Search results for: Multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 853

Search results for: Multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration

553 A Model to Study the Effect of Excess Buffers and Na+ Ions on Ca2+ Diffusion in Neuron Cell

Authors: Vikas Tewari, Shivendra Tewari, K. R. Pardasani

Abstract:

Calcium is a vital second messenger used in signal transduction. Calcium controls secretion, cell movement, muscular contraction, cell differentiation, ciliary beating and so on. Two theories have been used to simplify the system of reaction-diffusion equations of calcium into a single equation. One is excess buffer approximation (EBA) which assumes that mobile buffer is present in excess and cannot be saturated. The other is rapid buffer approximation (RBA), which assumes that calcium binding to buffer is rapid compared to calcium diffusion rate. In the present work, attempt has been made to develop a model for calcium diffusion under excess buffer approximation in neuron cells. This model incorporates the effect of [Na+] influx on [Ca2+] diffusion,variable calcium and sodium sources, sodium-calcium exchange protein, Sarcolemmal Calcium ATPase pump, sodium and calcium channels. The proposed mathematical model leads to a system of partial differential equations which have been solved numerically using Forward Time Centered Space (FTCS) approach. The numerical results have been used to study the relationships among different types of parameters such as buffer concentration, association rate, calcium permeability.

Keywords: Excess buffer approximation, Na+ influx, sodium calcium exchange protein, sarcolemmal calcium atpase pump, forward time centred space.

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552 Evaluation of Total Cross Section of Photo-Ionization of Helium in Weak Field on Base of Trajectory Method

Authors: Alexander B. Bichkov, Valery V. Smirnov

Abstract:

Total cross section of helium atom photo-ionization by weak short pulse is calculated using the variant of trajectory method, developed in our earlier work. The method enables simple estimation of total ionization probability (or cross section) without integration of differential one.

Keywords: Evaluation of Photo-Ionization, Helium, Trajectory Method

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551 Ahiska Turks in Philadelphia: Keeping Cultural Identity and Religion in a Multicultural Environment

Authors: Kenan Cetinkaya, Semanur Kodan

Abstract:

Ahiska Turks in the Philadelphia area maintain a very complex, cultural heritage which they have carried with them for centuries from Georgia to Uzbekistan then Russia and lastly to the USA. While facing very severe conditions in the last half of the last century, their passion for their language, religion and tradition allowed them to keep their cultural identity. In the paper, the Ahiska Turks’ sorrowful story is reviewed and their struggle with keeping their identity in a multicultural environment of the USA is examined in the context of the Philadelphia area.

Keywords: Ahiska Turks, identity, integration, Philadelphia, Turkish

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550 Self Organizing Analysis Platform for Wear Particle

Authors: Qurban A. Memon, Mohammad S. Laghari

Abstract:

Integration of system process information obtained through an image processing system with an evolving knowledge database to improve the accuracy and predictability of wear particle analysis is the main focus of the paper. The objective is to automate intelligently the analysis process of wear particle using classification via self organizing maps. This is achieved using relationship measurements among corresponding attributes of various measurements for wear particle. Finally, visualization technique is proposed that helps the viewer in understanding and utilizing these relationships that enable accurate diagnostics.

Keywords: Neural Network, Relationship Measurement, Selforganizing Clusters, Wear Particle Analysis.

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549 A Comparative Analysis of Performance and QoS Issues in MANETs

Authors: Javed Parvez, Mushtaq Ahmad Peer

Abstract:

Mobile Ad hoc networks (MANETs) are collections of wireless mobile nodes dynamically reconfiguring and collectively forming a temporary network. These types of networks assume existence of no fixed infrastructure and are often useful in battle-field tactical operations or emergency search-and-rescue type of operations where fixed infrastructure is neither feasible nor practical. They also find use in ad hoc conferences, campus networks and commercial recreational applications carrying multimedia traffic. All of the above applications of MANETs require guaranteed levels of performance as experienced by the end-user. This paper focuses on key challenges in provisioning predetermined levels of such Quality of Service (QoS). It also identifies functional areas where QoS models are currently defined and used. Evolving functional areas where performance and QoS provisioning may be applied are also identified and some suggestions are provided for further research in this area. Although each of the above functional areas have been discussed separately in recent research studies, since these QoS functional areas are highly correlated and interdependent, a comprehensive and comparative analysis of these areas and their interrelationships is desired. In this paper we have attempted to provide such an overview.

