Abstract:
The performance of a microstrip antenna has been known sensitive to substrate’s dielectric properties, which is dependent on the angle of laminate layers inside a composite laminated substrate. Modal analysis in spectral domain is applied to investigate the resonant frequency and radiation pattern of rectangular microstrip antenna on composite substrates. It is shown that the substrate’s dielectric properties are dependent upon the laminate angles, i.e., upon the orientation of the antenna relative to the substrate’s fiber direction. For the same operating frequency, the antenna size on composite substrates is larger than that on isotropic substrates, and the far field pattern is also more directional.

Abstract:
We study the isospectral deformations of the Eguchi-Hanson spaces along a torus isometric action in the noncompact noncommutative geometry. We concentrate on locality, smoothness and summability conditions of the nonunital spectral triples, and relate them to the geometric conditions to be noncommutative spin manifolds.

In high
performance aerospace systems where weight and aerodynamics are of major
concern, fiber reinforced composite laminates can be tailored to achieve
desirable mechanical properties and accommodate low-profile microstrip antenna.
This work aims at the analysis of microstrip antenna array embedded in
composite laminated substrates. The size of a single antenna is first
calculated by spectral domain analysis to model the effects of the substrate’s
electromagnetic property and the orientation of the laminate layers. The
antenna array as well as the feed network, composed of microstrip transmission
lines, quarter wave-length impedance transformers, and T-junction power
dividers, is then tuned to accommodate the effects of the coupling between the
antenna elements and the feed network loss. The performance of the 1 × 2, 1 × 4,
and 1 × 8 linear array and 2 × 2 and 2 × 4 planar array are shown to have
better directivity when embedded in composite laminated substrate compared with
those when attached on isotropic substrate. Both 1 × 2 and 1 × 4 arrays at 2.4
GHz are validated experimentally to achieve better coverage.

Abstract:
Utilizing the Schauder fixed point theorem to study existence on positive solutions of an integral equation, we obtain an upper bound of the critical value β involved in the Blasius problem, in particular, β < 18733/105= 0.18733. Previous results only presented a lower bound β ≥ 1/2 and numerical investigations β 0.3541.

Abstract:
The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk process in a one-dimensional lattice. Power law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions. This shows that power-law distributions in self-organized criticality may be caused by the balance of competitive interactions. At the mean time, the mean spatial size for avalanches with the same lifetime is found to increase in a power law with the lifetime.

Abstract:
A method is proposed for exactly calculating the partition function of a rectangular Ising lattice with the presence of a uniform external field. This approach is based on the method of the transfer matrix developed about seventy years ago for the rectangular Ising model in the absence of external field. The basis for the vector space is chosen as the eigenvectors of the diagonal part of the transfer matrix. The matrix elements for the non-diagonal part can be calculated very easily. Then the partition function and thermodynamical quantities can be evaluated. The limit of infinite lattice is discussed.

Abstract:
The effect of finite hadronization time is considered in the recombination model, and it is shown that the hadron multiplicity turns out to be proportional to the initial quark density and unitarity is conserved in the model. The baryon to meson ratio increases rapidly with the initial quark density due to competition among different channels.