Journal articles: 'Lavrentiev phenomenon'

1

Loewen, Philip D. "On The Lavrentiev Phenomenon." Canadian Mathematical Bulletin 30, no. 1 (March 1, 1987): 102–8. http://dx.doi.org/10.4153/cmb-1987-015-7.

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Cesari, L., and T. S. Angell. "On the Lavrentiev phenomenon." Calcolo 22, no. 1 (January 1985): 17–29. http://dx.doi.org/10.1007/bf02576198.

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Zolezzi, Tullio. "Wellposedness and the Lavrentiev Phenomenon." SIAM Journal on Control and Optimization 30, no. 4 (July 1992): 787–99. http://dx.doi.org/10.1137/0330043.

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Carstensen, C., and C. Ortner. "Analysis of a Class of Penalty Methods for Computing Singular Minimizers." Computational Methods in Applied Mathematics 10, no. 2 (2010): 137–63. http://dx.doi.org/10.2478/cmam-2010-0008.

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AbstractAmongst the more exciting phenomena in the field of nonlinear partial differential equations is the Lavrentiev phenomenon which occurs in the calculus of variations. We prove that a conforming finite element method fails if and only if the Lavrentiev phenomenon is present. Consequently, nonstandard finite element methods have to be designed for the detection of the Lavrentiev phenomenon in the computational calculus of variations. We formulate and analyze a general strategy for solving variational problems in the presence of the Lavrentiev phenomenon based on a splitting and penalization strategy. We establish convergence results under mild conditions on the stored energy function. Moreover, we present practical strategies for the solution of the discretized problems and for the choice of the penalty parameter.

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BAI, YU, and ZHI-PING LI. "A TRUNCATION METHOD FOR DETECTING SINGULAR MINIMIZERS INVOLVING THE LAVRENTIEV PHENOMENON." Mathematical Models and Methods in Applied Sciences 16, no. 06 (June 2006): 847–67. http://dx.doi.org/10.1142/s0218202506001376.

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A numerical method using the truncation technique on the integrand is developed for computing singular minimizers or singular minimizing sequences in variational problems involving the Lavrentiev phenomenon. It is proved that the method can detect absolute minimizers with various singularities whether the Lavrentiev phenomenon is involved or not. It is also proved that, when the absolute infimum is not attainable, the method can produce minimizing sequences. Numerical results on Manià's example and a two-dimensional problem involving the Lavrentiev phenomenon with continuous Sobolev exponent dependence, are given to show the efficiency of the method.

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BAI, YU, and ZHIPING LI. "NUMERICAL SOLUTION OF NONLINEAR ELASTICITY PROBLEMS WITH LAVRENTIEV PHENOMENON." Mathematical Models and Methods in Applied Sciences 17, no. 10 (October 2007): 1619–40. http://dx.doi.org/10.1142/s0218202507002406.

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A convergence theory is established for a truncation method in solving polyconvex elasticity problems involving the Lavrentiev phenomenon. Numerical results on a recent example by Foss et al., which has a polyconvex integrand and admits continuous singular minimizers, not only verify our convergence theorems but also provide a sharper estimate on the upper bound of a perturbation parameter for the existence of the Lavrentiev phenomenon in the example.

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Foss, M., W. Hrusa, and V. J. Mizel. "The Lavrentiev Phenomenon in Nonlinear Elasticity." Journal of Elasticity 72, no. 1-3 (2003): 173–81. http://dx.doi.org/10.1023/b:elas.0000018778.53392.b7.

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Carlson, Dean A. "Property (D) and the Lavrentiev phenomenon." Applicable Analysis 95, no. 6 (September 28, 2015): 1214–27. http://dx.doi.org/10.1080/00036811.2015.1057703.

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9

Gratwick, Richard. "Singular sets and the Lavrentiev phenomenon." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 145, no. 3 (June 2015): 513–33. http://dx.doi.org/10.1017/s0308210513001510.

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We show that non-occurrence of the Lavrentiev phenomenon does not imply that the singular set is small. Precisely, given a compact Lebesgue null subsetE⊆ ℝ and an arbitrary superlinearity, there exists a smooth strictly convex Lagrangian with this superlinear growth such that all minimizers of the associated variational problem have singular set exactlyEbut still admit approximation in energy by smooth functions.