Keywords: Bandwidth Reservation, Congestion, DynamicNetwork Topology, End-to-End Delay, Flexible QoS Model forMANET(FQMM), Hidden Terminal, Mobile AdhocNetwork(MANET), Packet Jitter, Queuing, Quality-of-Service(QoS), Relative Bandwidth Service Differentiation(RBSD), Resource ReSerVation Protocol (RSVP).

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548 Considering Assembly Operations and Product Structure for Manufacturing Cell Formation

Authors: M.B. Aryanezhad, J. Aliabadi

Abstract:

This paper considers the integration of assembly operations and product structure to Cellular Manufacturing System (CMS) design so that to correct the drawbacks of previous researches in the literature. For this purpose, a new mathematical model is developed which dedicates machining and assembly operations to manufacturing cells while the objective function is to minimize the intercellular movements resulting due to both of them. A linearization method is applied to achieve optimum solution through solving aforementioned nonlinear model by common programming language such as Lingo. Then, using different examples and comparing the results, the importance of integrating assembly considerations is demonstrated.

Keywords: Assembly operations and Product structure, CellFormation, Genetic Algorithm.

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547 Improved Plasmonic Demultiplexer Based on Tapered and Rectangular Slot MIM Waveguide

Authors: Aso Rahimzadegan, Seyyed Poorya Hosseini, Kamran Qaderi

Abstract:

In this paper, we have proposed two novel plasmonic demultiplexing structures based on metal-insulator-metal surfaces which, beside their compact size, have a very good transmission spectrum. The impact of the key internal parameters on the transmission spectrum is numerically analyzed by using the twodimensional (2D) finite difference time domain (FDTD) method. The proposed structures could be used to develop ultra-compact photonic wavelength demultiplexing devices for large-scale photonic integration.

Keywords: Photonic integrated devices, Plasmonics, Metalinsulator- metal (MIM) waveguide, Demultiplexers.

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546 The HDH Model for the Development of Creative Structural Thinking and Its Applications to Other Systems

Authors: Mosseri Avraham

Abstract:

Teaching structures and structural design in architectural studies is considered a difficult mission due to complex reasons and circumstances. This article proposes a new conceptual model (HDH) for teaching structures and structural design in architectural studies. Because of its systems-thinking orientation it is also relevant and applicable to other fields and systems. The HDH model was developed in order to encourage the integration of science and art, especially in relation to structures, in architectural studies.

Keywords: Structural Thinking, Conceptual Design, Teaching Structures, Systems Thinking.

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545 Modern Kazakhstan in Global World After Independence

Authors: Dmitri Men, Byong-soon Chun, Soon-ok Myong

Abstract:

The article deals with the problems of political and economic processes in Kazakhstan since independence in the context of globalization. It analyzes the geopolitical situation and selfpositioning processes in the world after the end of the "cold war". It examines the problems of internal economization of the Republic for 20 years of independence. The authors argue that the reforms proceeded in the economic sphere have brought ambiguous and tangible results. Despite the difficult economic and political conditions facing a world economical crisis the country has undergone fundamental and radical transformations in the whole socio-economic system

Keywords: Globalization, Kazakhstan, integration, economic processes, financial crisis, multi-vector.

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544 Framework for the Modeling of the Supply Chain Collaborative Planning Process

Authors: D. Pérez, M. M. E. Alemany

Abstract:

In this work, a framework to model the Supply Chain (SC) Collaborative Planning (CP) process is proposed. The main contributions of this framework concern 1) the presentation of the decision view, the most important one due to the characteristics of the process, jointly within the physical, organisation and information views, and 2) the simultaneous consideration of the spatial and temporal integration among the different supply chain decision centres. This framework provides the basis for a realistic and integrated perspective of the supply chain collaborative planning process and also the analytical modeling of each of its decisional activities.

Keywords: Collaborative Planning, Decision View, Distributed Decision-Making, Framework.

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543 The Stone in the Identity of the Landscape

Authors: Maria Diogo, Patrícia Diogo

Abstract:

The stone is a constituent part of the geological structure of the Territory, introducing himself as a subject that has always interconnected human and environment in the development of a discourse of meanings and symbols that reflect elements realized in different cultures and experiences. This action meant that the first settlements and their areas of influence gained importance in the field of humanization and spatial organization of the territory, not only for the appropriation that its inhabitants did, but mainly because the community regardless of their economic or social condition, used it as living space and cultural integration. These factors become decisive in the characterization of the landscape area in the northwest of Portugal, because the stone is a material that appears not only in the natural landscape, but is also a strong element in humanized landscape, becoming this relation the main characterization of the study area.

