It has been observed by different authors that QTAG-modules behave very much like torsion abelian groups. In this paper, in section 3, we characterize quasi-essential submodules (Theorem 3.9) and further find a characterization for an h-pure submodule to be a direct summand (Theorem 3.11). In section 4, we obtained a necessary and sufficient condition for a submodule to be contained in a minima...

A theoretical model for the laser-induced thermal lens effect in weakly absorbing media is derived. The model predicts the intensity variation in the far field of the laser beam in the presence of the lensing medium and takes into account the aberrant nature of the thermal lens. Some experimental results which support the validity of this approach are presented.

In this paper, the main purpose is to study existence of the global attractors for the weakly damped wave equation with nonlinear boundary conditions. To this end, we first show that the existence of a bounded absorbing set by the perturbed energy method. Secondly, we utilize the decomposition of the solution operator to verify the asymptotic compactness.

Stavskaya’s model is a one-dimensional Boolean probabilistic cellular automaton very similar to the contact and directed percolation processes. There is always an absorbing measure but close to the deterministic limit the model also shows a non-trivial invariant measure. We show that the latter “Stavskaya’s” measure is weakly Gibbsian with an exponentially decaying interaction potential.

We present measurements, by using two complementary methods, of the breakdown of atomic angular momentum selection rules in He-broadened Rb vapor. Atomic dark states are rendered weakly absorbing due to fine-structure mixing during Rb-He collisions. The effect substantially increases the photon demand for optical pumping of dense vapors.

Two Ag(I) ions, deprotonated 1-methyl-thymine (1MT-H)(-) and 1,3-dideaza-adenine (DDA), self-assemble in methanolic solution to a cationic [(Ag)2(1MT-H)(DDA)](+) complex as identified by electrospray ionization mass spectrometry. Assignment of vibrational bands and identification of the silver coordination pattern arise from comparison of one- and two-color Infrared Multiple Photon Dissociation...

Let R be a commutative ring with non-zero identity, S multiplicatively closed subset of and M unital R-module. In this paper, we define submodule N (N :R M) ? = to weakly S-primary if there exists s such that whenever m 0 , am N, then either sa ??(N or sm N. We present various properties characterizations concept (especially in faithful multiplication modules). Moreover, the behavior structure ...

We characterize absorption in finite idempotent algebras by means of Jónsson absorption and cube term blockers. As an application we show that it is decidable whether a given subset is an absorbing subuniverse of an algebra given by the tables of its basic operations.

Hollow-core photonic bandgap fibres (HC-PBFs) have emerged as a novel technology in the field of gas sensing. The long interaction pathlengths achievable with these fibres are especially advantageous for the detection of weakly absorbing gases. In this work, we demonstrate the good performance of a HC-PBF in the detection of the ν(2) + 2ν(3) band of methane, at 1.3 μm. The Q-branch manifold, at...

All rings are commutative with identity and all modules are unital. Let R be a ring, M an R-module and R(M), the idealization of M . Homogenous ideals of R(M) have the form I (+)N , where I is an ideal of R and N a submodule of M such that IM ⊆ N . A ring R (M) is called a homogeneous ring if every ideal of R (M) is homogeneous. In this paper we continue our recent work on the idealization of m...