Simple correction for perturbations of peak amplitudes in statistical models of overlap

Summary The application of statistical models of overlap (SMOs) to saturated separations is made possible by theory that addresses variable peak amplitudes. These amplitudes cause peak widths to vary, and this variation can be modeled by a random variable whose effect on the probability of overlap is expressed by a convolution integral. Modified probabilities of overlap are derived for both homogeneous and nonhomogeneous one-dimensional separations, and the new probabilities are compared to results determined from published computer simulations. The new theory can describe overlap at saturations that are 3 to 4 times larger than before. Previously reported experimental chromatograms are reinterpreted to show the capabilities of theory. The theoretical extension is an important step towards making SMOs into practical tools for screening analytical separations.     

Theoretical Definition of a Functional Group and the Molecular Orbital Paradigm

It is the purpose of this review to demonstrate that the empirical classification of the observations of chemistry in terms of the properties assigned to functional groups is a consequence of and is predicted by physics. This is accomplished by showing that the atoms and functional groups of chemistry can be identified with bounded space-filling objects whose properties are defined by quantum mechanics. The quantum mechanical definition of a group is combined with a new pictorial representation of its form to obtain a unified picture which should make it eminently recognizable to chemists. This picture, when combined with the demonstrated ability of these groups to recover the measured properties of atoms in molecules, is offered as one which meets the expectations a chemist associates with the concept of a functional group. The manner in which this physical definition of a group differs fundamentally from models of functional groups based upon molecular orbital theory is discussed.     

Oxazinins from toxic mussels: isolation of a novel oxazinin and reassignment of the C-2 configuration of oxazinin-1 and -2 on the basis of synthetic models

The analysis of a batch of toxic mussels (Mytilus galloprovincialis) from the Northern Adriatic Sea led to the isolation of a novel oxazinin, oxazinin-4. Its structure including the relative stereochemistry has been elucidated through extensive NMR analysis. A synthetic route to oxazinins has been crucial in establishing the absolute stereochemistry of oxazinin-4 and for reassigning the absolute C-2 configuration of oxazinin-1 and -2 previously isolated from toxic shellfish and stereostructurally characterized.     

主动冷却点阵夹层防热结构温度响应计算模型北大核心CSCD

针对点阵夹层结构主动热防护问题,建立了夹层结构面板和芯体导热与冷却剂对流耦合的非稳态传热理论模型,利用有限体积法离散控制方程并在MATLAB中进行了迭代求解.模型首次考虑了面板与夹芯杆之间的收缩热阻,并利用分离变量法得到了收缩热阻的近似解析解.基于单胞模型和周期性边界条件,模拟得到了模型所需的表面对流传热系数h_(b)和h_(fin).最后,选取多单胞计算工况进行数值模拟和理论模型对比,并讨论了收缩热阻对模型预测精度的影响.结果表明:理论模型能够准确预测夹层结构及内部流体的温度变化,理论与仿真之间的最大误差不超过1%;随着外加热流密度不断增大,忽略收缩热阻使得计算结果造成的误差不断增大;与数值模拟相比,理论模型可显著地减少计算时间并节省计算资源,尤其适用于非均匀、非稳态复杂热载荷下点阵夹层结构的温度响应计算.     

Multifractal analysis of Brownian zero set

We present a method for the derivation of the generating function and computation of critical exponents for several cluster models (staircase, bar-graph, and directed column-convex polygons, as well as partially directed self-avoiding walks), starting with nonlinear functional equations for the generating function. By linearizing these equations, we first give a derivation of the generating functions. The nonlinear equations are further used to compute the thermodynamic critical exponents via a formal perturbation ansatz. Alternatively, taking the continuum limit leads to nonlinear differential equations, from which one can extract the scaling function. We find that all the above models are in the same universality class with exponents _u =-1/2, _i =-1/3, and =2/3. All models have as their scaling function the logarithmic derivative of the Airy function.     

Disordered ground states for classical discrete-state problems in one dimension

It is known that one-dimensional lattice problems with a discrete, finite set of states per site generically have periodic ground states (GSs). We consider slightly less generic cases, in which the Hamiltonian is constrained by either spin (S) or spatial (I) inversion symmetry (or both). We show that such constraints give rise to the possibility ofdisordered GSs over a finite fraction of the coupling-parameter space—that is, without invoking any nongeneric fine tuning of coupling constants, beyond that arising from symmetry. We find that such disordered GSs can arise for many values of the number of statesk at each site and the ranger of the interaction. The Ising (k=2) case is the least prone to disorder:I symmetry allows for disordered GSs (without fine tuning) only forr5, whileS symmetry never gives rise to disordered GSs.     

The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice

Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2 and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second. Mathematics Subject Classification: 03E25, 03E35, 04A25.     

Optimality of a Threshold Policy in theM/M/ queue with repeated vacations

Consider anM/M/1 queueing system with server vacations where the server is turned off as soon as the queue gets empty. We assume that the vacation durations form a sequence of i.i.d. random variables with exponential distribution. At the end of a vacation period, the server may either be turned on if the queue is non empty or take another vacation. The following costs are incurred: a holding cost ofh per unit of time and per customer in the system and a fixed cost of each time the server is turned on. We show that there exists a threshold policy that minimizes the long-run average cost criterion. The approach we use was first proposed in Blanc et al. (1990) and enables us to determine explicitly the optimal threshold and the optimal long-run average cost in terms of the model parameters.     

The theoretical basis of column chromatography in multicomponent separations. Part 2: Peak capacity. Column systems with good selectivity

The selectivity of a column system, S, defined by equation 28, includes a variation coefficient (β) of plate number with capacity ratio which has a large influence on the peak capacity, as shown in Fig. 18. Some typical chromatograms are given. In order to predict S for a column system from Kovat's Index, equations 40 and 41 are given to calculate the constant of the carbon number rule for squalane at different temperatures or for different stationary phases. The specific retention value of heptane on squalane at different temperatures can be calculated from equation 42. The nonpolarity index, defined by equation 43, was used to calculate the retention value of heptane on various stationary phases. In liquid chromatography, the order of elution may be reversed by changing the composition of the eluent on the same chemically bonded silica (manufactured in China). The linear relations between the log retention values of different kinds of solutes or of a single solute on the silicas of different surface areas when using the same eluent are given.     

Solvent effects on 17O nuclear magnetic shielding: N-methylformamide in polar and apolar solutions

The solvent effect on ¹⁷O isotropic shielding was computed by different methods: the polarizable continuum model and a mixed approach, including a few real solvent molecules treated as the solute. The experimental data show that the behavior of protic and aprotic solvents is markedly different: we found that the continuum approach describes well the observed shielding at various dielectric constants for aprotic solvents, while the mixed procedure is needed when hydrogen bonds to the magnetic centre are present.Contribution to the Jacopo Tomasi Honorary Issue