Some research problems on the hadamard product and singular values of matrices

We pose some problems on the Hadamard product and singular values of matrices.     

Synthesis of lodopyridone

The total synthesis of the unusual 4-pyridone marine metabolite lodopyridone has been achieved by late stage manipulation of the related 4-pyrone. Key reactions include a Suzuki–Miyaura coupling to form the tetracyclic core and a modified Corey–Ganem–Gilman reaction to install the ethanolamide side-chain.     

Unital affine semigroups

Affine semigroups are convex sets on which there exists an associative binary operation which is affine separately in either variable. They were introduced by Cohen and Collins in 1959. We look at examples of affine semigroups which are of interest to matrix and operator theory and we prove some new results on the extreme points and the absorbing elements of certain types of affine semigroups. Most notably we improve a result of Wendel that every invertible element in a compact affine semigroup is extreme by extending this result to linearly bounded affine semigroups.     

Approximations for interactive Markov chains in discrete and continuous time

A class of models called interactive Markov chains is studied in both discrete and continuous time. These models were introduced by Conlisk and serve as a rich class for sociological modeling, because they allow for interactions among individuals. In discrete time, it is proved that the Markovian processes converge to a deterministic process almost surely as the population size becomes infinite. More importantly, the normalized process is shown to be asymptotically normal with specified mean vector and covariance matrix. In continuous time, the chain is shown to converge weakly to a diffusion process with specified drift and scale terms. The distributional results will allow for the construction of a likelihood function from interactive Markov chain data, so these results will be important for questions of statistical inference. An example from manpower planning is given which indicates the use of this theory in constructing and evaluating control policies for certain social systems.     

Enantioselective Cross-couplings between Halide Derivatives and Organometallics by Using Iron and Cobalt Catalysts: Formation of C−C Bonds

This review highlights the recent achievements of iron- and cobalt-catalyzed enantioselective cross-couplings of halide derivatives with organometallic reagents for the construction of C-C bonds. Synthetic applications of enantioselective cross-couplings to natural products and biologically active compounds are also covered showing the power of these cross-couplings in organic synthesis.     

A trotter product formula for random matrices

This note contains a generalization of the Trotter product formula to the setting of multiple linear systems of stochastic differential equations. From the result it follows that the solution of a system in Stratonovich form in a Lie algebra lies in the corresponding Lie group     

Available-To-Promise modeling for multi-plant manufacturing characterized by lack of homogeneity in the product: An illustration of a ceramic case

Lack of homogeneity in the product (LHP) appears in some production processes which incorporate raw materials that originate directly from nature and/or production processes with operations that confer heterogeneity to the characteristics of the outputs obtained, even when the inputs used are homogeneous. Poor LHP management may have a very negative impact on the customer service level and on the supply chains’ operation costs, especially when the customer needs to be served with homogeneous units of one same product. One of the key processes for suitable LHP management is the order-promising process. This work presents a mathematical programming order-promising model for make-to-stock environments with LHP. The model considers two objectives placed within a single objective by the weighted sum method. For the purpose of testing the validity of the proposed model and to evaluate the characteristics of the solutions obtained in different scenarios, numerical experiments based on realistic data from a ceramic tile company have been conducted. The results show that better results are obtained for the defined performance measures if multiple objectives are considered when promising orders than the single objective of maximizing profits. Furthermore, the superiority of the results obtained from the proposed model, if compared with current company practice, proves the model’s utility.     

Antioxidant product analysis of Folium Hibisci Mutabilis

Folium Hibisci Mutabilis, a new member of Chinese Pharmacopoeia, can treat some diseases induced by reactive oxygen species. The study prepared a lyophilized aqueous extract of Folium Hibisci Mutabilis (LAFHM). LAFHM was found to enrich eight flavonoids (i.e., quercetin, luteolin, hyperoside, isoquercitrin, rutin, kaempferol, tiliroside, and vitexin) by HPLC analysis. These flavonoids were further compared using antioxidant assays, where triliroside and vitexin always exhibited higher IC₅₀ values than the others. In ultra-performance liquid chromatography coupled with electrospray ionization quadrupole time-of-flight tandem mass spectrometry analysis, these flavonoids could basically give two characteristic m/z values (226 and 196) and their corresponding double m/z values (i.e., 602, 570, 926, 926, 570, 1186, and 862), when treated by 1,1-diphenyl-2-picryl-hydrazl radical (DPPH^?). Finally, the coupling products of DPPH^?-treated triliroside were investigated using computational chemistry. It was found that the –OH in para-coumaroyl moiety to have the lowest bond disassociation energy among all phenolic -OHs in the triliroside. In conclusion, Folium Hibisci Mutabilis contains the above eight antioxidant flavonoids. Despite of the different antioxidant levels, they can generally produce flavonoid-radical coupling product and flavonoid-flavonoid homodimer during antioxidant process. Especially, tiliroside uses para-coumaroyl as linker to construct a tiliroside-radical coupling product at the meta-carbon atom.     

Ion Product of Pure Water Characterized by Physics-Based Water Model

Pure water has been characterized for nearly a century, by its dissociation into hydronium (H₃O)¹⁺ and hydroxide (HO)^1- ions. As a chemical equilibrium reaction, the equilibrium constant, known as the ion product or the product of the equilibrium concentration of the two ion species, has been extensively measured by chemists over the liquid water temper-ature and pressure range. The experimental data have been nonlinear least-squares fitted to chemical thermodynamic-based equilibrium equations, which have been accepted as the industrial standard for 35 years. In this study, a new and statistical-physics-based water ion product equation is presented, in which, the ions are the positively charged protons and the negatively charged proton-holes or prohols. Nonlinear least squares fits of our equation to the experimental data in the 0-100 ℃ pure liquid water range, give a factor of two better precision than the 35-year industrial standard.