Keywords: Landscape, Men, Stone, Territory.

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542 An Automated Approach for Assembling Modular Fixtures Using SolidWorks

Authors: Uday Hameed Farhan, Majid Tolouei-Rad, Simona O'Brien

Abstract:

Modular fixtures (MFs) are very important tools in manufacturing processes in terms of reduction the cost and the production time. This paper introduces an automated approach for assembling MFs elements by employing SolidWorks as a powerful 3D CAD software. Visual Basic (VB) programming language was applied integrating with SolidWorks API (Application programming interface) functions. This integration allowed creating plug-in file and generating new menus in the SolidWorks environment. The menus allow the user to select, insert, and assemble MFs elements.

Keywords: Assembly automation, modular fixtures, SolidWorks, Visual Basic.

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541 Neurogenic Potential of Clitoria ternatea Aqueous Root Extract–A Basis for Enhancing Learning and Memory

Authors: Kiranmai S.Rai

Abstract:

The neurogenic potential of many herbal extracts used in Indian medicine is hitherto unknown. Extracts derived from Clitoria ternatea Linn have been used in Indian Ayurvedic system of medicine as an ingredient of “Medhya rasayana", consumed for improving memory and longevity in humans and also in treatment of various neurological disorders. Our earlier experimental studies with oral intubation of Clitoria ternatea aqueous root extract (CTR) had shown significant enhancement of learning and memory in postnatal and young adult Wistar rats. The present study was designed to elucidate the in vitro effects of 200ng/ml of CTR on proliferation, differentiation and growth of anterior subventricular zone neural stem cells (aSVZ NSC-s) derived from prenatal and postnatal rat pups. Results show significant increase in proliferation and growth of neurospheres and increase in the yield of differentiated neurons of aSVZ neural precursor cells (aSVZNPC-s) at 7 days in vitro when treated with 200ng/ml of CTR as compared to age matched control. Results indicate that CTR has growth promoting neurogenic effect on aSVZ neural stem cells and their survival similar to neurotrophic factors like Survivin, Neuregulin 1, FGF-2, BDNF possibly the basis for enhanced learning and memory.

Keywords: Anterior subventricular zone (aSVZ) neural stemcell, Clitoria ternatea, Learning and memory, Neurogenesis.

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540 Development Prospects of Education System in Modernization

Authors: Akbar Seraly, Kazbek Primbetov, Gulmira Abdiraiymova, Gulnapis Abdikerova

Abstract:

the article analyzes the development prospects of education system in Kazakhstan. Education is among key sources of culture and social mobility. Modern education must become civic which means availability of high quality education to all people irrespective of their racial, ethnic, religious, social, gender and any other differences. Socially focused nature of modernization of Kazakhstan-s society is predicated upon formation of a civic education model in the future. Kazakhstan-s education system undergoes intensive reforms first of all intended to achieve international education standards and integration into the global educational and information space.

Keywords: Education system, Kazakhstan , Modernization

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539 A Guide to the Implementation of Ambisonics Super Stereo

Authors: Alessio Mastrorillo, Giuseppe Silvi, Francesco Scagliola

Abstract:

This paper explores the decoding of Ambisonics material into 2-channel mixing formats, addressing challenges related to stereo speakers and headphones. We present the Universal HJ (UHJ) format as a solution, enabling the preservation of the entire horizontal plane and offering versatile spatial audio experiences. Our paper presents a UHJ format decoder, explaining its design, computational aspects, and empirical optimization. We discuss the advantages of UHJ decoding, potential applications, and its significance in music composition. Additionally, we highlight the integration of this decoder within the Envelop for Live (E4L) suite.

Keywords: Ambisonics, UHJ, quadrature filter, virtual reality, Gerzon, decoder, stereo, binaural, biquad.

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538 Experimental Study of Dynamic Characteristics of the Electromagnet Actuators with Linear Movement

Authors: Vultchan T. Gueorgiev, Racho M. Ivanov, Ivan S. Yatchev, Krastyo L. Hinov

Abstract:

An approach for experimental measurement of the dynamic characteristics of linear electromagnet actuators is presented. It uses accelerometer sensor to register the armature acceleration. The velocity and displacement of the moving parts can be obtained by integration of the acceleration results. The armature movement of permanent magnet linear actuator is acquired using this technique. The results are analyzed and the performance of the supposed approach is compared with the most commonly used experimental setup where the displacement of the armature vs. time is measured instead of its acceleration.

