A quick distributional way to the prime number theorem

We use distribution theory (generalized functions) to show the prime number theorem. No tauberian results are employed.     

Structural theorems for quasiasymptotics of distributions at the origin

An open question concerning the quasiasymptotic behavior of distributions at the origin is solved. The question is the following: Suppose that a tempered distribution has quasiasymptotic at the origin in S ′(?), then the tempered distribution has quasiasymptotic in D ′(?), does the converse implication hold? The second purpose of this article is to give complete structural theorems for quasiasymptotics at the origin. For this purpose, asymptotically homogeneous functions with respect to slowly varying functions are introduced and analyzed (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Velocity map imaging and theoretical study of the Coulomb explosion of CH3I under intense femtosecond IR pulses

The Coulomb explosion of CH(3)I in an intense (10-100 TW cm(-2)), ultrashort (50 fs) and nonresonant (804 nm) laser field has been studied experimentally and justified theoretically. Ion images have been recorded using the velocity map imaging (VMI) technique for different singly and multiply charged ion fragments, CH(3)(p+) (p = 1) and I(q+) (q ≤ 3), arising from different Coulomb explosion channels. The fragment kinetic energy distributions obtained from the measured images for these ion fragments show significantly lower energies than those expected considering only Coulomb repulsion forces. The experimental results have been rationalized in terms of one-dimensional wave packet calculations on ab initio potential energy curves of the different multiply charged species. The calculations reveal the existence of a potential energy barrier due to a bound minimum in the potential energy curve of the CH(3)I(2+) species and a strong stabilization with respect to the pure Coulombic repulsion for the higher charged CH(3)I(n+) (n = 3, 4) species.     

Energetics and structural properties, in the gas phase, of trans-hydroxycinnamic acids

We have studied the energetics and structural properties of trans-cinnamic acid (CA), o-, m-, and p-coumaric acids (2-, 3-, and 4-hydroxycinnamic acids), caffeic acid (3,4-dihydroxycinnamic acid), ferulic acid (4-hydroxy-3-methoxycinnamic acid), iso-ferulic acid (3-hydroxy-4-methoxycinnamic acid), and sinapic acid (3,5-dimethoxy-4-hydroxycinnamic acid). The experimental values of Δ(f)H(m)°(g), determined (in kJ·mol(-1)) for CA (-229.8 ± 1.9), p-coumaric acid (-408.0 ± 4.4), caffeic acid (-580.0 ± 5.9), and ferulic acid (-566.4 ± 5.7), allowed us to derive Δ(f)H(m)°(g) of o-coumaric acid (-405.6 ± 4.4), m-coumaric acid (-406.4 ± 4.4), iso-ferulic acid (-565.2 ± 5.7), and sinapic acid (-698.8 ± 4.1). From these values and by use of isodesmic/homodesmotic reactions, we studied the energetic effects of π-donor substituents (-OH and -OCH(3)) in cinnamic acid derivatives and in the respective benzene analogues. Our results indicate that the interaction between -OCH(3) and/or -OH groups in hydroxycinnamic acids takes place without significant influence of the propenoic fragment.     

Distributional versions of littlewood’s Tauberian theorem

We provide several general versions of Littlewood’s Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We employ two types of Tauberian hypotheses; the first kind involves distributional boundedness, while the second type imposes a one-sided assumption on the Cesàro behavior of the distribution. We apply these Tauberian results to deduce a number of Tauberian theorems for power series and Stieltjes integrals where Cesàro summability follows from Abel summability. We also use our general results to give a new simple proof of the classical Littlewood one-sided Tauberian theorem for power series.     

Structure of a spin-crossover Fe(II)–1,2,4-triazole polymer complex dispersed in an isotactic polystyrene matrix

Isotactic polystyrene (i-PS) was employed as a matrix to disperse a metallo-organic polymer of [Fe(II) (4-octadecyl-1,2,4-triazole)₃(ClO₄)₂] in order to obtain novel functional materials exhibiting thermal spin-crossover transition. A detailed investigation of the structure of the metallo-organic polymer and metallo-organic polymer/iPS blends has been carried out by DSC, WAXD and SAXS techniques as a function of temperature and metallo-organic polymer/iPS proportion.The results obtained confirm on the one hand that a structural transition associated with a change in the magnetic susceptibility of the metallo-organic polymer is preserved in the presence of i-PS. This transition was found to be associated to both, an inter-conversion of lamellar structures into hexagonal structures and to an increase of inter-sheet distances within the lamellar structures in metallo-organic polymer films prepared by casting from toluene solutions. On the other hand, an increase of the degree of crystallinity of the iPS is observed in the presence of the metallo-organic polymer which suggests some nucleating effect of the metallo-organic polymer in the crystallization of isotactic polystyrene.     

