20 research outputs found
Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks
Liouville field theory on a sphere is considered. We explicitly derive a
differential equation for four-point correlation functions with one degenerate
field . We introduce and study also a class of four-point
conformal blocks which can be calculated exactly and represented by finite
dimensional integrals of elliptic theta-functions for arbitrary intermediate
dimension. We study also the bootstrap equations for these conformal blocks and
derive integral representations for corresponding four-point correlation
functions. A relation between the one-point correlation function of a primary
field on a torus and a special four-point correlation function on a sphere is
proposed
Confinement-Induced Stiffening of Thin Elastomer Films: Linear and Nonlinear Mechanics vs Local Dynamics
Psychophysiological and sport activity of the student youth as an indicator and determinant of health-preserving culture development
The purpose of the study consisted in exploring specific features of the influence of social activity of student youth on the development of their health-promoting culture. In addition, the study was directed at searching for effective ways of encouraging and developing health-promoting culture among student youth by boosting activities in the sphere of student media. The subject of our study embraced the process of education and development of health-promoting culture among students through the inclusion of the media environment in the activity. Research methods comprised theoretical (analysis, classification, synthesis and generalization) and empirical ones (questionnaire "What is your creative potential"); "Communicative and organizational inclinations". On the basis of the results of the study, the authors of the paper specified and concretized the concepts of general culture and social activity of students through the implementation of creative activity in the media space. An additional education program for students has been designed and tested, the purpose of which is to increase social activity and the development of health-promoting culture in the youth milieu. The designed Program, in addition to the formation of competences in the field of social activity and the development of general culture, information support of events and coverage of the main news among students, is focused on developing students’ professional skills of humanities courses who participate in the media space activities. The significance of the study from a practical point of view lies in the fact that its results can be used in the educational process to boost social activity and develop health-promoting culture of students of higher educational and vocational institutions. The novelty of the study is based on the fact that the designed Program of additional education for students of higher educational and vocational institutions is not only an educational program for mastering educational material but is a practical platform for the implementation of both educational and professional activities. The program comprises methods, technologies and resources that allow students to participate in various events and projects, to express themselves as a creative person, the ability to communicate with society, and organize events. The results of the program implementation raise the general socialization of students; determine the direction of their professional activity; and also provide a foundation for public life in the framework of press services of state bodies and public organizations
The Salts of Copper Octafluoro- and Hexadecafluorophthalocyanines Containing [CuII(F8Pc)4–]2– Dianions and [CuF16Pc]− Monoanions
Photorefractive response in sillenite crystals with shallow traps by applying an alternating electric field
The Salts of Copper Octafluoro- and Hexadecafluorophthalocyanines Containing [Cu<sup>II</sup>(F<sub>8</sub>Pc)<sup>4–</sup>]<sup>2–</sup> Dianions and [CuF<sub>16</sub>Pc]<sup>−</sup> Monoanions
Crystalline anionic
salts with copper octafluoro- and hexadecafluorophthalocyanines, (Bu<sub>4</sub>N<sup>+</sup>)<sub>2</sub>[Cu<sup>II</sup>(F<sub>8</sub>Pc)<sup>4–</sup>]<sup>2–</sup>·2C<sub>6</sub>H<sub>4</sub>Cl<sub>2</sub> (<b>1</b>) and (PPN<sup>+</sup>)<sub>3</sub>[CuF<sub>16</sub>Pc]<sub>3</sub><sup>3–</sup>·2C<sub>6</sub>H<sub>5</sub>CN (<b>2</b>), where PPN<sup>+</sup> is
bis(triphenylphosphoranylidene)ammonium and Pc is phthalocyanine,
have been obtained. The absence of noticeable absorption in the NIR
range and DFT calculations for <b>1</b> indicate that both negative
charges are mainly localized on the Pc ligand, and that the [Cu<sup>II</sup>(F<sub>8</sub>Pc)<sup>4–</sup>]<sup>2–</sup> dianions are formed without reduction of Cu<sup>II</sup>. The magnetic
moment of 1.60 μ<sub>B</sub> corresponds to the contribution
of one <i>S</i> = 1/2 spin per dianion. The spin is localized
on the Cu<sup>II</sup> atom, which shows an EPR signal characteristic
of Cu<sup>II</sup>. Dianions are isolated in <b>1</b>, providing
only weak magnetic coupling of spins with a Weiss temperature of −4
K. Salt <b>2</b> contains closely packed π–π
stacks built of [CuF<sub>16</sub>Pc]<sup>−</sup> anions of
types I and II, and the interplanar distances are 3.187 and 3.275
Å. According to the DFT calculations, the [CuF<sub>16</sub>Pc]<sup>−</sup> anions of types I and II can have different charge
distributions, with localization of an extra electron on the copper
atoms to form diamagnetic [Cu<sup>I</sup>(F<sub>16</sub>Pc)<sup>2–</sup>]<sup>−</sup> monoanions or delocalization of an extra electron
on the F<sub>16</sub>Pc ligand to form [Cu<sup>II</sup>(F<sub>16</sub>Pc)<sup>•3–</sup>]<sup>•–</sup> having
an <i>S</i> = 1/2 (Cu<sup>II</sup>) + 1/2 (F<sub>16</sub>Pc<sup>•3–</sup>) spin state. In fact, at 300 K, the
magnetic moment of <b>2</b> of 3.25 μ<sub>B</sub> per
formula unit is rather close to the contribution from two [Cu<sup>II</sup>(F<sub>16</sub>Pc)<sup>•3–</sup>]<sup>•–</sup> (calculated μ<sub>eff</sub> is 3.46 μ<sub>B</sub>).
