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TY - JOUR. T1 - Theoretical and numerical investigations on shapes of planar lipid monolayer domains. AU - Wu, Hao. AU - Zhanchun Tu. PY - 2009. Y1 - 2009. N2 - Shapes of planar lipid monolayer domains at the air-water interface are theoretically and Shapes of planar lipid monolayer domains at the air-water interface are theoretically and numerically investigated by minimizing the formation energy of the domains, which consist of the surface energy, line tension energy, and dipole electrostatic energy. The shape equation, which describes boundary curves of the domains at equilibrium state, is derived from the first order variation of the formation energy. A relaxation method is proposed to find the numerical solutions of the shape equation. The theoretical and numerical results are in good agreement with previous experimental observation. Some new shapes not observed in previous experiments are also obtained, which awaits experimental confirmation in the future.. AB - Shapes of planar lipid ...
This course falls into two equal parts. The first part is devoted to a study of partial differential equations of the first order. Its orientation is very much geometrical. Here the solution of a partial differential equation is envisaged as a surface in the space of the dependent and independent variables. It is first shown how solution surfaces of the quasilinear Lagrange equation may be generated from families of curves. Knowledge of how to solve this equation enables us to find, by methods due to Charpit and Jacobi, so-called complete integrals of the general first-order partial differential equation. A complete integral may be viewed as a family of surfaces. Envelopes of this family, and of sub-families of this family, also solve the differential equation and give solutions known as singular integrals and general integrals.. The second half of the course deals with linear integral equations. Often many problems can be formulated in terms of an integral equation rather than the more ...
We consider the inertial range spectrum of capillary wave turbulence. Under the assumptions of weak turbulence, the theoretical surface elevation spectrum scales with wave number k as I[subscript η] ∼ k[superscript α], where α = α[subscript 0] = -19/4, energy (density) flux P as P[superscript 1/2]. The proportional factor C, known as the Kolmogorov constant, has a theoretical value of C = C[subscript 0] = 9.85 (we show that this value holds only after a formulation in the original derivation is corrected). The k[superscript -19/4] scaling has been extensively, but not conclusively, tested; the P[superscript 1/2] scaling has been investigated experimentally, but until recently remains controversial, while direct confirmation of the value of C[subscript 0] remains elusive. We conduct a direct numerical investigation implementing the primitive Euler equations. For sufficiently high nonlinearity, the theoretical k[superscript -19/4] and P[superscript 1/2] scalings as well as value of ...

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TY - JOUR. T1 - Integrating partner objectives in horizontal logistic optimisation models. AU - Defryn, C.. AU - Sorensen, K.. AU - Dullaert, Wout. PY - 2019/1. Y1 - 2019/1. N2 - In this paper a general solution framework is presented for optimising decisions in a horizontal logistics cooperation. The framework distinguishes between the objective of the group and the objectives of the individual partners in the coalition. Although the importance of the individual partner interests is often acknowledged in the literature, the proposed solution framework is the first to include these objectives directly into the objective function of the optimisation model. The solution framework is applied to a col- laborative variant of the clustered vehicle routing problem, for which we also create a set of benchmark instances. We find that by only considering a global coalition objective, the obtained solution is often suboptimal for some partners in the coalition. Providing a set of high quality alternative ...
Complex network theory in neuroscience; Graph theory in neuroscience Network theory is a branch of mathematics concerned with the analysis of the structure of graphs, the mathematical abstraction of...
View Notes - Lecture-7 from BIO 51310 at University of Texas. Thus far we have been assuming that the rates of various processes (distribution & elimination) are proportional to the drug
We investigate mathematical models for the dynamics between tumor cells, immune-effector cells, and cytokine interleukin-2 (IL-2). To better determine under what circumstances the tumor can be eliminated, we implement optimal control theory. We design two control functionals, the first functional having one control and the second having two controls, to maximize the effector cells and interleukin-2 concentration and to minimize the tumor cells. Next, we show that bang-bang optimal controls exist for each problem. Then, we characterize our optimal controls in terms of the solutions to the optimality system, which is the state system coupled with the adjoint system. Finally, we analyze the various optimal controls and optimality systems using numerical techniques.
