Toppling kings in multipartite tournaments by introducing new kings

Let and be two n-tuples of nonnegative integers. An all-4-kings n-partite tournament T(V₁,V₂,…V_n) is said to have a -property if there exists an n-partite tournament T₁(W₁,W₂,…,W_n) such that for each i∈{1,…,n}:

(1)

V_i⊆W_i;

(2)

exactly t_i 4-kings of V_i are not 4-kings in T₁;

(3)

exactly c_i 4-kings of W_i are not vertices of V_i.

We describe all pairs such that there exists an n-partite tournament having -property.     

Preimages of CR submanifolds with generic holomorphic maps

We investigate the notion of CR transversality of a generic holomorphic map f: ℂ ⁿ → ℂ ^m to a smooth CR submanifold M of ℂ ^m . We construct a stratification of the set of non-CR transversal points in the preimage M′ = f ⁻¹ (M) by smooth submanifolds, consisting of points where the CR dimension of M′ is constant. We show the existence of a Whitney stratification for sets which are locally diffeomorphic to the product of an open set and an analytic set. Work on this paper was supported by ARRS, Republic of Slovenia.     

Preparation and characterisation of poly(high internal phase emulsion) methacrylate monoliths and their application as separation media

Poly(glycidyl methacrylate-co-ethyleneglycol dimethacrylate) monolithic supports were prepared by radical polymerisation of the continuous phase of water in oil high internal phase emulsions. Morphology of monolithic materials was studied by scanning electron microscopy and mercury intrusion porosimetry. The ratio of phase volume and the degree of crosslinking influenced the void size and pore size distribution of resulting polymers. Void sizes between 1 and 10 microm were observed and average pore sizes around 100 nm. Polymers with 60, 75, 80 and 90% pore volume were prepared and even samples with highest pore volume showed good mechanical stability. They were modified to bear weak-anion exchange groups and tested on the separation of standard protein mixture containing myoglobin, conalbumine and trypsin inhibitor. Good separation was obtained in a very short time similar to the separation obtained by commercial methacrylate monoliths. However, higher dispersion was observed. Bovine serum albumin dynamic binding capacity for monolith with 90% porosity was close to 9 mg/ml.     

Photoelectrochemical behavior of molybdenum-modified nanoparticulate hematite electrodes

The preparation of molybdenum-modified hematite electrodes by means of chemical bath deposition and their photoelectrochemical behavior toward water oxidation are reported in this work. The addition of a molybdenum precursor to the bath solution for hematite deposition induces a remarkable change of morphology in the resulting film from (110)-oriented nanorods to polyhedral nanoparticles. Despite the resulting loss of order, by controlling the Mo/Fe molar ratio in the bath solution, a significant improvement of the water oxidation photocurrent is achieved compared to nanorod pristine hematite electrodes. Such a (photo)electrochemical enhancement is mainly explained by an effective surface state passivation in Mo-modified hematite films. FE-SEM, TEM, XRD, and XPS were employed for electrode structural and morphological characterization.

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Graphical abstract ?

     

Characterization of molecular complexity

We put forward a novel index of molecular complexity, ξ, taking into account the symmetry of a molecular graph and the specificity of structural components considered. The ξ index is defined as the sum of augmented valences of all mutually nonequivalent vertices in a molecular graph. The augmented valence of a vertex in a graph is the sum of its valence and valences of all neighboring vertices with the weight 1/2^d depending on their distance, d, from the vertex. The ξ index is examined on the set of octane isomers and some special classes of graphs. It is also compared with a certain number of alternative complexity measures considered in the literature. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003