Convergence of a penalty-finite element approximation for an obstacle problem

Summary This study establishes an error estimate for a penalty-finite element approximation of the variational inequality obtained by a class of obstacle problems. By special identification of the penalty term, we first show that the penalty solution converges to the solution of a mixed formulation of the variational inequality. The rate of convergence of the penalization is where is the penalty parameter. To obtain the error of finite element approximation, we apply the results obtained by Brezzi, Hager and Raviart for the mixed finite element method to the variational inequality.     

Protein identification by peptide mass fingerprinting and peptide sequence tagging with alternating scans of nano-liquid chromatography/infrared multiphoton dissociation Fourier transform ion cyclotron resonance mass spectrometry

We have developed a method for protein identification with peptide mass fingerprinting and sequence tagging using nano liquid chromatography (LC)/Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS). To achieve greater sensitivity, a nanoelectrospray (nano-ES) needle packed with reversed-phase medium was used and connected to the nano-ES ion source of the FTICR mass spectrometer. To obtain peptide sequence tag information, infrared multiphoton dissociation (IRMPD) was carried out in nano-LC/FTICR-MS analysis. The analysis involves alternating nano-ES/FTICR-MS and nano-ES/IRMPD-FTICR-MS scans during a single LC run, which provides sets of parent and fragment ion masses of the proteolytic digest. The utility of this alternating-scan nano-LC/IRMPD-FTICR-MS approach was evaluated by using bovine serum albumin as a standard protein. We applied this approach to the protein identification of rat liver diacetyl-reducing enzyme. It was demonstrated that this enzyme was correctly identified as 3-alpha-hydroxysteroid dehydrogenase by the alternating-scan nano-LC/IRMPD-FTICR-MS approach with accurate peptide mass fingerprinting and peptide sequence tagging.     

Dibenzylmagnesium-Initiated Anionic Oligomerizations of trans-Stilbene, 1,1-Diphenylethylene,and α-Methylstyrene in Hexamethylphosphortriamide

trans-Stilbene, 1, 1-diphenylethylene, and α-methylstyrene were allowed to react with dibenzylmagnesium to form their oligomers in hexamethylphosphortriamide (HMPA). One and two molecules of stilbene and 1, 1-diphenylethylene were incorporated into the magnesium carbon bond, and the carbanions obtained in HMPA were stable in analogy with the anionic living polymer having alkali cation as the gegenion in eithers. Intense coloration was observed during the reaction between α-methylstyrene and dibenzylmagnesium as well as in the case of stilbene and 1, 1-diphenylethylene. The low molecular weight products which were formed after a long time in the reaction between α-methylstyrene and dibenzylmagnesium were found to have no magnesium-carbon bond. It was considered that the cleavage of the propagating chain occurred gradually after the rapid propagation had proceeded to consume the monomer.     

Ishigadine A,a new canthin-6-one alkaloid from an Okinawan marine sponge Hyrtios sp.

A new indole alkaloid with the canthin-6-one skeleton, ishigadine A, has been isolated from an Okinawan marine sponge Hyrtios sp. The structure of ishigadine A was elucidated on the basis of spectroscopic analyses. Ishigadine A is a new canthin-6-one alkaloid possessing a hydroxy group, a 1,3-dimethyl-4-methylthioimidazolium, and a 1-propylguanidine. Ishigadine A is the third canthin-6-one alkaloid from sponges. Ishigadine A might be generated from l-arginine, l-histidine, and l-tryptophan. Ishigadine A exhibited moderate cytotoxicity against L1210 murine leukemia cells.     

Synthesis,Characterization, and Electronic Structures of Porphyrins Fused with Polycyclic Aromatic Ring Systems

A series of porphyrins fused with acenaphthylene, phenanthroline, and benzofluoranthene polycyclic aromatic rings were prepared by means of a 3+1 porphyrin synthesis approach and subsequent retro‐Diels–Alder reaction of bicyclo[2.2.2]octadiene‐fused precursors. Analysis of the magnetic circular dichroism spectra and the results of time‐dependent DFT calculations are used to identify the reasons for the trends observed in the wavelengths and relative intensities of the Q bands of the products. Michl's perimeter model is used as a conceptual framework to explain the changes in the relative energies of the frontier π‐molecular orbitals.     

