Jordan generalized derivations on triangular algebras

Let 𝒜 be a unital algebra and let ? be a unitary 𝒜-bimodule. We consider Jordan generalized derivations mapping from 𝒜 into ?. Our results on unitary algebras are applied to triangular algebras. In particular, we prove that any Jordan generalized derivation of a triangular algebra is a generalized derivation.     

Efficient chemoselective deprotection of silyl ethers using catalytic 1-chloroethyl chloroformate in methanol

Fast and chemoselective desilylation of silyl-protected alcohols was achieved using a catalytic amount of 1-chloroethyl chloroformate in methanol. With a minimal amount of 1-chloroethyl chloroformate as the source for anhydrous HCl, extremely efficient cleavage of silyl ethers of primary and secondary alcohols was accomplished, and chemoselective deprotection of one silyl ether in the presence of another silyl or other acid-labile group was possible through controlling the amount of the chloroformate and reaction time.     

Tris(pentafluorophenyl)silyl enol ethers: synthesis and aldol reactions

Silyl enol ethers bearing three pentafluorophenyl groups at the silicon atom are described. These compounds undergo uncatalyzed aldol reactions with aliphatic, α,β-unsaturated, and aromatic aldehydes. The observed reactivity is analyzed in terms of the Lewis acidity of the silyl fragment.     

First synthesis of 4-(arylsulfonyl)phenols by regioselective [3+3] cyclocondensations of 1,3-bis(silyloxy)-1,3-butadienes with 2-arylsulfonyl-3-ethoxy-2-en-1-ones

The formal [3+3] cyclization of 1,3-bis(silyloxy)-1,3-butadienes with readily available 2-arylsulfonyl-3-ethoxy-2-en-1-ones resulted in regioselective formation of 4-(arylsulfonyl)phenols.     

A Mild and Highly Efficient Method for the Preparation of Silyl Ethers using Fe(HSO4)3/Et3N by Chlorosilanes

A very efficient and mild procedure for preparation of silyl ethers from benzylic, allylic, propargilic alcohols, phenols, naphtoles and some of phenolic drugs with trimethylsilylchloride (TMSCl), triethylsilylchloride (TESCl) and t‐buthyldimethylsilyl chloride (TDSCl) ethers in the presence of Fe(HSO₄)₃/Et₃N in room temperature in excellent yields is reported. This procedure also allows the excellent selectivity for silylation of alcohols and phenols.     

Copper(I) Clusters with Trifunctional Silyl Amide Ligands. Synthesis and Crystal Structures of [Li(THF)4]2[Cu10{RSi(NPh)3}4] (R = Me,Ph, Vin)

Treatment of CuCl with the lithiated silyl amides RSi(NLiPh)₃ (R = Me, Ph, Vin) in THF as solvent led to the formation of the novel Cu^I cluster compounds [Li(THF)₄]₂[Cu₁₀{RSi(NPh)₃}₄]. For each of the three compounds the X‐ray crystal structure analysis revealed similar Si₄N₁₂Cu₁₀ cores which are based on cubane like Cu₈ cores bearing two additional peripheral copper atoms. The copper atoms are coordinated nearly linearly by the μ₅‐bridging silyl amide ligands with Cu–N distances in the range of 187.1(3) to 194.5(4) pm and N–Cu–N angles of 171.6(1) to 178.7(1)°. For each of the compounds the structural parameters are very similar which indicates that the structures are barely influenced by the different steric requirements of the organic groups bound to silicon.     

MgBr2·OEt2 mediated protection of alcohols with hexamethyldisilazane: An efficient catalytic route for the preparation of silyl ethers under solvent-free conditions

Various types of alcohols and phenols were rapidly protected by hexamethyldisilazane in good to excellent yields at room temperature in the presence of catalytic amount of magnesium bromide ethyl etherate under solvent-free conditions. Good to excellent chemoselectivity was demonstrated for competitive protection of primary hydroxyls in the presence of secondary and tertiary alcohols. Highly selective protection of phenols in the presence of aromatic amines was also demonstrated successfully.     

Vanishing Derivations and Co-Centralizing Generalized Derivations on Multilinear Polynomials in Prime Rings

Let R be a noncommutative prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, and f(x₁,…, x_n) be a multilinear polynomial over C, which is not central valued on R. Suppose that F and G are two generalized derivations of R and d is a nonzero derivation of R such that d(F(f(r))f(r) ? f(r)G(f(r))) = 0 for all r = (r₁,…, r_n) ∈ Rⁿ, then one of the following holds:

1. There exist a, p, q, c ∈ U and λ ∈C such that F(x) = ax + xp + λx, G(x) = px + xq and d(x) = [c, x] for all x ∈ R, with [c, a ? q] = 0 and f(x₁,…, x_n)² is central valued on R;

2. There exists a ∈ U such that F(x) = xa and G(x) = ax for all x ∈ R;

3. There exist a, b, c ∈ U and λ ∈C such that F(x) = λx + xa ? bx, G(x) = ax + xb and d(x) = [c, x] for all x ∈ R, with b + αc ∈ C for some α ∈C;

4. R satisfies s₄ and there exist a, b ∈ U and λ ∈C such that F(x) = λx + xa ? bx and G(x) = ax + xb for all x ∈ R;

5. There exist a′, b, c ∈ U and δ a derivation of R such that F(x) = a′x + xb ? δ(x), G(x) = bx + δ(x) and d(x) = [c, x] for all x ∈ R, with [c, a′] = 0 and f(x₁,…, x_n)² is central valued on R.

     

半素环上的右理想及其微商

R是半素环,d是R的微商,ρ是R的右理想,a是R中元素,如果对于ρ中的所有元素x,都有ad(x)ⁿ=0,其中n是一个固定的正整数,那么必有aρd(P)P=0.     

The reliability of measurements on electron energy distribution function in silane rf glow discharges

Electron energy distribution function (EEDF) is a key parameter of plasmas, which is directly proportional to the second derivative of the probe I-V characteristics. Because of an amplifying effect of unavoidable noises in the experimental probe I-V curves during the derivation process, the experimental I-V curves should be smoothed before performing the numerical derivation. This paper investigates the effect of adjustable factors used in the smoothing process on the deduced second derivative of the I-V curves, and an optimum group of the adjustable factors is selected to make the rms deviation of the smoothed I-V curves from the measured curves less than 1%. A simple differentiation circuit is designed and used to measure the EEDF parameter straightforwardly. It is the first time, so far as we know, to measure the EEDF parameters simultaneously by means of both numerical and circuit derivative methods under the same discharge conditions and on the same discharge equipment. The deviation between two groups of mean electron energy E and electron density n_e obtained by the above different methods is within about 7%. This apparently improves the reliability of the measurements of the EEDF parameters.