80 research outputs found
An Optimal Estimate of the --Variation
No full textA notion of Lr-δ-variation of a function in Lr which plays an essential role in the theory of the Henstock-Kurzweil integral for functions in Lr (HKr-integral) is studied. We obtain an improved, in fact the best possible, estimate from below for this variation via the classical variation. We show that the class of functions having a finite Lr-δ-variation on an interval coincides with the class of functions of bounded variation on this interval. As a by-product of the results of the paper we obtain a new proof of the uniqueness of the HKr-integral
Kurzweil-Henstock type integral on zero-dimensional group and some of its applications
No full textsummary:A Kurzweil-Henstock type integral on a zero-dimensional abelian group is used to recover by generalized Fourier formulas the coefficients of the series with respect to the characters of such groups, in the compact case, and to obtain an inversion formula for multiplicative integral transforms, in the locally compact case
Comparison of the Pr-integral with Burkill's integrals and some applications to trigonometric series
No full textIt is proved that the Pr-integral [9] which recovers a function from its derivative defined in the space Lr, 1 <= r < infinity, is properly included in Burkill's trigonometric CP-and SCP-integrals. As an application to harmonic analysis, a de La Vallee-Poussin-type theorem for the Pr-integral is obtained: convergence nearly everywhere of a trigonometric series to a Pr-integrable function f implies that this series is the Pr-Fourier series of f.(c) 2023 Elsevier Inc. All rights reserved
On the Coefficients of Multiple Series with Respect to Vilenkin System
No full textWe give a sufficient condition for coefficients of double series ∑∑ n,m a n,m χ n,m with respect to Vilenkin system to be convergent to zero when n + m →∞. This result can be applied to the problem of recovering coefficients of a Vilenkin series from its su
On the Lr-differentiability of two Lusin classes and a full descriptive characterization of the HKr-integral
No full textIt is proved that any function of a Lusin-type class, the class of ACGr-functions, is differentiable almost everywhere in the sense of a derivative defined in the space Lr, 1 ≤ r < ∞. This leads to a full descriptive characterization of a Henstock-Kurzweil-type integral, the HKr-integral, which serves to recover functions from their Lr-derivatives. The class ACGr is compared with the classical Lusin class ACG and it is shown that continuous ACG-functions can fail to be Lr-differentiable almost everywhere
Partition function, metastability, and kinetics of the escape transition for an ideal chain
No full textThe exact partition of the gaussian chain squeezed between two cylinders for a phase transition in a single macromolecule is analyzed. The polymer chain is squeezed between two pistons which results in abrupt transition from a confined coil state to an inhomogeneous conformation. The landau free energy is used in a one dimensional fokker-plank equation to predict the life-time of the metastable states. The analysis shows that the mean first passage time is estimated on the basis of the fokker-planck formalism.Baumgartner W, 2000, P NATL ACAD SCI USA, V97, P4005, DOI 10.1073-pnas.070052697; Carslaw H, 1947, CONDUCTION HEAT SOLI; Chaikin P.M., 2000, PRINCIPLES CONDENSED; De Gennes PG, 1979, SCALING CONCEPTS POL; de Gennes P.-G., 1993, PHYS LIQUID CRYSTALS; DESCLOIZEAUX G, 1990, POLYM SOLUTION THEIR; Doi M, 1986, THEORY POLYM DYNAMIC; EISENRIEGLER E, 1982, J CHEM PHYS, V77, P6296, DOI 10.1063-1.443835; Eisenriegler E., 1998, LECT NOTES PHYS, V508; Ennis J, 1999, PHYS REV E, V60, P6906, DOI 10.1103-PhysRevE.60.6906; Fleer G. J., 1993, POLYM INTERFACES; Flory PJ, 1953, PRINCIPLES POLYM CHE; Grosberg AY, 1994, STAT PHYS MACROMOLEC; GUFFOND MC, 1997, LANGMUIR, V13, P1591; Haupt BJ, 1999, LANGMUIR, V15, P3886, DOI 10.1021-la981112v; Hugel T, 2001, MACROMOLECULES, V34, P1039, DOI 10.1021-ma0009404; Hugel T, 2001, MACROMOL RAPID COMM, V22, P989, DOI 