Multistage estimation of the difference of locations of two negative exponential populations under a modified Linex loss function: Real data illustrations from cancer studies and reliability analysis

We have designed modified two-stage and purely sequential strategies to estimate the difference of location parameters from two independent negative exponential populations having unknown but proportional scale parameters under a modified Linex loss function. This article extends one-sample methodologies of Mukhopadhyay and Bapat (2016 Mukhopadhyay, N. and Bapat, S. R. (2016). Multistage Point Estimation Methodologies for a Negative Exponential Location under a Modified Linex Loss Function: Illustrations with Infant Mortality and Bone Marrow Data, Sequential Analysis 35: 175–206. http://dx.doi.org/10.1080/07474946.2016.1165532.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], Sequential Analysis). Some preliminary results are established along the lines of Mukhopadhyay and Hamdy (1984 Mukhopadhyay, N. and Hamdy, H. I. (1984). On Estimating the Difference of Location Parameters of Two Negative Exponential Distributions, Canadian Journal of Statistics 12: 67–76.[Crossref] , [Google Scholar], Canadian Journal of Statistics) and Mukhopadhyay and Darmanto (1988 Mukhopadhyay, N. and Darmanto, S. (1988). Sequential Estimation of the Difference of Means of Two Negative Exponential Populations, Sequential Analysis 7: 165–190.[Taylor &; Francis Online] , [Google Scholar], Sequential Analysis). We have resorted to Mukhopadhyay and Duggan (1997 Mukhopadhyay, N. and Duggan, W. T. (1997). Can a Two-Stage Procedure Enjoy Second Order Properties? Sankhya, Series A 59: 435–448. [Google Scholar], Sankhya, Series A) in developing asymptotic second-order properties for the modified two-stage methodology and to nonlinear renewal theory of Lai and Siegmund (1977 Lai, T. L. and Siegmund, D. (1977). A Nonlinear Renewal Theory with Applications to Sequential Analysis I, Annals of Statistics 5: 946–954.[Crossref], [Web of Science ®] , [Google Scholar], 1979 Lai, T. L. and Siegmund, D. (1979). A Nonlinear Renewal Theory with Applications to Sequential Analysis II, Annals of Statistics 7: 60–76.[Crossref], [Web of Science ®] , [Google Scholar], Annals of Statistics) and Woodroofe (1977 Woodroofe, M. (1977). Second Order Approximation for Sequential Point and Interval Estimation, Annals of Statistics 5: 984–995.[Crossref], [Web of Science ®] , [Google Scholar], Annals of Statistics) in addressing analogous properties under the purely sequential methodology. Then, we supplement with extensive sets of data analysis via computer simulations validating that both modified two-stage and purely sequential methods perform very well. Both methodologies are also illustrated and implemented using real datasets from cancer studies and reliability analysis.     

Nonparametric partially random sequential test under Phase II sampling: An illustration to monitor water samples for arsenic contamination

We introduce a class of nonparametric two-sample tests based on a new partially sequential sampling scheme. Existing partially sequential procedures based on inverse sampling schemes, pioneered by Wolfe (1977 Wolfe, D. A. (1977). On a Class of Partially Sequential Two Sample Test Procedure, Journal of American Statistical Association 72: 202–205.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and Orban and Wolfe (1980 Orban, J. and Wolfe, D. A. (1980). Distribution Free Partially Sequential Placement Procedure, Communications in Statistics - Theory &; Methods 9: 883–902.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), are updated in the light of random sequential sampling techniques, proposed by Mukhopadhyay and de Silva (2008 Mukhopadhyay, N. and de Silva, B. M. (2008). Theory and Applications of a New Methodology for the Random Sequential Probability Ratio Test, Statistical Methodology 5: 424–453.[Crossref] , [Google Scholar]). In a quality control setup, the present procedure can be looked upon as a Phase II on-line monitoring with rational subgroups of variable sizes where standards are unknown. We consider a training sample of prefixed size m as Phase I observations and adopt a random sequential sampling in Phase II. We discuss statistical methodologies in detail and provide some asymptotic results. Numerical results based on Monte Carlo are presented to justify asymptotic theory. We computationally investigate the power performances of the proposed test against some fixed alternative. We illustrate our procedure with real data related to water samples for monitoring arsenic contamination. Some concluding remarks along with possible future research problems are offered     

