Search results for: resuscitation order

Authors: Michael Wagner, Philipp Steinbauer, Andrea Katharina Lietz, Alexander Hoffelner, Johannes Fessler

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Background: Cardiopulmonary resuscitations are stressful situations in which vital decisions must be made within seconds. Lack of routine due to the infrequency of pediatric emergencies can lead to serious medical and communication errors. Virtual reality can fundamentally change the way simulation training is conducted in the future. It appears to be a useful learning tool for technical and non-technical skills. It is important to investigate the use of VR in providing a strong sense of presence within simulations. Methods: In this randomized study, we will enroll doctors and medical students from the Medical University of Vienna, who will receive learning material regarding the resuscitation of a one-year-old child. The study will be conducted in three phases. In the first phase, 20 physicians and 20 medical students from the Medical University of Vienna will be included. They will perform simulation-based training with a standardized scenario of a critically ill child with a hypovolemic shock. The main goal of this phase is to establish a baseline for the following two phases to generate comparative values regarding cognitive load and stress. In phase 2 and 3, the same participants will perform the same scenario in a VR setting. In both settings, on three set points of progression, one of three predefined events is triggered. For each event, three different stress levels (easy, medium, difficult) will be defined. Stress and cognitive load will be analyzed using the NASA Task Load Index, eye-tracking parameters, and heart rate. Subsequently, these values will be compared between VR training and traditional simulation-based training. Hypothesis: We hypothesize that the VR training and the traditional training groups will not differ in physiological response (cognitive load, heart rate, and heart rate variability). We further assume that virtual reality training can be used as cost-efficient additional training. Objectives: The aim of this study is to measure cognitive load and stress level during a real-life simulation training and compare it with VR training in order to show that VR training evokes the same physiological response and cognitive load as real-life simulation training.

Keywords: virtual reality, cognitive load, simulation, adaptive virtual reality training

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Authors: Hsin-Yi Huang, Ming-Sheng Liu, Jiun-Yan Shiau

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Planning the order picking lists of warehouses to achieve when the costs associated with logistics on the operational performance is a significant challenge. In e-commerce era, this task is especially important productive processes are high. Nowadays, many order planning techniques employ supervised machine learning algorithms. However, the definition of which features should be processed by such algorithms is not a simple task, being crucial to the proposed technique’s success. Against this background, we consider whether unsupervised algorithms can enhance the planning of order-picking lists. A Zone2 picking approach, which is based on using clustering algorithms twice, is developed. A simplified example is given to demonstrate the merit of our approach.

Keywords: order picking, warehouse, clustering, unsupervised learning

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Authors: H. Triki, Y. Hamaizi, A. El-Akrmi

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We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects.

Keywords: nonlinear Schrödinger equation, high-order effects, soliton solution

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Authors: Wilmer Osvaldo Martinez, Manuel Dario Hernandez, Juan Manuel Julio

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We propose to assess the performance of k forecast procedures by exploring the distributions of forecast errors and error losses. We argue that non systematic forecast errors minimize when their distributions are symmetric and unimodal, and that forecast accuracy should be assessed through stochastic loss order rather than expected loss order, which is the way it is customarily performed in previous work. Moreover, since forecast performance evaluation can be understood as a one way analysis of variance, we propose to explore loss distributions under two circumstances; when a strict (but unknown) joint stochastic order exists among the losses of all forecast alternatives, and when such order happens among subsets of alternative procedures. In spite of the fact that loss stochastic order is stronger than loss moment order, our proposals are at least as powerful as competing tests, and are robust to the correlation, autocorrelation and heteroskedasticity settings they consider. In addition, since our proposals do not require samples of the same size, their scope is also wider, and provided that they test the whole loss distribution instead of just loss moments, they can also be used to study forecast distributions as well. We illustrate the usefulness of our proposals by evaluating a set of real world forecasts.

Keywords: forecast evaluation, stochastic order, multiple comparison, non parametric test

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Authors: Zubdahe Noor, Haseeb Athar

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In this article, first a relation for conditional expectation is developed and then is used to characterize a general class of distributions F(x) = 1-e^(-ah(x)) through conditional expectation of difference of pair of generalized order statistics. Some results are reduced for particular cases. In the end, a list of distributions is presented in the form of table that are compatible with the given general class.

