Gabor systems and almost periodic functions

Inspired by results of Kim and Ron, given a Gabor frame in $L^2(\mathbb{R})$, we determine a non-countable generalized frame for the non-separable space ${\mathit{AP}}_2(\mathbb{R})$ of the Besicovic almost periodic functions. Gabor type frames for suitable separable subspaces of ${\mathit{AP}}_2(\mathbb{R})$ are constructed. We show furthermore that Bessel-type estimates hold for the AP norm with respect to a countable Gabor system using suitable almost periodic norms of sequences.     

Approximations in Sobolev spaces by prolate spheroidal wave functions

Recently, there is a growing interest in the spectral approximation by the Prolate Spheroidal Wave Functions (PSWFs) ${\psi }_{n,c},c>0$. This is due to the promising new contributions of these functions in various classical as well as emerging applications from Signal Processing, Geophysics, Numerical Analysis, etc. The PSWFs form a basis with remarkable properties not only for the space of band-limited functions with bandwidth c, but also for the Sobolev space $H^s([?1,1])$. The quality of the spectral approximation and the choice of the parameter c when approximating a function in $H^s([?1,1])$ by its truncated PSWFs series expansion, are the main issues. By considering a function $f\in H^s([?1,1])$ as the restriction to $[?1,1]$ of an almost time-limited and band-limited function, we try to give satisfactory answers to these two issues. Also, we illustrate the different results of this work by some numerical examples.     

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.     

Asymmetric Synthesis of a Quaternary Carbon Stereogenic Center by Organocatalysis Using a Primary Amino Acid and Its Salt

In this personal account, our recent developments on the asymmetric synthesis of a quaternary carbon stereogenic center by organocatalysis using a primary amino acid and its salt as a catalyst are described in three chapters: (1) conjugate addition to nitroalkenes and vinyl ketones, (2) nucleophilic addition to π-allyl palladium complexes, and (3) nucleophilic substitution reactions with allyl and propargyl halides. By these methods, asymmetric α-allylation of α-branched aldehydes and ketones smoothly proceeded to give γ-nitroaldehydes, ketoaldehydes, α-allylated aldehydes, and α-allylated β-ketoesters possessing a quaternary carbon stereogenic center in good yields with high enantioselectivities.     

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.     

酸溶-电感耦合等离子体发射光谱法测定白云石和菱镁石中主次元素

利用电感耦合等离子体原子发射光谱仪( ICP-AES)建立白云石和菱镁石中铝、钙、铁、镁、锰、磷、硅、锶的测定方法。研究了酸体系、温度及消解方式对试样消解的影响,结果表明,使用5 mL盐酸和硝酸混合酸(1：3)-0.75 mL氢氟酸-5 mL水以密闭消解的方式在150 ℃下消解白云石和菱镁石30min,并以2mL饱和硼酸络合多余的氢氟酸,可以得到澄清消解液。通过白云石和菱镁石中铝、钙、铁、镁、锰、磷、硅、锶的谱线干扰情况,选择Al 308.215 nm、Ca 318.127 nm、Fe 261.187 nm、Mg 277.983 nm、Mn 257.61 nm、P 213.618 nm、Si 251.611 nm、Sr 421.552 nm作为分析线,各元素的校准曲线在线性范围内线性关系良好,相关系数均不小于0.999。按照实验方法测定白云石和菱镁石标准物质,各元素结果的相对标准偏差 (RSD, n=6)为0.89~3.19%,测定值与认定值无显著性差异。本方法有效解决了白云石和菱镁石快速有效溶解及准确测定问题。     

Microorganisms as a Potential Source of Molecules to Control Trypanosomatid Diseases

Trypanosomatids are the causative agents of leishmaniasis and trypanosomiasis, which affect about 20 million people in the world’s poorest countries, leading to 95,000 deaths per year. They are often associated with malnutrition, weak immune systems, low quality housing, and population migration. They are generally recognized as neglected tropical diseases. New drugs against these parasitic protozoa are urgently needed to counteract drug resistance, toxicity, and the high cost of commercially available drugs. Microbial bioprospecting for new molecules may play a crucial role in developing a new generation of antiparasitic drugs. This article reviews the current state of the available literature on chemically defined metabolites of microbial origin that have demonstrated antitrypanosomatid activity. In this review, bacterial and fungal metabolites are presented; they originate from a range of microorganisms, including cyanobacteria, heterotrophic bacteria, and filamentous fungi. We hope to provide a useful overview for future research to identify hits that may become the lead compounds needed to accelerate the discovery of new drugs against trypanosomatids.     

Methylation of Cyanidin-3-O-Glucoside with Dimethyl Carbonate

The approach presented in this study is the first for the hemisynthesis of methylated anthocyanins. It was possible to obtain cyanidin-3-O-glucoside derivatives with different degrees of methylation. Cautious identification of 4′-, 5-, and 7-OH monomethylated derivatives was also accomplished. The methylation agent used was the “green chemical” dimethyl carbonate (DMC), which is characterized by low human and ecological toxicity. The influence of the temperature, reaction time, and amount of the required diazabicyclo[5.4.0]undec-7-en (DBU) catalyst on the formation of the products was examined. Compared to conventional synthesis methods for methylated flavonoids using DMC and DBU, the conditions identified in this study result in a reduction of reaction time, and an important side reaction, so-called carboxymethylation, was minimized by using higher amounts of catalyst.