Search results for: Hermitian positive definite solutions.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2741

Search results for: Hermitian positive definite solutions.

1961 Effect of Implementation of Nonlinear Sequence Transformations on Power Series Expansion for a Class of Non-Linear Abel Equations

Authors: Javad Abdalkhani

Abstract:

Convergence of power series solutions for a class of non-linear Abel type equations, including an equation that arises in nonlinear cooling of semi-infinite rods, is very slow inside their small radius of convergence. Beyond that the corresponding power series are wildly divergent. Implementation of nonlinear sequence transformation allow effortless evaluation of these power series on very large intervals..

Keywords: Nonlinear transformation, Abel Volterra Equations, Mathematica

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1960 Periodicity for a Semi–Ratio–Dependent Predator–Prey System with Delays on Time Scales

Authors: Kejun Zhuang

Abstract:

In this paper, the semi–ratio–dependent predator-prey system with nonmonotonic functional response on time scales is investigated. By using the coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained.

Keywords: Semi–ratio–dependent, predator–prey system, coincidence degree, time scales.

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1959 Integration Process of Industrial Design and Engineering Design

Authors: Kazuhide Sugiyama, Hiroshi Osada

Abstract:

Lately management strategy that put Industrial Design (ID) in its core is recognized more important, as technology and price alone cannot differentiate a product. The needs to shorten the time to develop a product also shorten the development period of ID, and it necessitates the ID process management. This research analyzes the status of integration process of ID and Engineering Design (ED) of office equipment that requires the collaboration of ID and ED to clarify the issues for the efficiency of the development and to propose solutions.

Keywords: Industrial Design (ID), Engineering Design (ED), Integration process, Office equipment

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1958 Factors Affecting Test Automation Stability and Their Solutions

Authors: Nagmani Lnu

Abstract:

Test automation is a vital requirement of any organization to release products faster to their customers. In most cases, an organization has an approach to developing automation but struggles to maintain it. It results in an increased number of flaky tests, reducing return on investments and stakeholders’ confidence. Challenges grow in multiple folds when automation is for User Interface (UI) behaviors. This paper describes the approaches taken to identify the root cause of automation instability in an extensive payments application and the best practices to address that using processes, tools, and technologies, resulting in a 75% reduction of effort.

Keywords: Automation stability, test stability, flaky test, test quality, test automation quality.

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1957 Estimating Reaction Rate Constants with Neural Networks

Authors: Benedek Kovacs, Janos Toth

Abstract:

Solutions are proposed for the central problem of estimating the reaction rate coefficients in homogeneous kinetics. The first is based upon the fact that the right hand side of a kinetic differential equation is linear in the rate constants, whereas the second one uses the technique of neural networks. This second one is discussed deeply and its advantages, disadvantages and conditions of applicability are analyzed in the mirror of the first one. Numerical analysis carried out on practical models using simulated data, and our programs written in Mathematica.

Keywords: Neural networks, parameter estimation, linear regression, kinetic models, reaction rate coefficients.

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1956 New Newton's Method with Third-order Convergence for Solving Nonlinear Equations

Authors: Osama Yusuf Ababneh

Abstract:

For the last years, the variants of the Newton-s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non-linear equations. These methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives. In this paper, we present a new Newton-s method based on contra harmonic mean with cubically convergent. Numerical examples show that the new method can compete with the classical Newton's method.

Keywords: Third-order convergence, non-linear equations, root finding, iterative method.

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1955 Crank-Nicolson Difference Scheme for the Generalized Rosenau-Burgers Equation

Authors: Kelong Zheng, Jinsong Hu,

Abstract:

In this paper, numerical solution for the generalized Rosenau-Burgers equation is considered and Crank-Nicolson finite difference scheme is proposed. Existence of the solutions for the difference scheme has been shown. Stability, convergence and priori error estimate of the scheme are proved. Numerical results demonstrate that the scheme is efficient and reliable.

Keywords: Generalized Rosenau-Burgers equation, difference scheme, stability, convergence.

