Search results for: meshes convergence

Authors: Hyuk Sang Yoo, Young Ju Son, Wei Mao, Myung Gu Kang, Sol Lee

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Biomedical applications of electrospun nanofibrous meshes have been received tremendous attentions because of their unique structures and versatilities as biomaterials. Incorporation of growth factors in fibrous meshes can be performed by surface-modification and encapsulation. Those growth factors stimulate differentiation and proliferation of specific types of cells and thus lead tissue regenerations of specific cell types. Topographical cues of electrospun nanofibrous meshes also increase differentiation of specific cell types according to alignments of fibrous structures. Wound healing treatments of diabetic ulcers were performed using nanofibrous meshes encapsulating multiple growth factors. Aligned nanofibrous meshes and those with random configuration were compared for differentiating mesenchymal stem cells into neuronal cells. Thus, nanofibrous meshes can be applied to drug delivery carriers and matrix for promoting cellular proliferation.

Keywords: nanofiber, tissue, mesh, drug

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Authors: Kwounghee Choi

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Technological convergence between the various sectors is expected to have a very large impact on future industrial and economy. This study attempts to do empirical approach between specific technologies’ classification. For technological convergence classification, it is necessary to set the target technology to be analyzed. This study selected target technology from national research and development plan. At first we found a source technology for analysis. Depending on the weight of source technology, NT-based, BT-based, IT-based, ET-based, CS-based convergence types were classified. This study aims to empirically show the concept of convergence technology and convergence types. If we use the source technology to classify convergence type, it will be useful to make practical strategies of convergence technology.

Keywords: technology convergence, source technology, convergence type, R&D strategy, technology classification

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Authors: Qiming Zhang, Youda Ye, Qinxue Jiang

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Accurate prediction of external flowfield and aero-heating at the wall of hypersonic vehicle is very crucial for the design of aircrafts. Unstructured/hybrid meshes have more powerful advantages than structured meshes in terms of pre-processing, parallel computing and mesh adaptation, so it is imperative to develop high-resolution numerical methods for the calculation of aerothermal environment on unstructured/hybrid meshes. The inviscid flux scheme is one of the most important factors affecting the accuracy of unstructured/ hybrid mesh heat flux calculation. Here, a new hybrid flux scheme is developed and the approach of interface type selection is proposed: i.e. 1) using the exact Riemann scheme solution to calculate the flux on the faces parallel to the wall; 2) employing Sterger-Warming (S-W) scheme to improve the stability of the numerical scheme in other interfaces. The results of the heat flux fit the one observed experimentally and have little dependence on grids, which show great application prospect in unstructured/ hybrid mesh.

Keywords: aero-heating prediction, computational fluid dynamics, hybrid meshes, hybrid schemes

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Authors: Sandeep Kaur Chouhan, Jatinderdeep Kaur, S. S. Bhatia

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The existence of sine and cosine series as a Fourier series, their L1-convergence seems to be one of the difficult question in theory of convergence of trigonometric series in L1-metric norm. In the literature so far available, various authors have studied the L1-convergence of cosine and sine trigonometric series with special coefficients. In this paper, we present a modified cosine and sine sums and criterion for L1-convergence of these modified sums is obtained. Also, a necessary and sufficient condition for the L1-convergence of the cosine and sine series is deduced as corollaries.

Keywords: conjugate Dirichlet kernel, Dirichlet kernel, L1-convergence, modified sums

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Authors: Yanni Chang, Dezhi Dai, Albert Y. Tong

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Piecewise linear interface calculation (PLIC) schemes are widely used in the volume-of-fluid (VOF) method to capture interfaces in numerical simulations of multiphase flows. Dynamic overset meshes can be especially useful in applications involving component motions and complex geometric shapes. In the present study, the VOF value of an acceptor cell is evaluated in a geometric way that transfers the fraction field between the meshes precisely with reconstructed interfaces from the corresponding donor elements. The acceptor cell value is evaluated by using a weighted average of its donors for most of the overset interpolation schemes for continuous flow variables. The weighting factors are obtained by different algebraic methods. Unlike the continuous flow variables, the VOF equation is a step function near the interfaces, which ranges from zero to unity rapidly. A geometric interpolation scheme of the VOF field in overset meshes for the PLIC-VOF method has been proposed in the paper. It has been tested successfully in quadrilateral/hexahedral overset meshes by employing several VOF advection tests with imposed solenoidal velocity fields. The proposed algorithm has been shown to yield higher accuracy in mass conservation and interface reconstruction compared with three other algebraic ones.

