线性模型中误差方差的二次型估计的可容许性问题

设有线性模型Y=(y₁…y_n)’=Xβ+ε=X(β₁…β_p)’+(ε₁…ε_n)’,这里n≥p,X已知,ε₁,…,ε_n相互独立,E(ε_i)=0,E(ε_i²)=σ²,E(ε_i³)=0,E(ε_i⁴)=3σ⁴,i=1,…,n,β∈R^p,0<σ~2<∞。令?={Y’AY:A≥0}。当损失函数为σ^-4(d-σ²)²且X=I_n或者X=1_n时,给出了 Y’AY(A≥0)在?中是σ₂的可容许估计的充分必要条件。又当ε～N(0,σ²I_n)时,给出了Y’AY(A≥0)在σ²的一切估计类中是可容许的充分条件。     

Skeleton and fractal scaling in complex networks

We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called a skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the property of the critical branching tree. The original fractal networks are viewed as a fractal skeleton dressed with local shortcuts. An in silico model with both the fractal scaling and the scale-invariance properties is also constructed. The framework of fractal networks is useful in understanding the utility and the redundancy in networked systems.     

Eta1 and eta2 complexes of lambda3-1,2,4,6-thiatriazinyls with CpCr(CO)x

The title heterocyclic radicals coordinate to either 17e CpCr(CO)3 or 15e CpCr(CO)2 moieties as one-electron or as three-electron donors, respectively; in the former the bonding is via the perpendicular p orbital of the sulfur atom, while in the latter bonding is via p(pi) orbitals on both sulfur and nitrogen.     

Optimal testing strategies in overlapped design process

Testing is an important activity in product development. Past studies, which are developed to determine the optimal scheduling of tests, often focused on single-stage testing of sequential design process. This paper presents an analytical model for the scheduling of tests in overlapped design process, where a downstream stage starts before the completion of upstream testing. We derive optimal stopping rules for upstream and downstream stages’ testing, together with the optimal time elapsed between beginning the upstream tests and beginning the downstream development. We find that the cost function is first convex then concave increasing with respect to upstream testing duration. A one-dimensional search algorithm is then proposed for finding the unique optimum that minimizes the overall cost. Moreover, the impact of different model parameters, such as the problem-solving capacity and opportunity cost, on the optimal solution is discussed. Finally, we compare the testing strategies in overlapped process with those in sequential process, and get some additional results. The methodology is illustrated with a case study at a handset design company.     

Two-dimensional crystal growth and stacking of bis(phthalocyaninato) rare earth sandwich complexes at the 1-phenyloctane/graphite interface

Initial stages of two-dimensional crystal growth of the double-decker sandwich complex Lu(Pc*)2 [Pc* = 2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyaninato] have been studied by scanning tunneling microscopy at the liquid/solid interface between 1-phenyloctane and highly oriented pyrolytic graphite. High-resolution images strongly suggest alignment of the double-decker molecules into monolayers with the phthalocyanine rings parallel to the surface. Domains were observed with either hexagonal or quadrate packing motifs, and the growing interface of the layer was imaged. Molecular resolution was achieved, and the face of the phthalocyanine rings appeared as somewhat diffuse circular features. The alkyl chains are proposed to be interdigitating to maintain planar side-by-side packing.     

Band-limited refinable functions for wavelets and framelets

Extending band-limited constructions of orthonormal refinable functions, a special class of periodic functions is used to generate a family of band-limited refinable functions. Characterizations of Riesz bases and frames formed by integer shifts of these refinable functions are obtained. Such families of refinable functions are employed to construct band-limited biorthogonal wavelet bases and biframes with desirable time-frequency localization.     

Tailoring the LCST of PNIPAAM‐b‐PLA‐b‐PNIPAAM Triblock Copolymers via Stereocomplexation

Poly(N‐isopropylacrylamide)‐block‐poly(l ‐lactic acid)‐block‐poly(N‐isopropylacrylamide) (PNIPAAM‐b‐PLLA‐b‐PNIPAAM) and PNIPAAM‐b‐PDLA‐b‐PNIPAAM triblock copolymers with varying polylactic acid (PLA) lengths are synthesized using a combination of ring‐opening polymerization and atom‐transfer radical polymerization. Results of ¹H NMR and gel permeation chromatography analyses show that the copolymers have a well‐defined triblock structure and the PLA segment lengths can be readily controlled with monomer feed ratio. Stereocomplexation between the enantiomeric PLA segments is confirmed with differential scanning calorimetry and wide‐angle X‐ray scattering. Dynamic light scattering experiments show that (1) the LCST of PNIPAAM in water could be tailored from 32 °C up to 38.5 °C by increasing the length of PLA segments and mixing copolymers of similar molecular weight with enantiomeric PLA segments to induce stereocomplexation, and (2) the LCST of each mixed copolymer system could be tailored within a 2–3 °C range of body temperature by manipulating the ratio of the enantiomeric copolymers in solution.

     

Higher Order Nonlinear Effect and Limitation of Soliton Propagation in Dispersive-Nonlinear Medium for Dispersion-Shifted Fiber

A computer simulation of the nonlinear Schrödinger equation is carried out to evaluate the impact of nonlinear susceptibility of a single mode fiber on the transmission of a soliton pulse. The third and fifth order nonlinear susceptibilities are considered in the simulation. The results show that the output soliton pulse shape strongly depends on the third order nonlinear susceptibility and gets distorted when the full width half maximum (FWHM) pulse width is of the order of 10ps or less.     

Nickel(II) meso‐Hydroxyporphyrin Complexes Revisited: Palladium‐Catalysed Synthesis,Electronic Structures of Derived Oxy Radicals,and Oxidative Coupling to a Dioxoporphodimethene Dyad

We report the synthesis and characterisation of new examples of meso‐hydroxynickel(II) porphyrins with 5,15‐diphenyl and 10‐phenyl‐5,15‐diphenyl/diaryl substitution. The OH group was introduced by using carbonate or hydroxide as nucleophile by using palladium/phosphine catalysis. The NiPor?OHs exist in solution in equilibrium with the corresponding oxy radicals NiPor?O^.. The 15‐phenyl group stabilises the radicals, so that the ¹H NMR spectra of {NiPor?OH} are extremely broad due to chemical exchange with the paramagnetic species. The radical concentration for the diphenylporphyrin analogue is only 1 %, and its NMR line‐broadening was able to be studied by variable‐temperature NMR spectroscopy. The EPR signals of NiPor?O^. are consistent with somewhat delocalised porphyrinyloxy radicals, and the spin distributions calculated by using density functional theory match the EPR and NMR spectroscopic observations. Nickel(II) meso‐hydroxy‐10,20‐diphenylporphyrin was oxidatively coupled to a dioxo‐terminated porphodimethene dyad, the strongly red‐shifted electronic spectrum of which was successfully modelled by using time‐dependent DFT calculations.