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...

We present a general semidefinite relaxation scheme for general n-variate quartic polynomial optimization under homogeneous quadratic constraints. Unlike the existing sum-of-squares (SOS) approach which relaxes the quartic optimization problems to a sequence of (typically large) linear semidefinite programs (SDP), our relaxation scheme leads to a (possibly nonconvex) quadratic optimization prob...

The dilaton theorem implies that the contribution to the dilaton potential from cubic interactions of all levels must be cancelled by the elementary quartic self-coupling of dilatons. We use this expectation to test the quartic structure of closed string field theory and to study the rules for level expansion. We explain how to use the results of Moeller to compute quartic interactions of state...

We detail the continued fraction expansion of the square root of the general monic quartic polynomial. We note that each line of the expansion corresponds to addition of the divisor at infinity, and interpret the data yielded by the general expansion. The paper includes a detailed ’reminder exposition’ on continued fractions of quadratic irrationals in function fields. A delightful ‘essay’ [16]...

A search for Higgs boson pair production via vector-boson fusion (VBF) in the $b\bar{b}b\bar{b}$ final state is carried out with ATLAS experiment using 126 fb$^{-1}$ of proton-proton collision data delivered at $\sqrt{s} = 13$ TeV by Large Hadron Collider. This sensitive to VBF additional heavy bosons that may decay into pairs, and a non-resonant topology it can constrain quartic coupling betwe...

This paper is focused on the bifurcation of critical periods from a quartic rigidly isochronous center under any small quartic homogeneous perturbations. By studying the number of zeros of the first several terms in the expansion of the period function in ε, it shows that under any small quartic homogeneous perturbations, up to orders 1 and 2 in ε, there are at most two critical periods bifurca...

We obtain the general solution of the generalized quartic functional equation f(x + my) + f(x - my) = 2(7m - 9)(m - 1)f(x) + 2m²(m² - 1)f(y)-(m - 1)² f(2x) + m²{f(x + y) + f(x - y)} for a fixed positive integer m. We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces. We also investigate the Hyers-Ulam stab...

The tree-level string effective action is known to contain quartic Riemann terms with coefficient $\zeta(3)\alpha'^3$. In the case of type II this first $\alpha'$ correction. We use requirement that reduced on a $d$-torus should have an $O(d,d)$ symmetry find B-field couplings up fifth order in fields. answer turns out surprisingly intricate structure.

In this work, we introduce a new type of generalised quartic functional equation and obtain the general solution. We then investigate stability results by using Hyers method in modular space for equations without Fatou property, ?b-condition both property. Moreover, with help fixed-point technique involving idea property spaces. Furthermore, suitable counter example is also demonstrated to prov...