Resistance distance in wheels and fans

The wheel graph is the join of a single vertex and a cycle, while the fan graph is the join of a single vertex and a path. The resistance distance between any two vertices of a wheel and a fan is obtained. The resistances are related to Fibonacci numbers and generalized Fibonacci numbers. The derivation is based on evaluating determinants of submatrices of the Laplacian matrix. A combinatorial argument is also illustrated. A connection with the problem of squaring a rectangle is described.     

Theoretical analysis of sonochemical degradation of phenol and its chloro-derivatives

Phenol and its chloro-derivatives contribute significantly to environmental pollution hazards due to their high degree of toxicity as well as improper disposal methods. Cavitation can be used successfully for degradation of phenolic compounds and the rates of degradation are dependent on the type of the primary pollutant in the system. In the present work, a theoretical explanation has been provided to explain the observed degradation trends of phenol and chlorophenols on the basis of concentration of the pollutant at the cavitation bubble/solution interface. Chemical stability of these compounds towards radical attack in the liquid phase has been discussed. It has been observed that chloro-derivates degrade much faster as compared to the parent compound due to higher hydrophobicity of chloro-derivates.     

Polarization and ESR studies of thermally pretreated γ-irradiated TiO2

Pellets of TiO₂ thermally pretreated at 450 and 540°C and -irradiated were polarized by d. c. field. The depolarization curves were resolved into different first order components having two and three depolarization constants. By heating the polarized pellets the Current Glow Peak curves were recorded where there were only two peaks around 65 and 400°C in case of pellets heated at 450°C and heated at 540°C and irradiated; and one more additional peak around 20°C in case of pellets heated at 540°C and heated at 450°C and irradiated thereon. In addition to those signals of O ₂ ^– and Ti³⁺ reported earlier there were distinctly four more, signals at g 1.933 and g 2.03, 2.036 and 2.043 appeared in case of samples heated at 540°C and heated at 450°C and irradiated thereon. The signal at g1.933 is attributed to Ti³⁺ ions in new phase Ti₄O₇ developed in heating at 540°C or due to irradiation and the rest of the signals are due to O _2ad ^– or O _ad ^– over the new phase near anion vacancy created.     

A matrix of permanents

If A is a matrix of order n×(n?2), n?3, denote by ā the n×n matrix whose (i,j)th entry is zero if i=j, and if i≠j, is the permanent of the submatrix of A obtained by deleting its ith and jth rows. It is shown that if A is a nonnegative n×(n?2) matrix, then ā is nonsingular if and only if A has no zero submatrix of n?1 lines. This is used to give precise consequences of the occurrence of equality in Alexandroff's inequality.     

Plasma synthesis of semiconductor nanocrystals for nanoelectronics and luminescence applications

Functional nanocrystals are widely considered as novel building blocks for nanostructured materials and devices. Numerous synthesis approaches have been proposed in the solid, liquid and gas phase. Among the gas phase approaches, low pressure nonthermal plasmas offer some unique and beneficial features. Particles acquire a unipolar charge which reduces or eliminates agglomeration; particles can be electrostatically confined in a reactor based on their charge; strongly exothermic reactions at the particle surface heat particles to temperatures that significantly exceed the gas temperature and facilitate the formation of high quality crystals. This paper discusses two examples for the use of low pressure nonthermal plasmas. The first example is that of a constricted capacitive plasma for the formation of highly monodisperse, cubic-shaped silicon nanocrystals with an average size of 35 nm. The growth process of the particles is discussed. The silicon nanocubes have successfully been used as building blocks for nanoparticle-based transistors. The second example focuses on the synthesis of photoluminescent silicon crystals in the 3–6 nm size range. The synthesis approach described has enabled the synthesis of macroscopic quantities of quantum dots, with mass yields of several mg/hour. Quantum yields for photoluminescence as high as 67% have been achieved.     

Indentation of a viscoelastic rubber covered roll by a rigid plane surface

Deformations of a viscoelastic rubberlike layer bonded to a rigid cylinder and indented by a rigid plane surface are studied by the finite element method. The constitutive relation assumed for the viscoelastic rubber is that proposed by Boltzman. Some of the assumptions made to simplify the work are that the roll cover is rotating at a uniform angular speed, steady state has reached, the deformations of the rubberlike layer are infinite-simal and the effect of inertia forces is negligible. Results presented include the pressure distribution at the contact surface and the stress distribution near the bond surface.     

Smith normal form of some distance matrices

We determine the Smith normal form of the distance matrices of unicyclic graphs and of the wheel graph with trees attached to each vertex.     

Reactivity of Binary Mixtures of La(III) Oxide and Cu(II) Oxalate or Nitrate and Synthesis of La(III) Cuprate

Reactivity of mixtures of La(III) oxide and Cu(II) oxalate/nitrate in hydrated as well as anhydrous state was studied using TG, DTA and XRD. Cu(II) oxide formed in the endothermic decomposition of mixture containing hydrated Cu(II) nitrate and La(III) oxide could not form La₂CuO₄ while Cu(II) oxide formed in the exothermic decomposition of mixture containing hydrated/anhydrous Cu(II) oxalate and La(III) oxide reacts with La(III) oxide and develops the phases CuLaO₃ and La₂CuO₄. The maximum reactivity with respect to the formation of La₂CuO₄phase was observed in mixture containing anhydrous Cu(II) oxalate. This revised version was published online in July 2006 with corrections to the Cover Date.