Investigating and ordering Quadrilaterals and their analogies in space—problem fields with various aspects

Problem fields with one or two generating problems and possibilities of varying existing problems give a good chance for self-activities of students and can be used for reaching different general aims. In this paper some topics concerning quadrilaterals will be presented. I hope they will animate teachers for more problem orientation in mathematics education. First we will reflect about different types of convex and non-convex quadrilaterals and possibilities of ordering them. Then we focus on middle-quadrilaterals and types of quadrilaterals with special middle-quadrilaterals as well as their logical ordering. Finally we investigate the analogies in space to the parallelogram and its sub-types and order them in the “house of parallelepipeds”.     

Hawking Radiation of Dirac Particles in a Nonuniformly Rectilinearly Accelerating Black Hole

The Hawking radiation of Dirac particles on the event horizon of a nonuniformly rectilinearly accelerating black hole is studied in this paper. First, we construct the symmetrized null tetrad from which the spin coefficients and Dirac equation are derived. Next, by proposing generalized tortoise coordinate transformation, the decoupling problem of the Dirac equation with nonzero rest mass is solved. Finally, by analytic continuation, the Hawking thermal spectrum formula of Dirac particle for nonuniformly rectilinearly accelerating black hole is obtained.     

Surface free energies of electroless Ni–P based composite coatings

Surface free energy of a solid surface gives a direct measure of intermolecular interactions at interfaces and has a strong influence on adsorption and adhesion behaviour. However few data are available for the surface free energies of electroless Ni–P based composition coatings. In this paper, the electroless Ni–P, Ni–P-surfactant, Ni–Cu–P, Ni–P–PTFE and Ni–Cu–P–PTFE composite coatings were prepared under various coating conditions. The chemical compositions, surface morphology and thickness of the coatings were measured using an energy dispersive X-ray microanalysis (EDX), a scanning electron microscope (SEM) and a digital micrometer respectively. The contact angles of water, diiodomethane and ethylene glycol on the coatings were measured automatically using dataphysics OCA-20 contact angle analyser. The surface free energy of the coatings and their components (e.g. dispersion, polar or acid/base portions) were calculated using various methods. The experimental results showed that the incorporation of surfactant or PTFE particles into Ni–P matrixes has a significant influence on the surface free energy of the coatings, while the incorporation of copper into Ni–P matrixes has no significant influence on the surface free energy of the coatings.     

Hydrogen indium vacancy complex VInH4 in n-type InP studied by positron-lifetime

Positron-lifetime experiments have been carried out on two undoped n-type liquid encapsulated Czochralski (LEC)-grown InP samples with different stoichiometric compositions in the temperature range 10-300 K. For temperatures below 120 K for P-rich InP and 100 K for In-rich InP, the positron average lifetime began to increase rapidly and then leveled off, which was associated with the charge state change of hydrogen indium vacancy complexes from (V_InH₄)⁺ to (V_InH₄)⁰. This phenomenon was more obvious in P-rich samples that have a higher concentration of V_InH₄. The transformation temperature of approximately 120 K suggests that the complex V_InH₄ is a donor defect and that the ionization energy is about 0.01 eV. The ionization of neutral V_InH₄ accounted for the decrease of the positron average lifetime when the sample was illuminated with a photon energy of 1.32 eV at 70 K. These results provide evidence for hydrogen complex defects in undoped LEC InP.     

Invariant set and attractor of nonautonomous functional differential systems

The paper is devoted to the invariant set and periodic attractor for nonautonomous functional differential systems. Some sufficient criteria of the invariant set and periodic attractor are derived. Particularly, we have provided an estimate on existence range of periodic attractor by using the properties of nonnegative matrices and differential inequality technique.     

Speciation Analysis of Inorganic Tin (Sn(II)/Sn(IV)) by Graphite Furnace Atomic Absorption Spectrometry Following Ion-Exchange Separation

A new method based on anion exchange resin separation and graphite furnace atomic absorption spectrometry (GFAAS) detection is proposed for the determination of inorganic tin species. The result showed that Sn(IV) was quantitatively retained on the resin when [HCl] = 9.0 mol · L⁻¹, but Sn(II) could not be adsorbed on the resin under the same condition. Thus, a separation of Sn(II) and Sn(IV) has been realized. When the concentration of NaOH solution was between 2.0–7.0 mol · L⁻¹, Sn(IV) that adsorbed on the resin could be eluated from the resin completely. Meanwhile, under the atmosphere and the nitrogen states, the translation between Sn(II) and Sn(IV) was investigated. Under the optimal conditions, the detection limit of Sn(IV) is 0.40 μg · L⁻¹ with RSD of 2.3% (n = 5, c = 2.0 μg · L⁻¹). The proposed method was applied to the speciation analysis of tin in different water samples and the recovery of total Sn was in the range of 98.7–101.7%. In order to verify the accuracy of the method, a certified reference water sample was analyzed and the results obtained were in good agreement with the certified value.     

On structure of small contractions of odd dimensional projective varieties

Let X be a smooth projective variety of dimension 2k-1 (k≥3) over the complex number field. Assume that fR: X→Y is a small contraction such that every irreducible component Ei of the exceptional locus of fR is a smooth subvariety of dimension k. It is shown that each Ei is isomorphic to the k-dimensional projective space Pk, the k-dimensional hyperquadric surface Qk in Pk 1, or a linear Pk-1-bundle over a smooth curve.     

Primes in quadratic progressions on average

In this paper, we establish a theorem on the distribution of primes in quadratic progressions on average.     

A numerically stable algorithm for two server queue models

In this paper, we consider a queueing system in which there are two exponential servers, each having his own queue, and arriving customers will join the shorter queue. Based on the results given in Flatto and McKean, we rewrite the formula for the probability that there are exactlyk customers in each queue, wherek = 0, 1,…. This enables us to present an algorithm for computing these probabilities and then to find the joint distribution of the queue lengths in the system. A program and numerical examples are given.