Functional analysis
Normed linear spaces. Contraction mapping theorem. Applications to differential and integral equations. Linear transformations. Product spaces and Fubini's theorem. Projection and self-adjoint operators. Gram-Schmidt orthonormalization. Fourier analysis.
Подобные документы
Absolute value of a complex number, and conjugate complex number. Integral powers and roots of complex numbers. Taylor’s and Laurent’s theorems. Evaluation of integral of meromorphic function. Fundamental elementary functions of complex variables.
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статья, добавлен 19.02.2016Using a generalized Dunkl translation, we obtain an analog of theorem 5.2 in Younis’ paper for the Dunkl transform for functions satisfying the (d, g)-Dunkl Lipschitz condition in the space L2(R,|x|2a+1dx). Consideration generalized Dunkl translation.
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статья, добавлен 24.01.2017Evidence the well-posedness of Fourier problems for anisotropic parabolic equations with variable exponents of nonlinearity without any assumptions on the solution behavior and growth of the initial data as time variable tends to minus in nity.
статья, добавлен 19.02.2016Investigation analytically specificity of numerical integration of ordinary second-order differential equations for systems with Coulomb and viscous friction. Developing and extending of modification of Runge-Kutta formulas for mentioned systems.
статья, добавлен 14.09.2016Combinatorial description. Teichmuller curves. Recurrence relation. Asymptotics of numbers of branched coverings of a torus, volumes of moduli spaces of holomorphic differentials. The character of the infinite wedge representation. Cylinder decomposition.
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статья, добавлен 30.10.2016Description of a variational graph-theoretic. Brief review of linear graph principles. Generate the equations of motion with elastic deformations, the flexible bodies are discretized using two types of finite elements. Discretize unidirectional bodies.
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статья, добавлен 29.01.2016- 40. Improving the mathematical model of the dynamics for underwater vehicles with asymmetrical hulls
Model of motion, which takes into account the asymmetry of hulls, infiltration processes and surface waves in the form of a system of nonlinear differential equations. Estimation of the error as a function of the magnitude of the initial velocities.
статья, добавлен 25.10.2016 - 41. Auto-Associative Models, Nonlinear Principal Component Analysis, Manifolds and Projection Pursuit
Auto-associative models as a new tool for building nonlinear principal component analysis methods. The successive approximations of a dataset by manifolds of increasing dimensions. The theoretical comparison between PCA and auto-associative models.
статья, добавлен 08.02.2013 The construction of lower-dimensional manifolds from high-dimensional data is an important task in data mining, machine learning and statistics. The authors consider principal manifolds as a regularized, non-linear empirical quantization error functional.
статья, добавлен 08.02.2013Teaching students of mathematical fields of training to inverse problems. Implementation of the scientific, educational potential of teaching university students inverse problems for differential equations. Computational methods of mathematical physics.
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учебное пособие, добавлен 25.11.2013The manual contains definitions, formulas, theorems of the differential calculus of functions of one variable. Derivative and its geometrical and physical meaning. Applying differential to approximate calculations. Extremum of function, the quotient rule.
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учебное пособие, добавлен 30.07.2016Putnam argues that, by reinterpretation, the Axiom of Constructibility can be saved from empirical refutation. This paper contends that this argument fails, which leaves Putnam’s sweeping appeal to the Lowenheim - Skolem Theorem inadequately motivated.
статья, добавлен 10.09.2012Prime and composite numbers. The fundamental theorem of arithmetic states. Sample factorizations. Review of elementary number theory. Some essential algorithms. RSA public-key cryptosystem. Finding squares through products. Large prime variations.
статья, добавлен 15.09.2012The unsupervised methods required to reduce the dimension of the data set and to extract meaningful biological information. This work shows that Independent Component Analysis is a promising approach for the analysis of genome-wide transcriptomic data.
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