Mathematical Modeling

A new kinetic model for the fluid catalytic cracking (FCC) riser is developed. An elementary reaction scheme, for the FCC, based on cracking of a large number of lumps in the form of narrow boiling pseudocomponents is proposed. The kinetic parameters are estimated using a semi-empirical approach based on normal probability distribution. The correlation proposed for the kinetic parameters' estimation contains four parameters that depend on the feed characteristics, catalyst activity, and coke forming tendency of the feed. This approach eliminates the need of determining a large number of rate constants required for conventional lumped models. The model seems to be more versatile than existing models and opens up a new dimension for making generic models suitable for the analysis and control studies of FCC units. The model also incorporates catalyst deactivation and two-phase flow in the riser reactor. Predictions of the model compare well with the yield pattern of industrial scale plant data reported in literature. ᭧

1] In the present contribution we focus our attention on the long-term behavior of meandering rivers, a very common pattern in nature. This class of dynamical systems is driven by the coexistence of various intrinsically nonlinear mechanisms which determine the possible occurrence of two different morphodynamic regimes: the subresonant and the superresonant regimes. Investigating the full range of morphodynamic conditions, we objectively compare the morphologic characteristics exhibited by synthetically generated and observed planimetric patterns. The analysis is carried out examining, through principal component analysis, a suitable set of morphological variables. We show that even in the presence of the strong filtering action exerted by cutoff processes, a closer, although not yet complete, similarity with natural meandering planforms can be achieved only by adopting a flow field model which accounts for the full range of morphodynamic regimes. We also introduce a new morphodynamic length scale, L m , associated with spatially oscillating disturbances. Once normalized with this length scale, the relevant morphologic features of the simulated long-term patterns (e.g., the probability density function of local curvature and the geometric characteristics of oxbow lakes) tend to collapse on two distinct behaviors, depending on the dominant morphologic regime.

This study examined the role of pregnancy-induced changes in wakefulness (or nonchemoreflex) and central chemoreflex drives to breathe, acid-base balance and female sex hormones in the hyperventilation of human pregnancy. Thirty-five healthy women were studied in the third trimester (TM 3 ; 36.3 ± 1.0 wks gestation; mean ± SD) and again 20.2 ± 7.8 wks postpartum (PP). An iso-oxic hyperoxic rebreathing procedure was used to evaluate wakefulness and central chemoreflex drives to breathe. At rest, arterialized venous blood was obtained for the estimation of arterial PCO 2 (PaCO 2 ) and [H + ]. Blood for the determination of plasma strong ion difference ([SID]), albumin ([Alb]), as well as serum progesterone ([P 4 ]) and 17-estradiol ([E 2 ]) concentrations was also obtained at rest. Wakefulness and central chemoreflex drives to breathe, [P 4 ] and [E 2 ], ventilation and V · CO 2 increased, whereas PaCO 2 and the central chemoreflex ventilatory recruitment threshold for PCO 2 (VRTCO 2 ) decreased from PP to TM 3 (all p<0.01). The reductions in PaCO 2 were not related to the increases in [P 4 ] and [E 2 ]. The alkalinizing effects of reductions in PaCO 2 and [Alb] were partly offset by the acidifying effects of a reduced [SID], such that arterial [H + ] was still reduced in TM 3 vs. PP (all p<0.001). A mathematical model of ventilatory control demonstrated that pregnancy-induced changes in wakefulness and central chemoreflex drives to breathe, acid-base balance, V · CO 2 and cerebral blood flow account for the reductions in PaCO 2 , [H + ] and VRTCO 2 . This is the first study to demonstrate that the hyperventilation and attendant hypocapnia/alkalosis of human pregnancy results from a complex interaction of pregnancy-induced changes in wakefulness and central chemoreflex drives to breathe, acid-base balance, metabolic rate and cerebral blood flow.

Hollow fiber membranes using Polyethersulfone (PES) were fabricated inhouse using phase inversion technique by modification with synthesized chargedsurface modifying macromolecules (cSMM). The cSMM comprise with end-group component of Hydroxybenzene sulfonate or Hydroxybenzene carboxylate. The electrical properties of the membranes were modeled by utilizing the combination of irreversible thermodynamic model, Steric-Hindrance Pore (SHP) model and Teorell-Meyer-Sievers (TMS) model. The negatively-charged of the modified hollow fiber membranes was calculated based on sodium chloride rejection performance. The analysis of the modeling results revealed that sulfonate induce negative 1.61 electrical properties compared to carboxylate that is negative 1.49 for the modified PES membranes.