Keywords: interpolation scheme, multiphase flows, overset meshes, PLIC-VOF method

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Authors: Israt Jahan Eshita

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Flows developed between two parallel disks have many engineering applications. Two types of non-swirling flows can be generated in such a domain. One is purely source flow in disc type domain (outward flow). Other is purely sink flow in disc type domain (inward flow). This situation often appears in some turbo machinery components such as air bearings, heat exchanger, radial diffuser, vortex gyroscope, disc valves, and viscosity meters. The main goal of this paper is to show the mesh convergence, because mesh convergence saves time, and economical to run and increase the efficiency of modeling for both sink and source flow. Then flow field is resolved using a very fine mesh near-wall, using enhanced wall treatment. After that we are going to compare this flow using standard k-epsilon, RNG k-epsilon turbulence models. Lastly compare some experimental data with numerical solution for sink flow. The good agreement of numerical solution with the experimental works validates the current modeling.

Keywords: hydraulic diameter, k-epsilon model, meshes convergence, Reynolds number, RNG model, sink flow, source flow, wall y+

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Authors: Rishikesh Yadav, Ramakanta Meher, Vishnu Narayan Mishra

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The main aim of this article is to investigate the statistical convergence of the summation of integral type operators and to obtain the weighted statistical convergence. The rate of statistical convergence by means of modulus of continuity and function belonging to the Lipschitz class are also studied. We discuss the convergence of the defined operators by graphical representation and put a better rate of convergence than the Szasz-Mirakjan-Kantorovich operators. In the last section, we extend said operators into bivariate operators to study about the rate of convergence in sense of modulus of continuity and by means of Lipschitz class by using function of two variables.

Keywords: The Szasz-Mirakjan-Kantorovich operators, statistical convergence, modulus of continuity, Peeters K-functional, weighted modulus of continuity

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Authors: Min Sang Lee, Hee Jae Shin, In Pyo Cha, Hyun Kyung Yoon, Seong Woo Hong, Min Jae Yu, Hong Gun Kim, Lee Ku Kwac

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In this paper, the electromagnetic shielding characteristics of an up-to-date typical carbon filler material, carbon fiber used with a metal mesh were investigated. Carbon fiber 12k-prepregs, where carbon fibers were impregnated with epoxy, were laminated with wire meshes, vacuum bag-molded and hardened to manufacture hybrid-type specimens, with which an electromagnetic shield test was performed in accordance with ASTM D4935-10, through which was known as the most excellent reproducibility is obtainable among electromagnetic shield tests. In addition, glass fiber prepress whose electromagnetic shielding effect were known as insignificant were laminated and formed with wire meshes to verify the validity of the electromagnetic shield effect of wire meshes in order to confirm the electromagnetic shielding effect of metal meshes corresponding existing carbon fiber 12k-prepregs. By grafting carbon fibers, on which studies are being actively underway in the environmental aspects and electromagnetic shielding effect, with hybrid-type wire meshes that were analyzed through the tests, in this study, the applicability and possibility are proposed.