10.1002-1521-3927(20010901)22:13989::AID-MARC9893.0.CO;2-D; Jimenez J, 1998, LANGMUIR, V14, P2598, DOI 10.1021-la971233f; Klushin LI, 2002, PHYS REV E, V66, DOI 10.1103-PhysRevE.66.036114; Landau L. D., 1976, STAT PHYS; Leermakers FAM, 2002, MACROMOLECULES, V35, P8640, DOI 10.1021-ma020718u; Milchev A, 1999, PHYS CHEM CHEM PHYS, V1, P2083, DOI 10.1039-a809795j; Milchev A, 1999, EUROPHYS LETT, V47, P675, DOI 10.1209-epl-i1999-00442-2; Muthukumar M, 2001, PHYS REV LETT, V86, P3188, DOI 10.1103-PhysRevLett.86.3188; Senden TJ, 2001, CURR OPIN COLLOID IN, V6, P95, DOI 10.1016-S1359-0294(01)00067-X; Sevick EM, 1999, MACROMOLECULES, V32, P6841, DOI 10.1021-ma990589q; Skvortsov AM, 2001, J CHEM PHYS, V115, P1586, DOI 10.1063-1.1374210; Skvortsov AM, 2000, J CHEM PHYS, V112, P7238, DOI 10.1063-1.481313; Skvortsov AM, 2001, PHYSICA A, V290, P445, DOI 10.1016-S0378-4371(00)00402-7; Skvortsov AM, 2002, EUROPHYS LETT, V58, P292, DOI 10.1209-epl-i2002-00636-0; Steels BM, 2000, J CHROMATOGR B, V743, P31, DOI 10.1016-S0378-4347(00)00199-7; Subramanian G, 1996, MACROMOLECULES, V29, P4045, DOI 10.1021-ma946439r; SUBRAMANIAN G, 1995, EUROPHYS LETT, V29, P285, DOI 10.1209-0295-5075-29-4-003; WILLIAMS DRM, 1995, J PHYS II, V9, P1417; Zhang WK, 2000, J PHYS CHEM B, V104, P10258, DOI 10.1021-jp000459f17191
'Every book is a part of life'
No full text© 2019, I. A. Ermakova. In her interview with the critic and scholar A. Skvortsov, the poet I. Ermakova discusses modern poetry, its authors and processes. Starting as a conversation about the poet's artistic evolution and mentioning her work as a translator, author of regular publications in various think journals, and her numerous poetic prizes, the interview gradually moves on to examining the contemporary poetic reality, which Ermakova describes as 'the era of Oleg Chukhontsev'. She argues that the value of Chukhontsev's poetry lies in its absolute precision of word choice and accurate and truthful depiction of familiar reality. In such an attempt to display the world undistorted, modern poets turn to related art forms, up to the cinematic, however few reach this level. The interview, therefore, provides Ermakova's assessment of the contemporary literary environment, her views on how one can join the literary process, and contemplations about the problem of the reader of modern poetry: whether they exist, and who they are
The Third Skvortsov Readings
No full textOn December 17, 2021, MGIMO University held the International Scientific Conference dedicated to the memory of Lev Ivanovich Skvortsov, outstanding linguist, lexicographer, Doctor of Philology, professor, author of many dictionaries and books on the culture of Russian spoken language. In the opening speech, his son Yaroslav Skvortsov, the Dean of the Faculty of International Journalism of MGIMO University, organizer and the permanent host of the Readings noted that the topic Do we speak Russian Correctly? Dynamics of Language Norms is also the title of Lev I. Skvortsov’s book, published 40 years ago and still topical. The Russian language still faces an influx of borrowed words, idioms and is prone to stylistic transformations induced by the media. Linguists, language teachers, journalists, and economists — all those interested in the conservation and development of the Russian language — came to the Suzdal Kremlin to discuss the current trends in language use and language teaching. The participants presented their ideas and research on various topics: Media variant of the language: from the usage to the norm (N. I. Klushina), Speech of YouTubers (E. V. Bykova), The concept of literacy in the Internet folklore (G. G. Slyshkin), Business slang in 2004 and today (Pogrebnyak E. V.) and others. By tradition, many departments of MGIMO University were presented at the conference. Editor-in-Chief of the Journal Concept: Philosophy, Religion, Culture, MGIMO Professor, Head of the Department of World Literature and Culture, writer Yury Pavlovich Simonov (Viazemsky) delivered a guest of honor speech. He remembered the deeds and ideals of Lev Ivanovich and urged everybody to find inspiration in the beauty of Russian nature that can only be described in the beautiful Russian language. This idea resonated with the director of Vladimir-Suzdal Reserve Museum S. E. Rybakov: Suzdal is the center of Russianness and is the right place to discuss its language. In the changing world, L. I. Skvortsov’s work reminds us of the importance of inspecting and rethinking norms that are to be adequate rather than rigid
