Exact and approximation product solutions form of heat equation with nonlocal boundary conditions using Ritz–Galerkin method with Bernoulli polynomials basis

In this article, a new method is introduced for finding the exact solution of the product form of parabolic equation with nonlocal boundary conditions. Approximation solution of the present problem is implemented by the Ritz–Galerkin method in Bernoulli polynomials basis. The properties of Bernoulli polynomials are first presented, then Ritz–Galerkin method in Bernoulli polynomials is used to reduce the given differential equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the techniques presented in this article for finding the exact and approximation solutions. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1143–1158, 2017     

Optimality conditions and duality results for nonsmooth vector optimization problems with the multiple interval-valued objective function

In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a (weakly) LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a (weakly) LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval-objective function are convex.     

Bolzano's Theorems for Holomorphic Mappings

The existence of a zero for a holomorphic functions on a ball or on a rectangle under some sign conditions on the boundary generalizing Bolzano's ones for real functions on an interval is deduced in a very simple way from Cauchy's theorem for holomorphic functions.A more complicated proof,using Cauchy's argument principle,provides uniqueness of the zero,when the sign conditions on the boundary are strict.Applications are given to corresponding Brouwer fixed point theorems for holomorphic functions.Extensions to holomorphic mappings from Cn to Cn are obtained using Brouwer degree.     

Renormalized solutions of elliptic equations with Robin boundary conditions

In the present paper, we consider elliptic equations with nonlinear and nonhomogeneous Robin boundary conditions of the type{-div(B(x, u)▽u) = f in ?,u = 0 on Γ_0,B(x, u)▽u·n→+γ(x)h(u) =g on Γ_1,where f and g are the element of L~1(?) and L~1(Γ_1), respectively. We define a notion of renormalized solution and we prove the existence of a solution. Under additional assumptions on the matrix field B we show that the renormalized solution is unique.     

一类1 < α < 2非局部条件下的脉冲分数阶微分方程mild解的存在性

本文研究了一类1 < α < 2非局部条件下的脉冲分数阶偏微分方程mild解的存在性问题.利用解算子的相关性质及Krasnoselskii不动点理论的方法,获得了这类方程的mild解并予以证明,且得到了解的存在性结果.     

Optimal portfolio execution under time-varying liquidity constraints

In this article, we take an algorithmic approach to solve the problem of optimal execution under time-varying constraints on the depth of a limit order book (LOB). Our algorithms are within the resilience model proposed by Obizhaeva and Wang (2013) with a more realistic assumption on the order book depth; the amount of liquidity provided by an LOB market is finite at all times. For the simplest case where the order book depth stays at a fixed level for the entire trading horizon, we reduce the optimal execution problem into a one-dimensional root-finding problem which can be readily solved by standard numerical algorithms. When the depth of the order book is monotone in time, we apply the Karush-Kuhn-Tucker conditions to narrow down the set of candidate strategies. Then, we use a dichotomy-based search algorithm to pin down the optimal one. For the general case, we start from the optimal strategy subject to no liquidity constraints and iterate over execution strategy by sequentially adding more constraints to the problem in a specific fashion until primal feasibility is achieved. Numerical experiments indicate that our algorithms give comparable results to those of current existing convex optimization toolbox CVXOPT with significantly lower time complexity.     

SMART: A data reporting standard for mass spectrometry imaging By Ying Xi,Alexandria L. Sohn,Alena N. Joignant,Stephanie M. Cologna,Boone M. Prentice and David C. Muddiman

Mass spectrometry imaging (MSI) is an important analytical technique that simultaneously reports the spatial location and abundance of detected ions in biological, chemical, clinical, and pharmaceutical studies. As MSI grows in popularity, it has become evident that data reporting varies among different research groups and between techniques. The lack of consistency in data reporting inherently creates additional challenges in comparing intra- and inter-laboratory MSI data. In this tutorial, we propose a unified data reporting system, SMART, based on the common features shared between techniques. While there are limitations to any reporting system, SMART was decided upon after significant discussion to more easily understand and benchmark MSI data. SMART is not intended to be comprehensive but rather capture essential baseline information for a given MSI study; this could be within a study (e.g., effect of spot size on the measured ion signals) or between two studies (e.g., different MSI platform technologies applied to the same tissue type). This tutorial does not attempt to address the confidence with which annotations are made nor does it deny the importance of other parameters that are not included in the current SMART format. Ultimately, the goal of this tutorial is to discuss the necessity of establishing a uniform reporting system to communicate MSI data in publications and presentations in a simple format to readily interpret the parameters and baseline outcomes of the data.     