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10

Heinricher, Arthur C., and Victor J. Mizel. "A New Example of the Lavrentiev Phenomenon." SIAM Journal on Control and Optimization 26, no. 6 (November 1988): 1490–503. http://dx.doi.org/10.1137/0326087.

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Heinricher, A. C., and V. J. Mizel. "The Lavrentiev phenomenon for invariant variational problems." Archive for Rational Mechanics and Analysis 102, no. 1 (March 1988): 57–93. http://dx.doi.org/10.1007/bf00250924.

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Foss, M., W. J. Hrusa, and V. J. Mizel. "The Lavrentiev Gap Phenomenon in Nonlinear Elasticity." Archive for Rational Mechanics and Analysis 167, no. 4 (May 1, 2003): 337–65. http://dx.doi.org/10.1007/s00205-003-0249-6.

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13

Buttazzo, Giuseppe, and Victor J. Mizel. "Interpretation of the Lavrentiev phenomenon by relaxation." Journal of Functional Analysis 110, no. 2 (December 1992): 434–60. http://dx.doi.org/10.1016/0022-1236(92)90038-k.

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14

Braides, A. "The Lavrentiev Phenomenon for Free Discontinuity Problems." Journal of Functional Analysis 127, no. 1 (January 1995): 1–20. http://dx.doi.org/10.1006/jfan.1995.1001.

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15

Cheng, Chih Wen, and Victor J. Mizel. "On the Lavrentiev phenomenon for autonomous second-order integrands." Archive for Rational Mechanics and Analysis 126, no. 1 (1994): 21–33. http://dx.doi.org/10.1007/bf00375694.

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16

Zaslavski, Alexander J. "Nonoccurrence of the Lavrentiev phenomenon for nonconvex variational problems." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 22, no. 5 (September 2005): 579–96. http://dx.doi.org/10.1016/j.anihpc.2004.10.004.

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Zaslavski, Alexander J. "Nonoccurrence of the Lavrentiev Phenomenon for Many Optimal Control Problems." SIAM Journal on Control and Optimization 45, no. 3 (January 2006): 1116–46. http://dx.doi.org/10.1137/050640370.

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18

Belloni, Marino. "Interpretation of Lavrentiev phenomenon by relaxation: the higher order case." Transactions of the American Mathematical Society 347, no. 6 (June 1, 1995): 2011–23. http://dx.doi.org/10.1090/s0002-9947-1995-1290714-9.

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Bousquet, Pierre, Carlo Mariconda, and Giulia Treu. "On the Lavrentiev phenomenon for multiple integral scalar variational problems." Journal of Functional Analysis 266, no. 9 (May 2014): 5921–54. http://dx.doi.org/10.1016/j.jfa.2013.12.020.

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Hüsseinov, Farhad. "Relaxation and nonoccurrence of the Lavrentiev phenomenon for nonconvex problems." Acta Mathematica Sinica, English Series 29, no. 6 (January 1, 2013): 1185–98. http://dx.doi.org/10.1007/s10114-013-1721-3.

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21

Kilpelainen, T., and P. Lindqvist. "The Lavrentiev Phenomenon and the Obstacle Problem for the Dirichlet Integral." Proceedings of the American Mathematical Society 123, no. 8 (August 1995): 2459. http://dx.doi.org/10.2307/2161275.

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Kilpeläinen, T., and P. Lindqvist. "The Lavrentiev phenomenon and the obstacle problem for the Dirichlet integral." Proceedings of the American Mathematical Society 123, no. 8 (August 1, 1995): 2459. http://dx.doi.org/10.1090/s0002-9939-1995-1264819-8.

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23

Zaslavski, Alexander J. "Nonoccurrence of the Lavrentiev phenomenon for many nonconvex constrained variational problems." Calculus of Variations and Partial Differential Equations 28, no. 3 (September 7, 2006): 351–81. http://dx.doi.org/10.1007/s00526-006-0047-8.

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LI, ZHIPING. "ELEMENT REMOVAL METHOD FOR SINGULAR MINIMIZERS IN PROBLEMS OF HYPERELASTICITY." Mathematical Models and Methods in Applied Sciences 05, no. 03 (May 1995): 387–99. http://dx.doi.org/10.1142/s0218202595000231.

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A numerical method called element removal method is applied to calculate singular minimizers in problems of hyperelasticity. The method overcomes the difficulty in finite element approximations caused by restrictions, such as det (I+∇u)>0, on admissible functions and can avoid Lavrentiev phenomenon if it does occur in the problem. The convergence of the method is proved.