Several components shows that the process of algebraic thinking on students in solving problems. One of these components is the process of using algebra as a tool for doing mathematical modelling. This study aims to reveal how the students' competency in making mathematical modelling for solving an algebraic problem. The descriptive qualitative study design was used to obtain an overview of the mathematical modelling competencies of nine students (15-16 years old) in Pekanbaru, Riau Province. Each participant received a test that contains an algebraic problem. The results of this study show that when students do mathematical modelling there are several errors as follows: (1) failure in making suppositions for the problem and simplifying the given situation; (2) failure in recognizing quantities that influence the given situation, to identify the key variable; (3) failure in construct relation between variable; and (4) failure in solving question within mathematical modelling.

Considering the undeniable importance of petroleum prices in making decisions with regard to politics and economy, Artificial Neural Networks as one of the most reliable methods in solving nonlinear problems was used in the present research to forecast petroleum prices. As for the training of the neural network, three consecutive years of data were used. Identifying first the most effective factors on the petroleum price, efforts were made to forecast the next-day as well as the next-week prices. Using these factors for three consecutive past days as the neural network inputs, the petroleum price for the following day was predicted. The data for the same day past three consecutive weeks were then used as inputs to the network to predict the price for the same day of the following week. On the daily time basis, the trained network provided an acceptable response with about 80% accuracy. Using a weekly time basis then, it was found that the network was able to predict with a 60%, accuracy. Noting that a higher risk is associated with the weekly than the daily time interval, such a performance in forecasting the petroleum price one week ahead of time can be considered acceptable indeed. These predicted prices are presented, indicating a quite acceptable set of results when compared with the actual values.

The basis of decision-making in the enterprise consists in formally representing the system and its subsystems in models which adequately capture those features which are necessary to reach consistent decisions. This work represents the elements of the enterprise which are included in mathematical models (i.e. decisions, parameters, constraints, performance indicators) in an ontology which captures the knowledge of the mathematical domain. Thus, this ontology relates the mathematical elements of the models to their corresponding semantic representation within the enterprise ontology. As a result, the mathematical symbolic abstractions of a given enterprise element in different models are directly linked to their actual unique meaning, and the integration of decisions in the enterprise is transparent and improved. The purpose of this work is illustrated in a case study related to capacity planning in the supply chain and scheduling problems.

This paper analyses the current progression of the coronavirus pandemic, with the help of a mathematical model based on differential equations. The model has been inspired by the standard SIR (Susceptible-Infected-Recovered) model in epidemiology. The model takes the effect of co-morbidities and vaccination into account. The susceptible population is split into healthy and co-morbid sub-compartments. A series of graphs is presented for the visual depiction of the situation at hand in the Indian context. Finally, a survey (carried out through an online questionnaire) based analysis of the perception of vaccination in the masses in general, and the medical community in particular, has also been presented.

Owing to the wide utilization of heat exchangers in industrial processes, their cost minimization is an important target for both designers and users. Traditional design approaches are based on iterative procedures which gradually change the design and geometric parameters to satisfy a given heat duty and constraints. Although well proven, this kind of approach is time consuming and may not lead to cost effective design as no cost criteria are explicitly accounted for. The present study explores the use of nontraditional optimization technique: called simulated annealing (SA), for design optimization of shell and tube heat exchangers from economic point of view. The optimization procedure involves the selection of the major geometric parameters such as tube diameters, tube length, baffle spacing, number of tube passes, tube layout, type of head, baffle cut etc and minimization of total annual cost is considered as design target. The presented simulated annealing technique is simple ...

