On the Fibonacci and Lucas p-numbers, their sums, families of bipartite graphs and permanents of certain matrices

In this paper we consider certain generalizations of the well-known Fibonacci and Lucas numbers, the generalized Fibonacci and Lucas p-numbers. We give relationships between the generalized Fibonacci p-numbers, F_p(n), and their sums, , and the 1-factors of a class of bipartite graphs. Further we determine certain matrices whose permanents generate the Lucas p-numbers and their sums.     

Synthesis, characterization and electro-spectroelectrochemical studies of four macrocyclic Schiff-base Co(II) complexes having N2O2 set of donor atoms

Four macrocyclic Schiff-base cobalt complexes, [CoL¹][NO₃]₂ · 3H₂O, [CoL²][NO₃]₂ · 4H₂O, [CoL³][NO₃]₂ · 4H₂O and [CoL⁴][NO₃]₂ · 2H₂O, were synthesized by reaction of salicylaldehyde derivatives with 1,4-bis(3-aminopropoxy)butane or (±)-trans-1,2-diaminocyclohexane and Co(NO₃)₂ · 6H₂O by template effect in methanol. The metals to ligand ratio of the complexes were found to be 1:1. The Co(II) complexes are proposed to be tetrahedral geometry. The macrocyclic Co(II) complexes are 1:2 electrolytes as shown by their molar conductivities (Λ_M) in DMF (dimethyl formamide) at 10^?3 M. The structure of Co(II) complexes is proposed from elemental analysis, Ft-IR, UV–visible spectra, magnetic susceptibility, molar conductivity measurements and mass spectra. Electrochemical and thin-layer spectroelectrochemical studies of the complexes were comparatively studied in the same experimental conditions. The electrochemical results revealed that all complexes displayed irreversible one reduction processes and their cathodic peak potential values (E _pc) were observed in around of ?1.14 to 0.95 V. It was also seen that [CoL¹][NO₃]₂ · 3H₂O and [CoL²][NO₃]₂ · 4H₂O exhibited one cathodic wave without corresponding anodic wave but, [CoL³][NO₃]₂ · 4H₂O and [CoL⁴][NO₃]₂ · 2H₂O showed one cathodic wave with corresponding anodic wave, probably due to the presence of different ligand nature even if the complexes have the same N₂O₂ donor set. In view of spectroelectrochemical studies [CoL³][NO₃]₂ · 4H₂O showed distinctive spectral changes in which the intensity of the band (λ = at 316 nm, assigned to n → π* transitions) decreased and a new broad band in a low intensity about 391 nm appeared as a result of the reduction process based on the cobalt center in the complex.     

Protein-template-driven formation of polynuclear iron species

Ferritins are iron-storage proteins capable of holding up to 4500 Fe(3+) ions within a single water-soluble protein shell made from 24 polypeptide chains. The Glu128Arg/Glu135Arg mutants of Escherichia coli and Rhodobacter capsulatus bacterioferritins are unable to associate into 24-meric structures, with dimers of polypeptide chains being their stable forms. The aerobic addition to these of up to 8-10 or 14-20 Fe(2+) ions per dimer, respectively, results in the oxidation of the added Fe(2+) to Fe(3+). Gel permeation chromatography and sedimentation equilibrium studies confirm that the Fe(3+) ions are associated with the polypeptide dimer, and the lack of intense EPR signals from magnetically isolated Fe(3+) ions confirms the formation of one or more antiferromagnetically coupled clusters of Fe(3+) ions. The effect of Fe(3+) chelators on iron-loaded subunit dimers is to remove the Fe(3+) from the protein, but to do so slowly, consistent with it not being merely adventitiously associated with protein. These data provide experimental support for the presence of nucleation centers for the mineral cores in bacterioferritins and indicate that these proteins are not simply acting as vessels in which hydrolysis of Fe(3+) occurs independent from the protein surface. From analyses of X-ray structures and amino acid sequence comparisons, possible nucleation sites are identified.     

Engineering reversible cell–cell interactions using enzymatically lipidated chemically self-assembled nanorings

Multicellular biology is dependent on the control of cell–cell interactions. These concepts have begun to be exploited for engineering of cell-based therapies. Herein, we detail the use of a multivalent lipidated scaffold for the rapid and reversible manipulation of cell–cell interactions. Chemically self-assembled nanorings (CSANs) are formed via the oligomerization of bivalent dihydrofolate reductase (DHFR²) fusion proteins using a chemical dimerizer, bis-methotrexate. With targeting proteins fused onto the DHFR² monomers, the CSANs can target specific cellular antigens. Here, anti-EGFR or anti-EpCAM fibronectin-DHFR² monomers incorporating a CAAX-box sequence were enzymatically prenylated, then assembled into the corresponding CSANs. Both farnesylated and geranylgeranylated CSANs efficiently modified the cell surface of lymphocytes and remained bound to the cell surface with a half-life of >3 days. Co-localization studies revealed a preference for the prenylated nanorings to associate with lipid rafts. The presence of antigen targeting elements in these bifunctional constructs enabled them to specifically interact with target cells while treatment with trimethoprim resulted in rapid CSAN disassembly and termination of the cell–cell interactions. Hence, we were able to determine that activated PBMCs modified with the prenylated CSANs caused irreversible selective cytotoxicity toward EGFR-expressing cells within 2 hours without direct engagement of CD3. The ability to disassemble these nanostructures in a temporally controlled manner provides a unique platform for studying cell–cell interactions and T cell-mediated cytotoxicity. Overall, antigen-targeted prenylated CSANs provide a general approach for the regulation of specific cell–cell interactions and will be valuable for a plethora of fundamental and therapeutic applications.