Keywords: generalized order statistics, order statistics, record values, conditional expectation, characterization

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Authors: Shubham Jaiswal

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In the present article, a drive is taken to compute the solution of spatial fractional order advection-dispersion equation having source/sink term with given initial and boundary conditions. The equation is converted to a system of ordinary differential equations using second-kind shifted Chebyshev polynomials, which have finally been solved using finite difference method. The striking feature of the article is the fast transportation of solute concentration as and when the system approaches fractional order from standard order for specified values of the parameters of the system.

Keywords: spatial fractional order advection-dispersion equation, second-kind shifted Chebyshev polynomial, collocation method, conservative system, non-conservative system

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Authors: Burcu Akyildiz, Cigdem Kadaifci, Y. Ilker Topcu, Burc Ulengin

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In today’s business environment, companies should make strategic decisions to gain sustainable competitive advantage. Order selection is a crucial issue among these decisions especially for steel production industry. When the companies allocate a high proportion of their design and production capacities to their ongoing projects, determining which customer order should be chosen among the potential orders without exceeding the remaining capacity is the major critical problem. In this study, it is aimed to identify and prioritize the evaluation factors for the customer order selection problem. Conjoint analysis is used to examine the importance level of each factor which is determined as the potential profit rate per unit of time, the compatibility of potential order with available capacity, the level of potential future order with higher profit, customer credit of future business opportunity, and the negotiability level of production schedule for the order.

Keywords: conjoint analysis, order prioritization, profit management, structural steel firm

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Authors: Huei Chu Weng, Chien-Hung Liu

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This paper presents a study on the effect of second-order slip and jump on forced convection through a long isothermally heated or cooled planar microchannel. The fully developed solutions of thermal flow fields are analytically obtained on the basis of the second-order Maxwell-Burnett slip and Smoluchowski jump boundary conditions. Results reveal that the second-order term in the Karniadakis slip boundary condition is found to contribute a negative velocity slip and then to lead to a higher pressure drop as well as a higher fluid temperature for the heated-wall case or to a lower fluid temperature for the cooled-wall case. These findings are contrary to predictions made by the Deissler model. In addition, the role of second-order slip becomes more significant when the Knudsen number increases.

Keywords: microfluidics, forced convection, gas rarefaction, second-order boundary conditions

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Authors: Ye Wang, Ickjai Lee

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Due to the widespread of mobile sensing, there is a strong need to handle trails of moving objects, trajectories. This paper proposes three visual analytic approaches for higher order information of trajectory data sets based on the higher order Voronoi diagram data structure. Proposed approaches reveal geometrical information, topological, and directional information. Experimental results demonstrate the applicability and usefulness of proposed three approaches.

Keywords: visual analytics, higher order information, trajectory datasets, spatio-temporal data

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Authors: M. Kang'ethe Simon, Nomngcoyiya Thanduxolo

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The aim of this article is to explore the role of selected cultural practices and assess how they can be a panacea in mitigating the state of social vices in South Africa. The article uses a review of literature methodology. Findings indicate that Africans were hoodwinked by white people to abandon their cultures for western based cultures. African cultures continue to weaken as they succumb to forces of westernization, eurocentrism, modernization, civilization, and globalization. Africans have realised that their cultures abandoned such as virginity testing, sexual mores and taboos and circumcision could be a panacea in mitigating some of the societal ills such as moral decadence and HIV/AIDS. The article urges for a resuscitation of cultural practices such as virginity testing, thigh sex (ukumetsha), circumcision and teachings that accompanied initiation schools; and societies to undergo an attitudinal and cultural paradigm shift that will consider the invaluable aspects of cultures that can effectuate and facilitate mitigation of social ills in African countries such as South Africa.

Keywords: virginity testing (reed dance), circumcision, initiation schools, African Renaissance, thigh sex, moral decadence, cultural custodians, state of anomie

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Authors: Elimhan N. Mahmudov

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The paper concerns the necessary and sufficient conditions of optimality for Cauchy problem of fourth order discrete (PD) and discrete-approximate (PDA) inclusions. The main problem is formulation of the fourth order adjoint discrete and discrete-approximate inclusions and transversality conditions, which are peculiar to problems including fourth order derivatives and approximate derivatives. Thus the necessary and sufficient conditions of optimality are obtained incorporating the Euler-Lagrange and Hamiltonian forms of inclusions. Derivation of optimality conditions are based on the apparatus of locally adjoint mapping (LAM). Moreover in the application of these results we consider the fourth order linear discrete and discrete-approximate inclusions.

