Experiments and Simulations of <Emphasis Type="Italic">n</Emphasis>-Heptane Spray Auto-Ignition in a Closed Combustion Chamber at Diesel Engine Conditions

Auto-igniting n-heptane sprays have been studied experimentally in a high pressure, high temperature constant volume combustion chamber with optical access. Ignition delay and the total pressure increase due to combustion are highly repeatable whereas the ignition location shows substantial fluctuations. Simulations have subsequently been performed by means of a first-order fully elliptic Conditional Moment Closure (CMC) code. Overall, the simulations are in good agreement with the experiment in terms of spray evolution, ignition delay and the pressure development. The sensitivity of the predictions with respect to the measured initial conditions, the spray modelling options as well as the chemical mechanism employed have been analysed. Strong sensitivity on the chemical mechanism and to the initial temperature on the predicted ignition delay is reported. The primary atomisation model did not affect strongly the predicted auto-ignition time, but a strong influence was found on the ignition location prediction.     

On the singularities of a constrained (incompressible-like) tensegrity-cytoskeleton model under equitriaxial loading

Singularity theory is applied for the study of the characteristic three-dimensional tensegrity-cytoskeleton model after adopting an incompressibility constraint. The model comprises six elastic bars interconnected with 24 elastic string members. Previous studies have already been performed on non-constrained systems; however, the present one allows for general non-symmetric equilibrium configurations. Critical conditions for branching of the equilibrium are derived and post-critical behaviour is discussed. Classification of the simple and compound singularities of the total potential energy function is effected. The theory is implemented into the cusp catastrophe for the case of one-dimensional branching of the buckling-allowed tensegrity model, and an elliptic umbilic singularity for compound branching of a rigid-bar model. It is pointed out that singularity studies with constraints demand a quite different mathematical approach than those without constraints.     

Symmetry groups and similarity solutions for a free convective boundary-layer problem

The free convective boundary-layer problem due to the motion of an elastic surface into an electrically conducting fluid is studied with group-theoretical methods. The symmetry groups admitted by the corresponding boundary value problem are obtained. Particular attention is paid on the group of scaling which provides the similarity solution of the problem. Also, the admissible form of the data, in order to be conformed to the obtained symmetries, is provided. Finally, with the use of the entailed similarity solution the problem is transformed into a boundary value problem of ODEs and is solved numerically.     

Universal Laurent series smooth up to a part of the boundary

We prove the generic existence of universal Laurent series in domains of infinite connectivity. The universal approximation is valid on a part of the boundary, while on another disjoint part of the boundary the universal function is smooth.     

Safe density ratio modeling

An important problem in logistic regression modeling is the existence of the maximum likelihood estimators. In particular, when the sample size is small, the maximum likelihood estimator of the regression parameters does not exist if the data are completely, or quasicompletely separated. Recognizing that this phenomenon has a serious impact on the fitting of the density ratio model–which is a semiparametric model whose profile empirical log-likelihood has the logistic form because of the equivalence between prospective and retrospective sampling–we suggest a linear programming methodology for examining whether the maximum likelihood estimators of the finite dimensional parameter vector of the model exist. It is shown that the methodology can be effectively utilized in the analysis of case–control gene expression data by identifying cases where the density ratio model cannot be applied. It is demonstrated that naive application of the density ratio model yields erroneous conclusions.     

Multiobjective evolutionary algorithms for complex portfolio optimization problems

This paper investigates the ability of Multiobjective Evolutionary Algorithms (MOEAs), namely the Non-dominated Sorting Genetic Algorithm II (NSGA-II), Pareto Envelope-based Selection Algorithm (PESA) and Strength Pareto Evolutionary Algorithm 2 (SPEA2), for solving complex portfolio optimization problems. The portfolio optimization problem is a typical bi-objective optimization problem with objectives the reward that should be maximized and the risk that should be minimized. While reward is commonly measured by the portfolio’s expected return, various risk measures have been proposed that try to better reflect a portfolio’s riskiness or to simplify the problem to be solved with exact optimization techniques efficiently. However, some risk measures generate additional complexities, since they are non-convex, non-differentiable functions. In addition, constraints imposed by the practitioners introduce further difficulties since they transform the search space into a non-convex region. The results show that MOEAs, in general, are efficient and reliable strategies for this kind of problems, and their performance is independent of the risk function used.     

Log-linear Poisson autoregression

We consider a log-linear model for time series of counts. This type of model provides a framework where both negative and positive association can be taken into account. In addition time dependent covariates are accommodated in a straightforward way. We study its probabilistic properties and maximum likelihood estimation. It is shown that a perturbed version of the process is geometrically ergodic, and, under some conditions, it approaches the non-perturbed version. In addition, it is proved that the maximum likelihood estimator of the vector of unknown parameters is asymptotically normal with a covariance matrix that can be consistently estimated. The results are based on minimal assumptions and can be extended to the case of log-linear regression with continuous exogenous variables. The theory is applied to aggregated financial transaction time series. In particular, we discover positive association between the number of transactions and the volatility process of a certain stock.