Facile synthesis of graft copolymers containing rigid poly(dialkyl fumarate) branches by macromonomer method

Graft copolymers show microphase separated structure as seen in block copolymers and have lower intrinsic viscosity than block copolymers because of a branching structure. Therefore, considering molding processability, especially for polymers containing rigid segments, graft copolymers are useful architectures. In this work, graft copolymers containing rigid poly(diisopropyl fumarate) (PDiPF) branches were synthesized by full free‐radical polymerization process. First, synthesis of PDiPF macromonomers by addition‐fragmentation chain transfer (AFCT) was investigated. 2,2‐Dimethyl‐4‐methylene‐pentanedioic acid dimethyl ester was found to be an efficient AFCT agent for diisopropyl fumarate (DiPF) polymerization because of the suppression of undesired primary radical termination, which significantly took place when common AFCT agent, methyl 2‐(bromomethyl)acrylate, was used. Copolymerization of PDiPF macromonomer with ethyl acrylate accomplished the generation of the graft copolymer having flexible poly(ethyl acrylate) backbone and rigid PDiPF branches. The graft copolymer showed a microphase separated structure, high transparency, and characteristic thermal properties to PDiPF and poly(ethyl acrylate). © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2474–2480     

Order-Stability in Complex Biological,Social, and AI-Systems from Quantum Information Theory

This paper is our attempt, on the basis of physical theory, to bring more clarification on the question “What is life?” formulated in the well-known book of Schrödinger in 1944. According to Schrödinger, the main distinguishing feature of a biosystem’s functioning is the ability to preserve its order structure or, in mathematical terms, to prevent increasing of entropy. However, Schrödinger’s analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schrödinger also appealed to the ambiguous notion of negative entropy. We apply quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of classical entropy. We consider a complex biosystem S composed of many subsystems, say proteins, cells, or neural networks in the brain, that is, S=(Si). We study the following problem: whether the compound system S can maintain “global order” in the situation of an increase of local disorder and if S can preserve the low entropy while other Si increase their entropies (may be essentially). We show that the entropy of a system as a whole can be constant, while the entropies of its parts rising. For classical systems, this is impossible, because the entropy of S cannot be less than the entropy of its subsystem Si. And if a subsystems’s entropy increases, then a system’s entropy should also increase, by at least the same amount. However, within the quantum information theory, the answer is positive. The significant role is played by the entanglement of a subsystems’ states. In the absence of entanglement, the increasing of local disorder implies an increasing disorder in the compound system S (as in the classical regime). In this note, we proceed within a quantum-like approach to mathematical modeling of information processing by biosystems—respecting the quantum laws need not be based on genuine quantum physical processes in biosystems. Recently, such modeling found numerous applications in molecular biology, genetics, evolution theory, cognition, psychology and decision making. The quantum-like model of order stability can be applied not only in biology, but also in social science and artificial intelligence.     

Structures and Reaction Mechanism of Novel Metal-Carbene Complexes Derived from Hypervalent Diazadiselenathiapentalenes

Abstract

Novel metal-carbene complexes (4) with a metallapentalene framework have been obtained from hypervalent diazadiselenathiapentalenes (3) by treating with Pt(PPh₃)₄, Pd(PPh₃)₄ and RhCl(PPh₃)₃. X-Ray investigations revealed that the central hypervalent sulfur atom in 3 was substituted by a metal atom to form M-Se bonds in the resultant metallapentalene framework.     

Total Synthesis of the 7,10‐Epimer of the Proposed Structure of Amphidinolide N,Part II: Synthesis of C17–C29 Subunit and Completion of the Synthesis

The total synthesis of 7,10‐epimer of the proposed structure of amphidinolide N was accomplished. The requisite chiral C17–C29 subunit was assembled stereoselectively via Keck allylation, Shi epoxidation, diastereoselective 1,3‐reduction, and a later oxidative synthesis of the THF framework. The C1–C13 and C17–C29 subunits were successfully coupled using a Enders RAMP “linchpin” as the C14–C16 three carbon unit, thereby controlling the chirality at C14 and C16. The labile allyl epoxy moiety was successfully constructed by Grieco–Nishizawa olefination at a final stage of the synthesis.     

Synthesis,Redox Properties,and Electronic Spectra of Sterically Crowded Triarylphosphines Conjugated with Electron Acceptors

Abstract

Synthesis, redox properties, and electronic spectra of the sterically crowded triarylphosphines conjugated with π-electron systems, especially electron acceptors such as carbonyl group, are briefly reviewed. The sterically crowded triarylphosphines conjugated with various π-electron systems were synthesized from the common synthetic intermediate, (bromoaryl)phosphine, by conventional manner. The sterically crowded triarylphosphines conjugated with the electron acceptors exhibit visible absorption and fluorescence with large Stokes shift. Large solvent effect, redshift in polar solvent, and good correlation with the difference of the oxidation potential of the phosphine moiety and the reduction potential of the acceptor moiety suggest polar excited state resulting from HOMO-LUMO transition.