We consider the size of large character sums, proving new lower bounds for ∆(N, q) = supχ6=χ0 mod q | ∑ n<N χ(n)| in almost all ranges of N . The proofs use the resonance method and saddle point analysis.

We show the existence of solutions for a second-order multi-point boundary-value problem at resonance on a half-line, where the dimension of the kernel of the differential operator is 2. Our main tools are the coincidence degree theory due to Mawhin, suitable operators, and algebraic methods. Our results are illustrated with an example.

A power allocation to active and reactive power in stochastic resonance is discussed for energy harvesting from noise. It is confirmed that active power can be increased at stochastic resonance, in the same way of the relationship between energy and phase at an appropriate setting in resonance. key words: stochastic resonance, white Gaussian noise, energy harvesting, active and reactive power, ...

A model-independent method for the determination of Breit-Wigner resonance parameters is presented. The method is based on eliminating the dependence on the choice of channel basis by analyzing the trace of the K and T matrices in the coupled-channel formalism, rather than individual matrix elements of the multichannel scattering matrix.

We obtain exact scattering solutions of the Dirac equation in 1 1 dimensions for a double square barrier vector potential. The potential bottom between the two barriers is chosen to be higher than 2mc2, whereas the top of the barriers is at least 2mc2 above the bottom. The relativistic version of the conventional double barrier transmission resonances is obtained for energies within ±mc2 from t...

This paper studies the particle motion when the tune is in the stable region close to the edge of linear sum resonance stopband. Results are found for the tune and the beta functions. Results are also found for the two solutions of the equations of motion. The results found are shown to be also valid for small accelerators where the large accelerator approximation may not be used.

In the present paper a dual frequency resonance antenna is achieved by introducing Lshaped slot in circular disk patch. It is analysed by using circuit theory concept. The resonance frequency is found to be 5.087 and 8.455 GHz and the 10 dB bandwidth of the proposed antenna for lower and upper resonance frequency is found to be 4.39 and 4.66 % respectively. It is easy to adjust the higher and l...

Incoherent photoproduction of pions on the deuteron in the first resonance region is investigated with special emphasis on single-spin asymmetries. For the elementary pion production operator an effective Lagrangian model which includes the standard pseudovector Born terms and a resonance contribution from the ∆(1232)-excitation is used. Single-spin asymmetries, both for charged and neutral pio...

It is shown that the random electric fields of charged dislocations in insulators should cause appreciable broadening of sharp resonance lines such as spin-resonance signals. The degree of broadening is very sensitive to the screening of the dislocations by charged point defects. Since the shape of the inhomogeneously broadened resonance line monitors the distribution of the internal fields, th...

The mechanosensory hair cells of many auditory receptor organs are tuned by an electrical resonance that increases their responses to stimulation over a narrow band of frequencies. The small oscillations of membrane potential characteristic of this phenomenon have previously been detectable only through intracellular electrode measurements, which are laborious and preclude analysis at the level...