Search results for: Functional analysis

Authors: S. M. Lee, J. H. Park, H. Y. Jung

Abstract:

This paper presents a method for functional projective H∞ synchronization problem of chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the novel feedback controller is established to not only guarantee stable synchronization of both drive and response systems but also reduce the effect of external disturbance to an H∞ norm constraint.

Keywords: Chaotic systems, functional projective H∞ synchronization, LMI.

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Authors: Han-hua Lu, Shun-yi Zhang, Yong Zheng, Ya-shi Wang, Li-juan Min

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From the perspective of system of systems (SoS) and emergent behaviors, this paper describes large scale application software systems, and proposes framework methods to further depict systems- functional and non-functional characteristics. Besides, this paper also specifically discusses some functional frameworks. In the end, the framework-s applications in system disintegrations, system architecture and stable intermediate forms are additionally dealt with in this in building, deployment and maintenance of large scale software applications.

Keywords: application software system, framework methods, system of systems, emergent behaviors

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Authors: Sim Hui Tee, Rodziah Atan, Abdul Azim Abd Ghani

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Inner class is a specialized class that defined within a regular outer class. It is used in some programming languages such as Java to carry out the task which is related to its outer class. The functional relatedness between inner class and outer class is always the main concern of defining an inner class. However, excessive use of inner class could sabotage the class cohesiveness. In addition, excessive inner class leads to the difficulty of software maintenance and comprehension. Our research aims at determining the minimum threshold for the functional relatedness of inner-outer class. Such minimum threshold is a guideline for removing or relocating the excessive inner class. Our research provides a feasible way for software developers to define inner classes which are functionally related to the outer class.

Keywords: Cohesion, functional relatedness of inner-outer class, inner class.

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Authors: Gülçin Tekin, Fethi Kadıoğlu

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In this study, the dynamic analysis of viscoelastic plates with variable thickness is examined. The solutions of dynamic response of viscoelastic thin plates with variable thickness have been obtained by using the functional analysis method in the conjunction with the Gâteaux differential. The four-node serendipity element with four degrees of freedom such as deflection, bending, and twisting moments at each node is used. Additionally, boundary condition terms are included in the functional by using a systematic way. In viscoelastic modeling, Three-parameter Kelvin solid model is employed. The solutions obtained in the Laplace-Carson domain are transformed to the real time domain by using MDOP, Dubner & Abate, and Durbin inverse transform techniques. To test the performance of the proposed mixed finite element formulation, numerical examples are treated.

Keywords: Dynamic analysis, inverse Laplace transform techniques, mixed finite element formulation, viscoelastic plate with variable thickness.

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Authors: Javed Parvez, Mushtaq Ahmad Peer

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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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Authors: Magda S. Taipina, Maria L. Garbelotti, Mariana G.B. Cadioli

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Banana is one of the most consumed fruits in the tropics and subtropics. Brazil accounts for about 9% of the world banana production. However, the production losses are as high as 30 to 40% and even much higher in some developing countries. The green banana flour is a complex carbohydrate source, including a high total starch (73.4%), resistant starch (17.5%) with functional properties. Gamma irradiation is considered to be an alternative method for food preservation. It has been performed due to the need of extending the shelf - life of foods, whilst maintaining their safety and avoiding one of the main concerns: the nutrient loss. In this work data about on the effects of ionizing radiation on the physicochemical analysis (carbohydrate, proteins, lipids, alimentary fiber, moistures and ashes) of Brazilian functional products (biscuits and bread) of the green banana pulp are presented. The caloric value was calculated. No significant difference was observed between the samples of irradiated and non – irradiated green banana biscuits with the following determinations: carbohydrates, proteins, alimentary fiber and ashes. Only a small significant difference was found in lipids (macronutrients). The results of physical chemical analysis of the irradiated and non- irradiated green banana bread non- irradiated showed no significant difference with the following determinations: carbohydrates, lipids (macronutrients), moisture, ashes and caloric value. A small difference was found in proteins (macronutrients). Irradiation of functional products (biscuits and bread) with doses of 1 and 3kGy maintained their original macronutrients content, showing good radioresistance.

Keywords: Irradiation, Functional Food, Nutritional value.