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1954 Developing a Conjugate Heat Transfer Solver

Authors: Mansour A. Al Qubeissi

Abstract:

The current paper presents a numerical approach in solving the conjugate heat transfer problems. A heat conduction code is coupled internally with a computational fluid dynamics solver for developing a couple conjugate heat transfer solver. Methodology of treating non-matching meshes at interface has also been proposed. The validation results of 1D and 2D cases for the developed conjugate heat transfer code have shown close agreement with the solutions given by analysis.

Keywords: Computational Fluid Dynamics, Conjugate Heat transfer, Heat Conduction, Heat Transfer

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1953 A Contractor for the Symmetric Solution Set

Authors: Milan Hladik

Abstract:

The symmetric solution set Σ sym is the set of all solutions to the linear systems Ax = b, where A is symmetric and lies between some given bounds A and A, and b lies between b and b. We present a contractor for Σ sym, which is an iterative method that starts with some initial enclosure of Σ sym (by means of a cartesian product of intervals) and sequentially makes the enclosure tighter. Our contractor is based on polyhedral approximation and solving a series of linear programs. Even though it does not converge to the optimal bounds in general, it may significantly reduce the overestimation. The efficiency is discussed by a number of numerical experiments.

Keywords: Linear interval systems, solution set, interval matrix, symmetric matrix.

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1952 Isolation and Identification Fibrinolytic Protease Endophytic Fungi from Hibiscus Leaves in Shah Alam

Authors: Mohd Sidek Ahmad, Zainon Mohd Noor, Zaidah Zainal Ariffin

Abstract:

Fibrin degradation is an important part in prevention or treatment of intravascular thrombosis and cardiovascular diseases. Plasmin like fibrinolytic enzymes has given new hope to patient with cardiovascular diseases by treating fibrin aggregation related diseases with traditional plasminogen activator which have many side effects. Various researches involving wide range of sources for production of fibrinolytic proteases, from bacteria, fungi, insects and fermented foods. But few have looked into endophytic fungi as a potential source. Sixteen (16) endophytic fungi were isolated from Hibiscus sp. leaves from six different locations in Shah Alam, Selangor. Only two endophytic fungi, FH3 and S13 showed positive fibrinolytic protease activities. FH3 produced 5.78cm and S13 produced 4.48cm on Skim Milk Agar after 4 days of incubation at 27°C. Fibrinolytic activity was observed; 3.87cm and 1.82cm diameter clear zone on fibrin plate of FH3 and S13 respectively. 18srRNA was done for identification of the isolated fungi with positive fibrinolytic protease. S13 had the highest similarity (100%) to that of Penicillium citrinum strain TG2 and FH3 had the highest similarity (99%) to that of Fusarium sp. FW2PhC1, Fusarium sp. 13002, Fusarium sp. 08006, Fusarium equiseti strain Salicorn 8 and Fungal sp. FCASAn-2. Media composition variation showed the effects of carbon nitrogen on protein concentration, where the decrement of 50% of media composition caused drastic decrease in protease of FH3 from 1.081 to 0.056 and also S13 from 2.946 to 0.198.

Keywords: Isolation, identification, fibrinolytic protease, endophytic fungi, Hibiscus leaves.

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1951 Fuzzy Shortest Paths Approximation for Solving the Fuzzy Steiner Tree Problem in Graphs

Authors: Miloš Šeda

Abstract:

In this paper, we deal with the Steiner tree problem (STP) on a graph in which a fuzzy number, instead of a real number, is assigned to each edge. We propose a modification of the shortest paths approximation based on the fuzzy shortest paths (FSP) evaluations. Since a fuzzy min operation using the extension principle leads to nondominated solutions, we propose another approach to solving the FSP using Cheng's centroid point fuzzy ranking method.

Keywords: Steiner tree, single shortest path problem, fuzzyranking, binary heap, priority queue.

