Stochastic Calculus with Respect to Gaussian Processes

Potential Analysis - In the present paper, we are going to show that outside a slim set in the sense of Malliavin (or quasi-surely), the signature path (which consists of iterated path integrals in...     

Spatiotemporal Studies of the One-Dimensional Coordination Polymer [Fe(ebtz)2(C2H5CN)2](BF4)2: Tug of War between the Nitrile Reorientation Versus Crystal Lattice as a Tool for Tuning the Spin Crossover Properties**

Reaction of 1,2-di(tetrazol-2-yl)ethane (ebtz) with Fe(BF₄)₂⋅6 H₂O in different nitriles yields one-dimensional coordination polymers [Fe(ebtz)₂(RCN)₂](BF₄)₂⋅nRCN (n=2 for R=CH₃ ( 1 ) and n=0 for R=C₂H₅ ( 2 ) C₃H₇ ( 3 ), C₃H₅ ( 4 ), CH₂Cl ( 5 )) exhibiting spin crossover (SCO). SCO in 1 and 3 – 5 is complete and occurs above 160 K. In 2 , it is shifted to lower temperatures and is accompanied by wide hysteresis (T_1/2^↓=78 K, T_1/2^↑=123 K) and proceeds extremely slowly. Isothermal (80 K) time-resolved single-crystal X-ray diffraction studies revealed a complex nature for the HS→LS transition in 2 . An initial, slow stage is associated with shrinkage of polymeric chains and with reduction of volume at 77 % (in relation to the difference between cell volumes V_HS−V_LS) whereas only 16 % of iron(II) ions change spin state. In the second stage, an abrupt SCO occurs, associated with breathing of the crystal lattice along the direction of the Fe–nitrile bonds, while the nitriles reorient. HS→LS switching triggered by light (808 nm) reveals the coupling of spin state and nitrile orientation. The importance of this coupling was confirmed by studies of [Fe(ebtz)₂(C₂H₅CN/C₃H₇CN)₂](BF₄)₂ mixed crystals ( 2 a , 2 b ), showing a shift of T_1/2 to higher values and narrowing of the hysteresis loop concomitant with an increase of the fraction of butyronitrile. This increase reduces the capability of nitrile molecules to reorient. Density functional theory (DFT) studies of models of 1 – 5 suggest a particular possibility of 2 to adopt a low (140–145°) value of its Fe-N-C(propionitrile) angle.     

Schatten properties,nuclearity and minimality of phase shift invariant spaces

We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.We use these results to prove that the pseudo-differential operator $\mathrm{Op}(a)$ is a Schatten-q operator from $M^{\infty }$ to $M^p$ and r-nuclear operator from $M^{\infty }$ to $M^r$ when $a\in M^r$ for suitable p, q and r in $(0,\infty ]$.     

2-Methyltetrahydrofuran (2-MeTHF) as a versatile green solvent for the synthesis of amphiphilic copolymers via ROP,FRP, and RAFT tandem polymerizations

2-methyltetrahydrofuran (2-MeTHF) is a readily available, inexpensive, neoteric, bio-based solvent. It has been adopted across a wide range of chemical processes including the batch manufacture of fine chemicals, enzymatic polycondensations and ring opening polymerizations. To reduce the environmental burden related to the synthesis of pharmaceutical-grade polymers based on lactide and caprolactone, we envisaged the use of 2-MeTHF. For the first time, we combined a series of metal-free and enzymatic ROPs with free radical and controlled RAFT polymerizations (carried out separately and in tandem) in 2-MeTHF, in order to easily tune the chemistry and the architecture of the final polymers. After a simple purification, the amphiphilic polymers were formulated into nanoparticles and tested for their cytocompatibility in three model cell lines, to assess their application as potential polymeric excipients for nanomedicines.     

New algorithms for maximum disjoint paths based on tree-likeness

Mathematical Programming - The aim of this paper is to show that every representative function of a maximally monotone operator is the Fitzpatrick transform of a bifunction corresponding to the...     

α-Diphenylphosphino-N-(pyrazin-2-yl)glycine as a ligand in Ni-catalyzed ethylene oligomerization

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