146 research outputs found

    ДослідТСння сорбції Ρ‚Π΅Ρ‚Ρ€Π°Π°Π»ΠΊΡ–Π»ΡŒΠ½ΠΈΡ… ΠΏΠΎΡ…Ρ–Π΄Π½ΠΈΡ… калікс[4]Π°Ρ€Π΅Π½Ρ–Π² Ρ– калікс[4]Ρ€Π΅Π·ΠΎΡ€Ρ†ΠΈΠ½Π°Ρ€Π΅Π½Ρ–Π² Π· ΠΏΠΎΠ²Π΅Ρ€Ρ…Π½Π΅ΡŽ LiChrosorb RP 18 ΠΌΠ΅Ρ‚ΠΎΠ΄Π°ΠΌΠΈ ОЀ Π’Π•Π Π₯ Ρ‚Π° молСкулярного модСлювання

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    Tetrahydroxycalix[4]arene, tetraalkoxycalix[4]arenes and tetraalkylcalix[4]resorcinarenes are capable to reversible adsorption on the surface of the hydrophobic support LiChrosorb RP 18 under conditions of the reversed-phase high performance liquid chromatography. The main chromatographic characteristics of tetrahydroxycalix[4]arene, a series of tetraalkoxycalix[4]arenes and tetraalkylcalix[4]resorcinarenes have been determined. It has been found that in the conditions selected (the mobile phase is acetonitrile/water, 86/14, v/v) the retention times of the compounds studied are in the wide range from 4.67 min to 88.0 min depending on the nature of the substituents in the macrocyclic skeleton of the molecule. Thus, the retention times increase with increase of the length of the alkyl substituents at the lower rim of the calixarene macrocycle. According to the molecular modelling data the most effective sorption is explained by the inclusion of LiChrosorb RP 18 octadecyl groups into the lipophilic cavity formed by the alkyl substituents at the lower rim of the macrocycle of calixarene/calixresorcinarene. Thus, the molecular cavity formed by the benzene rings remains opened for the Host-Guest complexation with the analyte molecules. This sorption of tetraalkoxycalix[4]arenes and tetraalkylcalix[4]arenes