Keywords: Dynamic characteristics, dynamic simulation, linearactuators.

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537 Identification of Coauthors in Scientific Database

Authors: Thiago M. R Dias, Gray F. Moita

Abstract:

The analysis of scientific collaboration networks has contributed significantly to improving the understanding of how does the process of collaboration between researchers and also to understand how the evolution of scientific production of researchers or research groups occurs. However, the identification of collaborations in large scientific databases is not a trivial task given the high computational cost of the methods commonly used. This paper proposes a method for identifying collaboration in large data base of curriculum researchers. The proposed method has low computational cost with satisfactory results, proving to be an interesting alternative for the modeling and characterization of large scientific collaboration networks.

Keywords: Extraction and data integration, Information Retrieval, Scientific Collaboration.

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536 Concept for Planning Sustainable Factories

Authors: T. Mersmann, P. Nyhuis

Abstract:

In the current economic climate, for many businesses it is generally no longer sufficient to pursue exclusively economic interests. Instead, integrating ecological and social goals into the corporate targets is becoming ever more important. However, the holistic integration of these new goals is missing from current factory planning approaches. This article describes the conceptual framework for a planning methodology for sustainable factories. To this end, the description of the key areas for action is followed by a description of the principal components for the systematization of sustainability for factories and their stakeholders. Finally, a conceptual framework is presented which integrates the components formulated into an established factory planning procedure.

Keywords: Factory Planning, Stakeholder, Systematization, Sustainability.

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535 Air Handling Units Power Consumption Using Generalized Additive Model for Anomaly Detection: A Case Study in a Singapore Campus

Authors: Ju Peng Poh, Jun Yu Charles Lee, Jonathan Chew Hoe Khoo

Abstract:

The emergence of digital twin technology, a digital replica of physical world, has improved the real-time access to data from sensors about the performance of buildings. This digital transformation has opened up many opportunities to improve the management of the building by using the data collected to help monitor consumption patterns and energy leakages. One example is the integration of predictive models for anomaly detection. In this paper, we use the GAM (Generalised Additive Model) for the anomaly detection of Air Handling Units (AHU) power consumption pattern. There is ample research work on the use of GAM for the prediction of power consumption at the office building and nation-wide level. However, there is limited illustration of its anomaly detection capabilities, prescriptive analytics case study, and its integration with the latest development of digital twin technology. In this paper, we applied the general GAM modelling framework on the historical data of the AHU power consumption and cooling load of the building between Jan 2018 to Aug 2019 from an education campus in Singapore to train prediction models that, in turn, yield predicted values and ranges. The historical data are seamlessly extracted from the digital twin for modelling purposes. We enhanced the utility of the GAM model by using it to power a real-time anomaly detection system based on the forward predicted ranges. The magnitude of deviation from the upper and lower bounds of the uncertainty intervals is used to inform and identify anomalous data points, all based on historical data, without explicit intervention from domain experts. Notwithstanding, the domain expert fits in through an optional feedback loop through which iterative data cleansing is performed. After an anomalously high or low level of power consumption detected, a set of rule-based conditions are evaluated in real-time to help determine the next course of action for the facilities manager. The performance of GAM is then compared with other approaches to evaluate its effectiveness. Lastly, we discuss the successfully deployment of this approach for the detection of anomalous power consumption pattern and illustrated with real-world use cases.

Keywords: Anomaly detection, digital twin, Generalised Additive Model, Power Consumption Model.

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534 Benefits of Polish Accession to the European Union for Air Transport

Authors: D. Tloczynski

Abstract:

The main aim of this article is to present a balance of the decade of Polish air transport market in the European Union having taking into account selected entities of the aviation market. This article analyzes the functioning of the Polish air transport market after the Polish accession to the European Union. During the study two main areas were pointed: shipping activity and activity of the airports. The most important benefits of integration and the benefits of introducing of the open sky policy were indicated. The last part of the article presents the perspectives of development of air traffic.

Keywords: Air transport, airports, development air transport, European Union, Poland.

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533 4D Flight Trajectory Optimization Based on Pseudospectral Methods

Authors: Kouamana Bousson, Paulo Machado

Abstract:

The optimization and control problem for 4D trajectories is a subject rarely addressed in literature. In the 4D navigation problem we define waypoints, for each mission, where the arrival time is specified in each of them. One way to design trajectories for achieving this kind of mission is to use the trajectory optimization concepts. To solve a trajectory optimization problem we can use the indirect or direct methods. The indirect methods are based on maximum principle of Pontryagin, on the other hand, in the direct methods it is necessary to transform into a nonlinear programming problem. We propose an approach based on direct methods with a pseudospectral integration scheme built on Chebyshev polynomials.

