On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials

Mathematics Subject Classification: 26A33

Mathematical Modeling for Studying Microbial Processes – Some Examples

Mathematical modeling may have different purposes in chemical and biochemical engineering sciences. One of them is to confirm or to reject kinetic models for certain processes, or to evaluate the importance of some transport phenomena on the net chemical or biochemical reaction rate. In the present paper different microbial processes are considered and modeled for evaluation of kinetic constants for batch and continuous processes accomplished by free and immobilized microbial cells. The practical examples are from the field of wastewater treatment and biosynthesis of products, like enzymes, lactic acid, gluconic acid, etc. By the aid of mathematical modeling the kinetics and the type of inhibition are specified for microbial wastewater denitrification and biodegradation of halogenated hydrocarbons. The importance of free and immobilized cells and their separate contribution to the overall microbial process is also evaluated for some fermentation processes: gluconic acid production, dichloroethane biodegradation, lactic acid fermentation and monochloroacetic acid biodegradation.

Client discourses on the process of seeking same-sex couple counselling

How same-sex couples manage the process of seeking help for their relationships is an under-researched area. Twelve semi-structured interviews were conducted with 16 people who had engaged in same-sex couple counselling, and were analysed using discourse analysis. The ways in which the couples positioned themselves as part of a 'minority group', or part of a generic group of couples struggling with relationship issues, impacted on how they discussed seeking help. We conclude that counsellors and psychotherapists need to be aware of the ways in which couples construct their relationships, and mindful of the tricky navigations around similarity to, and difference from, different-sex relationships. The impact of this on couples seeking therapeutic help is considered. © 2013 Taylor & Francis.

Business Modeling of the Application Architecture of the Bulgarian Folklore Artery

In an attempt to answer the need of wider accessibility and popularization of the treasury of Bulgarian folklore, a team from the Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences has planned to develop the Bulgarian folklore artery within the national project ―Knowledge Technologies for Creation of Digital Presentation and Significant Repositories of Folklore Heritage‖. This paper presents the process of business modeling of the application architecture of the Bulgarian folklore artery, which aids requirements analysis, application design and its software implementation. The folklore domain process model is made in the context of the target social applications—e-learning, virtual expositions of folklore artifacts, research, news, cultural/ethno-tourism, etc. The basic processes are analyzed and modeled and some inferences are made for the use cases and requirements specification of the Bulgarian folklore artery application. As a conclusion the application architecture of the Bulgarian folklore artery is presented.

Stability of the Inventory-Backorder Process in the (R; S) Inventory/Production Model

2000 Mathematics Subject Classification: 60G52, 90B30.

Group Comparisons on Cognitive Attributes Using the Least Squares Distance Model of Cognitive Diagnosis

2010 Mathematics Subject Classification: 62P15.

Revisiting goal-oriented models for self-aware systems-of-systems

Systems-of-systems (SoS) are systems resulted from the interaction among other independent constituent systems that collaborate to offer new functionalities towards accomplishing global missions. Each of these constituent systems accomplishes its individual missions and is able to contribute to the achievement of the global missions of the SoS, both being viewed as a set of associated goals. In the perspective of self-aware systems, SoS need to exhibit goal-awareness, i.e., They need to be aware of their own goals and of how their constituent systems contribute to their accomplishment. In this paper, we revisit goal-oriented concepts aiming at identifying and modeling goals at both SoS level and the constituent systems level. Moreover, we take advantage of such goal-oriented models to express the relationship among goals at these levels as well as to define how each constituent system can contribute to the accomplishment of global goals of an SoS. In addition, we shed light on important issues related to goal modeling in self-aware SoS to be addressed in future research.

Intenzitásalapú modellezés és a mértékcsere (Intensity-based modeling and thje change of measure)

A dolgozatban a hitelderivatívák intenzitásalapú modellezésének néhány kérdését vizsgáljuk meg. Megmutatjuk, hogy alkalmas mértékcserével nemcsak a duplán sztochasztikus folyamatok, hanem tetszőleges intenzitással rendelkező pontfolyamat esetén is kiszámolható az összetett kár- és csődfolyamat eloszlásának Laplace-transzformáltja. _____ The paper addresses questions concerning the use of intensity based modeling in the pricing of credit derivatives. As the specification of the distribution of the lossprocess is a non-trivial exercise, the well-know technique for this task utilizes the inversion of the Laplace-transform. A popular choice for the model is the class of doubly stochastic processes given that their Laplace-transforms can be determined easily. Unfortunately these processes lack several key features supported by the empirical observations, e.g. they cannot replicate the self-exciting nature of defaults. The aim of the paper is to show that by using an appropriate change of measure the Laplace-transform can be calculated not only for a doubly stochastic process, but for an arbitrary point process with intensity as well. To support the application of the technique, we investigate the e®ect of the change of measure on the stochastic nature of the underlying process.

