Spin–Orbit Charge-Transfer Intersystem Crossing (ISC) in Compact Electron Donor–Acceptor Dyads: ISC Mechanism and Application as Novel and Potent Photodynamic Therapy Reagents

Spin–orbit charge-transfer intersystem crossing (SOCT-ISC) is useful for the preparation of heavy atom-free triplet photosensitisers (PSs). Herein, a series of perylene-Bodipy compact electron donor/acceptor dyads showing efficient SOCT-ISC is prepared. The photophysical properties of the dyads were studied with steady-state and time-resolved spectroscopies. Efficient triplet state formation (quantum yield Φ_T=60 %) was observed, with a triplet state lifetime (τ_T=436 μs) much longer than that accessed with the conventional heavy atom effect (τ_T=62 μs). The SOCT-ISC mechanism was unambiguously confirmed by direct excitation of the charge transfer (CT) absorption band by using nanosecond transient absorption spectroscopy and time-resolved electron paramagnetic resonance (TREPR) spectroscopy. The factors affecting the SOCT-ISC efficiency include the geometry, the potential energy surface of the torsion, the spin density for the atoms of the linker, solvent polarity, and the energy matching of the ¹CT/³LE states. Remarkably, these heavy atom-free triplet PSs were demonstrated as a new type of efficient photodynamic therapy (PDT) reagents (phototoxicity, EC₅₀=75 nm ), with a negligible dark toxicity (EC₅₀=78.1 μm ) compared with the conventional heavy atom PSs (dark toxicity, EC₅₀=6.0 μm, light toxicity, EC₅₀=4.0 nm ). This study provides in-depth understanding of the SOCT-ISC, unveils the design principles of triplet PSs based on SOCT-ISC, and underlines their application as a new generation of potent PDT reagents.     

From SU(2) Gauge Theory to Qubits on the Fuzzy Sphere

We consider a classical pure SU(2) gauge theory, and make an ansatz, which separates the spatio-temporal degrees of freedom from the internal ones. This ansatz is gauge-invariant but not Lorentz invariant. In a limit case of the ansatz, obtained through a contraction map, and corresponding to a vacuum solution, the SU(2) gauge field reduces to an operator, which is the product of the generator of a global U(1) group times a Pauli matrix. We give a geometrical interpretation of the ansatz and of the contraction map in the framework of principal fiber bundles. Then, we identify the internal degrees of freedom of the gauge field with the non-commutative coordinates of the fuzzy sphere in the fundamental representation. In this way we obtain a qubit state.     

Crowd dynamics through non-local conservation laws

We present a Lax-Friedrichs type scheme to compute the solutions of a class of non-local and non-linear systems of conservation laws in several space dimensions. The convergence of the approximate solutions is proved by providing suitable L¹, L^∞ and BV uniform bounds. To illustrate the performances of the scheme, we consider an application to crowd dynamics. Numerical integrations show the formation of lanes in groups moving in opposite directions. This is joint work with R.M. Colombo (INDAM Unit, University of Brescia).     

Representing products of manifolds by edge-coloured graphs: the boundary case

In this paper we generalize the construction - introduced by Gagliardi and Grasselli in the closed case - of a coloured-graph representing the product of two manifolds, starting by two coloured graphs representing the manifolds themselves, to the boundary case. In particular we study the genus of the graph product of low dimensional manifold ( resp. n-spheres ) with m-disks. Received September 28, 1998; in final form January 5, 2000 / Published online October 11, 2000     

The Smoluchowski limit for a simple mechanical model

We consider a vertical stick constantly accelerated along thex-axis by a forceF and which elastically collides with point particles of the same mass (atoms). The atoms are initially Poisson distributed and are allowed to have four velocities only. It is shown that under suitable scaling of the system the displacementQ(t) of the stick satisfies a nontrivial CLT:Q(t)=vFt+D ^1/2 W(t) (Smoluchowski equation), where the values ofv andD depend on the fact that one atom may collide several times.     

Shortest Path Auction Algorithm Without Contractions Using Virtual Source Concept

In this paper, the problem of finding a shortest path tree rooted at a given source node on a directed graph (SPT) is considered. A new efficient algorithm based on a primal-dual approach is presented, which improves both the convergence and the complexity of the best known auction-like algorithm. It uses the virtual source (VS) concept based on the following consideration: when a node i is visited for the first time by any algorithm which preserves verified the dual admissibility conditions, then the shortest path (SP) from the source node to i is found. Therefore, the SP from the source to the remaining nodes may be computed by considering i as a virtual source.We propose a very efficient implementation of an auction-like algorithm that uses this concept and enables us to obtain a computational cost of O(n ²), where n is the number of nodes.Numerical experimentsare reported showing that the new method outdoes previously proposed auction-like algorithms and is highly competitive with other state-of-art SP approaches.     

On constant elasticity of substitution – Constant elasticity of transformation Directional Distance Functions

This paper aims to present non-linear CES (Constant Elasticity of Substitution)–CET (Constant Elasticity of Transformation) Directional Distance Functions. These measures inherit the structure of the standard Directional Distance Functions and that of the CES–CET technology. These functions allow non-parametric estimation of efficiency scores through linear programming method. Besides, the CES –CET technology gives the opportunity to explore α-returns to scale assumption for the new distance functions. The duality theory is investigated through pseudo profit, cost and revenue functions. The dual standpoint provides non-linear adjusted prices that can occur into non-linear pricing practices. An application is proposed to give an illustrative example of the primal CES–CET Directional Distance Functions.