Six extended-release formulations of tizanidine hydrochloride were prepared by direct compression technique using hydroxypropylmethylcellulose (HPMC) and ethylcellulose (EC). The drug release from these tablets was evaluated by analyzing the samples at 227 nm. Both model dependent and independent mathematical approaches were applied to investigate the extended release pattern and mechanism of tizanidine hydrochloride. About 87.8, 74.4, 85.1, 74.8, 70.8, and 56.2 % drug was released from F 1 to F 6 , respectively, in 12 h. Drug release kinetics indicated that drug release was best explained by Higuchi equation. The values of 'n' from Korsmeyer-Peppas model (0.45 to 0.89) supported anomalous or non-Fickian diffusion in first five formulations, whereas last formulation (F 6 ) with 'n' greater than 0.89 presented case-II relaxation or super case transport-II. In model independent approach, the values of first five formulations lies between 50 and 100, because of insignificant differences in their drug release whereas F 6 behaved differently. A retarding effect was observed with both of polymers depending upon their quantity. In F 3 and F 5 less retarding effect was observed than F 2 and F 5 because HPMC is hydrophilic and EC is hydrophobic polymer. When EC quantity increased, a decrease in release profile of tizanidine hydrochloride was observed.

This paper proposes a model for the reoccupation of ants in a region of attraction, using evolutive partial differential diffusion-advection equations, in which the population dispersion and velocity in directions x and y are fuzzy parameters. The domain under study contains an attractive region, representing areas with high concentrations of palatable host plants with better nutritious qualities. The algorithm developed here uses information about the foraging behavior of a leaf-cutting ant colony of the Amazon region in northern Brazil. In the first model, we determined the numerical solution of the partial differential deterministic equation with constant dispersion and velocity, without incorporating uncertainties that may occur in this type of biological phenomenon. In the second model, we calculated the numerical solution of the partial differential equation, determining the dispersion at each iteration and for each triangular finite element. The dispersion was determined from a fuzzy rule-based system that depends on the number of individuals of the population and on the characteristics of the terrain. In this model, we also considered the velocity along the x and y directions as a fuzzy parameter that depends on the ant movement characteristics on the terrain in the y and x directions, respectively. The two models produced solutions consistent with ant behavior in response to the proximity of an attractive region, as stated in the papers by Shepherd (1982) [2] and Vasconcelos (1999) [3], but the fuzzy model incorporates uncertainties that do occur in the biological phenomenon under study.

Models for drugs exhibiting target-mediated drug disposition (TMDD) play an important role in the investigation of biological products (Mager and Jusko 2001). These models are often overparameterized and difficult to converge. A simpler quasi-equilibrium (QE) approximation of the general model has been suggested (Mager and Krzyzanski 2005), but even this simpler form can be overparameterized when, for example, drug target level is not available. This work (a) introduces quasisteady-state (QSS) and Michaelis-Menten (MM) approximations of the TMDD model, (b) derives the relationships between the parameters of the TMDD, QE, QSS and MM models, (c) investigates the parameter ranges where the simplified approximations are equivalent to the TMDD model, (d) proposes an algorithm for establishing identifiability of these models, and (e) tests this algorithm on simulated datasets. The proposed QSS approximation is more general than the QE approximation: it degenerates into the QE approximation when the internalization rate of the drug-target complex is much smaller than its dissociation rate. The proposed identifiability analysis algorithm may be applied to provide justification for use of simplified approximations, avoiding use of incorrect parameter estimates of over-parameterized TMDD models while simultaneously saving time and resources required for the pharmacokinetics analysis of drugs with TMDD. The utility of the derived approximations and of the identifiability algorithm was demonstrated on the examples of the simulated data sets. The simulation examples indicated that the QSS model may be preferable to the QE model L. Gibiansky (B)

The discovery of nearly periodic vegetation patterns in arid and semi-arid regions motivated numerous model studies in the past decade. Most studies have focused on vegetation pattern formation, and on the response of vegetation patterns to gradients of the limiting water resource. The reciprocal question, what resource modifications are induced by vegetation pattern formation, which is essential to the understanding of dryland landscapes, has hardly been addressed. This paper is a synthetic review of model studies that address this question and the consequent implications for inter-specific plant interactions and species diversity. It focuses both on patch and landscape scales, highlighting bottom-up processes, where plant interactions at the patch scale give rise to spatial patterns at the landscape scale, and top-down processes, where pattern transitions at the landscape scale affect inter-specific interactions at the patch scale.

