Progress in Applied Mathematics
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<p><a title="Authors" href="/index.php/pam/author" target="_blank">Authors</a> <a title="Reviewers" href="/index.php/pam/reviewer" target="_blank">Reviewers</a> <a title="Editors" href="/index.php/pam/sectionEditor" target="_blank">Editors</a><strong> <em><a title="New Submission" href="/index.php/pam/author/submit/1" target="_blank">New Submission</a></em></strong></p>Canadian Research & Development Center of Sciences and Culturesen-USProgress in Applied Mathematics1925-251X<p>The authors agree that:</p><ol><li>Authors of reports of original research should present an accurate account of the work performed as well as an objective discussion of its significance.</li><li>The authors should ensure that they have written entirely original works, and if the authors have used the work and/or words of others that this has been appropriately cited or quoted.</li><li>An author should not in general publish manuscripts describing essentially the same research in more than one journal or primary publication. Submitting the same manuscript to more than one journal concurrently constitutes unethical publishing behavior and is unacceptable.</li><li>Authorship should be limited to those who have made a significant contribution to the conception, design, execution, or interpretation of the reported study. All those who have made significant contributions should be listed as co-authors. Where there are others who have participated in certain substantive aspects of the research project, they should be acknowledged or listed as contributors.</li><li>When an author discovers a significant error or inaccuracy in his/her own published work, it is the author’s obligation to promptly notify the journal editor or publisher and cooperate with the editor to retract or correct the paper. If the editor or the publisher learns from a third party that a published work contains a significant error, it is the obligation of the author to promptly retract or correct the paper or provide evidence to the editor of the correctness of the original paper.</li><li>The author assigns, conveys, and otherwise transfers all rights, title, interest, and copyright ownership in this “Work” to our journal when the "Work" is accepted for publication. "Work” means the material submitted for publication plus any other related material submitted.</li><li>The assignment of rights to our journal includes but is not expressly limited to rights to edit, publish, reproduce, distribute copies, prepare derivative works, include in indexes or search databases in print, electronic, or other media, whether or not in use at the time of execution of this agreement, and claim copyright in said work throughout the world for the full duration of the copyright and any renewals or extensions thereof.</li><li>If the authors cannot obey the previous terms and cause legal problems, the authors will take the full responsibilities.</li></ol>A New Yakushevich Model of Topological Solitons
http://www.cscanada.net/index.php/pam/article/view/j.pam.1925252820120402.1520
<p>Thanks to DNA interesting structure and its key role in the formation of life, many studies have been carried out on its properties and applications that have heretofore brought about great advances in science and technology such as biomedicine, agriculture, artificial intelligence, and even telecommunication. Topological solitons can be simulated through DNA strands when they are detached and they can travel along these strands because of DNA extremely high length/width ratio. Here, we investigate the topological soliton propagation through DNA strands and dispersion relation by employing the Yakushevich method and modifying a potential term in strand interaction. This paper also makes a comparison between our model’s results and previously achieved results.</p>Seyedali VedadAlireza Heidari2012-10-312012-10-314Estimation of Heteroscedasticity Effects in a Classical Linear Regression Model of a Cross-Sectional Data
http://www.cscanada.net/index.php/pam/article/view/j.pam.1925252820120402.1677
This paper investigates the effects of heteroscedasticity in the Classical Linear Regression Model (CLRM) of auditor's remuneration. Several efforts of building a realistic econometric model for Auditor's Remuneration with regards to core banking activities have been undertaken. The work involves the use of White heteroscedasticity and Newey-West test techniques to examine the presence of heteroscedasticity, which shows that heteroscedasticity is an inherent feature of cross-sectional data. The superiority of Weighted Least Squares (WLS) on Ordinary Least Squares (OLS) was put to test in estimating the parameters of Auditor’s Remuneration model designed as:\\<br />\hspace*{10mm} $ AR_i = \theta_0 + \theta_1 T A_i + \theta_2 T E_i + \theta_3 C D_i + \theta_4 P B T_i + \varepsilon$\\<br />\hspace*{6mm}And it was established that OLS is not appropriate for estimation if heteroscedasticity is present in research data, and that the model fitted using WLS is the most appropriate that is deemed fit for proper review of auditor's remuneration in banking industry.D. A. AgunbiadeN. O. Adeboye2012-10-312012-10-314Non-Central Beta Type 3 Distribution
http://www.cscanada.net/index.php/pam/article/view/j.pam.1925252820120402.1675