Ionized cluster beam deposition: Modeling, cluster size measurement and applications

Clusters are aggregations of atoms or molecules, generally intermediate in size between individual atoms and aggregates that are large enough to be called bulk matter. Clusters can also be called nanoparticles, because their size is on the order of nanometers or tens of nanometers. A new field has begun to take shape called nanostructured materials which takes advantage of these atom clusters. The ultra-small size of building blocks leads to dramatically different properties and it is anticipated that such atomically engineered materials will be able to be tailored to perform as no previous material could.^ The idea of ionized cluster beam (ICB) thin film deposition technique was first proposed by Takagi in 1972. It was based upon using a supersonic jet source to produce, ionize and accelerate beams of atomic clusters onto substrates in a vacuum environment. Conditions for formation of cluster beams suitable for thin film deposition have only recently been established following twenty years of effort. Zinc clusters over 1,000 atoms in average size have been synthesized both in our lab and that of Gspann. More recently, other methods of synthesizing clusters and nanoparticles, using different types of cluster sources, have come under development.^ In this work, we studied different aspects of nanoparticle beams. The work includes refinement of a model of the cluster formation mechanism, development of a new real-time, in situ cluster size measurement method, and study of the use of ICB in the fabrication of semiconductor devices.^ The formation process of the vaporized-metal cluster beam was simulated and investigated using classical nucleation theory and one dimensional gas flow equations. Zinc cluster sizes predicted at the nozzle exit are in good quantitative agreement with experimental results in our laboratory.^ A novel in situ real-time mass, energy and velocity measurement apparatus has been designed, built and tested. This small size time-of-flight mass spectrometer is suitable to be used in our cluster deposition systems and does not suffer from problems related to other methods of cluster size measurement like: requirement for specialized ionizing lasers, inductive electrical or electromagnetic coupling, dependency on the assumption of homogeneous nucleation, limits on the size measurement and non real-time capability. Measured ion energies using the electrostatic energy analyzer are in good accordance with values obtained from computer simulation. The velocity (v) is measured by pulsing the cluster beam and measuring the time of delay between the pulse and analyzer output current. The mass of a particle is calculated from m = (2E/v$\sp2).$ The error in the measured value of background gas mass is on the order of 28% of the mass of one N$\sb2$ molecule which is negligible for the measurement of large size clusters. This resolution in cluster size measurement is very acceptable for our purposes.^ Selective area deposition onto conducting patterns overlying insulating substrates was demonstrated using intense, fully-ionized cluster beams. Parameters influencing the selectivity are ion energy, repelling voltage, the ratio of the conductor to insulator dimension, and substrate thickness. ^

Capacity-based cost modeling for light rail and bus rapid transit systems

Choosing between Light Rail Transit (LRT) and Bus Rapid Transit (BRT) systems is often controversial and not an easy task for transportation planners who are contemplating the upgrade of their public transportation services. These two transit systems provide comparable services for medium-sized cities from the suburban neighborhood to the Central Business District (CBD) and utilize similar right-of-way (ROW) categories. The research is aimed at developing a method to assist transportation planners and decision makers in determining the most feasible system between LRT and BRT. ^ Cost estimation is a major factor when evaluating a transit system. Typically, LRT is more expensive to build and implement than BRT, but has significantly lower Operating and Maintenance (OM) costs than BRT. This dissertation examines the factors impacting capacity and costs, and develops cost models, which are a capacity-based cost estimate for the LRT and BRT systems. Various ROW categories and alignment configurations of the systems are also considered in the developed cost models. Kikuchi's fleet size model (1985) and cost allocation method are used to develop the cost models to estimate the capacity and costs. ^ The comparison between LRT and BRT are complicated due to many possible transportation planning and operation scenarios. In the end, a user-friendly computer interface integrated with the established capacity-based cost models, the LRT and BRT Cost Estimator (LBCostor), was developed by using Microsoft Visual Basic language to facilitate the process and will guide the users throughout the comparison operations. The cost models and the LBCostor can be used to analyze transit volumes, alignments, ROW configurations, number of stops and stations, headway, size of vehicle, and traffic signal timing at the intersections. The planners can make the necessary changes and adjustments depending on their operating practices. ^