Keywords: Carbon Fiber Reinforced Plastic(CFRP), Glass Fiber Reinforced Plastic(GFRP), stainless wire mesh, electromagnetic shielding

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Authors: Shuhua Lai, Kairui Chen

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In this paper, we present a fast and efficient mesh coarsening algorithm for 3D triangular meshes. Theis approach can be applied to very complex 3D meshes of arbitrary topology and with millions of vertices. The algorithm is based on the clustering of the input mesh elements, which divides the faces of an input mesh into a given number of clusters for clustering purpose by approximating the Centroidal Voronoi Tessellation of the input mesh. Once a clustering is achieved, it provides us an efficient way to construct uniform tessellations, and therefore leads to good coarsening of polygonal meshes. With proliferation of 3D scanners, this coarsening algorithm is particularly useful for reverse engineering applications of 3D models, which in many cases are dense, non-uniform, irregular and arbitrary topology. Examples demonstrating effectiveness of the new algorithm are also included in the paper.

Keywords: coarsening, mesh clustering, shape approximation, mesh simplification

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Authors: Amjad Naveed

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This study analysed the role of structural change in the process of labour productivity convergence at country and regional levels. Many forms of structural changes occurred within the European Union (EU) countries i.e. variation in sectoral employment share, changes in demand for products, variations in trade patterns and advancement in technology which may have an influence on the process of convergence. Earlier studies on convergence have neglected the role of structural changes which can have resulted in different conclusion on the nature of convergence. The contribution of this study is to examine the role of structural change in testing labour productivity convergence at various levels. For the empirical purpose, the data of 19 EU countries, 259 regions and 6 industries is used for the period of 1991-2009. The results indicate that convergence varies across regional and country levels for different industries when considered the role of structural change.

Keywords: labor produvitivty, convergence, structural change, panel unit root

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Authors: F. Berna Benli, Özgür Keskin

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Lately, many mathematicians have been studied the statistical convergence of a sequence of fuzzy numbers. We know that Lambda-statistically convergence is a kind of convergence between ordinary convergence and statistical convergence. In this paper, we will introduce the new kind of convergence such as λ-levelwise statistical convergence. Then, we will define the concept of the λ-levelwise statistical cluster and limit points of a sequence of fuzzy numbers. Also, we will discuss the relations between the sets of λ-levelwise statistical cluster points and λ-levelwise statistical limit points of sequences of fuzzy numbers. This work has been extended in this paper, where some relations have been considered such that when lambda-statistical limit inferior and lambda-statistical limit superior for lambda-statistically convergent sequences of fuzzy numbers are equal. Furthermore, lambda-statistical boundedness condition for different sequences of fuzzy numbers has been studied.

Keywords: fuzzy number, λ-levelwise statistical cluster points, λ-levelwise statistical convergence, λ-levelwise statistical limit points, λ-statistical cluster points, λ-statistical convergence, λ-statistical limit points

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Authors: Filipa Vasconcelos

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The administration of endoplasmic reticulum amino peptidases (ERAP1 or ERAP2) inhibitors can be used for therapeutic approaches against cancer and auto-immune diseases. However, one of the main shortcomings of drug delivery systems (DDS) is associated with the drug off-target distribution, which can lead to an increase in its side effects on the patient’s body. To overcome such limitations, the encapsulation of four representative compounds of ERAP inhibitors into Polycaprolactone (PCL), Polyvinyl-alcohol (PVA), crosslinked PVA, and PVA with nanoparticles (liposomes) electrospun fibrous meshes is proposed as a safe and controlled drug release system. The use of electrospun fibrous meshes as a DDS allows efficient solvent evaporation giving limited time to the encapsulated drug to recrystallize, continuous delivery of the drug while the fibers degrade, prevention of initial burst release (sustained release), tunable dosages, and the encapsulation of other agents. This is possible due to the fibers' small diameters and resemblance to the extracellular matrix (confirmed by scanning electron microscopy results), high specific surface area, and good mechanical strength/stability. Furthermore, release studies conducted on PCL, PVA, crosslinked PVA, and PVA with nanoparticles (liposomes) electrospun fibrous meshes with each of the ERAP compounds encapsulated demonstrated that they were capable of releasing >60%, 50%, 40%, and 45% of the total ERAP concentration, respectively. Fibrous meshes with ERAP_E compound encapsulated achieved higher released concentrations (75.65%, 62.41%, 56.05%, and 65.39%, respectively). Toxicity studies of fibrous meshes with encapsulated compounds are currently being accessed in vitro, as well as pharmacokinetics and dynamics studies. The last step includes the implantation of the drug-loaded fibrous meshes in vivo.

