Closure for the property of having a hamiltonian prism

We prove that a graph G of order n has a hamiltonian prism if and only if the graph Cl_4n/3–4/3(G) has a hamiltonian prism where Cl_4n/3–4/3(G) is the graph obtained from G by sequential adding edges between non‐adjacent vertices whose degree sum is at least 4n/3–4/3. We show that this cannot be improved to less than 4n/3–5. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 209–220, 2007     

The fourth power of the Fermat quotient

Let p be an odd prime and qp(a)=(ap−1−1)/p be the Fermat quotient with base a, p?a. The main purpose of this paper is to investigate the fourth power problem of qp(2) and deduce an explicit formula represented by a linear combination of Mirimanoff polynomial values.     

Synthesis of Novel Biologically Active Proflavine Ureas Designed on the Basis of Predicted Entropy Changes

A novel series of proflavine ureas, derivatives 11a–11i, were synthesized on the basis of molecular modeling design studies. The structure of the novel ureas was obtained from the pharmacological model, the parameters of which were determined from studies of the structure-activity relationship of previously prepared proflavine ureas bearing n-alkyl chains. The lipophilicity (LogP) and the changes in the standard entropy (ΔS°) of the urea models, the input parameters of the pharmacological model, were determined using quantum mechanics and cheminformatics. The anticancer activity of the synthesized derivatives was evaluated against NCI-60 human cancer cell lines. The urea derivatives azepyl 11b, phenyl 11c and phenylethyl 11f displayed the highest levels of anticancer activity, although the results were only a slight improvement over the hexyl urea, derivative 11j, which was reported in a previous publication. Several of the novel urea derivatives displayed GI₅₀ values against the HCT-116 cancer cell line, which suggest the cytostatic effect of the compounds azepyl 11b–0.44 μM, phenyl 11c–0.23 μM, phenylethyl 11f–0.35 μM and hexyl 11j–0.36 μM. In contrast, the novel urea derivatives 11b, 11c and 11f exhibited levels of cytotoxicity three orders of magnitude lower than that of hexyl urea 11j or amsacrine.     

Suspended bridges subjected to moving loads and support motions due to earthquake

The paper deals with the vibration of suspended bridges subjected to the simultaneous action of moving loads and vertical support motions due to earthquake. The basic partial integro-differential equation is applied to the vertical vibration of a suspended beam. The dynamic actions of traffic loads are modelled as a row of equidistant moving forces, while the earthquake is considered by vertical motions of supports. The governing equation is solved first analytically to receive an ordinary differential equation and next numerically. Moreover, the designed world's largest suspended bridge—Messina Bridge—is investigated (central span of length 3.3 km). The paper studies the effect of various lags of the earthquake arrival because the earthquake may appear at any time when the train moves along a large-span bridge. The modified Kobe earthquake records have been applied to calculations. The results indicate that the interaction of both the moving and seismic forces may substantially amplify the response of long-span suspended bridges in the vicinity of the supports and increase with the rising speed of trains.     

Stereospecific Synthesis of D -Glycero- D -ido-oct-2-ulose

 D-Glycero-D-gulo-heptose reacted with 2,2-dimethoxypropane to give its 2,3:6,7-di-O-isopropylidene derivative. Its base-catalyzed addition to formaldehyde resulted in the formation of 2,3:6,7-di-O-isopropylidene-2-C-(hydroxymethyl)-D-glycero-D-gulo-heptofuranose. After acid hydrolysis of this aldolization product, a new branched-chain aldose, 2-C-(hydroxymethyl)-D-glycero-D-gulo-heptose, was obtained, which was stereospecifically rearranged under the catalytic action of molybdic acid to D-glycero-D-ido-oct-2-ulose.     

A Characterization of the Interval Function of a (Finite or Infinite) Connected Graph

By the interval function of a finite connected graph we mean the interval function in the sense of H. M. Mulder. This function is very important for studying properties of a finite connected graph which depend on the distance between vertices. The interval function of a finite connected graph was characterized by the present author. The interval function of an infinite connected graph can be defined similarly to that of a finite one. In the present paper we give a characterization of the interval function of each connected graph.     

