Dimensions of triangulated categories via Koszul objects

Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings. As a consequence, one obtains bounds for the representation dimensions of certain Artin algebras.     

Elemental analysis of Pterocarpus Santalinus by PIXE and ICP-MS: chemometric approach

Journal of Radioanalytical and Nuclear Chemistry - A biomonitoring study of air pollution using lichen Flavoparmelia caperata (L.) Hale was conducted at indoor and outdoor environments of primary...     

Quantum Bit Commitment and the Reality of the Quantum State

Quantum bit commitment is insecure in the standard non-relativistic quantum cryptographic framework, essentially because Alice can exploit quantum steering to defer making her commitment. Two assumptions in this framework are that: (a) Alice knows the ensembles of evidence E corresponding to either commitment; and (b) system E is quantum rather than classical. Here, we show how relaxing assumption (a) or (b) can render her malicious steering operation indeterminable or inexistent, respectively. Finally, we present a secure protocol that relaxes both assumptions in a quantum teleportation setting. Without appeal to an ontological framework, we argue that the protocol’s security entails the reality of the quantum state, provided retrocausality is excluded.     

On Changes of Measure for Super Brownian Motion

Let be a superprocess under the measure P. We show the existence of probability measures which are absolutely continuous with respect to P, and whose Randon–Nikodym derivatives are suitably normalized functions of the self intersection local time of . These measures correspond to measure valued processes exhibiting a certain amount of (reinforcing) self interaction in terms of both the particle motion and the branching mechanism.     

Free summands of conormal modules and central elements in homotopy Lie algebras of local rings

If is a surjective local homomorphism with kernel , such that and the conormal module has a free summand of rank , then the degree central subspace of the homotopy Lie algebra of has dimension greater than or equal to . This is a corollary of the Main Theorem of this note. The techniques involved provide new proofs of some well known results concerning the conormal module.

     

Catalytic asymmetric synthesis of the central tryptophan residue of celogentin C

[reaction: see text] Chiral phase-transfer catalyst 5 containing an electron-deficient trifluorobenzyl moiety promoted the alkylation of glycine derivative 6 with propargyl bromide 7a in good yield and excellent ee. The resulting propargyl glycine 8 was converted to 14, the central tryptophan residue of Celogentin C, in two steps, with the Pd-catalyzed heteroannulation as the key transformation. This method promises to be an efficient route for the preparation of tryptophan derivatives possessing substitution on the indole ring.     

Geometric phase of a qubit interacting with a squeezed-thermal bath

We study the geometric phase of an open two-level quantum system under the influence of a squeezed, thermal environment for both non-dissipative as well as dissipative system-environment interactions. In the non-dissipative case, squeezing is found to have a similar influence as temperature, of suppressing geometric phase, while in the dissipative case, squeezing tends to counteract the suppressive influence of temperature in certain regimes. Thus, an interesting feature that emerges from our work is the contrast in the interplay between squeezing and thermal effects in non-dissipative and dissipative interactions. This can be useful for the practical implementation of geometric quantum information processing. By interpreting the open quantum effects as noisy channels, we make the connection between geometric phase and quantum noise processes familiar from quantum information theory.     

Catalytic epoxidation of cyclic vinylsilanes by ruthenium(II) complexes under aerobic conditions

A new methodology has been developed for the catalytic epoxidation of cyclic vinylsilanes using a ruthenium(II) bisoxazoline complex 2 with molecular oxygen. An attempt has been made to understand the role of -SiMe₃ group on the rate of epoxidation process.     

A lattice-based model of the kinetics of twin boundary motion

In this paper we derive a macroscopic kinetic law for twin boundary motion from a lattice dynamical model. The model is developed for compound and type-1 twins and it is explicitly illustrated for a Cu-Al-Ni shape memory alloy. The governing multiple-well energy is calculated using an effective interatomic potential; a Frenkel-Kontorowa type model is developed for the dynamics at the lattice scale; and a quasi-continuum approximation is used to determine the continuum-scale kinetics. The model predicts that compound twins in the Cu-Al-Ni shape memory alloy are an order of magnitude more mobile than type-1 twins which is consistent with experimental observations.