The Weiss temperature of −21.5 K indicates antiferromagnetic
coupling of spins, which can be modeled by stronger intermolecular
coupling between (F<sub>16</sub>Pc)<sup>•3–</sup> with <i>J</i><sub>1</sub>/<i>k</i><sub>B</sub> = −23.5
K and weaker intramolecular coupling between Cu<sup>II</sup> and (F<sub>16</sub>Pc)<sup>•3–</sup> with <i>J</i><sub>2</sub>/<i>k</i><sub>B</sub> = −8.1 K. This interaction
is realized in the {[Cu<sup>II</sup>(F<sub>16</sub>Pc)<sup>•3–</sup>]<sup>•–</sup>}<sub>2</sub> dimers separated by diamagnetic
[Cu<sup>I</sup>(F<sub>16</sub>Pc)<sup>2–</sup>]<sup>−</sup> species. In spite of the stacking arrangement of phthalocyanine
macrocycles in <b>2</b>, the inhomogeneous charge distribution
and nonuniform distances between the macrocycles should suppress electrical
conductivity
The Salts of Copper Octafluoro- and Hexadecafluorophthalocyanines Containing [Cu<sup>II</sup>(F<sub>8</sub>Pc)<sup>4–</sup>]<sup>2–</sup> Dianions and [CuF<sub>16</sub>Pc]<sup>−</sup> Monoanions
Crystalline anionic
salts with copper octafluoro- and hexadecafluorophthalocyanines, (Bu<sub>4</sub>N<sup>+</sup>)<sub>2</sub>[Cu<sup>II</sup>(F<sub>8</sub>Pc)<sup>4–</sup>]<sup>2–</sup>·2C<sub>6</sub>H<sub>4</sub>Cl<sub>2</sub> (<b>1</b>) and (PPN<sup>+</sup>)<sub>3</sub>[CuF<sub>16</sub>Pc]<sub>3</sub><sup>3–</sup>·2C<sub>6</sub>H<sub>5</sub>CN (<b>2</b>), where PPN<sup>+</sup> is
bis(triphenylphosphoranylidene)ammonium and Pc is phthalocyanine,
have been obtained. The absence of noticeable absorption in the NIR
range and DFT calculations for <b>1</b> indicate that both negative
charges are mainly localized on the Pc ligand, and that the [Cu<sup>II</sup>(F<sub>8</sub>Pc)<sup>4–</sup>]<sup>2–</sup> dianions are formed without reduction of Cu<sup>II</sup>. The magnetic
moment of 1.60 μ<sub>B</sub> corresponds to the contribution
of one <i>S</i> = 1/2 spin per dianion. The spin is localized
on the Cu<sup>II</sup> atom, which shows an EPR signal characteristic
of Cu<sup>II</sup>. Dianions are isolated in <b>1</b>, providing
only weak magnetic coupling of spins with a Weiss temperature of −4
K. Salt <b>2</b> contains closely packed π–π
stacks built of [CuF<sub>16</sub>Pc]<sup>−</sup> anions of
types I and II, and the interplanar distances are 3.187 and 3.275
Å. According to the DFT calculations, the [CuF<sub>16</sub>Pc]<sup>−</sup> anions of types I and II can have different charge
distributions, with localization of an extra electron on the copper
atoms to form diamagnetic [Cu<sup>I</sup>(F<sub>16</sub>Pc)<sup>2–</sup>]<sup>−</sup> monoanions or delocalization of an extra electron
on the F<sub>16</sub>Pc ligand to form [Cu<sup>II</sup>(F<sub>16</sub>Pc)<sup>•3–</sup>]<sup>•–</sup> having
an <i>S</i> = 1/2 (Cu<sup>II</sup>) + 1/2 (F<sub>16</sub>Pc<sup>•3–</sup>) spin state. In fact, at 300 K, the
magnetic moment of <b>2</b> of 3.25 μ<sub>B</sub> per
formula unit is rather close to the contribution from two [Cu<sup>II</sup>(F<sub>16</sub>Pc)<sup>•3–</sup>]<sup>•–</sup> (calculated μ<sub>eff</sub> is 3.46 μ<sub>B</sub>).
The Weiss temperature of −21.5 K indicates antiferromagnetic
coupling of spins, which can be modeled by stronger intermolecular
coupling between (F<sub>16</sub>Pc)<sup>•3–</sup> with <i>J</i><sub>1</sub>/<i>k</i><sub>B</sub> = −23.5
K and weaker intramolecular coupling between Cu<sup>II</sup> and (F<sub>16</sub>Pc)<sup>•3–</sup> with <i>J</i><sub>2</sub>/<i>k</i><sub>B</sub> = −8.1 K. This interaction
is realized in the {[Cu<sup>II</sup>(F<sub>16</sub>Pc)<sup>•3–</sup>]<sup>•–</sup>}<sub>2</sub> dimers separated by diamagnetic
[Cu<sup>I</sup>(F<sub>16</sub>Pc)<sup>2–</sup>]<sup>−</sup> species. In spite of the stacking arrangement of phthalocyanine
macrocycles in <b>2</b>, the inhomogeneous charge distribution
and nonuniform distances between the macrocycles should suppress electrical
conductivity