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Authors: Nittaya Kerdprasop, Kittisak Kerdprasop

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Frequent patterns are patterns such as sets of features or items that appear in data frequently. Finding such frequent patterns has become an important data mining task because it reveals associations, correlations, and many other interesting relationships hidden in a dataset. Most of the proposed frequent pattern mining algorithms have been implemented with imperative programming languages such as C, Cµ, Java. The imperative paradigm is significantly inefficient when itemset is large and the frequent pattern is long. We suggest a high-level declarative style of programming using a functional language. Our supposition is that the problem of frequent pattern discovery can be efficiently and concisely implemented via a functional paradigm since pattern matching is a fundamental feature supported by most functional languages. Our frequent pattern mining implementation using the Haskell language confirms our hypothesis about conciseness of the program. The performance studies on speed and memory usage support our intuition on efficiency of functional language.

Keywords: Association, frequent pattern mining, functionalprogramming, pattern matching.

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Authors: Vanessa Vasconcelos, Mariza A. S. Bigonha

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Understanding and using the functional paradigm is a challenge for many programmers. Looking for logical errors in code may take a lot of a developer’s time when a program grows in size. In order to facilitate both processes, this paper presents HaskellFL, a tool that uses fault localization techniques to locate a logical error in Haskell code. The Haskell subset used in this work is sufficiently expressive for those studying Functional Programming to get immediate help debugging their code and to answer questions about key concepts associated with the functional paradigm. HaskellFL was tested against Functional Programming assignments submitted by students enrolled at the Functional Programming class at the Federal University of Minas Gerais and against exercises from the Exercism Haskell track that are publicly available in GitHub. This work also evaluated the effectiveness of two fault localization techniques, Tarantula and Ochiai, in the Haskell context. Furthermore, the EXAM score was chosen to evaluate the tool’s effectiveness, and results showed that HaskellFL reduced the effort needed to locate an error for all tested scenarios. The results also showed that the Ochiai method was more effective than Tarantula.

Keywords: Debug, fault localization, functional programming, Haskell.

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Authors: Leszek Chybowski, Artur Bejger, Katarzyna Gawdzińska

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Subversion analysis is a tool used in the TRIZ (Theory of Inventive Problem Solving) methodology. This article introduces the history and describes the process of subversion analysis, as well as function analysis and analysis of the resources, used at the design stage when generating possible undesirable situations. The article charts the course of subversion analysis when applied to a fuel injection nozzle of a marine engine. The work describes the fuel injector nozzle as a technological system and presents principles of analysis for the causes of a cracked tip of the nozzle body. The system is modelled with functional analysis. A search for potential causes of the damage is undertaken and a cause-and-effect analysis for various hypotheses concerning the damage is drawn up. The importance of particular hypotheses is evaluated and the most likely causes of damage identified.

Keywords: Complex technical system, fuel injector, function analysis, importance analysis, resource analysis, sabotage analysis, subversion analysis, TRIZ.

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Authors: Lídia E. O. Cruz, Adriano P. C. Calvo, Renato J. Soares, Regiane A. Carvalho

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Individuals with non-specific chronic low back pain may present altered movement patterns during functional activities. However, muscle behavior before and after performing a functional task with different load conditions is not yet fully understood. The aim of this study is to analyze lumbar muscle activity before and after performing the functional task of picking up and placing an object on the ground (with and without load) in individuals with nonspecific chronic low back pain. 20 subjects with nonspecific chronic low back pain and 20 healthy subjects participated in this study. A surface electromyography was performed in the ilio-costal, longissimus and multifidus muscles to evaluate lumbar muscle activity before and after performing the functional task of picking up and placing an object on the ground, with and without load. The symptomatic participants had greater lumbar muscle activation compared to the asymptomatic group, more evident in performing the task without load, with statistically significant difference (p = 0,033) between groups for the right multifidus muscle. This study showed that individuals with nonspecific chronic low back pain have higher muscle activation before and after performing a functional task compared to healthy participants.

Keywords: Chronic low back pain, functional task, lumbar muscles, muscle activity.

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Authors: Theodore N.S. Karfakis, Anna Andrade

Abstract:

The aim of this study was to examine the dynamics of functional composition of a non flooded Amazonian forest in response to drought stress in terms of diameter growth, recruitment and mortality. The survey was carried out in the continuous forest of the Biological dynamics of forest fragments project 90 km outside the city of Manaus, state of Amazonas Brazil. All stems >10 cm dbh where identified to species level and monitored in 18 one hectare permanent sample plots from 1981 to 2004.For statistical analysis all species where aggregated in three ecological guilds. Two distinct drought events occurred in 1983 and 1997. Results showed that more early successional species performed better than later successional ones. Response was significant for both events but for the 1997 event this was more pronounced possibly because of the fact that the event was in the middle of the dry rather than the wet period as was the 1983 one.

