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Drawing on rich case studies of Baltimore City and Boston, this volume identifies policy factors and processes critical to the successful district-wide adoption of community schools. By applying the Multiple Streams Model (Kingdon) to comparative analysis of policy determination and the narratives of local stakeholders across a 16-year period, chapters illustrate the role of federal legislation, funding, and buy-in from coalitions, community leaders, and local advocates in ensuring policy adoption in Baltimore City. In contrast, Boston's more limited reforms are explained in light of local challenges and hindering dynamics. Ultimately, the volume offers key recommendations for stakeholders to drive successful policy uptake in urban school districts. Offering a new analysis of policy for community schools, this volume will be of interest to students, scholars, and researchers with an interest in school reform, as well as urban education.

General elliptic interface problem with variable coefficients and curvilinear interface is transformed into analogous problem with rectilinear interface. For the numerical solution of transformed problem a finite difference scheme with averaged right-hand side is proposed. Convergence rate estimate in discrete W21 norm, compatible with the smoothness of data, is obtained. [ABSTRACT FROM AUTHOR]

Chapter 62 of the book "Nutrition in Pediatrics: Basic Science & Clinical Applications" is presented. It examines the relationships between nutritional deficiency and anemia. Anemia refers to inadequate circulating red blood cell mass which prevent tissue hypoxia. This disease can be related to blood loss, decreased red cell production, increased red cell destruction, or a combination of these events. Vitamin and mineral deficiencies that have been implicated as causes of anemia ar mentioned.

In this paper we investigate the stability of the second-order operator-differential equation in Hilbert space, under perturbations of the operators, the initial conditions and right hand side of the equation. The estimates of strong stability in different norms are obtained. As an example, the strong stability of the hyperbolic problem is presented. [ABSTRACT FROM AUTHOR]

The new method for calculating the energy values of the hydrogen atom in a strong magnetic field (0 ≤ B ≤ 1013G ) with high degree of accuracy is developed in this paper. The proposed method is based on the Kantorovich method for solving eigenvalue problems. This method successfully reduces the given two dimensional spectral problem for the Schrödinger equation to the spectral problems for one one-dimensional equation and the system of ordinary second-order differential equations. The rate of convergence is examined numerically and is illustrated in the table. The results are in good agreement with the best one up to now and show that 12 significant digits are computed in the obtaining energy values. [ABSTRACT FROM AUTHOR]

Given the matrices A and E in , we consider, for the family , questions such as i) existence and analyticity of , and ii) limit as t→ ∞ of σ(A(t)), the spectrum of A(t). The answer depends on the Jordan structure of 0 ∈ σ (E), more precisely on the existence of trivial Jordan blocks (of size 1). The results of the theory of Homotopic Deviation are then used to analyse the convergence of Krylov methods in finite precision. Keywords: Sherman-Morrison formula, Schur complement, Jordan structure, frontier point, critical point, Ritz value, eigenprojection, analyticity, singularity, backward analysis, Krylov method. [ABSTRACT FROM AUTHOR]

The new iteration line-by-line method with a variable compensation parameter is proposed for solving a system of difference equations that arises from the implicit approximation of two-dimensional elliptic and parabolic differential equations. Calculations have shown that the method's convergence rate is insensitive to the variation of coefficients at high derivatives in differential equation and weakly depends on a quantity of grid nodes. The use of computational technology is especially effective on detailed grids and allows to reduce a necessary number of iteration steps up to two orders of magnitude as compared with the initial line-by-line method. Keywords: multidimensional differential equations, numerical calculations, difference equations, iteration methods. [ABSTRACT FROM AUTHOR]

We show that unlike the bright solitons, the parametrically driven kinks of the nonlinear Schrödinger equation are immune from instabilities for all damping and forcing amplitudes; they can also form stable bound states. In the undamped case, the two types of kinks and their complexes can stably travel with nonzero velocities. The bistability of the Bloch and Néel walls within the NLS contrasts the properties of these solutions within the Ginzburg-Landau equation, where they cannot stably coexist. [ABSTRACT FROM AUTHOR]

We consider problems of quantum mechanics of Kuryshkin which pass to eigenvalue problem of conventional quantum mechanics when passing to the limit. From the demand of experimental confirmation of the theory's results are derived linearized equations for eigenstates of observables. The method of solving derived equations is illustrated on an example of hydrogen-like atom, for which were constructed matrices Oij(H) and Oij(H2). An example of the solution is presented. [ABSTRACT FROM AUTHOR]

