The particle in a box problem inq-quantum mechanics

Aq-deformed,q-Hermitian kinetic energy operator is realised and hence aq-Schrödinger equation (q-SE) is obtained. Theq-SE for a particle confined in an infinite potential box is solved and the energy spectrum is found to have an upper bound.     

Reliable estimation via simulation

Leta ands denote the inter arrival times and service times in aGI/GI/1 queue. Let a⁽ⁿ⁾, s⁽ⁿ⁾ be the r.v.s. with distributions as the estimated distributions ofa ands from iid samples ofa ands of sizesn. Letw be a r.v. with the stationary distribution of the waiting times of the queue with input(a,s). We consider the problem of estimatingE[w ], > 0 and via simulations when (a ⁽ⁿ⁾,s⁽ⁿ⁾) are used as input. Conditions for the accuracy of the asymptotic estimate, continuity of the asymptotic variance and uniformity in the rate of convergence to the estimate are obtained. We also obtain rates of convergence for sample moments, the empirical process and the quantile process for the regenerative processes. Robust estimates are also obtained when an outlier contaminated sample ofa ands is provided. In the process we obtain consistency, continuity and asymptotic normality of M-estimators for stationary sequences. Some robustness results for Markov processes are included.     

Phase transitions and low-frequency dielectric dispersion in the solid phase of bromoform

Phase transitions in the solid phase of bromoform have been studied by dielectric and differential scanning calorimetric techniques. Two modifications of the solid phase, solid I and solid II, have been observed above and below about ?35°C respectively. Solid phase I exhibits clear Debye-type dispersion in the 0.5 to 100 kHz frequency region, while solid phase II exhibits complete dipole freezing.     

Ni selective sensors based on meso-tetrakis-{4-[tris-(4-allyl dimethylsilyl-phenyl)-silyl]-phenyl}porphyrin and (sal)2trien in poly(vinyl chloride) matrix

PVC-based membranes of meso-tetrakis-{4-[tris-(4-allyl dimethylsilyl-phenyl)-silyl]-phenyl}porphyrin (I) and (sal)₂trien (II) as electroactive material with dioctylphthalate (DOP), tri-n-butylphosphate (TBP), chloronapthalene (CN), dibutylphthalate (DBP) and dibutyl(butyl) phosphonate (DBBP) as plasticising solvent mediators have been found to act as Ni²⁺ selective sensor. The best performance was obtained with the sensor having a membrane of composition of I: sodium tetraphenyl borate: PVC in the ratio 5:5:150. The sensor exhibits Nernstian response in the activity range 2.5 × 10⁻⁶ to 1.0 × 10⁻¹ M, performs satisfactorily over wide pH range (2–5.5) with a fast response time (8 s). The sensor was found to work satisfactorily in partially non-aqueous media up to 20% (v/v) content of methanol or ethanol and acetone and could be used over a period of 4 months. Potentiometric selectivity coefficients determined by matched potential method (MPM) indicate excellent selectivity for Ni²⁺ ions. The sensors could be used successfully in the estimation of nickel in different brand of chocolates and also as an indicator electrode in potentiometric titration.     

Development of urethane acrylate composite ion-exchange membranes and their electrochemical characterization

With the objective of introducing antifouling characteristics into interpolymer types of cation and anion exchange membranes, the surface of these membranes was coated with a 12-microm-thick urethane acrylate layer and was cured by UV radiation of wavelengths 308 and 172 nm under a complete inert atmosphere. Different urethane acrylate composite ion exchange membranes developed were characterized in NaCl solution by measuring their ion-exchange capacity, volume fraction of water, contact angle with water, membrane conductance, and membrane potential. It was found that the electrochemical transport properties of urethane acrylate composite cation-exchange membranes were increased due to resonance stabilization of the urethane group, which acts as a weak acid and dissociates as a negatively charged urethane ion and a positively charged proton. This contributes toward the net charge density of the membrane matrix responsible for enhanced selectivity and conductivity, while for urethane acrylate composite anion-exchange membranes reduction in net charge density was responsible for reduction in electrochemical transport properties. Counterion transport number, permselectivity, and counterion diffusion coefficient values for these membranes were also estimated. Experiments were also carried out in higher homologs of sodium carboxylate solutions in order to observe the fouling tendencies of these membranes. It was concluded that it is possible to obtain antifouling characteristics of ion-exchange membranes by coating and curing thin hydrophilic layers of urethane acrylate on their surfaces without sacrificing their electrochemical transport properties.     

