syn/anti Diastereoselectivity in the Aldol Reaction of Aldehydes with the C(3) Carbanion of 1,3‐Dihydro‐2H‐1,4‐benzodiazepin‐2‐one

The aldol reaction of the C(3) carbanion of 7‐chloro‐1,3‐dihydro‐1‐methyl‐5‐phenyl‐2H‐1,4‐benzodiazepin‐2‐one ( 2 ) with a series of aromatic and aliphatic aldehydes at −78° afforded threo/erythro diastereoisomers 3 – 16 of 7‐chloro‐1,3‐dihydro‐3‐(hydroxymethyl)‐1‐methyl‐5‐phenyl‐2H‐1,4‐benzodiazepinones, substituted at the C(3) side chain, in a ratio from 55 : 45 to 94 : 6 (Scheme 1). Lewis acids exhibited limited effect on the syn/anti diastereoselectivity of this reaction, and kinetic control of the reaction was confirmed. ¹H‐NMR Data suggested the assignment of the threo relative configuration to the first‐eluted diastereoisomers 3 , 5 , 7 , and 9 on reversed‐phase HPLC, and the erythro configuration to the second‐eluted counterparts 4 , 6 , 8 , and 10 , respectively. The structures and relative configurations threo and erythro of the diastereoisomers 5 and 6 , respectively, were established by single‐crystal X‐ray analysis, confirming the assignment based on the ¹H‐NMR data. A tentative mechanistic explanation of the diastereoselectivity invokes the enolate anion of 1,3‐dihydro‐2H‐1,4‐benzodiazepin‐2‐one as the reactive species (Scheme 2). Acid‐catalyzed hydrolytic ring opening of 3 afforded threo‐β‐hydroxy‐phenylalanine 17 , whereas from 4 , the N‐(benzyloxy)carbonyl derivative 18 of erythro‐β‐hydroxy‐phenylalanine was obtained (Scheme 3); in both cases, neither elimination of H₂O from the C(3)−CHOH moiety nor epimerization at C(3) were observed. This result opens a new pathway to various configurationally uniform α‐amino‐β‐hydroxy carboxylic acids and their congeners of biological importance.     

Coumarin-Palladium(II) Complex Acts as a Potent and Non-Toxic Anticancer Agent against Pancreatic Carcinoma Cells

Pancreatic carcinoma still represents one of the most lethal malignant diseases in the world although some progress has been made in treating the disease in the past decades. Current multi-agent treatment options have improved the overall survival of patients, however, more effective treatment strategies are still needed. In this paper we have characterized the anticancer potential of coumarin-palladium(II) complex against pancreatic carcinoma cells. Cells viability, colony formation and migratory potential of pancreatic carcinoma cells were assessed in vitro, followed by evaluation of apoptosis induction and in vivo testing on zebrafish. Presented results showed remarkable reduction in pancreatic carcinoma cells growth both in vitro and in vivo, being effective at micromolar concentrations (0.5 μM). Treatments induced apoptosis, increased BAX/BCL-2 ratio and suppressed the expression of SOX9 and SOX18, genes shown to be significantly up-regulated in pancreatic ductal adenocarcinoma. Importantly, treatments of the zebrafish-pancreatic adenocarcinoma xenografts resulted in significant reduction in tumor mass, without provoking any adverse toxic effects including hepatotoxicity. Presented results indicate the great potential of the tested compound and the perspective of its further development towards pancreatic cancer therapy.     

Influence of surface modified TiO2 nanoparticles by gallates on the properties of PMMA/TiO2 nanocomposites

Nanocomposites based on poly(methyl methacrylate) (PMMA) and TiO₂ nanoparticles were synthesized by in situ radical polymerization of MMA in solution. The surface of TiO₂ nanoparticles was modified with four gallic acid esters (octyl, decyl, lauryl and cetyl gallate). The content of gallates present on the surface of TiO₂ was calculated from the TGA results. The influence of length of hydrophobic tail of amphiphilic alkyl gallates on dispersability of surface modified TiO₂ nanoparticles in PMMA matrix, the molecular weight and glass transition temperature of PMMA, as well as the thermal stability of the prepared PMMA/TiO₂ nanocomposites in nitrogen and air was investigated. The influence of content of TiO₂ nanoparticles on the properties of these nanocomposites was also examined. The formation of a charge transfer complex between the surface Ti atoms and the gallates was confirmed by FTIR and UV spectroscopy. TEM micrographs of the PMMA/TiO₂ nanocomposites revealed that degree of TiO₂ aggregation can be significantly lowered by increasing the length of aliphatic part of the used gallates. The molecular weight of PMMA slightly decreases with the increase of TiO₂ content, indicating that used TiO₂ nanoparticles act as radical scavengers during the polymerization of MMA. The presence of surface modified TiO₂ nanoparticles do not have an influence on the mobility of PMMA chain segments leading to the same values of glass transition temperature for all investigated samples. Thermal and thermo-oxidative stability of the PMMA matrix are improved by introducing TiO₂ nanoparticles modified with gallates.     

