Liouville theorem for weighted p-Lichnerowicz equation on smooth metric measure space

In this paper, let $(M^n,g,d\mu )$ be n-dimensional noncompact metric measure space which satisfies Poincaré inequality with some Ricci curvature condition. We obtain a Liouville theorem for positive weak solutions to weighted p-Lichnerowicz equation

${△}_{p,f}v+c{v}^{\sigma }=0,$

where $c\le 0,m>n\ge 1,1<p<\frac{m?1+\sqrt{(m?1)(m+3)}}{2},\sigma \le p?1$ are real constants.     

The character and the wave front set correspondence in the stable range

We relate the distribution characters and the wave front sets of unitary representation for real reductive dual pairs of type I in the stable range.     

Nano-sized Cu(II) and Zn(II) complexes and their use as a precursor for synthesis of CuO and ZnO nanoparticles: A study on their sonochemical synthesis,characterization, and DNA-binding/cleavage,anticancer, and antimicrobial activities

Two new divalent copper (C1) and zinc (C2) chelates having the formulae [M(PIMC)₂] (where M = Cu(II), Zn(II) and PIMC = Ligand [(E)-3-(((3-hydroxypyridin-2-yl)imino)methyl)-4H-chromen-4-one] were obtained and characterized by several techniques. Structures and geometries of the synthesized complexes were judged based on the results of alternative analytical and spectral tools supporting the proposed formulae. IR spectral data confirmed the coordination of the ligands to the copper and zinc centers as monobasic tridentate in the enol form. Thermal analysis, UV-Vis spectra and magnetic moment confirmed the geometry around the copper center to be tetrahedral, square pyramidal and octahedral. Study of the binding ability of the synthesized compounds with Circulating tumor DNA (CT-DNA) bas been evaluated applying UV-Vis spectral titration and viscosity measurements. The copper and zinc oxides were achieved from the copper and zinc nano-particles structures Schiff base complexes as the raw material after calcination for 5 hr at 600°C. On the other hand, synthesized of C1 and C2 NPs were used as suitable precursors to the preparation of CuO and ZnO NPs. Finally, the synthesized of the two complexes exhibited enhanced activity against the tested bacterial (Staphylococcus aureus and Escherichia Coli) and fungal strains (Candida albicans and Aspergillus fumigatus) as compared to HPIMC. Among all these synthesized compounds, C1 exhibits good cleaving ability compared to other newly synthesized C2.     

Design and development of a two‐dimensional system based on hydrophilic and reversed‐phase liquid chromatography with on‐line sample treatment for the simultaneous separation of excreted xenobiotics and endogenous metabolites in urine

In the present work we describe a two‐dimensional liquid chromatographic system (2D‐LC) with detection by mass spectrometry (MS) for the simultaneous separation of endogenous metabolites of clinical interest and excreted xenobiotics deriving from exposure to toxic compounds. The 2D‐LC system involves two orthogonal chromatographic modes, hydrophilic interaction liquid chromatography (HILIC) to separate polar endogenous metabolites and reversed‐phase (RP) chromatography to separate excreted xenobiotics of low and intermediate polarity. Additionally, the present proposal has the novelty of incorporating an on‐line sample treatment based on the use of restricted access materials (RAMs), which permits the direct injection of urine samples into the system. The work is focused on the instrumental coupling, studying all possible options and attempting to circumvent the problems of solvent incompatibility between the RAM device and the two chromatographic columns, HILIC and RP. The instrumental configuration developed, RAM‐HILIC‐RPLC‐MS/MS, allows the simultaneous assessment of urinary metabolites of clinical interest and excreted compounds derived from exposure to toxic agents with minimal sample manipulation. Thus, it may be of interest in areas such as occupational and environmental toxicology in order to explore the possible relationship between the two types of compounds. Copyright © 2015 John Wiley & Sons, Ltd.     

