112 research outputs found
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
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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 ([η<sup>1</sup>:η<sup>5</sup>-(Me<sub>2</sub>NCH<sub>2</sub>CH<sub>2</sub>)C<sub>2</sub>B<sub>9</sub>H<sub>10</sub>]TaMe<sub>3</sub> (<b>1</b>) and
[η<sup>1</sup>:η<sup>5</sup>-(MeOCH<sub>2</sub>CH<sub>2</sub>)C<sub>2</sub>B<sub>9</sub>H<sub>10</sub>]TaMe<sub>3</sub> (<b>8</b>)) with alkyl isonitriles have been studied.
Complex <b>1</b> reacted with 1 equiv of RNC (R = TMSCH<sub>2</sub>, Cy, and <sup><i>i</i></sup>Pr) to afford double
migratory insertion products [η<sup>1</sup>:η<sup>5</sup>-(Me<sub>2</sub>NCH<sub>2</sub>CH<sub>2</sub>)C<sub>2</sub>B<sub>9</sub>H<sub>10</sub>]Ta[η<sup>2</sup>-<i>C</i>,<i>N</i>-C(Me<sub>2</sub>)NCH<sub>2</sub>TMS]Me (<b>2</b>) and [σ:η<sup>1</sup>:η<sup>5</sup>-{MeN(CH<sub>2</sub>)CH<sub>2</sub>CH<sub>2</sub>}C<sub>2</sub>B<sub>9</sub>H<sub>10</sub>]Ta[N(<sup><i>i</i></sup>Pr)R]Me (R = Cy (<b>3</b>), <sup><i>i</i></sup>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 <sup>1</sup>H, <sup>13</sup>C, and <sup>11</sup>B 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-(CH<sub>2</sub>)<sub>3</sub>‑1,2‑C<sub>2</sub>B<sub>11</sub>H<sub>11</sub> with Nucleophiles: Scope and Mechanism
13-Vertex carborane, μ-1,2-(CH<sub>2</sub>)<sub>3</sub>-1,2-C<sub>2</sub>B<sub>11</sub>H<sub>11</sub> (<b>1</b>), reacted with
a series of nucleophiles (Nu) to give the cage carbon extrusion products
[μ-1,2-(CH<sub>2</sub>)<sub>3</sub>CH(Nu)-1-CB<sub>11</sub>H<sub>10</sub>]<sup>−</sup>, [μ-1,2-(CH<sub>2</sub>)<sub>2</sub>CH(Nu)CH<sub>2</sub>-1-CB<sub>11</sub>H<sub>10</sub>]<sup>−</sup>, and/or [μ-1,2-(CH<sub>2</sub>)<sub>2</sub>CHCH-1-CB<sub>11</sub>H<sub>10</sub>]<sup>−</sup>, depending on the nature of Nu and the reaction conditions.
The key intermediates for the formation of CB<sub>11</sub><sup>–</sup> anions were isolated and structurally characterized as [μ–η:η:η-7,8,10-(CH<sub>2</sub>)<sub>3</sub>CHB(Nu)-7-CB<sub>10</sub>H<sub>10</sub>]<sup>−</sup> (Nu = OMe, NEt<sub>2</sub>). 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 [η<sup>5</sup>:σ-(C<sub>9</sub>H<sub>6</sub>)(C<sub>2</sub>B<sub>10</sub>H<sub>10</sub>)]Ln(CH<sub>2</sub>C<sub>6</sub>H<sub>4</sub>‑<i>o</i>‑NMe<sub>2</sub>)(THF)<sub>2</sub>
Equimolar
reaction of 1-indenyl-1,2-carborane with Ln(CH<sub>2</sub>C<sub>6</sub>H<sub>4</sub>-<i>o</i>-NMe<sub>2</sub>)<sub>3</sub> in
THF gave highly constrained-geometry complexes [η<sup>5</sup>:σ-(C<sub>9</sub>H<sub>6</sub>)C<sub>2</sub>B<sub>10</sub>H<sub>10</sub>]Ln(CH<sub>2</sub>C<sub>6</sub>H<sub>4</sub>-<i>o</i>-NMe<sub>2</sub>)(THF)<sub>2</sub> (Ln = Y (<b>1a</b>), Gd (<b>1b</b>), Dy (<b>1c</b>)). They reacted
with RNCNR or 2,6-Me<sub>2</sub>C<sub>6</sub>H<sub>3</sub>NCS to generate the Ln–C<sub>alkyl</sub> insertion
products [η<sup>5</sup>:σ-(C<sub>9</sub>H<sub>6</sub>)C<sub>2</sub>B<sub>10</sub>H<sub>10</sub>]Ln[η<sup>2</sup><i>-</i>(RN)<sub>2</sub>C(CH<sub>2</sub>C<sub>6</sub>H<sub>4</sub>-<i>o</i>-NMe<sub>2</sub>)](THF) (R = TMS, Ln = Y
(<b>2a</b>), Gd (<b>2b</b>); R = <sup><i>t</i></sup>Bu, Ln = Y (<b>3a</b>)) or [η<sup>5</sup>:σ-(C<sub>9</sub>H<sub>6</sub>)C<sub>2</sub>B<sub>10</sub>H<sub>10</sub>]Dy[η<sup>2</sup><i>-</i>(2,6-Me<sub>2</sub>C<sub>6</sub>H<sub>3</sub>)NC(CH<sub>2</sub>C<sub>6</sub>H<sub>4</sub>-<i>o</i>-NMe<sub>2</sub>)S](THF)<sub>2</sub> (<b>4c</b>). Treatment
of <b>2a</b> with 1 equiv of R′NCNR′
to give the Y–C<sub>cage</sub> insertion complexes [η<sup>5</sup>:σ-(C<sub>9</sub>H<sub>6</sub>){N(R′)C(NR′)}C<sub>2</sub>B<sub>10</sub>H<sub>10</sub>]Y[η<sup>2</sup><i>-</i>{(TMS)N}<sub>2</sub>C(CH<sub>2</sub>C<sub>6</sub>H<sub>4</sub>-<i>o</i>-NMe<sub>2</sub>)] (R′ = Cy
(<b>5a</b>), <sup><i>i</i></sup>Pr (<b>6a</b>)). Similarly, unsaturated compounds Ph<sub>2</sub>CCO
and Py<sub>2</sub>CO (Py = 2-pyridyl) also inserted into the
Y–C<sub>cage</sub> bond in <b>2a</b> to yield [η<sup>5</sup>:σ-(C<sub>9</sub>H<sub>6</sub>){OC(CPh<sub>2</sub>)}C<sub>2</sub>B<sub>10</sub>H<sub>10</sub>]Y[η<sup>2</sup><i>-</i>{(TMS)N}<sub>2</sub>C(CH<sub>2</sub>C<sub>6</sub>H<sub>4</sub>-<i>o</i>-NMe<sub>2</sub>)] (<b>7a</b>) and [η<sup>5</sup>:σ-(C<sub>9</sub>H<sub>6</sub>){OC(Py)<sub>2</sub>}C<sub>2</sub>B<sub>10</sub>H<sub>10</sub>]Y[η<sup>2</sup><i>-</i>{(TMS)N)}<sub>2</sub>C(CH<sub>2</sub>C<sub>6</sub>H<sub>4</sub>-<i>o</i>-NMe<sub>2</sub>)](THF) (<b>8a</b>), respectively. In sharp
contrast to the earlier reports that the
nontraditional metal–C<sub>cage</sub> σ bonds in metal–carboranyl
complexes are generally inert toward electrophiles, the insertion
of unsaturated molecules into the Y–C<sub>cage</sub> 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
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