Abstract:
A tomographic method is considered that forms images from sets of spatially randomized source signals and receiver sensitivities. The method is designed to allow image reconstruction for an extended number of transmitters and receivers in the presence noise and without plane wave approximation or otherwise approximation on the size or regularity of source and receiver functions. An overdetermined set of functions are formed from the Hadamard product between a Gaussian function and a uniformly distributed random number set. It is shown that this particular type of randomization tends to produce well-conditioned matrices whose pseudoinverses may be determined without implementing relaxation methods. When the inverted sets are applied to simulated first-order scattering from a Shepp-Logan phantom, successful image reconstructions are achieved for signal-to-noise ratios (SNR) as low as 1. Evaluation of the randomization approach is conducted by comparing condition numbers with other forms of signal randomization. Image quality resulting from tomographic reconstructions is then compared with an idealized synthetic aperture approach, which is subjected to a comparable SNR. By root-mean-square-difference comparisons it is concluded that - provided a sufficient level of oversampling - the dynamic transmit and dynamic receive approach produces superior images, particularly in the presence of low SNR.

Abstract:
Field characterization methods using a scattering target in the absence of a point-like receiver have been well described in which scattering is recorded by a relatively large receiver located outside the field of measurement. Unfortunately, such methods are prone to artifacts due to averaging across the receiver surface. To avoid this problem while simultaneously increasing the gain of a received signal, the present study introduces a binary plate lens designed to focus spherically-spreading waves onto a planar region having a nearly-uniform phase proportional to that of the target location. The lens is similar to a zone plate, but modified to produce a bi-convex-like behavior, such that it focuses both planar and spherically spreading waves. A measurement device suitable for characterizing narrowband ultrasound signals in air is designed around this lens by coupling it to a target and planar receiver. A prototype device is constructed and used to characterize the field of a highly-focused 400 kHz air transducer along 2 radial lines. Comparison of the measurements with numeric predictions formed from nonlinear acoustic simulation showed good relative pressure correlation, with mean differences of 10% and 12% over center 3dB FWHM drop and 12% and 17% over 6dB.

Abstract:
We generalized the characterization of H-closedness for linearly ordered pospaces as follows: A pospace $X$ without an infinite antichain is an H-closed pospace if and only if $X$ is a directed complete and down-complete poset such that sup $L$ and inf $L$ are contained in the closure of $L$ for any nonempty chain $L$ in $X$.

Abstract:
We notice that Haynes-Hedetniemi-Slater Conjecture is true (i.e. $\gamma(G) \leq \frac{\delta}{3\delta -1}n$ for every graph $G$ of size $n$ with minimum degree $\delta \geq 4$, where $\gamma(G)$ is the domination number of $G$). Because the conjecture for $\delta =6$ follows from the estimate n (1 - \prod_{i= 1}^[\delta + 1} (\delta i)/(\delta i + 1) by W. E. Clark, B. Shekhtman, S. Suen [Upper bounds of the Domination Number of a Graph, Congressus Numerantium, 132 (1998), pp. 99-123.]

Abstract:
Let $M$ be an orientable connected closed surface and $f$ be an $R$-closed homeomorphism on $M$ which is isotopic to identity. Then the suspension of $f$ satisfies one of the following condition: 1) the closure of each element of it is minimal and toral. 2) there is a minimal set which is not locally connected. Moreover, we show that any positive iteration of an $R$-closed homeomorphism on a compact metrizable space is $R$-closed.

Abstract:
Let $\mathcal{F} $ be a pointwise almost periodic decomposition of a compact metrizable space $X$. Then $\mathcal{F} $ is $R$-closed if and only if $\hat{\mathcal{F}} $ is usc. Moreover, if there is a finite index normal subgroup $H$ of an $R$-closed flow $G$ on a compact manifold such that the orbit closures of $H$ consist of codimension $k$ compact connected elements and "few singularities" for $k = 1$ or 2, then the orbit class space of $G$ is a compact $k$-dimensional manifold with conners. In addition, let $v$ be a nontrivial $R$-closed vector field on a connected compact 3-manifold $M$. Then one of the following holds: 1) The orbit class space $M/ \hat{v}$ is $[0,1]$ or $S^1$ and each interior point of $M/ \hat{v}$ is two dimensional. 2) $\mathrm{Per}(v)$ is open dense and $M = \mathrm{Sing}(v) \sqcup \mathrm{Per}(v)$. 3) There is a nontrivial non-toral minimal set. On the other hand, let $G$ be a flow on a compact metrizable space and $H$ a finite index normal subgroup. Then we show that $G$ is $R$-closed if and only if so is $H$.

Abstract:
In this paper, we define the recurrence and "non-wandering" for decompositions. The following inclusion relations hold for codimension one foliation on a closed 3-manifolds: p.a.p. $\subsetneq$ recurrent $\subsetneq$ non-wandering.Though each closed 3-manifold has codimension one foliations, no codimension one foliations exist on some closed 3-manifolds.