ON THE CONVERGENCE OF MULTIPLICATIVE ITERATIVE ALGORITHMS WITH INEXACT LINE SEARCH

1.IntroductionIntillspaperweanalyzetheconvergenceonmultiplicativeiterativealgorithmsfortheIninimizationofadiffcrentiablefunctiondefinedonthepositiveorthantofR".ThealgorithmissllggestedbyEggermolltl'],andisrelatedtotheEM[2](Expextation--Maximization)algoritllnlforPositronemissiontonlography[']andimagereconstructi..14].Wecollsidertheproblenl"linf(x)s.t.x20.Themultiplicativeiterativealgorithmshavethel'orlniforj=l,2,',n,withAhdeterminedthroughalinesearch.Whilelusem[5]establishedanelegantconv…     

COMPACT COUPLED LINEAR TAPERED LINE BANDPASS FILTER WITH TWO TRANSMISSION ZEROS

A new compact bandpass filter composed of two coupled linear tapered line resonators (LTLRs) is designed. The two resonators are arranged in different layers. The filter has two transmission zeros on both sides of the passband. It has small size and steep response below its passband. It is also shown that this filter has 0.6 dB low insertion loss at the centre frequency and 10.5% 3dB bandwidth. This work was supported by the Development Foundation of Shanghai Educational Committee (217608) and Shanghai Leading Academic Discipline Project (T0102).     

A rational approximation and its applications to nonlinear partial differential equations on the whole line

An orthogonal system of rational functions is discussed. Some inverse inequalities, imbedding inequalities and approximation results are obtained. Two model problems are considered. The stabilities and convergences of proposed rational spectral schemes and rational pseudospectral schemes are proved. The techniques used in this paper are also applicable to other problems on the whole line. Numerical results show the efficiency of this approach.     

On the realization of Riemannian symmetric spaces in Lie groups

In this paper we give a realization of some symmetric space G/K as a closed submanifold P of G. We also give several equivalent representations of the submanifold P. Some properties of the set gK∩P are also discussed, where gK is a coset space in G.     

Challenging Students to View the Concept of Area in Triangles in a Broad Context: Exploiting the Features of Cabri-II

This study focuses on the constructions in terms of area and perimeter in equivalent triangles developed by students aged 12–15 years-old, using the tools provided by Cabri-Geometry II [Labore (1990). Cabri-Geometry (software), Université de Grenoble]. Twenty-five students participated in a learning experiment where they were asked to construct: (a) pairs of equivalent triangles “in as many ways as possible” and to study their area and their perimeter using any of the tools provided and (b) “any possible sequence of modifications of an original triangle into other equivalent ones”. As regards the concept of area and in contrast to a paper and pencil environment, Cabri provided students with different and potential opportunities in terms of: (a) means of construction, (b) control, (c) variety of representations and (d) linking representations, by exploiting its capability for continuous modifications. By exploiting these opportunities in the context of the given open tasks, students were helped by the tools provided to develop a broader view of the concept of area than the typical view they would construct in a typical paper and pencil environment.     

On the density of the space of continuous and uniformly continuous functions

For X a metrizable space and (Y,ρ) a metric space, with Y pathwise connected, we compute the density of (C(X,(Y,ρ)),σ)—the space of all continuous functions from X to (Y,ρ), endowed with the supremum metric σ. Also, for (X,d) a metric space and (Y,‖⋅‖) a normed space, we compute the density of (UC((X,d),(Y,ρ)),σ) (the space of all uniformly continuous functions from (X,d) to (Y,ρ), where ρ is the metric induced on Y by ‖⋅‖). We also prove that the latter result extends only partially to the case where (Y,ρ) is an arbitrary pathwise connected metric space.To carry such an investigation out, the notions of generalized compact and generalized totally bounded metric space, introduced by the author and A. Barbati in a former paper, turn out to play a crucial rôle. Moreover, we show that the first-mentioned concept provides a precise characterization of those metrizable spaces which attain their extent.