Keywords: Brazil, functional composition, drought, Amazonian non flooded forest.

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Authors: Nassima Cheikh, Abdelmadjid Cheikh, Said Hamou

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The objective of this work which is based on the approach of simultaneous engineering is to contribute to the development of a CIM tool for the synthesis of functional design dimensions expressed by average values and tolerance intervals. In this paper, the dispersions method known as the Δl method which proved reliable in the simulation of manufacturing dimensions is used to develop a methodology for the automation of the simulation. This methodology is constructed around three procedures. The first procedure executes the verification of the functional requirements by automatically extracting the functional dimension chains in the mechanical sub-assembly. Then a second procedure performs an optimization of the dispersions on the basis of unknown variables. The third procedure uses the optimized values of the dispersions to compute the optimized average values and tolerances of the functional dimensions in the chains. A statistical and cost based approach is integrated in the methodology in order to take account of the capabilities of the manufacturing processes and to distribute optimal values among the individual components of the chains.

Keywords: functional tolerances, manufacturing dispersions, simulation, CIM.

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Authors: Azza. S. Naik, S. S. Lele

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Indian subcontinent has a plethora of traditional medicine systems that provide promising solutions to lifestyle disorders in an 'all natural way'. Spices and oilseeds hold prominence in Indian cuisine hence the focus of the current study was to evaluate the bioactive molecules from Linum usitatissinum (LU), Lepidium sativum (LS), Nigella sativa (NS) and Guizotia abyssinica (GA) seeds. The seeds were characterized for functional lipids like omega-3 fatty acid, antioxidant capacity, phenolic compounds, dietary fiber and anti-nutritional factors. Analysis of the seeds revealed LU and LS to be a rich source of α-linolenic acid (41.85 ± 0.33%, 26.71 ± 0.63%), an omega 3 fatty acid (using GCMS). While studying antioxidant potential NS seeds demonstrated highest antioxidant ability (61.68 ± 0.21 TEAC/ 100 gm DW) due to the presence of phenolics and terpenes as assayed by the Mass spectral analysis. When screened for anti-nutritional factor cyanogenic glycoside, LS seeds showed content as high as 1674 ± 54 mg HCN / kg. GA is a probable good source of a stable vegetable oil (SFA: PUFA 1:2.3). The seeds showed diversified bioactive profile and hence further studies to use different bio molecules in tandem for the development of a possible 'nutraceutical cocktail' have been initiated..

Keywords: antioxidants, bioactives, functional lipids and oilseeds

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Authors: Ni Ni Soe , Masahiro Nakagawa

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Functional near infrared spectroscopy (fNIRS) is a practical non-invasive optical technique to detect characteristic of hemoglobin density dynamics response during functional activation of the cerebral cortex. In this paper, fNIRS measurements were made in the area of motor cortex from C4 position according to international 10-20 system. Three subjects, aged 23 - 30 years, were participated in the experiment. The aim of this paper was to evaluate the effects of different motor activation tasks of the hemoglobin density dynamics of fNIRS signal. The chaotic concept based on deterministic dynamics is an important feature in biological signal analysis. This paper employs the chaotic properties which is a novel method of nonlinear analysis, to analyze and to quantify the chaotic property in the time series of the hemoglobin dynamics of the various motor imagery tasks of fNIRS signal. Usually, hemoglobin density in the human brain cortex is found to change slowly in time. An inevitable noise caused by various factors is to be included in a signal. So, principle component analysis method (PCA) is utilized to remove high frequency component. The phase pace is reconstructed and evaluated the Lyapunov spectrum, and Lyapunov dimensions. From the experimental results, it can be conclude that the signals measured by fNIRS are chaotic.

Keywords: Chaos, hemoglobin, Lyapunov spectrum, motorimagery, near infrared spectroscopy (NIRS), principal componentanalysis (PCA).

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Authors: Asadollah Aghajani, Yaghoub Jalilian

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Using the concept of measure of noncompactness, we present some results concerning the existence, uniform local attractivity and global attractivity of solutions for a functional integral equation. Our results improve and extend some previous known results and based on weaker conditions. Some examples which show that our results are applicable when the previous results are inapplicable are also included.

