Comparative studies of femtosecond to microsecond laser pulses on selective pigmented cell injury in skin

Threshold radiant exposures for grossly apparent immediate whitening and ultrastructural alterations of melanosomes in black guinea pig skin were determined for a series of red visible laser pulses ranging from 4 x 10(-4) to 6.5 x 10(-14) s. Threshold exposures for melanosomal injury were found to be independent of pulsewidth when the pulsewidths were below the estimated thermal relaxation time of melanosomes. Threshold radiant exposures for melanosomal injury were found to increase when the pulsewidths were approximately equal to or above the thermal relaxation time of melanosomes. At longer pulse durations, fracturing of melanosomes was not observed despite the longer exposures necessary for injury. Instead, perimelanosomal vacuoles were noted. These findings are consistent with the theory of selective photothermolysis and provide evidence for the thermal initiation of melanosomal disruption.     

20-relative neighborhood graphs are hamiltonian

For any two points p and q in the Euclidean plane, define LUN_pq = { v | v ∈ R², d_pv < d_pq and d_qv < d_pq}, where d_uv is the Euclidean distance between two points u and v . Given a set of points V in the plane, let LUN_pq(V) = V ∩ LUN_pq. Toussaint defined the relative neighborhood graph of V, denoted by RNG(V) or simply RNG, to be the undirected graph with vertices V such that for each pair p,q ∈ V, (p,q) is an edge of RNG(V) if and only if LUN_pq (V) = ?. The relative neighborhood graph has several applications in pattern recognition that have been studied by Toussaint. We shall generalize the idea of RNG to define the k-relative neighborhood graph of V, denoted by kRNG(V) or simply kRNG, to be the undirected graph with vertices V such that for each pair p,q ∈ V, (p,q) is an edge of kRNG(V) if and only if | LUN_pq(V) | < k, for some fixed positive number k. It can be shown that the number of edges of a kRNG is less than O(kn). Also, a kRNG can be constructed in O(kn₂) time. Let E_c = {e_pq| p ∈ V and q ∈ V}. Then G_c = (V,E_c) is a complete graph. For any subset F of E_c, define the maximum distance of F as max_epq∈Fd_pq. A Euclidean bottleneck Hamiltonian cycle is a Hamiltonian cycle in graph G_c whose maximum distance is the minimum among all Hamiltonian cycles in graph G_c. We shall prove that there exists a Euclidean bottleneck Hamiltonian cycle which is a subgraph of 20RNG(V). Hence, 20RNGs are Hamiltonian.     

Note on a conjecture of toft

A conjecture of Toft [17] asserts that any 4-critical graph (or equivalently, every 4-chromatic graph) contains a fully odd subdivision ofK ₄. We show that if a graphG has a degree three nodev such thatG-v is 3-colourable, then eitherG is 3-colourable or it contains a fully oddK ₄. This resolves Toft's conjecture in the special case where a 4-critical graph has a degree three node, which is in turn used to prove the conjecture for line-graphs. The proof is constructive and yields a polynomial algorithm which given a 3-degenerate graph either finds a 3-colouring or exhibits a subgraph that is a fully odd subdivision ofK ₄. (A graph is 3-degenerate if every subgraph has some node of degree at most three.)     

WZW–Poisson manifolds

We observe that a term of the WZW-type can be added to the Lagrangian of the Poisson σ-model in such a way that the algebra of the first class constraints remains closed. This leads to a natural generalization of the concept of Poisson geometry. The resulting “WZW–Poisson” manifold M is characterized by a bivector Π and by a closed three-form H such that 1/2[Π,Π]_Schouten=H,ΠΠΠ.     

Macrodefect-Free Materials: Modification of Interfaces in Cement Composites by Polymer Grafting