AN IMPROVEMENT TO THE SSF MODEL FOR PREDICTION OF LIGHT PARTICLE DISPERSION

This study investigates the predicted motion of small, light particles using the stochastic separated flow models proposed by Shuen et al. (1983 Shuen , J. S. , Chen , L. D. , and Faeth , G. M. ( 1983 ). Evaluation of a stochastic model of particle dispersion in a turbulent round jet , AIChE J. , 29 , 167 – 170 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) and Lightstone and Raithby (1998 Lightstone , M. F. and Raithby , G. D. ( 1998 ). A stochastic model of particle dispersion in a turbulent gaseous environment , Combust. Flame , 113 , 424 – 441 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]). Model predictions are compared to the benchmark experiment of Snyder and Lumley (1971 Snyder , W. H. and Lumley , J. L. ( 1971 ). Some measurements of particle velocity autocorrelation functions in a turbulent flow , J. Fluid Mech. , 48 , 41 – 71 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) for particles released from a point source in grid-generated turbulence. It is found that the predictions of particle velocity variance and dispersion exhibit nonphysical waves. This behavior is explored in order to understand its mathematical basis arising from the model formulation. A modification to the model is presented. The modified model is successful in removing the characteristic waves.     

Multistage point estimation methodologies for a negative exponential location under a modified linex loss function: Illustrations with infant mortality and bone marrow data

We have designed Stein-type (Stein, 1945 Stein, C. (1945). A Two Sample Test for a Linear Hypothesis Whose Power Is Independent of the Variance, Annals of Mathematical Statistics 16: 243–258.[Crossref] , [Google Scholar], Annals of Mathematical Statistics) two-stage, modified two-stage (Mukhopadhyay and Duggan, 1997 Mukhopadhyay, N. and Duggan, W. T. (1997). Can a Two-Stage Procedure Enjoy Second Order Properties? Sankhya, Series A 59: 435–448. [Google Scholar], Sankhya, Series A), and purely sequential strategies (Chow and Robbins, 1965 Chow, Y. S. and Robbins, H. (1965). On the Asymptotic Theory of Fixed Width Sequential Confidence Intervals for the Mean, Annals of Mathematical Statistics 36: 457–462.[Crossref] , [Google Scholar], Annals of Mathematical Statistics) to estimate an unknown location parameter of a negative exponential distribution having an unknown scale parameter under a newly defined and modified Linex loss function. We aim at controlling the associated risk function per unit cost by bounding it from above with a fixed preassigned positive number, ω, and we emphasize both asymptotic first-order and asymptotic second-order properties for the modified two-stage and purely sequential estimation strategies. In developing asymptotic second-order properties for the modified two-stage methodology, we have heavily relied upon basic ideas rooted in Mukhopadhyay and Duggan (1997 Mukhopadhyay, N. and Duggan, W. T. (1997). Can a Two-Stage Procedure Enjoy Second Order Properties? Sankhya, Series A 59: 435–448. [Google Scholar]). In developing asymptotic second-order properties for the purely sequential methodology, however, we have heavily relied upon nonlinear renewal theory (Lai and Siegmund, 1977 Lai, T. L. and Siegmund, D. (1977). A Nonlinear Renewal Theory with Applications to Sequential Analysis I, Annals of Statistics 5: 946–954.[Crossref], [Web of Science ®] , [Google Scholar], 1979 Lai, T. L. and Siegmund, D. (1979). A Nonlinear Renewal Theory with Applications to Sequential Analysis II, Annals of Statistics 7: 60–76.[Crossref], [Web of Science ®] , [Google Scholar], Annals of Statistics; Woodroofe, 1977 Woodroofe, M. (1977). Second Order Approximation for Sequential Point and Interval Estimation, Annals of Statistics 5: 984–995.[Crossref], [Web of Science ®] , [Google Scholar], Annals of Statistics). Then, we take to extensive data analysis carried out via computer simulations when requisite sample sizes range from small to moderate to large. We find that the Stein-type two-stage estimation methodology oversamples significantly and yet the achieved risk is not close to preset goal ω. On the other hand, both modified two-stage and purely sequential estimation strategies perform remarkably well. We have validated their main theoretical first-order and second-order properties through simulated data. The latter methodologies have been illustrated and implemented using two real data sets from health studies, namely, infant mortality data and bone marrow data.     

