Quintic trigonometric Bézier curve with two shape parameters

The fifth degree of trigonometric Bézier curve called quintic with two shapes parameter is presented in this paper. Shape parameters provide more control on the shape of the curve compared to the ordinary Bézier curve. This technique is one of the crucial parts in constructing curves and surfaces because the presence of shape parameters will allow the curve to be more flexible without changing its control points. Furthermore, by changing the value of shape parameters, the curve still preserves its geometrical features thus makes it more convenient rather than altering the control points. But, to interpolate curves from one point to another or surface patches, we need to satisfy certain continuity constraints to ensure the smoothness not just parametrically but also geometrically

sj-docx-1-nms-10.1177_14614448231220346 – Supplemental material for But is it for us? Rural Chinese elders’ perceptions, concerns, and physical preferences regarding social robots

Supplemental material, sj-docx-1-nms-10.1177_14614448231220346 for But is it for us? Rural Chinese elders’ perceptions, concerns, and physical preferences regarding social robots by Xun “Sunny” Liu, Qi Shen and Jeffrey Hancock in New Media & Society</p

Synthesis of Dianionic β-Diketiminate Lanthanide Amides L′LnN(SiMe₃)₂(THF) by Deprotonation of the β-Diketiminate Ligand L (L = {[(2,6-<i>i</i>Pr₂C₆H₃)NC(CH₃)]₂CH}⁻) and the Transformation with [HNEt₃][BPh₄] to the Cationic Samarium Amide [LSmN(SiMe₃)₂][BPh₄]

Reaction of β-diketiminate lanthanide dichlorides LLnCl₂(THF)₂ (L = {[(2,6-<i>i</i>Pr₂C₆H₃)­NC­(CH₃)]₂CH}⁻) with 2 equiv of NaN­(SiMe₃)₂ in toluene afforded lanthanide amide complexes supported by a dianionic β-diketiminate ligand L′, L′LnN­(SiMe₃)₂(THF) (L′ <b>=</b>{(2,6-<i>i</i>Pr₂C₆H₃)­NC­(CH₂)­CHC­(CH₃)­N­(2,6-<i>i</i>Pr₂C₆H₃)}^2–, Ln = Yb (<b>1</b>), Y (<b>2</b>), Gd (<b>3</b>), Sm (<b>4</b>)), in moderate yields via deprotonation of L. Addition of a small amount of THF led to an increase of the yields of <b>1</b>–<b>4</b>. Lanthanide metals have a great influence on the deprotonation of L. The same reaction with LNdCl₂(THF)₂ did not afford the analogous complex L′NdN­(SiMe₃)₂(THF), but the normal diamide complex LNd­[N­(SiMe₃)₂]₂ (<b>5</b>) was isolated instead. The metathesis reaction of the triply bridged dichlorides of Sm, LSmCl­(μ-Cl)₃SmL­(THF), with 2 equiv of NaN­(SiMe₃)₂ yielded the diamide complexes LSm­[N­(SiMe₃)₂]₂ in toluene, while complex <b>4</b> was formed instead in a mixture of toluene and THF. In contrast, the same reactions with LYbCl­(μ-Cl)₃YbL­(THF) either in toluene or in a mixture of toluene and THF both afforded <b>1</b>. Treatment of <b>4</b> with [HNEt₃]­[BPh₄] in THF at room temperature gave the novel cationic Sm β-diketiminate amide complex [LSmN­(SiMe₃)₂(THF)₂]­[BPh₄] (<b>7</b>) in good yield. Complexes <b>1</b>–<b>5</b> and <b>7</b> have been confirmed by single-crystal X-ray structural analyses. The mechanism of deprotonation of L was discussed

Esterification of the Primary Benzylic C–H Bonds with Carboxylic Acids Catalyzed by Ionic Iron(III) Complexes Containing an Imidazolinium Cation

The first iron-catalyzed esterification of the primary benzylic C–H bonds with carboxylic acids using di-<i>tert</i>-butyl peroxide as an oxidant is achieved by novel ionic iron­(III) complexes containing an imidazolinium cation. The use of well-defined, air-stable, and available iron­(III) complex in a 5 mol % loading and readily available starting materials with a broad generality and outstanding sterically hindered tolerance renders this methodology a useful alternative to other protocols that are typically employed for the synthesis of benzyl esters

