Allene-alkyne cross-coupling for stereoselective synthesis of substituted 1,4-dienes and cross-conjugated trienes

Titanium-mediated cross-coupling of allenic alcohols with alkynes has been investigated. Divergent reaction pathways were discovered that provide either stereodefined 1,4-dienes or substituted cross-conjugated trienes. In short, allene substitution plays a critical role in the determination of reaction pathway.     

Ultrafast excited-state dynamics of adenine and monomethylated adenines in solution: implications for the nonradiative decay mechanism

The DNA base adenine and four monomethylated adenines were studied in solution at room temperature by femtosecond pump-probe spectroscopy. Transient absorption at visible probe wavelengths was used to directly observe relaxation of the lowest excited singlet state (S(1) state) populated by a UV pump pulse. In H(2)O, transient absorption signals from adenine decay biexponentially with lifetimes of 0.18 +/- 0.03 ps and 8.8 +/- 1.2 ps. In contrast, signals from monomethylated adenines decay monoexponentially. The S(1) lifetimes of 1-, 3-, and 9-methyladenine are similar to one another and are all below 300 fs, while 7-methyladenine has a significantly longer lifetime (tau = 4.23 +/- 0.13 ps). On this basis, the biexponential signal of adenine is assigned to an equilibrium mixture of the 7H- and 9H-amino tautomers. Excited-state absorption (ESA) by 9-methyladenine is 50% stronger than by 7-methyladenine. Assuming that ESA by the corresponding tautomers of adenine is unchanged, we estimate the population of 7H-adenine in H(2)O at room temperature to be 22 +/- 4% (estimated standard deviation). To understand how the environment affects nonradiative decay, we performed the first solvent-dependent study of nucleobase dynamics on the ultrafast time scale. In acetonitrile, both lowest energy tautomers of adenine are present in roughly similar proportions as in water. The lifetimes of the 9-substituted adenines depend somewhat more sensitively on the solvent than those of the 7-substituted adenines. Transient signals for adenine in H(2)O and D(2)O are identical. These solvent effects strongly suggest that excited-state tautomerization is not an important nonradiative decay pathway. Instead, the data are most consistent with electronic energy relaxation due to state crossings between the optically prepared (1)pipi* state and one or more (1)npi* states and the electronic ground state. The pattern of lifetimes measured for the monomethylated adenines suggests a special role for the (1)npi* state associated with the N7 electron lone pair.     

Quantification strategies for elemental imaging of biological samples using laser ablation-inductively coupled plasma-mass spectrometry

This review provides analysts with critical insights of current approaches for quantification by laser ablation-inductively coupled plasma-mass spectrometry in the field of elemental imaging. This encompasses both calibration strategies that have been used with success in imaging biological samples, as well as those with potential to improve analytical accuracy and precision if applied to imaging. Methods reviewed include the use of CRMs, laboratory prepared matrix matched standards, internal standardisation, online standard addition and a variety of novel approaches that makes elemental imaging accessible to a wider base of analysts. The importance of quantification and factors affecting its use in imaging will also be considered.     

A Fourier series formula for energy of measures with applications to Riesz products

In this paper we derive a formula relating the energy and the Fourier transform of a finite measure on the -dimensional torus which is similar to the well-known formula for measures on .

We apply the formula to obtain estimates on the Hausdorff dimension of Riesz product measures. These give improvements on the earlier, classical results which were based on completely different techniques.

     

Multipliers of spherical harmonics and energy of measures on the sphere

We consider the operator,f(Δ) for Δ the Laplacian, on spaces of measures on the sphere inR ^d , show how to determine a family of approximating kernels for this operator assuming that certain technical conditions are satisfied, and give estimates for theL²-norm off(Δ)μ in terms of the energy of the measure μ. We derive a formula, analogous to the classical formula relating the energy of a measure onR ^d with its Fourier transform, comparing the energy of a measure on the sphere with the size of its spherical harmonics. An application is given to pluriharmonic measures.     

Standard enthalpy of solution and formation of cesium chromate. Derived thermodynamic properties of the aqueous chromate,bichromate, and dichromate ions,alkali metal and alkaline earth chromates,and lead chromate

Calorimetric measurements of the enthalpy of solution of cesium chromate gave ΔH_soln = (7622 ± 24) cal_th mol^?1 for a dilution of Cs₂CrO₄·21128H₂O. This result, along with the enthalpy of dilution gave the standard enthalpy of solution, ΔH_soln^o = (7512 ± 31) cal_th mol^?1, whence the standard enthalpy of formation, ΔH_f⁰(Cs₂CrO₄, c, 298.15 K), was calculated to be ?(341.78 ± 0.46) kcal_th mol^?1. Recomputed thermodynamic data for the formation of the other alkali metal chromates have been tabulated. From their solubilities and enthalpies of solution, the standard entropies, S⁰(298 K), of BaCrO₄ and PbCrO₄ were estimated to be (38.9 ± 0.9) and (43.7 ± 1.2) cal_th K^?1 mol^?1, respectively. There is evidence that ΔH_f⁰(SrCrO₄, c, 298.15 K) may be in error. Thermochemical, solubility, and equilibrium data, have been combined to update the thermodynamic properties of the aqueous chromate (CrO₄^2?), bichromate (HCrO₄^?), and dichromate (Cr₂O₇^2?) ions. The new values at 298.15 K are as follows:

     

28.