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Cheng, Chih-Wen, and Victor J. Mizel. "On the Lavrentiev Phenomenon for Optimal Control Problems with Second-Order Dynamics." SIAM Journal on Control and Optimization 34, no. 6 (November 1996): 2172–79. http://dx.doi.org/10.1137/s0363012994261215.

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26

Bonfanti, Giovanni, and Arrigo Cellina. "The Nonoccurrence of the Lavrentiev Phenomenon for a Class of Variational Functionals." SIAM Journal on Control and Optimization 51, no. 2 (January 2013): 1639–50. http://dx.doi.org/10.1137/12086618x.

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27

Zaslavski, Alexander J. "Generic Nonoccurrence of the Lavrentiev Phenomenon for a Class of Optimal Control Problems." Journal of Dynamical and Control Systems 14, no. 1 (January 2008): 95–119. http://dx.doi.org/10.1007/s10883-007-9032-6.

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28

Mariconda, Carlo, and Giulia Treu. "Non-occurrence of the Lavrentiev phenomenon for a class of convex nonautonomous Lagrangians." Open Mathematics 18, no. 1 (February 17, 2020): 1–9. http://dx.doi.org/10.1515/math-2020-0001.

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Abstract We consider the classical functional of the Calculus of Variations of the form $$\begin{array}{} \displaystyle I(u)=\int\limits_{{\it\Omega}}F(x, u(x), \nabla u(x))\,dx, \end{array}$$ where Ω is a bounded open subset of ℝn and F : Ω × ℝ × ℝn → ℝ is a Carathéodory convex function; the admissible functions u coincide with a prescribed Lipschitz function ϕ on ∂Ω. We formulate some conditions under which a given function in ϕ + $\begin{array}{} \displaystyle W^{1,p}_0 \end{array}$(Ω) with I(u) < +∞ can be approximated in the W1,p norm and in energy by a sequence of smooth functions that coincide with ϕ on ∂Ω. As a particular case we obtain that the Lavrentiev phenomenon does not occur when F(x, u, ξ) = f(x, u) + h(x, ξ) is convex and x ↦ F(x, 0, 0) is sufficiently smooth.

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29

Avci, Mustafa, and Alexander Pankov. "Multivalued elliptic operators with nonstandard growth." Advances in Nonlinear Analysis 7, no. 1 (February 1, 2018): 35–48. http://dx.doi.org/10.1515/anona-2016-0043.

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AbstractThe paper is devoted to the Dirichlet problem for monotone, in general multivalued, elliptic equations with nonstandard growth condition. The growth conditions are more general than the well-known {p(x)} growth. Moreover, we allow the presence of the so-called Lavrentiev phenomenon. As consequence, at least two types of variational settings of Dirichlet problem are available. We prove results on the existence of solutions in both of these settings. Then we obtain several results on the convergence of certain types of approximate solutions to an exact solution.

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30

Ferriero, Alessandro. "The Approximation of Higher-Order Integrals of the Calculus of Variations and the Lavrentiev Phenomenon." SIAM Journal on Control and Optimization 44, no. 1 (January 2005): 99–110. http://dx.doi.org/10.1137/s0363012903437721.

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31

Alkhutov, Yu A., and V. V. Zhikov. "Hölder continuity of solutions to a degenerate elliptic equation in the presence of the Lavrentiev phenomenon." Applicable Analysis 93, no. 10 (July 10, 2014): 2057–75. http://dx.doi.org/10.1080/00036811.2014.936404.

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32

Sarychev, A. V. "First- and second-order integral functionals of the calculus of variations which exhibit the Lavrentiev phenomenon." Journal of Dynamical and Control Systems 3, no. 4 (October 1997): 565–88. http://dx.doi.org/10.1007/bf02463283.

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33

Treu, G., and S. Zagatti. "On the Lavrentiev Phenomenon and the Validity of Euler-Lagrange Equations for a Class of Integral Functionals." Journal of Mathematical Analysis and Applications 184, no. 1 (May 1994): 56–74. http://dx.doi.org/10.1006/jmaa.1994.1183.

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34

Mielke, Alexander, and Tomáš Roubíček. "Rate-independent elastoplasticity at finite strains and its numerical approximation." Mathematical Models and Methods in Applied Sciences 26, no. 12 (October 25, 2016): 2203–36. http://dx.doi.org/10.1142/s0218202516500512.

