Asymptotic Properties of Sums of Upper Records

Arnold and Villaseñor (1999) raised several questions for upper records, including characterizing all limit distributions of normalized partial sums of upper records. We provide some answers in the case when the distribution from which the samples are drawn is bounded above. When the distribution is not bounded above, we give sufficient conditions on the distribution for the properly normalized partial sums to converge to a standard normal distribution. We show that our conditions are general enough so that the examples provided by Arnold and Villaseñor (1999) are covered by our results.     

Quantum Dots (QDs) Based Fluorescent Sensor for the Selective Determination of Nimesulide

Fluorescent PET (Photoinduced Electron Transfer) has been of particular growth in recent times. A novel PET based fluorescent sensor using unmodified CdSe quantum dots (QDs) has been developed for the trace determination of Nimesulide (NIM). The sensor is based on the selective fluorescence quenching of quantum dots by NIM in presence of other NSAIDs and is found that intensity of quenching is linearly related to NIM concentration in the range 8.2?×?10^?7 – 4.01?×?10^?5?M. The mechanism of interaction is discussed. Finally, the potential application of the proposed method for the trace determination of NIM in pharmaceutical formulation is demonstrated.     

Rigorous Self-organised Criticality in the Modified Bak-Sneppen Model

We prove that a modified version of the Bak-Sneppen model obeys power law behaviour for avalanche duration and size. We do this through a coupling with a suitable branching process which is known to have power law behaviour at criticality.     

An absolute method for determination of misalignment of an immersion ultrasonic transducer

An absolute methodology has been developed for quantification of misalignment of an ultrasonic transducer using a corner-cube retroreflector. The amplitude based and the time of flight (TOF) based C-scans of the reflector are obtained for various misalignments of the transducer. At zero degree orientation of the transducer, the vertical positions of the maximum amplitude and the minimum TOF in the C-scan coincide. At any other orientation of the transducer with the horizontal plane, there is a vertical shift in the position of the maximum amplitude with respect to the minimum TOF. The position of the minimum (TOF) remains the same irrespective of the orientation of the transducer and hence is used as a reference for any misalignment of the transducer. With the measurement of the vertical shift and the horizontal distance between the transducer and the vertex of the reflector, the misalignment of the transducer is quantified. Based on the methodology developed in the present study, retroreflectors are placed in the Indian 500 MWe Prototype Fast Breeder Reactor for assessment of the orientation of the ultrasonic transducer prior to the under-sodium ultrasonic scanning for detection of any protrusion of the subassemblies.     

Convergence of tail sum for records

Suppose is the sequence of lower records from a distribution F, where F is continuous with . We derive conditions under which logarithm of the tail sum of records, ∑ _j=n ^∞ R _n ^(L) (F), properly centered and scaled, converge weakly. We also prove two results on Π-varying and regularly varying functions, which are of independent interest.     

On orthogonal ray graphs

An orthogonal ray graph is an intersection graph of horizontal and vertical rays (half-lines) in the xy-plane. An orthogonal ray graph is a 2-directional orthogonal ray graph if all the horizontal rays extend in the positive x-direction and all the vertical rays extend in the positive y-direction. We first show that the class of orthogonal ray graphs is a proper subset of the class of unit grid intersection graphs. We next provide several characterizations of 2-directional orthogonal ray graphs. Our first characterization is based on forbidden submatrices. A characterization in terms of a vertex ordering follows immediately. Next, we show that 2-directional orthogonal ray graphs are exactly those bipartite graphs whose complements are circular arc graphs. This characterization implies polynomial-time recognition and isomorphism algorithms for 2-directional orthogonal ray graphs. It also leads to a characterization of 2-directional orthogonal ray graphs by a list of forbidden induced subgraphs. We also show a characterization of 2-directional orthogonal ray trees, which implies a linear-time algorithm to recognize such trees. Our results settle an open question of deciding whether a (0,1)-matrix can be permuted to avoid the submatrices .     

Electrohydrodynamic transport of non‐symmetric electrolyte through porous wall of a microtube

Transport of salt through the wall of porous microtube is relevant in various physiological microcirculation systems. Transport phenomena based modeling of such system is undertaken in the present study considering a combined driving force consisting of pressure gradient and external electric field. Transport of salt is modeled in two domains, in the flow conduit and in the pores of porous wall of the microtube. The solute transport in the microtube is presented by convective‐diffusive mass balance and it is solved using integral method under the framework of boundary layer analysis. The wall of the microtube is considered to be consisting of series of straight parallel cylindrical pores with charged inner surface. The solute transport through the pores is considered to be composed of diffusive, convective and electric potential gradient governed by Nernst‐Planck equation. Transport in the microtube and pores is coupled through the osmotic pressure model for the solvent and Donnan equilibrium distribution for the solute. The simulated results agree remarkably well with the experimental data conducted by in‐house experimental set up. The charge density of the porous wall is estimated through the minimization of errors involved between the experimental and simulated data for different operating conditions.     

Magnetic Moment and Susceptibility Measurements of Mixed Rare Earth Oxalate Crystals

The growth of double rare earth oxalate crystals with a general chemical formula AB(C₂O₄)₃ · 10 H₂O (where A and H are Nd, Pr and Sm) is reported. The variation of the magnetic moment of these crystals with an external field is studied and the magnetic susceptibility and the effective magnetic moment are calculated. The observed effective magnetic moment of the crystals are in good agreement with those calculated on theoretical grounds.     

The effect of γ-ray-irradiated conducting polymer electrolyte and its application of dye-sensitized solar cells to building window glass system

Journal of Solid State Electrochemistry - In the present study, γ-ray-irradiated and un-irradiated PVA/PPy/KI/I2 conducting polymer electrolytes have been prepared for dye-sensitized solar...