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.     

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.