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。     

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.

     

Evolutionary snowdrift game incorporating costly punishment in structured populations

The role of punishment and the effects of a structured population in promoting cooperation are important issues. Within a recent model of snowdrift game (SG) incorporating a costly punishing strategy (P), we study the effects of a population connected through a square lattice. The punishers, who carry basically a cooperative (C) character, are willing to pay a cost α$\alpha$ so as to punish a non-cooperative (D) opponent by β$\beta$. Depending on α$\alpha$, β$\beta$, the cost-to-benefit ratio r$r$ in SG, and the initial conditions, the system evolves into different phases that could be homogeneous or inhomogeneous. The spatial structure imposes geometrical constraint on how one agent is affected by neighboring agents. Results of extensive numerical simulations, both for the steady state and the dynamics, are presented. Possible phases are identified and discussed, and isolated phases in the r–β$r\text{–}\beta$ space are identified as special local structures of strategies that are stable due to the lattice structure. In contrast to a well-mixed population where punishers are suppressed due to the cost of punishment, the altruistic punishing strategy can flourish and prevail for appropriate values of the parameters, implying an enhancement in cooperation by imposing punishments in a structured population. The system could evolve to a phase corresponding to the coexistence of C, D, and P strategies at some particular payoff parameters, and such a phase is absent in a well-mixed population. The pair approximation, a commonly used analytic approach, is extended from a two-strategy system to a three-strategy system. We show that the pair approximation can, at best, capture the numerical results only qualitatively. Due to the improper way of including spatial correlation imposed by the lattice structure, the approximation does not give the frequencies of C, D, and P accurately and fails to give the homogeneous AllD and AllP phases.     

A concise quantum mechanical treatment of the forced damped harmonic oscillator

By selecting a right generalized coordinate X, which contains the general solutions of the classical motion equation of a forced damped harmonic oscillator, we obtain a simple Hamiltonian which does not contain time for the oscillator such that Schrödinger equation and its solutions can be directly written out in X representation. The wave functin in x representation are also given with the help of the eigenfunctions of the operator \(\hat X\) in x representation. The evolution of \(\left\langle {\hat x} \right\rangle \) is the same as in the classical mechanics, and the uncertainty in position is independent of an external influence; one part of energy mean is quantized and attenuated, and the other is equal to the classical energy.     

Redox Communication within Multinuclear Iron–Sulfur Complexes Related to Electronic Interplay in the Active Site of [FeFe]Hydrogenase

The one‐electron oxidations of a Fe₂ complex lead to the formation of a persistent metal‐stabilized thiyl radical Fe₂ species, mixed‐valent Fe₄, and Fe₈ complexes. The unpaired spin in the Fe₂ radical species delocalizes over the Fe₂ and the aromatic dithiolate, mostly on the terminal sulfur. The subsequent dimerization of the singly oxidized Fe₂ to the Fe₄ retains the partial thiyl radical character. For an analogue with less steric hindrance, the π–π stacking interaction between the dithiolato aromatic rings induces generation of the Fe₈, in which process electronic structures of the species are modulated through reducing the thiyl radical to the thiolate. Electronic reorganization repeats when the Fe₈ is converted to Fe₄. Electronic interplay in the complexes decreases the energy gap of frontier MOs and buffers electronic impacts upon redox events. Easier accessible redox potentials and increased stability of the species are facilitated. The results demonstrate that electronic versatility of the benzenedithiolate exerts pronounced influences on electronic and coordination structure of the metal complexes.     

Monte Carlo simulation of Cu,Ni and Fe grade determination in borehole by PGNAA technique

A prompt gamma neutron activation analysis borehole logging method for copper, nickel and iron grade estimation is proposed. The performance of the method was simulated by MCNP5 code. Based on the theory of neutron–gamma distribution on the borehole condition, the BGO scintillator and ³He neutron tube are adopted to record gamma ray spectrum and thermal neutron simultaneously, and least square method is used for the characteristic gamma ray counts calculation in the high energy range. The results of detection limit of metal grade in borehole condition indicate that the effectiveness of this logging method.     

Existence of multi-solitary waves with logarithmic relative distances for the NLS equation

We construct 2-solitary wave solutions with logarithmic distance to the nonlinear Schrödinger equation,

$\mathrm{i}{?}_{t}u+\mathrm{\Delta }u+|u{|}^{p?1}u=0,t\in \mathbb{R},x\in {\mathbb{R}}^d,$

in mass-subcritical cases $1<p<1+\frac{4}{d}$ and mass-supercritical cases $1+\frac{4}{d}<p<\frac{d+2}{d?2}$, i.e. solutions $u(t)$ satisfying

${6u(t)?{\mathrm{e}}^{\mathrm{i}\gamma (t)}\sum _{k=1}^{2}Q(??x_k(t))6}_{H^1}\to 0$

and

$|x_1(t)?x_2(t)|～2\log ?t,\text{as}t\to +\infty ,$

where Q is the ground state. The logarithmic distance is related to strong interactions between solitary waves.In the integrable case ($d=1$ and $p=3$), the existence of such solutions is known by inverse scattering (E. Olmedilla, Multiple pole solutions of the nonlinear Schrödinger equation, Physica D 25 (1987) 330–346; T. Zakharov, A.B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Sov. Phys. JETP 34 (1972) 62–69). The mass-critical case $p=1+\frac{4}{d}$ exhibits a specific behavior related to blow-up, previously studied in Y. Martel, P. Raphaël (Strongly interacting blow up bubbles for the mass critical NLS, Ann. Sci. Éc. Norm. Supér. 51 (2018) 701–737).     

Thermal Pretreatment of Harvest Residues and Their Use in Anaerobic Co-digestion with Dairy Cow Manure

Several batch experiments were conducted on the anaerobic co-digestion of dairy cow manure (DCM) with three harvest residues (HR) (soybean straw, sunflower stalks, and corn stover). The influence of thermal pretreatment of HR on biogas production was investigated, where the HR were thermally pretreated at two different temperatures: T = 121 °C and T = 175 °C, during t = 30 and t = 90 min, respectively. All anaerobic co-digestion batch experiments were performed simultaneously under thermophilic regime, at T = 55 °C. Biogas and methane yields were significantly improved in experiments performed with corn stover thermally pretreated at 175 °C for 30 min (491.37 cm³/g VS and 306.96 cm³/g VS, respectively), if compared to experiments performed with untreated corn stover. The highest VS and COD removal rates were also observed in the same group of experiments and were 34.5 and 50.1%, respectively. The highest biogas and methane yields with soybean straw (418.93 cm³/g VS and 261.44 cm³/g VS, respectively) were obtained when soybean straw pretreated at 121 °C during 90 min. The highest biogas and methane yields with sunflower stalk (393.28 cm³/g VS and 245.02 cm³/g VS, respectively) were obtained when sunflower stalk was pretreated at 121 °C during 90 min.