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One of the main results of the present paper is contained in Theorem 2.1. The method of proof is based on martingale methods. For more information on viscosity solutions the reader is referred to [6]. Another feature of the presen...
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One of the main results of the present paper is contained in Theorem 2.1. The method of proof is based on martingale methods. For more information on viscosity solutions the reader is referred to [6]. Another feature of the present paper is the statement and proof of a generalized Noether theorem (Theorem 3.1) and its complex companion (Theorem 3.4). The proofs are of a computational character; they only depend on the properties of the generator of the diffusion and the corresponding carre du champ operator. They imitate and improve results obtained by Zambrini in [24]. Moreover the results solve problems posed in [22] (Problem 4, Theorem 16, pp. 257-258) and in para 2 of [23]. In particular see Problem 4 and the question prior and related to the suggested Theorem 6 on pp. 48-50 of [23]. The present paper extends the results in [21] considerably.
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The simplest model of a population is Malthus model. It states that the rate of change of the number of individuals in a population is proportional to the number of individuals so that populations modeled by this law grow or decay...
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The simplest model of a population is Malthus model. It states that the rate of change of the number of individuals in a population is proportional to the number of individuals so that populations modeled by this law grow or decay exponentially. Malthus model describes an unstructured population, that is a population in which individuals are not distinguishable. Models for structured populations may also display an overall exponential behavior. This is the case with the Lotka-McKendrick model for age-structured populations, where the so called persistent solutions occur, namely solutions that can be expressed as a product of a function of age (the stable distribution) and an exponentially growing function of time. The Lotka-McKendrick model has played an important role in demography, due to its simplicity and relatively good fit to data on a short time scale. Consequently, it remains the preferred theoretical paradigm in the study of human demography. The Malthus and the Lotka-McKendrick models are, however, linear. Usually non-linear population models are designed to avoid unlimited growth. In fact, through non-linear rates, it is possible to introduce those mechanisms that, in nature, produce containment of the population size.
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Flutter is an instability endemic to aircraft wings that occurs at high enough airspeed in subsonic flight, and sets a bound (flutter boundary) on attainable airspeed in the subsonic regime. As is to be expected we need to make ma...
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Flutter is an instability endemic to aircraft wings that occurs at high enough airspeed in subsonic flight, and sets a bound (flutter boundary) on attainable airspeed in the subsonic regime. As is to be expected we need to make many simplifying assumptions before we can obtain a mathematically tractable model. Here we limit ourselves to a long, slender, "high-aspect-ratio" wing (see Figure 1) so that we can simplify the wing model to a cantilever beam with two degrees of freedom - corresponding to plunge and pitch. The aerodynamics is assumed to be inviscid and incompressible, characterized by the small disturbance potential field equations. We simplify the problem further by invoking "typical section" theory, so that we can work with 2D aerodynamics (see Figure 2). In this way we finally arrive at a model describable in terms of a time-dependent boundary value problem for a set of partial differential (wave) equations. We show that the abstract version reduces to a convolution-semigroup equation in a Hilbert space, and the Flutter problem can then be characterized as the problem of determining system stability as a function of the airspeed, but determining the Flutter Boundary analytically is still an open problem, with room for further research. Numerical calculations on typical cases do however establish that the model does capture the known features of flutter. This material has already been reported, most recently in [1]. What is new in this paper is a self-contained mathematical development of the aerodynamic theory leading to the results quoted without proof in [1] in the calculation of the lift and moment. The structure model used derives from that of Goland [2] further elaborated in [3]. In the Aerodynamic part (which is the more difficult compared to the Structure Dynamics), key use is made of the results due to Sohngen and Tricomi [4] in their investigation of the airfoil equation. We begin in Section 2 with the stucture model. Section 3 is devoted to the aerodynamics, and the calculation of the aerodynamic lift and moment. Section 4 assembles the total aeroelastic system and develops the abstract convolution-semigroup equation.
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In our days, partial differential equations on multistructures have a width range of applications in continuum mechanics, aerodynamics, neurobiology, electronics and so on (cf. [5]). The most important questions are existence and ...