A Bayesian adaptive dose-finding algorithm for balancing individual- and population-level ethics in Phase I clinical trials

Multiple Bayesian adaptive designs have been proposed for Phase I clinical trials since the continual reassessment method (CRM) was proposed by O’Quigley et al. (1990). Focused on dose-finding in cancer studies, the CRM seeks to allocate new patients to an estimated maximum tolerable dose (MTD). Later, Whitehead and Brunier (1995 Whitehead, J. and Brunier, H. (1995). Continual Reassessment Method: Bayesian Decision Procedures for Dose Determining Experiments, Statistics in Medicine 14: 885–893.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) applied Bayesian decision theory to maximize statistical information for the MTD when allocating new patients. The two allocation rules reflect conflicting perspectives. The CRM emphasizes individual-level ethics, whereas the method of Whitehead and Brunier (1995 Whitehead, J. and Brunier, H. (1995). Continual Reassessment Method: Bayesian Decision Procedures for Dose Determining Experiments, Statistics in Medicine 14: 885–893.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) emphasizes population-level ethics. In the design of a Phase I clinical trial to investigate hyperthermic intraperitoneal chemotherapy (HIPEC) we sought to compromise the two perspectives. To this end, we propose a novel dose allocation design referred to as the balanced information gain method. We first decompose the loss function used by Whitehead and Brunier and then modify it with a tuning parameter that allows a trialist to differentially weigh individual- and population-level ethics based on their particular clinical setting. Simulation studies show that the proposed design provides a reasonable compromise between the distribution of the estimated MTD and the distribution of the number of observed adverse events per trial when compared to the two existing methods.     

A simulation model for settling tanks with varying cross-sectional area

A quasi-one-dimensional model of the process of continuous sedimentation in clarifier-thickeners (settlers) with variable cross-sectional area is presented. The partial differential equation (PDE) model extends the settler model advanced by Bürger et al. (2013 Bürger, R., Diehl, S., Farås, S., Nopens, I., and Torfs, E. (2013). A consistent modelling methodology for secondary settling tanks: A reliable numerical method, Water Sci. Technol. 68(1), 192–208.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), which assumes a constant cross section. A reliable numerical method that handles the special features of the nonlinear PDE is presented along with an advantageous time-step condition for continuous and batch sedimentation under the condition of a variable cross-sectional area. Simulations of continuous sedimentation show the effect of change of cross-sectional area in the concentration inside the vessel and in the underflow. Simulations of batch settling in cones illustrate the versatility of the numerical scheme to include a vertex, where the area shrinks to zero.     

Asymptotically optimal procedures in multivariate Bayesian sequential estimation

In this article, we consider the problem of multivariate Bayesian sequential estimation of the unknown mean vector. We propose a robust sequential procedure without using the prior information or any auxiliary data, which is similar to multivariate non-Bayesian sequential estimation by M. Ghosh et al. (1976 Ghosh, M., Sinha, B. K., and Mukhopadhyay, N. (1976). Multivariate Sequential Point Estimation, Journal of Multivariate Analysis 6: 281–294.[Crossref], [Web of Science ®] , [Google Scholar]). The proposed procedure, depending only on the present data but not on its distribution, is shown to be asymptotically as well as or better than the optimal fixed-sample-size procedures for the arbitrary distributions and asymptotically pointwise optimal and asymptotically optimal for multivariate exponential family with a large class of prior distributions.     