Narodil sa ako prvorodený syn Maxa Neumanna (po maď. Neumann Miksa) a Margaret Neumannovej. S rodičmi a pestúnkou komunikoval po maďarsky a po nemecky, v škole sa naučil po grécky, latinsky, anglicky a francúzsky[1], sám sa naučil hebrejčinu.. Von Neumann mal dvoch bratov: prvý (* 1907) sa stal lekárom v Chicagu a druhý (* 1911) sa stal právnikom vo Philadelphii. Von Neumann mal 10 rokov, keď jeho otcovi udelil šľachtický titul cisár František Jozef I.. Jeho otec bol skvelý bankár a právnik, svoje deti podporoval vo všestrannom vzdelaní. Ako šesťročný z hlavy delil osemciferné čísla a ako osemročný už ovládal diferenciálny a integrálny počet.. Roku 1913 ho rodičia zapísali na známe nemecké luteránske gymnázium, dnes nazývané Fasori Evangélikus Gimnázium. Matematiku ho tam učil László Rátz.. Neskôr študoval na univerzitách v Zürichu (vo Švajčiarsku) a v Budapešti, vo svojich 23 rokoch sa stal doktorom, v roku 1929 bol už profesorom ...
Represents the forefront of mathematical approaches on biological systems relating to networks, oscillations, and collective motions Brings together
TY - JOUR. T1 - Lioprotein oxidation and its significance for atherosclerosis: a mathematical approach. AU - Cobbold, C A. AU - Sherratt, J A. AU - Maxwell, S R J. PY - 2002. Y1 - 2002. M3 - Article. VL - 64. SP - 65. EP - 96. JO - Bulletin of Mathematical Biology. JF - Bulletin of Mathematical Biology. SN - 0092-8240. ER - ...
PENN S TATE Hypotheses and Events An hypothesis about a biological process is a statement about relationships within a biological system. Protein P induces transcription of gene X We define an event as a relationship between two biological entities, which we call agents.
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In this paper we discuss the existence and uniqueness of asymptotically almost automorphic and $S$-asymptotically $\omega$-periodic mild solutions to some abstract nonlinear integro-differential equation of neutral type with infinite delay. We apply our results to neutral partial differential equations with infinite delay.
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The Spatial Intelligence and Learning Center would like to invite interested researchers currently conducting spatial cognition and learning research to join this open network. If you would like to be involved, please contact the SILC Webmaster to request an invitation.. For more information, please see: Initiative 6: Build Spatial Learning as a Field .. ...
The deformed configurations of an inflated flat nonlinear membrane are obtained by the minimum potential energy principle. The deformed configurations of the membrane are assumed to be represented by a series of geometric admissible functions with unknown coefficients. The unknown coefficients that minimize the total potential energy of the deformed membrane are determined by Fletcher and Powells [1] method. The strain-energy-density function for the numerical calculations is assumed to have the Mooney form. The results for a particular case when the Mooney membrane reduces to the neo-Hookean membrane, agree with the previous results obtained by numerical integration of the corresponding equilibrium equations.. ...
Using an asymptotic analysis, we analytically calculate the dispersion and the field distribution of guided modes in an all-dielectric coaxial fiber. We compare the analytical results with those obtained from numerical calculations and find excellent agreement between them. We demonstrate that both the Bragg reflection and the total internal reflection play important roles in providing confinement and determining the dispersion characteristics of the coaxial fiber modes.. © 2002 Optical Society of America. Full Article , PDF Article ...
Abstract , References , Similar Articles , Additional Information Abstract: In this paper a family of implicit multistep methods for the solution of Volterra integral equations is derived. These methods together with an explicit Euler predictor permit the use of a variable step size when solving integral equations. Means of controlling the error and stability by varying the step size and the order of the method are described. Extensive numerical results are presented ...
The five days interdisciplinary workshop on all aspects of mathematical modelling and mathematical methods in virus dynamics and viral evolution is organised in the framework of an intended CRM Mathematics in Life Sciences series. The areas of interest of the workshop include (but not limited to) directions such as dynamics of virus within a host and in a community, antiviral therapy, immune response and immunity failure, HIV and AIDS, plant virus, viral evolution, bacteriophages and their possible use in antibacterial therapy, etc. Mathematical methods include deterministic (both, ODE and PDE) and stochastic modelling, control theory, networks, random processes, as well as other approaches and methods ...
