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Form Solutions (form + solution)

Distribution by Scientific Domains
Engineering33%
Mathematics and Statistics26%
Business, Economics, Finance and Accounting13%

Kinds of Form Solutions

  • closed form solution
    		•

    Selected Abstracts

    An Extended Analytical Approach to Credit Risk Management

    ECONOMIC NOTES, Issue 2 2002
    Alexandre Kurth
    Among the ,reduced form models' for measuring the credit risk of a bank's portfolio is CreditRisk+, which provides a closed,form solution for calculating the portfolio loss distribution based on an actuarial approach. The limitations of this model are well known, but they are often misinterpreted as being deeply embedded within the model. Dismantling the mathematical components of the model allows one to modify and extend it in several ways while remaining within an analytical approach. One of the most unattractive features is the orthogonality of the background factors or sectors as it hinders any resemblance to real,world macroeconomic indexes or industrial sectors and geographical areas. Among other extensions, which we mention briefly, we present in more detail how the original model can be amended to consider correlations among default risk sectors and among severity risk segments. These extensions are applied to real,life data, based on mortality rate data produced by the Italian Central Bank. (J.E.L.: C00, C51). [source]

    On the generation of conjugate flanks for arbitrary gear geometries

    GAMM - MITTEILUNGEN, Issue 1 2009
    A. Johann
    Abstract In this paper, we present a novel approach to three-dimensional mathematical gearing theory. We start from a general formulation of the so called basic law of gear kinematics. Based on that we derive an analytic closed form solution for the generation of conjugate tooth flanks, given a (local) parametric representation for any prescribed flank profile. Also, we study the problem of constructing pairs of tooth flanks that give rise to a prescribed surface of action. Surfaces of action will be represented in an implicit global rather than in a parametric way. To illustrate the general theory, we consider a number of specific examples including the standard involute profile for spur gears as well as a more sophisticated three-dimensional generalization of that (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

    On accurate boundary conditions for a shape sensitivity equation method

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2006
    R. Duvigneau
    Abstract This paper studies the application of the continuous sensitivity equation method (CSEM) for the Navier,Stokes equations in the particular case of shape parameters. Boundary conditions for shape parameters involve flow derivatives at the boundary. Thus, accurate flow gradients are critical to the success of the CSEM. A new approach is presented to extract accurate flow derivatives at the boundary. High order Taylor series expansions are used on layered patches in conjunction with a constrained least-squares procedure to evaluate accurate first and second derivatives of the flow variables at the boundary, required for Dirichlet and Neumann sensitivity boundary conditions. The flow and sensitivity fields are solved using an adaptive finite-element method. The proposed methodology is first verified on a problem with a closed form solution obtained by the Method of Manufactured Solutions. The ability of the proposed method to provide accurate sensitivity fields for realistic problems is then demonstrated. The flow and sensitivity fields for a NACA 0012 airfoil are used for fast evaluation of the nearby flow over an airfoil of different thickness (NACA 0015). Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Design of follow-up experiments for improving model discrimination and parameter estimation

    NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 8 2004
    Szu Hui Ng
    Abstract One goal of experimentation is to identify which design parameters most significantly influence the mean performance of a system. Another goal is to obtain good parameter estimates for a response model that quantifies how the mean performance depends on influential parameters. Most experimental design techniques focus on one goal at a time. This paper proposes a new entropy-based design criterion for follow-up experiments that jointly identifies the important parameters and reduces the variance of parameter estimates. We simplify computations for the normal linear model by identifying an approximation that leads to a closed form solution. The criterion is applied to an example from the experimental design literature, to a known model and to a critical care facility simulation experiment. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004 [source]

    Reduced-order suboptimal control design for a class of nonlinear distributed parameter systems using POD and ,,D techniques

    OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 3 2008
    Radhakant Padhi
    Abstract A new computational tool is presented in this paper for suboptimal control design of a class of nonlinear distributed parameter systems (DPSs). In this systematic methodology, first proper orthogonal decomposition-based problem-oriented basis functions are designed, which are then used in a Galerkin projection to come up with a low-order lumped parameter approximation. This technique has evolved as a powerful model reduction technique for DPSs. Next, a suboptimal controller is designed using the emerging ,,D technique for lumped parameter systems. This time domain control solution is then mapped back to the distributed domain using the same basis functions, which essentially leads to a closed form solution for the controller in a state-feedback form. We present this technique for the class of nonlinear DPSs that are affine in control. Numerical results for a benchmark problem as well as for a more challenging representative real-life nonlinear temperature control problem indicate that the proposed method holds promise as a good optimal control design technique for the class of DPSs under consideration. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Closed form solution of resin flow from multiple line gates in liquid composite molding