Pressure-induced phase transitions in Al2(WO4)3

The high pressure behavior of aluminum tungstate [Al₂(WO₄)₃] has been investigated up to ∼18 GPa with the help of Raman scattering studies. Our results confirm the recent observations of two reversible phase transitions below 3 GPa. In addition, we find that this compound undergoes two more phase transitions at ∼5.3 and ∼6 GPa before transforming irreversibly to an amorphous phase at ∼14 GPa.     

Gelation of aqueous pectin solutions: a dynamic light scattering study

We report the dynamic light scattering study of the gelation of aqueous solutions of the biopolymer, pectin, induced by the addition of calcium chloride. The time correlation function data are analyzed under the framework of the coupling model. As the solution enters the semidilute regime where gelation sets in, the relaxation process shows a stretched exponential behavior. The stretching exponent decreases and the characteristic time of the stretched exponential diverges as the system evolves to a gel. Aqueous pectin solutions in the presence of 0.1 M NaCl show similar behavior. Thus, the molecular relaxation modes of pectin solutions can be well described by the coupling model.     

A highly selective mercury electrode based on a diamine donor ligand

(H₂NCHMeCH₂NH₂)(H₂O)₂HgCl₂ (I) was synthesised, characterised and used for the fabrication of a potentiometric sensor for Hg²⁺ metal ions. Membrane having I as electroactive material, sodium tetraphenyl borate (NaTPB) as an anion excluder, dibutylamine (DBA) as plasticizer in PVC matrix in the percentage ratio of 10:3:150:150 (I:NaTPB:DBA:PVC) (w/w) exhibits a linear response to Hg²⁺ ions in a concentration range of 1.25 × 10⁻⁵ to 1.0 × 10⁻¹ M having a detection limit of 8.9 × 10⁻⁶ with a slope of 25 ± 0.1 mV over the pH range 6.6-9.3. Selectivity coefficients for Hg(II) relative to a number of interfering ions were investigated. The electrode is highly selective for Hg²⁺ ions over a large number of mono-, bi-, and trivalent cations. Normal interferents like Ag⁺ and Cd²⁺ do not interfere in the working of the electrode. The electrode has also been used successfully in mixtures having a 10% (v/v) methanol and acetone content without showing any considerable change in working concentration range or slope. These electrodes have been found to be chemically inert showing a fast response time of 10 s and were used over a period of 4 months with good reproducibility (s = ±0.2). The electrode was used for determination of mercury in binary mixtures with 100% recovery and thus the proposed sensor can be used for real sample analysis.     

Catalytic and electrocatalytic oxidation of aniline to nitrobenzene over vanadium silicate molecular sieves: VS-1 usingt-butyl hydroperoxide (TBHP) as oxidant

A comparison of the results of catalytic and electrocatalytic oxidation of aniline using VS-1 in the presence of H₂O₂ and TBHP indicates remarkable differences in conversion and selectivity. VS-1 catalyzes the oxidation of aniline selectively to nitrobenzene (73%) in the presence oft-butyl hydroperoxide (TBHP), while azoxybenzene (95.2%) is formed selectively when H₂O₂ is used. Cyclic voltammetric studies show a three-step oxidation of aniline to nitrobenzene in H₂O₂ but in the presence of TBHP only one step is observed. Electrocatalytic oxidation of aniline to nitrobenzene occurs at a potential 700 mV less than that corresponding to H₂O₂ as oxidant along with a selectivity of 91.8%. The enhancement of electrocatalytic rate is attributed to the stabilization of electron deficient transition state.     

Surprises in the design of anion receptors: calorimetry prevents false reasoning

Supplementing bicyclic guanidinium anion receptors with four sec-carboxamido groups leads to enhanced affinity for oxoanions, however, for a different reason than originally planned. Calorimetric analysis reveals that better binding is due to higher association entropies rather than more negative enthalpies. Thus, molecular design following geometric and functional complementarity principles may misguide supramolecular constructions aimed at a unique host-guest binding mode, as required, e.g., by self-assembly or catalysis.