Singularly Perturbed Linear and Semilinear Hyperbolic Systems: Kinetic Theory Approach to Some Folk’s Theorems

The fact that a solution of a wave equation with strong damping can be approximated by a solution of an appropriate diffusion equation has been common knowledge to physicists and mathematicians for a few decades. In numerous branches of science one can find attempts to prove this results by various ad hoc methods. However, it seems to be difficult to trace a rigorous and exhaustive treatment of the subject. By using a recently developed asymptotic procedure, first applied in kinetic theory, we present a systematic approach to a wide spectrum of singularly perturbed hyperbolic problems and we also hope that our method will provide new insight into the field.     

Aspects of Scalar Brane-World Cosmological Perturbations

We summarize an approach to deal with scalar brane-world cosmological perturbations based on Mukohyama's master equation. We also give its relation to one based on perturbing the effective Einstein's equations on the brane (involving the Weyl fluid).     

Decomposition of Vocal Cycle Length Perturbations into Vocal Jitter and Vocal Microtremor, and Comparison of Their Size in Normophonic Speakers

A statistical method that enables raw vocal cycle length perturbations to be decomposed into perturbations ascribed to vocal jitter and vocal tremor is presented, together with a comparison of the size of jitter and tremor. The method is based on a time series model that splits the vocal cycle length perturbations into uncorrelated cycle-to-cycle perturbations ascribed to vocal jitter and supra-cycle perturbations ascribed to vocal tremor. The corpus was composed of 114 vocal cycle length time series for sustained vowels [a], [i], and [u] produced by 22 male and 16 female normophonic speakers. The results were the following. First, 100 out of 114 time series were decomposed successfully by means of the time series model. Second, vocal perturbations ascribed to tremor were significantly larger than perturbations ascribed to jitter. Third, the correlation between vocal jitter and vocal tremor was moderate, but statistically significant. Fourth, small but statistically significant differences were observed among the three vowel timbres in the relative jitter and the arithmetic difference of jitter and tremor. Fifth, the differences between male and female speakers were not statistically significant in the relative raw perturbations, the relative jitter, or the modulation level owing to tremor.     

On harmonic analysis of causal operators

We follow the group representation theory approach to define causal operators on Banach modules and present some of their spectral properties.     

G-spaces and Fixed Point Sets

For a compact connected group G, in a compact free G-space M every closed subset is the fixed point set of an autohomeomorphism if the weight of M is not bigger than that of G. In a compact group with nonsingleton components, every closed subset is the fixed point set of an autohomeomorphism if and only if the weight of the whole group is not bigger than that of the component of the identity.     

局部对称共形平坦黎曼流形中紧致极小子流形的一个刚性定理

本文研究局部对称共形平坦黎曼流形中紧致极小子流形,得到了这类子流形第二基本形式模长平方关于外围空间Ricci曲率的—个拼挤定理,推广了文[1]中的结果.     

Newtonian versus relativistic nonlinear cosmology

Both for the background world model and its linear perturbations Newtonian cosmology coincides with the zero-pressure limits of relativistic cosmology. However, such successes in Newtonian cosmology are not purely based on Newton's gravity, but are rather guided ones by previously known results in Einstein's theory. The action-at-a-distance nature of Newton's gravity requires further verification from Einstein's theory for its use in the large-scale nonlinear regimes. We study the domain of validity of the Newtonian cosmology by investigating weakly nonlinear regimes in relativistic cosmology assuming a zero-pressure and irrotational fluid. We show that, first, if we ignore the coupling with gravitational waves the Newtonian cosmology is exactly valid even to the second order in perturbation. Second, the pure relativistic correction terms start appearing from the third order. Third, the correction terms are independent of the horizon scale and are quite small in the large-scale near the horizon. These conclusions are based on our special (and proper) choice of variables and gauge conditions. In a complementary situation where the system is weakly relativistic but fully nonlinear (thus, far inside the horizon) we can employ the post-Newtonian approximation. We also show that in the large-scale structures the post-Newtonian effects are quite small. As a consequence, now we can rely on the Newtonian gravity in analyzing the evolution of nonlinear large-scale structures even near the horizon volume.     

Novel Rat-race Hybrid Coupler for RF Front-end Module

In this paper, a novel compact rat-race hybrid coupler incorporating an improved beeline compact microstrip resonant cell(IB-CMRC) is presented firstly. The size of the coupler is reduced by 46.5% than conventional one due to IB-CMRC’s excellent slow-wave effect. The novel coupler possesses strong ability of high-order harmonic suppression (above 30 dB) in addition. The measured insertion loss is comparable to that of a conventional microstrip hybrid coupler. Great potential applications of this IB-CMRC can be explored in MICs and MMICs to reduce the circuits size, suppress harmonics and improve the overall performance of the RF front-end module.     

Real perturbations of complex polynomials

In this article the dynamics of generic C^r (r ≥ 3) perturbations of complex polynomials are considered. The attention is focused on the determination of the existence of large or invariant components of the complement of the basin of ∞, where the interesting dynamics occur.     

RELATIVELY WEAKLY COMPACT SETS IN THE DEN JOY SPACE

Some topological Properties of the completion H of the Denjoy space are studied. In particular sufficient conditions for a subsets of H be relatively compact and characterizations for a subsets of H be restively weakly compact are given.