This letter proposes closed form solutions to the L2sensitivity minimization of second-order state-space digital filters with real poles. We consider two cases of second-order digital filters: distinct real poles and multiple real poles. In case of second-order digital filters, we can express the L2-sensitivity of second-order digital filters by a simple linear combination of exponential functi...

Two-dimensional Hamiltonian systems admitting second invariants which are quartic in the momenta are investigated using the Jacobi geometrization of the dynamics. This approach allows for a unified treatment of invariants at both arbitrary and fixed energy. In the differential geometric picture, the quartic invariant corresponds to the existence of a fourth rank Killing tensor. Expressing the J...

the stability problem of the functional equation was conjectured by ulam and was solved by hyers in the case of additive mapping. baker et al. investigated the superstability of the functional equation from a vector space to real numbers.in this paper, we exhibit the superstability of $m$-additive maps on complete non--archimedean spaces via a fixed point method raised by diaz and margolis.

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This paper presents several results on images of various configurations of conics. We extract information about the plane from single and multiple views of known and unknown conics, based on planar homography and conic correspondences. We show that a single conic section cannot provide sufficient information. Metric rectification of the plane can be performed from a single view if two conics ca...

Solving a quadratic equation P (x) = ax + bx+ c = 0 with real coefficients is known to middle school students. Solving the equation over the quaternions is not straightforward. Huang and So [2] give a complete set of formulas, breaking it into several cases depending on the coefficients. From a result of the second author in [10], zeros of P (x) can be expressed in terms of the zeros of a real ...

Electromagnetic fields and media can be compactly represented by applying the four-dimensional differential-form formalism. In particular, classes of linear (bi-anisotropic) media can be defined in terms of the medium dyadic mapping between the electromagnetic two-forms. As a continuation to the process started by medium dyadics satisfying linear and quadratic algebraic equations, the class of ...

The very good performance of modern density functional theory for molecular geometries and harmonic vibrational frequencies has been well established. We investigate the performance of density functional theory (DFT) for quartic force fields, vibrational anharmonicity and rotationvibration coupling constants, and thermodynamic functions beyond the RRHO (rigid rotorharmonic oscillator) approxima...

The uniqueness has been proved by Piatetskiî-Sapiro and Safarevic. The proof of existence is outlined below. Let o be the closed point of A = Spec C[[t] ]. Let An be the finite covering of A obtained by extracting an nth. root of t; let on be the closed point of An. A family of surfaces over An is a flat, projective map ƒ: Xn —> An such that the generic fiber is smooth, connected, and two dimen...

We present a computational approach for finding all integral solutions of the equation y2 = 1k + 2k + · · ·+xk for even values of k. By reducing this problem to that of finding integral solutions of a certain class of quartic equations closely related to the Pell equations, we are able to apply the powerful computational machinery related to quadratic number fields. Using our approach, we deter...