Inviscid Models Generalizing the Two-dimensional Euler and the Surface Quasi-geostrophic Equations

Any classical solution of the two-dimensional incompressible Euler equation is global in time. However, it remains an outstanding open problem whether classical solutions of the surface quasi-geostrophic (SQG) equation preserve their regularity for all time. This paper studies solutions of a family of active scalar equations in which each component u _j of the velocity field u is determined by the scalar θ through \({u_j =\mathcal{R}\Lambda^{-1}P(\Lambda) \theta}\) , where \({\mathcal{R}}\) is a Riesz transform and Λ = (?Δ)^1/2. The two-dimensional Euler vorticity equation corresponds to the special case P(Λ) = I while the SQG equation corresponds to the case P(Λ) = Λ. We develop tools to bound \({\|\nabla u||_{L^\infty}}\) for a general class of operators P and establish the global regularity for the Loglog-Euler equation for which P(Λ) = (log(I + log(I ? Δ))) ^γ with 0 ≦ γ ≦ 1. In addition, a regularity criterion for the model corresponding to P(Λ) = Λ ^β with 0 ≦ β ≦ 1 is also obtained.     

Strained Ammonium Precursors for Radiofluorinations

The increasing application of positron emission tomography (PET) in nuclear medicine has stimulated the extensive development of a multitude of novel and versatile techniques to introduce fluorine-18, especially for the radiolabelling of biologically or pharmacologically active molecules. Taking into consideration that the introduction of fluorine-18 (t_1/2=109.8 min) mostly proceeds under harsh conditions, radiolabelling of such molecules represents a challenge and is of enormous interest. Ideally, it should proceed in a regioselective manner under mild physiological conditions, in an acceptable time span, with high yields and high specific activities. Special attention has been drawn to 2-fluoroethyl and 3-fluoropropyl groups, which are often the active sites of radiofluorinated compounds. Precursors containing an ammonium leaving group – such as a strained azetidinium or aziridinium moiety – can help to overcome these obstacles leading to a convenient and mild introduction of [¹⁸F]fluoride with high radiochemical yields.     

On The Cut-off Parameters in the Bosonization Technique

Jordan's boson representation and cut-off repolarization for the one-dimensional two-fermion model (TFT) is used to get the equivalence of the model with the two-dimensional Coulomb gas and sine-Gordon model. The scaling equations for the coupling constants are thereby obtained up to the third order.     

Dynamic kinetic resolution of transient hemiketals: a strategy for the desymmetrisation of prochiral oxetanols

Identification of an electron poor trifluoroacetophenone allows the formation of uniquely stable hemiketals from prochiral oxetanols. When exposed to a cobalt(ii) catalyst, efficient ring-opening to densely functionalized dioxolanes is observed. Mechanistic studies suggest an unprecedented redox process between the cobalt(ii) catalyst and the hemiketal that initiates the oxetane-opening. Based on this observation, a dynamic kinetic resolution of the transient hemiketals is explored that uses a Katsuki-type ligand for stereoinduction (up to 99 : 1 dr and 96 : 4 er) and allows a variety of 1,3-dioxolanes to be accessed (20 examples up to 98% yield).

Desymmetrization of prochiral oxetanols via an electron-deficient hemiketal intermediate is achieved. Key to this process is the catalyst''s chiral recognition of one of the two hemiketal enantiomers enabling an efficient dynamic kinetic resolution.     

An inequality concerning the growth bound of an evolution family and the norm of a convolution operator

Let \(\mathcal {U}=\{U(t,s)\}_{t\ge s\ge 0}\) be a strongly continuous and exponentially bounded evolution family acting on a complex Banach space X and let \(\mathcal {X}\) be a certain Banach function space of X-valued functions. We prove that the growth bound of the family \(\mathcal {U}\) is less than or equal to \(-\frac{1}{c(\mathcal {U}, \mathcal {X})}\) provided that the convolution operator \(f\mapsto \mathcal {U}*f\) acts on \(\mathcal {X}.\) It is well known that under the latter assumption, the convolution operator is bounded and then \(c(\mathcal {U}, \mathcal {X})\) denotes (ad-hoc) its norm in \(\mathcal {L}(\mathcal {X}).\) As a consequence, we prove that if \(\sup \nolimits _{s\ge 0}\int \nolimits _{s}^\infty \Vert U(t,s)\Vert dt=u_1(\mathcal {U})<\infty ,\) then \(\omega _0(\mathcal {U})u_1(\mathcal {U})\le -1.\) Finally, we give an example showing that the accuracy of the estimates may be quite accurate.     