Spatial-temporal mining of archived automatic vehicle location (AVL) data for transit service planning applications

An Automatic Vehicle Location (AVL) system is a computer-based vehicle tracking system that is capable of determining a vehicle's location in real time. As a major technology of the Advanced Public Transportation System (APTS), AVL systems have been widely deployed by transit agencies for purposes such as real-time operation monitoring, computer-aided dispatching, and arrival time prediction. AVL systems make a large amount of transit performance data available that are valuable for transit performance management and planning purposes. However, the difficulties of extracting useful information from the huge spatial-temporal database have hindered off-line applications of the AVL data. ^ In this study, a data mining process, including data integration, cluster analysis, and multiple regression, is proposed. The AVL-generated data are first integrated into a Geographic Information System (GIS) platform. The model-based cluster method is employed to investigate the spatial and temporal patterns of transit travel speeds, which may be easily translated into travel time. The transit speed variations along the route segments are identified. Transit service periods such as morning peak, mid-day, afternoon peak, and evening periods are determined based on analyses of transit travel speed variations for different times of day. The seasonal patterns of transit performance are investigated by using the analysis of variance (ANOVA). Travel speed models based on the clustered time-of-day intervals are developed using important factors identified as having significant effects on speed for different time-of-day periods. ^ It has been found that transit performance varied from different seasons and different time-of-day periods. The geographic location of a transit route segment also plays a role in the variation of the transit performance. The results of this research indicate that advanced data mining techniques have good potential in providing automated techniques of assisting transit agencies in service planning, scheduling, and operations control. ^

An investigation of location effect on trip production using artificial neural networks

As traffic congestion exuberates and new roadway construction is severely constrained because of limited availability of land, high cost of land acquisition, and communities' opposition to the building of major roads, new solutions have to be sought to either make roadway use more efficient or reduce travel demand. There is a general agreement that travel demand is affected by land use patterns. However, traditional aggregate four-step models, which are the prevailing modeling approach presently, assume that traffic condition will not affect people's decision on whether to make a trip or not when trip generation is estimated. Existing survey data indicate, however, that differences exist in trip rates for different geographic areas. The reasons for such differences have not been carefully studied, and the success of quantifying the influence of land use on travel demand beyond employment, households, and their characteristics has been limited to be useful to the traditional four-step models. There may be a number of reasons, such as that the representation of influence of land use on travel demand is aggregated and is not explicit and that land use variables such as density and mix and accessibility as measured by travel time and congestion have not been adequately considered. This research employs the artificial neural network technique to investigate the potential effects of land use and accessibility on trip productions. Sixty two variables that may potentially influence trip production are studied. These variables include demographic, socioeconomic, land use and accessibility variables. Different architectures of ANN models are tested. Sensitivity analysis of the models shows that land use does have an effect on trip production, so does traffic condition. The ANN models are compared with linear regression models and cross-classification models using the same data. The results show that ANN models are better than the linear regression models and cross-classification models in terms of RMSE. Future work may focus on finding a representation of traffic condition with existing network data and population data which might be available when the variables are needed to in prediction.

Business process quantitative analysis and optimization for service industries

The total time a customer spends in the business process system, called the customer cycle-time, is a major contributor to overall customer satisfaction. Business process analysts and designers are frequently asked to design process solutions with optimal performance. Simulation models have been very popular to quantitatively evaluate the business processes; however, simulation is time-consuming and it also requires extensive modeling experiences to develop simulation models. Moreover, simulation models neither provide recommendations nor yield optimal solutions for business process design. A queueing network model is a good analytical approach toward business process analysis and design, and can provide a useful abstraction of a business process. However, the existing queueing network models were developed based on telephone systems or applied to manufacturing processes in which machine servers dominate the system. In a business process, the servers are usually people. The characteristics of human servers should be taken into account by the queueing model, i.e. specialization and coordination. ^ The research described in this dissertation develops an open queueing network model to do a quick analysis of business processes. Additionally, optimization models are developed to provide optimal business process designs. The queueing network model extends and improves upon existing multi-class open-queueing network models (MOQN) so that the customer flow in the human-server oriented processes can be modeled. The optimization models help business process designers to find the optimal design of a business process with consideration of specialization and coordination. ^ The main findings of the research are, first, parallelization can reduce the cycle-time for those customer classes that require more than one parallel activity; however, the coordination time due to the parallelization overwhelms the savings from parallelization under the high utilization servers since the waiting time significantly increases, thus the cycle-time increases. Third, the level of industrial technology employed by a company and coordination time to mange the tasks have strongest impact on the business process design; as the level of industrial technology employed by the company is high; more division is required to improve the cycle-time; as the coordination time required is high; consolidation is required to improve the cycle-time. ^

