Thermal stability of organoclays with mono- and di-alkyl cationic surfactants

In this study, mono- and di-alkyl cationic surfactants were used to prepare organoclays through ion exchange and the prepared organoclays were characterised by X-ray diffraction (XRD) and thermogravimetric analysis (TG). Larger basal spacings were observed in the interlayer of the organoclays intercalated with DDDMA than organoclays intercalated with DDTMA. The DTG curves identify the thermal stability of organoclays intercalated with two different types of surfactants (DDTMA and DDDMA) and the different arrangements of the surfactant molecules intercalated in the montmorillonite. Both organoclays intercalated with organic surfactant molecules proved to be thermally stable at high temperature. This study provides an understanding of the structure and properties of organoclays, which will enhance the potential applications of organoclays in environmental remediation.     

Practical Method for Analysis of Immiscible Displacement in Laboratory Core Tests

Abstract. An accurate analytical interpretation method to determine the Leverett function (f_w)and its derivative (f_w) from immiscible displacement data in core plugs is presented. Linear equations are developed to describe the displacement processes occurring before and after breakthrough. A quadratic function is introduced to represent the saturation distribution along the cores. The relationships derived in this study can be used for analysis of core tests involving constant injection rates and constant pressure differences. The applicability, practicality, and accuracy of the new analytical method are verified by means of the experimental data obtained in the present study and by those reported in the literature.     

A Ramsey-Type Result for Convex Sets

Given a family of n convex compact sets in the plane, one canalways choose n of them which are either pairwise disjoint orpairwise intersecting. On the other hand, there exists a familyof n segments in the plane such that the maximum size of a subfamilywith pairwise disjoint or pairwise intersecting elements inn^log2/log5 n^0·431.     

3-Alkyl-1-benzoxepin-5-on-Derivate und 2-Alkyl-1, 4-naphthochinone aus 2-Acylaryl-propargyläthern

3-Alkyl-1-benzoxepin-5-one derivatives and 2-alkyl-1,4-naphtoquinones from 2-acylaryl propargyl ethers. It was found that 3-alkyl-1-benzoxepin-5(2H)-ones of type B can be synthesized by treating 2-acylaryl propargyl ethers of type A with sodium methylsulfinyl methide (NaMSM, dimesyl sodium) (Scheme 13). Oxepinone derivatives of type B undergo ring contraction with base (also NaMSM) to yield the quinol derivatives C which, oxidize (during work-up), if R² = H, to the 1,4-naphthoquinones D (Scheme 13). The propargyl ethers used are listed in Scheme 1. The naphthalene derivatives 1 and 3 give oxepinones (E- 9 and a mixture of 14/15 respectively), whereas the expected oxepinone from 2 is transformed directly into the quinone 11 (Scheme 2, 3 and 5). Isomerizations of 2-acetylphenyl propargyl ethers ( 4, 5 and 6 ) (Schemes 6, 7 and 8) are less successful because of side reactions. If however the acetyl group is replaced by a propionyl or substituted propionyl group (as in ethers 7 and 8 ) oxepinones are obtained again in good yield (Scheme 9). The mechanistic pathway for the transformation of naphthyl propargyl ethers (and phenyl derivatives) under influence of NaMSM is shown in Scheme 10. The base-catalysed conversion of 4-phenyl-l-benzoxepin-5(2H)-one,benzo[f]furo[2,3-c](10 H)-oxepin-4-oncsand 3-methoxy-G,11- dihydro-dibenzo[b, e]loxepin-11-oneinto thc corresponding quinones has been reported [13] [20] [21]. The conversion of 2-acylaryl propargyl others via the isolable benzoxepin-5-one derivativcs or directly into the specifically substituted 1,4-naphthoquinone derivatives is of synthetic interest.     

The number of large prime divisors of consecutive integers

Let ?(N) > 0 be a function of positive integers N and such that ?(N) → 0 and N^?(N) → ∞ as N → + ∞. Let Nν_N(n:…) be the number of positive integers n ≤ N for which the property stated in the dotted space holds. Finally, let g(n; N, ?, z) be the number of those prime divisors p of n which satisfy N^Z?(N) ? p ? N^?(N), 0 < z < 1 In the present note we show that for each k = 0, ±1, ±2,…, as N → ∞, limv_N(n : g(n; N, ?, z) ? g(n + 1; N, ?z) = k) exists and we determine its actual value. The case k = 0 induced the present investigation. Our solution for this value shows that the natural density of those integers n for which n and n + 1 have the same number of prime divisors in the range (1) exists and it is positive.     

Solution of Scott's Problem on the Number of Directions Determined by a Point Set in 3-Space

Let P be a set of n points in R³, not all in a common plane. We solve a problem of Scott (1970) by showing that the connecting lines of P assume at least 2n - 5 different directions if n is odd and at least 2n - 7 if n is even. The bound for odd n is sharp.     

Degenerate Dirichlet Problems Related to the Invariant Measure of Elasto-Plastic Oscillators

A stochastic variational inequality is proposed to model a white noise excited elasto-plastic oscillator. The solution of this inequality is essentially a continuous diffusion process for which a governing diffusion equation is obtained to study the evolution in time of its probability distribution. The diffusion equation is degenerate, but using the fact that the degeneracy occurs on a bounded region we are able to show the existence of a unique solution satisfying the desired properties. We prove the ergodic properties of the process and characterize the invariant measure. Our approach relies on extending Khasminskii’s method (Stochastic Stability of Differential Equations, Sijthoff and Noordhoff, 1980), which in the present context leads to the study of degenerate Dirichlet problems with nonlocal boundary conditions. This research was partially supported by a grant from CEA, Commissariat à l’énergie atomique and by the National Science Foundation under grant DMS-0705247.     

Synthesis of D- and L-5-Oxaproline and of a New Captopril Analogue

The 1,3-dipolar cycloaddition of the C-t-butyloxycarbonyl-N -mannosyl-nitrone 5 , formed in situ from the partially protected D -mannose-oxime 3 and the glyoxylate 4 , to ethylene gave preferentially the (3S)-N-glycosyl-isoxazolidine 6 which was transformed into the 3-isoxazolidine-carboxylate (L -5-oxaproline ester) 12 and into some derivatives thereof. The (S)-configuration of 12 was proved by chemical correlation with a derivative of L -asparagine. The D -5-oxaproline ester was obtained from the corresponding N-ribosyl-nitrone 24 . Two protected dipeptides containing either C-terminal- ( 28 ) or N-terminal-5-oxaproline (= Opro) ( 30 ) were synthesized. Starting from 12 , the analogue 1 of captopril® ( 2 ) was prepared and its activity as an inhibitor of the angiotensin-converting-enzyme (ACE) was examined.