Keywords: difference, optimization, fourth, approximation, transversality

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Authors: Jerome Dalphinis, Vishal Patel

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The Bailiwick of Jersey is an island British crown dependency situated off the coast of France. Jersey General Hospital’s emergency department sees approximately 40,000 patients a year. It’s outside the NHS, with secondary care being free at the point of care. Sedation is a continuum which extends from a normal conscious level to being fully unresponsive. Procedural sedation produces a minimally depressed level of consciousness in which the patient retains the ability to maintain an airway, and they respond appropriately to physical stimulation. The goals of it are to improve patient comfort and tolerance of the procedure and alleviate associated anxiety. Indications can be stratified by acuity, emergency (cardioversion for life-threatening dysrhythmia), and urgency (joint reduction). In the emergency department, this is most often achieved using a combination of opioids and benzodiazepines. Some departments also use ketamine to produce dissociative sedation, a cataleptic state of profound analgesia and amnesia. The response to pharmacological agents is highly individual, and the drugs used occasionally have unpredictable pharmacokinetics and pharmacodynamics, which can always result in progression between levels of sedation irrespective of the intention. Therefore, practitioners must be able to ‘rescue’ patients from deeper sedation. These practitioners need to be senior clinicians with advanced airway skills (AAS) training. It can lead to adverse effects such as dangerous hypoxia and unintended loss of consciousness if incorrectly undertaken; studies by the National Confidential Enquiry into Patient Outcome and Death (NCEPOD) have reported avoidable deaths. The Royal College of Emergency Medicine, UK (RCEM) released an updated ‘Safe Sedation of Adults in the Emergency Department’ guidance in 2017 detailing a series of standards for staff competencies, and the required environment and equipment, which are required for each target sedation depth. The emergency department in Jersey undertook audit research in 2018 to assess their current practice. It showed gaps in clinical competency, the need for uniform care, and improved documentation. This spurred the development of a checklist incorporating the above RCEM standards, including contraindication for procedural sedation and difficult airway assessment. This was approved following discussion with the relevant heads of departments and the patient safety directorates. Following this, a second audit research was carried out in 2019 with 17 completed checklists (11 relocation of joints, 6 cardioversions). Data was obtained from looking at the controlled resuscitation drugs book containing documented use of ketamine, alfentanil, and fentanyl. TrakCare, which is the patient electronic record system, was then referenced to obtain further information. The results showed dramatic improvement compared to 2018, and they have been subdivided into six categories; pre-procedure assessment recording of significant medical history and ASA grade (2 fold increase), informed consent (100% documentation), pre-oxygenation (88%), staff (90% were AAS practitioners) and monitoring (92% use of non-invasive blood pressure, pulse oximetry, capnography, and cardiac rhythm monitoring) during procedure, and discharge instructions including the documented return of normal vitals and consciousness (82%). This procedural sedation checklist is a safe intervention that identifies pertinent information about the patient and provides a standardised checklist for the delivery of gold standard of care.

Keywords: advanced airway skills, checklist, procedural sedation, resuscitation

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Authors: Aurelija Burinskiene

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This paper presents the study for an e-commerce warehouse. The study is aiming to improve order fulfillment activity by identifying the strategy presenting the best performance. A simulation model was proposed to reach the target of this research. This model enables various scenario tests in an e-commerce warehouse, allowing them to find out for the best order fulfillment strategy. By using simulation, model authors investigated customers’ orders representing on-line purchases for one month. Experiments were designed to evaluate various order picking methods applicable to the fulfillment of customers’ orders. The research uses cost components analysis and helps to identify the best possible order picking method improving the overall performance of e-commerce warehouse and fulfillment service to the customers. The results presented show that the application of order batching strategy is the most applicable because it brings distance savings of around 6.7 percentage. This result could be improved by taking an assortment clustering action until 8.34 percentage. So, the recommendations were given to apply the method for future e-commerce warehouse operations.