Let $X$ and $Y$ be independent random variables, $X$ having a gamma distribution with shape parameter $a$ and $Y$ having a non-central<br />gamma distribution with shape and non-centrality parameters $b$ and<br />$\delta$, respectively. Define $ W ={X}/(X + 2 Y)$. Then, the random<br />variable $W$ has a non-central beta type 3 distribution, $W\sim<br />\textnormal{NCB3} (a,b;\delta)$. In this article we study several of its<br />properties. We also give a multivariate generalization of the<br />non-central beta type 3 distribution and derive its properties.Daya K. NagarYeison Arley Ramirez-Vanegas2012-10-312012-10-314Nonoscillation for System of Neutral Delay Dynamic Equation on Time Scales
http://www.cscanada.net/index.php/pam/article/view/j.pam.1925252820120402.1785
In this paper, by fixed theorem, some sufficient conditions for<br />nonoscillation of the system of neutral delay dynamic equations on time scales $\mathbb{T}$ are established. Our results as special case when $\mathbb{T}=R$ and $\mathbb{T}=N$, involve and improve some known results.G. H. LiuL. CH. Liu2012-10-312012-10-314An Introduction to the Generator of the Function Space
http://www.cscanada.net/index.php/pam/article/view/j.pam.1925252820120402.1981
The paper would introduce a concept of the generator of the function space. The generator is a more fundamental function than the basis, that the function space can be generated by the shifts and the linear combination of the generator. Various related properties of the generator are presented.Zongmin Wu2012-10-312012-10-314An Explicit Solution for Perpetual American Put Options in a Markov-Modulated Jump Diffusion Model
http://www.cscanada.net/index.php/pam/article/view/j.pam.1925252820120402.3025
This paper is concerned with the pricing of perpetual American put options when the dynamics of the risky underlying asset are driven by a jump diffusion with Markovian switching. By using the ``modified smooth pasting'' technique, we derive an explicit optimal stopping rule and the corresponding value function in a closed form. Finally, we present a numerical example to illustrate the application of the exact solution.Jinying TongZhenzhong Zhang2012-10-312012-10-314Statistical Analysis of MOBVE Distribution with TFR Model Under Step-Stress Accelerated Life Test
http://www.cscanada.net/index.php/pam/article/view/j.pam.1925252820120402.ZT301
We obtain the maximum likelihood estimates of parameters of MOBVE distribution with tampered failure rate model under step-stress accelerated life test. Thereafter we show the feasibility of this method by using the Monte-Carlo simulation.Ping ZhangXiaoling XuRonghua WangBeiqing Gu2012-10-312012-10-314A General Model on Intertemporal Measure Correlation
http://www.cscanada.net/index.php/pam/article/view/j.pam.1925252820120402.ZT937
In this paper, we proposed the error growth curve model for the integration of intertemporal measure errors correlation which usually exist in quality control process. This model can work well in the usual error distributions, such as normal, uniform, Rayleigh and some other error distributions. Simulation results show that the proposed estimators of the model parameters perform well especially in small sample situations.Fuxiang Liu2012-10-312012-10-314Extension of Some Polynomial Inequalities to the Polar Derivative
http://www.cscanada.net/index.php/pam/article/view/j.pam.1925252820120402.2135
Let $p(z)$ be a polynomial of degree $n$ and ${D_\propto }p(z) = np(z) + (\propto - z)p'(z)$ denote the polar derivative of the polynomial $p(z)$ with respect to the point $\propto$. In this paper we obtain an inequality for the polar derivative of a polynomial which is an improvement of the result recently proved by Mir, Baba and Pukhta (2011) [Thai Journal of Mathematics, 9(2), 291--298].M. S. Pukhta2012-10-312012-10-314Lacunary Statistical Convergence of Sequences of Sets
http://www.cscanada.net/index.php/pam/article/view/j.pam.1925252820120402.2264
Several notions of convergence for subsets of metric space appear in the literature. In this paper we define lacunary statistical convergence for sequences of sets and study in detail the relationship between other convergence concepts.UGUR ULUSUFATIH NURAY2012-10-312012-10-314Comparison of Optimality Criteria of Reduced Models for Response Surface Designs with Restricted Randomization
http://www.cscanada.net/index.php/pam/article/view/j.pam.1925252820120402.1517
In this work, $D-$, $G-$, and $A-$ efficiencies and the scaled average prediction variance, $IV$ criterion, are computed and compared for second-order split-plot central composite design. These design optimality criteria are evaluated across the set of reduced split-plot central composite design models for three design variables under various ratios of the variance components (or degrees of correlation $d$). It was observed that $D$, $A$, $G$, and $IV$ for these models strongly depend on the values of $d$; they are robust to changes in the interaction terms and vary dramatically with the number of, and changes in the squared terms.Angela U. ChukwuYisa Yakubu2012-10-312012-10-314Special Topic: ADVANCES IN STATISTICAL METHODS
http://www.cscanada.net/index.php/pam/article/view/2920
The special issue may focus on publishing recent developments of statistical methods for biological, medical and pharmaceutical research. Application of statistical methods has recently been dominated by biostatistical and bioinformatics research including clinical study, survival analysis, genetics and microarray analysis. Advanced statistical methods are being developed for analyzing high-dimensional microarray data as well as various observational data with outliers and measurement errors. The special issue would be a suitable venue for publishing such new developments in statistical research.CSCanada PAM2012-10-312012-10-314Robust Inference for Incomplete Binary Longitudinal Data
