Equations Involving the Mean of Almost Periodic Measures

2009 ◽  
pp. 125-133
Author(s):  
Silvia-Otilia Corduneanu
Keyword(s):  
Almost Periodic ◽  
The Mean

scholarly journals Planar Waves of the Buffered Bistable System

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Xiaohuan Wang ◽  
Guangying Lv
Keyword(s):  
Large Time ◽  
Mean Curvature Flow ◽  
Large Time Behavior ◽  
Bistable System ◽  
Time Behavior ◽  
Almost Periodic ◽  
Drift Term ◽  
Planar Front ◽  
Special Cases ◽  
The Mean

This paper is concerned with the large time behavior of disturbed planar fronts in the buffered bistable system inℝn(n≥2). We first show that the large time behavior of the disturbed fronts can be approximated by that of the mean curvature flow with a drift term for all large time up tot=+∞. And then we prove that the planar front is asymptotically stable inL∞(ℝn)under ergodic perturbations, which include quasiperiodic and almost periodic ones as special cases.

scholarly journals Distribution of Small Values of Bohr Almost Periodic Functions with Bounded Spectrum

2019 ◽  
pp. 571-578
Author(s):  
Wayne M. Lawton
Keyword(s):  
Periodic Function ◽  
Riemann Hypothesis ◽  
Mahler Measure ◽  
Trigonometric Polynomials ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Periodic Functions ◽  
The Mean ◽  
Relationship Of ◽  
The Relationship

For f a nonzero Bohr almost periodic function on R with a bounded spectrum we proved there exist Cf > 0 and integer n > 0 such that for every u > 0 the mean measure of the set f x : jf(x)j < u g is less than Cf u1=n: For trigonometric polynomials with n + 1 frequencies we showed that Cf can be chosen to depend only on n and the modulus of the largest coefficient of f: We showed this bound implies that the Mahler measure M(h); of the lift h of f to a compactification G of R; is positive and discussed the relationship of Mahler measure to the Riemann Hypothesis

scholarly journals Accumulation distribution in terre adélie, antarctica: effect of meteorological parameters

1986 ◽  
Vol 32 (112) ◽  
pp. 486-500 ◽  
Author(s):  
P. Pettre ◽  
J.F. Pinglot ◽  
M. Pourchet ◽  
L. Reynaud
Keyword(s):  
Surface Roughness ◽  
Spatial Distribution ◽  
Meteorological Parameters ◽  
Mean Value ◽  
Almost Periodic ◽  
Data Set ◽  
Periodic Oscillations ◽  
Terre Adélie ◽  
The Mean ◽  
Spatio Temporal

AbstractAlong the 1040 km extending from Cape Prud’homme (lat. 66°41’S., long. 139°55’ E.), near Dumont d’Urville station, to Dome C (lat. 74°39’S., long. 124°10’E.), the variations in annual accumulation can be analysed by a division of the entire data set into three sub-sets depending on the types of measurements and the character of the spatial distribution. Along the first 33 km, from the coast to stake E40, annual measurements show considerable inter-annual variability, 52% of which can be explained by the spatio-temporal homogeneity of the balance distribution. However, we obtain a better result (64%) for the fluctuation homogeneity standardized using the standard deviation. This means that there is a strong space-time dis-tribution structure, characterized by an equal variation of the balance around the mean value specific to each location. This is so in spite of the existence of considerable surface roughness (sastrugi), the influence of which should be reduced by averaging values around each stake. From stake E40 to stake R60, a distance of 170 km, the almost periodic oscillations in the accumulation with a wavelength close to 40 km can be explained by the formation of a gravity-inertia wave, disturbing the geostrophic equilibrium, occurring at the break in slope 200 km from the coast. The very low values of accumulation for stakes D55 and D58S show that the oscillations were almost stationary during the study period (about 25 years). Finally, along the 840 km from stake R60 to Dome C we can observe a decrease in accumulation resulting from the decrease in mean temperature.

scholarly journals Conditional Oscillation of Half-Linear Differential Equations with Coefficients Having Mean Values

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Petr Hasil ◽  
Robert Mařík ◽  
Michal Veselý
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Linear Differential Equations ◽  
Almost Periodic ◽  
Mean Values ◽  
Conditional Oscillation ◽  
The Mean ◽  
Linear Differential ◽  
Positive Coefficients ◽  
Oscillation Constant

We prove that the existence of the mean values of coefficients is sufficient for second-order half-linear Euler-type differential equations to be conditionally oscillatory. We explicitly find an oscillation constant even for the considered equations whose coefficients can change sign. Our results cover known results concerning periodic and almost periodic positive coefficients and extend them to larger classes of equations. We give examples and corollaries which illustrate cases that our results solve. We also mention an application of the presented results in the theory of partial differential equations.

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