Environmental concerns coupled with the depletion of fuel sources has led to research on ethanol, fuel cells, and even generating electricity from vibrations. Much of the research in these areas is stalling due to expensive or environmentally contaminating processes, however recent breakthroughs in materials and production has created a surge in research on waste heat energy harvesting devices. The thermoelectric generators (TEGs) used in waste heat energy harvesting are governed by the Thermoelectric, or Seebeck, effect, generating electricity from a temperature gradient. Some research to date has featured platforms such as heavy duty diesel trucks, model airplanes, and automobiles, attempting to either eliminate heavy batteries or the alternator. A motorcycle is another platform that possesses some very promising characteristics for waste heat energy harvesting, mainly because the exhaust pipes are exposed to significant amounts of air flow. A 1995 Kawasaki Ninja 250R was used for these trials. The module used in these experiments, the Melcor HT3-12-30, produced an average of 0.4694 W from an average temperature gradient of 48.73 • C. The mathematical model created from the Thermoelectric effect equation and the mean Seebeck coefficient displayed by the module produced an average error from the experimental data of 1.75%. Although the module proved insufficient to practically eliminate the alternator on a standard motorcycle, the temperature data gathered as well as the examination of a simple, yet accurate, model represent significant steps in the process of creating a TEG capable of doing so.

Diabetes mellitus is a disease characterized by a range of metabolic complications involving an individual&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s blood glucose levels, and its main regulator, insulin. These complications can vary largely from person to person depending on their current biophysical state. Biomedical research day-by-day makes strides to impact the lives of patients of a variety of diseases, including diabetes. One large stride that is being made is the generation of techniques to assist physicians to ``personalize medicine&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;. From available physiological data, biological understanding of the system, and dimensional analysis, a differential equation-based mathematical model was built in a sequential matter, to be able to elucidate clearly how each parameter correlates to the patient&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s current physiological state. We developed a simple mathematical model that accurately simulates the dynamics between glucose, insulin, and pancreatic $\beta$-cells throughout disease progression with constraints to maintain biological relevance. The current framework is clearly capable of tracking the patient&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s current progress through the disease, dependent on factors such as latent insulin resistance or an attrite $\beta$-cell population. Further interests would be to develop tools that allow the direct and feasible testing of how effective a given plan of treatment would be at returning the patient to a desirable biophysical state.

Single-unit recordings of vestibular afferents from the semicircular canals of squirrel monkeys have shown that the cupular time constant (T c) is between 5 and 6 sec. Such recordings obviously cannot be performed in humans, and the corresponding values have thus been inferred to be somewhat longer based on their size and on the cupulaendolymph system. The ocular motor response of the rotational vestibulo-ocular reflex (rVOR) is characterized by longer time constants, typically between 15 and 20 sec, due to the so-called velocity storage mechanism (VSM), which prolongs the time constant of the afferents through central processing. Recent studies have attempted to determine the time constant of the cupula by fitting the slow phase velocity (SPV) of the response to postrotational stimuli using a mathematical model of the rVOR processing. To this goal they considered the processing of head velocity due to the peripheral vestibular organs and to the VSM. The resulting estimates of T c are lower than expected, averaging about 4 sec. These modeling approaches, though, neglect both the processing of the final common pathway and the adaptation shown by the discharge of primary vestibular afferents. Here we argue that such an approach may be bound to underestimate the duration of the rVOR time constants.

A mathematical model is developed in algorithmic form for the steady-state simulation of gasketed plate heat exchangers with generalized configurations. The configuration is defined by the number of channels, number of passes at each side, fluid locations, feed connection locations and type of channel-flow. The main purposes of this model are to study the configuration influence on the exchanger performance and to further develop a method for configuration optimization. The main simulation results are: temperature profiles in all channels, thermal effectiveness, distribution of the overall heat transfer coefficient and pressure drops. Moreover, the assumption of constant overall heat transfer coefficient is analyzed.

The formation of vegetation patterns has been widely studied and discussed over the years and it has been related to two different mechanisms: depletion of water in the center of vegetation patches and production of toxicity by the decomposition of plant residues in soil. In this work we present a spatially explicit model that combines these two processes showing that negative plant-soil feedbacks can explain the development of different vegetation patterns also when water is not a limiting factor. This also demonstrates that the toxicity effects may change the stability properties of the vegetation patterns.

We discuss a model illustrating how the outcome of repeated endotoxin administration experiments can emerge as a natural consequence of the tightly regulated signaling pathways and also highlight the importance of a dual negative feedback regulation including PI3K/Akt and IRAK-M (IRAK3). We identify the relative time scales of the onset and the magnitude of the stimulus as key determinants of outcome in repeated administration experiments. The results of our simulations involve potentiated response, tolerance, and protective tolerance. Moreover, the knockout of negative regulators shows that IRAK-M is a necessary and sufficient factor for generation of endotoxin tolerance (ET). The effects of the knockout of IRAK-M gene or administration of PI3K inhibitor do yield predictions that have been verified experimentally. Finally, the pretreatment with PI3K inhibitor reveals the interaction between these two negative regulations.