http://www.cscanada.net/index.php/pam/article/view/j.pam.1925252820120402.S0803
<p>Missing data occur in many longitudinal studies. When data are nonignorably missing, it is necessary to incorporate the missing data mechanism into the observed data likelihood function. A full likelihood analysis of nonignorable missing data is complicated algebraically, and often requires intensive computation, especially when there are many follow-up times. To avoid such computational difficulties, pseudo-likelihood methods have been proposed in the literature under minimal parametric assumptions. However, like the classical maximum likelihood estimators, these pseudo-likelihood estimators are also sensitive to potential outliers in the data. In this article, we propose and explore a robust method in the framework of a pseudo-likelihood function that is derived under the working assumption that the longitudinal responses are independent over time. The performance of the proposed robust method is investigated in simulations. The method is also illustrated in an example using actual data on CD4 counts from clinical trials of HIV-infected patients.</p>Sanjoy K. Sinha2012-10-312012-10-314Between-Subject and Within-Subject Model Mixtures for Classifying HIV Treatment Response
http://www.cscanada.net/index.php/pam/article/view/j.pam.1925252820120402.S0801
We present a method for using longitudinal data to classify individuals into clinically-relevant population subgroups. This is achieved by treating ``subgroup'' as a categorical covariate whose value is unknown for each individual, and predicting its value using mixtures of models that represent ``typical'' longitudinal data from each subgroup. Under a nonlinear mixed effects model framework, two types of model mixtures are presented, both of which have their advantages. Following illustrative simulations, longitudinal viral load data for HIV-positive patients is used to predict whether they are responding -- completely, partially or not at all -- to a new drug treatment.Cyprien MbogningKevin BleakleyMarc Lavielle2012-10-312012-10-314Constrained Statistical Inference: A Hybrid of Statistical Theory, Projective Geometry and Applied Optimization Techniques
http://www.cscanada.net/index.php/pam/article/view/j.pam.1925252820120402.S923
In many data applications, in addition to determining whether a given risk factor affects an outcome, researchers are often interested in whether the factor has an increasing or decreasing effect. For instance, a clinical trial may test which dose provides the minimum effect; a toxicology study may wish to determine the effect of increasing exposure to a harmful contaminant on human health; and an economist may wish to determine an individual's optimal preferences subject to a budget constraint. In such situations, constrained statistical inference is typically used for analysis, as estimation and hypothesis testing incorporate the parameter orderings, or restrictions, in the methodology. Such methods unite statistical theory with elements of projective geometry and optimization algorithms. In many different models, authors have demonstrated constrained techniques lead to more efficient estimates and improved power over unconstrained methods, albeit at the expense of additional computation. In this paper, we review significant advancements made in the field of constrained inference, ranging from early work on isotonic regression for several normal means to recent advances of constraints in Bayesian techniques and mixed models. To illustrate the methods, a new analysis of an environmental study on the health effects in a population of newborns is provided.Karelyn D. Davis2012-10-312012-10-314Joint Modeling of All-Cause Mortality and Longitudinally Measured Serum Albumin
http://www.cscanada.net/index.php/pam/article/view/j.pam.1925252820120402.S853
In clinical studies, longitudinal and survival data are often obtained simultaneously from the same individual. Linear mixed effects models are widely used for analyzing longitudinal continuous outcome data, while survival models are used for analyzing time-to-event data. It is a common practice to analyze these longitudinal and time-to-event data separately. However, when multivariate outcomes are obtained from a given individual, they can be correlated by nature, and one can attain considerable gain in efficiency by jointly analyzing the outcomes. An objective of this study is to analyze such multivariate data by jointly modeling longitudinally measured continuous outcomes and time-to-event data. In this joint modeling, we formulate a joint likelihood function for both outcomes and use the maximum likelihood method to estimate the parameters in the two sub-models (longitudinal and survival models). We demonstrate the merits of joint modeling by considering a joint analysis of longitudinally measured serum albumin (biomarker) and time-to-all-cause mortality data obtained from a hemodialysis (HEMO) study. This HEMO study was a large NIH (National Institute of Health) sponsored multicenter clinical trial contrasting the effects of dialysis dose and dialysis membrane permeability in end-stage renal disease patients receiving hemodialysis. We find that the parameter estimates obtained under joint modeling of HEMO data are more efficient than those obtained under separate modeling of the outcome variables.Abdus SattarSanjoy K. SinhaChristos ArgyropoulosMark Unruh2012-10-312012-10-314