Multicellular biology is dependent on the control of cell-cell interactions. The prenylated antigen-targeted CSANs provide a general approach for the regulation of specific cell-cell interactions and will be valuable for a plethora of fundamental and therapeutic applications.     

Synthesis, Spectroscopic and Electrochemical Investigations of Two vic-Dioximes and Their Mononuclear Ni（Ⅱ）, Cu（Ⅱ） and Co（Ⅱ） Metal Complexes Containing Morpholine Group

Two vic-dioxime ligands （LxH2） containing morpholine group have been synthesized from 4-[2-（dimethylaminoethyl）] morpholine with anti-phenylchloroglyoxime or anti-monochloroglyoxime in absolute THF at -15 ℃. Reaction of two vic-dioxime ligands with MCl2·nH2O （M： Ni, Cu or Co and n=2 or 6） salts in 1 ： 2 molar ratio afforded metal complexes of type [M（LxH）2] or [M（LxH）2·2H2O]. All of metal complexes are non-electrolytes as shown by their molar conductivities （Am） in DMF （dimethyl formamide） at 10^-3 mol·L^-1. Structures of the ligands and metal complexes have been solved by elemental analyses, FT-IR, UV-Vis, ^1H NMR and ^13C NMR, magnetic susceptibility measurements, molar conductivity measurements. Furthermore, redox properties of the metal complexes were investigated by cyclic voltammetry.     

Synthesis of 4,4′-biquinazoline alcohols as chiral catalysts in enantioselective alkynylation of aldehydes with phenyl acetylene

Optically active propargylic alcohols are important chiral-building blocks in asymmetric synthesis, while the asymmetric addition of a terminal alkyne to an aldehyde is one of the most important procedures to prepare these chiral-building blocks. In this work, a family of chiral 4,4′-biquinazoline alcohols has been conveniently prepared from the easily accessible (S)-2-acetoxycarboxylic acid chlorides by reaction sequences beginning with condensation and followed by key synthetic steps including chlorination, nickel(0)-mediated homocoupling, and deprotection in addition to being examined as potential ligands in the enantioselective addition of phenylacetylene to aldehydes. These chiral ligands can be combined with Ti(OiPr)₄ and then used to catalyze the asymmetric addition of zinc acetylide, produced in situ by the reaction of phenylacetylene with diethylzinc, to aldehydes. The best enantiomeric excess obtained in this study was 75%.     

A reformulation for the stochastic lot sizing problem with service-level constraints

We study the stochastic lot-sizing problem with service level constraints and propose an efficient mixed integer reformulation thereof. We use the formulation of the problem present in the literature as a benchmark, and prove that the reformulation has a stronger linear relaxation. Also, we numerically illustrate that it yields a superior computational performance. The results of our numerical study reveals that the reformulation can optimally solve problem instances with planning horizons over 200 periods in less than a minute.     

The orthopalladation dinuclear [Pd(L1)(μ-OAc)]2, [Pd(L2)(μ-OAc)]2 and mononuclear [Pd(L3)2] complexes with [N, C, O] or [N, O] containing ligands: Synthesis, spectral characterization, electrochemistry and catalytic properties

Treatment of the salicylaldimine ligands (L₁H, L₂H, L₃H, L₄H and L₅H) with palladium(II) acetate in absolute ethanol gave the orthopalladation dinuclear [Pd(L₁)(μ-OAc)]₂, [Pd(L₂)(μ-OAc)]₂ and mononuclear [Pd(L₃)₂] with the tetradentate ligands [N, C, O] or [N, O] moiety. The ligands L₁H and L₂H are coordinated through the imine nitrogen and aromatic ortho carbon atoms, whereas the ligand L₃H coordinated through the imine nitrogen and phenolic oxygens atoms. The Pd(II) complexes have a square-planar structure and were found to be effective catalysts for the hydrogenation of both nitrobenzene and cyclohexene. These metal complexes were also tested as catalysts in Suzuki-Miyaura coupling of aryl bromide in the presence of K₂CO₃. The catalytic studies showed that the introduction of different groups on the salicyl ring of the molecules effected the catalytic activity towards hydrogenation of nitrobenzene and cyclohexene in DMF at 25 and 45 °C. The Pd(II) complexes easily prepared from cheap materials could be used as versatile and efficient catalysts for different C-C coupling reactions (Suzuki-Miyaura reactions). The structure of ligands and their complexes was characterized by UV-Vis, FT-IR, ¹H and ¹³C NMR, elemental analysis, molar conductivity, as well as by electrochemical techniques.     

Generalized ICM for image segmentation based on Tsallis statistics

In this paper, the iterated conditional modes optimization method of a Markov random field technique for image segmentation is generalized based on Tsallis statistics. It is observed that, for some q$q$ entropic index values the new algorithm performs better segmentation than the classical one. The proposed algorithm also does not have a local minimum problem and reaches a global minimum energy point although the number of iterations remains the same as ICM. Based on the findings of the new algorithm, it can be expressed that the new technique can be used for the image segmentation processes in which the objects are Gaussian or nearly Gaussian distributed.