on the LiChrosorb RP 18 surface can significantly improve its resolution ability in RP HPLC analysis. The influence of replacement of tetrahydroxycalix[4]arene hydroxyl protons with the alkyl groups on the conformation of the macrocycle has been studied.ВСтрагидроксикаликс[4]Π°Ρ€Π΅Π½, тСтраалкоксикаликс[4]Π°Ρ€Π΅Π½Ρ‹ ΠΈ тСтраалкилкаликс[4]Ρ€Π΅Π·ΠΎΡ€Ρ†ΠΈΠ½Π°Ρ€Π΅Π½Ρ‹ ΠΎΠ±Ρ€Π°Ρ‚ΠΈΠΌΠΎ ΡΠΎΡ€Π±ΠΈΡ€ΡƒΡŽΡ‚ΡΡ Π½Π° повСрхности Π³ΠΈΠ΄Ρ€ΠΎΡ„ΠΎΠ±Π½ΠΎΠΉ насадки LiChrosorb RP 18 Π² условиях ΠΎΠ±Ρ€Π°Ρ‰Π΅Π½Π½ΠΎ-Ρ„Π°Π·Π½ΠΎΠΉ высокоэффСктивной Тидкостной Ρ…Ρ€ΠΎΠΌΠ°Ρ‚ΠΎΠ³Ρ€Π°Ρ„ΠΈΠΈ. ΠžΠΏΡ€Π΅Π΄Π΅Π»Π΅Π½Ρ‹ основныС хроматографичСскиС характСристики тСтрагидроксикаликс[4]Π°Ρ€Π΅Π½Π°, сСрии тСтраалкоксикаликс[4]Π°Ρ€Π΅Π½ΠΎΠ² ΠΈ тСтраалкилкаликс[4]Ρ€Π΅Π·ΠΎΡ€Ρ†ΠΈΠ½Π°Ρ€Π΅Π½ΠΎΠ². УстановлСно, Ρ‡Ρ‚ΠΎ Π² Π²Ρ‹Π±Ρ€Π°Π½Π½Ρ‹Ρ… условиях (подвиТная Ρ„Π°Π·Π° – Π°Ρ†Π΅Ρ‚ΠΎΠ½ΠΈΡ‚Ρ€ΠΈΠ»/Π²ΠΎΠ΄Π° Π² ΡΠΎΠΎΡ‚Π½ΠΎΡˆΠ΅Π½ΠΈΠΈ 86/14 ΠΏΠΎ ΠΎΠ±ΡŠΠ΅ΠΌΡƒ) Π²Ρ€Π΅ΠΌΠ΅Π½Π° удСрТивания исслСдуСмых соСдинСний находятся Π² ΡˆΠΈΡ€ΠΎΠΊΠΎΠΌ Π΄ΠΈΠ°ΠΏΠ°Π·ΠΎΠ½Π΅ 4.67-88.0 ΠΌΠΈΠ½ Π² зависимости ΠΎΡ‚ ΠΏΡ€ΠΈΡ€ΠΎΠ΄Ρ‹ замСститСлСй Π² макроцикличСском скСлСтС ΠΌΠΎΠ»Π΅ΠΊΡƒΠ»Ρ‹. ΠŸΡ€ΠΈ этом врСмя удСрТивания возрастаСт ΠΏΠΎ ΠΌΠ΅Ρ€Π΅ увСличСния Π΄Π»ΠΈΠ½Ρ‹ Π°Π»ΠΊΠΈΠ»ΡŒΠ½Ρ‹Ρ… замСститСлСй Π½Π° Π½ΠΈΠΆΠ½Π΅ΠΌ ΠΎΠ±ΠΎΠ΄Π΅ каликсарСнового ΠΌΠ°ΠΊΡ€ΠΎΡ†ΠΈΠΊΠ»Π°. Богласно Π΄Π°Π½Π½Ρ‹ΠΌ молСкулярного модСлирования Π½Π°ΠΈΠ±ΠΎΠ»Π΅Π΅ эффСктивная сорбция происходит Π·Π° счСт Π²ΠΊΠ»ΡŽΡ‡Π΅Π½ΠΈΡ ΠΎΠΊΡ‚Π°Π΄Π΅Ρ†ΠΈΠ»ΡŒΠ½ΠΈΡ… Π³Ρ€ΡƒΠΏΠΏ насадки Π² Π»ΠΈΠΏΠΎΡ„ΠΈΠ»ΡŒΠ½ΡƒΡŽ ΠΏΠΎΠ»ΠΎΡΡ‚ΡŒ, ΠΎΠ±Ρ€Π°Π·ΠΎΠ²Π°Π½Π½ΡƒΡŽ Π°Π»ΠΊΠΈΠ»ΡŒΠ½Ρ‹ΠΌΠΈ замСститСлями Π½ΠΈΠΆΠ½Π΅Π³ΠΎ ΠΎΠ±ΠΎΠ΄Π° ΠΌΠ°ΠΊΡ€ΠΎΡ†ΠΈΠΊΠ»Π° каликсарСна/каликсрСзорцинарСна. ΠŸΡ€ΠΈ этом молСкулярная ΠΏΠΎΠ»ΠΎΡΡ‚ΡŒ, сформированная Π±Π΅Π½Π·ΠΎΠ»ΡŒΠ½Ρ‹ΠΌΠΈ ΠΊΠΎΠ»ΡŒΡ†Π°ΠΌΠΈ ΠΌΠ°ΠΊΡ€ΠΎΡ†ΠΈΠΊΠ»Π°, остаСтся ΠΎΡ‚ΠΊΡ€Ρ‹Ρ‚ΠΎΠΉ для комплСксообразования с ΠΌΠΎΠ»Π΅ΠΊΡƒΠ»Π°ΠΌΠΈ Π°Π½Π°Π»ΠΈΡ‚ΠΎΠ². Вакая сорбция тСтраалкоксикаликс[4]Π°Ρ€Π΅Π½ΠΎΠ² ΠΈ тСтраалкилкаликс[4]Ρ€Π΅Π·ΠΎΡ€Ρ†ΠΈΠ½Π°Ρ€Π΅Π½ΠΎΠ² Π½Π° повСрхности хроматографичСской насадки LiChrosorb RP 18 ΠΌΠΎΠΆΠ΅Ρ‚ сущСствСнно ΡƒΠ»ΡƒΡ‡ΡˆΠΈΡ‚ΡŒ Π΅Π΅ ΡΠ΅Π»Π΅ΠΊΡ‚ΠΈΠ²Π½ΠΎΡΡ‚ΡŒ ΠΏΠΎ ΠΎΡ‚Π½ΠΎΡˆΠ΅Π½ΠΈΡŽ ΠΊ Π°Π½Π°Π»ΠΈΡ‚Π°ΠΌ Π² условиях ΠΎΠ±Ρ€Π°Ρ‰Π΅Π½Π½ΠΎ-Ρ„Π°Π·Π½ΠΎΠΉ высокоэффСктивной Тидкостной Ρ…Ρ€ΠΎΠΌΠ°Ρ‚ΠΎΠ³Ρ€Π°Ρ„ΠΈΠΈ. ИсслСдовано влияниС Π·Π°ΠΌΠ΅Π½Ρ‹ Π³ΠΈΠ΄Ρ€ΠΎΠΊΡΠΈΠ»ΡŒΠ½Ρ‹Ρ… ΠΏΡ€ΠΎΡ‚ΠΎΠ½ΠΎΠ² тСтрагидроксикаликс[4]Π°Ρ€Π΅Π½Π° Π°Π»ΠΊΠΈΠ»ΡŒΠ½Ρ‹ΠΌΠΈ Π³Ρ€ΡƒΠΏΠΏΠ°ΠΌΠΈ Π½Π° ΠΊΠΎΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΡŽ макроцикличСского скСлСта ΠΌΠΎΠ»Π΅ΠΊΡƒΠ»Ρ‹.ВСтрагідроксикалікс[4]Π°Ρ€Π΅Π½, тСтраалкоксикалікс[4]Π°Ρ€Π΅Π½ΠΈ Ρ‚Π° тСтраалкілкалікс[4]Ρ€Π΅Π·ΠΎΡ€Ρ†ΠΈΠ½Π°Ρ€Π΅Π½ΠΈ Π·Π΄Π°Ρ‚Π½Ρ– Π΄ΠΎ ΠΎΠ±Π΅Ρ€Π½Π΅Π½ΠΎΡ— сорбції Π½Π° ΠΏΠΎΠ²Π΅Ρ€Ρ…Π½Ρ– Π³Ρ–Π΄Ρ€ΠΎΡ„ΠΎΠ±Π½ΠΎΡ— насадки LiChrosorb RP 18 Π² ΡƒΠΌΠΎΠ²Π°Ρ… ΠΎΠ±Π΅Ρ€Π½Π΅Π½ΠΎ-Ρ„Π°Π·Π½ΠΎΡ— високоСфСктивної Ρ€Ρ–Π΄ΠΈΠ½Π½ΠΎΡ— Ρ…Ρ€ΠΎΠΌΠ°Ρ‚ΠΎΠ³Ρ€Π°Ρ„Ρ–Ρ—. Π’ΠΈΠ·Π½Π°Ρ‡Π΅Π½Ρ– основні Ρ…Ρ€ΠΎΠΌΠ°Ρ‚ΠΎΠ³Ρ€Π°Ρ„Ρ–Ρ‡Π½Ρ– характСристики тСтрагідроксикалікс[4]Π°Ρ€Π΅Π½Ρƒ, Π½ΠΈΠ·ΠΊΠΈ тСтраалкоксикалікс[4]Π°Ρ€Π΅Π½Ρ–Π² Ρ‚Π° тСтраалкілкалікс[4]Ρ€Π΅Π·ΠΎΡ€Ρ†ΠΈΠ½Π°Ρ€Π΅Π½Ρ–Π². ВстановлСно, Ρ‰ΠΎ Ρƒ Π²ΠΈΠ±Ρ€Π°Π½ΠΈΡ… ΡƒΠΌΠΎΠ²Π°Ρ… (Ρ€ΡƒΡ…ΠΎΠΌΠ° Ρ„Π°Π·Π° – Π°Ρ†Π΅Ρ‚ΠΎΠ½Ρ–Ρ‚Ρ€ΠΈΠ»/Π²ΠΎΠ΄Π° Ρƒ ΡΠΏΡ–Π²Π²Ρ–Π΄Π½ΠΎΡˆΠ΅Π½Π½Ρ– 86/14 Π·Π° об’ємом) час утримання дослідТуваних сполук Π·Π½Π°Ρ…ΠΎΠ΄ΠΈΡ‚ΡŒΡΡ Π² ΡˆΠΈΡ€ΠΎΠΊΠΎΠΌΡƒ Π΄Ρ–Π°ΠΏΠ°Π·ΠΎΠ½Ρ– 4.67-88.0 Ρ…Π² Π² залСТності Π²Ρ–Π΄ ΠΏΡ€ΠΈΡ€ΠΎΠ΄ΠΈ замісників Ρƒ ΠΌΠ°ΠΊΡ€ΠΎΡ†ΠΈΠΊΠ»Ρ–Ρ‡Π½ΠΎΠΌΡƒ кістяку каліксарСну. ΠŸΡ€ΠΈ Ρ†ΡŒΠΎΠΌΡƒ час утримання зростає ΠΏΠΎ ΠΌΡ–Ρ€Ρ– Π·Π±Ρ–Π»ΡŒΡˆΠ΅Π½Π½Ρ Π΄ΠΎΠ²ΠΆΠΈΠ½ΠΈ Π°Π»ΠΊΡ–Π»ΡŒΠ½ΠΈΡ… замісників Π½Π° Π½ΠΈΠΆΠ½ΡŒΠΎΠΌΡƒ Π²Ρ–Π½Ρ†Ρ– каліксарСнового ΠΌΠ°ΠΊΡ€ΠΎΡ†ΠΈΠΊΠ»Ρƒ. Π—Π³Ρ–Π΄Π½ΠΎ Π· Π΄Π°Π½ΠΈΠΌΠΈ молСкулярного модСлювання Π½Π°ΠΉΠ±Ρ–Π»ΡŒΡˆ Π΅Ρ„Π΅ΠΊΡ‚ΠΈΠ²Π½Π° сорбція Π²Ρ–Π΄Π±ΡƒΠ²Π°Ρ”Ρ‚ΡŒΡΡ Π·Π° Ρ€Π°Ρ…ΡƒΠ½ΠΎΠΊ Π²ΠΊΠ»ΡŽΡ‡Π΅Π½Π½Ρ ΠΎΠΊΡ‚Π°Π΄Π΅Ρ†ΠΈΠ»ΡŒΠ½ΠΈΡ… Π³Ρ€ΡƒΠΏ насадки LiChrosorb RP 18 Π² Π»Ρ–ΠΏΠΎΡ„Ρ–Π»ΡŒΠ½Ρƒ ΠΏΠΎΡ€ΠΎΠΆΠ½ΠΈΠ½Ρƒ, ΡƒΡ‚Π²ΠΎΡ€Π΅Π½Ρƒ Π°Π»ΠΊΡ–Π»ΡŒΠ½ΠΈΠΌΠΈ замісниками ниТнього вінця ΠΌΠ°ΠΊΡ€ΠΎΡ†ΠΈΠΊΠ»Ρƒ каліксарСну/каліксрСзорцинарСну. ΠŸΡ€ΠΈ Ρ†ΡŒΠΎΠΌΡƒ молСкулярна ΠΏΠΎΡ€ΠΎΠΆΠ½ΠΈΠ½Π°, сформована Π±Π΅Π½Π·Π΅Π½ΠΎΠ²ΠΈΠΌΠΈ ΠΊΡ–Π»ΡŒΡ†ΡΠΌΠΈ ΠΌΠ°ΠΊΡ€ΠΎΡ†ΠΈΠΊΠ»Ρƒ, Π·Π°Π»ΠΈΡˆΠ°Ρ”Ρ‚ΡŒΡΡ Π²Ρ–Π΄ΠΊΡ€ΠΈΡ‚ΠΎΡŽ для комплСксоутворСння Π· ΠΌΠΎΠ»Π΅ΠΊΡƒΠ»Π°ΠΌΠΈ Π°Π½Π°Π»Ρ–Ρ‚Ρ–Π².Π’Π°ΠΊΠ° сорбція тСтраалкоксикалікс[4]Π°Ρ€Π΅Π½Ρ–Π² Ρ‚Π° тСтраалкілкалікс[4]Ρ€Π΅Π·ΠΎΡ€Ρ†ΠΈΠ½Π°Ρ€Π΅Π½Ρ–Π² Π½Π° ΠΏΠΎΠ²Π΅Ρ€Ρ…Π½Ρ– Ρ…Ρ€ΠΎΠΌΠ°Ρ‚ΠΎΠ³Ρ€Π°Ρ„Ρ–Ρ‡Π½ΠΎΡ— насадки Ρ‚ΠΈΠΏΡƒ LiChrosorb RP 18 ΠΌΠΎΠΆΠ΅ суттєво ΠΏΠΎΠ»Ρ–ΠΏΡˆΠΈΡ‚ΠΈ Ρ—Ρ— Ρ€ΠΎΠ·Π΄Ρ–Π»ΡŒΠ½Ρƒ Π·Π΄Π°Ρ‚Π½Ρ–ΡΡ‚ΡŒ ΠΏΠΎ Π²Ρ–Π΄Π½ΠΎΡˆΠ΅Π½Π½ΡŽ Π΄ΠΎ Π°Π½Π°Π»Ρ–Ρ‚Ρ–Π² Π² ΡƒΠΌΠΎΠ²Π°Ρ… ΠΎΠ±Π΅Ρ€Π½Π΅Π½ΠΎ-Ρ„Π°Π·Π½ΠΎΡ— високоСфСктивної Ρ€Ρ–Π΄ΠΈΠ½Π½ΠΎΡ— Ρ…Ρ€ΠΎΠΌΠ°Ρ‚ΠΎΠ³Ρ€Π°Ρ„Ρ–Ρ—. ДослідТСно Π²ΠΏΠ»ΠΈΠ² Π·Π°ΠΌΡ–Π½ΠΈ Π³Ρ–Π΄Ρ€ΠΎΠΊΡΠΈΠ»ΡŒΠ½ΠΈΡ… ΠΏΡ€ΠΎΡ‚ΠΎΠ½Ρ–Π² тСтрагідроксикалікс[4]Π°Ρ€Π΅Π½Ρƒ Π°Π»ΠΊΡ–Π»ΡŒΠ½ΠΈΠΌΠΈ Π³Ρ€ΡƒΠΏΠ°ΠΌΠΈ Π½Π° ΠΊΠΎΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†Ρ–ΡŽ ΠΌΠ°ΠΊΡ€ΠΎΡ†ΠΈΠΊΠ»Ρ–Ρ‡Π½ΠΎΠ³ΠΎ кістяка ΠΌΠΎΠ»Π΅ΠΊΡƒΠ»ΠΈ