Some optimal variance stopping problems revisited with an application to the Italian Ftse-Mib stock index

Optimal variance stopping (O.V.S.) problems are a new class of optimal stopping problems that differ from the classical ones because of their non linear (quadratic) dependence on the expectation operator. These problems were introduced by Pedersen (2011 Pedersen, J. L. (2011). Explicit Solutions to Some Optimal Variance Stopping Problems, Stochastics 83: 505–518.[Taylor &; Francis Online] , [Google Scholar]), who provided an effective solution method and derived the explicit solutions to the O.V.S. problem for some important examples of diffusion processes. In this article, we analyze the examples of Pedersen (2011 Pedersen, J. L. (2011). Explicit Solutions to Some Optimal Variance Stopping Problems, Stochastics 83: 505–518.[Taylor &; Francis Online] , [Google Scholar]) in light of the results in Buonaguidi (2015 Buonaguidi, B. (2015). A Remark on Optimal Variance Stopping Problems, Journal of Applied Probability 52: 1187–1194.[Crossref], [Web of Science ®] , [Google Scholar]), where an alternative method for solving an O.V.S. problem was developed: this method is based on the solution of a constrained optimal stopping problem, whose maximization, over all the admissible constraints, returns the solution to the O.V.S. problem. Using real data on the Italian Ftse-Mib stock index, we also discuss how the solution to the O.V.S. problem for a geometric Brownian motion can be used in trading strategies.     

Thermal Effects in Evaporation from Binary Liquid Mixtures

Thermal effects are considered assuming a volatile component evaporates from a binary liquid mixture in a very long tube. The work is an extension of the work of Chebbi and Selim (2006 Chebbi, R., and Selim, M. S. (2006). The Stefan problem of evaporation of a volatile component from a binary liquid mixture, Heat Mass Transfer, 42(3), 238–247.[Crossref], [Web of Science ®] , [Google Scholar]) (isothermal case) to include evaporative cooling. A similarity solution is provided for the gas–liquid interface temperature and the temperature profiles in the liquid and gas phases. The analysis accounts for the motion of the gas–liquid interface and shows evaporative cooling as expected. The magnitude of evaporative cooling is found significant when volatility of the volatile component is sufficiently high. The validity of the approximations used in the solution is addressed.     

Adhesive Contact of a Compliant Sphere to an Elastic Coated Substrate: The Thin Film Limit

Experimental results for adhesive contacts on substrates coated with elastomeric thin films have recently been obtained by Tardivat and Léger [1 Tardivat , C. and Léger L. , J. Adhesion Sci. Technol. 15 , 1055 – 1078 ( 2001 ).[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] by the so-called Johnson-Kendall-Roberts (JKR) test, which provides both adhesion energy and elastic modulus. These data show that on substrates coated with thin films the adhesion and effective elastic modulus of the sphere depend upon the film thickness. In keeping with the experimental conditions, we try to interpret these data using a simple model [4 Barthel , E. and Perriot , A. , J. Phys. D: Appl. Phys. 40, 1059–1067 (2007).[Crossref] , [Google Scholar]] in the thin film limit, i.e., when the film thickness is small compared with the contact radius. Although the film does impact the local crack tip stress field, we show that no effect on the macroscopic contact variables is expected for the adhesion to coated substrates in such confined geometries. The deviations from the experimental results are ascribed to the idealized contact boundary conditions assumed in the model.     

Partial Sequential Tests for Generalized Behrens-Fisher Problem

Abstract

In this article we study the problem of finding a locally most powerful sequentially planned test in a one-sided sequentially planned testing problem for stochastic processes of the exponential class with continuous time parameter, thereby applying the theory of optimal sampling in continuous time (cf. Roters, 1995b Roters , M. ( 1995b ). The Theory of Optimal Sampling in Continuous Time with Applications to Sequentially Planned Decision Procedures, Habilitationsschrift, Universität Trier.  [Google Scholar] 1997 Roters , M. ( 1997 ). The Theory of Optimal Sampling in Continuous Time, Forschungsbericht 97-25, FB IV Mathematik/Informatik, Universit ät Trier. [CSA]  [Google Scholar]). The theory presented here extends the discrete-time results of Berk (1975 Berk , R. H. ( 1975 ). Locally Most Powerful Sequential Tests , Annals of Statistics 3 : 373 – 381 . [CSA] [Crossref], [Web of Science ®] , [Google Scholar]) and Schmitz (1993 Schmitz , N. ( 1993 ). Optimal Sequentially Planned Decision Procedures , Lecture Notes in Statistics 79 , New York : Springer-Verlag .[Crossref] , [Google Scholar]).     