This article is concerned with the theoretical analysis of the functionally graded magneto-electro-thermoelastic hollow sphere due to uniform surface heating. We analyze the transient thermoelastic problem for a functionally graded hollow sphere constructed of the spherical isotropic and linear magneto-electro-thermoelastic materials using a laminated composite mode as one of theoretical approximation in the spherically symmetric state. As an illustration, we carry out numerical calculations for a functionally graded hollow sphere constructed of piezoelectric and magnetostrictive materials and examine the behaviors in the transient state. The effects of the nonhomogeneity of material on the stresses, electric potential, and magnetic potential are investigated.
After you successfully download, extract, and import the scenario (archive file Templates.zip), open the Templates project in the designer perspective. Double click on the Disease Model scenario and you should see a series of empty nested project (see Figure 2). The nested models within the scenario are named to make it easy to see what elements should be added to each model. In Figure 2 we navigated to the libraries of prebuilt models. The Models Tab contains folders with geographic information by country. In this example we pick Japan, and the prebuilt model with admin 0,1,2 data including the Human population data. ...
After you successfully download, extract, and import the scenario (archive file Templates.zip), open the Templates project in the designer perspective. Double click on the Disease Model scenario and you should see a series of empty nested project (see Figure 2). The nested models within the scenario are named to make it easy to see what elements should be added to each model. In Figure 2 we navigated to the libraries of prebuilt models. The Models Tab contains folders with geographic information by country. In this example we pick Japan, and the prebuilt model with admin 0,1,2 data including the Human population data. ...
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Use mathematical representations to support the claim that atoms, and therefore mass, are conserved during a chemical reaction. [Clarification Statement: Emphasis is on using mathematical ideas to communicate the proportional relationships between masses of atoms in the reactants and the products, and the translation of these relationships to the macroscopic scale using the mole as the conversion from the atomic to the macroscopic scale. Emphasis is on assessing students use of mathematical thinking and not on memorization and rote application of problem-solving techniques.] [Assessment Boundary: Assessment does not include complex chemical reactions.] ...
The utility of Potential Future Exposure (PFE) for counterparty trading limits is being challenged by new market developments, notably widespread regulatory Initial Margin (using stressed 99% 10-day exposure), and netting of trade and collateral flows. In addition, PFE has other drawbacks: lack of comparability across counterparties; lack of consistency with credit mitigation; insensitivity to exposure distribution changes above its reference quantile; exclusion of existing credit losses (i.e. incurred CVA). We introduce the concept of Potential Future Loss (PFL) which combines expected shortfall (ES) and loss given default (LGD) as a replacement for PFE. With two extensions to include existing credit losses (Adjusted PFL) and consistency with credit mitigation (Protected Adjusted PFL) both new and pre-existing challenges are resolved. We provide theoretical background and illustrate with numerical examples.. Based on joint work with: Benjamin Poncet (Lloyds) and Chris Kenyon (MUFG ...
The transport cross section (TCS) is calculated from the differential elastic-scattering cross sections. The latter were calculated using the relativistic Dirac partial wave analysis, as described by Walker [1]. The scattering potential was obtained from the self-consistent Dirac-Hartree-Fock electron density for free atoms [2] with the local exchange potential of Furness and McCarthy [3]. The numerical calculations were performed with the algorithm described by Salvat and Mayol [4]. ...
The transport cross section (TCS) is calculated from the differential elastic-scattering cross sections. The latter were calculated using the relativistic Dirac partial wave analysis, as described by Walker [1]. The scattering potential was obtained from the self-consistent Dirac-Hartree-Fock electron density for free atoms [2] with the local exchange potential of Furness and McCarthy [3]. The numerical calculations were performed with the algorithm described by Salvat and Mayol [4]. ...
Bézier Curves. Representing free-form shape. CAD/CAM software requires shape to be represented mathematically Standard mathematical representations such as y=f(x) very problematic Overcome using parametric representations. The simplest parametric curve. The Line: L (p) = (1-p) L 0 + p L 1 Slideshow 6853301 by hanna-delgado
log in you can tag this publication with additional keywords A publication can refer to another publication (outgoing references) or it can be referred to by other publications (incoming references).. ...
