Image Restoration: A General Wavelet Frame Based Model and Its Asymptotic Analysis

Image restoration is one of the most important areas in imaging science. Mathematical tools have been widely used in image restoration, where wavelet frame based approach is one of the successful examples. In this paper, we introduce a generic wavelet frame based image restoration model, called the "general model", which includes most of the existing wavelet frame based models as special cases. Moreover, the general model also includes examples that are new to the literature. Motivated by our earlier studies [1-3], We provide an asymptotic analysis of the general model as image resolution goes to infinity, which establishes a connection between the general model in discrete setting and a new variatonal model in continuum setting. The variational model also includes some of the existing variational models as special cases, such as the total generalized variational model proposed by [4]. In the end, we introduce an algorithm solving the general model and present one numerical simulation as an example

Tuning ice nucleation with counterions on polyelectrolyte brush surfaces

Heterogeneous ice nucleation (HIN) on ionic surfaces is ubiquitous in a wide range of atmospheric aerosols and at biological interfaces. Despite its great importance in cirrus cloud formation and cryopreservation of cells, organs, and tissues, it remains unclear whether the ion-specific effect on ice nucleation exists. Benefiting from the fact that ions at the polyelectrolyte brush (PB)/water interface can be reversibly exchanged, we report the effect of ions on HIN on the PB surface, and we discover that the distinct efficiency of ions in tuning HIN follows the Hofmeister series. Moreover, a large HIN temperature window of up to 7.8°C is demonstrated. By establishing a correlation between the fraction of ice-like water molecules and the kinetics of structural transformation from liquid- to ice-like water molecules at the PB/water interface with different counterions, we show that our molecular dynamics simulation analysis is consistent with the experimental observation of the ion-specific effect on HIN

On the Successiveness of the Two Extreme Cold Events in China during the 2020/21 Winter According to Cold Air Trajectories

Two extreme cold air events successively hit China during 28–31 December 2020 (the late 2020 event) and during 6–8 January 2021 (the early 2021 event), which caused great losses. These two events have received extensive attention in relation to synoptic weather systems and remote forcing. Although it has been noted that a near-surface cool condition can greatly impact tropospheric circulation, its role in the successiveness of two such extreme cold waves remains unclear. This study focused on cold air pathways from the Lagrangian perspective, and explored the potential influence of cold air over the key region in terms of connecting the two cold events using a piecewise potential vorticity inversion. With the obtained results, three cold air sources with three corresponding air routes were identified in the two cold events. The northern pathway dominated the late 2020 event, in which the cold air intruded from the eastern Laptev Sea and moved southward to China. In contrast, the early 2021 event was mainly associated with the northwestern pathway in which the cold air came from the Ural Mountains and moved clockwise. Notably, cold air traveling along the western route from western Lake Balkhash arrived at the north of the Tianshan Mountains earlier and amplified the positive height anomaly in situ. Moreover, such an enhanced positive height anomaly moved the direction of the cold air from the northern and northwestern routes southward and thus played a key role in the successiveness of the two extreme cold events

On the Successiveness of the Two Extreme Cold Events in China during the 2020/21 Winter According to Cold Air Trajectories

Two extreme cold air events successively hit China during 28–31 December 2020 (the late 2020 event) and during 6–8 January 2021 (the early 2021 event), which caused great losses. These two events have received extensive attention in relation to synoptic weather systems and remote forcing. Although it has been noted that a near-surface cool condition can greatly impact tropospheric circulation, its role in the successiveness of two such extreme cold waves remains unclear. This study focused on cold air pathways from the Lagrangian perspective, and explored the potential influence of cold air over the key region in terms of connecting the two cold events using a piecewise potential vorticity inversion. With the obtained results, three cold air sources with three corresponding air routes were identified in the two cold events. The northern pathway dominated the late 2020 event, in which the cold air intruded from the eastern Laptev Sea and moved southward to China. In contrast, the early 2021 event was mainly associated with the northwestern pathway in which the cold air came from the Ural Mountains and moved clockwise. Notably, cold air traveling along the western route from western Lake Balkhash arrived at the north of the Tianshan Mountains earlier and amplified the positive height anomaly in situ. Moreover, such an enhanced positive height anomaly moved the direction of the cold air from the northern and northwestern routes southward and thus played a key role in the successiveness of the two extreme cold events

Tantallacarborane Mediated Consecutive C–C and C–N Coupling Reactions of Alkyl Isonitriles: A Facile Route to N‑Heterocycles

Reactions of tantallacarborane methyl complexes ([η¹:η⁵-(Me₂NCH₂CH₂)­C₂B₉H₁₀]­TaMe₃ (<b>1</b>) and [η¹:η⁵-(MeOCH₂CH₂)­C₂B₉H₁₀]­TaMe₃ (<b>8</b>)) with alkyl isonitriles have been studied. Complex <b>1</b> reacted with 1 equiv of RNC (R = TMSCH₂, Cy, and ^<i>i</i>Pr) to afford double migratory insertion products [η¹:η⁵-(Me₂NCH₂CH₂)­C₂B₉H₁₀]­Ta­[η²-<i>C</i>,<i>N</i>-C­(Me₂)­NCH₂TMS]­Me (<b>2</b>) and [σ:η¹:η⁵-{MeN­(CH₂)­CH₂CH₂}­C₂B₉H₁₀]­Ta­[N­(^<i>i</i>Pr)­R]­Me (R = Cy (<b>3</b>), ^<i>i</i>Pr (<b>4</b>)). However, treatment of <b>1</b> or <b>8</b> with 4 equiv of alkyl isonitriles gave two fused six-membered <i>N</i>-heterocycles <b>5</b>–<b>7</b> and <b>9</b> via consecutive C–C/C-N bond-forming reactions. All new complexes were characterized by ¹H, ¹³C, and ¹¹B NMR spectra as well as elemental analyses. Their structures were further confirmed by single-crystal X-ray analyses. The results show that aryl and alkyl isonitriles exhibit significantly different reactivity patterns. This work also offers a very efficient method for the synthesis of N-heterocycles