    POLYMER COMPOSITES, Issue 8 2010
    B. Markicevic
    The resin flow from multiple line injection into a fibrous porous medium is investigated analytically and experimentally. The flow in a rectangular porous medium is created by placing two inlets: a channel along one of the domain edges, and a manifold placed in the center of the domain perpendicular to the first inlet on the top surface of the porous medium. It is demonstrated that two distinct sub-regions of the porous medium exist: inner sub-region which is filled by the liquid from the manifold, and outer sub-region that is filled by fluid from the channel. In the experiments, the following geometric parameters are varied: channel cross-sectional area, mold width, and thickness to investigate how the processing parameters influence which part of the overall domain is filled by fluid from a specific inlet. Neither fluid nor porous medium are varied throughout the study. For nonconstrained flow, an analytical model is formulated to predict the interface between the two sub-regions which is called the inner sub-region thickness. Both, implicit and explicit solutions are found, where the explicit solution is represented as inverse Lambert function. The solution relies on one physical constant which is a function of the pressure gradients and the directional permeabilities of the fibrous preform. Comparisons between experimental and analytical results reveal an excellent agreement for various sets of geometric parameters. This research should prove useful in understanding the flow in composites manufacturing when resin is injected simultaneously from multiple gates and channels. POLYM. COMPOS., 31:1434,1441, 2010. © 2009 Society of Plastics Engineers [source]

    Flow front measurements and model validation in the vacuum assisted resin transfer molding process

    POLYMER COMPOSITES, Issue 4 2001
    R. Mathuw
    Through-thickness measurements were recorded to experimentally investigate the through thickness flow and to validate a closed form solution of the resin flow during the vacuum assisted resin transfer molding process (VARFM). During the VART'M process, a highly permeable distribution medium is incorporated into the preform as a surface layer and resin is inftised Into the mold, under vacuum. During Infusion, the resin flaws preferentially across the surface and simultaneously through the thickness of the preform, giving rise to a three dimensional-flow front. The time to fill the mold and the shape of the flow front, which plays a key role in dry spot formation, are critical for the optimal manufacture of large composite parts. An analytical model predicts the flow times and flow front shapes as a function of the properties of the preform, distribution media and resin. It was found that the flow front profile reaches a parabolic steady state shape and the length of the region saturated by resin is proportional to the square root of the time elapsed. Experimental measurements of the flow front in the process were carried out using embedded sensors to detect the flow of resin through the thickness of the preform layer and the progression of flow along the length of the part. The time to fill the part, the length of flow front and its shapes show good agreement between experiments and the analytical model. The experimental study demonstrates the need for control and optimization of resin injection during the manufacture of large parts by VARTM. [source]

    Computer programs for estimating substrate flux into steady-state biofilms from pseudoanalytical solutions

    COMPUTER APPLICATIONS IN ENGINEERING EDUCATION, Issue 1 2002
    Chetan T. Goudar
    Abstract Fixed-film processes employing microorganisms attached to an inert surface (biofilms) are widely used for biological treatment of municipal and industrial wastewater. For optimal design and analysis of these processes, mathematical models are necessary that describe the dynamics of contaminant transport within these biofilms and the associated contaminant utilization by the microorganisms. However, these governing equations that typically involve Fickian diffusion for contaminant transport and Monod kinetics for contaminant utilization are inherently nonlinear and have no closed form solutions except under special conditions. This can restrict their use in the classroom as cumbersome numerical techniques must be used for their solution. This problem is well documented in the literature and several authors have presented pseudoanalytical solutions that replace numerical solutions with algebraic equations. In the present study, we present pseudoanalytical solution-based computer programs for estimating substrate flux and biofilm thickness for a steady-state biofilm. Depending upon the intended end use, these programs can either partially or totally automate the solution process. In the partial automation mode, they can serve to enhance student understanding of important concepts related to steady-state biofilms, while complete automation can help bring more challenging and realistic problems associated with steady-state biofilms into the classroom. The programs have been tested on MATLAB version 5.0 and are available as freeware for educational purposes. © 2002 Wiley Periodicals, Inc. Comput Appl Eng Educ 10: 26,32, 2002; Published online in Wiley InterScience (www.interscience.wiley.com.); DOI 10.1002/cae.10017 [source]

    Dynamic response of a soft soil layer to flow and periodical disturbance

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2003
    Ping-Cheng Hsieh
    Abstract The dynamic response of a soft soil layer of finite thickness under the mutual effects of flow and periodical disturbance at the free surface is discussed in this work. The homogeneous water is governed by potential theory and the soil layer obeys Biot's theory of poroelasticity. The boundary-value problem is solved by an analytical algorithm, in which the wave number is found first. Secondly, the closed form solutions are found by a two-parameter perturbation method with the boundary-layer correction. The results are also compared with those of the poroelastic soil layer of infinite thickness to show the impermeable rigid boundary effect. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Modeling of the catalytic removal of CO and NO in dry combustion gases