Data analytics is a unique field where you will learn insights needed to make sense of data, research, and observations from everyday life. You will learn how to apply a data-driven approach to problem solving, but will not only learn about tools, methods, and techniques, or the latest trends, but also more generic insights: why do certain approaches work, why the field is so popular, what common mistakes are made, and so on. You will also learn that data analytics is part science and part `art, since in applying methods and searching for findings there is a creative component.. Throughout the workshops you will work on several individual DA assignments, on predefined problems/datasets, using R tools, with a focus on the Life Sciences & Health domain. However, many of these assignments allow for freedom for your own individual approach. Most assignments involve real-world and relevant data sets, often connected to active research. The lectures will provide the theoretical background of how a DA ...
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79036 avhandlingar från svenska högskolor och universitet. Avhandling: A Complex Adaptive System Approach on Logistics - Implications of adopting a complexity perspective.
James Case Fragile Dominion: Complexity and the Commons. By Simon Levin, Helix Books (a division of Perseus Books), Reading, Massachusetts, 1999, 250 pages, $27 hardcover,$17 paperback.. Simon Levin---whose PhD and earliest positions were in mathematics---is the Moffett Professor of Biology at Princeton University, as well as the founding director of the Princeton Environmental Institute and a member of the Science Board of the Santa Fe Institute. As the author or editor of more than 25 books on biology, ecology, and biodiversity,* he is a leading contributor to some of the most politically sensitive branches of science. In the book under review, Levin explains why he believes the biosphere to constitute a complex adaptive system (CAS)---in the sense of the systems studied by John H. Holland---and why he deems biodiversity to be an essential ingredient thereof.. Since bursting on the scene little more than a decade ago, Hollands brain-children (which include genetic algorithms as well as ...
Research in this group spans a broad spectrum underpinned by the rigorous treatment and analysis of linear and nonlinear partial differential equations (PDEs).. This ranges from PDEs arising in geometry, physics and mechanics to those in control theory, finance and material sciences.. A core of our activities is on calculus of variations and geometric and harmonic analysis and there are subgroups with major interests in geometric measure theory, spectral theory, function spaces, dynamical systems, fluid mechanics, nonlinear elasticity and homogenisation.. For details see the Research tab.. ...
It is challenging to evaluate complex adaptive systems that often do not comprise easily observable processes that lead to easily measurable outcomes.5,8,35,56 Instead, these systems, such as in primary care, often have a plurality of aims and interests that sometimes conflict; they are influenced by their external environment, whose effects on the system could be minimal or profound; and the impact of the external forces often change with time.5,8 In traditional QI of mechanical processes, measurements are often at the level of an individual step. Ideally, it is more appropriate to measure complex adaptive systems at the level of the final outcome of interest.5. Which is not to suggest that all aspects of a complex adaptive system are completely unmeasurable. Parts of a primary care practice may be fairly linear and simple, others might best be imagined as a complicated set of linear processes, and other parts reflect an adaptive system.36 At the macro level, decades of research show that ...
In the present paper, experimental and numerical investigation of a laboratory oil furnace have been done to study the effect of inlet air swirl angle on temperature and generating of pollutant CO and NO. The Concentration of pollutant CO and NO on the centerline of the furnace have been measured using ...
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This book develops a morphodynamical approach of spatial networks with a particular emphasis on infrastructure networks such as streets, roads and transportation networks (subway, train). The author p
In this paper, four different forms of a model to describe the dynamics of autoimmune diseases (with emphasis on Guillain-Barré syndrome) are proposed. In the first two cases, the immune response is supposed to be linear, while in the other two cases it is supposed to be in the Holling type III form. In case of linear immune response, the model has a basic reproduction number and shows forward bifurcation. However, in the nonlinear Holling type III immune response cases, the model does not have a basic reproduction number and two positive equilibria do exist for a range of the parameters. The stability analysis of the models steady states has been established. Our analytical results have been illustrated by numerical simulations.
Partial differential equations arise in the mathematical modeling of many physical, chemical, and biological phenomena. They play a crucial role in diverse subject areas, such as fluid dynamics, electromagnetism, material science, astrophysics, financial modeling, and hydrogeology, for example. This course is an introduction to partial differential equations with emphasis on the wave, diffusion and Laplace equations. The focus will be on understanding the physical meaning and mathematical properties of solutions of partial differential equations. Methods of solutions include separation of variables using orthogonal series, transform methods, method of characteristics, and some numerical methods. 3 sh.. Prerequisites: MATH 420.. ...
Modern information processing systems show such complex properties as distribution, parallelism, interaction, time dependency, and nondeterminism. For critical applications, mathematical methods are needed to model the systems and to support their development and validation. Impressive progress in mathematical methods for programming software systems makes it possible to think about unifying the different approaches. This book gives a comprehensive overview of existing methods and presents some of the most recent results in applying them. The main topics are: advanced programming techniques, foundations of systems engineering, mathematical support methods, and application of the methods. The approaches presented are illustrated by examples and related to other approaches.
From BioPortfolio: After uncovering the progression of HIV infection in the brain thanks to a new mathematical model developed by a UAlberta research team, clinicians and research...
SUMMARY: Critical care environments are complex and dynamic. To adapt to such environments, clinicians may be required to make alterations to their workflows resulting in deviations from standard procedures. Some of these deviations are errors which can result in harmful outcomes. On the other hand, some of the deviations can be innovations, which are dynamic adjustments to the protocols made by people to adapt the current operational conditions and achieve high accuracy and efﬁciency. However, there is very little known about the underlying cognitive processes that are related to errors and innovations. In this work, deviations from standards in trauma critical care are studied.. METHODS: Field observations were conducted in a Level 1 Trauma unit. A total of 30 Trauma cases were observed and the collected data was analyzed using measures that included customized activity-error-innovation ontology, time-stamps and expertise of the team members. Activities tracked were compared to the Advance ...
Hurricane: component air and water molecules, multiple atoms bonded together. The physical and chemical phenomena associated with the molecule such as charge, size, shape, and potential energy reflect the constituent atoms, the types of bonds between them and the topology of the bonding. Charged molecules dissolve in aqueous solutions (water). Uncharged molecules dissolve in lipid bilayers. transiently present; It obeys physical laws; energy within hurricane can interact with (reflect) external ...
Genetic programming is a form of evolutionary computation that evolves programs and program-like executable structures for developing reliable time-and cost-effective applications. It does this by breeding programs over many generations, using the principles of natural selection, sexual recombination, and mutuation. This third volume of Advances in Genetic Programming highlights many of the recent technical advances in this increasingly popular field.. ...
Thomas E Kottke, MD, MSPH; Jacquelyn A Huebsch, RN, PhD; Paul McGinnis, MD; Jolleen M Nichols, RN; Emily D Parker, PhD; Juliana O Tillema, MPA; Michae
The Santa Fe Institute is the gathering point for the study of complexity|CAS a new reactionary approach to science. In some disciplines we are might ex...
An accurate cell-integrated semi Lagrangian and semi-implicit scheme based on step-functions. A new and very accurate cell-integrated semi Lagrangian (CISL) two time level scheme has been formulated and tested for the shallow water equations in a plane channel model with realistic variation of the Coriolis-parameter and including topography. The implementation includes semi-implicit time stepping of the gravity wave terms. Furthermore, two-dimensional advection of passive tracers has been tested in idealized flows as well as in a fully general flow.. Regarding basic features, the new formulation is based on step-functions, which implicitly are advected with the flow across cell boundaries. The scheme is exact in case of passive advection by a flow that is constant in time and space. This means that the accuracy is of indefinite order. In addition to this attractive feature the scheme shows very small numerical dispersion in fully non-linear and divergent flows and in such flows the scheme is ...
Get this from a library! Introduction to integral equations with applications. [Abdul J Jerri] -- Abdul Jerri has revised his highly applied book to make it even more useful for scientists and engineers, as well as mathematicians. Covering the fundamental ideas and techniques at a level ...
