Functions and Equations
M27 Inverse Circ Functions and Equations.pdf
... 1 Evaluate values involving inverse circular functions. 2 Solve equations involving inverse circular functions.[r] ...
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Functional equations from generating functions: a novel approach to deriving identities for the Bernstein basis functions
... sis functions as well as a novel derivation for the two-term formula for the derivatives of the nth degree Bernstein basis ...functional equations, we give new deriva- tions for the sum and alternating sum ...
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Lyapunov functions and strict stability of Caputo fractional differential equations
... differential equations is the stability of ...differential equations causes many ...Lyapunov functions to study a nonlinear Caputo fractional differential equation is ...differential equations are ...
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Linear equations and functions ALGEBRAIC MODELLING
... This chapter, Linear equations and functions, revised algebraic skills and introduced the concept of the linear function and its applications. Make sure you master the algebraic techniques required to ...
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The application of block pulse functions for solving higher order differential equations with multi point boundary conditions
... differential equations associated with multi-point boundary ...pulse functions frequently have been applied to approximate the solution of ordinary differential equations associated with the initial ...
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Phase functions as solutions of integral equations
... The radiative transfer equation (RTE), which models light propagation in scattering media, contains two un- known functions: the radiance and the scattering phase function. Usually, the phase function is modeled ...
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Nonparametric estimating equations for circular probability density functions and their derivatives
... estimating equations for circular density estimation (and its derivatives) where local versions of population trigonometric moments are equated with their empirical ...of functions at a point, as opposed to ...
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Application of new basis functions for solving nonlinear stochastic differential equations
... pulse functions [7], but we use from the stochastic operational matrix based on properties of the NBFs without ...of equations, moreover, the computational cost of operations is ...
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On Applications of Generalized Functions in the Discontinuous Beam Bending Differential Equations
... differential Equations. This problem is solved by the use of generalized functions, among which is the well known Dirac delta ...differential Equations of a Timoshenko beam with jump discontinuities ...
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Lyapunov functions for linear nonautonomous dynamical equations on time scales
... Lyapunov functions are a very useful tool for investigating the behaviour of dynamical ...differential equations of many types [15] as well as difference equations ...Lyapunov functions on time ...
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An application of Lauricella hypergeometric functions to the generalized heat equations
... conduction equations into ordinary differential equations, therefore, precise so- lutions can be easily obtained ...differential equations with the modified Riemann-Liouville derivative ...
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Mean periodic functions and ordinary differential equations
... For E E = if the ¢R, the space of all complex-valued continuous functions defined on the real line and equipped with the topology of convergence uniform on all compact subsets of R, Schw[r] ...
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The solving integro-differential equations of fractional order with the ultraspherical functions
... differential equations for mathematical modeling of real world physical problems has been widely developed in recent years, ...generalized functions ap- proaches ...
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On Solutions of a System of Wiener-Hopf Integral Equations
... Proof. For part (a), we take a contour that encloses the spectrum of G but does not enclose zero. For part (b), sup- pose, λ(x) and µ(x), respectively, represent the largest and the smallest eigenvalues of G(x). The ...
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Stochastic Differential Equations: Models and Numerics - Free Computer, Programming, Mathematics, Technical Books, Lecture Notes and Tutorials
... We can state our problem in optimal control terms as the maximization of an objective function, the expected profit from selling electricity power during a given period, with respect to control functions, like the ...
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Existence Theorems for First Order Equations on Time Scales with Carathéodory Functions
... first-order equations on time ...Carath´eodory functions which are more general than continuous functions used for systems studied in 6, ...first-order equations of time scale with ...
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On certain Heun functions, associated functions of discrete variables, and applications
... mulas (Section 4) and integral equations (Section 6). The coefficients of these series constitute orthogonal (J-orthogonal or biorthogonal) bases in certain se- quence spaces (Sections 3 and 5). Some of them are ...
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Superlinear Equations Involving Nonlinearities Limited by Asymptotically Homogeneous Functions
... the nonlinearity f is superlinear at zero, and it is located near infinity between two func- tions that belong to a class of functions where the Ambrosetti-Rabinowitz condition is satisfied. More precisely, we ...
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Numerical Solution to Euler–Cauchy Equation with Neumann Boundary Conditions Using B-Spline Collocation Method
... basis functions are used as the basis in B-spline collocation method whereas the base functions which are used in normal collocation method are the polynomials vanishes at the boundary ...
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Numerical Solution of Singular IVPs of Lane-Emden Type Using Integral Operator and Radial Basis Functions
... Lane-Emden equations as singular initial value prob- lems is ...Lane-Emden equations to integral equations and interpolation by radial basis functions ...integral equations to the ...
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