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Gradient plasticity at large strains with kinematic hardening is analyzed as quasistatic rate-independent evolution. The energy functional with a frame-indifferent polyconvex energy density and the dissipation is approximated numerically by finite elements and implicit time discretization, such that a computationally implementable scheme is obtained. The nonself-penetration as well as a possible frictionless unilateral contact is considered and approximated numerically by a suitable penalization method which keeps polyconvexity and simultaneously bypasses the Lavrentiev phenomenon. The main result concerns the convergence of the numerical scheme toward energetic solutions. In the case of incompressible plasticity and of nonsimple materials, where the energy depends on the second derivative of the deformation, we derive an explicit stability criterion for convergence relating the spatial discretization and the penalizations.

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35

LI, ZHIPING. "NUMERICAL METHODS FOR MINIMIZERS AND MICROSTRUCTURES IN NONLINEAR ELASTICITY." Mathematical Models and Methods in Applied Sciences 06, no. 07 (November 1996): 957–75. http://dx.doi.org/10.1142/s0218202596000390.

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A standard finite element method and a finite element truncation method are applied to solve the boundary value problems of nonlinear elasticity with certain nonconvex stored energy functions such as those of St. Venant-Kirchhoff materials. Finite element solutions are proved to exist and of the form of minimizers in appropriate sets of admissible finite element functions for both methods. Convergence of the finite element solutions to a solution in the form of a minimizer or microstructure for the boundary value problem is established. It is also shown that in the presence of Lavrentiev phenomenon the finite element truncation method can overcome the difficulty and converges to the absolute minimum while the standard finite element method converges to a pseudominimum which is a minimum in a slightly smaller set of admissible functions.

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36

Mazowiecka, Katarzyna, and Paweł Strzelecki. "The Lavrentiev gap phenomenon for harmonic maps into spheres holds on a dense set of zero degree boundary data." Advances in Calculus of Variations 10, no. 3 (July 1, 2017): 303–14. http://dx.doi.org/10.1515/acv-2015-0040.

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AbstractWe consider the set of smooth zero degree maps {\psi\colon\mathbb{S}^{2}\to\mathbb{S}^{2}} which have the following properties: (i) There is a unique minimizing harmonic map {u\colon\mathbb{B}^{3}\to\mathbb{S}^{2}} which agrees with ψ on the boundary of the unit ball. (ii) The map u has at least N singular points in {\mathbb{B}^{3}}. (iii) The Lavrentiev gap phenomenon holds for ψ, i.e., the infimum of the Dirichlet energies {E(w)} of all smooth extensions {w\colon\mathbb{B}^{3}\to\mathbb{S}^{2}} of ψ is strictly larger than the Dirichlet energy {\int_{\mathbb{B}^{3}}\lvert\nabla u|^{2}} of the (irregular) minimizer u. For each positive integer N, we prove that this set is dense in the set {\mathcal{S}} of all smooth zero degree maps {\phi\colon\mathbb{S}^{2}\to\mathbb{S}^{2}} endowed with the {W^{1,p}}-topology, where 1 \leqp ¡ 2. This result is sharp since it fails in the {W^{1,2}}-topology of {\mathcal{S}}.

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37

De Arcangelis, Riccardo. "The Lavrentieff phenomenon for quadratic functionals." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 125, no. 2 (1995): 329–39. http://dx.doi.org/10.1017/s0308210500028055.

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The paper provides an example of an integral functional in more than two dimensions, with a symmetric and positively defined quadratic integrand q, exhibiting the Lavrentieff phenomenon on a ball B and on a linear boundary datum u0, i.e. for whichThe example is also utilised to discuss nonidentity between some relaxation procedures for a quadratic integral functional and to provide a weighted Sobolev space in the Hilbert case in which smooth functions are not dense.

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Antonio Corbo, Esposito, and Riccardo De Arcagelis. "The Lavrentieff phenomenon And Different processes of Homogenization." Communications in Partial Differential Equations 17, no. 9-10 (January 1992): 1503–38. http://dx.doi.org/10.1080/03605309208820894.

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39

Pastukhova, Svetlana E. "Degenerate equations of monotone type: Lavrent'ev phenomenon and attainability problems." Sbornik: Mathematics 198, no. 10 (October 31, 2007): 1465–94. http://dx.doi.org/10.1070/sm2007v198n10abeh003892.