Electronic spectra and transitions of the fullerene C₆₀     

Sydney Leach  Michel Vervloet  Alain Despr  s  Emilienne Br  heret  Jonathan P. Hare  T. John Dennis  Harold W. Kroto  Roger Taylor  David R. M. Walton 《Chemical physics》1992,160(3):451-466

Absorption spectra of C₆₀ have been measured in the ranges (a) 190–700 nm in n-hexane solutions at 300 K, (b) 390–700 nm in n-hexane and in 3-methylpentane solutions at 77 K. 40 vibronic bands were observed. They exhibit a large range of bandwidths and intensities, whose significance is discussed. Assignment of electronic transitions has been carried out using the results of theoretical calculations. Vibronic structures have been analyzed within the framework of theories of electronic transitions of polyatomic molecules applied to the I_h symmetry group. Nine allowed ¹T_1u−¹A_g transitions have been assigned in the 190–410 nm region. Observed and calculated allowed transition energies and oscillator strengths are compared. Detailed vibronic analyses of the 1 ¹T_1u−1 ¹A_g and 2 ¹T_1u−1 ¹A_g transitions illustrate the role of Jahn-Teller couplings. Orbitally forbidden singlet-singlet transitions are observed between 410 and 620 nm. Their vibronic structures were analyzed in terms of concurrent Herzberg-Teller and Jahn-Teller vibronic interactions. The 77 K spectra provided useful information on hot bands and on other aspects of the analyses. Vibronic bands belonging to triplet←singlet transitions were detected between 620 and 700 nm.     

29.

Computing the Principal Branch of log-Gamma     

D.E.G Hare 《Journal of Algorithms in Cognition, Informatics and Logic》1997,25(2):221-236

Thelog-Gammafunction is an important special function of mathematics, and its principal branch is required in many applications. We develop here the mathematics required to evaluate the principal branch to arbitrary precision, including a new bound for the error in Stirling's asymptotic series. We conclude with a discussion of the implementation of the principal branch of the log-Gamma function in the Maple symbolic algebra system, starting with version Maple V, Release 3.     

30.

The energy of signed measures     

Kathryn E. Hare  Maria Roginskaya 《Proceedings of the American Mathematical Society》2004,132(2):397-406

We generalize the concept of energy to complex measures of finite variation. We show that although the energy dimension of a measure can exceed that of its total variation, it is always less than the Hausdorff dimension of the measure. As an application we prove a variant of the uncertainty principle.

     

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	$\text{S}{}^0\text{/}\text{cal}{}_{\mathrm{th}}\text{K}{}^{\mathrm{?1}}\text{mol}{}^{\mathrm{?1}}$	$\text{ΔH}{}_{\mathrm{f}}{}^0\text{/kcal}{}_{\mathrm{th}}\text{mol}{}^{\mathrm{?1}}$	$\text{ΔG}{}_{\mathrm{f}}{}^0\text{/kcal}{}_{\mathrm{th}}\text{mol}{}^{\mathrm{?1}}$
CrO42?(aq)	(13.8 ± 0.5)	?(210.93 ± 0.45)	?(174.8 ± 0.5)
HCrO4?(aq)	(46.6 ± 1.8)	?(210.0 ± 0.7)	?(183.7 ± 0.5)
Cr2O72?(aq)	(67.4 ± 3.9)	?(356.5 ± 1.5)	?(312.8 ± 1.0)

Electronic spectra and transitions of the fullerene C60

Absorption spectra of C₆₀ have been measured in the ranges (a) 190–700 nm in n-hexane solutions at 300 K, (b) 390–700 nm in n-hexane and in 3-methylpentane solutions at 77 K. 40 vibronic bands were observed. They exhibit a large range of bandwidths and intensities, whose significance is discussed. Assignment of electronic transitions has been carried out using the results of theoretical calculations. Vibronic structures have been analyzed within the framework of theories of electronic transitions of polyatomic molecules applied to the I_h symmetry group. Nine allowed ¹T_1u−¹A_g transitions have been assigned in the 190–410 nm region. Observed and calculated allowed transition energies and oscillator strengths are compared. Detailed vibronic analyses of the 1 ¹T_1u−1 ¹A_g and 2 ¹T_1u−1 ¹A_g transitions illustrate the role of Jahn-Teller couplings. Orbitally forbidden singlet-singlet transitions are observed between 410 and 620 nm. Their vibronic structures were analyzed in terms of concurrent Herzberg-Teller and Jahn-Teller vibronic interactions. The 77 K spectra provided useful information on hot bands and on other aspects of the analyses. Vibronic bands belonging to triplet←singlet transitions were detected between 620 and 700 nm.     

Computing the Principal Branch of log-Gamma

Thelog-Gammafunction is an important special function of mathematics, and its principal branch is required in many applications. We develop here the mathematics required to evaluate the principal branch to arbitrary precision, including a new bound for the error in Stirling's asymptotic series. We conclude with a discussion of the implementation of the principal branch of the log-Gamma function in the Maple symbolic algebra system, starting with version Maple V, Release 3.     

The energy of signed measures

We generalize the concept of energy to complex measures of finite variation. We show that although the energy dimension of a measure can exceed that of its total variation, it is always less than the Hausdorff dimension of the measure. As an application we prove a variant of the uncertainty principle.