Esterification of the Primary Benzylic C–H Bonds with Carboxylic Acids Catalyzed by Ionic Iron(III) Complexes Containing an Imidazolinium Cation

The first iron-catalyzed esterification of the primary benzylic C–H bonds with carboxylic acids using di-<i>tert</i>-butyl peroxide as an oxidant is achieved by novel ionic iron­(III) complexes containing an imidazolinium cation. The use of well-defined, air-stable, and available iron­(III) complex in a 5 mol % loading and readily available starting materials with a broad generality and outstanding sterically hindered tolerance renders this methodology a useful alternative to other protocols that are typically employed for the synthesis of benzyl esters

Synthesis of a Naphthalene-Bridged Bis(guanidinato)ytterbium(II) Complex and an Unexpected Pathway in Its Reaction with CH₃CN, <i>p</i>‑ClC₆H₄CH₂CN, and Ph₂CHCN

A novel binuclear ytterbium­(II) complex supported by a naphthalene-bridged bis­(guanidinate) ligand, [Yb­(μ-L)­(THF)]₂ (<b>1</b>; L = 1,8-C₁₀H₆{NC­(N^<i>i</i>Pr)­(NH^<i>i</i>Pr)}₂), was synthesized by the reduction reaction of [Yb­(L)­Cl­(THF)₂] with Na/K alloy in THF and structurally characterized. The reactions of <b>1</b> with CH₃CN and <i>p</i>-ClC₆H₄CH₂CN resulted in the formation of the corresponding binuclear (crotononitrileamido)­ytterbium­(III) complexes [Yb­(L)­(μ­(<i>N,N′</i>)-N­(H)­C­(Me)C­(H)­CN)­(THF)]₂ (<b>2</b>) and [Yb­(L)­(μ­(<i>N</i>,<i>N</i>′)-N­(H)­C­(CH₂C₆H₄<i>-p</i>-Cl)C­(C₆H₄<i>-p</i>-Cl)­CN)­(THF)]₂ (<b>3</b>) via metalation of the nitrile, followed by insertion of a second nitrile molecule. Treatment of <b>1</b> with the bulkier Ph₂CHCN afforded the mononuclear (keteniminato)­ytterbium­(III) complex [Yb­(L)­(NCCPh₂)­(THF)₂] (<b>4</b>) by deprotonation of Ph₂CHCN. The molecular structures of <b>2</b>–<b>4</b> have been determined

Bis(β-diketiminate) Rare-Earth-Metal Borohydrides: Syntheses, Structures, and Catalysis for the Polymerizations of l‑Lactide, ε‑Caprolactone, and Methyl Methacrylate

Reaction of LnCl₃ (Ln = Y, Yb) with 2 equiv of NaL^2,6‑ipr2_Ph (L^2,6‑ipr2_Ph = [(2,6-^<i>i</i>Pr₂C₆H₃)­NC­(Me)­CHC­(Me)­N­(C₆H₅)]⁻) afforded the chlorides (L^2,6‑ipr2_Ph)₂YCl (<b>1</b>) and (L^2,6‑ipr2_Ph)₂YbCl (<b>2</b>). Crystal structure analysis revealed <b>2</b> to be the unsolvated monomer. Treatment of the chlorides <b>1</b> and <b>2</b> with NaBH₄ in a 1/1 molar ratio in THF led to the preparation of the monoborohydrides (L^2,6‑ipr2_Ph)₂LnBH₄ (Ln = Y (<b>3</b>), Yb (<b>4</b>)) in good yields. Reaction of LnCl₃ (Ln = Y, Yb) with 2 equiv of NaL^2‑Me (L^2‑Me = [N­(2-MeC₆H₄)­C­(Me)]₂CH^–) in THF, followed by treatment with 1 equiv of NaBH₄, afforded the monoborohydrides (L^2‑Me)₂LnBH₄ (Ln = Y (<b>5</b>), Yb (<b>6</b>)). Complexes <b>3</b>–<b>6</b> were fully characterized, including X-ray crystal structure analyses. Complexes <b>3</b>–<b>6</b> are isostructural. The central metal in each complex is ligated by two β-diketiminate ligands and one η³-BH₄^– group in a distorted trigonal bipyramid. Complexes <b>3</b>–<b>6</b> were found to be highly active in the ring-opening polymerization of l-lactide (l-LA) and ε-caprolactone (ε-CL) to give polymers with relatively narrow molar mass distributions. The activity depends on both the central metal and the ligand (Y > Yb and L^2,6‑ipr2_Ph > L^2‑Me). The best control over the molar mass was found for complex <b>6</b>. The <i>M</i>_n(obsd) values (<i>M</i>_n = the number-average molar mass) of the resulting PCL are in good agreement with <i>M</i>_n(calcd), with a ratio of monomer to <b>6</b> of up to 1000. The polymerization kinetics of l-LA in THF at 20 °C by complex <b>6</b> displays a first-order dependence on the monomer concentration. Notably, the binary <b>6</b>/^<i>i</i>PrOH system exhibited an “immortal” nature and proved able to quantitatively convert 10 000 equiv of l-LA with up to 200 equiv of ^<i>i</i>PrOH per metal initiator. All the obtained PLAs showed monomodal, narrow distributions (<i>M</i>_w/<i>M</i>_n = 1.06–1.11), with the <i>M</i>_n values decreasing proportionally with an increasing amount of ^<i>i</i>PrOH. Complex <b>4</b> can also initiate the polymerization of methyl methacrylate (MMA) at −40 °C with high activity, affording the PMMA with 83.3% syndiotacticity