Keywords: Functional integral equation, fixed-point, measure of noncompactness, attractive solution, asymptotic stability.

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Authors: Kyung-Jung Lee, Young-Hun Ki, Hyun-Sik Ahn

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In this paper, we propose a hardware and software design method for automotive Electronic Control Units (ECU) considering the functional safety. The proposed ECU is considered for the application to Electro-Mechanical Actuator systems and the validity of the design method is shown by the application to the Electro-Mechanical Brake (EMB) control system which is used as a brake actuator in Brake-By-Wire (BBW) systems. The importance of a functional safety-based design approach to EMB ECU design has been emphasized because of its safety-critical functions, which are executed with the aid of many electric actuators, sensors, and application software. Based on hazard analysis and risk assessment according to ISO26262, the EMB system should be ASIL-D-compliant, the highest ASIL level. To this end, an external signature watchdog and an Infineon 32-bit microcontroller TriCore are used to reduce risks considering common-cause hardware failure. Moreover, a software design method is introduced for implementing functional safety-oriented monitoring functions based on an asymmetric dual core architecture considering redundancy and diversity. The validity of the proposed ECU design approach is verified by using the EMB Hardware-In-the-Loop (HILS) system, which consists of the EMB assembly, actuator ECU, a host PC, and a few debugging devices. Furthermore, it is shown that the existing sensor fault tolerant control system can be used more effectively for mitigating the effects of hardware and software faults by applying the proposed ECU design method.

Keywords: BBW (Brake-By-wire), EMB (Electro-Mechanical Brake), Functional Safety, ISO26262.

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Authors: Nurcan Tuncbag, Turkan Haliloglu, Ozlem Keskin

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Understanding the cell's large-scale organization is an interesting task in computational biology. Thus, protein-protein interactions can reveal important organization and function of the cell. Here, we investigated the correspondence between protein interactions and function for the yeast. We obtained the correlations among the set of proteins. Then these correlations are clustered using both the hierarchical and biclustering methods. The detailed analyses of proteins in each cluster were carried out by making use of their functional annotations. As a result, we found that some functional classes appear together in almost all biclusters. On the other hand, in hierarchical clustering, the dominancy of one functional class is observed. In the light of the clustering data, we have verified some interactions which were not identified as core interactions in DIP and also, we have characterized some functionally unknown proteins according to the interaction data and functional correlation. In brief, from interaction data to function, some correlated results are noticed about the relationship between interaction and function which might give clues about the organization of the proteins, also to predict new interactions and to characterize functions of unknown proteins.

Keywords: Pair-wise protein interactions, DIP database, functional correlations, biclustering.

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Authors: Setareh Shekarsaraei, Marjan Moridi, Nasser L. Hadipour

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In this study, nuclear magnetic resonance spectroscopy and nuclear quadrupole resonance spectroscopy parameters of 14N (Nitrogen in imidazole ring) in N–H…O hydrogen bonding for Histidine hydrochloride monohydrate were calculated via density functional theory. We considered a five-molecule model system of Histidine hydrochloride monohydrate. Also we examined the trends of environmental effect on hydrogen bonds as well as cooperativity. The functional used in this research is M06-2X which is a good functional and the obtained results has shown good agreement with experimental data. This functional was applied to calculate the NMR and NQR parameters. Some correlations among NBO parameters, NMR and NQR parameters have been studied which have shown the existence of strong correlations among them. Furthermore, the geometry optimization has been performed using M062X/6-31++G(d,p) method. In addition, in order to study cooperativity and changes in structural parameters, along with increase in cluster size, natural bond orbitals have been employed.

Keywords: Hydrogen bonding, Density Functional Theory (DFT), Natural bond Orbitals (NBO), cooperativity effects.

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Authors: Ayesha Zaman, Tanvir Atahary, Shahida Rafiq

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Functional Magnetic Resonance Imaging(fMRI) is a noninvasive imaging technique that measures the hemodynamic response related to neural activity in the human brain. Event-related functional magnetic resonance imaging (efMRI) is a form of functional Magnetic Resonance Imaging (fMRI) in which a series of fMRI images are time-locked to a stimulus presentation and averaged together over many trials. Again an event related potential (ERP) is a measured brain response that is directly the result of a thought or perception. Here the neuronal response of human visual cortex in normal healthy patients have been studied. The patients were asked to perform a visual three choice reaction task; from the relative response of each patient corresponding neuronal activity in visual cortex was imaged. The average number of neurons in the adult human primary visual cortex, in each hemisphere has been estimated at around 140 million. Statistical analysis of this experiment was done with SPM5(Statistical Parametric Mapping version 5) software. The result shows a robust design of imaging the neuronal activity of human visual cortex.

