Superconvergent interpolants for Gaussian collocation solutions of mixed order BVODE systems

<abstract><p>The high quality COLSYS/COLNEW collocation software package is widely used for the numerical solution of boundary value ODEs (BVODEs), often through interfaces to computing environments such as Scilab, R, and Python. The continuous collocation solution returned by the code is much more accurate at a set of mesh points that partition the problem domain than it is elsewhere; the mesh point values are said to be superconvergent. In order to improve the accuracy of the continuous solution approximation at non-mesh points, when the BVODE is expressed in first order system form, an approach based on continuous Runge-Kutta (CRK) methods has been used to obtain a superconvergent interpolant (SCI) across the problem domain. Based on this approach, recent work has seen the development of a new, more efficient version of COLSYS/COLNEW that returns an error controlled SCI.</p> <p>However, most systems of BVODEs include higher derivatives and a feature of COLSYS/COLNEW is that it can directly treat such mixed order BVODE systems, resulting in improved efficiency, continuity of the approximate solution, and user convenience. In this paper we generalize the approach mentioned above for first order systems to obtain SCIs for collocation solutions of mixed order BVODE systems. The main contribution of this paper is the derivation of generalizations of continuous Runge-Kutta-Nyström methods that form the basis for SCIs for this more general problem class. We provide numerical results that (ⅰ) show that the SCIs are much more accurate than the collocation solutions at non-mesh points, (ⅱ) verify the order of accuracy of these SCIs, and (ⅲ) show that the cost of utilizing the SCIs is a small fraction of the cost of computing the collocation solution upon which they are based.</p></abstract>

Quality assessment of the contact center while implementation the IP IVR system by using teletraffic theory

The paper considers the form of taking into account the specialization of information needs. An analysis of the work of modern call centers has been carried out. The authors noted the effectiveness of using IVR devices, operators, and consultants for differentiated customer service and the need to take feedback into account when forming the revenue stream of applications. The models make it possible to determine the leading indicators of the quality of service for applications arriving at the call center. Formal expressions for descriptions are derived from the input parameters' values and the model's stationary probability. The relationships between the characteristics of the call center that regulate the intensity of incoming and outgoing calls, call processing through 3CXPhone, corporate mail, and social networks were obtained using Global Statistic. The developed methodology for organizing information and reference systems makes it possible to consider modern trends in the development of call centers. The paper presents the results of research using the IP IVR system. The results of calculating service characteristics are given for two different types of calls with mixed order ω=(0.5; 0.7; 0.9). The presented results were obtained by using experimental data of the JSC Kazakhtelecom's call center. For the calculations, the authors used the formulas of the teletraffic theory for a mixed service system. It also assesses the extent of combined service model effects for the contact center's call quality. It is shown that the probability of lost calls depends on the incoming load. The obtained results show that the mixed order for incoming calls servicing affects the probability of service failure.

Impact of Public Capital Expenditure on Inflation Rate in Nigeria

This paper examines the impact of public capital expenditure on inflation rate in Nigeria. The data for the study were sourced from various issues of the Central Bank of Nigeria’s statistical bulletin. The data was subjected to unit root test using Augmented Dickey fuller (ADF) approach to ascertain the time series properties. Descriptive statistics was used to assess the socioeconomic characteristics of the variables. Due to the mixed order of integration witnessed in the unit root, ARDL- Autoregressive Distributed Lag approach was used for cointegration and regression analysis. The result found that Public capital expenditure is negatively and statistically significant (tcal = -2.903) in influencing Inflation Rate in Nigeria. This outcome is highly directional in the sense that prudent and productive spending will always subdue inflation in any economy; therefore, this study recommend that government should increase its investment in production sectors and encourage skilful and willing citizens to participate, since this would reduce the expenses being incurred on business as a result low currency value and raise the profitability of firms.