Synthesis of Group 4 Metal Complexes Stabilized by an Amine-Bridged Bis(phenolato) Ligand and Their Catalytic Behavior in Intermolecular Hydroamination Reactions

Zirconium and titanium complexes <b>1</b> and <b>2</b>, bearing an amine-bridged bis­(phenolato) ligand, have been synthesized and characterized. Although <b>1</b> and <b>2</b> were inactive in catalyzing intermolecular hydroamination reactions, cationic complexes generated in situ from treatment of <b>1</b> and <b>2</b> with borate [Ph₃C]­[B­(C₆F₅)₄], respectively, were found to be highly active. In general, excellent yields (up to >99%) and 100% regioselectivity for a broad range of terminal alkynes and anilines were observed within a reaction time of 1 h. Reactions with internal alkynes of moderate sterics also led to good yields and moderate regioselectivity. A kinetic study was also conducted, which provided some insights into the mechanism of hydroamination reactions

Synthesis of Group 4 Metal Complexes Stabilized by an Amine-Bridged Bis(phenolato) Ligand and Their Catalytic Behavior in Intermolecular Hydroamination Reactions

Zirconium and titanium complexes <b>1</b> and <b>2</b>, bearing an amine-bridged bis­(phenolato) ligand, have been synthesized and characterized. Although <b>1</b> and <b>2</b> were inactive in catalyzing intermolecular hydroamination reactions, cationic complexes generated in situ from treatment of <b>1</b> and <b>2</b> with borate [Ph₃C]­[B­(C₆F₅)₄], respectively, were found to be highly active. In general, excellent yields (up to >99%) and 100% regioselectivity for a broad range of terminal alkynes and anilines were observed within a reaction time of 1 h. Reactions with internal alkynes of moderate sterics also led to good yields and moderate regioselectivity. A kinetic study was also conducted, which provided some insights into the mechanism of hydroamination reactions

Evaluation of Bacterial Expansin EXLX1 as a Cellulase Synergist for the Saccharification of Lignocellulosic Agro-Industrial Wastes

<div><p>Various types of lignocellulosic wastes extensively used in biofuel production were provided to assess the potential of EXLX1 as a cellulase synergist. Enzymatic hydrolysis of natural wheat straw showed that all the treatments using mixtures of cellulase and an optimized amount of EXLX1, released greater quantities of sugars than those using cellulase alone, regardless of cellulase dosage and incubation time. EXLX1 exhibited different synergism and binding characteristics for different wastes, but this can be related to their lignocellulosic components. The cellulose proportion could be one of the important factors. However, when the cellulose proportion of different biomass samples exhibited no remarkable differences, a higher synergism of EXLX1 is prone to occur on these materials, with a high proportion of hemicellulose and a low proportion of lignin. The information could be favorable to assess whether EXLX1 is effective as a cellulase synergist for the hydrolysis of the used materials. Binding assay experiments further suggested that EXLX1 bound preferentially to alkali pretreated materials, as opposed to acid pretreated materials under the assay condition and the binding preference would be affected by incubation temperature.</p></div