Reaction of 13-Vertex Carborane μ‑1,2-(CH₂)₃‑1,2‑C₂B₁₁H₁₁ with Nucleophiles: Scope and Mechanism

13-Vertex carborane, μ-1,2-(CH₂)₃-1,2-C₂B₁₁H₁₁ (<b>1</b>), reacted with a series of nucleophiles (Nu) to give the cage carbon extrusion products [μ-1,2-(CH₂)₃­CH­(Nu)-1-CB₁₁H₁₀]⁻, [μ-1,2-(CH₂)₂­CH­(Nu)­CH₂-1-CB₁₁H₁₀]⁻, and/or [μ-1,2-(CH₂)₂­CHCH-1-CB₁₁H₁₀]⁻, depending on the nature of Nu and the reaction conditions. The key intermediates for the formation of CB₁₁^– anions were isolated and structurally characterized as [μ–η:η:η-7,8,10-(CH₂)₃­CHB­(Nu)-7-CB₁₀H₁₀]⁻ (Nu = OMe, NEt₂). The reaction mechanism is thus proposed, which involves the attack of Nu at the most electron-deficient cage boron, followed by H-migration to one of the cage carbons, leading to the formation of the intermediate. Nu-migration gives the products

Reactivity of Traditional Metal–Carbon (Alkyl) versus Nontraditional Metal–Carbon (Cage) Bonds in Organo-Rare-Earth Metal Complexes [η⁵:σ-(C₉H₆)(C₂B₁₀H₁₀)]­Ln(CH₂C₆H₄‑<i>o</i>‑NMe₂)(THF)₂

Equimolar reaction of 1-indenyl-1,2-carborane with Ln­(CH₂C₆H₄-<i>o</i>-NMe₂)₃ in THF gave highly constrained-geometry complexes [η⁵:σ-(C₉H₆)­C₂B₁₀H₁₀]­Ln­(CH₂C₆H₄-<i>o</i>-NMe₂)­(THF)₂ (Ln = Y (<b>1a</b>), Gd (<b>1b</b>), Dy (<b>1c</b>)). They reacted with RNCNR or 2,6-Me₂C₆H₃NCS to generate the Ln–C_alkyl insertion products [η⁵:σ-(C₉H₆)­C₂B₁₀H₁₀]­Ln­[η²<i>-</i>(RN)₂C­(CH₂C₆H₄-<i>o</i>-NMe₂)]­(THF) (R = TMS, Ln = Y (<b>2a</b>), Gd (<b>2b</b>); R = ^<i>t</i>Bu, Ln = Y (<b>3a</b>)) or [η⁵:σ-(C₉H₆)­C₂B₁₀H₁₀]­Dy­[η²<i>-</i>(2,6-Me₂C₆H₃)­NC­(CH₂C₆H₄-<i>o</i>-NMe₂)­S]­(THF)₂ (<b>4c</b>). Treatment of <b>2a</b> with 1 equiv of R′NCNR′ to give the Y–C_cage insertion complexes [η⁵:σ-(C₉H₆)­{N­(R′)­C­(NR′)}­C₂B₁₀H₁₀]­Y­[η²<i>-</i>{(TMS)­N}₂­C­(CH₂C₆H₄-<i>o</i>-NMe₂)] (R′ = Cy (<b>5a</b>), ^<i>i</i>Pr (<b>6a</b>)). Similarly, unsaturated compounds Ph₂CCO and Py₂CO (Py = 2-pyridyl) also inserted into the Y–C_cage bond in <b>2a</b> to yield [η⁵:σ-(C₉H₆)­{OC­(CPh₂)}­C₂B₁₀H₁₀]­Y­[η²<i>-</i>{(TMS)­N}₂C­(CH₂C₆H₄-<i>o</i>-NMe₂)] (<b>7a</b>) and [η⁵:σ-(C₉H₆)­{OC­(Py)₂}­C₂B₁₀H₁₀]­Y­[η²<i>-</i>{(TMS)­N)}₂­C­(CH₂C₆H₄-<i>o</i>-NMe₂)]­(THF) (<b>8a</b>), respectively. In sharp contrast to the earlier reports that the nontraditional metal–C_cage σ bonds in metal–carboranyl complexes are generally inert toward electrophiles, the insertion of unsaturated molecules into the Y–C_cage σ bond in <b>2a</b> represents the first example of this type of reactions. These results shed some light on how to activate the nontraditional metal–carbon (cage) bonds in metal–carboranyl complexes. All new complexes were characterized by spectroscopic techniques and elemental analyses. Some were further confirmed by single-crystal X-ray analyses

Palladium-Catalyzed Regioselective Intramolecular Coupling of <i>o</i>‑Carborane with Aromatics via Direct Cage B–H Activation

Palladium-catalyzed intramolecular coupling of <i>o</i>-carborane with aromatics via direct cage B–H bond activation has been achieved, leading to the synthesis of a series of <i>o</i>-carborane-functionalized aromatics in high yields with excellent regioselectivity. In addition, the site selectivity can also be tuned by the substituents on cage carbon atom