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Mariconda, Carlo. "Equi-Lipschitz minimizing trajectories for non coercive, discontinuous, non convex Bolza controlled-linear optimal control problems." Transactions of the American Mathematical Society, Series B 8, no. 29 (November 2, 2021): 899–947. http://dx.doi.org/10.1090/btran/80.

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This article deals with the Lipschitz regularity of the “approximate” minimizers for the Bolza type control functional of the form \[ J t ( y , u ) ≔ ∫ t T Λ ( s , y ( s ) , u ( s ) ) d s + g ( y ( T ) ) J_t(y,u)≔\int _t^T\Lambda (s,y(s), u(s))\,ds+g(y(T)) \] among the pairs ( y , u ) (y,u) satisfying a prescribed initial condition y ( t ) = x y(t)=x , where the state y y is absolutely continuous, the control u u is summable and the dynamic is controlled-linear of the form y ′ = b ( y ) u y’=b(y)u . For b ≡ 1 b\equiv 1 the above becomes a problem of the calculus of variations. The Lagrangian Λ ( s , y , u ) \Lambda (s,y,u) is assumed to be either convex in the variable u u on every half-line from the origin (radial convexity in u u ), or partial differentiable in the control variable and satisfies a local Lipschitz regularity on the time variable, named Condition (S). It is allowed to be extended valued, discontinuous in y y or in u u , and non convex in u u . We assume a very mild growth condition, actually a violation of the Du Bois-Reymond–Erdmann equation for high values of the control, that is fulfilled if the Lagrangian is coercive as well as in some almost linear cases. The main result states that, given any admissible pair ( y , u ) (y,u) , there exists a more convenient admissible pair ( y ¯ , u ¯ ) (\overline y, \overline u) for J t J_t where u ¯ \overline u is bounded, y ¯ \overline y is Lipschitz, with bounds and ranks that are uniform with respect to t , x t,x in the compact subsets of [ 0 , T [ × R n [0,T[\times \mathbb {R}^n . The result is new even in the superlinear case. As a consequence, there are minimizing sequences that are formed by pairs of equi-Lipschitz trajectories and equi-bounded controls. A new existence and regularity result follows without assuming any kind of Lipschitzianity in the state variable. We deduce, without any need of growth conditions, the nonoccurrence of the Lavrentiev phenomenon for a wide class of Lagrangians containing those that satisfy Condition (S), are bounded on bounded sets “well” inside the effective domain and are radially convex in the control variable. The methods are based on a reparametrization technique and do not involve the Maximum Principle.

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Esposito, A. Corbo, and T. Durante. "Complete representation of some functionals showing the Lavrentieff phenomenon." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 131, no. 4 (August 2001): 811–32. http://dx.doi.org/10.1017/s0308210500001128.

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The functional F(u) = ∫Bf(x, Du) is considered, where B is the unit ball in R2, u varies in the set of the locally Lipschitz functions on R2 and f belongs to a family containing, as model case, the following integrand: The computation of the relaxed functional F̄ is provided yielding an explicit representation formula.This formula nevertheless is not integral, because F̄ is not a measure and does not coincide with the obvious extension of F over all W1,p(B).This phenomenon is essentially due to the non-standard growth behaviour of f(x, z) in the variable z.

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Dani, Keshav, William J. Hrusa, and Victor J. Mizel. "Lavrentiev's phenomenon for totally unconstrained variational problems in one dimension." Nonlinear Differential Equations and Applications 7, no. 4 (December 2000): 435–46. http://dx.doi.org/10.1007/pl00001434.

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De Arcangelis, Riccardo, Sara Monsurrò, and Elvira Zappale. "On the relaxation and the Lavrentieff phenomenon for variational integrals with pointwise measurable gradient constraints." Calculus of Variations and Partial Differential Equations 21, no. 4 (December 2004): 357–400. http://dx.doi.org/10.1007/s00526-003-0259-0.

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Chlebicka, Iwona, Piotr Gwiazda, and Anna Zatorska–Goldstein. "Parabolic equation in time and space dependent anisotropic Musielak–Orlicz spaces in absence of Lavrentiev's phenomenon." Annales de l'Institut Henri Poincaré C, Analyse non linéaire 36, no. 5 (August 2019): 1431–65. http://dx.doi.org/10.1016/j.anihpc.2019.01.003.