Keywords: Echo Planner Imaging, Event related Response, General Linear Model, Visual Neuronal Response.

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Authors: Sachin Bhalekar, Varsha Daftardar-Gejji

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In the present paper, we present a modification of the New Iterative Method (NIM) proposed by Daftardar-Gejji and Jafari [J. Math. Anal. Appl. 2006;316:753–763] and use it for solving systems of nonlinear functional equations. This modification yields a series with faster convergence. Illustrative examples are presented to demonstrate the method.

Keywords: Caputo fractional derivative, System of nonlinear functional equations, Revised new iterative method.

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Authors: Kassem Saleh

Abstract:

Decision Support System (DSS) are interactive software systems that are built to assist the management of an organization in the decision making process when faced with nonroutine problems in a specific application domain. Non-functional requirements (NFRs) for a DSS deal with the desirable qualities and restrictions that the DSS functionalities must satisfy. Unlike the functional requirements, which are tangible functionalities provided by the DSS, NFRs are often hidden and transparent to DSS users but affect the quality of the provided functionalities. NFRs are often overlooked or added later to the system in an ad hoc manner, leading to a poor overall quality of the system. In this paper, we discuss the development of NFRs as part of the requirements engineering phase of the system development life cycle of DSSs. To help eliciting NFRs, we provide a comprehensive taxonomy of NFRs for DSSs.

Keywords: Decision support system, Development, Elicitation, Non-functional requirements, Taxonomy

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Authors: Yanling Zhu

Abstract:

In this paper, a predator-prey model with Holling III type functional response is studied. It is interesting that the system is always uniformly persistent, which yields the existence of at least one positive periodic solutions for the corresponding periodic system. The result improves the corresponding ones in [11]. Moreover, an example is illustrated to verify the results by simulation.

Keywords: Predator-prey model, Uniformly persistence, Comparisontheorem, Holling III type functional response.

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Authors: M. Volpini, D. Alves, A. Horta, M. Borges, P. Reis

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The gait pattern in people that present motor limitations foment the demand for auxiliary locomotion devices. These artifacts for movement assistance vary according to its shape, size and functional features, following the clinical applications desired. Among the ortheses of lower limbs, the ankle-foot orthesis aims to improve the ability to walk in people with different neuromuscular limitations, although they do not always answer patients' expectations for their aesthetic and functional characteristics. The purpose of this study is to explore the possibility of using new design in additive manufacturer to reproduce the shape and functional features of a ankle-foot orthesis in an efficient and modern way. Therefore, this work presents a study about the performance of the mechanical forces through the analysis of finite elements in an ankle-foot orthesis. It will be demonstrated a study of distribution of the stress on the orthopedic device in orthostatism and during the movement in the course of patient's walk.

Keywords: Additive manufacture, new designs, orthoses, finite elements.

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Authors: S. Mozuriunaite

Abstract:

Contemporary metropolitan areas and large cities are dynamic, rapidly growing and continuously changing. Thus, urban transformations and mutations are not a new phenomenon, but rather a continuous process. Basic factors of urban transformation are related to development of technologies, globalisation, lifestyle, etc., which in combination with local factors have generated an extremely great variety of urban development conditions. This article discusses the main urbanisation processes in Lithuania during last 50-year period and social factors affecting urban functional mutations.

Keywords: Dispersion, functional mutations, urbanisation, urban mutations, social factors.

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Authors: Gesine Hellwig

Abstract:

Functional imaging procedures for the non-invasive assessment of tissue microcirculation are highly requested, but require a mathematical approach describing the trans- and intercapillary passage of tracer particles. Up to now, two theoretical, for the moment different concepts have been established for tracer kinetic modeling of contrast agent transport in tissues: pharmacokinetic compartment models, which are usually written as coupled differential equations, and the indicator dilution theory, which can be generalized in accordance with the theory of lineartime- invariant (LTI) systems by using a convolution approach. Based on mathematical considerations, it can be shown that also in the case of an open two-compartment model well-known from functional imaging, the concentration-time course in tissue is given by a convolution, which allows a separation of the arterial input function from a system function being the impulse response function, summarizing the available information on tissue microcirculation. Due to this reason, it is possible to integrate the open two-compartment model into the system-theoretic concept of indicator dilution theory (IDT) and thus results known from IDT remain valid for the compartment approach. According to the long number of applications of compartmental analysis, even for a more general context similar solutions of the so-called forward problem can already be found in the extensively available appropriate literature of the seventies and early eighties. Nevertheless, to this day, within the field of biomedical imaging – not from the mathematical point of view – there seems to be a trench between both approaches, which the author would like to get over by exemplary analysis of the well-known model.