For a nonlinear model of a wastewater treatment process the input-output static caracteristics are studied with respect to uncertainties in process parameters. Computer simulations and visualizations are performed in Maple to show how these uncertainties influence the efficiency of the bioreactor. [ABSTRACT FROM AUTHOR]

Tank reactors with different mixers are very often used for many chemical and biological processes. For their effective use is necessary to know in details hydrodynamics and mass transfer which take place in them. For many practically important cases the experimental study of these processes is very expensive, very difficult or impossible. This is why recently mathematical modelling of the complex swirling flows in such reactors becomes an effective method for investigation of the behavior of the fluids in these reactors. This paper presents mathematical model and numerical results for viscous swirling flow in a cylindrical tank reactor with a mixer. The model is based on the Navier-Stokes equations in cylindrical co-ordinate system. These equations are written in terms of the stream function, vorticity and the momentum of the tangential component of the velocity. The flow is supposed to be stationary and axis-symmetric. A special attention is devoted to the correct formulation of the boundary conditions. A numerical algorithm for studying this motion of the fluid is proposed in [6]. The grid for the discretization of the equations is nonuniform. Difference scheme of Alternating Direction Implicit Method for solving Navier-Stokes equations is used. Numerical results for the stream function, the velocity field and the momentum of the tangential velocity for different Reynolds numbers are obtained by this numerical algorithm. The results are presented graphically. They are discussed and compared with results of other authors. It is observed a very good agreement between them. Keywords: Stirred tank reactor, Navier - Stokes equations; axis-symmetrical swirling viscous flow, numerical investigation. [ABSTRACT FROM AUTHOR]

A second order singularly perturbed differential equation with nonlinear source term modelling chemical processes on semi-infinite interval is considered. The question of transformation of the boundary conditions to a finite interval is studied. We proved that the problem posed on a finite interval does not involve a distinct boundary layer and can be solved with the use of an upwind difference scheme that is uniformly convergent with respect to the small parameter. Numerical experiments are discussed. [ABSTRACT FROM AUTHOR]

An iterative procedure of finding a solution of the initial value problem for a linear anisotropic system of elasticity with polynomial data is described. 3-D images and animated movies of elastic wave propagations in different anisotropic crystals are generated. These images are collected in the library of images. Keywords: 3-D simulation, anisotropic solids, initial value problem, wave propagation. [ABSTRACT FROM AUTHOR]

In this paper, we develop a probabilistic model for estimation of the numbers of cache misses during the sparse matrix-vector multiplication (for both general and symmetric matrices) and the Conjugate Gradient algorithm for 3 types of data caches: direct mapped, s-way set associative with random or with LRU replacement strategies. Using HW cache monitoring tools, we compare the predicted number of cache misses with real numbers on Intel x86 architecture with L1 and L2 caches. The accuracy of our analytical model is around 96%. [ABSTRACT FROM AUTHOR]

The paper is devoted to the eigenvalue problem for a second order strongly elliptic operator. The problem is considered on curved domains, which require interpolated boundary conditions in approximating finite element formulation. The necessary triangulations for solving the eigenvalue problem consists of isoparametric elements of degree n, where n is any integer greater than two. An approximating numerical quadrature eigenvalue problem is investigated. The considered convergence analysis is a crucial point for estimating of the error in approximating eigenvalues. An isoparametric approach is the basic tool for proving the convergence. Keywords: eigenvalue problem, isoparametric FEM, numerical integration. [ABSTRACT FROM AUTHOR]

Results of numerical simulation of soliton-like propagation of two interacting femtosecond laser pulses in bulk media with radial symmetry are presented. Propagation is analysed under conditions of SHG with strong self-action and remarkable phase mismatch for nonzero input amplitudes of both waves. Two NLSE in two spatial coordinates and time with quadratic and cubic nonlinearities govern the process. Numerical simulation was made on the base of conservative difference scheme, taking into account the conservation laws of the problem. Long-time approximation of flat beam profiles was used to reveal the conditions of soliton-like propagation. [ABSTRACT FROM AUTHOR]

An effective difference method is proposed for finding of eigenvalues and eigenfunctions of a nonlinear Shrödinger equation (NLSE) with a cubic nonlinearity, describing the light beam propagation in an optical fiber. The methodical recommendations are given for the NLSE eigenfunctions construction depending on the nonlinearity coefficient and the transverse size of a waveguide. [ABSTRACT FROM AUTHOR]