The use of artificial neural networks (ANNs) for nonlinear modeling of symmetric and nonsymmetric peaks in capillary zone electrophoresis (CZE) and in optimization of CZE methods was studied. It was shown that ANNs can be used to estimate peak parameters and in combination with experimental design can be applied for efficient prediction of optimal separation conditions. The great advantage is that no use of the explicit model of the separation process and no knowledge of the physicochemical constants are needed.

Salmonella spp. has recently been involved in a number of food-borne outbreaks with a high impact on pharmaceuticals, food safety, and the economy. These outbreaks have increased the need to understand the behavior of this microorganism under conventional and new technologies applied to reduce its presence in food products. In the last twenty years, a number of emerging food processing technologies have been proposed as alternatives to thermal food processing. Studies have proven that these technologies ensure microbial inactivation while producing foods with better nutritional and sensory characteristics. Salmonella is one of the target microorganisms under study for these novel technologies showing encouraging results. Salmonella inactivation using conventional and novel technologies often does not follow first order kinetics, posing the need for models that adequately describe its survival curves and have predictive ability. This manuscript presents a summary of some of the emerging technologies used to inactivate Salmonella species in different food products and model systems, along with their inactivation patterns. It also reviews the models currently proposed to describe and estimate Salmonella inactivation under conventional thermal treatments and their applicability and limitations to characterize the survival curves obtained during exposure to novel technologies.

The present paper describes the development of a
monitoring, analysis and diagnosis system of power plant
equipments based on strain measurements. The objective
is to help companies increase availability and reduce
maintenance costs. The aim is the integrity evaluation of
a main steam and a hot reheat steam piping through
inspection, strain monitoring and computational
diagnosis.
The benefits are, among others, reduction in the
uncertainty of the remaining life prediction and reduction
of work, through process automation and integration and
real time monitoring (through the Internet) of the
operational condition of the equipment. Thus, greater
confidence and availability of the monitored generating
unit is sought as well as cost reduction as a consequence
of reduced frequency of unnecessary unit stops and
greater speed in decision making due to more precise
follow up of the operational condition of the targetequipment
and of its remaining life.

"Formal methods aim to apply mathematically-based techniques to the development of computer-based systems, especially at the specification level, but also down to the implementation level. This aids early detection and avoidance of errors through increased understanding. It is also beneficial for more rigorous testing coverage. This talk presents the use of formal methods on a real project. The Z notation has been used to specify a large-scale high integrity system to aid in air traffic control. The system has been implemented directly from the Z specification using SPARK Ada, an annotated subset of the Ada programming language that includes assertions and tool support for proofs. The Z specification has been used to direct the testing of the software through additional test design documents using tables and fragments of Z. In addition, Mathematica has been used as a test oracle for algorithmic aspects of the system. In summary, formal methods can be used successfully in all phases of the lifecycle for a large software project with suitably trained engineers, despite limited tool support.
"

The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model comprises two general methods for, namely a macroscopic transformation and mathematical transformation method. The problem of transformation is formally expressed and four special cases of transformation are considered. Simulations to confirm the feasibility of the proposed models and transformation methods are presented. Comparison between the two transformation methods is also reported.

Performance is a key feature of large-scale computing systems. However, the achieved performance when a certain program is executed is significantly lower than the maximal theoretical performance of the large-scale computing system. The model-based performance evaluation may be used to support the performance-oriented program development for large-scale computing systems. In this paper we present a hybrid approach for performance modeling and prediction of parallel and distributed computing systems, which combines mathematical modeling and discrete-event simulation. We use mathematical modeling to develop parameterized performance models for components of the system. Thereafter, we use discreteevent simulation to describe the structure of system and the interaction among its components. As a result, we obtain a highlevel performance model, which combines the evaluation speed of mathematical models with the structure awareness and fidelity of the simulation model. We evaluate empirically our approach with a real-world material science program that comprises more than 15,000 lines of code.