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In our days, partial differential equations on multistructures have a width range of applications in continuum mechanics, aerodynamics, neurobiology, electronics and so on (cf. [5]). The most important questions are existence and regularity results for stationary or nonstationary (linear or nonlinear) equations, spectral theory, control theory and numerical analysis, all reveal the specific character of the multistructure in question. This topic starts with the study of equations on one-dimensional stratified sets (also called topological networks or geometrical graphs) at the end of the 70th's with the works of G. Lumer [16, 17] and Y.V. Pokornyi [32, 25]. Diffusion equations on topological networks were first considered in [16, 17, 18] (see also [4, 7, 9, 14, 19]). Spectral theory on such objects (system composed of strings or beams) is also of great interest and reveals specific features of these structures which help to describe their properties [3, 6, 8, 11, 13, 19, 20, 25, 33, 34].
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In this work we analyze an S.I. epidemic model with age dependence and a heterogeneous spatial structure. Our main motivation rests on a tentative qualitative comparison in Naulin between continuous models and matrix population mo...
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In this work we analyze an S.I. epidemic model with age dependence and a heterogeneous spatial structure. Our main motivation rests on a tentative qualitative comparison in Naulin between continuous models and matrix population models, i.e., discrete models, with age and space structures of the S.E.I.R. form, used in modelling the propagation of rabies in red fox populations (Vulpes vulpes) in Suppo et al. [19]; see also Naulin [17]. A derivation of continuous S.E.I.R.models from the corresponding matrix models is found in Naulin [18], along the lines of Cushing [7] and Gurtin [10]. Then, the first question to address is a global (in time) existence problem. While this does not pose any problem for matrix population models because they are set in an explicit form, X(t + 1) = P(t, X(t))X(t) where P(t,X) is the reproduction matrix (Caswell [5]), this is far from being obvious for continuous models with age dependence because they are both non linear and non local. A further feature is that population fluxes are age dependent and may contain a transport term, as it is the case for territorial populations where juveniles must find their own territory to settle down and reproduce ([17]), [19]. This yields new age dependent mathematical problems much more structured than the one usullly considered (see the books of Webb [20], Iannelli [11] and Anita [3]).
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One of the main topics in modern mathematical finance is the pricing of contingent claims. The standard framework is built on a partial equilibrium analysis, the evolution of the underlying asset price or of the interest rate is d...
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One of the main topics in modern mathematical finance is the pricing of contingent claims. The standard framework is built on a partial equilibrium analysis, the evolution of the underlying asset price or of the interest rate is described by a stochastic process and then the price of a contingent claim is obtained imposing the no-arbitrage condition, i.e., given the evolution of the exogenous variables (underlying asset price-interest rate) the contingent claim is priced in such a way that there are no opportunities to make money from nothing. The price of a contingent claim can be interpreted from two different perspectives. It can be viewed as the solution of a Cauchy problem defined by the no-arbitrage Partial Differential Equation (PDE) and by the final payoff of the contingent claim as initial condition (PDE approach) or as the expectation of the final payoff under the risk-neutral probability measure nested in the stochastic process for the underlying asset price once the no-arbitrage condition is imposed (Probabilistic Approach). The two approaches are related by the well known Feynman-Kac theorem which states that the classical solution of the Cauchy problem admits a stochastic representation, i.e., the expectation of the final payoff under the probability measure associated with the no-arbitrage PDE (the risk-neutral probability measure), see [15].
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The fundamental objectives and purposes of this paper are to introduce a new registered and dedicated web site with virtual URL name as "civil-air.com". This active new web site has being designed and implemented for the project m...
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The fundamental objectives and purposes of this paper are to introduce a new registered and dedicated web site with virtual URL name as "civil-air.com". This active new web site has being designed and implemented for the project management technology and aircraft engineering technique distributed through the Wide Area Network( WAN )system for both inheritance and the international project management purpose. Because of the spaces limitation so that only essential background be reviewed in the Historical Background Review section and the some related system window views are shown in the Case Study section. At the end Conclusions section there are some recommendation comments and proposals are made. In case study section some important experienced practices included such as : customer data base structure, registration page for member, privacy policy in general, terms of service between ISP and customers, legal issues, virtual URL account statistics, channels of communication, interactivity and site responsive to visitors' input, CGI modules and Java applet, special surveys and forms, customer secure data transfer, security data base maintenance and how to promote a web site from the business point of view will be presented and described with detail. The last section of this paper is the conclusions in which the E-business and CBT are proposed for a similar web site of national knowledge banking system. The authors and their colleagues are also hoped that there are chances of cooperation in the domain area of IT. (Information Technology) & K.E. (Knowledge Engineering) technique's application to the development of Great Western China.
