Analytical evaluation of lower critical hydrostatic pressure for imperfect cylindrical shells of moderate length

The paper applies generalized power series to determine effectively the lower critical hydrostatic pressure for imperfect cylindrical shells. The basic equations were assumed in the form derived by W.A. Nash. Two variants as regards the number of circumferential half-wavelengths are discussed: m constant during buckling, thus corresponding to upper critical pressure, and m furnishing minimal value of lower critical pressure. It is found that the dependence of lower critical pressure on an imperfection parameter V is linear, i.e. smaller than in the case of the upper critical pressure which decreases with $\text{V}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$.     

Direct Synthesis of Amphiphilic α-, β-, and γ-Cyclodextrins

ABSTRACT

The clean one step synthesis of the amphiphilic α-, β-, and γ-cyclodextrins starting from per-(6-bromo-6-deoxy)-α-, -β-, and -γ-cyclodextrins is described. The role of the lipophilic tail is played by various aryl groups (phenyl, p-bromophenyl, p-O-butoxyphenyl, p-pentylphenyl, and o-, m-, and p-nitrophenyl) linked by a thioether bridge to the position C-6 of each glucopyranose unit. The yields of the S-alkylation reactions were very high (85-95%).     

Alkali metal cation complexation by 1,3-alternate,mono-ionisable calix[4]arene-benzocrown-6 compounds

Alkali metal cation extraction behaviour for two series of 1,3-alternate, mono-ionisable calix[4]arene-benzocrown-6 compounds is examined. In Series 1, the proton-ionisable group (PIG) is a substituent on the benzo group of the polyether ring that directs it away from the crown ether cavity. In Series 2, the PIG is attached to one para position in the calixarene framework, thereby positioning it over the crown ether ring. Competitive solvent extraction of alkali metal cations from aqueous solutions into chloroform shows high Cs⁺ efficiency and selectivity. Single-species extraction pH profiles of Cs⁺ for Series 1 and 2 ligands with the same PIG are very similar. Thus, association of Cs⁺ with the calixcrown ring is more important than the position of the PIG relative to the crown ether cavity. Solid-state structures of two unionised ligands from Series 2 are presented. Also described is a crystal containing two different ionised ligand–Cs⁺ complexes.     

Isolation of terpenoids from Pimpinella anisum essential oil by high‐performance counter‐current chromatography

High‐performance counter‐current chromatography was successfully used for the isolation and purification of terpenoid compounds from the essential oil of Pimpinella anisum L. A two‐phase solvent system composed of n‐heptane/methanol/ethyl acetate/water (5:2:5:2, v/v/v/v) was suitable for the purification of linalool, terpinen‐4‐ol, α‐terpineol, p‐anisaldehyde, while n‐heptane/methanol (1:1, v/v) was used for the isolation of anethole and foeniculin. A scale‐up process from analytical to preparative was developed. Additionally, a stepwise gradient elution was applied and instead of two different runs, 40 min each, one 80 min separation was performed; although the time of separation remains the same, it was possible to repeat the efficiency even if the water‐containing mobile phase was changed to a nonaqueous system. The obtained essential oil, as well as purified compounds, was analyzed by GC. A total of 0.64 mg of linalool, 0.52 mg of terpinen‐4‐ol, 0.10 mg of α‐terpineol, 0.62 mg of p‐anisaldehyde, 15 mg of anethole, and 2.12 mg of foeniculin were obtained from 210 mg of the essential oil of P. anisum L. in a short time with purities of 99, 98, 94, 93.54, 93, and 93.6%, respectively.     

