Representation Formulae for Solutions to Some Classes of Higher Order Systems and Related Liouville Theorems

Let m ≥ 1 be an integer and N > 2m. Let μ be a positive Radon measure on . We study necessary and sufficient conditions on possible distributional solutions of , that guarantee the validity of the representation formula a.e. on , where and c(2m) is a positive constant depending on m and N. Several consequences are derived. In particular we prove Liouville theorems for systems of higher order elliptic inequalities and weighted form of Hardy-Littlewood-Sobolev systems of integral equations. Received: March 2008     

The Square of Opposition and the Four Fundamental Choices

Each predicate of the Aristotelian square of opposition includes the word “is”. Through a twofold interpretation of this word the square includes both classical logic and non-classical logic. All theses embodied by the square of opposition are preserved by the new interpretation, except for contradictories, which are substituted by incommensurabilities. Indeed, the new interpretation of the square of opposition concerns the relationships among entire theories, each represented by means of a characteristic predicate. A generalization of the square of opposition is achieved by not adjoining, according to two Leibniz’ suggestions about human mind, one more choice about the kind of infinity; i.e., a choice which was unknown by Greek’s culture, but which played a decisive role for the birth and then the development of modern science. This essential innovation of modern scientific culture explains why in modern times the Aristotelian square of opposition was disregarded. This work was completed with the support of our -pert.     

On a Submersion Between Reinhart Lightlike Manifolds and Semi-Riemannian Manifolds

In this paper, we introduce a new submersion, namely, screen lightlike submersion between a lightlike manifold and a semi-Riemannian manifold. We give an example and obtain a characterization for lightlike manifold to be Reinhart under such submersion. Then, we investigate the geometry of a screen lightlike submersion when the total manifold is a Reinhart lightlike manifold. Received: March 6, 2007 Revised: October 4, 2007 and November 2, 2007 Accepted: December 6, 2007     

Positive Elements and Automatic Continuity of Algebra Morphisms

We use positive elements of Hermitian algebras to give results on automatic continuity of algebra morphisms. Consequences and applications are also given.      

Controlled growth for synthesizing a compact mordenite membrane

Controlling the growth of zeolite crystals on a porous alumina support is essential for preparing a compact zeolite membarne. First, mordenite seed crystals applied on a nonporous -alumina disk were grown and morphological change of mordenite crystals were observed in the course of growth. Then, mordenite membranes were synthesized on a porous -alumina tube under the same conditions employed in the study using the alumina disks. We found that seed crystal growth was widely controllable by changing water content in reaction solution, which resulted in better control of the morphology of mordenite crystals for synthesizing a thin compact mordenite membrane. Separation properties for mordenite membranes were studied in water–hydrogen binary system at 473 K with 10 kPa of water partial pressure, where no capillary condensation was expected in non-zeolitic pores. Separation factor for a mordenite membrane with a few defects was poor; however, a defect-free mordenite membrane prepared under a suitable condition highly separated steam from hydrogen.     

Polymerization effects on molecular dynamics of n-ethylene glycol dimethacrylates followed by dielectric relaxation spectroscopy

A detailed dielectric characterization of n-ethylene glycol dimethacrylate monomers with n = 2 and 4 is provided. Besides the α relaxation associated to the glass transition, two secondary relaxation processes were detected: the γ process assigned to the twisting motions within the ethylene glycol moiety, and the β process related with hindered rotations of carboxylic groups. While the relaxation time of the γ process is independent of the size of the ethylene glycol group, the β process deviates to higher times with increasing n. Upon polymerization the α process goes to extinction, faster in the 4-ethylene monomer, with a concomitant depletion of the β process that remains at higher polymerization degrees relatively to the α process, thus acting as a more sensitive probe to evaluate conversion. The height decrease of α and β processes of monomers with the polymerization progress, occurs without significant changes of position. At intermediate states of polymerization, a new relaxation process evolves being only detectable in a narrow temperature range. In the end, the polymer networks show, in addition to the γ_pol relaxation identical to the γ relaxation of the monomer, a β_pol relaxation with similar features to the β relaxation found in poly n-alkyl methacrylates originated by a π flip of the ester unit accompanied by a restricted main chain rearrangement. The main dielectric relaxation corresponding to the swollen polymer network should appear at quite high temperatures already in early stages of the polymerization process because phase segregation occurs and only a limited amount of liquid monomer plasticizes the newly formed material.     

