On second order degree of graphs

Given a vertex v of a graph G the second order degree of v denoted as d 2(v) is defined as the number of vertices at distance 2 from v.In this paper we address the following question:What are the sufficient conditions for a graph to have a vertex v such that d2(v) ≥ d(v),where d(v) denotes the degree of v? Among other results,every graph of minimum degree exactly 2,except four graphs,is shown to have a vertex of second order degree as large as its own degree.Moreover,every K-4-free graph or every maximal planar graph is shown to have a vertex v such that d2(v) ≥ d(v).Other sufficient conditions on graphs for guaranteeing this property are also proved.     

Solving the discrete-continuous project scheduling problem via its discretization

In this paper a discrete-continuous project scheduling problem is considered. In this problem activities simultaneously require discrete and continuous resources. The processing rate of each activity depends on the amount of the continuous resource allotted to this activity at a time. All the resources are renewable ones. The activities are nonpreemtable and the objective is to minimize the makespan. Discretization of this problem leading to a classical (i.e. discrete) project scheduling problem in the multi-mode version is presented. A simulated annealing (SA) approach to solving this problem is described and tested computationally in two versions: with and without finding an optimal continuous resource allocation for the final schedule. In the former case a nonlinear solver is used for solving a corresponding convex programming problem. The results are compared with the results obtained using SA for the discrete-continuous project scheduling problem where the nonlinear solver is used for exact solving the continuous part in each iteration. The results of a computational experiment are analyzed and some conclusions are included.     

Mikro-permanganometrisehe Studien

Ohne Zusammenfassung     

New Finding of the Glass Transition Phenomenon in Surfactant Gel Phase: The Binary System of Water and Dioctadecyldimethyl-Ammonium Chloride

Differential scanning calorimetry on the two-component system of dioctadecyldimethylammonium chloride (DOAC)–water was carried out in the temperature region from 80 °C down to -100 °C. As the result, a new type of glassy state was found around at -40 °C for the supercooled complete gel phase.     

4-(Pyrrolidinyl)methoxybenzoic acid derivatives as a potent, orally active VLA-4 antagonist

A novel series of benzoic acid derivatives as VLA-4 antagonists were synthesized. Optimization, focusing on activity and lipophilicity needed for cell permeability, resulted in the identification of 15b and 15e with good activity (IC50 = 1.6 nM each) and moderate lipophilicity (Log D = 2.0, 1.8). Furthermore, 15e demonstrated efficacy in murine asthma model by an oral dose of 30 mg/kg.     

Review: Different types of ordering

Homogeneous structures A_xB_y with identical A–A or B–B self‐coordination numbers T₁, T₂, T₃, of nearest, next‐nearest and third neighbors are selected. The maximum T_i values are 2 2 2 (1D row), 6 6 6 (2D hexagonal net) and 12 6 24 (3D cubic close‐packing). Reduced T₁ or T₂ values for A_xB_y can be related with attractive or repulsive A–A (or B–B) interactions. A single set of T₁ T₂ T₃; y/x values was obtained for y/x = 1–4 and 6. The y/x = 2 structures of three equivalent positions A, B and C are unfavourable for A = ⊕ and B = ⊖ charge or direction of magnetic moments. The spatial distribution of positive and negative potential near A⁺ and B⁻ positions gives rise to neutral C positions. Frustrated magnetic moments at C positions are disordered. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Circularly polarized luminescence (CPL) characteristics of hydrophobic pyrene derivatives/γ-cyclodextrin (γ-CD) complexes in aqueous solution dissolved by grinding

Circularly polarized luminescence (CPL) organic dyes are currently receiving a great interest, but there are still not many reported observations of CPL spectra of hydrophobic dyes from aqueous solution. We have prepared hydrophobic pyrene derivatives and dissolved them into aqueous solutions with γ-cyclodextrin (γ-CD) by using grinding technique. Among these derivatives, (pyrene-1-carbonyl)serine (PySer) forms a spatially restricted dimer in the hydrophobic chiral cavity of γ-CD and exhibits excimer emission with a high quantum yield of Φ_f?=?0.68. In addition, circular dichroism and CPL signals were induced for the complex. The strong g_CPL value of g_CPL?=?+?2.2?×?10^?3 was obtained, which may be attributed to the interaction between the hydroxyl groups in the side chain of PySer with those of γ-CD and it strengthens the chiral dimeric structure.

Graphic abstract

     

Radical cyclopolymerization of dimethacrylates bearing rigid adamantane-like core derived from naturally occurring myo-inositol

Dimethacrylates with rigid adamantane-like cores were synthesized from myo-inositol orthoester via a sequence of (a) acylation or silylation of the equatorially oriented hydroxyl group, followed by (b) attachment of methacrylate groups on the axially oriented hydroxyl groups. The radical homopolymerization of these compounds proceeded via cyclopolymerization without crosslinking, as the two axially oriented methacrylate groups were fixed in close proximity with each other. The dimethacrylates underwent radical copolymerization with methyl methacrylate (MMA) to afford the corresponding polymethacrylates, exhibiting high glass transition temperatures (T_g), due to the introduction of the rigid orthoester moieties originating from the monomers and the macrocyclic structures formed via intramolecular cyclization of the two methacrylate groups of the monomers. The polymers obtained by polymerization of the dimethacrylate bearing a silylated hydroxyl group served as precursors of hydroxyl-bearing polymers, which also exhibited high T_g due to the formation of a hydrogen bonding network between the hydroxyl groups.