On Word Equations Originated from Discrete Dynamical Systems Related to Antisymmetric Cubic Maps with Some Applications

In this article, we solve some word equations originated from discrete dynamical systems related to antisymmetric cubic map. These equations emerge when we work with primitive and greatest words. In particular, we characterize all the cases for which <β₁β₁>=<β₂β₂> where β₁ and β₂ are the greatest words in <<β₁>> and <<β₂>> of M(n).     

Asymptotic Behavior of the Stock Price Distribution Density and Implied Volatility in Stochastic Volatility Models

We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process and the density of the stock price process in the Stein-Stein and the Heston model. We find explicit formulas for leading terms in asymptotic expansions of these densities and give error estimates. As an application of our results, sharp asymptotic formulas for the implied volatility in the Stein-Stein and the Heston model are obtained.     

Direct probing of sorbent-solvent interactions for amylose tris(3,5-dimethylphenylcarbamate) using infrared spectroscopy, X-ray diffraction, solid-state NMR, and DFT modeling

The sorbent-solvent interactions for amylose tris(3, 5-dimethylphenylcarbamate) (ADMPC) with five commonly used solvents, hexane, methanol, ethanol, 2-propanol (IPA), and acetonitrile (ACN), are studied using attenuated total reflection infrared spectroscopy (ATR-IR) of thin sorbent films, X-ray diffraction (XRD) of thin films, (13)C cross polarization/magic angle spinning (CP/MAS) and MAS solid state NMR of polymer-coated silica beads (commercially termed "Chiralpak AD"), and DFT modeling. The ADMPC-polymer-coated silica beads are used commercially for analytical and preparative scale separations of chiral enantiomers. The polymer forms helical rods with intra- and inter-rod hydrogen bonds (H-bonds). There are various nm-sized cavities formed between the polymer side-chains and rods. The changes in the H-bonding states of the C=O and NH groups of the polymer upon absorption of each of the five solvents at 25 degrees C are determined with ATR-IR. The IR wavenumbers, the H-bonding interaction energies, and the H-bonding distances of the polymer side-chains with each of the solvent molecules are predicted using the DFT/B3LYP/6-311+g(d,p) level of theory. The changes in the polymer crystallinity upon absorption of each solvent are characterized with XRD. The changes in the polymer crystallinity and the H-bonding states of C=O groups are also probed with (13)C CP/MAS solid-state NMR. The changes in the polymer side-chain mobility are detected using (13)C MAS solid-state NMR. The H-bonding states of the polymer change upon absorption of each polar solvent and usually result in an increase in the polymer crystallinity and the side-chain mobility. The polymer rods are reorganized upon solvent absorption, and the distance between the rods increases with the increase in the solvent molecular size. These results have implications for understanding the role of the solvent in modifying the structure and behavior of the polymer sorbents.     

On the Topology of Real Algebraic Plane Curves

We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and critical points, is also relevant. A challenge is to compute efficiently this information for the given coordinate system even if the curve is not in generic position. Previous methods based on the cylindrical algebraic decomposition use sub-resultant sequences and computations with polynomials with algebraic coefficients. A novelty of our approach is to replace these tools by Gröbner basis computations and isolation with rational univariate representations. This has the advantage of avoiding computations with polynomials with algebraic coefficients, even in non-generic positions. Our algorithm isolates critical points in boxes and computes a decomposition of the plane by rectangular boxes. This decomposition also induces a new approach for computing an arrangement of polylines isotopic to the input curve. We also present an analysis of the complexity of our algorithm. An implementation of our algorithm demonstrates its efficiency, in particular on high-degree non-generic curves.     

On the Asymptotic Depth of Multigraded Modules

The aim of this article is to establish, among other results, the asymptotic stability of the depth of the graded pieces of a nonstandard multigraded module. As a corollary, we get the asymptotic stability of the depth of the graded pieces of the multigraded Rees algebra defined by a finite set of ideals and their associated multigraded rings.     

On the Analytic Type of Artin Algebras

In this paper we give a complete analytic classification of Artin Gorenstein almost stretched algebras, i.e., Artin Gorenstein algebras with Hilbert function {1, n, 2,…, 2, 1,…, 1}.     

Electrochemical and photochemical approaches for the synthesis of the C28–C38 fragment of okadaic acid

Okadaic acid, a potent and selective inhibitor of Protein Phosphatases 1 and 2A (PP1 and PP2A), is widely used as a probe for various biochemical processes. We describe herein two innovative methods for the synthesis of the terminal C28–C38 fragment of the natural polyether. Suárez photochemical oxidative cyclization and electrochemical oxidation of malonates to their ketals equivalents have been successfully applied for the assembly of the key spiroketal core.     

Visible-Light Augmented Lithium Storage Capacity in a Ruthenium(II) Photosensitizer Conjugated with a Dione-Catechol Redox Couple

Controlling redox activity of judiciously appended redox units on a photo-sensitive molecular core is an effective strategy for visible light energy harvesting and storage. The first example of a photosensitizer - electron donor coordination compound in which the photoinduced electron transfer step is used for light to electrical energy conversion and storage is reported. A photo-responsive Ru-diimine module conjugated with redox-active catechol groups in [Ru(II)(phenanthroline-5,6-diolate)₃]⁴⁻ photosensitizer can mediate photoinduced catechol to dione oxidation in the presence of a sacrificial electron acceptor or at the surface of an electrode. Under potentiostatic condition, visible light triggered current density enhancement confirmed the light harvesting ability of this photosensitizer. Upon implementation in galvanostatic charge-discharge of a Li battery configuration, the storage capacity was found to be increased by 100 %, under 470 nm illumination with output power of 4.0 mW/cm⁻². This proof-of-concept molecular system marks an important milestone towards a new generation of molecular photo-rechargeable materials.     

A Catalyst and Solvent Free Route for the Synthesis of N-Substituted Pyrrolidones from Levulinic Acid

An efficient, metal-free, catalyst-free and solvent-free methodology for the reductive amination of levulinic acid with different anilines has been developed using HBpin as the reducing reagent. This protocol offers an excellent method to avoid solvents and added catalysts on the synthesis of different kinds of N-substituted pyrrolidones under metal free conditions. It is also the first report for the synthesis of different pyrrolidones by solvent-free as well as catalyst-free methods. The proposed mechanism for the formation of pyrrolidone has been supported by DFT calculations and control experiments.