Keywords: Pseudospectral Methods, Trajectory Optimization, 4DTrajectories

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532 Building Relationship Network for Machine Analysis from Wear Debris Measurements

Authors: Qurban A Memon, Mohammad S. Laghari

Abstract:

Integration of system process information obtained through an image processing system with an evolving knowledge database to improve the accuracy and predictability of wear debris analysis is the main focus of the paper. The objective is to automate intelligently the analysis process of wear particle using classification via self-organizing maps. This is achieved using relationship measurements among corresponding attributes of various measurements for wear debris. Finally, visualization technique is proposed that helps the viewer in understanding and utilizing these relationships that enable accurate diagnostics.

Keywords: Relationship Network, Relationship Measurement, Self-organizing Clusters, Wear Debris Analysis, Kohonen Network

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531 On the Combination of Patient-Generated Data with Data from a Secure Clinical Network Environment – A Practical Example

Authors: Jeroen S. de Bruin, Karin Schindler, Christian Schuh

Abstract:

With increasingly more mobile health applications appearing due to the popularity of smartphones, the possibility arises that these data can be used to improve the medical diagnostic process, as well as the overall quality of healthcare, while at the same time lowering costs. However, as of yet there have been no reports of a successful combination of patient-generated data from smartphones with data from clinical routine. In this paper we describe how these two types of data can be combined in a secure way without modification to hospital information systems, and how they can together be used in a medical expert system for automatic nutritional classification and triage.

Keywords: Data integration, disease-related malnutrition, expert systems, mobile health.

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530 Bernstein-Galerkin Approach for Perturbed Constant-Coefficient Differential Equations, One-Dimensional Analysis

Authors: Diego Garijo

Abstract:

A numerical approach for solving constant-coefficient differential equations whose solutions exhibit boundary layer structure is built by inserting Bernstein Partition of Unity into Galerkin variational weak form. Due to the reproduction capability of Bernstein basis, such implementation shows excellent accuracy at boundaries and is able to capture sharp gradients of the field variable by p-refinement using regular distributions of equi-spaced evaluation points. The approximation is subjected to convergence experimentation and a procedure to assemble the discrete equations without a background integration mesh is proposed.

Keywords: Bernstein polynomials, Galerkin, differential equation, boundary layer.

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529 Distinction between Manifestations of Diabetic Retinopathy and Dust Artifacts Using Three-Dimensional HSV Color Space

Authors: Naoto Suzuki

Abstract:

Many ophthalmologists find it difficult to distinguish between small retinal hemorrhages and dust artifacts when using fundus photography for the diagnosis of diabetic retinopathy. Six patients with diabetic retinopathy underwent fundus photography, which revealed dust artifacts in the photographs of some patients. We constructed an experimental device similar to the optical system of the fundus camera and colored the fundi of the artificial eyes with khaki, sunset, rose and sunflower colors. Using the experimental device, we photographed dust artifacts using each artificial eyes. We used Scilab 5.4.0 and SIVP 0.5.3 softwares to convert the red, green, and blue (RGB) color space to the hue, saturation, and value (HSV) color space. We calculated the differences between the areas of manifestations and perimanifestations and the areas of dust artifacts and periartifacts using average HSVs. The V values in HSV for the manifestations were as follows: hemorrhages, 0.06 ± 0.03; hard exudates, −0.12 ± 0.06; and photocoagulation marks, 0.07 ± 0.02. For dust artifacts, visualized in the human and artificial eyes, the V values were as follows: human eye, 0.19 ± 0.03; khaki, 0.41 ± 0.02; sunset, 0.43 ± 0.04; rose, 0.47 ± 0.11; and sunflower, 0.59 ± 0.07. For the human and artificial eyes, we calculated two sensitivity values of dust artifacts compared to manifestation areas. V values of the HSV color space enabled the differentiation of small hemorrhages, hard exudates, and photocoagulation marks from dust artifacts.

Keywords: Diabetic retinopathy, HSV color space, small hemorrhages, hard exudates, photocoagulation marks.