Cooling towers are widely used in many industrial and utility plants as a cooling medium, whose thermal performance is of vital importance. Despite the wide interest in cooling tower design, rating and its importance in energy conservation, there are few investigations concerning the integrated analysis of cooling systems. This work presents an approach for the systemic performance analysis of a cooling water system. The approach combines experimental design with mathematical modeling. An experimental investigation was carried out to characterize the mass transfer in the packing of the cooling tower as a function of the liquid and gas flow rates, whose results were within the range of the measurement accuracy. Then, an integrated model was developed that relies on the mass and heat transfer of the cooling tower, as well as on the hydraulic and thermal interactions with a heat exchanger network. The integrated model for the cooling water system was simulated and the temperature results agree with the experimental data of the real operation of the pilot plant. A case study illustrates the interaction in the system and the need for a systemic analysis of cooling water system. The proposed mathematical and experimental analysis should be useful for performance analysis of real-world cooling water systems.

a b s t r a c t Some industrial processes frequently change due to various factors, such as alterations of feedstocks and compositions, different manufacturing strategies, fluctuations in the external environment and various product specifications. Most multivariate statistical techniques are under the assumption that the process has one nominal operation region. The performance of it is not good when they are used to monitor the process with multiple operation regions. In this paper, we developed an effective approach for monitoring multi-mode continuous processes with the following improvements. 1). Offline mode identification algorithm is proposed to identify (i) stable modes, (ii) transitional modes between two stable modes, and (iii) noise. 2). According to the data distribution, proper multivariate statistical algorithm is selected automatically to realize fault detection for each mode. 3). When online monitoring, the right model is chosen based on Mode Transformation Probability (MTP), which makes full use of the empirical knowledge hidden in offline data. This method can enhance realtime performance of online mode identification for continuous process and timely monitoring can be further realized. The proposed method is illustrated by application in furnace temperature system of continuous annealing line. The effectiveness of mode identification and fault detection is demonstrated in the results.

This paper presents a deterministic model for monitoring the impact of drug resistance on the transmission dynamics of malaria in a human population. The model has a diseasefree equilibrium, which is shown to be globally-asymptotically stable whenever a certain threshold quantity, known as the effective reproduction number, is less than unity. For the case when treatment does not lead to resistance development, the model has a wild strain-only equilibrium whenever the reproduction number of the wild strain exceeds unity. It is shown, using linear and nonlinear Lyapunov functions, coupled with the LaSalle Invariance Principle, that this equilibrium is globally-asymptotically stable for a special case. The model has a resistant strain-only equilibrium, which is globally-asymptotically stable whenever its reproduction number is greater than unity and exceeds that of the wild strain. In this case, the two strains undergo competitive exclusion, where the strain with the higher reproduction number displaces the other. Further, for the case when treatment does not lead to resistance development, the model can have no coexistence equilibrium or a continuum of coexistence equilibria. When treatment leads to resistance development, the model can have a unique coexistence equilibrium or a resistant-only equilibrium. This coexistence equilibrium is shown to be locally-asymptotically stable, using a technique based on Krasnoselskii sub-linearity argument. Numerical simulations of the model show that for high treatment rates, the resistant strain can dominate, and drive out, the wild strain. Finally, when the two strains co-exist, the proportion of individuals with the resistant strain at steady-state decreases with increasing rate of resistance development.

The extraction-back extraction column of low concentration species by means of an organic closed loop flow, considered as liquid membrane, was modelled then simulated, using some simplifying assumptions. The main hypotheses are: the aqueous phase is perfectly mixed, the drops of the organic phase are lumped into a plug-flow inner cylinder co-axial with the aqueous phase, and the organic phases under the sieve and on the top of the column are perfectly mixed also. The dynamic model of the extraction-back extraction column is, then, applied to the recovery of the hydrocarboxylic acids. The mathematical model, reduced through orthogonal collocation to a system of ordinary differential equations, was solved using a self-adaptive (RK)-type method. Its validation was done based on batch experimental data; the optimal model parameters (the specific mass transfer coefficients for both extraction and back-extraction zones), ensuring the agreement with the experiment, were found by means of a modified genetic algorithm technique. Then, a sensitivity analysis was done, to grasp the behaviour of the system with respect to the main operating parameters-the organic flow in the closed loop, the partition coefficient and the buffer volume.

