A sufficient condition for a graph to be hamiltonian

Those non-hamiltonian graphsG withn vertices are characterized, which satisfy the Ore-type degree-conditiond(x)+d(y)n–2 for each pairx,yM of different nonadjacent vertices whereM consists of two vertices ofG. As an application a theorem on hamiltonian connectivity of graphs is given. Furthermore, a condition is presented which is sufficient for the existence of a covering of a graph by two disjoint paths with prescribed set of startpoints and prescribed set of endpoints. A class of graphs is described which have no covering of this kind.     

Symmetries and correlation inequalities for classicaln-vector models

We describe a new class of single spin measures on then-dimensional sphereS _r ⁿ of radiusr (n 4) for which Lebowitz-type [J. Lebowitz,J. Stat. Phys. 16:463 (1977)] inequalities hold. This is achieved by an appropriate parametrization ofS _r ⁿ . The above class includes the uniform measures onxs Rⁿ ¦x¦ r for any 0 p r. The second topic of this paper is an abstract formulation of the first Griffiths inequality [R. B. Griffiths,J. Math. Phys. 8:478 (1967)] and the underlying symmetry property.     

Synthesis and characterization of the open-framework barium bisphosphonate [Ba3(O3PCH2NH2CH2PO3)2(H2O)4].3H2O

Following the strategy of using polyfunctional phosphonic acids for the synthesis of open-framework metal phosphonates, the phosphonocarboxylic acid (H2O3PCH2)2NCH2C6H4COOH was used in the hydrothermal synthesis of new Ba phosphonates. Its decomposition led to the first open-framework barium phosphonate [Ba3(O3PCH2NH2CH2PO3)2(H2O)4].3H2O. The synthesis was also successfully performed using iminobis(methylphosphonic acid), (H2O3PCH2)2NH, as a starting material, and the synthesis was optimized to obtain as a pure material. The reaction setup as well as the pH are the dominant parameters, and only a diffusion-controlled reaction led to the desired compound. The crystal structure was solved from single-crystal data: monoclinic; C2/c; a=2328.7(2), b=1359.95(7), and c=718.62(6) pm; beta=98.732(10) degrees ; V=2249.5(3)x10(6) pm3; Z=4; R1=0.036; and wR2=0.072 (all data). The structure of [Ba3(O3PCH2NH2CH2PO3)2(H2O)4].3H2O is built up from BaO8 and BaO10 polyhedra forming BaO chains and layers, respectively. These are connected to a three-dimensional metal-oxygen-metal framework with the iminobis(methylphosphonic acid) formally coating the inner walls of the pores. The one-dimensional pores (3.6x4 A) are filled with H2O molecules that can be thermally removed. Thermogravimetric investigations and temperature-dependent X-ray powder diffraction demonstrate the stability of the crystal structure up to 240 degrees C. The uptake of N,N-dimethylformamide and H2O by dehydrated samples is demonstrated. Furthermore, IR, Raman, and 31P magic-angle-spinning NMR data are also presented.     

Renormalization group treatment of phase transitions in ferromagnetic superconductors

We investigate the nature of the phase transition from the superconducting to the uniformly ordered magnetic phase in ferromagnetic superconductors by renormalization group methods. For this purpose Halperin, Lubensky, Ma's application of the-expansion to pure superconductors is extended to include the influence of magnetic order as well. Our treatment shows that in the vicinity of the ferromagnetic to superconducting phase-boundary critical fluctuations of the magnetization are absorbed into fluctuations of the magnetic field. As a consequence the transition always is first order. An additional indication to the dominance of electromagnetic effects is the irrelevance of the coupling corresponding to spin flip scattering.     

Zerlegung total gerichteter Graphen in Kreise

The following statements are valid:The complete directed graph ¯K_n, n1 (mod 2p), is decomposable into directed 2p-cycles.The complete directed bipartite graph ¯K_m,n is decomposable into 2p-cycles if p is a divisor of m and np.If p is a prime, then this condition is necessary, too.The complete directed graph ¯K_n, n12, is decomposable into 6-cycles if and only if 6     

On index formulas for manifolds with metric horns

In this paper was discuss the index problem for geometric differential operators (Spin–Dirac opreatorm Gauβ–Bonnet operator, Singnature operator) on manifolds with metric horns. On singular manifolds these operators in general do not unique closed extensions. But there always exist two extremal extensions D$sub:min$esub:and D$sub:max$esub: We describe the quotient D (D$sub:max$esub:)/D(D$sub:esub:) explicitely in geometric resp.topological terms of the base manifolds of the metric horns.

We derive index formulas for the3 Spin–Dirac and GauβBonnet operator. For the Singnature operator we present a partial result.     

Genotoxicity and Cytotoxicity of 4-Nonylphenol Ethoxylate on Lymphocytes as Assessed by the Comet Assay

Surfactants, which are prevalent at industrial sites and in the environment generally, are potential risk factors in human carcinogenesis. The widespread industrial use of surfactants such as 4-alkylphenol ethoxylates and their prevalence in many cleaning products have provoked studies about surfactant concentrations in water and their toxicity levels. Up to now, these substances have mainly been tested on aquatic organisms. Though tests on human cell lines are rare. The alkaline Comet assay was performed to evaluate the genotoxicity of 4-nonylphenol ethoxylate, a biodegradable product of 4-alkylphenol ethoxylate, in human lymphocytes. Concentrations tested ranged from 0.15 to 150 µg/mL. Test concentrations of 10 to 15 µg/mL caused an increase level of DNA migration in human cells, but without inducing excessive toxicity (viability > 80%). Though induced levels of DNA migration starting at concentrations of 30 µg/mL may have been due to excessive levels of cytotoxicity (viability < 70%). Based on these data, 4-nonylphenol ethoxylate can induce DNA damage in human lymphocytes but at higher concentrations than are normally found in river or drinking water. However, considering the prevalence of surfactants, the measured genotoxicity of these substances is of concern. Further investigations on human target cells are necessary to evaluate the carcinogenic impact of surfactants and reconsider their environmental acceptance.     

Allyl sulfides and α‐substituted acrylates as addition–fragmentation chain transfer agents for methacrylate polymer networks

The rapid and uncontrolled nature of network formation from di(meth)acrylate monomers produces high shrinkage stress and results in polymers with oftentimes brittle mechanical properties. Methods for regulating polymerization and network formation are sought. One option is the use of addition–fragmentation chain transfer (AFCT) agents, which are well known to control molecular weight and molecular weight distribution of monofunctional (meth)acrylates. A series of novel and previously described AFCT reagents were synthesized and screened with laser flash photolysis to determine reactivity. Well‐performing AFCT reagents were then tested in polymerizations with monofunctional and difunctional methacrylates. With monofunctional monomers, the molecular weight and polydispersity of the resultant linear polymers tend to decrease with the addition of AFCT agent. In copolymerization with dimethacrylate monomers, the AFCT agents were found to substantially lower and sharpen the glass transition. Sharpness of the glass transition is here indicative of a more regular and homogenous network. After coupling of the instruments, photorheology was performed simultaneously with real‐time IR to show an increase in monomer conversion at the time of gelation, which appears to have a positive effect on reducing shrinkage stress. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 394–406