Keywords: drug delivery, electrospinning, ERAP inhibitors, liposomes

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Authors: Neha Bhardwaj

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In this paper, we consider positive linear operators and study the Voronovskaya type result of the operator then obtain an error estimate in terms of the higher order modulus of continuity of the function being approximated and its A-statistical convergence. Also, we compute the corresponding rate of A-statistical convergence for the linear positive operators.

Keywords: Poisson distribution, Voronovskaya, modulus of continuity, a-statistical convergence

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Authors: Berkay Buluş, Aytekin İşman, Kübra Yüzüncüyıl

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Developments in media and communication technologies have changed the way we use media. The importance of convergence culture has been increasing day by day within the framework of these developments. With new media, it is possible to say that social networks are the most powerful platforms that are integrated to this digitalization process. Although social networks seem like the place that people can socialize, they can also be utilized as places of production. On the other hand, audience has become users within the framework of transformation from national to global broadcasting. User generated contents make conventional media and new media collide. In this study, these communication platforms will be examined not as platforms that replace one another but mediums that unify each other. In the light of this information, information that is produced by users regarding new media platforms and all new media use practices are called convergence culture. In other words, convergence culture means intersections of conventional and new media. In this study, examples of convergence culture will be analyzed in detail.

Keywords: new media, convergence culture, convergence, use of new media, user generated content

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Authors: Alexandre Marin, Alexandra Bac, Laurent Astart

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New numerical methods for PDE resolution (such as Finite Volumes (FV) or Virtual Elements Method (VEM)) open new needs in terms of meshing of domains of interest, and in particular, polyhedral meshes have many advantages. One way to build such meshes consists of constructing Restricted Voronoi Diagrams (RVDs) whose boundaries respect the domain of interest. By minimizing a function defined for RVDs, the shapes of cells can be controlled, e.g., elongated according to user-defined directions or adjusted to comply with given aspect ratios (anisotropy) and density variations. In this paper, our contribution is threefold: First, we introduce a new gradient formula for the Voronoi tessellation energy under a continuous anisotropy field. Second, we describe a meshing algorithm based on the optimisation of this function that we validate against state-of-the-art approaches. Finally, we propose a hierarchical approach to speed up our meshing algorithm.

Keywords: anisotropic Voronoi diagrams, meshes for numerical simulations, optimisation, volumic polyhedral meshing

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Authors: Marian Sagat, Mariana Remesikova

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In civil engineering, there is a problem how to industrially produce tensile membrane structures that are non-developable surfaces. Nondevelopable surfaces can only be developed with a certain error and we want to minimize this error. To that goal, the non-developable surfaces are cut into plates along to the geodesic curves. We propose a numerical algorithm for finding approximations of open geodesics on meshes and surfaces based on geodesic curvature flow. For practical reasons, it is important to automatize the choice of the time step. We propose a method for automatic setting of the time step based on the diagonal dominance criterion for the matrix of the linear system obtained by discretization of our partial differential equation model. Practical experiments show reliability of this method. Because approximation of the model is made by numerical method based on classic derivatives, it is necessary to solve obstacles which occur for meshes with sharp corners. We solve this problem for big family of meshes with sharp corners via special rotations which can be seen as partial unfolding of the mesh. In practical applications, it is required that the approximation of geodesic has its vertices only on the edges of the mesh. This problem is solved by a specially designed pointing tracking algorithm. We also partially solve the problem of finding geodesics on meshes with holes. We implemented the whole algorithm in Rhinoceros (commercial 3D computer graphics and computer-aided design software ). It is done by using C# language as C# assembly library for Grasshopper, which is plugin in Rhinoceros.