A difference scheme for problem of femtosecond pulse interaction with semiconductor is proposed in the case of nonlinear dependencies of light energy absorption coefficient and mobility of free electrons from electric field strength. Comparison of some difference schemes efficiency for computation of various regimes of laser pulse interaction with semiconductor is carried out. It is shown that approach developed by us allows to analyze regimes for which difference schemes known earlier are unsuitable. [ABSTRACT FROM AUTHOR]

A Conservative difference scheme is proposed for a problem of three femtosecond pulses interaction in medium with quadratic nonlinearity. Second order dispersion and dispersion of nonlinear response are taking into account under the consideration of femtosecond pulses propagation in nonlinear optical fiber. [ABSTRACT FROM AUTHOR]

In this paper we develop two resultant based methods for the computation of the Greatest Common Divisor (GCD) of two polynomials. Let S be the resultant Sylvester matrix of the two polynomials. We modified matrix S to S*, such that the rows with non-zero elements under the main diagonal, at every column, to be gathered together. We constructed modified versions of the LU and QR procedures which require only the of floating point operations than the operations performed in the general LU and QR algorithms. Finally, we give a bound for the error matrix which arises if we perform Gaussian elimination with partial pivoting to S*. Both methods are tested for several sets of polynomials and tables summarizing all the achieved results are given. Keywords: Greater Common Divisor, Sylvester matrix, Gaussian elimination, QR factorization. [ABSTRACT FROM AUTHOR]

In the present work a numerical model of the heat transfer of a hot free thin viscous film attached on a rectangular colder frame is proposed. If the film is cooled down to its solidification temperature the Stefan boundary condition for the heat flux jump is introduced and a part of the liquid film is transformed into a rigid one. The film is assumed to be under the action of the capillary forces and attractive intermolecular van der Waals forces and to be symmetric to a middle plane. Taking the film thickness as a small parameter, the thermal-dynamic problem in its one-dimensional form is solved numerically by a conservative finite difference scheme on a staggered grid. [ABSTRACT FROM AUTHOR]

By analogy with the theory of good lattice points for the numerical integration of rapidly convergent Walsh series, in the present paper the author use the Price functional system and Haar type functional system, defined in the generalized number system, for numerical integration. We consider two classes of functions, whose Fourier-Price and Fourier-Haar coefficients satisfy specific conditions. For this classes we obtain the exact orders of the error of the quadrature formula with good lattice points, constructed in the generalized number system. Keywords: Numerical integration, Good lattice points, Price functions, Haar type functions, Estimation of the error. [ABSTRACT FROM AUTHOR]

This paper discusses how to control the accuracy of inexact matrix-vector products in restarted GMRES. We will show that the GMRES iterations can be performed with relatively low accuracy. Furthermore, we will study how to compute the residual at restart and propose suitable strategies to control the accuracy of the matrix-vector products in this computation. [ABSTRACT FROM AUTHOR]

Multivariate ideal interpolation schemes are deeply connected with H-bases. Both the definition of a H-basis and of an ideal interpolation space depend of the notion of degree used in the grading decomposition of the polynomial spaces. We studied, in the case of bivariate polynomials, a generalized degree, introduced by T. Sauer and named w-degree. This article give some theoretical results that allow us to construct algorithms for calculus of the dimension of the homogeneous spaces of bivariate polynomials of w - degree n. We implemented these algorithms in C++ language. The analysis of the results obtained, leads us to another theoretical conjecture which we proved in the end. [ABSTRACT FROM AUTHOR]

The aim of this article is to introduce and to study a generalization of the error order of interpolation, named λ - error order of interpolation. This generalization makes possible a deeper analysis of the error in the interpolation process. We derived the general form of the λ - error order of interpolation and then we applied it for many choices of the functional λ. [ABSTRACT FROM AUTHOR]

In this paper, the finite difference scheme for solving the Cauchy problem for the simplified Euler system in a class of discountinuous functions, which describes irrational flow of fluid by neglecting the viscosity and temperature effects is investigated. For this purpose, firstly the Euler system is decomposed with respect to its coordinates. Then an auxiliary problem which is superiour to the main problem in terms of obtaining the solution is introduced, and shown that the solutions of this auxiliary problem are smoother than the solutions of the main problem. Additionally, the auxiliary problem provides to develop effective and efficient algorithms. Keywords: Computational hydrodynamics, compressible and incompressible flow, Euler systems, numerical modeling, shock waves. [ABSTRACT FROM AUTHOR]