In deep water, the amplitude spectrum, a(k) in figure 5a, shows that, while the second-order bound wave components account for some of the energy transfers to the higher wavenumbers (and hence higher frequencies), comparisons with the fully nonlinear BST model indicate significant additional transfers for k,0.05 rad m−1. Furthermore, comparisons between the second- and third-order bound wave solutions confirm that the latter contribution is very small. Further evidence of this is provided in figure 5b,c. In terms of the resulting deep-water wave profile, figure 5b shows that, while the general shape of the wave group is similar to that predicted by linear dispersion, the fully nonlinear wave profile (BST) is higher and steeper than that predicted by linear, second- or even third-order bound wave solutions; the difference in terms of the crest elevation (see insert) is 17, 8 and 7 per cent, respectively. Furthermore, the fact that the maximum crest elevation calculated to third order is only ...
We will prove the main theorems of local and global class field theory in the first part of this semester (as sketched at the end of last semester). In the remaining part, our additional topics may include central simple algebras and quaternion algebras, Lubin-Tate formal groups (explicit local class field theory), CM elliptic curves (explicit class field theory for imaginary quadratic fields), (possibly) Drinfeld modules (explicit class field theory for global function fields), local and global Tate duality theorems (c.f., Serres Galois cohomology [1]) and (possibly) Langlands classification of representations of tori.. 01/30/2013. ...
A series of experiments on three-dimensional near fling was carried out. Two pairs of plates, rectangular and triangular, were selected, and the distance between the rotation axes of the two plates of each pair was varied. The motion of the plates as well as the forces and the moment were measured, and the interference between the two plates of a pair was studied. In addition, a method of numerical calculation was developed to aid in the understanding of the experimental results. The interference between the two plates of a pair, which acted to increase both the added mass of each plate and the hydrodynamic force due to dynamic pressure, was noted only when the opening angle between the plates was small. The hydrodynamic forces were strongly influenced by separated vortices that occurred during the rotation. A method of numerical calculation, which took into account the effect both of interference between the plates and of separated vortices, was developed to give adequate accuracy in ...
Provides a broad spectrum of numerical techniques and real life applications of these techniques All fundamentally important aspects of numerical
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In the recent paper Well-posedness and regularity for a generalized fractional Cahn--Hilliard system, the same authors derived general well-posedness and regularity results for a rather general system of evolutionary operator equations having the structure of a Cahn--Hilliard system. The operators appearing in the system equations were fractional versions in the spectral sense of general linear operators A and B having compact resolvents and are densely defined, unbounded, selfadjoint, and monotone in a Hilbert space of functions defined in a smooth domain. The associated double-well potentials driving the phase separation process modeled by the Cahn--Hilliard system could be of a very general type that includes standard physically meaningful cases such as polynomial, logarithmic, and double obstacle nonlinearities. In the subsequent paper Optimal distributed control of a generalized fractional Cahn--Hilliard system (Appl. Math. Optim. (2018), https://doi.org/10.1007/s00245-018-9540-7) by ...
Mechanical and civil engineers have created a new mathematical method to design better structures, machines and versatile computer-controlled robots called robot manipulators.
Computational and Mathematical Methods in Medicine publishes research and review articles focused on the application of mathematics to problems arising from the biomedical sciences.
Neumann University is a private, Catholic, co-educational college in the Franciscan tradition. It is located in Aston, PA, a suburb south of Philadelphia. Neumann emphasizes respect for individuals, concern for the environment, and social responsibility. The University offers undergraduate degrees in a broad variety of subjects, seven graduate programs, and an accelerated bachelors degree program for adults.
Neumann University is a private, Catholic, co-educational college in the Franciscan tradition. It is located in Aston, PA, a suburb south of Philadelphia. Neumann emphasizes respect for individuals, concern for the environment, and social responsibility. The University offers undergraduate degrees in a broad variety of subjects, seven graduate programs, and an accelerated bachelors degree program for adults.
Many processes in physics, the life sciences and technology that evolve in time are modeled by initial and boundary value problems for partial differential or integro-differential equations. The resulting mathematical theory of Evolution Equations involves tools from many fields of mathematical analysis, notably from functional analysis, operator theory and partial differential equations. This course is a self-contained introduction to the subject. It covers background materials like duality theory, the Bochner integral, vector-valued analytic functions, distributions and Fourier multipliers, vector-valued Laplace transforms, Tauberian theorems, asymptotic analysis, and spectral theory for closed operators on Banach spaces. The theory of Cauchy problems and operator semigroups will be developed completely in the spirit of Laplace transforms. Existence and uniqueness, regularity, numerical approximation, and asymptotic behavior of solutions will be covered and diverse applications to concrete ...
