Uniqueness for Quasi-variational Inequalities

This paper presents a uniqueness result for a quasi-variational inequality QVI(1) that, in contrast to existing results, does not require the projection mapping on a variable closed and convex set to be a contraction. Our basic idea is to find a simple QVI(0), for example a variational inequality, for which we can show the existence of a unique solution. Further, exploiting some nonsingularity condition, we will guarantee the existence of a continuous solution path from the unique solution of QVI(0) to a solution of QVI(1). Finally, we can show that the existence of a second different solution of QVI(1) contradicts the nonsingularity condition. Moreover, we present some matrix-based sufficient conditions for our nonsingularity assumption, and we discuss these assumptions in the context of generalized Nash equilibrium problems with quadratic cost and affine linear constraint functions.     

Millisecond pulsars with r-modes as steady gravitational radiators

Millisecond pulsars (MSPs) probably achieve their fast rotation by mass transfer from their companion stars in low-mass x-ray binaries (LMXBs). The lack of MSPs and LMXBs rotating near breakup has been attributed to the accretion torque being balanced, at fast rotation, by gravitational radiation, perhaps caused by an unstable oscillation mode. It has been argued that internal dissipation involving hyperons may cause LMXBs to evolve into a quasisteady state, with nearly constant rotation rate, temperature, and mode amplitude. We show that MSPs descending from these LMXBs spend a long time in a similar state, as extremely steady sources of gravitational waves and thermal x rays, while they spin down due to gravitational radiation and the standard magnetic torque. Observed MSP braking torques already place meaningful constraints on this scenario.     

Sparse blind deconvolution and demixing through <Emphasis Type="Italic">ℓ</Emphasis><Subscript>1,2</Subscript>-minimization

This paper concerns solving the sparse deconvolution and demixing problem using ? _1,2-minimization. We show that under a certain structured random model, robust and stable recovery is possible. The results extend results of Ling and Strohmer (Inverse Probl. 31, 115002 2015), and in particular theoretically explain certain experimental findings from that paper. Our results do not only apply to the deconvolution and demixing problem, but to recovery of column-sparse matrices in general.     

A Carbene‐Extended ATRA Reaction

Atom‐transfer radical addition (ATRA) reactions have gained a strong foothold in organic synthesis by virtue of their operational simplicity, synthetic versatility, and perfect atom economy. A rich chemical space can be accessed through clever combinations of the simple starting materials. Many variations of this general motif have been reported. However, the vast majority involve the addition of an organic halide across a C=C double bond, resulting in the formation of 1,2‐bifunctional products. This report introduces a significant expansion of this general reactivity concept to give 1,3‐bifunctional adducts through the combination of 1,1‐ATRA to a carbenoid and 1,2‐ATRA to an alkyne. Both processes operate under mild conditions (RT, 5 h) with the same commercial catalyst (CoBr₂, dppbz).     

Synthese,Struktur und einige Reaktionen [N-(N′,N′,N″,N″-tetramethyl)-guanidinyl]-substituierter Phosphorylverbindungen

Synthesis, Structure, and some Reactions of N-(N′,N′,N″,N″-tetramethyl)guanidinyl-substituted Phosphoryl Compounds The tetramethylguanidinyl-substituted phosphoryl compounds 1 – 10 were prepared in the reaction of the appropriate chlorophosphoryl compounds with either N′,N′,N″,N″-tetramethylguanidine (HTMG) or N-trimethylsilyl-(N′,N′,N″,N″-tetramethyl)guanidine (TMSTMG). With methyl iodide 1 reacted with N-alkylation to give the ammonium salt 11. 1 reacted with BF₃ · Et₂O at both imino nitrogen atoms with formation of the bis-BF₃-adduct 12 . The X-ray structure determination of phenylphosphonic acid-bis(N′,N′,N″,N″-tetramethylguanidinide) 3 shows shortened PN-bonds and widened PNC-angles, consistent with the partial double bond character of the PN-bond.     