MDF materials are chemically bonded ceramic materials free of the macrodefects typical of hydraulic cement-based materials. MDF materials arising through reactions of sulfo-aluminate-ferrite belitic (SAFB) clinkers and/or Portland cements (PC) with two types of water-soluble polymer (hydroxy-propylmethyl cellulose {HPMC}, polyphosphate glass {poly-P}) are discussed. Mixes of low energy SAFB clinkers with Portland cement, HPMC and, especially poly-P comprise promising cross-linked compositions additional to the better known MDF materials formed from high alumina cement with polyvinylalcohol/acetate. The principles of co-ordination of P and C atoms (of the polymer) with Al and Fe atoms (originating from the cement) are highlighted from spectroscopic information on next-nearest-neighbour interactions, along with the effects of second co-ordination spheres. Polymers modify the interface through functional bonding/grafting of polymer chains onto the surfaces of cement grains. Both the cross-linked atomic structure and the interface coincide well with the model of functional polymers and represent a new type of atomic-level structure in polymer-modified cements. Interpretation is based on previous magnetic resonance and thermal analysis studies. The compactness of Al(Fe)-O-P cross-links reduces transport through the interfaces, increasing the interfacial interactions and resisting the unfavourable uptake of moisture and carbonation.     

Modeling hyperelastic behavior of rubber: A novel invariant‐based and a review of constitutive models

A constitutive phenomenological model completing the Gent‐Thomas concept is carried out to formulate laws governing the hyperelastic behavior of incompressible rubber materials. It is shown that the phenomenological Gent‐Thomas model (1958) and the constrained chain model (1992) give similar precise results at small to moderate deformation. On the other hand, comparisons of the outcome of the proposed model with that of the molecular model from the combined concepts of Flory‐Erman and Boyce‐Arruda (2000), and with those of the phenomenological models of Ogden (1982), Yeoh‐Fleming (1997), Pucci‐Saccomandi (2002) and Beda (2005) are made. Residual inconveniences raised by attractive continuum models in rubber elasticity literature have been successfully overcome. Results from both the statistical and phenomenological mechanics concepts are compared with the data of some useful classical materials (rubbers of Treloar, Rivlin‐Saunders, Pak‐Flory and Yeoh‐Fleming). The results permit one to see salient equivalence of the two theories for a more reliable prediction of stress‐stretch response for all states of any mode of deformation. A complete and exhaustive analysis of the Mooney plot that combines small and very large extension‐compression has been quite essential in assessing the validity of models. A method of identification of material parameters is presented and data of the simple tension suffice for the determination of the parameter values. It is shown that the ordinary identification procedures, such as the usual least squares, a very much used numerical method in materials investigation, can be unsuitable in some cases of hyperelastic modeling. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1713–1732, 2007     

Anodic stripping coulometry with collection for absolute trace analysis of lead, using flow-through electrochemical cells with porous working electrodes

Summary Flow-through electrochemical cells with porous working electrodes made of crushed reticulated vitreous carbon and plated with mercury were used for absolute analysis of trace amounts of lead by anodic stripping coulometry with collection (ASCWC) in a flow system. The role of mercury coating, flow rate and pH were investigated. The coulombic content of the collection peak corresponded to the theoretical values calculated by Faraday's law in a concentration range from about 10^–9 to 10^–6 mol/l. The relative error and the relative standard deviation was +0.15% and 0.8%, respectively for 2×10^–6 mol/l analyte concentration. The absolute detection limit (3 s) was 0.1 ng of Pb, the linear response range 7×10⁴. One leave from: Department of Analytical Chemistry, Slovak Technical University, CS-812 37 Bratislava, Czechoslovakia     

On α-I-continuous and α-I-open functions

Montgomery and Vaughan improved a theorem of Erd?s and Fuchs for an arbitrary sequence. Sárközy extended this theorem of Erd?s and Fuchs for two arbitrary sequences which are "near" in a certain sense. Using the idea of Jurkat (differentiation of the generating function), we will extend similarly the result of Montgomery and Vaughan for "sufficiently near" sequences.     

Analytical and numerical investigation of two families of Lorenz-like dynamical systems

We investigate two families of Lorenz-like three-dimensional nonlinear dynamical systems (i) the generalized Lorenz system and (ii) the Burke–Shaw system. Analytical investigation of the former system is possible under the assumption (I) which in fact concerns four different systems corresponding to  = ±1, m = 0, 1.

(I)

The fixed points and stability characteristics of the Lorenz system under the assumption (I) are also classified. Parametric and temporal (t → ∞) asymptotes are also studied in connection to the memory of both the systems. We calculate the Lyapunov exponents and Lyapunov dimension for the chaotic attractors in order to study the influence of the parameters of the Lorenz system on the attractors obtained not only when the assumption (I) is satisfied but also for other values of the parameters σ, r, b, ω and m.