B(C6F5)3-Catalyzed Aza-Friedel–Crafts Reaction of Indolizines with 2-Aryl-3H-indol-3-ones

A Friedel–Crafts reaction of indolizines with 2-aryl-3H-indol-3-ones catalyzed by B(C₆F₅)₃ is described. This protocol gives access to indolizine derivatives that are valuable building blocks in synthetic and pharmaceutical chemistry. The reaction proceeds under mild conditions, affording various C2-quaternary indolin-3-ones based on indolizine with high yields and regioselectivities. Moreover, the synthetic transformations of the target products were realized by N-methylation and trifluoromethane sulfonation.     

Composite Mesoporous Silica Nanoparticles with Dual-color Afterglow for Cross-correlation-based Living Cell Imaging

Room temperature phosphorescence (RTP) materials are characterized with emission after removing the excitation source. Such long-lived emission feature possesses great potential in biological fluorescence imaging because it enables a way regarding temporal dimension for separating the interference of autofluorescence and common noises typically encountered in conventional fluorescence imaging. Herein, we constructed a new type of mesoporous silica nanoparticles (MSNs)-based composite nanoparticles (NPs) with dual-color long-lived emission, namely millisecond-level green phosphorescence and sub-millisecond-level delayed red fluorescence by encapsulating a typical RTP dye and Rhodamine dye in the cavities of the MSNs with the former acting as energy donor (D) while the latter as acceptor (A). Benefiting from the close D-A proximity, energy match between the donor and the acceptor and the optimized D/A ratio in the composite NPs, efficient triplet-to-singlet Förster resonance energy transfer (TS-FRET) in the NPs occurred upon exciting the donor, which enabled dual-color long-lived emission. The preliminary results of dual-color correlation imaging of live cells based on such emission feature unequivocally verified the unique ability of such NPs for distinguishing the false positive generated by common emitters with single-color emission feature.     

Redox Properties and in Vivo Magnetic Resonance Imaging of Cyclodextrin-Polynitroxides Contrast Agents

This paper reports the synthesis, characterization and in vivo application of water-soluble supramolecular contrast agents (Mw: 5–5.6 kDa) for MRI obtained from β-cyclodextrin functionalized with different kinds of nitroxide radicals, both with piperidine structure ( CD2 and CD3 ) and with pyrrolidine structure ( CD4 and CD5 ). As to the stability of the radicals in presence of ascorbic acid, CD4 and CD5 have low second order kinetic constants (≤0.05 M⁻¹ s⁻¹) compared to CD2 (3.5 M⁻¹ s⁻¹) and CD3 (0.73 M⁻¹ s⁻¹). Relaxivity (r₁) measurements on compounds CD3 - CD5 were carried out at different magnetic field strength (0.7, 3, 7 and 9.4 T). At 0.7 T, r₁ values comprised between 1.5 mM⁻¹ s⁻¹ and 1.9 mM⁻¹ s⁻¹ were found while a significant reduction was observed at higher fields (r₁≈0.6-0.9 mM⁻¹ s⁻¹ at 9.4 T). Tests in vitro on HEK293 human embryonic kidney cells, L929 mouse fibroblasts and U87 glioblastoma cells indicated that all compounds were non-cytotoxic at concentrations below 1 μmol mL⁻¹. MRI in vivo was carried out at 9.4 T on glioma-bearing rats using the compounds CD3 - CD5 . The experiments showed a good lowering of T₁ relaxation in tumor with a retention of the contrast for at least 60 mins confirming improved stability also in vivo conditions.