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Chlebicka, Iwona, Piotr Gwiazda, and Anna Zatorska-Goldstein. "Renormalized solutions to parabolic equations in time and space dependent anisotropic Musielak–Orlicz spaces in absence of Lavrentiev's phenomenon." Journal of Differential Equations 267, no. 2 (July 2019): 1129–66. http://dx.doi.org/10.1016/j.jde.2019.02.005.

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Korabel’nikova, E. A. "Anxiety disorders in children with attention deficit/hyperactivity disorder." Russian Journal of Woman and Child Health 3, no. 4 (2020): 302–8. http://dx.doi.org/10.32364/2618-8430-2020-3-4-302-308.

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Aim: to assess the prevalence and presentations of anxiety in preschool children with attention deficit/hyperactivity disorder (ADHD). Patients and Methods: preschoolers (4–6 years) and their parents were enrolled. 30 children with ADHD and their parents were included in the study group and 15 healthy children and their parents were included in the control group. The study was performed in Moscow kindergartens. Clinical anamnestic, experimental psychological (Р. Temple, М. Dorkey, and Е.W. Amen anxiety test adapted by V.M. Astapov; “Fears in Houses” test modified by M.A. Panfilova; questionnaire for anxiety in children for a teacher and parents by G.P. Lavrent’eva and T.M. Titarenko), and statistical tests were applied. Results: in children with ADHD, a significantly higher level of anxiety was reported as demonstrated by Р. Temple, М. Dorkey, and Е.W. Amen anxiety test results (i.e., the test completed by children themselves). The percentage of children with 15 fears or more was significantly higher in the study group compared to the control group. Most preschoolers from both groups experience so-called age-related fears. In addition, age-inappropriate social fears (e.g., a fear of punishment or a fear of being late for kindergarten) were revealed in children with ADHD. These fears were much more common in the study group compared to the control group. Conclusions: our findings demonstrate a higher level of anxiety in children with ADHD compared to healthy children. Therefore, anxiety may be regarded as an ADHD-associated factor. In addition to typical age-related fears, children with ADHD experience so-called social fears. This phenomenon illustrates a fear of disapproval and punishment and a propensity for low self-esteem. KEYWORDS: attention deficit/hyperactivity disorder, anxiety disorders, preschoolers. FOR CITATION: Korabel’nikova E.A. Anxiety disorders in children with attention deficit/hyperactivity disorder. Russian Journal of Woman and Child Health. 2020;3(4):302–308. DOI: 10.32364/2618-8430-2020-3-4-302-308.

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Karbovska, Karolina. "Personal image: introduction to legal discourse." Law and innovations, no. 4 (36) (December 15, 2021): 117–23. http://dx.doi.org/10.37772/2518-1718-2021-4(36)-17.

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Problem setting. Intensive development of public relations, digitalization and commercialization of new spheres of life, growing popularity of the media sphere necessitates civil protection not only the privacy of individuals who are popular and recognizable, but also their right to publicity, which is directly related to lawful use of intangible benefits that belong to a person and shape his image. Analysis of recent researches and publications. Among the world's most prominent researchers of image as a social phenomenon are R. Burns, I. Hoffman, W. James, J. Rotter, L. Holl, and others. Domestic studies of image are represented by the works of Atamanskaya K.I., Barny N.V., Krynychna I.P., Lavrentiya A.S., Palekha Y.I., Panteleychuk I.V., Fedoriva T.V., Shcherbak N. V. and other representatives of various social sciences. The purpose of the article is to outline general scientific approaches to defining the concept of image, distinguishing it from related concepts and identifying promising areas of civil law research of image. Article’s main body. The concept of image is more often used in the information space, which leads to an increase in public demand for the legal definition of this concept and the settlement of issues related to the protection of the image of both individuals and legal entities. Image is the object of study of various branches of social science and studied by them in a variety of manifestations and aspects. Based on the analysis of a number of approaches to image definition by representatives of various sciences, it can be concluded that image considered as: (a) a communication tool that is a manipulative technology to influence public consciousness; (b) marketing tool to promote goods, works and services; (c) the external and psychological image of the public person through which society identifies him as an individual. Considering the image of an individual from the standpoint of a systematic approach, in particular a multilevel set of different components - personal intangible assets, we believe that reputation is an element of the image of an individual and should be considered as its structural component. From the standpoint of interdisciplinary research, the concepts of image and personal brand should be considered as synonymous, from a legal point of view, despite their similarity, they are formed by different objects of civil rights, although within the protection of the individual's right to protection and personal brand. Conclusions and prospects for the development. In view of the above, it can be concluded that the image of an individual is a complex, interdisciplinary concept. It is a holistic, stable image of a particular person that exists in society, and is characterized by the indivisibility of its external and internal characteristics, the corresponding personal, professional and social qualities. The constituent legal elements of the image are (a) personal intangible assets: the right to a name, the right to an image, the right to individuality, personal reputation; (b) objects of intellectual property rights: means of personalization: personal brand, trademark, trade name and others.