Application of reversed-phase high-performance liquid chromatography with fluorimetric detection for simultaneous assessment of global DNA and total RNA methylation in Lepidium sativum: effect of plant exposure to Cd(II) and Se(IV)

In the present work, application of the previously established reversed-phase liquid chromatography procedure based on fluorescent labeling of cytosine and methylcytosine moieties with 2-bromoacetophenone (HPLC-FLD) is presented for simultaneous evaluation of global DNA and total RNA methylation at cytosine carbon 5. The need for such analysis was comprehended from the recent advances in the field of epigenetics that highlight the importance of non-coding RNAs in DNA methylation and suggest that RNA methylation might play a similar role in the modulation of genetic information, as previously demonstrated for DNA. In order to adopt HPLC-FLD procedure for DNA and RNA methylation analysis in a single biomass extract, two extraction procedures with different selectivity toward nucleic acids were examined, and a simplified calibration was designed allowing for evaluation of methylation percentage based on the ratio of chromatographic peak areas: cytidine/5-methylcytidine for RNA and 2´-deoxycytidine/5-methyl-2′-deoxycytidine for DNA. As a proof of concept, global DNA and total RNA methylation were determined in Lepidium sativum hydroponically grown in the presence of different Cd(II) or Se(IV) concentrations, expecting that plant exposure to abiotic stress might affect not only global DNA but also total RNA methylation. The results obtained showed the increase of DNA methylation in the treated plants up to concentration levels 2 mg?L^?1 Cd and 1 mg?L^?1 Se in the growth medium. For higher stressors’ concentration, global DNA methylation tended to decrease. Most importantly, an inverse correlation was found between DNA and RNA methylation levels (r?=??0.6788, p?=?0.031), calling for further studies of this particular modification of nucleic acids in epigenetic context.     

Metal ion extraction by cone p-tert-butylcalix[4]arene-1,3-crown-5 with two N-(X)sulfonyl carbamoylmethoxy side arms and -1,3-monothiacrown-5 analogues

Four cone p-tert-butylcalix[4]arene-1,3-monothiacrown-5 ligands each with two N-(X)sulfonyl carbamoylmethoxy side arms are synthesized for comparison with analogs having only oxygen heteroatoms in the crown ether ring. Solvent extractions of hard alkali metal and alkaline earth metal cations, intermediate Pb²⁺, and soft Hg²⁺ from aqueous solutions into chloroform by these ligands are utilized to probe the effects of sulfur replacement in the crown ether ring on metal ion complexation.     

The Lagrange-Newton method for state constrained optimal control problems

Local convergence of the Lagrange-Newton method for optimization problems with two-norm discrepancy in abstract Banach spaces is investigated. Based on stability analysis of optimization problems with two-norm discrepancy, sufficient conditions for local superlinear convergence are derived. The abstract results are applied to optimal control problems for nonlinear ordinary differential equations subject to control and state constraints.This research was completed while the second author was a visitor at the University of Bayreuth, Germany, supported by grant No. CIPA3510CT920789 from the Commission of the European Communities.     

Some representations of midconvex set-valued functions

Summary In this note we establish conditions under which every midconvex set-valued function can be represented as sum of an additive function and a convex set-valued function. These results improve some theorems obtained in [8], [10] and [3]. Some results on local Jensen selections of midconvex set-valued functions are also given.     

Sensitivity analysis for parametric control problems with control-state constraints

Parametric nonlinear control problems subject to vector-valued mixed control-state constraints are investigated. The model perturbations are implemented by a parameter p of a Banach-space P. We prove solution differentiability in the sense that the optimal solution and the associated adjoint multiplier function are differentiable functions of the parameter. The main assumptions for solution differentiability are composed by regularity conditions and recently developed second-order sufficient conditions (SSC). The analysis generalizes the approach in [16, 20] and establishes a link between (1) shooting techniques for solving the associated boundary value problem (BVP) and (2) SSC. We shall make use of sensitivity results from finite-dimensional parametric programming and exploit the relationships between the variational system associated to BVP and its corresponding Riccati equation.Solution differentiability is the theoretical backbone for any numerical sensitivity analysis. A numerical example with a vector-valued control is presented that illustrates sensitivity analysis in detail.