A novel analytical model and energy analysis of thermal stresses in two-phase composites

This paper deals with analytical modelling of thermal stresses in a multi-particle-matrix system with isotropic spherical particles. These particles are periodically distributed in an isotropic infinite matrix. This model system which is characterized by microstructural parameters (particle volume fraction, particle radius) is applicable to two-phase composites of a precipitate-matrix type with isotropic phases. The thermal stresses originate during a cooling process due to a difference in thermal expansion coefficients. The analytical modelling which is based on fundamental equations of solid continuum mechanics represents a combination of different mathematical procedures applied to equilibrium and compatibility equations. This novel analytical model is compared with that which is based on mathematical procedures applied to the equilibrium equations only. The energy analysis of both analytical models which is applied to the SiC-Al₂O₃ composite is presented.     

Thermal-stress induced phenomena in two-component material： part I

The paper deals with analytical fracture mechanics to consider elastic thermal stresses acting in an isotropic multi-particle-matrix system. The multi-particle-matrix system consists of periodically distributed spherical particles in an infinite matrix. The thermal stresses originate during a cooling process as a consequence of the difference αm - αp in thermal expansion coefficients between the matrix and the particle, αm and αp, respectively. The multi-particle-matrix system thus represents a model system applicable to a real two-component material of a precipitation-matrix type. The infinite matrix is imaginarily divided into identical cubic cells. Each of the cubic cells with the dimension d contains a central spherical particle with the radius R, where d thus corresponds to inter-particle distance. The parameters R, d along with the particle volume fraction v = v（R, d） as a function of R, d represent microstructural characteristics of a twocomponent material. The thermal stresses are investigated within the cubic cell, and accordingly are functions of the microstructural characteristics. The analytical fracture mechanics includes an analytical analysis of the crack initiation and consequently the crack propagation both considered for the spherical particle （q = p） and the cell matrix （q = m）. The analytical analysis is based on the determination of the curve integral Wcq of the thermal-stress induced elastic energy density Wq. The crack initiation is represented by the determination of the critical particle radius Rqc = Rqc（V）. Formulae for Rqc are valid for any two-component mate- rial of a precipitate-matrix type. The crack propagation for R 〉 Rqc is represented by the determination of the function fq describing a shape of the crack in a plane perpendicular     

Observation of stimulated Raman scattering in polar tetragonal crystals of barium antimony tartrate trihydrate,Ba[Sb2((+)C4H2O6)2]·3H2O

The non‐centrosymmetric polar tetragonal (P 4₁) barium antimony tartrate trihydrate, Ba[Sb₂((+)C₄H₂O₆)₂]·3H₂O, was found to be an attractive novel semi‐organic crystal manifesting numerous χ ⁽²⁾‐ and χ ⁽³⁾‐nonlinear optical interactions. In particular, with picosecond single‐ and dual‐wavelength pumping SHG and THG via cascaded parametric four‐wave processes were observed. High‐order Stokes and anti‐Stokes lasing related to two SRS‐promoting vibration modes of the crystal, with ω_SRS1 ≈ 575 cm^?1 and ω_SRS2 ≈ 2940 cm^?1, takes place. Basing on a spontaneous Raman investigation an assignment of the two SRS‐active vibration modes is discussed.

     

Finite-Size Effects in Non-neutral Two-Dimensional Coulomb Fluids

Thermodynamic potential of a neutral two-dimensional (2D) Coulomb fluid, confined to a large domain with a smooth boundary, exhibits at any (inverse) temperature \(\beta \) a logarithmic finite-size correction term whose universal prefactor depends only on the Euler number of the domain and the conformal anomaly number \(c=-1\). A minimal free boson conformal field theory, which is equivalent to the 2D symmetric two-component plasma of elementary \(\pm e\) charges at coupling constant \(\Gamma =\beta e^2\), was studied in the past. It was shown that creating a non-neutrality by spreading out a charge Qe at infinity modifies the anomaly number to \(c(Q,\Gamma ) = - 1 + 3\Gamma Q^2\). Here, we study the effect of non-neutrality on the finite-size expansion of the free energy for another Coulomb fluid, namely the 2D one-component plasma (jellium) composed of identical pointlike e-charges in a homogeneous background surface charge density. For the disk geometry of the confining domain we find that the non-neutrality induces the same change of the anomaly number in the finite-size expansion. We derive this result first at the free-fermion coupling \(\Gamma \equiv \beta e^2=2\) and then, by using a mapping of the 2D one-component plasma onto an anticommuting field theory formulated on a chain, for an arbitrary even coupling constant.