Weighted bounds for multilinear operators with non-smooth kernels

Let $T$ be a multilinear integral operator which is bounded on certain products of Lebesgue spaces on $\mathbb R^n$. We assume that its associated kernel satisfies some mild regularity condition which is weaker than the usual H\"older continuity of those in the class of multilinear Calder\'on-Zygmund singular integral operators. In this paper, given a suitable multiple weight $\vec{w}$, we obtain the bound for the weighted norm of multilinear operators $T$ in terms of $\vec{w}$. As applications, we exploit this result to obtain the weighted bounds for certain singular integral operators such as linear and multilinear Fourier multipliers and the Riesz transforms associated to Schr\"odinger operators on $\mathbb{R}^n$. Our results are new even in the linear case

Application of Spherical Copper Oxide (II) Water Nano-fluid as a Potential Coolant in a Boiling Annular Heat Exchanger

Convective boiling heat transfer coefficient of spherical CuO (II) nanoparticles dispersed in water is experimentally quantified inside the vertical heat exchanger. Influence of different operating parameters including applied heat and mass fluxes, sub-cooling temperature and concentration of nano-fluid on forced convection and nucleate boiling heat transfer mechanisms is experimentally investigated and briefly discussed. Results show that by increasing heat and mass fluxes, the heat transfer coefficient considerably increases for both heat transfer regions, while by increasing the nanoparticle weight concentration, the heat transfer coefficient increases in convective heat transfer (about 35 % at the maximum concentration) and deteriorates the heat transfer coefficient (about 9 % at maximum concentration) in nucleate boiling region due to the formation of nanoparticle deposition on heating surface. Experimental results are then compared to well-known correlations. Results of comparisons reveal good agreement between experimental data and those obtained by some correlations. In addition, thermo-physical properties of CuO nano-fluid are experimentally measured and represented, which are a good reference for other nano-fluid-related studies

New bounds for bilinear Calderón-Zygmund operators and applications

In this work we extend Lacey’s domination theorem to prove the pointwise control of bilinear Calderón–Zygmund operators with Dini–continuous kernel by sparse operators. The precise bounds are carefully tracked following the spirit in a recent work of Hytönen, Roncal and Tapiola. We also derive new mixed weighted estimates for a general class of bilinear dyadic positive operators using multiple $A_\infty$ constants inspired in the Fujii-Wilson and Hrusˇcˇev classical constants. These estimates have many new applications including mixed bounds for multilinear Calderón–Zygmund operators and their commutators with $BMO$ functions, square functions and multilinear Fourier multipliers.Analytic-probabilistic methods for borderline singular integrals; MTM2015-63699-P "Análisis Complejo, Espacios de Banach y Operadores

Topological Quantum Computing with Only One Mobile Quasiparticle

In a topological quantum computer, universal quantum computation is performed by dragging quasiparticle excitations of certain two dimensional systems around each other to form braids of their world lines in 2+1 dimensional space-time. In this paper we show that any such quantum computation that can be done by braiding $n$ identical quasiparticles can also be done by moving a single quasiparticle around n-1 other identical quasiparticles whose positions remain fixed.Comment: 4 pages, 5 figure

Topological Quantum Compiling

A method for compiling quantum algorithms into specific braiding patterns for non-Abelian quasiparticles described by the so-called Fibonacci anyon model is developed. The method is based on the observation that a universal set of quantum gates acting on qubits encoded using triplets of these quasiparticles can be built entirely out of three-stranded braids (three-braids). These three-braids can then be efficiently compiled and improved to any required accuracy using the Solovay-Kitaev algorithm.Comment: 20 pages, 20 figures, published versio

Braid Topologies for Quantum Computation

In topological quantum computation, quantum information is stored in states which are intrinsically protected from decoherence, and quantum gates are carried out by dragging particle-like excitations (quasiparticles) around one another in two space dimensions. The resulting quasiparticle trajectories define world-lines in three dimensional space-time, and the corresponding quantum gates depend only on the topology of the braids formed by these world-lines. We show how to find braids that yield a universal set of quantum gates for qubits encoded using a specific kind of quasiparticle which is particularly promising for experimental realization.Comment: 4 pages, 4 figures, minor revision

A new bifunctional hybrid nanostructure as an active platform for photothermal therapy and MR imaging

As a bi-functional cancer treatment agent, a new hybrid nanostructure is presented which can be used for photothermal therapy by exposure to one order of magnitude lower laser powers compared to similar nanostructures in addition to substantial enhancment in magnetic resonance imaging (MRI) contrast. This gold-iron oxide hybrid nanostructure (GIHN) is synthesized by a cost-effective and high yield water-based approach. The GIHN is sheilded by PEG. Therefore, it shows high hemo and biocompatibility and more than six month stability. Alongside earlier nanostructures, the heat generation rate of GIHN is compareable with surfactnat-capped gold nanorods (GNRs). Two reasons are behind this enhancement: Firstly the distance between GNRs and SPIONs is adjusted in a way that the surface plasmon resonance of the new nanostructure is similar to bare GNRs and secondly the fraction of GNRs is raised in the hybrid nanostructure. GIHN is then applied as a photothermal agent using laser irradiation with power as low as 0.5 W.cm−2 and only 32% of human breast adenocarcinoma cells could survive. The GIHN also acts as a dose-dependent transvers relaxation time (T2) MRI contrast agent. The results show that the GINH can be considered as a good candidate for multimodal photothermal therapy and MRI

The effect of Setarud (IMOD�) on angiogenesis in transplanted human ovarian tissue to nude mice

Background: One of the promising methods in fertility preservation among women with cancer is cryopreservation of ovarian cortex but there are many drawbacks such as apoptosis and considerable reduction of follicular density in the transplanted ovary. One solution to reduce ischemic damage is enhancing angiogenesis after transplantation of ovarian cortex tissue. Objective: The aim of this study was to investigate the effect of Setarud, on angiogenesis in transplanted human ovarian tissue. Materials and Methods: In this case control study, twenty four nude mice were implanted subcutaneously, with human ovarian tissues, from four women. The mice were randomly divided into two groups (n=12): the experimental group was treated with Setarud, while control group received only vehicle. Each group was divided into three subgroups (n=4) based on the graft recovery days post transplantation (PT). The transplanted fragments were removed on days 2, 7, and 30 PT and the expression of Angiopoietin-1, Angiopoietin-2, and Vascular endothelial growth factor at both gene and protein levels and vascular density were studied in the grafted ovarian tissues. Results: On the 2nd and 7th day PT, the level of Angiopoietin-1 gene expression in case group was significantly lower than that in control group, while the opposite results were obtained for Angiopoietin-2 and Vascular endothelial growth factor. These results were also confirmed at the protein level. The density of vessels in Setarud group elevated significantly on day 7 PT compared to pre-treatment state. Conclusion: Our results showed that administration of Setarud may stimulates angiogenesis in transplanted human ovarian tissues, although further researches are needed before a clear judgment is made. � 2015, Research and Clinical Center for Infertitlity. All rights reserved