On the number of reducible polynomials of bounded naive height

We prove an asymptotical formula for the number of reducible integer polynomials of degree d and of naive height at most T when \({T \to \infty}\) . The main term turns out to be of the form \({\kappa_d T^d}\) for each \({d \geq 3}\) , where the constant \({\kappa_d}\) is given in terms of some infinite Dirichlet series involving the volumes of symmetric convex bodies in \({\mathbb{R}^d}\) . For d = 2, we prove that there are asymptotically \({\kappa_2 T^2 \,\text{log} T}\) of such polynomials, where \({\kappa_2:=6(3\sqrt{5}+2\,\text{log} (1+\sqrt{5}) -2 \,\text{log}\, 2)/\pi^2}\) . Earlier results in this direction were given by van der Waerden, Pólya and Szegö, Dörge, Chela, and Kuba.     

Two-photon excitation of substituted enediynes

Electronic spectroscopy of nine benzannelated enediynes and a related fulvene was studied under one-photon and two-photon excitation conditions. We utilize measured absorbance and emission spectra and time-resolved fluorescence decays of these molecules to calculate their radiative lifetimes and fluorescence quantum yields. The fluorescence quantum yields for the other compounds were referenced to the fluorescence quantum yield of compound 3 and used to determine relative two-photon absorption cross-sections. Further insight into experimental studies has been achieved using time-dependent density functional (TD-DFT) computations. The probability of two-photon absorption (TPA) increases noticeably for excitation to the higher excited states. The photophysical properties of benzannelated enediynes are sensitive to substitutions at both the core and the periphery of the enediyne chromophore. Considerably enhanced two-photon absorption is observed in an enediyne with donor substitution in the middle and acceptor substitution at the termini. Excited states with B symmetry are not active in TPA spectra. From a practical point of view, this study extends the range of wavelengths applicable for activation of the enediyne moiety from 350 to 600 nm and provides a rational basis for future studies in this field. Our theoretical computations confirmed that lowest energy TPA in benzannelated enediynes involves different orbitals than lowest energy one-photon absorbance and provided further support to the notion that introduction of donor and acceptor substituents at different ends of a molecule increases TPA.     

Observation of a photoexcited state of a paramagnetic transition metal complex by time-resolved electron paramagnetic resonance spectroscopy

The first observation of a spin polarized excited state of a paramagnetic metal-complex using time-resolved electron paramagnetic resonance (TREPR) spectroscopy is reported for octaethylporphinatooxovanadium(iv). The TREPR spectra show well resolved orientation dependent hyperfine splitting to the I = 7/2 vanadium nucleus. The reduction of the hyperfine splitting by a factor of 3 compared to the ground state and the observation of a multiplet pattern of spin polarization allow the TREPR spectra to be assigned to the excited quartet state of the complex. The spin polarization patterns evolve with time and it is postulated that this is a result of the equilibration between the lowest excited quartet and doublet states.     

Alteration of the Axial Met Ligand to Electron Acceptor A0 in Photosystem I: An Investigation of Electron Transfer at Different Temperatures by Multifrequency Time-Resolved and CW EPR

The ambient temperature and low-temperature electron transfer properties of Photosystem I (PS I) from the M688N_PsaA and M668N_PsaB mutant strains of the cyanobacterium Synechocystis sp. PCC 6803 are studied using transient electron paramagnetic resonance (EPR) and continuous-wave (CW) EPR. The two mutations are expected to alter the midpoint potentials of, and the reorganization energies around, the primary electron chlorophyll acceptors A_0A and A_0B, which should lead to a change in the yield and/or rate of electron transfer to the phylloquinone acceptors A_1A and A_1B, respectively. At ambient temperature it is known that both quinone acceptors are active in electron transfer. At low temperature there are at least two fractions that undergo either reversible or irreversible electron transfer. The EPR data of the two PS I variants are used to investigate the relationship between these low-temperature fractions and the ambient temperature electron transfer pathway. The results show that mutation in the PsaA-branch increases the rate of $ {\text{A}}_{{1{\text{A}}}}^{. - } $ to F_X electron transfer at ambient temperature, while the corresponding mutation in the PsaB-branch has no effect on the electron transfer rate observable by transient EPR. An analysis of the complete time/field datasets from both variants suggests that the yield of electron transfer in the branch carrying the mutation is reduced. The mutations have no effect on the low-temperature CW EPR spectra of the iron–sulfur clusters if the samples are frozen under illumination but they both cause a decrease in the yield of reduced F_A and F_B if the samples are frozen in the dark and then illuminated. The PsaA-branch mutation greatly reduces the intensity and changes the polarization pattern of the radical pair $ {\text{P}}_{700}^{ + } {\text{A}}_{1}^{. - } $ . Possible causes of the changes in the polarization pattern are discussed and it is suggested that the mutations introduce structural heterogeneity in the vicinity of the A₀ binding site. No clear correlation between the yield of electron transfer in a particular branch and the yield of stable charge separation is found.     

Standards for the measurement of diffuse reflectance – an overview of available materials and measurement laboratories

As part of the Intersociety Colour Council (ISCC) effort to update ISCC Guide 89-1, a survey of manufacturers and national measurement laboratories was undertaken. This survey was to determine availability of artifact standards and measurement services related to colour. The results were presented as a poster paper at the Third Oxford Conference on Spectrometry in July, 1998.     

Ⅰ类超晶格势阱中能级分布及电子跃迁规律研究

在研究大量实验曲线的基础上,指出势阱所有能级均有一定的宽度,电子或空穴在各能级中出现的概率符合正态分布,从理论上分析了I类超晶格和双势垒单势阱的发光光谱与吸收光谱.解释了GaAs/Ga1－xAlxAs多量子阱和超晶格吸收光谱吸收边及量子阱变窄时各吸收峰的“蓝移现象”及GaAs/Ga1－xAlxAs双势垒单量子阱样品的电流—电压特性曲线及电导—电压特性曲线的特征和出现的“负阻效应”.     

New Acrylamidinium Salts by Condensation Between Acetamidinium Salts and Aromatic Aldehydes

The well-known N,N,N′,N′-tetramethyl acetamidinium salt condenses; smoothly, without any base, with (hetero)aromatic aldehydes to give a series of cinnamamidinium salts. Amide acetals react as well to form trimethine cyanines.     

Relative-error bounds for the LU decomposition via the GTH algorithm

Summary. Recently the author showed that the Grassmann-Taksar-Heyman (GTH) algorithm computes the steady-state distribution of a finite-state Markov chain with low relative error. Here it is shown that the LU decomposition computed in the course of the GTH algorithm also has low relative error. The proof requires a refinement of the methods used in the earlier paper. Received September 2, 1994 / Revised version received July 17, 1995     

A combinatorial decomposition of simplicial complexes

We find a decomposition of simplicial complexes that implies and sharpens the characterization (due to Björner and Kalai) of thef-vector and Betti numbers of a simplicial complex. It generalizes a result of Stanley, who proved the acyclic case, and settles a conjecture of Stanley and Kalai.