Some Applications of a Polynomial Inequality to Global Optimization

In this paper, we use the Ehlich-Zeller-Gärtel inequality to derive an algorithm for finding the global minima of polynomials over hyperrectangles as well as to provide a bounding method for the branch-and-bound algorithm. The latter application of the inequality results in an improved algorithm which gives simultaneously a decreasing upper bound and an increasing lower bound for the global minimum at each iteration. The algorithm can be used also to find the Lipschitz constant of a polynomial.     

Chiral copper-bipyridine complexes: Synthesis, characterization and mechanistic studies on asymmetric cyclopropanation

Chiral bipyridine ligands of different steric properties when reacted with CuCl₂ formed orange, yellow or green solids of new copper(II) complexes, [Cu(L)Cl₂] (L = L2-6), in good yield. Together with [Cu(L1)Cl₂], these complexes were characterized in solution by UV-Vis spectroscopy and cyclic voltammetry. The complexes give d-d transitions between 860 and 970 nm, and exhibit one quasi-reversible Cu(II)/Cu(I) couple between +0.405 V and +0.516 V versus NHE. Two of the copper(II) complexes, [Cu(L5)Cl₂] and [Cu(L6)Cl₂], and a copper(I) complex of L1, [Cu(L1)Cl], were characterized by X-ray crystallography. The triflate derivatives of both the Cu(I) and Cu(II) complexes are active catalysts towards the cyclopropanation of ethyl diazoacetate with styrene. The asymmetric induction suffers when the size difference between the alkyl and alkoxyl groups was minimized. The mechanism of the cyclopropanation was studied with kinetic and competition experiments. The rate is first order in catalyst and ethyl diazoacetate, inverse order with styrene and is strongly affected by the counterion.     

Design, synthesis and biological characterization of novel inhibitors of CD38

Human CD38 is a novel multi-functional protein that acts not only as an antigen for B-lymphocyte activation, but also as an enzyme catalyzing the synthesis of a Ca(2+) messenger molecule, cyclic ADP-ribose, from NAD(+). It is well established that this novel Ca(2+) signaling enzyme is responsible for regulating a wide range of physiological functions. Based on the crystal structure of the CD38/NAD(+) complex, we synthesized a series of simplified N-substituted nicotinamide derivatives (Compound 1-14). A number of these compounds exhibited moderate inhibition of the NAD(+) utilizing activity of CD38, with Compound 4 showing the highest potency. The crystal structure of CD38/Compound 4 complex and computer simulation of Compound 7 docking to CD38 show a significant role of the nicotinamide moiety and the distal aromatic group of the compounds for substrate recognition by the active site of CD38. Biologically, we showed that both Compounds 4 and 7 effectively relaxed the agonist-induced contraction of muscle preparations from rats and guinea pigs. This study is a rational design of inhibitors for CD38 that exhibit important physiological effects, and can serve as a model for future drug development.     

Two-photon induced luminescence, singlet oxygen generation, cellular uptake and photocytotoxic properties of amphiphilic Ru(II) polypyridyl-porphyrin conjugates as potential bifunctional photodynamic therapeutic agents

Two Ru(II) polypyridyl-porphyrin and Zn(II) porphyrin conjugates (Ru-L and Ru-Zn-L) have been synthesized and their photophysical properties studied. The two conjugates, which contained a hydrophobic tetraphenylporphyrin L conjugated via an acetylide linker at its β-position with a hydrophilic Ru(II) polypyridyl complex, showed high singlet oxygen quantum yields (>70%) and substantial two-photon absorption cross-sections (~500 GM). Ru-L gave strong emissions at ~660 and ~733 nm through linear or two-photon excitation. Solvatochromism was observed in the fluorescence spectra of Ru-L and Ru-Zn-L, where in less polar solvents (i.e., toluene and dichloromethane) their fluorescence emissions became slightly blue-shifted with a 3-fold reduction in intensity relative to those observed in polar solvents (i.e., acetonitrile and methanol). Cell-based studies of these complex conjugates were conducted using human nasopharyngeal carcinoma HK-1 and cervical carcinoma HeLa cells on which Ru-L showed rapid cellular uptake, low dark-cytotoxicity, and high photo-cytotoxicity. Furthermore, Ru-L can be excited and emits in the "biological window"in vitro, making it a potential potent new generation photodynamic therapeutic agent capable of singlet oxygen generation and in vitro near-infrared emission.     

A mild and efficient palladium-catalyzed cyanation of aryl chlorides with K4[Fe(CN)6

An efficient palladium-catalyzed cyanation of aryl chlorides is established. In the presence of a highly effective Pd/CM-phos catalyst, cyanation of aryl chlorides proceeds at 70 °C in general, which is the mildest reaction temperature achieved so far for this process. Common functional groups such as keto, aldehyde, ester, nitrile and -NH(2), and heterocyclic coupling partners including N-H indoles are well tolerated. Moreover, a sterically hindered nonactivated ortho,ortho-disubstituted electrophile is shown to be a feasible coupling partner in cyanation.     

Palladium-catalyzed oxidative C-H bond coupling of steered acetanilides and aldehydes: a facile access to ortho-acylacetanilides

A palladium-catalyzed oxidative C-H bond functionalization/ortho-acylation of acetanilides using easily accessible aldehyde as the acyl source is described. In the presence of a Pd(TFA)(2) catalyst and tert-butylhydroperoxide at 90 °C in general, an array of ortho-acylacetanilides can be afforded in good yields.     

A versatile palladium catalyst system for Suzuki-Miyaura coupling of alkenyl tosylates and mesylates

A general and effective palladium system for Suzuki-Miyaura coupling of alkenyl electrophiles under mild reaction conditions is reported. With the Pd(OAc)(2)/CM-phos system, a variety of alkenyl tosylates are coupled well with ArB(OH)(2). Moreover, the first successful examples of using alkenyl mesylates in alkenylation are also described.     

Epoxidation of alkenes and oxidation of alcohols with hydrogen peroxide catalyzed by a manganese(V) nitrido complex

The manganese(V) nitrido complex (PPh(4))(2)[Mn(N)(CN)(4)] is an active catalyst for alkene epoxidation and alcohol oxidation using H(2)O(2) as an oxidant. The catalytic oxidation is greatly enhanced by the addition of just one equivalent of acetic acid. The oxidation of ethene by this system has been studied computationally by the DFT method.     

On the Integrability of the Abel and of the Extended Liénard Equations

Acta Mathematicae Applicatae Sinica, English Series - We present some exact integrability cases of the extended Liénard equation y″ + f(y)(y′)n + k(y)(y′)m + g(y)y′ +...     

On Ivády’s bounds for the gamma function and related results

Periodica Mathematica Hungarica - We prove that the inequality $$\begin{aligned} \Gamma (x+1)\le \frac{x^2+\beta }{x+\beta } \end{aligned}$$ holds for all $$x\in [0,1]$$ , $$\beta \ge {\beta...