Asymptotic exponentiality of the first exit time of the Shiryaev–Roberts diffusion with constant positive drift

We consider the first exit time of a Shiryaev–Roberts diffusion with constant positive drift from the interval [0,A] with A>0 fixed. We show that the moment generating function (Laplace transform) of a suitably standardized version of the first exit time converges to that of the unit-mean exponential distribution as A→+∞. The proof is explicit in that the moment generating function of the first exit time is first expressed analytically and in a closed form and then the desired limit as A→+∞ is evaluated directly. The result is of importance in the area of quickest change-point detection, and its discrete-time counterpart has been previously established—although in a different manner—by Pollak and Tartakovsky (2009a Pollak, M. and Tartakovsky, A. G. (2009a). Asymptotic Exponentiality of the Distribution of First Exit Times for a Class of Markov Processes with Applications to Quickest Change Detection, Theory of Probability and Its Applications 53: 430–442.[Crossref], [Web of Science ®] , [Google Scholar]).     

EXPERIMENTAL MEASUREMENTS OF FOAMING TENDENCIES IN AQUEOUS GAS SWEETENING SOLUTIONS CONTAINING MDEA OVER A TEMPERATURE RANGE OF 297–358 K AND A PRESSURE RANGE OF 101–500 KPA

This work presents experimental measurements of foaming tendencies and break times for 50 wt% aqueous solutions of MDEA in contact with nitrogen, methane, and ethane gases from atmospheric pressure to 500 kPa and temperatures from 297 to 358 K. The effect of various contaminants including methanol, HEP (1,4- bis-2-hydroxyethyl piperazine), hexane, and carboxylic acids ranging from formic to dodecanoic acid was investigated. Only those systems containing carboxylic acids heavier than valeric acid exhibited foaming. Foaming tendency in systems containing carboxylic acids was worsened by the addition of methanol and HEP, although the difference was moderate. Foaming was shown to be worse at lower pressure and at higher temperature. Foaming in MDEA systems was shown to be substantially worse than that measured previously by McCarthy and Trebble (1996 McCarthy , J. and Trebble , M. A. ( 1996 ). An experimental investigation into the foaming tendency of diethanolamine gas sweetening solutions , Chemi. Eng. Commun. , 144 , 159 – 171 [CSA] [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) for aqueous systems of DEA.     

FLUIDIZED BED PRESSURE DROP IN PROMOTED GAS-SOLID BEDS WITH COAXIAL ROD,DISK, AND BLADE TYPE PROMOTERS

Bed pressure drop equations have been formulated for gas-solid fluidized beds with different types of promoters using Ergun's equation (Ergun, 1952 Ergun, S. 1952. Fluid flow through packed columns. Chem. Eng. Prog., 48(2): 89[Web of Science ®] , [Google Scholar]) and experimental data. Four rod promoters, seven disk promoters, along with one blade promoter were used in beds supported on five different distributors with open areas of 12.9%, 8.96%, 5.74%, 3.23%, and 1.43% of the column section. The predicted values of bed pressure drop using a modified (i.e., modified numerical constant) Burke-Plummer (Burke and Plummer, 1928 Burke, F. E. and Plummer, W. B. 1928. Gas flow through packed columns. Ind. Eng. Chem., 20: 1196[Crossref] , [Google Scholar]) equation were compared with the corresponding experimental as well as the respective values obtained with the help of Kumar et al. (submitted) and traditional gas-solid fluidized bed equations.     

