Diode laser absorption measurements obtained with two-tone frequency-modulation spectroscopy (TTFMS) are combined with tomography to produce spatially resolved quantitative images of fluid flows. The high sensitivity, good accuracy, and high stability of TTFMS absorption measurements permit optical-absorption tomography to be performed with low noise on extremely weakly absorbing objects. The m...

Let R be a commutative ring with identity and let M be a torsion free R-module. Several characterizations of distributive modules are investigated. Indeed, among other equivalent conditions, we prove that M is distributive if and only if any primal submodule of M is irreducible, and, if and only if each submodule of M can be represented as an intersection of irreducible isolated components. MSC...

Let Γ=(V,E) be a graph and ‎W_(‎a)={w_1,…,w_k } be a subset of the vertices of Γ and v be a vertex of it. The k-vector r_2 (v∣ W_a)=(a_Γ (v,w_1),‎…‎ ,a_Γ (v,w_k)) is the adjacency representation of v with respect to W in which a_Γ (v,w_i )=min{2,d_Γ (v,w_i )} and d_Γ (v,w_i ) is the distance between v and w_i in Γ. W_a is called as an adjacency resolving set for Γ if distinct vertices of ...

Let R be a commutative ring with identity and M be a unitary R-module. Let : S(M) −! S(M) [ {;} be a function, where S(M) is the set of submodules ofM. Suppose n 2 is a positive integer. A proper submodule P of M is called(n − 1, n) − -prime, if whenever a1, . . . , an−1 2 R and x 2 M and a1 . . . an−1x 2P(P), then there exists i 2 {1, . . . , n − 1} such that a1 . . . ai−1ai+1 . . . an−1x 2 P...

A bolometer consists of a thermometer with heat capacity C mounted on an absorbing substrate, weakly coupled to a bath at temperature T0 via a thermal conductance G ( Figure 1 ). Resistive bolometers (including both composite and transition-edge bolometers) use the temperature dependence of a resistive element to measure the infrared signal incident on the absorber. In steady-state operation, t...

Far field X-ray grating interferometry achieves extraordinary phase sensitivity in imaging weakly absorbing samples, provided that the grating period is within the transverse coherence length of the X-ray source. Here we describe a cost-efficient process to fabricate large area, 100 nm half-pitch hard X-ray phase gratings with an aspect ratio of 32. The nanometric gratings are suitable for ordi...

The basic premise behind the retrieval is to iterate the mixing ratios of two aerosol models for each size mode. (Weakly and a strongly absorbing aerosol models are used for the fine mode, sea salt and dust models are used for the coarse mode.) Ideally, the retrieval will produce the mixing ratios that best describe the measured radiances at 3-4 wavelengths. (The mixing ratio of dust and sea sa...

Let $G$ be a group with identity $e$. $R$ commutative $G$-graded ring non-zero identity, $S\subseteq h(R)$ multiplicatively closed subset of and $M$ graded $R$-module. In this article, we introduce study the concept $S$-1-absorbing prime submodules. A submodule $N$ $(N:_{R}M)\cap S=\emptyset$ is said to prime, if there exists an $s_{g}\in S$ such that whenever $a_{h}b_{h'}m_{k}\in N$, then eith...

let $n$ be a submodule of a module $m$ and a minimal primary decomposition of $n$ is known‎. ‎a formula to compute baer's lower nilradical of $n$ is given‎. ‎the relations between classical prime submodules and their nilradicals are investigated‎. ‎some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated‎.

let $n$ be a submodule of a module $m$ and a minimal primary decomposition of $n$ is known‎. ‎a formula to compute baer's lower nilradical of $n$ is given‎. ‎the relations between classical prime submodules and their nilradicals are investigated‎. ‎some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated‎.