Keywords: geodesic, geodesic curvature flow, mesh, Rhinoceros software

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Authors: Sonia Sonia

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This paper presents a family of iterative scheme for solving nonlinear systems of equations which have wide application in sciences and engineering. The proposed iterative family is based upon some parameters which generates many different iterative schemes. This family is completely derivative free and uses first of divided difference operator. Moreover some numerical experiments are performed and compared with existing methods. Analysis of convergence shows that the presented family has fourth-order of convergence. The dynamical behaviour of proposed family and local convergence have also been discussed. The numerical performance and convergence region comparison demonstrates that proposed family is efficient.

Keywords: convergence, divided difference operator, nonlinear system, Newton's method

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Authors: Ahmad Alhawarat, Mustafa Mamat, Mohd Rivaie, Ismail Mohd

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Conjugate gradient method has been enormously used to solve large scale unconstrained optimization problems due to the number of iteration, memory, CPU time, and convergence property, in this paper we find a new class of nonlinear conjugate gradient coefficient with global convergence properties proved by exact line search. The numerical results for our new βK give a good result when it compared with well-known formulas.

Keywords: conjugate gradient method, conjugate gradient coefficient, global convergence

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Authors: César Garza

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In supervised binary classification and regression problems, it is well-known that learnability is equivalent to a uniform convergence of the hypothesis class, and if a problem is learnable, it is learnable by empirical risk minimization. For the general learning setting of unsupervised learning tasks, there are non-trivial learning problems where uniform convergence does not hold. We present here the task of learning centers of mass with an extra feature that “activates” some of the coordinates over the unit ball in a Hilbert space. We show that the learning problem is learnable under a stable RLM rule. We introduce a family of distributions over the domain space with some mild restrictions for which the sample complexity of uniform convergence for these problems must grow logarithmically with the dimension of the Hilbert space. If we take this dimension to infinity, we obtain a learnable problem for which the uniform convergence property fails for a vast family of distributions.

Keywords: statistical learning theory, learnability, uniform convergence, stability, regularized loss minimization

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Authors: Aayushi Somani, Siba P. Samal

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Three-dimensional (3D) meshes are data structures, which store geometric information of an object or scene, generally in the form of vertices and edges. Current technology in laser scanning and other geometric data acquisition technologies acquire high resolution sampling which leads to high resolution meshes. While high resolution meshes give better quality rendering and hence is used often, the processing, as well as storage of 3D meshes, is currently resource-intensive. At the same time, web applications for data processing have become ubiquitous owing to their accessibility. For 3D meshes, the advancement of 3D web technologies, such as WebGL, WebVR, has enabled high fidelity rendering of huge meshes. However, there exists a gap in ability to stream huge meshes to a native client and browser application due to high network latency. Also, there is an inherent delay of loading WebGL pages due to large and complex models. The focus of our work is to identify the challenges faced when such meshes are streamed into and processed on hand-held devices, owing to its limited resources. One of the solutions that are conventionally used in the graphics community to alleviate resource limitations is mesh compression. Our approach deals with a two-step approach for random accessible progressive compression and its parallel implementation. The first step includes partition of the original mesh to multiple sub-meshes, and then we invoke data parallelism on these sub-meshes for its compression. Subsequent threaded decompression logic is implemented inside the Web Browser Engine with modification of WebGL implementation in Chromium open source engine. This concept can be used to completely revolutionize the way e-commerce and Virtual Reality technology works for consumer electronic devices. These objects can be compressed in the server and can be transmitted over the network. The progressive decompression can be performed on the client device and rendered. Multiple views currently used in e-commerce sites for viewing the same product from different angles can be replaced by a single progressive model for better UX and smoother user experience. Can also be used in WebVR for commonly and most widely used activities like virtual reality shopping, watching movies and playing games. Our experiments and comparison with existing techniques show encouraging results in terms of latency (compressed size is ~10-15% of the original mesh), processing time (20-22% increase over serial implementation) and quality of user experience in web browser.

