A new application method for nonoscillation criteria of Hille-Wintner type

The present paper deals with nonoscillation problem for the Sturm–Liouville half-linear differential equation

$$\begin{aligned} \big (r(t)\phi _p(x')\big )' + c(t)\phi _p(x) = 0, \end{aligned}$$

where r, \(c\!:[a,\infty ) \rightarrow \mathbb {R}\) are continuous functions, \(r(t) > 0\) for \(t \ge a\), and \(\phi _p(z) = |z|^{p-2}z\) with \(p > 1\). The purpose of this paper is to show that it is possible to broaden the application range of Hille-Wintner type nonoscillation criteria. To this end, we derive a comparison theorem by means of Riccati’s technique. Our result is new even in the linear case that \(p = 2\). By the obtained result, we can compare two differential equations having a different power p of the above-mentioned type. To illustrate our comparison theorem, we present two examples of which all non-trivial solutions of the Sturm-Liouville linear differential equation are nonoscillatory even if \(\int _a^t\!\frac{1}{r(s)}ds\int _t^\infty \!\!c(s)ds\) or \(\int _t^\infty \!\!\frac{1}{r(s)}ds\int _a^t\!c(s)ds\) is less than the lower bound \(-3/4\).

     

Lattice surfaces and smallest triangles

We calculate the area of the smallest triangle and the area of the smallest virtual triangle for many known lattice surfaces. We show that our list of the lattice surfaces for which the area of the smallest virtual triangle greater than \(1\over 20\) is complete. In particular, this means that there are no new lattice surfaces for which the area of the smallest virtual triangle is greater than .05. Our method follows an algorithm described by Smillie and Weiss and improves on it in certain respects.     

Admissibility of linear estimators with respect to inequality constraints under some loss functions

In this paper, we study the issue of admissibility of linear estimated functions of parameters in the multivariate linear model with respect to inequality constraints under a matrix loss and a matrix balanced loss. Under the matrix loss, when the model is not constrained, the results in the class of non-homogeneous linear estimators [Xie, 1989, Chinese Sci. Bull., 1148–1149; Xie, 1993, J. Multivariate Anal., 1071–1074] showed that the admissibility under the matrix loss and the trace loss is equivalent. However, when the model is constrained by the inequality constraints, we find this equivalency is not tenable, our result shows that the admissibility of linear estimator does not depend on the constraints again under this matrix loss, but it is contrary under the trace loss [Wu, 2008, Linear Algebra Appl., 2040–2048], and it is also relative to the constraints under another matrix loss [He, 2009, Linear Algebra Appl., 241–250]. Under the matrix balanced loss, the necessary and sufficient conditions that the linear estimators are admissible in the class of homogeneous and non-homogeneous linear estimators are obtained, respectively. These results will support the theory of admissibility on the linear model with inequality constraints.     

The Analysis of Phenolic Compounds in Walnut Husk and Pellicle by UPLC-Q-Orbitrap HRMS and HPLC

Husk and pellicle as the agri-food waste in the walnut-product industry are in soaring demand because of their rich polyphenol content. This study investigated the differential compounds related to walnut polyphenol between husk and pellicle during fruit development stage. By using ultra-high performance liquid chromatography-quadrupole-orbitrap (UHPLC-Q-Orbitrap), a total of 110 bioactive components, including hydrolysable tannins, flavonoids, phenolic acids and quinones, were tentatively identified, 33 of which were different between husk and pellicle. The trend of dynamic content of 16 polyphenols was clarified during walnut development stage by high-performance liquid chromatography (HPLC). This is the first time to comprehensive identification of phenolic compounds in walnut husk and pellicle, and our results indicated that the pellicle is a rich resource of polyphenols. The dynamic trend of some polyphenols was consistent with total phenols. The comprehensive characterization of walnut polyphenol and quantification of main phenolic compounds will be beneficial for understanding the potential application value of walnut and for exploiting its metabolism pathway.     

Two New Aristolochic Acid Analogues from the Roots of Aristolochia contorta with Significant Cytotoxic Activity

Twelve compounds, including two new aristolochic acid analogues with a formyloxy moiety (9–10) and 10 known aristolochic acid derivates (1–8 and 11–12), were obtained from the roots of Aristolochia contorta. Their structures were elucidated using extensive spectroscopic methods. Their cytotoxic activity in human proximal tubular cells HK-2 was evaluated by the MTT method, which has been widely used to assess cell viability. Among these molecules, compounds 3 and 9 were found to be more cytotoxic. Furthermore, molecular modeling was used to evaluate, for the first time, the interactions of compounds 3 and 9 with the target protein organic anionic transporter 1 (OAT1) that plays a key role in mediating aristolochic acid nephropathy. Structure–activity relationships are briefly discussed.     

Advances in nucleic acid architectures for electrochemical sensing

Nucleic acid–based electrochemical sensors are ideally suited to the detection of molecular targets for which enzymatic detection or direct electrochemical oxidation – reduction reactions are not possible. Moreover, the versatility of nucleic acids in their ability to bind a great variety of target types, from small molecules to single-entity mesoscopic targets, makes them attractive receptors for the development of electrochemical biosensors. In this brief opinion piece, we discuss field advances from the past two years. We hope the works highlighted here will inspire the community to pursue creative designs enabling the detection of larger and more complex targets with a specific focus on analytical validation and translation into preclinical or clinical applications.     

Nonflammable nonaqueous electrolytes for lithium batteries

As the energy density of state-of-the-art lithium (Li)-ion batteries (LIBs) increases, the safety concern of LIBs using liquid electrolytes is drawing increasing attention. Flammability of electrolytes is a critical link of the overall safety performance of LIBs and Li metal batteries. For this reason, intensive efforts have been devoted to suppressing the flammability of liquid electrolytes. In this short review, the common approaches to reduce the flammability of the nonaqueous liquid electrolytes will be summarized. The advantages and limitations of these approaches will also be discussed.     

Evaluation of Poly(glycidyl methacrylate)-Coated Column for Enantioseparation with Azithromycin Lactobionate and Clindamycin Phosphate as Chiral Selectors in Capillary Electrophoresis

Chromatographia - In this study, a poly(glycidyl methacrylate) nanoparticle (PGMA NP)-coated column system with two antibiotics as selector was constructed for enantioseparation. The PGMA NP...     

1H NMR Reassignment for Z/E-Benzomalvins B and Absolute Configuration of Benzomalvin C

Chemistry of Natural Compounds - Benzomalvins B, C, and E (1, 2, and 3) were simultaneously obtained from the marine fungus Aspergillus sp. isolated from the soft coral Sinularia sp., collected...