Mathematical analysis of the waves propagation through a rectangular material structure in space-time

We consider propagation of waves through a spatio-temporal doubly periodic material structure with rectangular microgeometry in one spatial dimension and time. Both spatial and temporal periods in this dynamic material are assumed to be the same order of magnitude. Mathematically the problem is governed by a standard wave equation t(ρut)−z(kuz)=0 with variable coefficients. We consider a checkerboard microgeometry where variables cannot be separated. The rectangles in a space-time checkerboard are assumed filled with materials differing in the values of phase velocities but having equal wave impedance . The difference between dynamic materials and classical static composites is that in the former case the design variables will also be time dependent. Within certain parameter ranges, the formation of distinct and stable limiting characteristic paths, i.e., limit cycles, was observed in [K.A. Lurie, S.L. Weekes, Wave propagation and energy exchange in a spatio-temporal material composite with rectangular microstructure, J. Math. Anal. Appl. 314 (2006) 286-310]; such paths attract neighboring characteristics after a few time periods. The average speed of propagation along the limit cycles remains the same throughout certain ranges of structural parameters, and this was called in [K.A. Lurie, S.L. Weekes, Wave propagation and energy exchange in a spatio-temporal material composite with rectangular microstructure, J. Math. Anal. Appl. 314 (2006) 286-310] a plateau effect. Based on numerical evidence, it was conjectured in [K.A. Lurie, S.L. Weekes, Wave propagation and energy exchange in a spatio-temporal material composite with rectangular microstructure, J. Math. Anal. Appl. 314 (2006) 286-310] that a checkerboard structure is on a plateau if and only if it yields stable limit cycles and that there may be energy concentrations over certain time intervals depending on material parameters. In the present work we give a more detailed analytic characterization of these phenomena and provide a set of sufficient conditions for the energy concentration that was predicted numerically in [K.A. Lurie, S.L. Weekes, Wave propagation and energy exchange in a spatio-temporal material composite with rectangular microstructure, J. Math. Anal. Appl. 314 (2006) 286-310].     

A parameterized approach to modeling and forecasting mortality

A new method is proposed of constructing mortality forecasts. This parameterized approach utilizes Generalized Linear Models (GLMs), based on heteroscedastic Poisson (non-additive) error structures, and using an orthonormal polynomial design matrix. Principal Component (PC) analysis is then applied to the cross-sectional fitted parameters. The produced model can be viewed either as a one-factor parameterized model where the time series are the fitted parameters, or as a principal component model, namely a log-bilinear hierarchical statistical association model of Goodman [Goodman, L.A., 1991. Measures, models, and graphical displays in the analysis of cross-classified data. J. Amer. Statist. Assoc. 86(416), 1085-1111] or equivalently as a generalized Lee-Carter model with p interaction terms. Mortality forecasts are obtained by applying dynamic linear regression models to the PCs. Two applications are presented: Sweden (1751-2006) and Greece (1957-2006).     

Optimal intervention policies for a multidimensional simple epidemic process

We consider a deterministic simple epidemic process in which the susceptibles are exposed to n+1 diseases. It is assumed that one disease is relatively harmless while the others cause serious symptoms. Policies for introducing infection by the harmless disease are considered and, under a suitable cost structure, the optimal policy that minimises the future cost for every initial state is found. For the corresponding stochastic model, the optimal policy is found by implementing a suitable dynamic programming algorithm, and is compared numerically with the optimal policy for the deterministic model.     

A reassessment of the Snyman–Fatti dynamic search trajectory method for unconstrained global optimization

The aim of this paper is to present a thorough reassessment of the Snyman–Fatti (SF) Multi-start Global Minimization Algorithm with Dynamic Search Trajectories, first published twenty years ago. The reassessment is done with reference to a slightly modified version of the original method, the essentials of which are summarized here. Results of the performance of the current code on an extensive set of standard test problems commonly in use today, are presented. This allows for a fair assessment to be made of the performance of the SF algorithm relative to that of the popular Differential Evolution (DE) method, for which test results on the same standard set of test problems used here for the SF algorithm, are also given. The tests show that the SF algorithm, that requires relatively few parameter settings, is a reliably robust and competitive method compared to the DE method. The results also indicate that the SF trajectory algorithm is particularly promising to solve minimum potential energy problems to determine the structure of atomic and molecular clusters.     

On estimates for the Fourier-Bessel integral transform in the space <Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript>(ℝ<Subscript>+</Subscript>)

Two estimates useful in applications are proved for the Fourier-Bessel integral transform in L ₂(?₊) as applied to some classes of functions characterized by a generalized modulus of continuity.     

Lp approximation by Bernstein-Kantorovich quasi-interpolants

Bernstein-Kantorovich quasi-interpolants K(2r-1) n (f, x) are considered and direct,inverse and equivalence theorems with Ditzian-Totik modulus of smoothness ω2rψ(f, t)p (1 ≤ p≤+∞) are obtained.     

L p approximation by Bernstein-Kantorovich quasi-interpolants

Bernstein-Kantorovich quasi-interpolants K^（2r-1）n（f, x） are considered and direct, inverse and equivalence theorems with Ditzian-Totik modulus of smoothness ω^2rφ（f, t）p （1 ≤ p ≤＋∞） are obtained.     

A dynamic programming algorithm for the single-machine scheduling problem with release dates and deteriorating processing times

We consider a scheduling problem in which the processing time of each job deteriorates, i.e. it increases as time passes after the release date of the job. We present a dynamic programming algorithm coupled with upper bounding and lower bounding techniques to compute exact solutions. We report on problem instances of different size and we analyze the dependence between the ranges to which the data belong and the computing time.     

Partitions with initial repetitions

A variety of interesting connections with modular forms, mock theta functions and Rogers- Ramanujan type identities arise in consideration of partitions in which the smaller integers are repeated as summands more often than the larger summands. In particular, this concept leads to new interpretations of the Rogers Selberg identities and Bailey＇s modulus 9 identities.     

Dynamic versus static ultrasonic sample treatment for the solid-liquid pre-concentration of mercury from human urine

Dynamic and static ultrasonic procedures involving ultrasonic bath and tandem focused ultrasound (i.e. two probes were used in the same sample treatment) have been assessed in order to implement a reliable solid-liquid back extraction of mercury from commercial resins (dowex and chelex-100), previously used to concentrate Hg(II) from treated urine. The urine had been previously treated with an advanced oxidation process provided by the conjunction of potassium permanganate, hydrochloric acid and high intensity focused ultrasound, which allowed that organic matter degradation was achieved in less than 3 min. 95 ± 10% of mercury in the certified urine and 97 ± 6% of the spiked methyl-mercury was recovered with the dowex resin plus the static ultrasonic procedure, whilst 96 ± 11% of the spiked mercury was recovered with the dowex resin plus the dynamic procedure, for which ultrasonication was not necessary. The Hg pre-concentration factor used in this work was 8 (20 mL of urine to 2.5 mL of acid), but different volume ratios can be used in order to increase this factor.