A collocation method for systems of nonlinear ordinary differential equations

A collocation method based on piecewise polynomials is applied to boundary value problems for mth order systems of nonlinear ordinary differential equations. Optimal a priori estimates are obtained for the error of approximation in the maximum norm and superconvergence is verified at particular points.     

Ziziphus nummularia Attenuates the Malignant Phenotype of Human Pancreatic Cancer Cells: Role of ROS

Pancreatic cancer (PC) is the fourth leading cause of all cancer-related deaths. Despite major improvements in treating PC, low survival rate remains a major challenge, indicating the need for alternative approaches, including herbal medicine. Among medicinal plants is Ziziphus nummularia (family Rhamnaceae), which is a thorny shrub rich in bioactive molecules. Leaves of Ziziphus nummularia have been used to treat many pathological conditions, including cancer. However, their effects on human PC are still unknown. Here, we show that the treatment of human pancreatic ductal adenocarcinoma cells (Capan-2) with Ziziphus nummularia ethanolic extract (ZNE) (100–300 μg/mL) attenuated cell proliferation in a time- and concentration-dependent manner. Pretreatment with N-acetylcysteine, an ROS scavenger, attenuated the anti-proliferative effect of ZNE. In addition, ZNE significantly decreased the migratory and invasive capacity of Capan-2 with a concomitant downregulation of integrin α₂ and increased cell–cell aggregation. In addition, ZNE inhibited in ovo angiogenesis as well as reduced VEGF and nitric oxide levels. Furthermore, ZNE downregulated the ERK1/2 and NF-κB signaling pathways, which are known to drive tumorigenic and metastatic events. Taken together, our results suggest that ZNE can attenuate the malignant phenotype of Capan-2 by inhibiting hallmarks of PC. Our data also provide evidence for the potential anticancer effect of Ziziphus nummularia, which may represent a new resource of novel anticancer compounds, especially ones that can be utilized for the management of PC.     

Pairwise epistemic conditions for correlated rationalizability

We provide a foundation for correlated rationalizability by means of pairwise epistemic conditions imposed only on some pairs of players. Indeed, we show that pairwise mutual belief, for some pairs of players, of (i) the game payoffs, (ii) rationality, and (iii) deeming possible only strategy profiles that receive positive probability by the actual conjectures suffice for correlated rationalizability when there is a common prior. Moreover, we show that our epistemic conditions do not require nor imply mutual belief of rationality. Finally, we discuss the relationship between correlated rationalizability and Nash equilibrium on the basis of the respective pairwise epistemic conditions for each of the two concepts.     

A fuzzy difference equation with an application

Difference equations arise in the modeling of many interesting problems. “Measurements” of data or specified information for an underlying problem may be imprecise or only partially specified. This motivates us to initiate a study of “fuzzy difference equations.” In this paper, we will formulate and solve a given difference equation in the fuzzy setting and give a general method for dealing with any first order difference equation.     

A short and convenient chemical route to optically pure 2-methyl chromanmethanols. Total asymmetric synthesis of beta-, gamma-, and delta-tocotrienols

With use of inexpensive commercially available raw materials, chromanmethanol precursors to the natural beta-, gamma-, and delta-tocotrienols have been prepared in high yield. Enzymatic resolution afforded chiral chromanmethanols in high enantiomeric excess. Subsequent attachment of the farnesyl side chain was high yielding, thus allowing the preparation of asymmetric beta-, gamma-, and delta-tocotrienols in one final step wherein simultaneous deprotection of the phenol and removal of the sulfone group occurs. This chemistry provides the first synthesis of natural-series beta-tocotrienol.     

Effects of protonation on the spectroscopic properties of tetrapyridoacridine (TPAC) mono- and dinuclear Ru(II) complexes in their ground and (3)MLCT excited states

The spectroscopic behavior of mono- and dinuclear Ru(II) complexes (P, T, PP and TT, Figure 1) that contain the extended planar ligand tetrapyrido[3,2-a:2',3'-c:3' ',2' '-h:2' ',3' '-j]acridine (TPAC) and either 1,10-phenanthroline (phen) or 1,4,5,8-tetraazaphenanthrene (tap) as ancillary ligands is examined in water and as a function of the pH. These four complexes luminesce in aqueous solution. The analyses of the data in absorption lead to the pKa values in the ground state, and the data in emission show that the excited 3MLCT states are much more basic than the ground state. When the complex contains tap ligands (T and TT), a decrease in pH transforms the luminescent excited basic form into another luminescent excited protonated species, which emits more bathochromically. In contrast, with phen ancillary ligands (P and PP), the protonated excited state does not luminesce. The rate constant of first protonation of the 3MLCT state is diffusion controlled, except for the dinuclear PP complex, whose protonation takes place on the nitrogen of the acridine motif. For P, in which the protonation process is the fastest, it would take place on the nitrogen atoms of the nonchelated phen moiety of the TPAC ligand. These results allow also us to gain information on the localization of the excited electron in the 1MLCT state populated upon absorption as well as in the relaxed 3MLCT emissive state. Moreover as these complexes are interesting for their study with DNA, it can be concluded from these data that a portion of the excited species in interaction with DNA will be protonated.     

Spherulitic growth of hen egg-white lysozyme crystals

In protein crystallography, spherulites are considered the result of a failed crystallization experiment. Understanding the formation of these structures may contribute to finding methods to prevent their formation. Here, we present an in situ study on lysozyme spherulites grown from sodium nitrate and sodium thiocyanate solutions, investigating their morphology and growth kinetics using optical microscopy. In a morphodrom, we indicate the conditions at which spherulites form for the lysozyme-nitrate system, showing that liquid-liquid phase separation is not a prerequisite to form sheaflike spherulites and that supersaturation is not the only factor determining their creation. Despite their sheaflike morphology, the spherulites all appear to be formed through heterogeneous nucleation. The spherulites are of a new polymorphic form and are less stable than the monoclinic form. For a single needle, growth kinetics indicate surface processes to be the rate-limiting step during growth, but for an entire spherulite volume, diffusion still plays a role. Spherulites simulated by using a time-dependent, tip-splitting model are found to compare well to experimentally observed spherulites.