Solubility of gases in liquids. 18. High-precision determination of Henry fugacities for argon in liquid water at 2 to 40°C

The solubility of argon in pure liquid water was measured at ca. 100 kPa and from 2 to 40°C using an analytical method characterized by an imprecision of about ±0.05%. From the experimental results, Henry fugacities H _2,1 (T,P _s,1 ) (also known as Henry's Law constants or Henry coefficients) at the vapor pressure P _s,1 of water as well as Ostwald coefficients L _2,1 at infinite dilution were obtained. Measurements were made at roughly 0.5°C and/or 1° intervals between 2 and 8°C (region I), and at 5°C intervals above 10°C (region II). A difference plot lnH _2,1 /T suggests an unusual temperature dependence in region I, i.e., between 2 and 8°C. Because of this, the data were treated separately in two parts corresponding to these two regions. Our results are compared with the recent high-precision data of Krause and Benson (Henry fugacities), and with calorimetrically determined quantities (enthalpies and heat capacities of solution). Finally, experimental results are compared with values calculated via scaled particle theory.Communicated in part at the 2^nd International Symposium on Solubility Phenomena in Newark, New Jersey, August 12–15, 1986, and at the 4^th ISSP in Troy, New York, July 20–August 3, 1990.     

Bismuth compounds in organic synthesis. A one-pot synthesis of homoallyl ethers and homoallyl acetates from aldehydes catalyzed by bismuth triflate

[reaction: see text] Three one-pot methods for the conversion of aldehydes to homoallyl ethers catalyzed by Bi(OTf)(3).xH(2)O (1 < x < 4) have been developed. The one-pot synthesis of homoallyl ethers can be achieved either by in situ generation of the acetal followed by its reaction with allyltrialkylsilane or by a three-component synthesis in which the aldehyde, trimethylorthoformate or an alkoxytrimethylsilane and allyltrimethylsilane are mixed together in the presence of bismuth triflate (0.1-1.0 mol %). In addition, a three-component synthesis of homoallyl acetates, which is achieved by reacting the aldehyde, acetic anhydride, and allyltrimethylsilane in the presence of bismuth triflate (3.0-5.0 mol %), has been developed. The use of a relatively nontoxic, easy to handle, and inexpensive catalyst adds to the versatility of these methods.     

A simple and versatile method for the synthesis of acetals from aldehydes and ketones using bismuth triflate

Acetals are obtained in good yields by treatment of aldehydes and ketones with trialkyl orthoformate and the corresponding alcohol in the presence of 0.1 mol % Bi(OTf)3.4H2O. A simple procedure for the formation of acetals of diaryl ketones has also been developed. The conversion of carbonyl compounds to the corresponding 1,3-dioxolane using ethylene glycol is also catalyzed by Bi(OTf)3.4H2O (1 mol %). Two methods, both of which avoid the use of benzene, have been developed.     

Environment friendly organic synthesis using bismuth compounds. An efficient method for carbonyl-ene reactions catalyzed by bismuth triflate

Bismuth triflate (0.1 mol %) is a highly efficient catalyst for the cyclization of citronellal 1, a reaction that yields a ratio of 80:20 of isopulegol 2 and neoisopulegol 3. This methodology has also been extended to the synthesis of substituted piperidines. The bismuth triflate catalyzed ene reaction of aldehyde 4 gives a 70:30 mixture of piperidines 5 and 6. The advantages of these methods include the use of a highly efficient catalyst that is relatively nontoxic, cheap and easy to handle.     

Characterization of $(c)$-Riordan Arrays, Gegenbauer-Humbert-Type Polynomial Sequences, and $(c)$-Bell Polynomials

Here presented are the definitions of(c)-Riordan arrays and(c)-Bell polynomials which are extensions of the classical Riordan arrays and Bell polynomials.The characterization of(c)-Riordan arrays by means of the A-and Z-sequences is given,which corresponds to a horizontal construction of a(c)-Riordan array rather than its definition approach through column generating functions.There exists a one-to-one correspondence between GegenbauerHumbert-type polynomial sequences and the set of(c)-Riordan arrays,which generates the sequence characterization of Gegenbauer-Humbert-type polynomial sequences.The sequence characterization is applied to construct readily a(c)-Riordan array.In addition,subgrouping of(c)-Riordan arrays by using the characterizations is discussed.The(c)-Bell polynomials and its identities by means of convolution families are also studied.Finally,the characterization of(c)-Riordan arrays in terms of the convolution families and(c)-Bell polynomials is presented.     

P分之一Riordan矩阵及恒等式构造

For an integer p≥2 we construct vertical and horizontal one-pth Riordan arrays from a Riordan array.When p=2 one-pth Riordan arrays are reduced to well known half Riordan arrays.The generating functions of the A-sequences of vertical and horizontal one-pth Riordan arrays are found.The vertical and horizontal one-pth Riordan arrays provide an approach to construct many identities.They can also be used to verify some well known identities readily.     

A Unified Approach to Generalized Stirling Functions

Here presented is a unified approach to generalized Stirling functions by using generalized factorial functions, k-Gamma functions, generalized divided difference, and the unified expression of Stirling numbers defined in [16]. Previous well-known Stirling functions introduced by Butzer and Hauss [4], Butzer, Kilbas, and Trujilloet [6] and others are included as particular cases of our generalization. Some basic properties related to our general pattern such as their recursive relations, generating functions, and asymptotic properties are discussed,which extend the corresponding results about the Stirling numbers shown in [21] to the defined Stirling functions.     

Bismuth compounds in organic synthesis. Deprotection of ketoximes using bismuth bromide-bismuth triflate

Ketoximes undergo deprotection in CH₃CN/acetone/H₂O (3:6:1) in the presence of 20-40 mol% BiBr₃/5 mol% Bi(OTf)₃. Bismuth(III) salts are relatively non-toxic, insensitive to air and inexpensive. These features coupled with the use of a relatively non-toxic solvent system make this method an attractive alternative to existing routes for deprotection of ketoximes.     

Monotone iterative technique for periodic boundary value problems with causal operators

In this paper, we develop the monotone iterative technique for periodic boundary value problems with causal operators.