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528 An Integrated Predictor for Cis-Regulatory Modules

Authors: Darby Tien-Hao Chang, Guan-Yu Shiu, You-Jie Sun

Abstract:

Various cis-regulatory module (CRM) predictors have been proposed in the last decade. Several well-established CRM predictors adopted different categories of prediction strategies, including window clustering, probabilistic modeling and phylogenetic footprinting. Appropriate integration of them has a potential to achieve high quality CRM prediction. This study analyzed four existing CRM predictors (ClusterBuster, MSCAN, CisModule and MultiModule) to seek a predictor combination that delivers a higher accuracy than individual CRM predictors. 465 CRMs across 140 Drosophila melanogaster genes from the RED fly database were used to evaluate the integrated CRM predictor proposed in this study. The results show that four predictor combinations achieved superior performance than the best individual CRM predictor.

Keywords: Cis-regulatory module, transcription factor binding site.

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527 Design and Control of an Integrated Plant for Simultaneous Production of γ-Butyrolactone and 2-Methyl Furan

Authors: Ahtesham Javaid, Costin S. Bildea

Abstract:

The design and plantwide control of an integrated plant where the endothermic 1,4-butanediol dehydrogenation and the exothermic furfural hydrogenation is simultaneously performed in a single reactor is studied. The reactions can be carried out in an adiabatic reactor using small hydrogen excess and with reduced parameter sensitivity. The plant is robust and flexible enough to allow different production rates of γ-butyrolactone and 2-methyl furan, keeping high product purities. Rigorous steady state and dynamic simulations performed in AspenPlus and AspenDynamics to support the conclusions.

Keywords: Dehydrogenation and hydrogenation, Reaction coupling, Design and control, Process integration.

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526 Regional Medical Imaging System

Authors: Michal Javornik, Otto Dostal, Karel Slavicek

Abstract:

The purpose of this article is to introduce an advanced system for the support of processing of medical image information, and the terminology related to this system, which can be an important element to a faster transition to a fully digitalized hospital. The core of the system is a set of DICOM compliant applications running over a dedicated computer network. The whole integrated system creates a collaborative platform supporting daily routines in the radiology community, developing communication channels, supporting the exchange of information and special consultations among various medical institutions as well as supporting medical training for practicing radiologists and medical students. It gives the users outside of hospitals the tools to work in almost the same conditions as in the radiology departments.

Keywords: DICOM, Integration, Medical Education, MedicalImaging

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525 Efficient Use of Energy through Incorporation of a Gas Turbine in Methanol Plant

Authors: M. Azadi, N. Tahouni, M. H. Panjeshahi

Abstract:

A techno-economic evaluation for efficient use of energy in a large scale industrial plant of methanol is carried out. This assessment is based on integration of a gas turbine with an existing plant of methanol in which the outlet gas products of exothermic reactor is expanded to power generation. Also, it is decided that methanol production rate is constant through addition of power generation system to the existing methanol plant. Having incorporated a gas turbine with the existing plant, the economic results showed total investment of MUSD 16.9, energy saving of 3.6 MUSD/yr with payback period of approximately 4.7 years.

Keywords: Energy saving, Gas turbine, Methanol, Power generation.

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524 On the Mathematical Structure and Algorithmic Implementation of Biochemical Network Models

Authors: Paola Lecca

Abstract:

Modeling and simulation of biochemical reactions is of great interest in the context of system biology. The central dogma of this re-emerging area states that it is system dynamics and organizing principles of complex biological phenomena that give rise to functioning and function of cells. Cell functions, such as growth, division, differentiation and apoptosis are temporal processes, that can be understood if they are treated as dynamic systems. System biology focuses on an understanding of functional activity from a system-wide perspective and, consequently, it is defined by two hey questions: (i) how do the components within a cell interact, so as to bring about its structure and functioning? (ii) How do cells interact, so as to develop and maintain higher levels of organization and functions? In recent years, wet-lab biologists embraced mathematical modeling and simulation as two essential means toward answering the above questions. The credo of dynamics system theory is that the behavior of a biological system is given by the temporal evolution of its state. Our understanding of the time behavior of a biological system can be measured by the extent to which a simulation mimics the real behavior of that system. Deviations of a simulation indicate either limitations or errors in our knowledge. The aim of this paper is to summarize and review the main conceptual frameworks in which models of biochemical networks can be developed. In particular, we review the stochastic molecular modelling approaches, by reporting the principal conceptualizations suggested by A. A. Markov, P. Langevin, A. Fokker, M. Planck, D. T. Gillespie, N. G. van Kampfen, and recently by D. Wilkinson, O. Wolkenhauer, P. S. Jöberg and by the author.

Keywords: Mathematical structure, algorithmic implementation, biochemical network models.

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