Optimal linear interpolation of multiple missing values

Statistical Inference for Stochastic Processes - The problem of linear interpolation in the context of a multivariate time series having multiple (possibly non-consecutive) missing values is...     

A study of properties of adaptive quadratic grids for three-dimensional near-surface field computations

Curved geometries and the corresponding near-surface fields typically require a large number of linear computational elements. High-order numerical solvers have been primarily used with low-order meshes. There is a need for curved, high-order computational elements. Typical near-surface meshes consist of hexahedral and/or prismatic elements. The present work studies the employment of quadratic meshes that are relatively coarse for field simulations. Directionally quadratic high-order elements are proposed for the near-surface field regions. The quadratic meshes are compared with the conventional low-order ones in terms of accuracy and efficiency. The cases considered include closed surface volume calculations, as well as computation of gradients of several analytic fields. A special method of adaptive local quadratic meshes is proposed and evaluated. Truncation error analysis for quadratic grids yields comparison with the conventional linear hexahedral/prismatic meshes, which are subject to typical distortions such as stretching, skewness, and torsion.     

Exit Times,Overshoot and Undershoot for a Surplus Process in the Presence of an Upper Barrier

We study the movement of a surplus process with initial capital u in the presence of two barriers: a lower barrier at zero and an upper barrier at b (b > u). More specifically, we consider the behaviour of the surplus: (a) in continuous time; and (b) only at claim arrival times. For each of these cases, we find the expected time until the process exits the interval [0,b]. We also obtain results related to the undershoot and overshoot of the surplus which, in particular for case (b) above, are derived under the assumption that the distribution of claim sizes and/or claim interarrival times belongs to the mixed Erlang class. In the final section we discuss the implementation of the methods in a number of examples using computer algebra software. These examples illustrate the efficiency of the methods even in fairly complicated cases.     

Il'iushin's postulate and resulting thermodynamic conditions on elasto-plastic coupling

Il'iushin's postulate is restated within a general thermodynamic strain space formulation of rate independent plasticity by means of plastic internal variables. This yields a general expression in terms of appropriate thermodynamic potentials. A combination of a thermodynamic condition, derived from the general development, with the results of Il'iushin's postulate, furnishes explicit conditions on elasto-plastic coupling. A specific example is presented, with the plastic work being the only plastic internal variable. Necessary and sufficient consitbns on the elastic moduli and their change with plastic deformation are derived, for the thermodynamic condition to be satisfied.     

Elasto-plastic coupling within a thermodynamic strain space formulation of plasticity

Elasto-plastic coupling is studied within a general thermodynamic train space formulation of rate-independent plasticity by means of plastic internal variables. The strain space formulation offers a unified approach in treating both stable and unstable material behavior simultaneously. The conditions on elasto-plastic coupling are imposed by the second law of thermodynamics and the consistency equation in the strain space formulation, and are expressed by two inequalities. This is further illustrated by specific examples where explicit necessary and sufficient conditions on the elastic moduli and their change with plastic deformation are derived for the two inequalities to be satisfied.     

Time-dependent density functional theory molecular dynamics simulation of doubly charged uracil in gas phase

We use time-dependent density functional theory and Born-Oppenheimer molecular dynamics methods to investigate the fragmentation of doubly ionized uracil in gas phase. Different initial electronic excited states of the dication are obtained by removing electrons from different inner-shell orbitals of the neutral species. We show that shape-equivalent orbitals lead to very different fragmentation patterns revealing the importance of the intramolecular chemical environment. The results are in good agreement with ionion coincidence measurements of uracil collision with 100 keV protons.     

Desirability-based optimization and its sensitivity analysis for the perindopril and its impurities analysis in a microemulsion LC system

In the current paper the application of multiobjective optimization (MOOP) technique, via Derringer's desirability function, to a microemulsion liquid chromatographic (MELC) method is described. Chromatographic separation of perindopril tert-butylamine and its four impurities was selected as the case study. Central composite design (CCD) with fractional factorial design, ± 0.5 α star design and four replications in central point was applied for a response surface study, in order to examine in depth the effects of the most important factors. As factors that influence the system mostly (i) content of ethyl acetate and (ii) butyl acetate in composite internal phase, (iii) content of sodium dodecyl sulfate (surfactant) and (iv) n-butanol (co-surfactant), as well as (v) pH of the mobile phase were selected. Retention factor of (a) perindoprilat and (b) impurity Y 31 and (c) resolution factor for impurities Y 32 and 33 were chosen for simultaneous optimization. By adjustment of the importance coefficients and weights, according to defined objectives, the optimal mobile phase composition was predicted to be: 0.24% w/v butyl acetate, 0.3% w/v ethyl acetate, 2% w/v SDS, 7.75% w/v n-butanol and pH of the mobile phase 3.7. The sensitivity analysis of desirability function for these optimal conditions was conducted for the first time in LC separations, by applying a sensitivity procedure. The performed sensitivity analysis confirmed that the higher overall desirability does not necessarily mean a better solution. The accuracy of prediction might be affected if the optimal levels of input variables, achieved from several design points, end up with equal settings and different corresponding overall desirability. In our study this was not the issue, which confirmed the adequacy of predicted optimum.