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Parfenova, A. G., and M. V. Safonova. "FEATURES OF THE ACTIVITY OF MODERN ADOLESCENTS AND POSSIBILITY OF ITS DEVELOPMENT WITH THE HELP OF A SUBJECT-SPATIAL COMPONENT OF THE EDUCATIONAL ENVIRONMENT." Bulletin of Krasnoyarsk State Pedagogical University named after V.P. Astafiev 59, no. 1 (March 30, 2022): 68–84. http://dx.doi.org/10.25146/1995-0861-2022-59-1-318.

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Statement of the problem. The article fixes the relevance of the problem of student activity, since any human manifestations are associated with the phenomenon of activity, emphasizes the importance of studying the nature of activity, the mechanisms of its development and manifestation in order to determine possible ways of its purposeful formation. The purpose of the article is to analyze the results of the study of various manifestations of the activity of the personality of adolescents and to discuss the possibilities of the subject-spatial environment of educational institutions as a means of contributing to the formation of the activity of the personality of a modern schoolchild. The theoretical and methodological basis of the research includes activity-based (V.V. Davydov, M.M. Makhmutov, etc.); personality-activity-based (V.P. Zinchenko, V.A. Slastenin), systemic (B.F. Lomov, V.A. Hansen), ecological (J. Gibson), integrative (A.A. Volochkov) approaches, as well as the theory of personality activity (S.L. Rubinstein, L.S. Vygotsky, B.F. Lomov, K.A. Abulkhanova-Slavskaya), research in the field of environmental psychology (M.Chernoushek, K. Levin, J. Gibson, V.A. Yasvin). 155 students of grades 6–8 of MBOU “Secondary school No. 157” of Krasnoyarsk took part in the study. To analyze the results, the following samples were formed: all respondents studying separately in grades 6, 7, 8. The methods of WAM (well-being, activity, mood) developed by V.A. Doskin, N.A. Lavrentieva, V.B. Sharai and M.P. Miroshnikov were used; the method of diagnosing the components of socially-oriented activity by R.M. Shamionov; the method of diagnosing the components of subjective adaptivity “Readiness for action and evaluation of the implementation of action” by L.M. Kolpakova, S.V. Khusainova. Observation was also used as a research method. When processing the results, methods of average analysis, ranking, and qualitative analysis were used. Research results. According to the study of social activity, adolescents are motivated to be with others and be active in interaction and communication, but they have insufficient indicative basis for its implementation, they do not see opportunities for activity, which is accompanied by negative experiences and is expressed in low overall activity. Teenagers rarely initiate any actions, offer solutions, in order for the activity to manifest itself, efforts on the part of a teacher, mentor are required. That is, we can talk about reactivity in response to the demands of the school environment, rather than about our own activity. Teenagers find it difficult to choose such forms of their actions and behavior that would allow them to harmonize their own interests and the interests of others, rely on internal meanings and beliefs and combine them with the requirements of the society. Internal contradictions lead to emotional tension, negative experiences and rejection of activity as a defensive strategy to avoid failure. After passing through the physiological storm in the acute puberty period, from the point of view of the functional state, adolescents are ready to be active, but psychologically the realization of different types of activity is hindered by the difficulty in finding their own ways of its manifestation, consistent with the requirements of the social environment, as well as conditions in the educational environment that limit the manifestations of activity or do not contribute to the emergence of the need for activity. Conclusion. In adolescence, we can talk about the presence of a certain readiness of adolescents to be proactive in the educational environment, but unwillingness, inability to show it. In many ways, this may be due to environmental factors that set a certain well-being, mood, readiness for active actions. As one of the means of developing the activity of adolescents, we offer a co-participating design of the subject-spatial component of the educational environment.

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Burganova, Maria A. "LETTER FROM THE EDITOR." Scientific and analytical journal Burganov House. The space of culture 17, no. 5 (December 10, 2021): 8–9. http://dx.doi.org/10.36340/2071-6818-2021-17-5-8-9.