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This plant construction project has just been completed by the joint effort of Chinese and Japaness leading engineering and construction companies. The plant is a new production line of Purified Terephthalic Acid (PTA), the capaci...
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This plant construction project has just been completed by the joint effort of Chinese and Japaness leading engineering and construction companies. The plant is a new production line of Purified Terephthalic Acid (PTA), the capacity of which is designed for 262,000 tons per annum (8,200 hours base). The plant is located at Luoyang, Henan Province, the People's Republic of China, about 1,000 kilometers inland from Tianjin. Chiyoda Corporation's role as the engineering and procurement contractor was as the supplier ofj licenses and know-how, basic engineering, supply of specific items of equipment and materials, technical service and supervising construction / commissioning / start-up and training. The detailed engineering was performed by SINOPEC Luoyang Petro-Chemical Engineering Company. The main construction was carried out by SINOPEC The Fifth Construction Company with the supervision of Chiyoda, under the overall control of the end-user, SINOPEC Luoyang Petro-Chemical Complex. The contract was signed by China Petro-Chemical International Company (SINOPEC Inter) and Chiyoda Corporation on January 30, 1997, and the work started effectively on May 26, 1997. The mechanical completion was scheduled for March 2000 and completed on March 18, 2000 just as planned. Following the mechanical completion, the raw materials were initially charged on May 25, and the first production of PTA meeting the specification was delivered on May 29. As the performance test is scheduled for this coming August, this project is at the very last stage and project members are making every effort to complete it. Two topics are highlighted. First of all, no lost time accident has been recorded at the Job-site to this date. Secondly, we are proud that we could manage without any trouble the long haul of equipment and materials such as huge-sized reactor, towers and compressor, which were barged from Shanghai to Wuhan on the Yangtze River, and then transported to Luoyang by trailer. Some other materials were transported from Tianjin Xingang Seaport to the deep inland Luoyang by train, a distance of nearly 1,000 kilometers.
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For a grid-connected AC microgrid (MG), when a fault occurs at the microgrid, adaptive overcurrent (OC) or directional overcurrent (DOC) relays must be activated as fast as possible to protect all distributed generation (DG) units...
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For a grid-connected AC microgrid (MG), when a fault occurs at the microgrid, adaptive overcurrent (OC) or directional overcurrent (DOC) relays must be activated as fast as possible to protect all distributed generation (DG) units and loads. Fault currents inside the grid-connected AC microgrid can be significantly varied because fault current contributions from the main grid and DG units are different depending on various fault locations, fault types, and high penetration of inverter-based distributed generators (IBDGs) and rotating-based distributed generators (RBDGs) in the microgrid. A traditional fault analysis method cannot be applicable for AC microgrids with the presence of both rotating-based distributed generators and inverter-based distributed generators. Therefore, this paper proposes a simplified and automated fault current estimation approach for grid-connected AC microgrids, which is effective to quickly and accurately calculate fault current contributions from IBDGs and RBDGs and the grid fault current contribution to any faulted sections in the microgrid. This simplified and automated fault current calculation approach is mainly focused on grid-connected and small-sized low-voltage (LV) AC microgrids with the support of communication system. Under the grid-connected operation mode of the MG, fault tripping current thresholds of adaptive OC/DOC relays can be properly adjusted by the proposed fault analysis method. In particular, relying on fault current distribution coefficients of IBDGs, RBDGs, and the utility grid, pick-up currents of the adaptive OC/DOC relays in the LV AC microgrid are instantly and accurately self-adjusted according to different MG configurations as well as the operation status of DG units during the grid-connected mode.
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