Design,synthesis, and preliminary evaluation as antimicrobial activity of novel spiro-1, 3-thiazolidine C-acyclic nucleoside analogs

Synthesis of a new class of 1, 3-thiazolidine nucleoside analogs is described. Reaction of 2-amino-2-deoxy-D-glucopyranose hydrochloride 2 with carbon disulfide yielded 5-hydroxy-4-(D-arabino-1, 2, 3, 4-tetrahydroxybutyl)-thiazolidin-2-thione 3, which on acetylation yielded 5-acetoxy-4-(D-arabino-1, 2, 3, 4-tetraacetoxy-butyl)-thiazolidin-2-thione 4. The acetylated sugar 4 reacted with hydrazonoyl chlorides 1a–f, affording the 5-acetoxy-4-(D-arabino-1, 2, 3, 4-tetraacetoxybutyl)-spiro-1 Chen, H., Fan, Y-H., Natarajan, A., Guo, Y., Iyasere, J., Harbinski, F., Luus, L., Christ, W., Aktas, H. and Halperin, J. A. 2004. Bioorg. Med. Chem. Lett., 14: 5401–5405. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar] 3 Nasr, M. N., Gineinah, M. M. and El-Bendary, E. R. 2003. Arch. Pharm., 336: 560–566. [Crossref] , [Google Scholar]thiazolidine-2,2′ -1 Chen, H., Fan, Y-H., Natarajan, A., Guo, Y., Iyasere, J., Harbinski, F., Luus, L., Christ, W., Aktas, H. and Halperin, J. A. 2004. Bioorg. Med. Chem. Lett., 14: 5401–5405. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar] 3 Nasr, M. N., Gineinah, M. M. and El-Bendary, E. R. 2003. Arch. Pharm., 336: 560–566. [Crossref] , [Google Scholar] 4 Belleau, B., Brasilli, L., Chan, L. and Zacheri, B. 1993. Cameron J. Bioorg. Med. Chem. Lett., 3: 1723–1928. [Crossref], [Web of Science ®] , [Google Scholar]thiadiazole derivatives 8a–f. The antibacterial activity of the novel 1, 3-thiazolidine-2,2′ -spiro- 1 Chen, H., Fan, Y-H., Natarajan, A., Guo, Y., Iyasere, J., Harbinski, F., Luus, L., Christ, W., Aktas, H. and Halperin, J. A. 2004. Bioorg. Med. Chem. Lett., 14: 5401–5405. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar] 3 Nasr, M. N., Gineinah, M. M. and El-Bendary, E. R. 2003. Arch. Pharm., 336: 560–566. [Crossref] , [Google Scholar] 4 Belleau, B., Brasilli, L., Chan, L. and Zacheri, B. 1993. Cameron J. Bioorg. Med. Chem. Lett., 3: 1723–1928. [Crossref], [Web of Science ®] , [Google Scholar]thiadiazole nucleoside analogs is highlighted. All compounds with free NH group in the thiazolidine series 8a–f showed significant biological activity against all the standard strains.     

Experimental study and hydrodynamic modeling of countercurrent liquid–solid system with batch liquid

It is known that a transient effluent outlet concentration is obtained with a batch of adsorbent solids in any operation. A preferred steady state outlet concentration can be achieved with a continuous flow of solids. In the present work, information on pressure profiles, the total pressure drop across the column and holdup of solids are experimentally obtained for various solid flow rates, particle sizes and densities in a countercurrent liquid–solid system. These experimental results are compared with the prediction obtained using a phenomenological model containing continuity and momentum balance equations. The dominant drag force term was expressed in terms of various drag equations. The drag expression developed by Foscolo et al. (1983 Foscolo, P. U., Gibilaro, L. G., and Waldram, S. P. (1983). A unified model for particulate expansion of fluidized beds and flow in fixed porous media, Chem. Eng. Sci., 38(8), 1251–1260.[Crossref], [Web of Science ®] , [Google Scholar]) could predict the axial profiles of pressure drop and holdup, and the effect of various parameters on total pressure drop and solid holdup most satisfactorily.     