A methodological framework for modeling pavement maintenance costs for projects with performance-based contracts

Performance-based maintenance contracts differ significantly from material and method-based contracts that have been traditionally used to maintain roads. Road agencies around the world have moved towards a performance-based contract approach because it offers several advantages like cost saving, better budgeting certainty, better customer satisfaction with better road services and conditions. Payments for the maintenance of road are explicitly linked to the contractor successfully meeting certain clearly defined minimum performance indicators in these contracts. Quantitative evaluation of the cost of performance-based contracts has several difficulties due to the complexity of the pavement deterioration process. Based on a probabilistic analysis of failures of achieving multiple performance criteria over the length of the contract period, an effort has been made to develop a model that is capable of estimating the cost of these performance-based contracts. One of the essential functions of such model is to predict performance of the pavement as accurately as possible. Prediction of future degradation of pavement is done using Markov Chain Process, which requires estimating transition probabilities from previous deterioration rate for similar pavements. Transition probabilities were derived using historical pavement condition rating data, both for predicting pavement deterioration when there is no maintenance, and for predicting pavement improvement when maintenance activities are performed. A methodological framework has been developed to estimate the cost of maintaining road based on multiple performance criteria such as crack, rut and, roughness. The application of the developed model has been demonstrated via a real case study of Miami Dade Expressways (MDX) using pavement condition rating data from Florida Department of Transportation (FDOT) for a typical performance-based asphalt pavement maintenance contract. Results indicated that the pavement performance model developed could predict the pavement deterioration quite accurately. Sensitivity analysis performed shows that the model is very responsive to even slight changes in pavement deterioration rate and performance constraints. It is expected that the use of this model will assist the highway agencies and contractors in arriving at a fair contract value for executing long term performance-based pavement maintenance works.

Integrated surface-ground water modeling in wetlands with improved methods to simulate vegetative resistance to flow

In topographically flat wetlands, where shallow water table and conductive soil may develop as a result of wet and dry seasons, the connection between surface water and groundwater is not only present, but perhaps the key factor dominating the magnitude and direction of water flux. Due to their complex characteristics, modeling waterflow through wetlands using more realistic process formulations (integrated surface-ground water and vegetative resistance) is an actual necessity. This dissertation focused on developing an integrated surface – subsurface hydrologic simulation numerical model by programming and testing the coupling of the USGS MODFLOW-2005 Groundwater Flow Process (GWF) package (USGS, 2005) with the 2D surface water routing model: FLO-2D (O’Brien et al., 1993). The coupling included the necessary procedures to numerically integrate and verify both models as a single computational software system that will heretofore be referred to as WHIMFLO-2D (Wetlands Hydrology Integrated Model). An improved physical formulation of flow resistance through vegetation in shallow waters based on the concept of drag force was also implemented for the simulations of floodplains, while the use of the classical methods (e.g., Manning, Chezy, Darcy-Weisbach) to calculate flow resistance has been maintained for the canals and deeper waters. A preliminary demonstration exercise WHIMFLO-2D in an existing field site was developed for the Loxahatchee Impoundment Landscape Assessment (LILA), an 80 acre area, located at the Arthur R. Marshall Loxahatchee National Wild Life Refuge in Boynton Beach, Florida. After applying a number of simplifying assumptions, results have illustrated the ability of the model to simulate the hydrology of a wetland. In this illustrative case, a comparison between measured and simulated stages level showed an average error of 0.31% with a maximum error of 2.8%. Comparison of measured and simulated groundwater head levels showed an average error of 0.18% with a maximum of 2.9%. The coupling of FLO-2D model with MODFLOW-2005 model and the incorporation of the dynamic effect of flow resistance due to vegetation performed in the new modeling tool WHIMFLO-2D is an important contribution to the field of numerical modeling of hydrologic flow in wetlands.