On the gaps in the Fourier expansion of cusp forms

In this paper we obtain some results on the gap function which measures the size of gaps in the Fourier expansion of cusp forms that are not linear combinations of forms with complex multiplication. We also investigate the nonvanishing of Fourier coefficients of such cusp forms along rational multiples of linear forms in two variables.      

Diels‐alder click reaction for the preparation of polycarbonate block copolymers

The Diels‐Alder reaction as a click reaction strategy is applied to the preparation of well‐defined polycarbonate (PC)‐block copolymers. A well‐defined α‐anthracene‐terminated polycarbonate (PC‐anthracene) is prepared using 9‐anthracene methanol as an initiator in the ring opening polymerization of benzyl 5‐methyl‐2‐oxo‐1,3‐dioxane‐5‐carboxylate in CH₂Cl₂ at room temperature for 5 h. Next, a well‐defined α‐furan protected maleimide‐terminated‐poly(ethylene glycol) (PEG₁₁‐MI or PEG₃₇‐MI), ‐poly(methyl methacrylate) (PMMA₂₆‐MI), and ‐poly(ε‐caprolactone) (PCL₂₇‐MI) were clicked with the PC‐anthracene at reflux temperature of toluene to yield their corresponding PC‐based block copolymers (PC‐b‐PEG, PC‐b‐PMMA, and PC‐b‐PCL). The homopolymer precursors and their block copolymers were characterized by using the GPC, NMR and UV analysis. © 2013 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Novel ETFE based radiation grafted poly(styrene sulfonic acid-co-methacrylonitrile) proton conducting membranes with increased stability

Styrene radiation grafted ETFE based proton conducting membranes are subject to degradation under fuel cell operating conditions and show a poor stability. Lifetimes exceeding 250 h can only be achieved with crosslinked membranes. In this study, a novel approach based on the increase of the intrinsic oxidative stability of uncrosslinked membranes is reported. Hence, the co-grafting of styrene with methacrylonitrile (MAN), which possesses a protected α-position and strong dipolar pendant nitrile group, onto 25 μm ETFE base film was investigated. Styrene/MAN co-grafted membranes were compared to a styrene based membrane in durability tests in single H₂/O₂ fuel cells. It is shown that the incorporation of MAN considerably improves the chemical stability, yielding fuel cell lifetimes exceeding 1000 h. The membrane preparation based on the co-grafting of styrene and MAN offers the prospect of tuning the MAN content and introduction of a crosslinker to enhance the oxidative stability of the resulting fuel cell membranes.     

Constrained thermal denaturation of DNA under fixed linking number

A DNA molecule with freely fluctuating ends undergoes a sharp thermal denaturation transition upon heating. However, in circular DNA chains and some experimental setups that manipulate single DNA molecules, the total number of turns (linking number) is constant at all times. The consequences of this additional topological invariant on the melting behaviour are nontrivial. Below, we investigate the melting characteristics of a homogeneous DNA where the linking number along the melting curve is preserved by supercoil formation in duplex portions. We obtain the mass fraction and the number of loops and supercoils below and above the melting temperature. We also argue that a macroscopic loop appears at T _c and calculate its size as a function of temperature.     

Cyclic homo and block copolymers through sequential double click reactions

Well‐defined linear α‐anthracene‐ω‐maleimide functionalized polystyrene (l‐Anth‐PS‐MI) and linear α‐alkyne‐ω‐maleimide functionalized poly(tert‐butyl acrylate) (l‐alkyne‐PtBA‐MI) homopolymers, and linear α‐anthracene‐ω‐maleimide functionalized PS‐b‐PtBA (l‐Anth‐PS‐b‐PtBA‐MI) and linear α‐anthracene‐ω‐maleimide functionalized PS‐b‐poly(ε‐caprolactone) (PCL) (l‐Anth‐PS‐b‐PCL‐MI) block copolymers were obtained via combination of atom transfer radical polymerization (ATRP)/ring opening polymerization (ROP) and azide‐alkyne click reaction strategy. Subsequently, these linear homo and block copolymers were efficiently clicked via Diels‐Alder reaction to give their corresponding cyclic homo and block copolymers at reflux temperature of toluene for 48 h under 7–4 × 10^?5 M conditions. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Multidimensional averages and Dirichlet convolution

In this paper we study average values of arithmetical functions of several variables and present a module theoretic interpretation of these averages. Research of Alexandru Zaharescu is supported by NSF grant number DMS-0456615.     

