We introduce a class of scattering passive linear systems motivated by examples from mathematical physics. The state space of the system is X = H ⊕ E, where H and E are Hilbert spaces. We also have a Hilbert space E0 which is dense in E, with continuous embedding, and E ′ 0 is the dual of E0 with respect to the pivot space E. The input space is the same as the output space, and it is denoted by...

Let X be a compact Hausdorff space and M a metric space. E0(X,M) is the set of f ∈ C(X,M) such that there is a dense set of points x ∈ X with f constant on some neighborhood of x. We describe some general classes of X for which E0(X,M) is all of C(X,M). These include βN\N, any nowhere separable LOTS, and any X such that forcing with the open subsets of X does not add reals. In the case thatM is...

The apoE knockout (E0) mouse is one of the most widely used animal models of atherosclerosis, and there may be similarities to chylomicron remnant-induced atherosclerosis in humans. Although the lesions of these mice contain large numbers of cholesteryl ester (CE)-laden macrophages (foam cells), E0 plasma lipoproteins are relatively weak inducers of cholesterol esterification in macrophages. Pr...

The results of a theoretical study of the one-, two- and three-water hydrolyses of carbodiimide and the one- and two-water hydrolyses of methyleneimine are presented. All structures were optimized and characterized at the MP2(full)/6-31G* level of theory. Energies for the one-water hydrolysis of carbodiimide were determined at numerous higher levels of theory, up to the QCISD(T)(fc)/6-311+G(3df...

A non-linear functional Q[u, v] is given that governs the loss, respectively gain, of (doubly degenerate) eigenvalues of fourth order differential operators L = ∂ + ∂ u ∂ + v on the line. Apart from factorizing L as A∗A+E0, providing several explicit examples, and deriving various relations between u, v and eigenfunctions of L, we find u and v such that L is isospectral to the free operator L0 ...

Due to economical and environmental issues, utilization of mineral wastes, e.g. iron ore mine tailing (IOMT), as road materials can be recommended as a sustainable alternative. In the present study, mechanical properties, as well as resistance to freezing and thawing cycles (F-T) of low plasticity clay soil stabilized with different percentages of Portland cement (0, 6, 9, 12 and 15%) and diffe...

Let Fe be the set of faulty edges of Sn and E0 be the edge set of some pairwise vertex-disjoint paths of Sn. All edges of E0 lie on a Hamiltonian cycle of Sn−Fe, if |Fe| ≤ n−3, |E0| ≤ 2n−5−2|Fe| and lie on a Hamiltonian path P (u, v) where d(u, v) is odd, |Fe| ≤ n− 3, |E0| ≤ 2n− 7− 2|Fe| .

The reduced mass of the effective quantum particle for inversion mode ν2 phosphine molecule PH3 is known to be a position dependent one. In present article spectrum considered with help Schrödinger equation (SE) and corresponding modified double-well potential. SE shown exactly solvable. results are used analysis pertinent experimental data available in literature. We based on reliable value ν2...