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1950 The Role of Internal Function of Organization for The Successful Implementation of Good Corporate Governance

Authors: Aries Susanty

Abstract:

The inability to implement the principles of good corporate governance (GCG) as demonstrated in the surveys is due to a number of constraints which can be classified into three; namely internal constraints, external constraints, and constraints coming from the structure of ownership. The issues in the internal constraints mentioned are related to the function of several elements of the company. As a business organization, corporation is unable to achieve its goal to successfully implement GCG principles since it is not support by its internal elements- functions. Two of several numbers of internal elements of a company are ethical work climate and leadership style of the top management. To prove the correlation between internal function of organization (in this case ethical work climate and transformational leadership) and the successful implementation of GCG principles, this study proposes two hypotheses to be empirically tested on thirty surveyed organizations; eleven of which are state-owned companies and nineteen are private companies. These thirty corporations are listed in the Jakarta Stock Exchange. All state-owned companies in the samples are those which have been privatized. The research showed that internal function of organization give support to the successful implementation of GCG principle. In this research we can prove that : (i) ethical work climate has positive significance of correlation with the successful implementation of social awareness principle (one of principles on GCG) and, (ii) only at the state-owned companies, transformational leadership have positive significance effect to forming the ethical work climate.

Keywords: Good Corporate Governance Principles, Ethical Work Climate, Transformational Leadership

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1949 A Survey of WhatsApp as a Tool for Instructor-Learner Dialogue, Learner-Content Dialogue, and Learner-Learner Dialogue

Authors: Ebrahim Panah, Muhammad Yasir Babar

Abstract:

Thanks to the development of online technology and social networks, people are able to communicate as well as learn. WhatsApp is a popular social network which is growingly gaining popularity. This app can be used for communication as well as education. It can be used for instructor-learner, learner-learner, and learner-content interactions; however, very little knowledge is available on these potentials of WhatsApp. The current study was undertaken to investigate university students’ perceptions of WhatsApp used as a tool for instructor-learner dialogue, learner-content dialogue, and learner-learner dialogue. The study adopted a survey approach and distributed the questionnaire developed by Google Forms to 54 (11 males and 43 females) university students. The obtained data were analyzed using SPSS version 20. The result of data analysis indicates that students have positive attitudes towards WhatsApp as a tool for Instructor-Learner Dialogue: it easy to reach the lecturer (4.07), the instructor gives me valuable feedback on my assignment (4.02), the instructor is supportive during course discussion and offers continuous support with the class (4.00). Learner-Content Dialogue: WhatsApp allows me to academically engage with lecturers anytime, anywhere (4.00), it helps to send graphics such as pictures or charts directly to the students (3.98), it also provides out of class, extra learning materials and homework (3.96), and Learner-Learner Dialogue: WhatsApp is a good tool for sharing knowledge with others (4.09), WhatsApp allows me to academically engage with peers anytime, anywhere (4.07), and we can interact with others through the use of group discussion (4.02). It was also found that there are significant positive correlations between students’ perceptions of Instructor-Learner Dialogue (ILD), Learner-Content Dialogue (LCD), Learner-Learner Dialogue (LLD) and WhatsApp Application in classroom. The findings of the study have implications for lectures, policy makers and curriculum developers.

Keywords: Instructor-learner dialogue, learners-contents dialogue, learner-learner dialogue, WhatsApp.

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1948 APPLE: Providing Absolute and Proportional Throughput Guarantees in Wireless LANs

Authors: Zhijie Ma, Qinglin Zhao, Hongning Dai, Huan Zhang

Abstract:

This paper proposes an APPLE scheme that aims at providing absolute and proportional throughput guarantees, and maximizing system throughput simultaneously for wireless LANs with homogeneous and heterogenous traffic. We formulate our objectives as an optimization problem, present its exact and approximate solutions, and prove the existence and uniqueness of the approximate solution. Simulations validate that APPLE scheme is accurate, and the approximate solution can well achieve the desired objectives already.

Keywords: IEEE 802.11e, throughput guarantee, priority.

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1947 Flexible Technologies of Granulated Complex Fertilizers

Authors: Andrey M. Norov, Denis A. Pagaleshkin, Pavel S. Fedotov, Viacheslav M. Kolpakov, Konstantin G. Gorbovskiy

Abstract:

The article focuses on the latest research and developments (R&D) aimed at the development of plants for production of complex phosphorus-containing fertilizers which are in line with the principles of the best available techniques (BAT). The advantages of the implemented technical solutions are given. The paper describes developed options of flexible technologies for schemes with DGD (drum granulator dryer) and for schemes with AG-DD (ammoniator-granulator and dryer drum).

