Unexpected formation of β, meso-directly linked diporphyrins under Adler–Longo reaction conditions

Unexpected formation of β, meso-directly linked diporphyrin products has been described in the reactions of β-formyl porphyrins with pyrrole under Adler–Longo reaction conditions. Preliminary mechanistic studies indicates that β-dipyrromethane substituted porphyrin structure is the crucial intermediate for the formation of diporphyrin product.     

Partially conserved axial-vector current inS-matrix theory

Mandelstam’s argument that PCAC follows from assigning Lorentz quantum numberM=1 to the massless pion is examined in the context of multiparticle dual resonance model. We construct a factorisable dual model for pions which is formulated operatorially on the harmonic oscillator Fock space along the lines of Neveu-Schwarz model. The model has bothm _π andm _ϱ as arbitrary parameters unconstrained by the duality requirement. Adler self-consistency condition is satisfied if and only if the conditionmϱ²−mπ²=1/2 is imposed, in which case the model reduces to the chiral dual pion model of Neveu and Thorn, and Schwarz. The Lorentz quantum number of the pion in the dual model is shown to beM=0.     

Quasigraded lie algebras,Kostant-Adler scheme,and integrable hierarchies

Using special anisotropic quasigraded Lie algebras, we obtain a number of new hierarchies of integrable nonlinear equations in partial derivatives admitting zero-curvature representations. Among them are an anisotropic deformation of the Heisenberg magnet hierarchy, a matrix and vector generalization of the Landau—Lifshitz hierarchies, new types of matrix and vector anisotropic chiral-field hierarchies, and other types of anisotropic hierarchies.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 2, pp. 329–345, February, 2005.     

Semi-parametric Estimation of the Hölder Exponent of a Stationary Gaussian Process with Minimax Rates

Let (X(t))_t∈[0,1] be a centered Gaussian process with stationary increments such that IE[(X_{u+t-X_u)²] = C|t|^s+r(t). Assume that there exists an extra parameter β > 0 and a polynomial P of degree smaller than s + β such that |r(t)-P(t)| is bounded with respect to |t|^s+β. We consider the problem of estimating the parameter s ∈ (0,2) in the asymptotic framework given by n equispaced observations in [0, 1]. Adding possibly stronger regularity conditions to r, we define classes of such processes over which we show that s cannot be estimated at a better rate than n^{min(1/2, β)}. Then, we study increment (or, more generally, discrete variation) estimators. We obtained precise bounds of the bias of the variance which show that the bias mainly depend on the parameter β and the variance on two terms, one depending on the parameter s and one on some regularity properties of r. A central limit theorem is given when the variance term relying on s dominates the bias and the other variance term. Eventually, we exhibit an estimator which achieves the minimax rate over a wide range of classes for which sufficient regularity conditions are assumed on r. This revised version was published online in August 2006 with corrections to the Cover Date.     

高频超声联合PSV、RI、Adler血流分级在甲状腺良恶性结节中的诊断价值

本研究探讨高频超声联合彩色多普勒超声参数在诊断甲状腺良恶性结节中的价值。选取40例甲状腺癌患者作为观察组,42例甲状腺良性结节患者作为对照组,比较两组、不同N和T分期患者高频超声联合彩色多普勒超声参数,并对数据进行统计分析。两组结节形态、边界、回声、钙化超声征象比较,差异具有统计学意义(P<0.05)。观察组A/T_C、A/T_L、TI-RADS分级评分、PSV、RI、Adler血流分级评分高于对照组(P<0.05)。各参数联合诊断恶性甲状腺结节的AUC为0.902,诊断N1分期的AUC为0.879,诊断Ⅲ+Ⅳ分期的AUC为0.915,均大于任一单一参数(P<0.05)。可见采用高频超声、彩色多普勒超声联合观测甲状腺结节征象与A/T_C、A/T_L、TI-RADS分级、PSV、RI、Adler分级,可诊断结节性质,并能评估恶性结节患者术前肿瘤分期,为临床治疗、决策提供量化参考。