The TLM 102 defines a new generation of Neumann studio microphones. This applies not only to the design of the microphone but also to the price. The reduced overall size contributes to an exceptionally compact appearance, which unites all of the typical design components of a Neumann microphone. The harmonious proporti
This is the second volume in a projected five-volume survey of numerical linear algebra and matrix algorithms. It treats the numerical solution of dense and large-scale eigenvalue problems with an emphasis on algorithms and the theoretical background required to understand them. The notes and reference sections contain pointers to other methods along with historical comments. The book is divided into two parts: dense eigenproblems and large eigenproblems. The first part gives a full treatment of the widely used QR algorithm, which is then applied to the solution of generalized eigenproblems and the computation of the singular value decomposition. The second part treats Krylov sequence methods such as the Lanczos and Arnoldi algorithms and presents a new treatment of the Jacobi-Davidson method. These volumes are not intended to be encyclopedic, but provide the reader with the theoretical and practical background to read the research literature and implement or modify new algorithms.. ...
TY - JOUR. T1 - Eigenvalue curve veering in stressed structures: an experimental study. AU - du Bois, Jonathan Luke. AU - Adhikari, Sondipon. AU - Lieven, Nick A.J.. PY - 2009/5/1. Y1 - 2009/5/1. N2 - There have been extensive research works on the veering phenomenon in dynamic systems. As eigenvalues change under parametric variation, converging loci are commonly seen to veer away suddenly in a small region of the graph such that the modes swap trajectories. All of the modal properties are swapped in the process, leading to some curious behaviour in the transition zone. Theoretical studies of this behaviour have been reported for half a century but despite this heritage, explicit references to experimental results are scarce. In this paper detailed experimental and numerical investigations on veering are reported. The parameter varied is the internal pre-load of a redundant frame. An FE model is presented and stress stiffening approximations are employed to obtain a tangent stiffness for a ...
Problem solving and modelling are fundamental themes of the course - representing real world situations in a mathematical form and then using appropriate methods and techniques to analyse the situation, translating results back from mathematics to the actual problem situation. You will build on the mathematics that you have already studied, further extending your knowledge of calculus and linear algebra. You will also be introduced to mathematical modelling and learn how to approach building a mathematical representation of a real world problem.. Statistics is another important feature (the course assumes no prior knowledge in this area). Modern technology facilitates the collection of massive datasets which require new statistical techniques to analyse them. The focus within the course is on statistical thinking rather than the routine of how to perform a particular calculation. You will learn about the full problem solving cycle of planning, data collection, analysis and interpretation of ...
We present a novel Process Algebra designed for multi-scale integration modelling: Process Algebra with Layers (PAL). The unique feature of PAL is the modularisation of scale into integrated layers: Object and Population. An Object can represent a molecule, organelle, cell, tissue, organ or any organism. Populations hold specific types of Object, for example, life stages, cell phases and infectious states. The syntax and semantics of this novel language are presented. A PAL model of the multi-scale system of cell growth and damage from cancer treatment is given. This model allows the analysis of different scales of the system. The Object and Population levels give insight into the length of a cell cycle and cell population growth respectively. The PAL model results are compared to wet laboratory survival fractions of cells given different doses of radiation treatment [1]. This comparison shows how PAL can be used to aid in investigations of cancer treatment in systems biology.. Keywords ...
We confirm a conjecture, about neat embeddings of cylindric algebras, made in 1969 by J. D. Monk, and a later conjecture by Maddux about relation algebras obtained from cylindric algebras. These ...
We investigate a nonlocal reaction diffusion equation with absorption under Neumann boundary. We obtain optimal conditions on the exponents of the reaction and absorption terms for the existence of solutions blowing up in finite time, or for the global existence and boundedness of all solutions. For the blowup solutions, we also study the blowup rate estimates and the localization of blowup set. Moreover, we show some numerical experiments which illustrate our results.