Light-Activated Carbon Monoxide Prodrugs Based on Bipyridyl Dicarbonyl Ruthenium(II) Complexes

Two photoactivatable dicarbonyl ruthenium(II) complexes based on an amide-functionalised bipyridine scaffold (4-position) equipped with an alkyne functionality or a green-fluorescent BODIPY (boron-dipyrromethene) dye have been prepared and used to investigate their light-induced decarbonylation. UV/Vis, FTIR and ¹³C NMR spectroscopies as well as gas chromatography and multivariate curve resolution alternating least-squares analysis (MCR-ALS) were used to elucidate the mechanism of the decarbonylation process. Release of the first CO molecule occurs very quickly, while release of the second CO molecule proceeds more slowly. In vitro studies using two cell lines A431 (human squamous carcinoma) and HEK293 (human embryonic kidney cells) have been carried out in order to characterise the anti-proliferative and anti-apoptotic activities. The BODIPY-labelled compound allows for monitoring the cellular uptake, showing fast internalisation kinetics and accumulation at the endoplasmic reticulum and mitochondria.     

Gadolinium Photocatalysis: Dearomative [2+2] Cycloaddition/Ring‐Expansion Sequence with Indoles

Lanthanide photocatalysts are much less investigated in synthetic chemistry than rare and expensive late transition metals. We herein introduce Gd^III photocatalysis of a highly regioselective, intermolecular [2+2] photocycloaddition/ring‐expansion sequence with indoles, which could provide divergent access to cyclopenta[b]indoles and indolines. A simple and commercially available Gd(OTf)₃ salt is sufficient for this visible‐violet‐light‐induced transformation. The reaction proceeds either through a transient or start‐to‐end dearomatization cascade and shows excellent regioselectivity (usually >95:5 r.r.), broad scope (59 examples), good functional group tolerance and facile scale‐up under mild, direct visible‐light‐excitation conditions. Mechanistic investigations reveal that direct excitation of the Gd(OTf)₃/indole mixture gives an excited state intermediate, which undergoes the subsequent [2+2] cycloaddition and cyclobutane‐expansion cascade.     

Scientific investigations of the Imperial Gates from the Petrindu wooden church,Salaj County,Romania

In order to preserve and restore the Imperial Gates from the Petrindu wooden church, Salaj County, Romania, (map location—latitude, longitude: 46.97, 23.19), the scientific investigation of the wooden support and painting materials (ground and pigments) was performed, employing Fourier‐transform infrared spectroscopy (FTIR), X‐ray fluorescence spectroscopy, and 3D scanning. FTIR spectroscopy offered information about the wooden degradation stage, whereas X‐ray fluorescence and FTIR spectroscopic methods were employed for structural painting materials characterization. The structural data can be correlated with the artistic, theological, and historical analysis of this religious patrimony object. After obtaining information about the wooden support and painting materials, the Imperial Gates were 3D digitized using state of the art laser scanning technology. The digital 3D model obtained was restored in a virtual environment and converted into an interactive 3D model that can be used for Romanian cultural heritage digital dissemination.     

Sensitivity Analysis for a Class of H 0 1 ${{H_{0}^{1}}}$ -Elliptic Variational Inequalities of the Second Kind

Set-Valued and Variational Analysis - We study the stability of solutions to ${H_{0}^{1}}$ -elliptic variational inequalities of the second kind that contain a non-differentiable Nemytskii...