Keywords: e-commerce, order, fulfilment, strategy, simulation

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Authors: Gabriel A. Orozco

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The purpose of this article is to make an approach to the Security Studies, exposing their theories and concepts to understand the role that have had in the interpretation of the changes and continuities of the world order and their impact on policies or decision-making facing the problems of the 21st century. The aim is to build a bridge between the security studies as a subfield and the meaning that has been given to the world order. The idea of epistemic communities serves as a methodological proposal about the different programs of research in security studies, showing their influence in the realities of States, intergovernmental organizations and transnational forces, moving to implement, perpetuate and project a vision of the world order.

Keywords: security studies, epistemic communities, international, relations

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Authors: Venkatesh Pulletikurthi, Karthik B. Ariyur, Luciano Castillo

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The system identification from the turbulence wakes will lead to the tactical advantage to prepare and also, to predict the trajectory of the opponents’ movements. A low-order modeling technique, POD, is used to predict the object based on the wake pattern and compared with pre-trained image recognition neural network (NN) to classify the wake patterns into objects. It is demonstrated that low-order modeling, POD, is able to predict the objects better compared to pretrained NN by ~30%.

Keywords: the bluff body wakes, low-order modeling, neural network, system identification

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Authors: Ali Afaghi, Sehraneh Ghaemi

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The coordination of the multi-agent systems has been one of the interesting topic in recent years, because of its potential applications in many branches of science and engineering such as sensor networks, flocking, underwater vehicles and etc. In the most of the related studies, it is assumed that the dynamics of the multi-agent systems are integer-order and linear and the multi-agent systems with the fractional-order nonlinear dynamics are rarely considered. However many phenomena in nature cannot be described within integer-order and linear characteristics. This paper investigates the leader-following consensus problem for a class of nonlinear fractional-order multi-agent systems based on observer-based cooperative control. In the system, the dynamics of each follower and leader are nonlinear. For a multi-agent system with fixed directed topology firstly, an observer-based consensus protocol is proposed based on the relative observer states of neighboring agents. Secondly, based on the property of the stability theory of fractional-order system, some sufficient conditions are presented for the asymptotical stability of the observer-based fractional-order control systems. The proposed method is applied on a five-agent system with the fractional-order nonlinear dynamics and unavailable states. The simulation example shows that the proposed scenario results in the good performance and can be used in many practical applications.

Keywords: fractional-order multi-agent systems, leader-following consensus, nonlinear dynamics, directed graphs

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Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali

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We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.

Keywords: explicit group iterative method, finite difference, fourth order compact, Poisson equation

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Authors: Elhadj Bounadja, Mohand Oulhadj Mahmoudi, Abdelkader Djahbar, Zinelaabidine Boudjema

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In this paper we present a novel fuzzy second-order sliding mode control (FSOSMC) for wind energy conversion system based on a doubly-fed induction generator (DFIG). The proposed control strategy combines a fuzzy logic and a second-order sliding mode for the DFIG control. This strategy presents attractive features such as chattering-free, compared to the conventional first and second order sliding mode techniques. The use of this method provides very satisfactory performance for the DFIG control. The overall strategy has been validated on a 1.5-MW wind turbine driven a DFIG using the Matlab/Simulink.

Keywords: doubly fed induction generator, fuzzy second-order sliding mode controller, wind energy

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Authors: Ramandeep Behl, S. S. Motsa

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The main focus of this manuscript is to provide a highly efficient two-point sixth-order family of super-Halley type methods that do not require any second-order derivative evaluation for obtaining simple roots of nonlinear equations, numerically. Each member of the proposed family requires two evaluations of the given function and two evaluations of the first-order derivative per iteration. By using Mathematica-9 with its high precision compatibility, a variety of concrete numerical experiments and relevant results are extensively treated to confirm t he t heoretical d evelopment. From their basins of attraction, it has been observed that the proposed methods have better stability and robustness as compared to the other sixth-order methods available in the literature.