In Electrical engineering programs, a class and field of study known as signals and systems (S and S) is often seen as the cut class for EE careers, and is dreaded by some students as such. Depending on the school, undergraduate EE students generally take the class as juniors or seniors, normally depending on the number and level of previous linear algebra and differential equation classes they have taken.[16]. The field studies input and output signals, and the mathematical representations between them known as systems, in four domains: Time, Frequency, s and z. Since signals and systems are both studied in these four domains, there are 8 major divisions of study. As an example, when working with continuous time signals (t), one might transform from the time domain to a frequency or s domain; or from discrete time (n) to frequency or z domains. Systems also can be transformed between these domains like signals, with continuous to s and discrete to z.. Although S and S falls under and ...
Differential Equations with Boundary-Value Problems (Metric Version), 9th edition, by Dennis G. Zill and published by Cengage Learning, provides a thorough treatment of topics typically covered in a first course in Differential Equations, as well as an introduction to boundary-value problems and partial differential equations. This proven and easy-to-understand book speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, Remarks boxes, definitions, and more. The WebAssign component for this text engages students with immediate feedback, a complete eBook, and a question bank of end-of-section exercises ...
Critical percolation phase and thermal Berezinskii-Kosterlitz-Thouless transition in a scale-free network with short-range and long-range random ...
In this paper, we advocate for a more harmonized approach to model development for additive manufacturing (AM) processes, through classification and metamodeling that will support AM process model composability, reusability, and integration. We review several types of AM process models and use the direct metal powder bed fusion AM process to provide illustrative examples of the proposed classification and metamodel approach. We describe how a coordinated approach can be used to extend modeling capabilities by promoting model composability. As part of future work, a framework is envisioned to realize a more coherent strategy for model development and deployment.. ...
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All known living systems share a number of basal features: (a) they are complex, containing large numbers of interacting components; (b) they are hierarchically organized (from molecules and their assemblies to cell organelles, to cells, to tissues, to organs, to organisms, to populations, to communities, to ecosystems); (c) they are the product of adaptive processes like natural selection; and (d) they are responsive in that they adapt their state and behaviour to changes in local conditions.. It is a major challenge to understand the functioning of such complex adaptive systems, to predict their responses to changing conditions, and to steer these systems in a desired direction, e.g. by increasing their capacity to adapt to human-induced environmental change. Meeting this challenge comes, for the first time in human history, within reach.. As a result of the omics revolution, biological data of unprecedented scope, depth and detail have become available. On the computational side, major ...
Ideal for ages 11-16+. Twin line 10+2 digit natural textbook display. Multi-replay. Matrix/vector. S-VPAM logic. Slide-on hard plastic case. Regression analysis. Calculus (numerical integration, numerical derivative). Physical constants. Metric conversions. Equations (polynomial, simultaneous). It is ideal for all Advanced Studies The FX991ESPLUS is Dual power and has 417 Functions Numeric calculation tools for differentiation, integration and summation Co-ordinate conversions between Polar and Rectangular values with Polynomial, simultaneous and general equation solvers
A text which students can actually READ and use to learn intermediate algebra and which instructors can use as a genuinely supportive framework from which to teach algebra Intermediate Algebra with Applications features an easy-to-read presentation, an emphasis on problem-solving skills, a wealth of well-chosen, illustrative examples, and uniquely structured problem sets ...
In this work, we study numerically a model which describes cell dwarfism. It consists in a pure initial value problem for a first order partial differential equation, that can be applied to the description of the evolution of diseases as thalassemia. We design two numerical methods that prevent the use of the characteristic curve x = 0, and derive their optimal rates of convergence. Numerical experiments are also reported in order to demonstrate the predicted accuracy of the schemes. Finally, a comparison study on their efficiency is presented ...
In this work, we study numerically a model which describes cell dwarfism. It consists in a pure initial value problem for a first order partial differential equation, that can be applied to the description of the evolution of diseases as thalassemia. We design two numerical methods that prevent the use of the characteristic curve x = 0, and derive their optimal rates of convergence. Numerical experiments are also reported in order to demonstrate the predicted accuracy of the schemes. Finally, a comparison study on their efficiency is presented ...