Generalized Connected Functions with Respect to Cones

In this paper, generalized connected functions with respect to cones such as quasi cone-connected, pseudo cone-connected, strongly pseudo cone-connected, and strictly pseudo cone-connected functions are introduced; necessary and sufficient optimality conditions are obtained for a weak minimum, a minimum, and a strong minimum of a vector-valued minimization problem. A Mond–Weir type dual is associated, and weak and strong duality results are established.     

Solvent effects on chemical processes. 3. Surface tension of binary aqueous organic solvents

The surface tension of binary solvents is modelled by analogy to solvation effects arising from solvent-solute interactions. Competitive exchange equilibria are postulated between solvent component I (water) and solvent component 2 (organic cosolvent) for solute, which in this case is air; the solvation shell is thus the surface phase. A quantitative relationship is given between surface tension and mole fractions x₁ and x₂, the model parameters being exchange equilibrium constants K₁ and K₂. The equation is analyzed, it is applied to literature surface tension data, and it is compared with an earlier model from this laboratory. Curve-fits are very good, and the parameters appear to possess physical significance.     

Synthesis of oleylamine capped copper nanocrystals via thermal reduction of a new precursor

The present investigation reports the novel synthesis of copper nanocrystals using thermal reduction, and their physicochemical characterization. The copper nanocrystal powder has been prepared using [bis(2-hydroxyacetophenato)copper(II)] as a precursor. The effect of oleylamine and triphenylphosphine on the particle morphology has been investigated. Transmission electron microscopy (TEM) analysis has demonstrated that the copper nanocrystals have an average diameter of about 3 nm. The as-prepared copper nanocrystals were characterized by XRD, SEM, TEM, EDX, UV–Vis and FTIR.     

Temperature controlled synthesis of SrCO3 nanorods via a facile solid-state decomposition rout starting from a novel inorganic precursor

Strontium carbonate nanorods have been successfully synthesized via solid-state decomposition of a new precursor, [Sr(Pht)(H₂O)₂]. The obtained nanorods were found to be orthorhombic with the length of 70-100 nm and the diameter of about 10-15 nm. The Effect of calcinations temperature on morphology and purity of the products has been investigated. Strontium carbonate nanorods were formed at 500 °C. The products were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM) and Fourier transform infrared (FT-IR) spectroscopy. In addition, further evidence for the purity and stoichiometry of the product was obtained by XPS (X-ray photoelectron spectroscopy) spectrum.     

Hitting probabilities for systems of non-linear stochastic heat equations with multiplicative noise

We consider a system of d non-linear stochastic heat equations in spatial dimension 1 driven by d-dimensional space-time white noise. The non-linearities appear both as additive drift terms and as multipliers of the noise. Using techniques of Malliavin calculus, we establish upper and lower bounds on the one-point density of the solution u(t, x), and upper bounds of Gaussian-type on the two-point density of (u(s, y),u(t, x)). In particular, this estimate quantifies how this density degenerates as (s, y) → (t, x). From these results, we deduce upper and lower bounds on hitting probabilities of the process ${\{u(t,x)\}_{t \in \mathbb{R}_+, x\in [0,1]}}$ , in terms of respectively Hausdorff measure and Newtonian capacity. These estimates make it possible to show that points are polar when d ≥ 7 and are not polar when d ≤ 5. We also show that the Hausdorff dimension of the range of the process is 6 when d > 6, and give analogous results for the processes ${t \mapsto u(t,x)}$ and ${x \mapsto u(t,x)}$ . Finally, we obtain the values of the Hausdorff dimensions of the level sets of these processes.     

Strong approximations in a charged-polymer model

We study the large-time behavior of the charged-polymer Hamiltonian H _n of Kantor and Kardar [Bernoulli case] and Derrida, Griffiths, and Higgs [Gaussian case], using strong approximations to Brownian motion. Our results imply, among other things, that in one dimension the process {H _[nt]}_0≤t≤1 behaves like a Brownian motion, time-changed by the intersection local-time process of an independent Brownian motion. Chung-type LILs are also discussed.     

Chung's law for integrated Brownian motion

The small ball problem for the integrated process of a real-valued Brownian motion is solved. In sharp contrast to more standard methods, our approach relies on the sample path properties of Brownian motion together with facts about local times and Lévy processes.

     

Brownian sheet images and Bessel-Riesz capacity

We show that the image of a 2-dimensional set under -dimensional, 2-parameter Brownian sheet can have positive Lebesgue measure if and only if the set in question has positive ()-dimensional Bessel-Riesz capacity. Our methods solve a problem of J.-P. Kahane.

     

Images of the Brownian sheet

An -parameter Brownian sheet in maps a non-random compact set in to the random compact set in . We prove two results on the image-set :

(1) It has positive -dimensional Lebesgue measure if and only if has positive -dimensional capacity. This generalizes greatly the earlier works of J. Hawkes  (1977), J.-P. Kahane  (1985), and Khoshnevisan (1999).

(2) If , then with probability one, we can find a finite number of points such that for any rotation matrix that leaves in , one of the 's is interior to . In particular, has interior-points a.s. This verifies a conjecture of T. S. Mountford  (1989).

This paper contains two novel ideas: To prove (1), we introduce and analyze a family of bridged sheets. Item (2) is proved by developing a notion of ``sectorial local-non-determinism (LND).' Both ideas may be of independent interest.

We showcase sectorial LND further by exhibiting some arithmetic properties of standard Brownian motion; this completes the work initiated by Mountford (1988).

     

Thermal decomposition route for synthesis of Mn3O4 nanoparticles in presence of a novel precursor

The synthesis of manganese oxide (Mn₃O₄) nanoparticles by using thermal decomposition and its physicochemical characterization are being reported in present investigation. As a new precursor, [bis(2-hydroxy-1-naphthaldehydato)manganese(II)] complex was used in the presence of oleylamine (C₁₈H₃₇N) as both surfactant and solvent to control the size of resulting nanoparticle. The products were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), Fourier transform infrared (FT-IR) spectroscopy, thermogravimetric analysis (TGA), X-ray photoelectron spectroscopy (XPS) and Raman spectrum. Synthesized manganese oxide nanoparticles have a tetragonal structure with average size of 9–24 nm. The phase pure samples were characterized by using X-ray photoelectron spectroscopy (XPS) for Mn 2p level. The values of binding energies are consistent with the relative values are reported in the literature. As a comparison between two methods, the novel precursor thermally was treated in solid state reaction in different temperature, 400, 500, and 600 °C and the products were characterized by SEM images. Magnetic property of the as-prepared Mn₃O₄ nanoparticle shows a ferromagnetic behavior with high saturation magnetization and coercivity.