U-Shape by Quadratic Equation: A Best-fit for Modelling Hemodynamic Changes in the DCCS Task

General Linear Modelling (GLM) has been widely employed to estimate the hemodynamic changes evoked by cognitive processing, which are more likely to be nonlinear than linear. First, this study re-analyzed the fNIRS data (N = 38, Mage = 5.0 years, SD = 0.69 years, 17 girls) collected in the Mixed-Order Design Dimensional Change Card Sort (DCCS) task. The results indicated that the quadratic equation was better than GLM to model HbO changes in this task. Second, analysis of a new set of data indicated that the Habit-DisHabit design of DCCS was more effective in identifying the neural correlates of cognitive shifting than the Mixed-Order Design. Third, this study found that the Non-users were more attentive and engaged than the Heavy-users, with a slower but more steady increase of brain activation in BA8 and BA9.

Effects of Orthographic Consistency on Bilingual Reading: Human and Computer Simulation Data

English serves as today’s lingua franca, a role not eased by the inconsistency of its orthography. Indeed, monolingual readers of more consistent orthographies such as Italian or German learn to read more quickly than monolingual English readers. Here, we assessed whether long-lasting bilingualism would mitigate orthography-specific differences in reading speed and whether the order in which orthographies with a different regularity are learned matters. We studied high-proficiency Italian-English and English-Italian bilinguals, with at least 20 years of intensive daily exposure to the second language and its orthography and we simulated sequential learning of the two orthographies with the CDP++ connectionist model of reading. We found that group differences in reading speed were comparatively bigger with Italian stimuli than with English stimuli. Furthermore, only Italian bilinguals took advantage of a blocked presentation of Italian stimuli compared to when stimuli from both languages were presented in mixed order, suggesting a greater ability to keep language-specific orthographic representations segregated. These findings demonstrate orthographic constraints on bilingual reading, whereby the level of consistency of the first learned orthography affects later learning and performance on a second orthography. The computer simulations were consistent with these conclusions.

A Refinement-by-Superposition hp-Method for H(curl)- and H(div)-Conforming Discretizations

We present an application of refinement-by-superposition (RBS) <i>hp</i>-refinement in computational electromagnetics (CEM), which permits exponential rates of convergence. In contrast to dominant approaches to <i>hp</i>-refinement for continuous Galerkin methods, which rely on constrained-nodes, the multi-level strategy presented drastically reduces the implementation complexity. Through the RBS methodology, enforcement of continuity occurs by construction, enabling arbitrary levels of refinement with ease and without the practical (but not theoretical) limitations of constrained-node refinement. We outline the construction of the RBS <i>hp</i>-method for refinement with <i>H</i>(curl)- and <i>H</i>(div)-conforming finite cells. Numerical simulations for the 2-D finite element method (FEM) solution of the Maxwell eigenvalue problem demonstrate the effectiveness of RBS <i>hp</i>-refinement. An additional goal of this work, we aim to promote the use of mixed-order (low- and high-order) elements in practical CEM applications.

A Refinement-by-Superposition hp-Method for H(curl)- and H(div)-Conforming Discretizations

We present an application of refinement-by-superposition (RBS) <i>hp</i>-refinement in computational electromagnetics (CEM), which permits exponential rates of convergence. In contrast to dominant approaches to <i>hp</i>-refinement for continuous Galerkin methods, which rely on constrained-nodes, the multi-level strategy presented drastically reduces the implementation complexity. Through the RBS methodology, enforcement of continuity occurs by construction, enabling arbitrary levels of refinement with ease and without the practical (but not theoretical) limitations of constrained-node refinement. We outline the construction of the RBS <i>hp</i>-method for refinement with <i>H</i>(curl)- and <i>H</i>(div)-conforming finite cells. Numerical simulations for the 2-D finite element method (FEM) solution of the Maxwell eigenvalue problem demonstrate the effectiveness of RBS <i>hp</i>-refinement. An additional goal of this work, we aim to promote the use of mixed-order (low- and high-order) elements in practical CEM applications.