In signal processing, four functions of one variable are commonly used. They are the signal in time, the spectrum, the auto-correlation function of the signal, and the auto-correlation function of the spectrum. The variables of these functions are denoted, respectively, as time, frequency, lag, and doppler. In time–frequency analysis, these functions of one variable are extended to quadratic fu...

Ambient mechanical vibrations have emerged as a viable energy source for low-power wireless sensor nodes aiming the upcoming era of the 'Internet of Things'. Recently, purposefully induced dynamical nonlinearities have been exploited to widen the frequency spectrum of vibration energy harvesters. Here we investigate some critical inconsistencies between the theoretical formulation and applicati...

It is shown that an even partition A∪B of the set R = {1, 2, . . . , p− 1} of positive residues modulo an odd prime p is the partition into quadratic residues and quadratic non-residues if and only if the elements of A and B satisfy certain additive properties, thus providing a purely additive characterization of the set of quadratic residues. 1 Additive properties of quadratic residues An inte...

ABSTRACT. A Steiner surface is the generic case of a quadratically parameterizable quartic surface used in geometric modeling. This paper studies quadratic parameterizations of surfaces under the angle of Classical Invariant Theory. Precisely, it exhibits a collection of covariants associated to projective quadratic parameterizations of surfaces, under the actions of linear reparameterization a...

In signal processing, four functions of one variable are commonly used. They are the signal in time, the spectrum, the auto-correlation function of the signal, and the auto-correlation function of the spectrum. The variables of these functions are denoted, respectively, as time, frequency, lag, and doppler. In time-frequency analysis, these functions of one variable are extended to quadratic fu...

In 1940, Ulam 1 gave a wide-ranging talk before a mathematical colloquium at the University of Wisconsin, in which he discussed a number of important unsolved problems. Among those was the following question concerning the stability of homomorphisms. Let G1 be a group, and let G2 be a metric group with a metric d ·, · . Given ε > 0, does there exist a δ > 0 such that if a function h : G1 → G2 s...

Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4 . In particular, Bag and Samanta 5 , following Cheng and Mordeson 6 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 7 . T...

In this paper, we investigate the stability problems for a functional equation f(ax + y) + af(x − y) − a2+3a 2 f(x) −a(a−1) 2 f(−x)− f(y) − af(−y) = 0 by using the fixed point method. Mathematics Subject Classification: Primary 39B82, 39B62; Secondary 47H10