On harmonic typically real mappings

In this paper, we prove that a univalent orientation-preserving harmonic mapping defined on the unit disk U with the normalization f(0)=0, , is a typically real mapping, if f(U) is a starlike domain with respect to the origin or f(U) is convex in one direction.     

Zero–One Law for some Brownian Functionals

We prove that for a>0, (B _t) one-dimensional standard Brownian motion and ₀=inf{t>0 : B _t=0} the following zero–one law is valid

Manganese Dioxide Mediated Stereoselective, One-step Synthesis of Novel Steroidal (6R)-Spiro-1’,2’,4’-triazoline-3’-thiones

Oxidative cyclization of 5α-cholestan-6-one thiosemicarbazone (1), its 3β-chloro (2) and 3β-acetoxy (3) analogues with active manganese dioxide at room temperature afforded selectively the corresponding (6R)-spiro-1’,2’,4’-triazoline-3’-thiones 4—6. This synthesis has the advantages of mild reaction conditions, easy handling, easily available reagent and high yields. The products have been characterized by analytical and spectral data.     

Combined finite difference and spectral methods for the numerical solution of hyperbolic equation with an integral condition

In this work the combined finite difference and spectral methods have been proposed for the numerical solution of the one‐dimensional wave equation with an integral condition. The time variable is approximated using a finite difference scheme. But the spectral method is employed for discretizing the space variable. The main idea behind this approach is that we can get high‐order results. The new method is used for two test problems and the numerical results are obtained to support our theoretical expectations. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Simultaneous reversible addition fragmentation chain transfer and ring‐opening polymerization

The simultaneous ring‐opening polymerization (ROP) of ε‐caprolactone (ε‐CL) and 2‐hydroxyethyl methacrylate (HEMA) polymerization via reversible addition fragmentation chain transfer (RAFT) chemistry and the possible access to graft copolymers with degradable and nondegradable segments is investigated. HEMA and ε‐CL are reacted in the presence of cyanoisopropyl dithiobenzoate (CPDB) and tin(II) 2‐ethylhexanoate (Sn(Oct)₂) under typical ROP conditions (T > 100 °C) using toluene as the solvent in order to lead to the graft copolymer PHEMA‐g‐PCL. Graft copolymer formation is evidenced by a combination of size‐exclusion chromatography (SEC) and NMR analyses as well as confirmed by the hydrolysis of the PCL segments of the copolymer. With targeted copolymers containing at least 10% weight of PHEMA and relatively small PHEMA backbones (ca. 5,000–10,000 g mol^?1) the copolymer grafting density is higher than 90%. The ratio of free HEMA‐PCL homopolymer produced during the “one‐step” process was found to depend on the HEMA concentration, as well as the half‐life time of the radical initiator used. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3058–3067, 2008     

One‐pot synthesis of star‐block copolymers using double click reactions

3‐Arm star‐block copolymers, (polystyrene‐b‐poly(methyl methacrylate))₃, (PS‐b‐PMMA)₃, and (polystyrene‐b‐poly(ethylene glycol))₃, (PS‐b‐PEG)₃, are prepared using double‐click reactions: Huisgen and Diels–Alder, with a one‐pot technique. PS and PMMA blocks with α‐anthracene‐ω‐azide‐ and α‐maleimide‐end‐groups, respectively, are achieved using suitable initiators in ATRP of styrene and MMA, respectively. However, PEG obtained from a commercial source is reacted with 3‐acetyl‐N‐(2‐hydroxyethyl)‐7‐oxabicyclo[2.2.1]hept‐5‐ene‐2‐carboxamide (7) to give furan‐protected maleimide‐end‐functionalized PEG. Finally, PS/PMMA and PS/PEG blocks are linked efficiently with trialkyne functional linking agent 1,1,1‐tris[4‐(2‐propynyloxy)phenyl]‐ethane 2 in the presence of CuBr/N,N,N′,N″,N″‐pentamethyldiethylenetriamine (PMDETA) at 120 °C for 48 h to give two samples of 3‐arm star‐block copolymers. The results of the peak splitting using a Gaussian deconvolution of the obtained GPC traces for (PS‐b‐PMMA)₃ and (PS‐b‐PEG)₃ displayed that the yields of target 3‐arm star‐block copolymers were found to be 88 and 82%, respectively. © Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 7091–7100, 2008     

Convenient Preparation of α-Tert-Butyl N-Blocked Glutamates Through γ-Allyl Ester Protection

Utilisation of γ-allyl ester protection of glutamates provides a convenient route to the synthesis of Z-Glu-OBu^t, Tr-Glu-OBu^t and (Boc)2-Glu-OBu^t.     

Contractive projections on Banach algebras

In this paper, we explore the properties of projections of norm one on general Banach algebras, in particular the relation with conditional expectations for algebras which arise in harmonic analysis.     

A partial order in the knot table II

A partial order on the set of the prime knots can be defined by the existence of a surjective homomorphism between knot groups. In the previous paper, we determined the partial order in the knot table. In this paper, we prove that 31 and 41 are minimal elements. Further, we study which surjection a pair of a periodic knot and its quotient knot induces, and which surjection a degree one map can induce.     

An intrinsic approach to Lichnerowicz conjecture

In this paper we give a proof of Lichnerowicz conjecture for compact simply connected manifolds which is intrinsic in the sense that it avoids thenice embeddings into eigenspaces of the Laplacian. Even if one wants to use these embeddings, this paper gives a more streamlined proof. As a byproduct, we get a simple criterion for a polynomial to be a Jacobi polynomial.