Validation of a Simple HPLC-Based Method for Lysine Quantification for Ruminant Nutrition

Robust and selective quantification methods are required to better analyze feed supplementation effectiveness with specific amino acids. In this work, a reversed-phase high-performance liquid chromatography method with fluorescence detection is proposed and validated for lysine quantification, one of the most limiting amino acids in ruminant nutrition and essential towards milk production. To assess and widen method applicability, different matrices were considered: namely Li₂CO₃ buffer (the chosen standard reaction buffer), phosphate buffer solution (to mimic media in cellular studies), and rumen inoculum. The method was validated for all three matrices and found to be selective, accurate (92% ± 2%), and precise at both the inter- and intra-day levels in concentrations up to 225 µM, with detection and quantification limits lower than 1.24 and 4.14 µM, respectively. Sample stability was evaluated when stored at room temperature, 4 °C, and −20 °C, showing consistency for up to 48 h regardless of the matrix. Finally, the developed method was applied in the quantification of lysine on real samples. The results presented indicate that the proposed method can be applied towards free lysine quantification in ruminant feeding studies and potentially be of great benefit to dairy cow nutrition supplementation and optimization.     

Single‐Electron Self‐Exchange between Cage Hydrocarbons and Their Radical Cations in the Gas Phase

We show that the radical cations of adamantane (C₁₀H₁₆^.+, 1 H^.+) and perdeuteroadamantane (C₁₀D₁₆^.+, 1 D^.+) are stable species in the gas phase. The radical cation of adamantylideneadamantane (C₂₀H₂₈^.+, 2 H^.+) is also stable (as in solution). By using the natural ¹³C abundances of the ions, we determine the rate constants for the reversible isergonic single‐electron transfer (SET) processes involving the dyads 1 H^.+/ 1 H, 1 D^.+/ 1 D and 2 H^.+/ 2 H. Rate constants for the reaction 1 H^.++ 1 D? 1 H+ 1 D^.+ are also determined and Marcus’ cross‐term equation is shown to hold in this case. The rate constants for the isergonic processes are extremely high, practically collision‐controlled. Ab initio computations of the electronic coupling (H_DA) and the reorganization energy (λ) allow rationalization of the mechanism of the process and give insights into the possible role of intermediate complexes in the reaction mechanism.     

Precise and traceable carbon isotope ratio measurements by multicollector ICP-MS: what next?

This article reviews recent developments in the use of multicollector inductively coupled plasma mass spectrometry (MC-ICP-MS) to provide high-precision carbon isotope ratio measurements. MC-ICP-MS could become an alternative method to isotope ratio mass spectrometry (IRMS) for rapid carbon isotope ratio determinations in organic compounds and characterisation and certification of isotopic reference materials. In this overview, the advantages, drawbacks and potential of the method for future applications are critically discussed. Furthermore, suggestions for future improvements in terms of precision and sensitivity are made. No doubt, this is an exciting analytical challenge and, as such, hurdles will need to be cleared.     

Synthesis and characterization of new polymeric ionic liquid microgels

A new two‐step route toward the synthesis of polymeric ionic liquid microgel particles is presented. In the first step, hydrophilic microparticles were prepared by the concentrated emulsion polymerization of the ionic liquid 1‐vinyl‐3‐ethylimidazolium bromide in the presence of small amounts of N,N‐dimethylenebisacrylamide as a crosslinking agent. In the second step, the bromide anion was exchanged in water with different anions such as BF, CF₃SO, (CF₃SO₂)₂N^?, (CF₃CF₂SO₂)₂N^?, and dodecylbenzenesulfonate, and this resulted in the coagulation of the microparticles, which were easily recovered by filtration. The obtained polymeric ionic liquid microparticles could be swollen in a very broad range of organic solvents, including apolar organic solvents. As an application, glucose oxidase was encapsulated inside polymeric ionic liquid microparticles, which were used in an amperometric biosensor. The response of the biosensor showed excellent values that strongly depended on the nature of the polymeric ionic liquid counteranion in the order of Br^? > BF > (CF₃SO₂)₂N^?. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3958–3965, 2006