Let χ denote the space of all gai sequences and Λ the space of all analytic sequences. First we show that the set E = { s(k) : k = 1, 2, 3, · · · } is a determining set for χM . The set of all finite matrices transforming χM into FKspace Y denoted by (χM : Y ) . We characterize the classes (χM : Y ) when Y = (c0)π , cπ, χM , `π, `s,Λπ, hπ. In summary we have the following table: ↗ (c0)π cπ χM `...

this is true for indicator functions, since ∫ 1Adπ = π(A) = ∫ A hπ,μdμ by definition of the Radon-Nikodym derivative. Then by linearity of the integral, the claim is also true for simple functions. Then we can show the claim for non-negative measurable functions, by approximating by simple functions. Indeed, if f ≥ 0 is measurable, then there exists a sequence of simple functions 0 ≤ sn ↑ f suc...

A bis-urea-functionalized pillar[5]arene has been synthesized and shown to form [2]pseudorotaxanes spontaneously with linear alkyl dicarboxylates in highly polar solvent DMSO, in which the hydrogen bonding interactions between the bis-urea hydrogens and dicarboxylate oxygens play an important role in stabilizing the novel [2]pseudorotaxanes alongside C-Hπ interactions.

The synthesis of new Schiff base-like ligands with extended π-system and their iron complexes is described. Some of the iron(ii) complexes with N-heterocycles as axial ligands show spin crossover behaviour. The influence of the extended aromatic system on cooperative interactions is investigated by single crystal X-ray structure analysis, X-ray powder diffraction, and magnetic measurements. A c...

We introduce the concepts of degree inertia, diG(H), and compression, dcG(H), a finitely generated subgroup H given group G. For case direct products free-abelian free groups, we compute compression give an upper bound for inertia. Imposing some technical assumptions to supremum involved in definition notion called restricted diG′(H), and, again Zm×Fn, provide explicit formula relating it inert...

We compute the photon asymmetry for near threshold parity violating (PV) pion photoproduction through sub-leading order. We find a potentially significant contribution from new PV low-energy constants not considered previously. We observe that a measurement of this asymmetry may help clarify the theoretical intepretation of backward angle PV electron-proton scattering, provided that the PV πNN ...

In this letter, we propose to investigate Λ hypernuclei for the A 15 mass region by using pionic decay. The Project aims to determine precisely the binding energies of light hypernuclei, investigate production of exotic hypernuclei, and study impurity nuclear physics and the medium effect of baryons. ≤ These investigations will fully utilize the unique parameters (high intensity, small emittanc...

In this paper, we define invariant tensor product and study invariant tensor products associated with discrete series representations. Let G(V1) × G(V2) be a pair of classical groups diagonally embedded in G(V1 ⊕ V2). Suppose that dimV1 < dimV2. Let π be a discrete series representation of G(V1 ⊕ V2). We prove that the functor π⊗G(V1) maps unitary representations of G(V1) to unitary representat...

By using 1-methyl-4-(carbomethoxy)pyridinium (MCMP+) as counterions, two iodoargentate hybrids, 1D [MCMP][AgI2] (1) and 3D [MCMP][Ag3I4] (2) have been synthesized and they exhibit rare electron transfer photochromism with a fast response rate, a wide response range and a long-lived charge-separated state in iodometallate systems. Noteworthily, the marked differences in the structure and photoch...