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The Cubic Symplectic Theta Function
Journal of Mathematical Sciences, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Generalized Cubic Functional Equation
Acta Mathematica Sinica, English Series, 2005The author solves the functional equation \[ f_1(2x+y)+f_2(2x-y)=f_3(x+y)+f_4(x-y)+f_5(x), \qquad x,y \in \mathbb R, \] where \(f_1, f_2, f_3, f_4, f_5: \mathbb R \to \mathbb R\). The general solution, obtained by elementary methods, is made up via diagonal of multiadditive symmetric functions. This result is then extended to the case of functions from
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Cubic Identities of Theta Functions
The Ramanujan Journal, 1998A number of useful and interesting cubic identities involving theta functions are available in Ramanujan's Lost Note book. In this paper several theorems are established, in order to prove, some of these cubic identities. For proving the theorems the author employed addition formulas, the Jacobi triple product identity and the quintuple product ...
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A Green’s function for a cubic lattice
Journal of Mathematical Physics, 1978The following Green’s function for a cubic lattice is evaluated exactly and expressed in terms of the complete elliptic integrals of the first kind: G (E) = (1/π3) ℱℱℱπ0 dxdydz/[E −a1cosx−a2cosy−a3cosz−a2cosycosz−a1 coszcosx].
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Mathematical Proceedings of the Cambridge Philosophical Society, 1979
Although the classification of affine cubic curves was undertaken by Newton(4), in one of the first major exercises ever in coordinate geometry (see Cayley(2) for a fuller account), a parallel study of cubic functions seems not to have been contemplated till recently.
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Although the classification of affine cubic curves was undertaken by Newton(4), in one of the first major exercises ever in coordinate geometry (see Cayley(2) for a fuller account), a parallel study of cubic functions seems not to have been contemplated till recently.
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The generalized cubic functional equation and the stability of cubic Jordan $$*$$ ∗ -derivations
ANNALI DELL'UNIVERSITA' DI FERRARA, 2013Several definitions of ``cubic functional equations'' have been already given. Here, the authors introduce a new one: \[ \begin{multlined} f(x+my)+f(x-my) =2(2\cos\left(\frac{m\pi}{2}\right)+m^2-1)f(x)\\ -\frac{1}{2}(\cos\left(\frac{m\pi}{2}\right)+m^2-1)f(2x) +m^4(f(x+y)+f(x-y)), \end{multlined} \] where \(m\) is an integer not less than 2.
Bodaghi, Abasalt +2 more
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Mathematical Proceedings of the Cambridge Philosophical Society, 1980
The classification of affine cubic functions in the real case is a fairly easy corollary of that in the complex case (9). However as the results can be easily interpreted by diagrams, one can obtain a much richer understanding. For example, the question of which types of cubic curve occur as level curves of which types of function is now much less ...
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The classification of affine cubic functions in the real case is a fairly easy corollary of that in the complex case (9). However as the results can be easily interpreted by diagrams, one can obtain a much richer understanding. For example, the question of which types of cubic curve occur as level curves of which types of function is now much less ...
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Biomechanical Analysis with Cubic Spline Functions
Research Quarterly. American Alliance for Health, Physical Education and Recreation, 1977Abstract The purpose of this study was to determine if the cubic spline could provide accurate smoothed estimates of displacement-time functions and corresponding time derivatives for typical biomechanical data obtained from cinematographical records. Various experiments were conducted to ascertain a procedure for determining the error associated with ...
T M, McLaughlin +2 more
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Cubic hermite and cubic spline fractal interpolation functions
AIP Conference Proceedings, 2012Despite that the spline theory is a well studied topic, its relationship with the fractal theory is novel. Fractal approach offers a single specification for a large class of interpolants of which the classical spline is a particular member, and hence possesses considerable flexibility in the choice of an interpolant.
A. K. B. Chand, P. Viswanathan
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Integral of negative powers of cubic functions
Applied Mathematics Letters, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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