Keywords: basins of attraction, nonlinear equations, simple roots, super-Halley

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Authors: Ahmad Shah Farhat

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Background: Prenatal asphyxia or birth asphyxia is the medical situation resulting from a newborn infant that lasts long enough during the birth process to cause physical harm, usually to the brain. Human umbilical cord blood (UCB) is a well-established source of hematopoietic stem/progenitor cells (HSPCs) for allogeneic stem cell transplantation. These can be used clinically to care for children with malignant diseases. Low O2 can cause in proliferation and differentiation of stem cells. Method: the cord blood of 11 infants with 3-5 Apgar scores or need to cardiac pulmonary Resuscitation as an asphyxia group and ten normal infants with more than 8 Apgar scores as the normal group was collected, and after isolating hematopoietic stem cells, the cells were cultured in enriched media for 14 days to compare the numbers of colonies by microscope. Results: There was a significant difference in the number of RBC precursor colonies (red colonies) in cultured media with 107 cord blood hematopoietic stem cells of infants who were exposed to hypoxemia in two wells of palate. There was not a significant difference in the number of white cell colonies in the two groups in the two wells of the plate. Conclusion: Hypoxia in the perinatal period can cause the increase of hematopoietic stem cells of cord blood, special red precursor stem cells in vitro, like an increase of red blood cells in the body when exposed to low oxygen conditions. Thus, it will be usable.

Keywords: asphyxia, neonre, stem cell, red cell

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Authors: Pardeep Singh, Kamlesh Dutta

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Many languages have fixed sentence structure and others are free word order. The accuracy of anaphora resolution of syntax based algorithm depends on structure of the sentence. So, it is important to analyze the structure of any language before implementing these algorithms. In this study, we analyzed the sentence structure exploiting the case marker in Hindi as well as some special tag for subject and object. We also investigated the word order for Hindi. Word order typology refers to the study of the order of the syntactic constituents of a language. We analyzed 165 news items of Ranchi Express from EMILEE corpus of plain text. It consisted of 1745 sentences. Eight file of dialogue based from the same corpus has been analyzed which will have 1521 sentences. The percentages of subject object verb structure (SOV) and object subject verb (OSV) are 66.90 and 33.10, respectively.

Keywords: anaphora resolution, free word order languages, SOV, OSV

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Authors: H. Booke, R. Nordmeier

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Sudden cardiac arrest is sometimes eye-witnessed by kids. Mostly, their (grand-)parents are affected by sudden cardiac arrest, putting these kids under enormous psychological pressure: Although they are more than desperate to help, they feel insecure and helpless and are afraid of causing harm rather than realizing their chance to help. Even years later, they may blame themselves for not having helped their beloved ones. However, the absolute majority of school children - at least in Germany - is not educated to provide first aid. Teaching young kids (5th grade) in basic life support thus may help to save lives while washing away the kids' fear from causing harm during cardio-pulmonary resuscitation. A teaching of circulatory and respiratory (patho-)physiology, followed by hands-on training of basic life support for every single child, was offered to each school in our district. The teaching was performed by anesthesiologists, and the program was called 'kids can save lives'. However, before enrollment in this program, the entire class must have had lessons in biology with a special focus on heart and circulation as well as lung and gas exchange. More than 1.000 kids were taught and trained in basic life support, giving them the knowledge and skills to provide basic life support. This may help to reduce the rate of failure to provide first aid. Therefore, educating young kids in basic life support may not only help to save lives, but it also may help to prevent any feelings of guilt because of not having helped in cases of eye-witnessed sudden cardiac arrest.

Keywords: teaching, children, basic life support, cardiac arrest, CPR

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Authors: Eric Sanchis

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Although there does not exist a definitive consensus on a precise definition of a complex system, it is generally considered that a system is complex by nature. The presented work illustrates a different point of view: a system becomes complex only with regard to the question posed to it, i.e., with regard to the problem which has to be solved. A complex system is a couple (question, object). Because the number of questions posed to a given object can be potentially substantial, complexity does not present a uniform face. Two types of complex systems are clearly identified: first-order complex systems and second-order complex systems. First-order complex systems physically exist. They are well-known because they have been studied by the scientific community for a long time. In second-order complex systems, complexity results from the system composition and its articulation that are partially unknown. For some of these systems, there is no evidence of their existence. Vagueness is the keyword characterizing this kind of systems. Autonomy and free will, two mental productions of the human cognitive system, can be identified as second-order complex systems. A classification based on the properties structure makes it possible to discriminate complex properties from the others and to model this kind of second order complex systems. The final outcome is an implementable synthetic property that distinguishes the solid aspects of the actual property from those that are uncertain.