Generally, computer system is handled by the English language only. But the person who is unaware of the English language and structure of query language cannot handle the system. This paper proposed a new approach for accessing the database easily without knowing English. So, the database is accessed with the help of natural languages such as Hindi, Marathi etc. Natural language processing (NLP) is the study of mathematical and computational modeling of various aspects of language and the development of a wide range of systems. Natural Language Processing holds great promise for making computer interfaces that are easier to use for people, since people will be able to talk to the computer in their own language, rather than learn a specialized language of computer commands.

Mathematical modeling is an important step for developing many advanced technologies in various domains such as network security, data mining and etc…  This lecture introduces a process  that the speaker summarizes from his past practice of mathematical modeling and  algorithmic solutions in IT industry, as  an applied mathematician, algorithm specialist or software engineer , and even as an  entrepreneur.  A practical problem from DLP  system will be used as an example for creating math models and providing algorithmic solutions.

In teaching an introduction to the finite element method at the undergraduate level, a prudent mix of theory and applications is often sought. In many cases, analysts use the finite element method to perform parametric studies on potential designs to size parts, weed out less desirable design scenarios, and predict system behavior under load. In this book, we discuss common pitfalls encountered by many finite element analysts, in particular, students encountering the method for the first time. We present a variety of simple problems in axial, bending, torsion, and shear loading that combine the students' knowledge of theoretical mechanics, numerical methods, and approximations particular to the finite element method itself. We also present case studies in which analyses are coupled with experiments to emphasize validation, illustrate where interpretations of numerical results can be misleading, and what can be done to allay such tendencies. Challenges in presenting the necessary mix of theory and applications in a typical undergraduate course are discussed. We also discuss a list of tips and rules of thumb for applying the method in practice.

In this paper we have established a mathematical model on diabetes mellitus under the influence of ingested glucose where glucose and insulin both are affected by the externally ingested glucose. The ingested glucose is the external source of glucose that is coming from the source of food and assumed to follow the logistic growth. With the introduction of ingested glucose and its impact on the glucose as well as on insulin, a three variable mathematical model is established. The stability of the model is discussed under various equilibrium conditions. Numerical simulations are used to validate and describe the stability of the proposed model.

Coloring of fuzzy graphs has many real life applications in combinatorial optimization problems like traffic light system, exam scheduling, register allocation, etc. In this paper, the concept of fuzzy chromatic polynomial of fuzzy graph is introduced and defined based on í µí»¼-cuts of fuzzy graph. Two different types of fuzziness to fuzzy graph are considered in the paper. The first type was fuzzy graph with crisp vertex set and fuzzy edge set and the second type was fuzzy graph with fuzzy vertex set and fuzzy edge set. Depending on this, the fuzzy chromatic polynomials for some fuzzy graphs are discussed. Some interesting remarks on fuzzy chromatic polynomial of fuzzy graphs have been derived. Further, some results related to the concept are proved. Lastly, fuzzy chromatic polynomials for complete fuzzy graphs and fuzzy cycles are studied and some results are obtained.

Various melt spinning embodiments have been developed over the past 30 years and have been widely used, particularly at bench-scale for the production of metallic glasses. Much of the processing science has been developed 'as-needed' by the metallurgical community. Commercial scale-up has been limited, primarily because of the difficulty in maintaining good product quality. As yet, pilot-scale, and larger, single stage melt-spinning machines have not become industrially sig-I would like to acknowledge my funding sources. I received a Fulbright Scholarship to initially aid my doctoral studies in 2001 and a Graduate School Fellowship to support me in my first year. The bulk of my support has come from the National Science Foundation. Support in the laboratory comes from ALCOA, primarily arranged by Dave Stevenson and Greg Hildeman. The most remarkable part of my experience at Cornell has been the people I have met and friends I have made. These friends have been an important part of v my graduate school experience. They include Alejandro Becerra-Arteaga, Nikolas

Several real-time PCR (rtPCR) quantification techniques are currently used to determine the expression levels of individual genes from rtPCR data in the form of fluorescence intensities. In most of these quantification techniques, it is assumed that the efficiency of rtPCR is constant. Our analysis of rtPCR data shows, however, that even during the exponential phase of rtPCR, the efficiency of the reaction is not constant, but is instead a function of cycle number. In order to understand better the mechanisms belying this behavior, we have developed a mathematical model of the annealing and extension phases of the PCR process. Using the model, we can simulate the PCR process over a series of reaction cycles. The model thus allows us to predict the efficiency of rtPCR at any cycle number, given a set of initial conditions and parameter values, which can mostly be estimated from biophysical data. The model predicts a precipitous decrease in cycle efficiency when the product concentration reaches a sufficient level for template-template reannealing to compete with primer-template annealing; this behavior is consistent with available experimental data. The quantitative understanding of rtPCR provided by this model can allow us to develop more accurate methods to quantify gene expression levels from rtPCR data.