A technique for adaptive conjugate smoothing of discontinuous fields is presented in the paper. The described technique is applicable in various engineering problems and is especially effective when hybrid numerical - experimental methodologies are used. Adaptive smoothing strategy is illustrated for a discontinuous plain stress field problem when photoelastic fringes representing the variation of stress are constructed in virtual projection plane. Keywords: Finite element method, adaptive smoothing, visualization [ABSTRACT FROM AUTHOR]

The one-phase Stefan problem in enthalpy formulation, describing the freezing of initially supercooled droplets that impact on solid surfaces, is solved numerically by the finite volume method on a non-orthogonal body fitted coordinate system, numerically generated. The general case of third order boundary conditions on the droplet is considered. The numerical results for the simple case of a spherical droplet touching a surface at first order boundary conditions are validated well by the known 1D asymptotic solution. The proposed solution method occurs faster than another method, based on ADI implicit finite-difference scheme in cylindrical coordinates, for the same droplet shapes. [ABSTRACT FROM AUTHOR]

The paper deals with the condition number estimation and the computation of residual-based forward error estimates in the numerical solution of the matrix Riccati equations. Efficient, LAPACK-based condition and error estimators are proposed involving the solution of triangular Lyapunov equations along with one-norm computation. [ABSTRACT FROM AUTHOR]

Large scale air pollution models are powerful tools, designed to meet the increasing demand in different environmental studies. The atmosphere is the most dynamic component of the environment, where the pollutants can be moved quickly on far distnce. Therefore the air pollution modeling must be done in a large computational domain. Moreover, all relevant physical, chemical and photochemical processes must be taken into account. In such complex models operator splitting is very often applied in order to achieve sufficient accuracy as well as efficiency of the numerical solution. The Danish Eulerian Model (DEM) is one of the most advanced such models. Its space domain (4800 × 4800 km) covers Europe, most of the Mediterian and neighboring parts of Asia and the Atlantic Ocean. Efficient parallelization is crucial for the performance and practical capabilities of this huge computational model. Different splitting schemes, based on the main processes mentioned above, have been implemented and tested with respect to accuracy and performance in the new version of DEM. Some numerical results of these experiments are presented in this paper. [ABSTRACT FROM AUTHOR]

Let ϕ be analytic iterative vector function with fixed point α and integer order p > 1. It is proved that for each approximation z0 of α and enough close to α the corresponding iterative process zk + 1=ϕ(zk) converges to α with order p. Using this result we give new shorter proofs for convergence of some well known iterative methods and of iterative methods proposed by authors for solving of nonlinear equations and systems of equations. [ABSTRACT FROM AUTHOR]

A new method is proposed for finding all maxima and minima of a multivariable function f in a box . In this method, the maxima and the minima are calculated by dividing into subregions recursively and bounding the ranges of f in the each subregion applying affine arithmetic[1 2] and discarding the subregions which don't possess the possibility of including the point that the maximum (minimum) value occurs. Moreover, to discard more subregions in initial stage, i.e. to speed the new method, two algorithms are introduced. And to show the efficiency of the new method, some numerical examples are implemented. [ABSTRACT FROM AUTHOR]

We consider the problem of computing transitive closure of a given directed graph on the regular bidirectional systolic array. The designed array has n PEs, where n is a number of nodes in the graph. This is an optimal number for a given problem size. [ABSTRACT FROM AUTHOR]

This paper presents a dynamical model of an active control system for seismic-resistant building structures. Three optimal performance indexes: LQR, discrete time-dependent non-integral and generalized LQR, based on linear quadratic optimization are considered. The maximum structural response and maximum active control force versus control design parameters are studied. The influence of the time increment used in response analysis on the algorithm is investigated. Numerical examples illustrate the effectiveness of the proposed algorithms in reducing the structural response . [ABSTRACT FROM AUTHOR]

In this paper a general model is developed for the simulation of one dimensional diffusion annealing. Our main interest is the determination of the diffusion coefficient from measured values at discrete space-time points within the sample. The method is based on a suitable reduction of the pde to a system of odes by a second order finite difference space discretization. The inverse problem is solved by implementation of the Levenberg-Marquardt method. This allows the estimation of the parameters and the determination of Cramér-Rao lower bounds. [ABSTRACT FROM AUTHOR]

QR algorithm for eigenproblems is often applied with single or double shift strategies. To save computation effort, double implicit shift technique is employed. In Watkins and Elsner[1], a higher-order shift strategy, generalized Rayleigh quotient shift strategy, is introduced. In this paper, we give a generalization of the double implicit shift technique for the higher-order strategy, and compare the computation cost for different orders with numerical experiments. [ABSTRACT FROM AUTHOR]