Dynamical stability of the response of oscillators with discontinuous or steep first derivative of restoring characteristic

The influence of factors which can lead to incorrect prediction of dynamical stability of the periodic response of oscillators which contain a non-linear restoring characteristic with discontinuous or steep first derivative is considered in this paper. For that purpose, a simple one degree-of-freedom system with a piecewise-linear force-displacement relationship subjected to a harmonic excitation is analysed. Stability of the periodic response obtained in the frequency domain by the incremental harmonic balance method is determined by using the Floquet–Liapounov theorem. Responses in the time domain are obtained by digital simulation. The accuracy of determining the eigenvalues of the monodromy matrix (in the considered example) significantly depend on the corrective vector norm r , the accuracy of numerical determination of the times when the system undergoes a stiffness change, and on the number of step functions M (used in the Hsu's procedure), only for r >1×10⁻⁵,>1×10⁻⁵ and M<2000. Otherwise, except if the maximum modulus of the eigenvalues of the monodromy matrix is very close to unity, their influence on estimation of dynamical stability is minor. On the contrary, neglecting very small harmonic terms of the actual time domain response can cause a very large error in the evaluation of the eigenvalues of the monodromy matrix, and so they can lead to incorrect prediction of the dynamical stability of the solution, regardless of whether the maximum modulus of the eigenvalues of the monodromy matrix is close to unity or not.     

Concentration effects on irreversible colloid cluster aggregation and gelation of silica dispersions

Effects of particle concentration on the irreversible aggregation of colloidal silica are studied using in situ destabilization via the ionic strength increase derived from the enzymatic hydrolysis of urea by urease. Aggregation is monitored by time-resolved optical density and dynamic light scattering measurements. It terminates at a gel boundary, signaled by a prominent increase of the optical density and incipient non-ergodicity. Raman scattering is used to demonstrate that the enzymatic reaction continues, well beyond gelation for the compositions studied here, until the urea is consumed. Calibration of the ionic conductivity permits for constructing stability diagrams in terms of particle and salt concentration. As with reversible gelation, the process exhibits a collective character in that lower ionic strengths are required for gelation of concentrated dispersions and vice versa. However, light scattering demonstrates that the gel boundary is preceded here by a line marking the transition from reversible to irreversible cluster formation, with the two transition boundaries tracking each other. Comparisons are made with dispersions destabilized by direct addition of salt solutions, which gel under very different conditions.     

Graphs for small multiprocessor interconnection networks

Let D be the diameter of a graph G and let λ₁ be the largest eigenvalue of its (0, 1)-adjacency matrix. We give a proof of the fact that there are exactly 69 non-trivial connected graphs with (D + 1)λ₁ ? 9. These 69 graphs all have up to 10 vertices and were recently found to be suitable models for small multiprocessor interconnection networks. We also examine the suitability of integral graphs to model multiprocessor interconnection networks, especially with respect to the load balancing problem. In addition, we classify integral graphs with small values of (D + 1)λ₁ in connection with the load balancing problem for multiprocessor systems.     

A mixed integer linear programming formulation of the maximum betweenness problem

This paper considers the maximum betweenness problem. A new mixed integer linear programming (MILP) formulation is presented and validity of this formulation is given. Experimental results are performed on randomly generated instances from the literature. The results of CPLEX solver, based on the proposed MILP formulation, are compared with results obtained by total enumeration technique. The results show that CPLEX optimally solves instances of up to 30 elements and 60 triples in a short period of time.     

Karamata functions and differential equations: Achievements from the 20th century

This paper presents the major achievements of the 20th century regarding Karamata functions and the theory of differential equations, made mostly by V. Mari?, M. Tomi?, E. Omey, J.L. Geluk. The connection between these notions was first noticed by V.G. Avakumovi? (1910–1990). Slowly and regularly varying functions were introduced by J. Karamata (1902–1967). A group of mathematicians from the Karamata School of classical mathematical analysis were pioneers in research on these functions and their role in the theory of differential equations. Special attentions is given to the study of the Thomas–Fermi, Emden–Fowler and Friedmann equations, as well as the classical second order linear differential equations.