In the past this research efforts in optimizing earthwork processes focused mainly on minimizing transportation costs and mass haul distances, respectively. This kind of optimization problem, well known as earthwork allocation problem can be solved by applying linear programming techniques. As a result, the most cost-efficient cut-to-fill assignments will be found. In this article, starting from an optimal cut-to-fill assignment, we formulate a new corresponding combinatorial optimization problem. This earthwork section division problem arises when a large road project is divided into several linear construction sections and tendered to different normally non-cooperating construction companies. The optimization objective is to partition the optimized cut-to-fill-assignments in different earthwork sections with minimal earth movements between them. This problem is subjected to certain user-defined constraints, like number of sections, minimal and maximal section-length, etc. The proposed solution model will be integrated into an earthwork modeling and assessment system which allows performing a quantity take-off from a roadway model to provide the necessary input data for the optimization algorithms.

In this project, we have developed the basic codes of the Kalman filter by applying to a linear system and we have validated that by the Sequential Importance Sampling (SIS)algorithm of Particle filter using Monte Carlo simulations. The problem of degeneracy in the SIS Algorithm has also been explored in the project.

Abstract-this paper presents a study of the approaches taken to model and simulate power systems of an industrial plant. Even the best-designed electric systems occasionally experience short-circuits resulting in abnormally high currents. To predict the behavior of these short ...

Разработана математическая модель для расчета температуры полосы при горячей прокатке на стане 2000 ПАО «Северсталь», основанная на методе конечных разностей. Созданный компьютерный модуль, реализующий эту модель, включен в интегральную компьютерную модель горячей прокатки на стане 2000 (STAN 2000), с помощью которой проведены расчеты температуры в середине поверхности 164 полос 30 марок стали (с широким диапазоном изменения химического состава) после второй, пятой и 12-й клетей, а также перед смоткой в рулон. Полученные результаты хорошо согласуются с показаниями соответствующих пирометров. Средние абсолютные погрешности расчета отмеченных температур соответственно: 8,4; 10,6; 14,1 и 16,4 °C.

Based on the generalized van der Waals theory, a cubic equation of state (the van der Waals equation) was extended to describe the behavior of pure fluids and mixtures confined in porous solids. Each pore was assumed to be a cylinder with a continuous and homogeneous surface. Fluid molecules were assumed spherical, interacting with each other and with the wall of the pore through square-well potentials. Pairwise additivity was assumed for the attractive parts of all interaction potentials. The repulsive part of the equation of state for confined fluids was modeled based on literature data for the packing of hard spheres in cylinders. The effect of pore size on fluid properties was explicitly represented in the model, allowing its application to both confined and bulk fluids thus providing a consistent description of adsorption systems for all pore sizes. The resulting equation of state has two fitting parameters for each component of the fluid, which are related to the interaction between the fluid molecules and the pore walls. Calculations of pure fluid adsorption were carried out in order to analyze the sensitivity of the model to its fitting parameters and to pore size. It was found that the model is able to describe different types of adsorption isotherms. The model correlated experimental data of pure fluid adsorption quite well and was then used to predict the adsorption of several binary mixtures and one ternary mixture with no additional fitting, with good results. The methodological framework presented here can be extended to other widely used equations of state for modeling confined fluids.

Velocity measurements were carried out in the nip and translational regions of a co-rotating, self-wiping, twin-screw extruder using laser Doppler anemometry. Signi®cantly higher values of axial and tangential velocity components were measured in the nip region, indicating that the¯uid accelerated as it moved through the nip. The local volume¯ow rates in the nip and translational regions were calculated from the measured velocity ®eld. The volume¯ow rate in the nip was about four times higher than that in the translational region, indicating the positive displacement character of the nip region. The total volume¯ow rate calculated over the entire cross-section of the extruder was in agreement with the experimentally measured volume¯ow rate. Ó