Keywords: Functional imaging, Tracer kinetic modeling, LTIsystem, Indicator dilution theory / convolution approach, Two-Compartment model.

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Authors: C. S. Marques, M. J. Reis Lima, J. Oliveira, E. Teixeira-Lemos

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The growing concerns for physical wellbeing and health have been reflected in the way we choose food in our table. Nowadays, we are all more informed consumers and choose healthier foods. On the other hand, stroke, cancer and atherosclerosis may be somehow minimized by the intake of some bioactive compounds present in food, the so-called nutraceuticals and functional foods. The aim of this work was to make a revision of the published studies about the effects of some bioactive compounds, namely lycopene in human health, in the prevention of diseases, thus playing the role of a functional food. Free radical in human body can induce cell damage and consequently can be responsible for the development of some cancers and chronic diseases. Lycopene is one of the most powerful antioxidants known, being the predominant carotenoid in tomato. The respective chemistry, bioavailability, and its functional role in the prevention of several diseases will be object of this work. On the other hand, the inclusion of lycopene in some foods can also be made by biotechnology and represents a way to recover the wastes in the tomato industry with nutritional positive effects in health.

Keywords: Tomato, lycopene, bioavailability, functional foods, carotenoids, cancer and antioxidants.

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Authors: Yanling Zhu

Abstract:

In this paper, a higher order nonlinear neutral functional differential equation with distributed delay is studied by using the continuation theorem of coincidence degree theory. Some new results on the existence of periodic solutions are obtained.

Keywords: Neutral functional differential equation, higher order, periodic solution, coincidence degree theory.

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Authors: Xianqing Liu, Shouming Zhong, Lijiang Xiang

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In this paper, a stochastic predator-prey system with Bedding-DeAngelis functional response is studied. By constructing a suitable Lyapunov founction, sufficient conditions for species to be stochastically permanent is established. Meanwhile, we show that the species will become extinct with probability one if the noise is sufficiently large.

Keywords: Stochastically permanent, extinct, white noise, Bedding-DeAngelis functional response.

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Authors: B. L. Ho, L. Shi, D. F. Wang, V. C. T. Mok

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The brain’s functional connectivity while temporally non-stationary does express consistency at a macro spatial level. The study of stable resting state connectivity patterns hence provides opportunities for identification of diseases if such stability is severely perturbed. A mathematical model replicating the brain’s spatial connections will be useful for understanding brain’s representative geometry and complements the empirical model where it falls short. Empirical computations tend to involve large matrices and become infeasible with fine parcellation. However, the proposed analytical model has no such computational problems. To improve replicability, 92 subject data are obtained from two open sources. The proposed methodology, inspired by financial theory, uses multivariate regression to find relationships of every cortical region of interest (ROI) with some pre-identified hubs. These hubs acted as representatives for the entire cortical surface. A variance-covariance framework of all ROIs is then built based on these relationships to link up all the ROIs. The result is a high level of match between model and empirical correlations in the range of 0.59 to 0.66 after adjusting for sample size; an increase of almost forty percent. More significantly, the model framework provides an intuitive way to delineate between systemic drivers and idiosyncratic noise while reducing dimensions by more than 30 folds, hence, providing a way to conduct attribution analysis. Due to its analytical nature and simple structure, the model is useful as a standalone toolkit for network dependency analysis or as a module for other mathematical models.

Keywords: Functional magnetic resonance imaging, multivariate regression, network hubs, resting state functional connectivity.

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Authors: Mei Li, Fahui Zhai

Abstract:

In this paper, the definitions of the quaternion measure and the quaternion vector measure are introduced. The relation between the quaternion measure and the complex vector measure as well as the relation between the quaternion linear functional and the complex linear functional are discussed respectively. By using these relations, the necessary and sufficient condition to determine the quaternion vector measure is given.

Keywords: Quaternion, Quaternion measure, Quaternion vector measure, Quaternion Banach space, Quaternion linear functional.

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