Context equivalence of semigroups

Two semigroups are called strongly Morita equivalent if they are contained in a Morita context with unitary bi-acts and surjective mappings. We consider the notion of context equivalence which is obtained from the notion of strong Morita equivalence by dropping the requirement of unitariness. We show that context equivalence is an equivalence relation on the class of factorisable semigroups and describe factorisable semigroups that are context equivalent to monoids or groups, and semigroups with weak local units that are context equivalent to inverse semigroups, orthodox semigroups or semilattices.     

Morita invariants for semigroups with local units

In this paper we study Morita invariants for strongly Morita equivalent semigroups with local units of various kinds. Among others we prove that, under a certain condition of this kind, congruence lattices are preserved by strong Morita equivalence.     

Tensor Products and Preservation of Weighted Limits,for S-Posets

We prove that the functor of tensor multiplication by a right S-poset (S is a pomonoid) preserves all small weighted limits if and only if this S-poset is cyclic and projective. We also show that this functor preserves all finite pie-limits if and only if the S-poset is a filtered colimit of S-posets isomorphic to S _S .     

Effect of light polarization on holographic recording in glassy azocompounds and chalcogenides

Light polarization effects on a holographic grating recording in a glassy chalcogenide a-As₄₀S₁₅Se₄₅ film has been experimentally studied and compared with previously studied glassy molecular azobenzene film 8a at 633, using s − s,p − p, CE-1 and CE-2 circular-elliptic recording-beam polarizations (differing by light electric field rotation directions). The azocompound exhibited much higher self-diffraction efficiency (SDE) and diffraction efficiency whereas chalcogenide was more sensitive. Their recording efficiency polarization dependences also were different. SDE up to 45% was achieved in 8a with p − p and up to 2.6% in a-As₄₀S₁₅Se₄₅ with CE-2 polarized recording beams. The polarization changes in the diffraction process were studied as well in these and other materials (11, 16, 19 and a-As₂S₃ film, LiTaO₃:Fe crystal). It was found that light polarization changes in the process of diffraction from gratings recorded vectorially by s−p polarizations depended on chemical composition, wavelength, and exposure time. Vector gratings with SDE up to 25% were recorded in 8a, rotating a linear polarization by 90°. No light polarization changes were found in azobenzene 19 and chalcogenide films and in LiTaO₃:Fe crystal, thus showing a vector recording of scalar holograms. The recording mechanisms in azocompounds and chalcogenides are discussed and compared.     

Molecular routes for spin cluster qubits

We report on real molecular complexes and propose strategies that explore the possibility of implementation of specific quantum computation architectures with molecular spin systems. We focus on Cr3+ carboxylate derivatives and use the Loss-DiVincenzo scheme as reference.     

Isolated heterometallic Cr7Ni rings grafted on Au(111) surface

A study of the deposition of heterometallic antiferromagnetically coupled rings onto gold surfaces is reported. Two new {Cr7Ni} rings, [NH2nPr2][Cr7NiF8(3-tpc)16] (1) (where 3-tpc=3-thiophenecarboxylate) and [nBuNH2CH2CH2SH] [Cr7NiF8(O2CtBu)16] (2) have been made and structurally characterized. They have been deposited from the liquid phase on Au(111) and the adsorbed molecules compared by means of scanning tunneling microscopy (STM) and X-ray photoemission spectroscopy (XPS). In both cases a two-dimensional distribution of individually accessible {Cr7Ni} heterometallic rings on the gold surface has been obtained, exploiting the direct grafting of sulfur-functionalized clusters. There is a competition between the chemisorption of the {Cr7Ni} clusters and a thiolic self-assembled monolayer (SAM) formed by free ligands. In 2, the presence of a single sulfur ligand should force the molecule to graft with the ring axis normal to the surface. The cluster stability in the STM images and the S-2p energy positions demonstrate, for both functionalizations, the strength of the grafting with the gold surface.     

Strong Morita equivalence of semigroups with local units

In this paper we study Morita contexts for semigroups. We prove a Rees matrix cover connection between strongly Morita equivalent semigroups and investigate how the existence of a unitary Morita semigroup over a given semigroup is related to the existence of a ‘good’ Rees matrix cover of this semigroup.