    Synthesis of Macrocyclic Stereoisomers Substituted with Oligolactide Fragments

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    Β© 2018, Pleiades Publishing, Ltd. Acylation of cone and 1,3-alternate stereoisomers of hydrazides of p-tert-butylthaicalix[4]arene tetrasubstituted at the lower rim with S,S-lactide in dimethylsulfoxide has afforded the macrocyclic oligolactide derivatives containing 16 (cone) to 24 (1,3-alternate) lactide fragments. It has been shown that nanosized aggregates (80 nm) are formed with silver nitrate in the case of the cone stereoisomer containing the oligolactide fragments at one side of the macrocyclic rim, whereas submicron particles (400 nm) are formed in the case of the 1,3-alternate conformation when the substituents are at different sides of the macrocycle

    The thermodynamics of molecular recognition in supramolecular systems based on calyxarenes

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    The publications of the authors concerned with seeking simple structure-property relations for the thermodynamic parameters of intermolecular interactions in solid guest-host inclusion compounds with the participation of three receptors, namely, tert-butylcalyx[4]arene, tert-butylthiocalyx[4]arene, and 2,2β€²-bis(9-hydroxy-9-fluorenyl)biphenyl, are briefly reviewed. Rules determining structure-property correlations can exist for guest-host inclusion compounds. Generally, the correlations obtained are nonlinear

    Stabilization of silica nanoparticles dispersions by surface modification with silicon derivative of thiacalix[4]arene

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    Β© 2015, Springer Science+Business Media Dordrecht. For the first time, silica nanopowder functionalized with thiacalixarene derivatives was synthesized by ultrasonication of nanoparticles (diameter 23.7Β Β±Β 2.4Β nm) with organosilicon derivative of thiacalixarene in glacial acetic acid. The protocol resulted in the formation of colloidal solution of low-disperse (polydispersity index of 0.11) submicron-sized (diameter 192.5Β nm) clusters of nanoparticles according to the dynamic light scattering data. As defined by scanning electron microscopy (SEM), mean diameter of thiacalixarene-functionalized nanoparticles is equal to 25.5Β Β±Β 2.5Β nm and the shape is close to spherical. SEM images confirm low aggregation of thiacalixarene-modified nanoparticle compared to initial silica nanopowder (mean diameter of aggregates 330 and 429Β nm, correspondingly). According to the thermogravimetry/differential scanning calorimetry and elemental analysis of the nanoparticles obtained, 5Β % of the powder mass was related to thiacalixarene units. The effect of thiacalixarene functionalization of silica nanoparticles on linear polydimethylsiloxane (PDMS)β€”silica dispersions was modeled to achieve high resistance toward liquid media required for similar sol–gel prepared PDMS-based materials applied for solid-phase microextraction. In such a manner, the influence of thiacalixarene-modified nanofiller on thermal stability and resistance against polar organic solvents was estimated. Similarity of decomposition temperature of both thiacalixarene-functionalized nanoparticles and non-functionalized silica nanoparticles was found. Swelling/solubility behavior observed was related to partial dissolution of PDMS/silica (10Β % mixture) in alcohols. Thiacalixarene-functionalized silica particles exerted significantly higher resistance of PDMS/silica composites toward alcohol solvents

