Moments of wishart distribution

Moments of central and noncentral Wishart distributions are obtained by differentiating their characteristic functions applying matrix derivative techniques, using a special operator which takes into account the symmetry of the matrices. As a special case, higher moments of the multivariate normal distribution are obtained, arranged automatically in a square matrix form     

Conductivity as a Sensor for Monitoring Relative Magnesium Corrosion Rates in Real‐time,in Serum‐containing Media under Cell Culture Conditions

Because controlling the corrosion rate of magnesium metal will be crucial to the success of biomedical implants containing pure magnesium or magnesium alloys, many ways have been sought to improve in vitro tests to analyze corrosion rates, and also to identify new methods of preparing or post‐processing magnesium. In this work, for an in vitro assay, we explored the use of a commercially available conductivity sensor to study magnesium corrosion under cell culture conditions that duplicate many physiologically appropriate parameters. With this sensor, we studied the corrosion of two previously untested magnesium single crystal samples that differed in surface treatments that could alter corrosion rates. The results show that the relative conductivity changes in (mS/cm) over the total time of immersion were proportional to the corrosion rates in (mm/y) and also to the total magnesium released, as detected by inductively coupled plasma mass spectrometry (ICP‐MS).     

Syntheses of 3-Chloro-7-[(Chlorocarbonyl)Methoxy]-4-Methylcoumarin

Two efficient syntheses of 3-chloro-7-[(chlorocarbonyl)methoxy]-4-methylcoumarin are described, one utilizing traditional chemistry starting from 3-chloro-7-hydroxy-4-methylcoumarin, while the other uses a novel reagent, sulfuryl chloride/thionyl chloride, in a one-pot reaction starting from 7-(carboxymethoxy)-4-methylcoumarin.     

Isoregic Thienylene‐Phenylene Polymers: The Effects of Structural Variation and Application to Photovoltaic Devices

Isoregic conjugated polymers composed of thiophene and dialkoxybenzene units were designed to harvest incident light in the mid‐visible energy range (band gap of 2.1 eV). Poly(1,4‐bis(2‐thienyl)‐2,5‐diheptoxybenzene) (PBTB(OC₇H₁₅)₂) and poly(1,4‐bis(2‐thienyl)‐2,5‐didodecyloxybenzene) (PBTB(OC₁₂H₂₅)₂) have shown significant photovoltaic performance as an electron donor when used in tandem with the electron acceptor [6, 6]‐phenyl C₆₁‐butyric acid methyl ester (PCBM) in bulk hetero‐junction photovoltaic devices. Photovoltaic devices incorporating PBTB(OC₇H₁₅)₂ and PCBM have shown AM1.5 efficiencies of ～0.6% with a short circuit current density of 2.5 mA/cm², an open circuit voltage of 0.74 V, and a fill factor of 0.32. Incident Photon‐to‐Current Efficiency (IPCE) of the device was found to be ca. 16% at 410 nm. In order to examine the relationship between the molecular structure of the polymers and their electronic energy levels, and to correlate this with photovoltaic performance, optoelectronic and electrochemical results are discussed in relation to the I‐V characteristics of the devices. Additionally, a computer‐aided simulation is used to gain further insight into the effect of polymer structure on the energetic relationships in the bulk heterojunction devices.     

Expanding conceptions of utility: middle school students’ perspectives on the usefulness of mathematics

This research explores how adolescents conceptualize the usefulness of mathematics. Integrating sociocultural theory with the study of utility value, this study uses open-ended survey items and interview tasks to examine conceptions of usefulness among a group of predominantly Latinx middle school students. Findings reveal that students primarily conceptualized the usefulness of mathematics in two ways. First, students considered the applicability of mathematics content, focusing on applications of mathematics in everyday life and future jobs/careers. Second, students considered the usefulness of features of the learning experience, such as the form of interaction and structure of the activity. Both conceptions are compared to existing conceptions of usefulness in the literature, and implications for classroom practice and future research are discussed.     

Synthesis of Amino Acid Derived Cyclic Phosphorus Ylides

Abstract

We recently reported the thermal elimination of Ph₃PO from suitably protected aminoacyl ylides 1 as a route to acetylenic amino acid analogues 2. Pyrolysis of ylides such as 3 with a free amino group takes a different course. Ethanol is eliminated to give the c h i d cyclic ylides 4 which can be viewed as 3-triphenylphosphoranylidene tetramic acids. Specific examples prepared include 4 (R = Me, Pri), the parent compound 5 (from glycine) and the six-membered ring compound 6 (from p-alanine). Using a similar approach, bicyclic ylides such as 7 (from proline) can be prepared. In the case of the glutamate derived ylide 8, thermolysis initially gives a mixturc of 9 and 10 but these both cyclise to the bicyclic product 11 with time. The structure and reactivity of these interesting cyclic ylides are now being examined.     