It was recently shown that block-circulant preconditioners applied to a conjugate gradient method used to solve structured sparse linear systems arising from 2D or 3D elliptic problems have good numerical properties and a potential for high parallel efficiency. The asymptotic estimate for their convergence rate is as for the incomplete factorization methods but the efficiency of the parallel algorithms based on circulant preconditioners are asymptotically optimal. In this paper parallel performance of a circulant block-factorization based preconditioner applied to a 3D model problem is investigated. The aim of this presentation is to analyze the performance and to report on the experimental results obtained on shared and distributed memory parallel architectures. A portable parallel code is developed based on Message Passing Interface (MPI) and OpenMP (Open Multi Processing) standards. The performed numerical tests on a wide range of parallel computer systems clearly demonstrate the high level of parallel efficiency of the developed parallel code. [ABSTRACT FROM AUTHOR]

We give an algorithm to obtain formulae and values for minors of skew Hadamard and conference matrices. One step in our algorithm allows the (n-j) × (n-j) minors of skew Hadamard and conference matrices to be given in terms of the minors of a 2j-1 × 2j-1 matrix. In particular we illustrate our algorithm by finding explicitly all the (n-3) × (n-3) minors of such matrices. [ABSTRACT FROM AUTHOR]

The sensitivity of generalized matrix Lyapunov equations relative to perturbations in the coefficient matrices is studied. New local and non-local perturbation bounds are obtained. [ABSTRACT FROM AUTHOR]

Approximations to the volume integrals with logarithmic kernels are obtained as solutions to finite difference schemes on the regular grid in a rectangular domain, which contains the domain of integration. Two types of right-hand sides in the finite difference equations are constructed - the first one includes some double and line integrals and the second one is fully discrete. The error estimates (optimal with respect to the smoothness of the volume integral) for both types of right-hand sides are obtained for volume integrals in appropriate Besov spaces. Keywords: volume integrals, integral equations, particular solution, Poisson equation. [ABSTRACT FROM AUTHOR]

A technique combined the Rothe method with two-grid (coarse and fine) algorithm of Xu [18] for computation of numerical solutions of nonlinear parabolic problems with various boundary conditions is presented. For blow-up solutions we use a decreasing variable step in time, according to the growth of the solution. We give theoretical results, concerning convergence of the numerical solutions to the analytical ones. Numerical experiments for comparison the accuracy of the algorithm with other known numerical schemes are discussed. [ABSTRACT FROM AUTHOR]

The Farey tree is a binary tree containing all rational numbers from [0, 1] in ordered way. It is constructed hierarchically, level by level, using the Farey mediant sum. Some extreme properties of the Farey sum tree, i.e., the set of points {p+q} associated with Farey tree in the way that rationals {p/q} belong to k-th level of the Farey tree are investigated. [ABSTRACT FROM AUTHOR]

A numerical approach for solving systems of nonautonomous ordinary differential equations (ODEs) is proposed under suitable assumptions. This approach is based on expansion of the solutions of ODEs by Volterra series and allows to estimate the distance between the obtained approximation and the true trajectory. [ABSTRACT FROM AUTHOR]

A technique combining the Rothe method with the immersed interface method (IIM) of R. Leveque and Z. Li, [8] for numerical solution of parabolic interface problems in which the jump of the flux is proportional to a given function of the solution is developed. The equations are discretized in time by Rothe's method. The space discretization on each time level is performed by the IIM. Numerical experiments are presented. AMS Subject Classification: 65N06, 35K55, 35K57. Keywords: immersed interface method, nonlinear parabolic problems, delta-Dirac function, finite difference schemes, Cartesian grids. [ABSTRACT FROM AUTHOR]

Adaptive filtering is an important subfield of digital signal processing having been actively researched for more than four decades and having important applications such as noise cancellation, system identification, and telecommunications channel equalization. In this paper we provide a novel framework for adaptive filtering based on the theory stationary iterative linear equation solvers. We show that a large number of established, and some quite novel, adaptive filtering algorithms can be interpreted as special cases of a generic update equation forming the cornerstone of our framework. The novelty of our contribution is the casting of the adaptive filtering problem as a problem in numerical linear algebra facilitating a clearer understanding and a unified analysis of the various algorithms. [ABSTRACT FROM AUTHOR]