Development of an Aerosol Dynamics Model for Dry Deposition Process Using the Moment Method

An aerosol dynamics model for dry deposition process is developed based on the moment method. Since it is hard to fully apply the moment method to the widely used dry deposition velocity expressions based on the resistance theory, the dry deposition velocity expression by Raupach et al. (2001) Raupach, M. R., Briggs, P. R., Ahmad, N. and Edge, V. E. 2001. Endosulfan Tansport: II. Modeling airborne Dispersal and Deposition by Spray and Vapor. J. Environ. Qual., 30: 729–740. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar] is used. Detailed deposition mechanisms such as Brownian diffusion, gravitational settling, and impaction are considered in the expression. To verify the validity of the derived dynamic equation, aerosol dynamics for the dry deposition process is estimated with the expressions of Raupach et al. (2001) Raupach, M. R., Briggs, P. R., Ahmad, N. and Edge, V. E. 2001. Endosulfan Tansport: II. Modeling airborne Dispersal and Deposition by Spray and Vapor. J. Environ. Qual., 30: 729–740. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar], of Wesely (1989) Wesely, M. L. 1989. Parameterizations of Surface Resistance to Gaseous Dry Deposition in Regional-Scale, Numerical Models. Atmos. Environ., 23: 1293–1304. [Crossref], [Web of Science ®] , [Google Scholar] modified for particles (Seinfeld and Pandis 1998 Seinfeld, J. H. and Pandis, S. N. 1998. Atmospheric Chemistry and Physics, 958–996. New York, , USA: Wiley.  [Google Scholar]), in CMAQ, and with constant value used in RAINS-ASIA. Those expressions give different dynamics. Generally, the result for this study is between the result of modified Wesely's expression and CMAQ. When using the modified Wesely's expression with the number of sections being equal or smaller than 10, the resultant size distribution does not give the peak shape accurately.     

Author's response

This article contains the author's responses to the five discussion papers commenting on the results presented in Nikiforov (2016 Nikiforov, I. V. (2016). Sequential Detection/Isolation of Abrupt Changes, Sequential Analysis 35: 268–301.[Taylor &; Francis Online] , [Google Scholar]). The quickest detection/isolation of abrupt changes is the generalization of the quickest detection of abrupt changes to the case of M post-change hypotheses. It is necessary to detect the change in distribution as soon as possible and to indicate which hypothesis is true after a change occurs.     

Study on the Preparation and Characterization of Biodegradable Polylactide/SiO2–TiO2 Hybrids

In this study, the silicic acid produced from sodium metasilicate hydrate and titanium tetraisopropylate were chosen as the ceramic precursors for the modification of biodegradable polylactide (PLA) through an in situ sol-gel process and the melt blending method. In addition, acrylic acid grafted polylactide (PLA-g-AA) was studied as an alternative to PLA. Hybrids were characterized by Fourier transform infrared spectroscopy, ²⁹ Kumar , P. ; Badrinarayanan , M.S. ; Sastry , M. Nanocrystalline TiO₂ studied by optical, FTIR and X-ray photoelectron spectroscopy: correlation to presence of surface states . Thin Solid Films 2000 , 358 , 122 – 130 .[Crossref], [Web of Science ®] , [Google Scholar]Si solid-state nuclear magnetic resonance (NMR), thermogravimetry analysis (TGA), scanning electron microscope (SEM), and Instron mechanical tester. The result was that properties of the PLA-g-AA/SiO₂–TiO₂ hybrid were superior to those of the PLA/SiO₂–TiO₂ hybrid. This was because the carboxylic acid groups of acrylic acid acted as coordination sites for the silica-titania phase to allow the formation of stronger chemical bonds. The ²⁹ Kumar , P. ; Badrinarayanan , M.S. ; Sastry , M. Nanocrystalline TiO₂ studied by optical, FTIR and X-ray photoelectron spectroscopy: correlation to presence of surface states . Thin Solid Films 2000 , 358 , 122 – 130 .[Crossref], [Web of Science ®] , [Google Scholar]Si solid-state NMR showed that Si atoms coordinated around SiO₄ units were predominantly Q₃ and Q₄. The 10 wt.% SiO₂–TiO₂ content gave the maximum values of tensile strength and glass transition temperature in PLA/SiO₂–TiO₂ and PLA-g-AA/SiO₂–TiO₂ both because excess SiO₂–TiO₂ particles caused separation between the organic and inorganic phases.