Keywords: 3D compression, 3D mesh, 3D web, chromium, client-server architecture, e-commerce, level of details, parallelization, progressive compression, WebGL, WebVR

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Authors: Ramandeep Behl, Prashanth Maroju, S. S. Motsa

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In this paper, we study the semilocal convergence of a fifth order iterative method using recurrence relation under the assumption that first order Fréchet derivative satisfies the Hölder condition. Also, we calculate the R-order of convergence and provide some a priori error bounds. Based on this, we give existence and uniqueness region of the solution for a nonlinear Hammerstein integral equation of the second kind.

Keywords: Holder continuity condition, Frechet derivative, fifth order convergence, recurrence relations

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Authors: Vladimir V. Iakovlev, Erin T. Carey, John Steege

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The use of polypropylene mesh devices for Pelvic Organ Prolapse (POP) spread rapidly during the last decade, yet our knowledge of the mesh-tissue interaction is far from complete. We aimed to perform a thorough pathological examination of explanted POP meshes and describe findings that may explain mechanisms of complications resulting in product excision. We report a spectrum of important findings, including nerve ingrowth, mesh deformation, involvement of detrusor muscle with neural ganglia, and polypropylene degradation. Analysis of these findings may improve and guide future treatment strategies.

Keywords: transvaginal, mesh, nerves, polypropylene degradation

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Authors: Firano Zakaria, Filali Adib Fatine

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The issue f convergence in theoretical models (classical or Keynesian) has been widely discussed. The results of the work affirm that most countries are seeking to get as close as possible to a steady state in order to catch up with developed countries. In this paper, we have retested this question whether it is absolute or conditional. The results affirm that the degree of convergence of countries like Morocco is very low and income is still far from its equilibrium state. Moreover, the analysis of financial convergence, of the countries in our panel, states that the pace in this sector is more intense: countries are converging more rapidly in financial terms. The question arises as to why, with a fairly convergent financial system, growth does not respond, yet the financial system should facilitate this economic convergence. Our results confirm that the degree of information exchange between the financial system and the economic system did not change significantly between 1985 and 2017. This leads to the hypothesis that the financial system is failing to serve its role as a creator of information in developing countries despite all the reforms undertaken, thus making the existence of an economic demon in the Maxwell prevail.

Keywords: economic convergence, financial convergence, financial system, entropy

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Authors: Andreas Aceranti, Guido Bighiani, Francesca Crotto, Marco Colorato, Stefania Zaghi, Marino Zanetti, Simonetta Vernocchi

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The management of eye parameters such as convergence, accommodation, and miosis is very complex; in fact, both the neurovegetative system and the complex Oculocephalgiria system come into play. We have found the effectiveness of the "highvelocity low amplitude" technique directed on C7-T1 (where the cilio-spinal nucleus of the budge is located) in improving the convergence parameter through the measurement of the point of maximum convergence. With this research, we set out to investigate whether the improvement obtained through the High Velocity Low Amplitude maneuver lasts over time, carrying out a pre-manipulation measurement, one immediately after manipulation and one month after manipulation. We took a population of 30 subjects with both refractive and non-refractive problems. Of the 30 patients tested, 27 gave a positive result after the High Velocity Low Amplitude maneuver, giving an improvement in the point of maximum convergence. After a month, we retested all 27 subjects: some further improved the result, others kept, and three subjects slightly lost the gain obtained. None of the re-tested patients returned to the point of maximum convergence starting pre-manipulation. This result opens the door to a multidisciplinary approach between ophthalmologists and osteopaths with the aim of addressing oculomotricity and convergence deficits that increasingly afflict our society due to the massive use of devices and for the conduct of life in closed and restricted environments.