Keywords: Ammoniator-granulator and dryer drum, drum granulator dryer, phosphorus-containing fertilizer technology, PK-, NPK-, PKS- and NPKS-fertilizers, wet phosphoric acid.

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1946 Comparative Analysis of Two Modeling Approaches for Optimizing Plate Heat Exchangers

Authors: Fábio A. S. Mota, Mauro A. S. S. Ravagnani, E. P. Carvalho

Abstract:

In the present paper the design of plate heat exchangers is formulated as an optimization problem considering two mathematical modelling. The number of plates is the objective function to be minimized, considering implicitly some parameters configuration. Screening is the optimization method used to solve the problem. Thermal and hydraulic constraints are verified, not viable solutions are discarded and the method searches for the convergence to the optimum, case it exists. A case study is presented to test the applicability of the developed algorithm. Results show coherency with the literature.

Keywords: Plate heat exchanger, optimization, modeling, simulation.

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1945 Surveillance for African Swine Fever and Classical Swine Fever in Benue State, Nigeria

Authors: A. Asambe, A. K. B. Sackey, L. B. Tekdek

Abstract:

A serosurveillance study was conducted to detect the presence of antibodies to African swine fever virus (ASFV) and Classical swine fever virus in pigs sampled from piggeries and Makurdi central slaughter slab in Benue State, Nigeria. 416 pigs from 74 piggeries across 12 LGAs and 44 pigs at the Makurdi central slaughter slab were sampled for serum. The sera collected were analysed using Indirect Enzyme Linked Immunosorbent Assay (ELISA) test kit to test for antibodies to ASFV, while competitive ELISA test kit was used to test for antibodies to CSFV. Of the 416 pigs from piggeries and 44 pigs sampled from the slaughter slab, seven (1.7%) and six (13.6%), respectively, tested positive to ASFV antibodies and was significantly associated (p < 0.0001). Out of the 12 LGAs sampled, Obi LGA had the highest ASFV antibody detection rate of (4.8%) and was significantly associated (p < 0.0001). None of the samples tested positive to CSFV antibodies. The study concluded that antibodies to CSFV were absent in the sampled pigs in piggeries and at the Makurdi central slaughter slab in Benue State, while antibodies to ASFV were present in both locations; hence, the need to keep an eye open for CSF too since both diseases may pose great risk in the study area. Further studies to characterise the ASFV circulating in Benue State and investigate the possible sources is recommended. Routine surveillance to provide a comprehensive and readily accessible data base to plan for the prevention of any fulminating outbreak is also recommended.

Keywords: African swine fever, classical swine fever, piggery, slaughter slab, surveillance.

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1944 Haar wavelet Method for Solving Initial and Boundary Value Problems of Bratu-type

Authors: S.G.Venkatesh, S.K.Ayyaswamy, G.Hariharan

Abstract:

In this paper, we present a framework to determine Haar solutions of Bratu-type equations that are widely applicable in fuel ignition of the combustion theory and heat transfer. The method is proposed by applying Haar series for the highest derivatives and integrate the series. Several examples are given to confirm the efficiency and the accuracy of the proposed algorithm. The results show that the proposed way is quite reasonable when compared to exact solution.

Keywords: Haar wavelet method, Bratu's problem, boundary value problems, initial value problems, adomain decomposition method.

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1943 Genetic-Based Planning with Recursive Subgoals

Authors: Han Yu, Dan C. Marinescu, Annie S. Wu, Howard Jay Siegel

Abstract:

In this paper, we introduce an effective strategy for subgoal division and ordering based upon recursive subgoals and combine this strategy with a genetic-based planning approach. This strategy can be applied to domains with conjunctive goals. The main idea is to recursively decompose a goal into a set of serializable subgoals and to specify a strict ordering among the subgoals. Empirical results show that the recursive subgoal strategy reduces the size of the search space and improves the quality of solutions to planning problems.

Keywords: Planning, recursive subgoals, Sliding-tile puzzle, subgoal interaction, genetic algorithms.

