Daytime Reactions of 1,8‐Cineole in the Troposphere

Relative rate coefficients for the gas‐phase reaction of chlorine atoms (Cl) and hydroxyl radicals (OH) with 1,8‐cineole were determined by Fourier‐transform infrared (FTIR) spectroscopy between 285 and 313 K at atmospheric pressure. The temperature dependence of both reactions shows simple Arrhenius behaviour which can be represented by the following expressions (in units of cm³ molecule^?1s^?1): k(1,8‐cineole+OH)=(6.28±6.53)×10^?8exp[(?2549.3±155.7)/T] and k(1,8‐cineole+Cl)=(1.35±1.07)×10^?10exp[(?151.6±237.7)/T]. Major products of the titled reactions were identified by solid‐phase microextraction (SPME) coupled to a GC‐MS. Additionally, the first step of the reaction was theoretically studied by ab initio calculations and a reaction mechanism is proposed.     

Temperature dependence of ESR anisotropy in La7/8Sr1/8MnO3

We report X-ray diffraction, DC-susceptibility, electron spin resonance (ESR), and dilatometry measurements carried out on an La_7/8Sr_1/8MnO₃ single crystal. Thermal expansion was measured along different crystallographic axes using a three-terminal dilatometer. The sharp anomalies observed in the temperature dependence of Δl/l allowed us to locate the Jahn–Teller transition at T_JT=285(1) K. ESR experiments were carried out in the paramagnetic regime from 220 to 570 K, at 9.4 GHz. We measured the ESR line width ΔH_pp(T) with the magnetic field parallel to the crystallographic directions [1 0 0] and [0 0 1], referred to the orthorhombic (Pbnm) axes. We correlate the temperature dependence of ΔH_pp with the structural changes of the lattice.     

Hardy-type estimates for Dirac operators

We prove some Hardy type inequalities related to the Dirac operator by elementary methods, for a large class of potentials, which even includes measure valued potentials. Optimality is achieved by the Coulomb potential. When potentials are smooth enough, our estimates provide some spectral information on the operator.     

Simulation of CPMAS Signals at High Spinning Speeds

The spin dynamics of anS( )I_Nsystem during the CP mixing time of continuous wave and variable amplitude cross-polarization magic angle spinning (CWCPMAS and VACPMAS) experiments is discussed. The signal enhancement of a low abundantSspin, coupled to a set ofN= 6 coupled spins withI= , is evaluated as a function of the length of the mixing time. For CWCPMAS this signal is first evaluated in the frequency domain and then transformed to the time domain. These calculations provide some additional insight into the CP spin dynamics and enable a practical approach toward the evaluation of CP signals of large spin systems. In addition the adiabatic character of the ramped VACPMAS experiments is discussed andS-spin signals of a spin system withN= 6 are simulated. Estimates of the upper bounds of the CP signals as a function of the number ofIspins in anS( )I_Nsystem are given and compared with the calculated values.     

Polynomial time approximation schemes for dense instances of minimum constraint satisfaction

It is known that large fragments of the class of dense Minimum Constraint Satisfaction (MIN‐CSP) problems do not have polynomial time approximation schemes (PTASs) contrary to their Maximum Constraint Satisfaction analogs. In this paper we prove, somewhat surprisingly, that the minimum satisfaction of dense instances of kSAT ‐formulas, and linear equations mod 2, Ek‐LIN2, do have PTASs for any k. The MIN‐Ek‐LIN2 problems are equivalent to the k‐ary versions of the Nearest Codeword problem, the problem which is known to be exceedingly hard to approximate on general instances. The method of solution of the above problems depends on the development of a new density sampling technique for k‐uniform hypergraphs which could be of independent interest. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 73–91, 2003     

Functionalization of carbon nanofibers (CNFs) through atom transfer radical polymerization for the preparation of poly(tert‐butyl acrylate)/CNF materials: Spectroscopic,thermal, morphological,and physical characterizations

Vapor‐grown carbon nanofibers (CNFs) were oxidized and functionalized for atom transfer radical polymerization (ATRP) of tert‐butyl acrylate (t‐BA) from the surface of the CNFs. The materials were characterized by solubility tests, Fourier‐transform infrared (FTIR) spectroscopy, Raman spectroscopy, thermogravimetric analysis (TGA), X‐ray diffraction (XRD), and scanning electron microscopy. The FTIR and electron microscopy results suggest that ATRP process was successfully used to graft poly(tert‐butyl acrylate) (poly(t‐BA)) chains from the surface of the fibers. Raman results strongly indicate the partial degradation of the graphitic layer of CNFs because of the chemical treatments. TGA results suggest that the presence of poly(t‐BA) leads to a decrease of the initial degradation temperature of the fibers. XRD and electron microscopy results indicate that the microstructure of fibers was not destroyed because of the oxidation and functionalization processes. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3326–3335, 2008     

On the maximum cardinality of a consistent set of arcs in a random tournament

For any tournament T on n vertices, let h(T) denote the maximum number of edges in the intersection of T with a transitive tournament on the same vertex set. Sharpening a previous result of Spencer, it is proved that, if T_n denotes the random tournament on n vertices, then, $\text{P}$$\text{(h(T}{}_{\mathrm{n}}\text{) ≤}\text{1}\text{2}\text{(}{}_2{}^{\mathrm{n}}\text{) + 1.73n}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{) → 1}$ as n → ∞.     

Perturbation theory of p-adic Fredholm and semi-Fredholm operators

The main goal of this paper is to prove that Fredholm and semi-Fredholm operators between p-adic (or non-archimedean) Banach spaces, as well as the index of those that are Fredholm, are preserved when they are perturbed by a small operator. In this way we obtain the non-archimedean counterparts of some well-known results of classical Operator Theory. For non-spherically complete fields the classical techniques are no longer valid in the p-adic context, which forces us to seek a completely different way to attack the problem. The p-adic concept of orthogonality will be one of the key tools to get our purpose.