Keywords: point of maximum convergence, HVLA, improvement in PPC, convergence

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Authors: A. B. Bolkhir, A. Elshafie, T. K. Yousif

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This paper highlights the methods of error estimation in finite element analysis (FEA) results. It indicates that the modeling error could be eliminated by performing finite element analysis with successively finer meshes or by extrapolating response predictions from an orderly sequence of relatively low degree of freedom analysis results. In addition, the paper eliminates the round-off error by running the code at a higher precision. The paper provides application in finite element analysis results. It draws a conclusion based on results of application of methods of error estimation.

Keywords: finite element analysis (FEA), discretization error, round-off error, mesh refinement, richardson extrapolation, monotonic convergence

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Authors: Sudhakar Kadiyala, Sripad R. Naik

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Large cavern in Bhutan Himalayas is being monitored since the construction period. The behavior of the cavern is being monitored for last 16 years. Instrumentation includes measurement of convergence of high walls by geodetic monitoring, load on the support systems with load cells and instrumented bolts. Analysis of the results of instrumentation showed that during the construction period of the cavern, the convergence of the cavern varied from 181 - 233 mm in the unit bay area with maximum convergence rate of 2.80mm/day. Whereas during the operational period the total convergence observed was in the range of 21 to 45 mm during a period of 11.30 years with convergence rate of 0.005 to 0.011 mm/day. During the last five years, there were no instances of high tensile stress recorded by the instrumented bolts. Load on the rock bolts have shown stabilization trend at most of the locations. This paper discusses in detail the results of long-term monitoring using the geotechnical instruments and how the data is being used in 3D numerical model to confirm the stability of the cavern.

Keywords: convergence, displacements, geodetic monitoring, long-term stability

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Authors: T. Martini, J. M. Martínez

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An algorithmic acceleration strategy based on quasi-Newton (or secant) methods is displayed for address the practical problem of accelerating the convergence of the Newton-Lagrange method in the case of convergence to critical multipliers. Since the Newton-Lagrange iteration converges locally at a linear rate, it is natural to conjecture that quasi-Newton methods based on the so called secant equation and some minimal variation principle, could converge superlinearly, thus restoring the convergence properties of Newton's method. This strategy can also be applied to accelerate the convergence of algorithms applied to fixed-points problems. Computational experience is reported illustrating the efficiency of this strategy to solve fixed-point problems with linear convergence rate.

Keywords: algorithmic acceleration, fixed-point problems, nonlinear programming, quasi-newton method

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Authors: Guillaume Leduc

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In this paper, we describe a broad setting under which the error of the approximation can be quantified, controlled, and for which convergence occurs at a speed of n⁻¹ for European and American options. We describe how knowledge of the error allows for arbitrarily fast acceleration of the convergence.

Keywords: random walk approximation, European and American options, rate of convergence, option pricing

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Authors: Zhifeng Kong

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Over-parameterized neural networks have attracted a great deal of attention in recent deep learning theory research, as they challenge the classic perspective of over-fitting when the model has excessive parameters and have gained empirical success in various settings. While a number of theoretical works have been presented to demystify properties of such models, the convergence properties of such models are still far from being thoroughly understood. In this work, we study the convergence properties of training two-hidden-layer partially over-parameterized fully connected networks with the Rectified Linear Unit activation via gradient descent. To our knowledge, this is the first theoretical work to understand convergence properties of deep over-parameterized networks without the equally-wide-hidden-layer assumption and other unrealistic assumptions. We provide a probabilistic lower bound of the widths of hidden layers and proved linear convergence rate of gradient descent. We also conducted experiments on synthetic and real-world datasets to validate our theory.

Keywords: over-parameterization, rectified linear units ReLU, convergence, gradient descent, neural networks

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Authors: Sharfi Dirar, Shihab Elhaj, Ahmed El Fatih

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Computational fluid dynamics were used to simulate and study the heated water boiler tube for both normal and rifled tube with a refinement of the mesh to check the convergence. The operation condition was taken from GARRI power station and used in a boundary condition accordingly. The result indicates the rifled tube has higher heat transfer efficiency than the normal tube.

Keywords: boiler tube, convergence check, normal tube, rifled tube

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