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1942 The Effect of Religious Tourist Motivation and Satisfaction on Behavioral Intention

Authors: Tao Zhang, Nan Yan

Abstract:

In recent years, the Chaoshan area, a special place located in the southeast of Guangdong province in China, actively protects religious heritage and is developing religious tourism, which is attracting many expatriate Chinese who are coming back for travel and to worship. This paper discussed three questions. Firstly, what is the current situation about the different social background of tourists’ motivation, satisfaction and behavioral intention? Secondly, is there a relationship between the motivation, satisfaction and behavioral intention and the different social backgrounds of tourists? Thirdly, what is the relationship between religious tourists’ motivation, satisfaction and behavioral intention? The research methods use a combination of qualitative analysis and quantitative analysis. Qualitative analysis uses the method of observation and interviews. Convenient sampling technique was used for quantitative analysis. The study showed that the different social backgrounds of tourists’ forms diverse cognition and experiences about religious tourism, and their motivations, satisfaction and behavioral intention as tourists vary. Tourists’ motivation and satisfaction has a positive phase relation. Tourists’ motivation with satisfaction as the intervening variable also has a positive phase effect on tourists’ behavior intention. The result shows that religious tourists’ motivations include experiencing a religious atmosphere, and having a rest and recreation. The result also shows that religious tourists want to travel with their family members and friends. While traveling, religious tourists like to talk with Buddhist monks or nuns. Compared to other tourism types, religious tourists have higher expectations about temple environment, traveling experience, peripheral service and temple management.

Keywords: Behavioral intension, motivation, religious tourism, satisfaction.

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1941 A New Approach to Annotate the Text's of the Websites and Documents with a Quite Comprehensive Knowledge Base

Authors: Mohammad Yasrebi, Mehran Mohsenzadeh, Mashalla Abbasi-Dezfuli

Abstract:

Machine-understandable data when strongly interlinked constitutes the basis for the SemanticWeb. Annotating web documents is one of the major techniques for creating metadata on the Web. Annotating websites defines the containing data in a form which is suitable for interpretation by machines. In this paper, we present a new approach to annotate websites and documents by promoting the abstraction level of the annotation process to a conceptual level. By this means, we hope to solve some of the problems of the current annotation solutions.

Keywords: Knowledge base, ontology, semantic annotation, semantic web.

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1940 Study Concerning the Energy-to-Mass Ratio in Pneumatic Muscles

Authors: Tudor Deaconescu, Andrea Deaconescu

Abstract:

The utilization of pneumatic muscles in the actuation of industrial systems is still in its early stages, hence studies on the constructive solutions which include an assessment of their functional performance with a focus on one of the most important characteristics-energy efficiency are required. A quality indicator that adequately reflects the energy efficiency of an actuator is the energy-to-mass ratio. This ratio is computed in the paper for various types and sizes of pneumatic muscles manufactured by Festo, and is subsequently compared to the similar ratios determined for two categories of pneumatic cylinders.

Keywords: Pneumatic cylinders, pneumatic muscles, energy-to-mass ratio, muscle stroke.

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1939 Comparison between XGBoost, LightGBM and CatBoost Using a Home Credit Dataset

Authors: Essam Al Daoud

Abstract:

Gradient boosting methods have been proven to be a very important strategy. Many successful machine learning solutions were developed using the XGBoost and its derivatives. The aim of this study is to investigate and compare the efficiency of three gradient methods. Home credit dataset is used in this work which contains 219 features and 356251 records. However, new features are generated and several techniques are used to rank and select the best features. The implementation indicates that the LightGBM is faster and more accurate than CatBoost and XGBoost using variant number of features and records.

Keywords: Gradient boosting, XGBoost, LightGBM, CatBoost, home credit.

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1938 Complex Fuzzy Evolution Equation with Nonlocal Conditions

Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

Abstract:

The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups.