Synthesis and Structure of Monomeric,Trimeric, and Mixed Phenylcyanamides

In a new synthetic approach phenylcyanamide (Hpca) was synthesized by methylation of phenylthiourea followed by a basic work‐up. All products along the synthetic route have been fully characterized by means of NMR, IR, and X‐ray studies. The first structural report of neutral mixed crystals of phenylcyanamide containing monomeric and trimeric Hpca is presented. Examination of these intriguing mixed crystals revealed the formation of distinct layers of monomeric and trimeric Hpca. These layers are interconnected by weak hydrogen bonds. The trimer represents triphenylisomelamine, which readily isomerizes to the triphenylmelamine in the melt, in accord with computations at the B3LYP level, indicating an exothermic process (ΔH=?49.4 kcal mol^?1). Pure trimeric Hpca (triphenylisomelamine) was obtained either by recrystallization of the mixed crystals from boiling water or by trimerization of monomeric Hpca in isopropanol for 12 h under reflux conditions. For comparison tritylcyanamide (Htca) and potassium phenylcyanamide as an [18]crown‐6 complex [K([18]crown‐6)pca] have been synthesized, and the solid‐state structures were determined using X‐ray diffraction techniques. The thermal behavior was studied by thermo‐analytical experiments. In agreement with the experimental results, computations predict an exothermic cyclotrimerization process for Hpca (ΔH=?41.3 kcal mol^?1).     

Carbon incorporation in Pd(111) by adsorption and dehydrogenation of ethene

The decomposition of ethene on the Pd(111) surface was studied at effective pressures in the 10(-8) to 10(-7) mbar range and at sample temperatures between 300 and 700 K, using an effusive capillary array beam doser for directional adsorption, LEED, AES, temperature programmed reaction, and TDS. In the temperature range of 350-440 K increasingly stronger dehydrogenation of the ethene molecule is observed. Whereas at 350 K an ethylidyne adlayer is still present after adsorption, already at temperatures around 440 K complete coverage of the surface by carbon is attained, while the bulk still retains the properties of pure Pd. Beyond 440 K a steady-state surface C coverage is established, which decreases with temperature and is determined by detailed balancing between the ethene gas-phase adsorption rate and the migration rate of carbon into the Pd bulk. This process gives rise to the formation of a "partially carbon-covered Pd(x)C(y) surface". Above 540 K the surface-bulk diffusion of adsorbed carbon becomes fast, and in the UHV experiment the ethene adsorption rate becomes limited by the ethene gas-phase supply. The carbon bulk migration rate and the steady-state carbon surface coverage were determined as a function of the sample temperature and the ethene flux. An activation energy of 107 kJ mol(-1) for the process of C diffusion from surface adsorption sites into the subsurface region was derived in the temperature range of 400-650 K by modeling the C surface coverage as a function of temperature on the basis of steady-state reaction kinetics, assuming a first-order process for C surface-subsurface diffusion and a second-order process for C(ads) formation by dissociative C2H4 adsorption.     

Chemoenzymatic approaches toward dechloroansamitocin P-3

[reaction: see text] The enantioselective total synthesis of proansamitocin, a key biosynthetic intermediate of the highly potent antitumor agent ansamitocin P-3, is described which bears a diene-ene RCM as the key macrocyclization step. Feeding of proansamitocin to an AHBA block mutant Actinosynnema pretiosum (HGF073) yielded ansamitocin P-3 as well as dechloroansamitocin P-3, the latter also being formed upon fermentation in the presence of 3-amino-5-methoxybenzoic acid.     

Enzyme activity control by responsive redoxpolymers

A new thermoresponsive poly-N-isopropylacrylamide (PNIPAM)-ferrocene polymer was synthesized and characterized. PNIPAMFoxy bears additional oxirane groups which were used for attachment by a self-assembly process on a cysteamine-modified gold electrode to create a thin hydrophilic film. The new redox polymer enabled electrical communication between the cofactor pyrrolinoquinoline quinone (PQQ) of soluble glucose dehydrogenase (sGDH) and the electrode for sensitive detection of this enzyme as a prospective protein label. The temperature influence on the redox polymer/enzyme complex was investigated. An inverse temperature response behavior of surface bound PNIPAMFoxy compared to the soluble polymer was found and is discussed in detail. The highest efficiency of mediated electron transfer for the immobilized PNIPAMFoxy with sGDH was observed at 24 degrees C, which was twice as high as that of its soluble counterpart. A steady-state electrooxidation current densitiy of 4.5 microA.cm-2 was observed in the presence of 10 nM sGDH and 5 mM glucose. A detection limit of 0.5 nM of soluble PQQ-sGDH was obtained.