Synthesis,characterization and antioxidant,antibacterial activity Zn2+, Cu2+, Ni2+ and Co2+, complexes of ligand [2-(thiophen-2-yl)-1-(thiophen-2-ylmethyl)-1H-benzo[d]imidazole]

New metal complexes of (Zn(II), Co(II), Ni(II) and Cu(II)) based on the ligand 2-(thiophen-2-yl)-1-(thiophen-2-ylmethyl)-1H-benzo[d]imidazole] were synthesized, whose structures were determined with the different spectroscopic techniques ¹H NMR,¹³C NMR, FT-IR, UV–Visible and by mass spectrometry. The thermal analysis was performed by TG-DTA. The antioxidant activity of the ligand and its complexes was evaluated by DPPH (2,2-diphenyl-1-picrylhydrazyl) method, in comparison with the synthetic antioxidant, ascorbic acid. The results obtained showed that the antioxidant activity of the ligand and its complexes is moderate and that the copper complex has a high activity that exceeds that of ascorbic acid. Antimicrobial activity of the ligand and its metal complexes was studied against two Gram-positive bacteria: Bacillus subtilis ILP1428B, Staphylococcus aureus CIP543154 and two Gram-negative bacteria: Pseudomonas aeruginosa ATCC27653, Escherichia coli CIP5412 (American Type Culture Collection)the activity data show that the metal complexes are more potent than the free ligand.     

Thermal degradation of trimethylolpropane/adipic acid hyperbranched poly(ester)s

Hyperbranched poly(ester)s offer attractive features for applications in a number of areas, particularly as platforms for the support of controlled release actives in the agricultural and biomedical fields. Such materials have been generated from trimethylolpropane and adipic acid, and fully characterized using chromatographic, spectroscopic, and thermal methods. The thermal stability of these polymers has been assessed using thermogravimetry and infrared spectroscopy. The degradation characteristics of these materials have been compared to those of two linear adipic acid polymers. The prominent feature of the thermal degradation of the hyperbranched poly(ester)s is ether formation while that for the comparable linear poly(ester)s is ester pyrolysis resulting in chain scission.     

An MRI‐Sensitive,Non‐Photobleachable Porphysome Photothermal Agent

Photothermal therapy makes use of photothermal sensitizers and laser light to thermally ablate diseased tissues. Porphysome nanoparticles offer a nontoxic alternative to inorganic nanocrystals for the efficient conversion of light into heat. Mn³⁺ ions were incorporated directly into the building blocks of our porphysome nanoparticles, thus imparting MRI sensitivity while simultaneously improving photostability and maintaining high photothermal efficiency. Mn porphysomes are as photothermally effective as free‐base porphysomes and can rival gadolinium diethylenetriaminepentaacetate (Gd‐DTPA) for MRI contrast generation. Their MRI contrast generation, photothermal efficiency, and photostability are unprecedented for an all‐organic nanoparticle composed of a single functional component.     

Selective ion-molecule reactions of lactams with dimethyl ether ions

The ion-molecule reactions of dimethyl ether ions CH₃OCH₃ ⁺ and (CH₃OCH₃)H⁺, and four- to seven-membered ring lactams with methyl substituents in various positions were characterized by using a quadrupole ion trap mass spectrometer and a triple-quadrupole mass spectrometer. In both instruments, the lactams were protonated by dimethyl ether ions and formed various combinations of [M + 13] ⁺, [M + 15] ⁺, and [M + 45] ⁺ adduct ions, as well as unusual [M + 3] ⁺ and [M + 16] ⁺ adduct ions. An additional [M + 47] ⁺ adduct ion was formed in the conventional chemical ionization source of the triple-quadrupole mass spectrometer. The product ions were isolated and collisionally activated in the quadrupole ion trap to understand formation pathways, structures, and characteristic dissociation pathways. Sequential activation experiments were performed to elucidate fragment ion structures and stepwise dissociation sequences. Protonated lactams dissociate by loss of water, ammonia, or methylamine; ammonia and carbon monoxide; and water and ammonia or methylamine. The [M + 16] ⁺ products, which are identified as protonated lactone structures, are only formed by those lactams that do not have an N-methyl substituent. The ion-molecule reactions of dimethyl ether ions with lactams were compared with those of analogous amides and lactones.