    AICHE JOURNAL, Issue 3 2010
    C. Treviño
    Abstract Catalytic removal of pollutants in dry combustion gases in a planar stagnation-point flow over a platinum foil is studied using both numerical and analytical tools. The governing equations have been numerically integrated with the Newton technique, and the response curve has been obtained as functions of temperature and the mixture concentrations. Using the appropriate stoichiometry, the additional oxygen needed to reduce the NO and to achieve complete oxidation of CO has been obtained. The asymptotic analysis leads to an algebraic equation for the surface coverage of empty sites as a function of two nondimensional parameters: the mass transfer number, relating the residence time to the chemical time (sort of Damköhler number), and a parameter, which relates the desorption rate to the adsorption rate of carbon monoxide and depends strongly on temperature. Critical conditions of ignition (light-off) and extinction are identified and closed form solutions are obtained for these phenomena. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source]

    Optimal Redistribution with Heterogeneous Preferences for Leisure

    JOURNAL OF PUBLIC ECONOMIC THEORY, Issue 4 2002
    Robin Boadway
    This paper examines the properties of the optimal nonlinear income tax when preferences are quasi,linear in leisure and individuals differ in their ability and their preferences for leisure. The government seeks to redistribute income. It can perfectly observe the level of endogenous income but cannot observe either ability or preferences. The heterogeneity of preferences leads to problems of comparability between individual utilities which challenge the design of redistributive schemes. We analyze the consequences of adopting a utilitarian social welfare function where the government is allowed to give different weights to individuals with different preferences. Under this particular social objective and given the quasi,linearity of preferences, we are able to obtain closed,form solutions for the marginal tax rates and to examine the progressivity of the tax system according to the weights used. [source]

    Resonance shifting and plane impedance calculations for a rectangular cavity in printed circuit board using closed form solutions

    MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 2 2009
    K. Cantrell
    Abstract A method for arbitrarily shifting the dominant mode frequency of a rectangular cavity in printed circuit boards (PCBs) is presented. Standard closed-form and analytic solutions are used to determine the frequency, quality factor, and impedance of the cavity. Calculations are compared with 3D full wave finite element method (FEM) solutions. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 452,455, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24080 [source]

    The local theory of the cosmic skeleton

    MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2009
    D. Pogosyan
    ABSTRACT The local theory of the critical lines of two- and three-dimensional random fields that underline the cosmic structures is presented. In the context of cosmological matter distribution, the subset of critical lines of the three-dimensional density field serves to delineate the skeleton of the observed filamentary structure at large scales. A stiff approximation used to quantitatively describe the filamentary skeleton shows that the flux of the skeleton lines is related to the average Gaussian curvature of the (N , 1) dimensional sections of the field. The distribution of the length of the critical lines with threshold is analysed in detail, while the extended descriptors of the skeleton , its curvature and singular points , are introduced and briefly described. Theoretical predictions are compared to measurements of the skeleton in realizations of Gaussian random fields in two and three dimensions. It is found that the stiff approximation accurately predicts the shape of the differential length, allows for analytical insight and explicit closed form solutions. Finally, it provides a simple classification of the singular points of the critical lines: (i) critical points; (ii) bifurcation points and (iii) slopping plateaux. [source]

    Warehouse sizing to minimize inventory and storage costs

    NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 4 2001
    Mark Goh
    Abstract This paper considers a warehouse sizing problem whose objective is to minimize the total cost of ordering, holding, and warehousing of inventory. Unlike typical economic lot sizing models, the warehousing cost structure examined here is not the simple unit rate type, but rather a more realistic step function of the warehouse space to be acquired. In the cases when only one type of stock-keeping unit (SKU) is warehoused, or when multiple SKUs are warehoused, but, with separable inventory costs, closed form solutions are obtained for the optimal warehouse size. For the case of multi-SKUs with joint inventory replenishment cost, a heuristic with a provable performance bound of 94% is provided. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 299,312, 2001 [source]

    On Gene Ranking Using Replicated Microarray Time Course Data

    BIOMETRICS, Issue 1 2009
    Yu Chuan Tai
    Summary Consider the ranking of genes using data from replicated microarray time course experiments, where there are multiple biological conditions, and the genes of interest are those whose temporal profiles differ across conditions. We derive a multisample multivariate empirical Bayes' statistic for ranking genes in the order of differential expression, from both longitudinal and cross-sectional replicated developmental microarray time course data. Our longitudinal multisample model assumes that time course replicates are independent and identically distributed multivariate normal vectors. On the other hand, we construct a cross-sectional model using a normal regression framework with any appropriate basis for the design matrices. In both cases, we use natural conjugate priors in our empirical Bayes' setting which guarantee closed form solutions for the posterior odds. The simulations and two case studies using published worm and mouse microarray time course datasets indicate that the proposed approaches perform satisfactorily. [source]