricate patterned nonlinear crystals and to shape beams in two‐dimensions with high conversion efficiency. The one‐dimensional case is experimentally demonstrated by converting a fundamental Gaussian beam into Hermite‐Gaussian beams at the second harmonic in a KTiOPO₄ crystal. The two‐dimensional case is demonstrated by generating Hermite‐Gaussian and Laguerre‐Gaussian beams in a stoichiometric lithium tantalate crystal. The suggested scheme enables broad wavelength tuning by simply tilting the crystal.     

Stanley decompositions in localized polynomial rings

We introduce the concept of Stanley decompositions in the localized polynomial ring S _f where f is a product of variables, and we show that the Stanley depth does not decrease upon localization. Furthermore it is shown that for monomial ideals ${J \subset I \subset S_f}$ the number of maximal Stanley spaces in a Stanley decomposition of I/J is an invariant of I/J. For the proof of this result we introduce Hilbert series for ${\mathbb{Z}^n}$ -graded K-vector spaces.     

Nonlinear computer-generated holograms

We propose a novel technique for arbitrary wavefront shaping in quadratic nonlinear crystals by introducing the concept of computer-generated holograms (CGHs) into the nonlinear optical regime. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into the first three Hermite-Gaussian beams at the second harmonic in a stoichiometric lithium tantalate nonlinear crystal, and we characterize its efficiency dependence on the fundamental power and the crystal temperature. Nonlinear CGHs open new possibilities in the fields of nonlinear beam shaping, mode conversion, and beam steering.     

Problems on polytopes, their groups, and realizations

Summary The paper gives a collection of open problems on abstract polytopes that were either presented at the \emph{Polytopes Day in Calgary} or motivated by discussions at the preceding \emph{Workshop on Convex and Abstract Polytopes\/} at the Banff International Research Station in May~2005.     

A procedure to compute prime filtration

Let K be a field, S = K[x ₁, … x _n ] be a polynomial ring in n variables over K and I ⊂ S be an ideal. We give a procedure to compute a prime filtration of S/I. We proceed as in the classical case by constructing an ascending chain of ideals of S starting from I and ending at S. The procedure of this paper is developed and has been implemented in the computer algebra system Singular.     

Tuning the Electrochemical Performance of Titanium Carbide MXene by Controllable In Situ Anodic Oxidation

MXenes are a class of two‐dimensional (2D) transition metal carbides, nitrides and carbonitrides that have shown promise for high‐rate pseudocapacitive energy storage. However, the effects that irreversible oxidation have on the surface chemistry and electrochemical properties of MXenes are still not understood. Here we report on a controlled anodic oxidation method which improves the rate performance of titanium carbide MXene (Ti₃C₂T_x, T_x refers to ‐F, =O, ‐Cl and ‐OH) electrodes in acidic electrolytes. The capacitance retention at 2000 mV s^?1 (with respect to the lowest scan rate of 5 mV s^?1) increases gradually from 38 % to 66 % by tuning the degree of anodic oxidation. At the same time, a loss in the redox behavior of Ti₃C₂T_x is evident at high anodic potentials after oxidation. Several analysis methods are employed to reveal changes in the structure and surface chemistry while simultaneously introducing defects, without compromising electrochemically active sites, are key factors for improving the rate performance of Ti₃C₂T_x. This study demonstrates improvement of the electrochemical performance of MXene electrodes by performing a controlled anodic oxidation.