Mechanical desorption of a single chain: Unusual aspects of phase coexistence at a first-order transition
No full textThe phase transition occurring when a single polymer chain adsorbed at a planar solid surface is mechanically desorbed is analyzed in two statistical ensembles. In the force ensemble, a constant force applied to the nongrafted end of the chain (that is grafted at its other end) is used as a given external control variable. In the z-ensemble, the displacement z of this nongrafted end from the surface is taken as the externally controlled variable. Basic thermodynamic parameters, such as the adsorption energy, exhibit a very different behavior as a function of these control parameters. In the thermodynamic limit of infinite chain length the desorption transition with the force as a control parameter clearly is discontinuous, while in the z-ensemble continuous variations are found. However, one should not be misled by a too-naive application of the Ehrenfest criterion to consider the transition as a continuous transition: rather, one traverses a two-phase coexistence region, where part of the chain is still adsorbed and the other part desorbed and stretched. Similarities with and differences from two-phase coexistence at vapor-liquid transitions are pointed out. The rounding of the singularities due to finite chain length is illustrated by exact calculations for the nonreversal random walk model on the simple cubic lattice. A new concept of local order parameter profiles for the description of the mechanical desorption of adsorbed polymers is suggested. This concept give evidence for both the existence of two-phase coexistence within single polymer chains for this transition and the anomalous character of this two-phase coexistence. 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Analytical theory of finite-size effects in mechanical desorption of a polymer chain
No full textWe discuss a unique system that allows exact analytical investigation of first- and second-order transitions with finite-size effects: mechanical desorption of an ideal lattice polymer chain grafted with one end to a solid substrate with a pulling force applied to the other end. We exploit the analogy with a continuum model and use accurate mapping between the parameters in continuum and lattice descriptions, which leads to a fully analytical partition function as a function of chain length, temperature (or adsorption strength), and pulling force. The adsorption-desorption phase diagram, which gives the critical force as a function of temperature, is nonmonotonic and gives rise to re-entrance. We analyze the chain length dependence of several chain properties (bound fraction, chain extension, and heat capacity) for different cross sections of the phase diagram. Close to the transition a single parameter (the product of the chain length N and the deviation from the transition point) describes all thermodynamic properties. We discuss finite-size effects at the second-order transition (adsorption without force) and at the first-order transition (mechanical desorption). The first-order transition has some unusual features: The heat capacity in the transition region increases anomalously with temperature as a power law, metastable states are completely absent, and instead of a bimodal distribution there is a flat region that becomes more pronounced with increasing chain length. The reason for this anomaly is the absence of an excess surface energy for the boundary between adsorbed and stretched coexisting phases (this boundary is one segment only): The two states strongly fluctuate in the transition point. 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