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1937 Characteristics of Nanosilica-Geopolymer Nanocomposites and Mixing Effect

Authors: H. Assaedi, F. U. A. Shaikh, I. M. Low

Abstract:

This paper presents the effects of mixing procedures on mechanical properties of flyash-based geopolymer matrices containing nanosilica (NS) at 0.5%, 1.0%, 2.0%, and 3.0% by weight. Comparison is made with conventional mechanical dry-mixing of NS with flyash and wet-mixing of NS in alkaline solutions. Physical and mechanical properties are investigated using X-Ray Diffraction (XRD) and Scanning Electron Microscope (SEM). Results show that generally the addition of NS particles enhanced the microstructure and improved flexural and compressive strengths of geopolymer nanocomposites. However, samples, prepared using dry-mixing approach, demonstrate better physical and mechanical properties comparing to wet-mixing samples.

Keywords: Geopolymer, mechanical properties, nanosilica.

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1936 A Study on using N-Pattern Chains of Design Patterns based on Software Quality Metrics

Authors: Niloofar Khedri, Masoud Rahgozar, MahmoudReza Hashemi

Abstract:

Design patterns describe good solutions to common and reoccurring problems in program design. Applying design patterns in software design and implementation have significant effects on software quality metrics such as flexibility, usability, reusability, scalability and robustness. There is no standard rule for using design patterns. There are some situations that a pattern is applied for a specific problem and this pattern uses another pattern. In this paper, we study the effect of using chain of patterns on software quality metrics.

Keywords: Design Patterns, Design patterns' Relationship, Software quality Metrics, Software Engineering.

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1935 Local Stability Analysis of Age Structural Model for Herpes Zoster in Thailand

Authors: P. Pongsumpun

Abstract:

Herpes zoster is a disease that manifests as a dermatological condition. The characteristic of this disease is an irritating skin rash with blisters. This is often limited to one side of body. From the data of Herpes zoster cases in Thailand, we found that age structure effects to the transmission of this disease. In this study, we construct the age structural model of Herpes zoster in Thailand. The local stability analysis of this model is given. The numerical solutions are shown to confirm the analytical results.

Keywords: Age structural model, Herpes zoster, local stability, Numerical solution.

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1934 A Preliminary Analysis of Sustainable Development in the Belgrade Metropolitan Area

Authors: S. Zeković, M. Vujošević, T. Maričić

Abstract:

The paper provides a comprehensive analysis of the sustainable development in the Belgrade Metropolitan Region - BMA (level NUTS 2) preliminary evaluating the three chosen components: 1) economic growth and developmental changes; 2) competitiveness; and 3) territorial concentration and industrial specialization. First, we identified the main results of development changes and economic growth by applying Shift-share analysis on the metropolitan level. Second, the empirical evaluation of competitiveness in the BMA is based on the analysis of absolute and relative values of eight indicators by Spider method. Paper shows that the consideration of the national share, industrial mix and metropolitan/regional share in total Shift share of the BMA, as well as economic/functional specialization of the BMA indicate very strong process of deindustrialization. Allocative component of the BMA economic growth has positive value, reflecting the above-average sector productivity compared to the national average. Third, the important positive role of metropolitan/regional component in decomposition of the BMA economic growth is highlighted as one of the key results. Finally, comparative analysis of the industrial territorial concentration in the BMA in relation to Serbia is based on location quotient (LQ) or Balassa index as a valid measure. The results indicate absolute and relative differences in decrease of industry territorial concentration as well as inefficiency of utilizing territorial capital in the BMA. Results are important for the increase of regional competitiveness and territorial distribution in this area as well as for improvement of sustainable metropolitan and sector policies, planning and governance on this level.

Keywords: Belgrade Metropolitan Area (BMA), Comprehensive analysis/evaluation, economic growth and competitiveness, sustainable development.

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1933 Approximate Solution of Nonlinear Fredholm Integral Equations of the First Kind via Converting to Optimization Problems

Authors: Akbar H. Borzabadi, Omid S. Fard

Abstract:

In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To this purpose, we consider two stages of approximation. First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems and optimal control problems. Finally numerical examples is proposed.

Keywords: Fredholm integral equation, Optimization method, Optimal control, Nonlinear and linear programming

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1932 On the Strong Solutions of the Nonlinear Viscous Rotating Stratified Fluid

Authors: A. Giniatoulline

Abstract:

A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid.

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