    Particle Propagation on a Circle with a Point Interaction

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    We study a particle propagation on a circle in the presence of a point interaction. We show that the one-particle Feynman kernel can be written into the sum of reflected and transmitted trajectories which are weighted by the elements of the n-th power of the scattering matrix evaluated on a line with a point interaction. As a by-product we find three-parameter family of trace formulae as a generalization of the Poisson summation formula.Comment: 21 pages, 12 figure

    Sorption of hydrocarbons by leached chernozem

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    The sorption of n-octane, n-nonane, n-decane, decalin, and p-xylene on oven-dried and differently wetted leached chemozem, zeolite-bearing rock, and limestone was studied using static headspace-gas chromatography. It was found that leached chernozem exhibits a high capacity for selective sorption of hydrocarbons and has significantly heterogeneous sorption sites. Thermodynamic parameters of sorption, specific surface of sorbents, and the fractal dimension of soil surface were determined. An increase in the soil moisture content significantly inhibited the sorption of the hydrocarbons studied. Copyright Β© 2003 by MAIK "Nauka/Interperiodica" (Russia)

    Configuration effect of the tert-butylthiacalix[4]arene tetracarboxy derivative on its receptor properties toward vaporous organic compounds

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    The effect of carboxy groups and the stable conformation of tert-butylcalix[4]arenes containing four carboxymethoxy substituents at the lower rim on their receptor properties toward organic substances and water was studied for the systems with guest vapor and solid host. For this purpose, the compositions of clathrates formed in these systems, their thermal stability, and parameters of the host-guest affinity were determined by the quartz microbalance method, thermogravimetry, thermogravimetry combined with differential scanning calorimetry and mass spectrometry, and static headspace gas chromatography. The introduction of four carboxymethoxy groups into tert-butylthiacalix[4]arene enhances its receptor capacity and affinity to water and aliphatic alcohols and decreases the thermal stability of the most part of the studied clathrates with hydrophobic guests except benzene. The studied tert-butylthiacalix[4]arene derivatives can be promising receptors for use in mass-sensitive sensors of the quartz microbalance type to methanol and ethanol vapors. Β© 2009 Springer Science+Business Media, Inc

    Non-Weyl asymptotics for quantum graphs with general coupling conditions

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    Inspired by a recent result of Davies and Pushnitski, we study resonance asymptotics of quantum graphs with general coupling conditions at the vertices. We derive a criterion for the asymptotics to be of a non-Weyl character. We show that for balanced vertices with permutation-invariant couplings the asymptotics is non-Weyl only in case of Kirchhoff or anti-Kirchhoff conditions, while for graphs without permutation numerous examples of non-Weyl behaviour can be constructed. Furthermore, we present an insight helping to understand what makes the Kirchhoff/anti-Kirchhoff coupling particular from the resonance point of view. Finally, we demonstrate a generalization to quantum graphs with nonequal edge weights.Comment: minor changes, to appear in Pierre Duclos memorial issue of J. Phys. A: Math. Theo

    One-dimensional Dirac operators with zero-range interactions: Spectral, scattering, and topological results

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    17 pagesInternational audienceThe spectral and scattering theory for 1-dimensional Dirac operators with mass mm and with zero-range interactions are fully investigated. Explicit expressions for the wave operators and for the scattering operator are provided. These new formulae take place in a representation which links, in a suitable way, the energies βˆ’βˆž-\infty and +∞+\infty, and which emphasizes the role of Β±m\pm m. Finally, a topological version of Levinson's theorem is deduced, with the threshold effects at Β±m\pm m automatically taken into account

    Effect of the Polarizability of Organic Compounds on Isotherms of Sorption of Their Vapors with Solid tert-Butylcalix[4]arene

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    The stoichiometry and free energy of formation of saturated solid host-guest complexes were determined from the sorption isotherms of the vapors of organic compounds of various classes with solid tert-butylcalix[4]arene and from their limiting activity coefficients in toluene at 298 K. The contribution of the supramolecular effect to the free energy of formation of these complexes was estimated. The complexation stoichiometry and the observed supramolecular effect decrease with increasing molar refraction of the guest compound. The complexation stoihiometry is a step function of the molar refraction of the guest molecule
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