A numerical approach to solve the model of an electromechanical system

In this paper, the model of an electromechanical system, which is a system of linear differential equations, is studied. Haar wavelet collocation method (HWCM) is applied for finding the approximate solution of the model. HWCM reduces the system of the model into a matrix‐vector form that contains the unknown Haar coefficients, and these coefficients are easily calculated. To demonstrate the validity and applicability of HWCM, numerical solutions of the system for different parameter values in the system are presented. The obtained results demonstrate the efficiency and accuracy of the method. All of the computations are performed via a program written in Mathematica.     

Three‐arm star ring opening metathesis polymers via alkyne‐azide click reaction

The click chemistry strategy is successfully applied for the preparation of three‐arm star (A₃) ring opening metathesis polymers. A well‐defined monoazide end‐functionalized poly(N‐ethyl oxanorbornene) and a poly(N‐butyl oxanorbornene) obtained via ring opening metathesis polymerization using first generation Grubbs' catalyst are simply clicked with the trisalkyne core affording the synthesis of target star polymers. The obtained star polymers are characterized via nuclear magnetic resonance spectroscopy and gel permeation chromatography (GPC). The deconvolution analyses of GPC traces reveal that the click reaction efficiency for the star formation strongly depends on the chemical nature and the molecular weight of ROM polymers. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 2344–2351, 2009     

Delayed myelination in a rhizomelic chondrodysplasia punctata case: MR spectroscopy findings

Rhizomelic chondrodysplasia punctata is a member of genetic peroxisomal disorders. Delayed myelination, which is probably related to the inadequacy of plasmalogens biosynthesis, is an important feature of this disorder. Direct assessment of neuropathologic aspects of RCDP syndrome such as neuronal degeneration and delayed myelination is possible with MR spectroscopy.In this report, MR spectroscopy findings (decreased Cho/Cr and increased Ins-Gly/Cr ratios and increased levels of mobile lipids) of a rhizomelic chondrodysplasia punctata case supporting delayed myelination are presented. This is the second report of MR spectroscopy examination of the specific brain metabolic changes associated with rhizomelic chondrodysplasia punctata.     

Proton MR spectroscopy features of normal appearing white matter in neurofibromatosis type 1

To determine whether differences exist between neurofibromatosis type 1 (NF1) patients with or without focal lesions and healthy normal volunteers in the metabolite ratios of normal appearing white matter, 27 patients with NF1 (with parenchymal lesion, MR positive, n: 17; without parenchymal lesions, MR negative, n: 10) and 20 healthy volunteers underwent MRI and short TE (31 ms) proton MR spectroscopy (MRS). In 17 patients with parenchymal lesions, 61 focal lesions were detected by MRI. MRS was performed from normal appearing frontal and posterior parietal white matter (FWM and PWM) in NF1 and from control groups. NAA/Cr, Cho/Cr and MI/Cr ratios were calculated. Significant increase in Cho/Cr and MI/Cr ratios were found in FWM and PWM in MR negative and positive groups when compared to control group. NAA/Cr ratio in MR positive group was significantly decreased in FWM compared to control group. There were no significant differences between FWM and PWM in all metabolite ratios of MR negative group. MI/Cr ratio in MR positive group was significantly elevated in PWM compared to FWM. Metabolite changes detected by MRS could indicate demyelination and gliosis in normal appearing white matter in all NF1 patients, and additionally neuroaxonal damage in the FWM of NF1 patients with focal lesions. For that reason, in the clinical evaluation and follow-up of these patients MRS features of normal appearing white matter should be considered in addition to focal lesions.