LiNi0.5Mn1.5O4-xFx高电压电极高温保存下的电化学行为

采用溶胶-凝胶法结合高温热处理制备了锂离子电池用5 V正极材料LiNi0.5Mn1.5O4-xFx(x=0, 0.1). 通过X射线衍射(XRD)、扫描电子显微镜(SEM)和低温氮吸附法(BET)表征了粉体材料的结构、表面形貌和比表面特性, 并以其为正极材料装配电池后, 在85 ℃下高温保存24 h, 测量了保存前后电池的一系列电化学性质变化. 结果表明, 高温保存时电池开路电压会因自放电而较快地下降. 材料的比表面积和氟掺杂显著地影响电池的电压保持能力. 比表面积愈大, 电压保持时间愈短. 氟掺杂有利于提高电池在高温条件下的电压稳定性, 并可以改善电极与电解液之间的界面性质,使充放电性能更好.     

Metabolic Tumor Imaging with Rapidly Signal-Enhanced 1-13C-Pyruvate-d3

The metabolism of malignant cells differs significantly from that of healthy cells and thus, it is possible to perform metabolic imaging to reveal not only the exact location of a tumor, but also intratumoral areas of high metabolic activity. Herein, we demonstrate the feasibility of metabolic tumor imaging using signal-enhanced 1-¹³C-pyruvate-d₃, which is rapidly enhanced via para-hydrogen, and thus, the signal is amplified by several orders of magnitudes in less than a minute. Using as a model, human melanoma xenografts injected with signal-enhanced 1-¹³C-pyruvate-d3, we show that the conversion of pyruvate into lactate can be monitored along with its kinetics, which could pave the way for rapidly detecting and monitoring changes in tumor metabolism.     

Analysis of steroidal glycoalkaloids and their metabolites in Solanum nigrum fruits based on liquid chromatography-tandem mass spectrometry and molecular networking

Solanum nigrum fruit is like a treasure house for anticancer drugs because of its steroidal alkaloids. However, the clinical treatment of cancer mainly uses immature fruits, which can cause a toxic reaction if eaten directly, while mature fruits are eaten as fruit. In order to clarify the reasons for the differences in pharmacodynamics and toxicity between them, we studied the composition and metabolism of steroidal alkaloids in fruits of different maturities based on liquid chromatography-tandem mass spectrometry and molecular networking. As a result, 114 steroidal glycoalkaloids were identified. During fruit ripening, the aglycones of steroidal alkaloids mainly undergo hydroxylation and carboxylation, and the sugar side chains mainly undergo acylation and glycosylation reactions. Furthermore, 219 steroidal alkaloids were identified in a metabolism experiment in rats. Metabolic processes include deglycosylation, redox, sulfuric acid binding, acetyl binding, and glucuronic acid-binding. Steroidal alkaloids in mature fruits have high molecular weight and polarity, which are difficult to absorb, and most of them are excreted through feces and urine, which may be the reason for their poor efficacy. This study lays a foundation for research on the biosynthesis of steroidal alkaloids and provides potential candidates for the discovery of new steroidal alkaloid anticancer drugs.     

Optical coherence tomography based imaging of dental demineralisation and cavity restoration in 840 nm and 1310 nm wavelength regions

In this paper, a study of in-house built optical coherence tomography (OCT) system with a wavelength of 840 nm for imaging of dental caries, progress in demineralisation and cavity restoration is presented. The caries when imaged with the 840 nm OCT system showed minute demineralisation in the order of 5 μm. The OCT system was also proposed to study the growth of lesion and this was demonstrated by artificially inducing caries with a demineralisation solution of pH 4.8. The progress of carious lesion to a depth of about 50–60 μm after 60 hours of demineralisation was clearly observed with the 840 nm OCT system. The tooth samples were subjected to accelerated demineralisation condition at pH of approximately 2.3 to study the adverse effects and the onset of cavity formation was clearly observed. The restoration of cavity was also studied by employing different restorative materials (filled and unfilled). In the case of restoration without filler material (unfilled), the restoration boundaries were clearly observed. Overall, results were comparable with that of the widely used 1310 nm OCT system. In the case of restoration with filler material, the 1310 nm OCT imaging displayed better imaging capacity due to lower scattering than 840 nm imaging.