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Dear readers, We are pleased to present to you Issue 5, 2021, of the scientific and analytical journal Burganov House. The Space of Culture. Upon the recommendation of the Expert Council of the Higher Attestation Commission, the journal is included in the List of Leading Peer-reviewed Scientific Journals and Publications in which the main scientific results of theses for the academic degrees of doctor and candidate of science must be published. The journal publishes scientific articles by leading specialists in various humanitarian fields, doctoral students, and graduate students. Research areas concern topical problems in multiple areas of culture, art, philology, and linguistics. This versatility of the review reveals the main specificity of the journal, which represents the current state of the cultural space. The journal traditionally opens with the Academic Interview rubric. In this issue, we present an interview with Alexander Burganov, Academician of the Russian Academy of Arts, an outstanding Russian sculptor, National Artist of Russia, Doctor of Art History, Professor, Director of the Burganov House Moscow State Museum, interviewed by Irina Sedova, the Head of the 20th Century Sculpture Department of the State Tretyakov Gallery. This dialogue became part of the sculptor’s creative evening at the State Tretyakov Gallery, which included a personal exhibition, donation of the sculptural work Letter, screening of a special film and a dialogue with the audience in the format of an interactive interview. In the article “The Apocalypse Icon from the Kremlin’s Assumption Cathedral. Dating and Historical Context”, T. Samoilova points out the similarities between some motifs of the Apocalypse iconography and the motifs of Botticelli’s illustrations to the Divine Comedy, as well as the role of a line in both artworks which testifies to the influence of the Renaissance art on icon painting of the late 15th — early 16th centuries. Studying palaeography and stylistic features of the icon, the author clarifies the dates and believes that the icon was most likely painted after 1500, in the first decade of the 16th century. P. Tsvetkova researches the features of the development of the Palladian architectural system in Italy, in the homeland of Andrea Palladio. On the examples of specific monuments, drawings and projects created during two and a half centuries, the author analyses the peculiarities of the style transformation in the work of Palladio’s followers, the continuity of tradition, deviations from canonical rules. In the article “Artistic Features of the Northern White Night Motif in the Landscapes of Alexander Borisov and Louis Apol”, I. Yenina conducts art analysis and compares the works of the Russian “artist of eternal ice”, A. Borisov, and the Dutch “winter artist”, L. Apol. They were the first to depict such a phenomenon as a white night in the Far North. V. Slepukhin studies the artworks of the first decades of the Soviet era in the article “Formation of the Image of a New Hero in Russian Art of 1920- 1930”. The author concludes that the New Hero in the plastic arts of the 1920s–1930s was formed as a reflection of social ideals. The avant-garde artists searched for the Hero’s originality in the images of aviators, peasants, women. The artists of socialist realism began to form the images of the “typical” heroes of the time — warriors, athletes, rural workers, scientists, as new “people of the Renaissance”. In the article “Dialogues of the Avant-garde”, A. N. Lavrentyev presents a comparative analysis of spatial constructions created by the Russian Avant-Garde Artist Alexander Rodchenko and the famous kinetic European and American artist Alexander Calder in the first half of the 20th century. Wei Xiao continues his analysis of contemporary art in the article “Chinese Sculpture in the New Era”. The author notes that the art of sculpture is in many ways a reflection of social change, both in terms of cultural content and practice. The author emphasises the need for cultural identity to preserve national traditions and spirituality. Xu Yanping’s article “The Dynamics of the Choral Culture Development in China in the 1930s on the Example of Huang Tzi’s Oratorio Eternal Regret” is a scientific study of a particular phase of the active entry of Chinese choral music into the sphere of the oratorio genre, directly related to the name of the great Chinese composer, Huang Tzi. It also highlights the issues of the country’s political life in the 1930s, which actively influenced the creation of nationwide singing movements and new choral works in the country. The author believes that the oratorio Eternal Regret presented in the article is a unique creation that organically combines ethnic musical material and Western composition techniques. The publication is addressed to professionals specialising in the theory and practice of the fine arts and philology and all those interested in the arts and culture.

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Bonfanti, Giovanni, and Arrigo Cellina. "On the non-occurrence of the Lavrentiev phenomenon." Advances in Calculus of Variations 6, no. 1 (January 1, 2013). http://dx.doi.org/10.1515/acv-2011-0002.

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Journal articles on the topic 'Lavrentiev phenomenon'

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