Keywords: autonomy, free will, synthetic property, vaporous complex systems

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

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In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: dissipation, oscillatory solutions, phase-lag, Runge-Kutta methods

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Authors: Henri Champliaud, Zhengkun Feng, Ngan Van Lê, Javad Gholipour

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In this article, a method is presented to effectively estimate the deformed shape of a thick plate due to line heating. The method uses a fifth order spline interpolation, with up to C3 continuity at specific points to compute the shape of the deformed geometry. First and second order derivatives over a surface are the resulting parameters of a given heating line on a plate. These parameters are determined through experiments and/or finite element simulations. Very accurate kriging models are fitted to real or virtual surfaces to build-up a database of maps. Maps of first and second order derivatives are then applied on numerical plate models to evaluate their evolving shapes through a sequence of heating lines. Adding an optimization process to this approach would allow determining the trajectories of heating lines needed to shape complex geometries, such as Francis turbine blades.

Keywords: deformation, kriging, fifth order spline interpolation, first, second and third order derivatives, C3 continuity, line heating, plate forming, thermal forming

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Authors: A. M. Sagir

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This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: block method, hybrid, linear multistep, self-starting, third order ordinary differential equations

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Authors: Mahdi Shamsi, Tohid Yousefi Rezaii, Siavash Eftekharifar

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Compressed sensing (CS) is a new powerful mathematical theory concentrating on sparse signals which is widely used in signal processing. The main idea is to sense sparse signals by far fewer measurements than the Nyquist sampling rate, but the reconstruction process becomes nonlinear and more complicated. Common dilemma in sparse signal recovery in CS is the lack of knowledge about sparsity order of the signal, which can be viewed as model order selection procedure. In this paper, we address the problem of sparsity order estimation in sparse signal recovery. This is of main interest in situations where the signal sparsity is unknown or the signal to be recovered is approximately sparse. It is shown that the proposed method also leads to some kind of signal denoising, where the observations are contaminated with noise. Finally, the performance of the proposed approach is evaluated in different scenarios and compared to an existing method, which shows the effectiveness of the proposed method in terms of order selection as well as denoising.

Keywords: compressed sensing, data denoising, model order selection, sparse representation

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Authors: Mohamed Suleiman, Zarina Bibi Ibrahim, Nor Ain Azeany, Khairil Iskandar Othman

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In this paper, a class of variable order fully implicit multistep Block Backward Differentiation Formulas (VOBBDF) using uniform step size for the numerical solution of stiff ordinary differential equations (ODEs) is developed. The code will combine three multistep block methods of order four, five and six. The order selection is based on approximation of the local errors with specific tolerance. These methods are constructed to produce two approximate solutions simultaneously at each iteration in order to further increase the efficiency. The proposed VOBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with single order Block Backward Differentiation Formula (BBDF). Numerical results shows the advantage of using VOBBDF for solving ODEs.

Keywords: block backward differentiation formulas, uniform step size, ordinary differential equations

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Authors: Parshanth Maroju, Ramandeep Behl, Sandile S. Motsa

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In this study, we proposed a simple and interesting family of fourth-order multi-point methods without memory for obtaining simple roots. This family requires only three functional evaluations (viz. two of functions f(xn), f(yn) and third one of its first-order derivative f'(xn)) per iteration. Moreover, the accuracy and validity of new schemes is tested by a number of numerical examples are also proposed to illustrate their accuracy by comparing them with the new existing optimal fourth-order methods available in the literature. It is found that they are very useful in high precision computations. Further, the dynamic study of these methods also supports the theoretical aspect.

Keywords: basins of attraction, nonlinear equations, simple roots, Newton's method

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Authors: Sandeep Singh

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In this article, two classes of iterative schemes are proposed for approximating solutions of nonlinear systems of equations whose orders of convergence are six and eight respectively. Sixth order scheme requires the evaluation of two vector-functions, two first Fr'echet derivatives and three matrices inversion per iteration. This three-step sixth-order method is further extended to eighth-order method which requires one more step and the evaluation of one extra vector-function. Moreover, computational efficiency is compared with some other recently published methods in which we found, our methods are more efficient than existing numerical methods for higher and medium size nonlinear system of equations. Numerical tests are performed to validate the proposed schemes.

Keywords: Nonlinear systems, Computational complexity, order of convergence, Jarratt-type scheme

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