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.     

Synthesis,characterization and biological activities of <Emphasis Type="Italic">N</Emphasis>-heteroaromatic hydrazones and their complexes with Pd(II), Pt(II) and Cd(II)

Condensation derivatives of ethyl hydrazinoacetate with 2-formylpyridine and quinoline-2-carboxaldehyde were synthesized. Pd(II), Pt(II) and Cd(II) complexes with the 2-formylpyridine derivative and a Cd(II) complex with the quinoline-2-carboxaldehyde derivative were synthesized and characterized by spectroscopic techniques. In the complexes, both ligands are coordinated in neutral NN bidentate modes, while the remaining two coordination sites are occupied by chloride. All compounds showed biological activity when tested against Escherichia coli, Bacillus subtilis and Staphylococcus aureus.     

The Voronoi Identity via the Laplace Transform

The classical Voronoi identity $$\Delta (x) = - \frac{2}{\pi }\sum\limits_{n = 1}^\infty {d(n)} \left( {\frac{x}{n}} \right)^{1/2} \left( {K_1 (4\pi \sqrt {xn} ) + \frac{\pi }{2}Y_1 (4\pi \sqrt {xn} )} \right)$$ is proved in a relatively simple way by the use of the Laplace transform. Here Δ(x) denotes the error term in the Dirichlet divisor problem, d(n) is the number of divisors of n and K_1, Y_1 are the Bessel functions. The method of proof may be used to yield other identities similar to Voronoi's.     

Size of supramolecular SNARE complex: membrane-directed self-assembly

Full length v-SNARE protein in lipid vesicles when exposed to t-SNARE-reconstituted lipid membrane results in the self-assembly of a t-/v-SNARE complex in a ring pattern, forming pores, and establishing continuity between the opposing bilayers. It is known that smaller vesicles fuse more efficiently than larger ones, and hence the curvature of secretory vesicles may dictate the potency and efficacy of their fusion at the cell plasma membrane. The diameter of t- and v-SNARE vesicles may, therefore, reflect the size of the t-/v-SNARE complex formed. In the present study, this hypothesis was tested, and results from the study demonstrate that the size of the t-/v-SNARE complex is directly proportional to the vesicle diameter (R2 = 0.9725).     

Physico-chemical processes in metal-oxide-semiconductor transistors with thick gate oxide during high electric field stress

A complete study of the defects created in the gate oxide and at the gate oxide/substrate interface of metal-oxide-semiconductor transistors with thick gate oxide (t_ox > 10 nm) during high electric field stress, and the mechanisms responsible for these defects creation have been given. In addition, some results of positive/negative high electric field stress with constant gate voltage of commercial n-channel power metal-oxide-semiconductor transistors with thick gate oxide of 100 nm, have been explained using this study.     

Reactivity of haloethanes with hydroxyl radicals: Effects of basis set and correlation energy on reaction energetics

Ab initio calculations on fluoroethane reactions with the hydroxyl radical have been carried out at different levels of theory. The convergence of reaction barriers and reaction enthalpies has been systematically investigated with respect to the size and quality of the basis set and the treatment of correlation energy. The G2 and MP2 barrier heights and reaction enthalpies show the best agreement with the experimental data. The split valence basis sets of triple-zeta quality supplemented by diffuse and polarization functions are necessary to reproduce experimental values for barrier heights and reaction enthalpies at the MP2 level of theory. The full counterpoise correction was used to calculate the basis set superposition error for several standard basis sets, including polarization and diffuse functions. The smallest counterpoise corrections are associated with basis sets that contain polarization and diffuse functions, the diffuse functions being the most effective in reducing BSSE. However, in our case, the uncorrected barrier heights are in better agreement with experimental results than the counterpoise-corrected data. Thus, at the MP2 level of theory, which seems to be dictated for larger electronic systems of chemical interest, the optimal approach is to increase the basis set to the maximum size affordable and to use results without counterpoise corrections for the calculation of reaction barriers. A viable alternative is the use of G2 theory because its results for the barrier heights and reaction enthalpies are in excellent agreement with the experimental data. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1190–1199     

The Effect of Dia2 Protein Deficiency on the Cell Cycle,Cell Size,and Recruitment of Ctf4 Protein in Saccharomyces cerevisiae

Cells have evolved elaborate mechanisms to regulate DNA replication machinery and cell cycles in response to DNA damage and replication stress in order to prevent genomic instability and cancer. The E3 ubiquitin ligase SCF^Dia2 in S. cerevisiae is involved in the DNA replication and DNA damage stress response, but its effect on cell growth is still unclear. Here, we demonstrate that the absence of Dia2 prolongs the cell cycle by extending both S- and G2/M-phases while, at the same time, activating the S-phase checkpoint. In these conditions, Ctf4—an essential DNA replication protein and substrate of Dia2—prolongs its binding to the chromatin during the extended S- and G2/M-phases. Notably, the prolonged cell cycle when Dia2 is absent is accompanied by a marked increase in cell size. We found that while both DNA replication inhibition and an absence of Dia2 exerts effects on cell cycle duration and cell size, Dia2 deficiency leads to a much more profound increase in cell size and a substantially lesser effect on cell cycle duration compared to DNA replication inhibition. Our results suggest that the increased cell size in dia2∆ involves a complex mechanism in which the prolonged cell cycle is one of the driving forces.