Uniqueness property for quasiharmonic functions

In this paper we consider class of continuous functions, called quasiaharmonic functions, admitting best approximations by harmonic polynomials. In this class we prove a uniqueness theorem by analogy with the analytic functions

Удовольствие и интерес к игре как основа подхода к проектированию детской игровой площадки

The article considers design of children’s playgrounds. The design traditions in modern architectural school are discussed, the problem of “the game” is identified and the term “pleasure” is focused. The conclusion is that we need a new approach to design children’s playgrounds in order to interest children in the age group from six to fifteen.В статье рассматривается проектирование детских игровых площадок. Обсуждаются традиции проектирования в современных архитектурных школах, ставится проблема «игры» и центральное внимание уделяется термину «удовольствие». В заключении делается вывод, что нужен новый подход к проектированию детских игровых площадок, для того чтобы заинтересовать детей возрастом от 6 до 15 лет

Nonlinear self-adjointness and conservation laws

The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self-adjointness and quasi self-adjointness introduced earlier by the author. It is shown that the equations possessing the nonlinear self-adjointness can be written equivalently in a strictly self-adjoint form by using appropriate multipliers. All linear equations possess the property of nonlinear self-adjointness, and hence can be rewritten in a nonlinear strictly self-adjoint. For example, the heat equation $u_t - \Delta u = 0$ becomes strictly self-adjoint after multiplying by $u^{-1}.$ Conservation laws associated with symmetries can be constructed for all differential equations and systems having the property of nonlinear self-adjointness

The Impact of Cultural Familiarity on Students’ Social Media Usage in Higher Education

Using social media (SM) in Higher education (HE) becomes unavoidable in the new teaching and learning pedagogy. The current generation of students creates their groups on SM for collaboration. However, SM can be a primary source of learning distraction due to its nature, which does not support structured learning. Hence, derived from the literature, this study proposes three learning customised system features, to be implemented on SM when used in Higher Education HE. Nevertheless, some psychological factors appear to have a stronger impact on students’ adoption of SM in learning than the proposed features. A Quantitative survey was conducted at a university in Uzbekistan to collect 52 undergraduate students’ perception of proposed SM learning customised features in Moodle. These features aim to provide localised, personalised, and privacy control self-management environment for collaboration in Moodle. These features could be significant in predicting students’ engagement with SM in HE. The data analysis showed a majority of positive feedback towards the proposed learning customised SM. However, the surveyed students’ engagement with these features was observed as minimal. The course leader initiated a semi-structured interview to investigate the reason. Although the students confirmed their acceptance of the learning customised features, their preferences to alternate SM, which is Telegram overridden their usage of the proposed learning customized SM, which is Twitter. The students avoided the Moodle integrated Twitter (which provided highly accepted features) and chose to use the Telegram as an external collaboration platform driven by their familiarity and social preferences with the Telegram since it is the popular SM in Uzbekistan. This study is part of an ongoing PhD research which involves deeper frame of learners’ cognitive usage of the learning management system. However, this paper exclusively discusses the cultural familiarity impact of student’s adoption of SM in HE

Group Analysis of the Novikov Equation

We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing conserved vectors associated with symmetries of differential equations, we find the conservation law corresponding to the dilations symmetry and show that other symmetries do not provide nontrivial conservation laws. Then we investigat the invariant solutions

Classification of conservation laws of compressible isentropic fluid flow in n>1 spatial dimensions

For the Euler equations governing compressible isentropic fluid flow with a barotropic equation of state (where pressure is a function only of the density), local conservation laws in $n>1$ spatial dimensions are fully classified in two primary cases of physical and analytical interest: (1) kinematic conserved densities that depend only on the fluid density and velocity, in addition to the time and space coordinates; (2) vorticity conserved densities that have an essential dependence on the curl of the fluid velocity. A main result of the classification in the kinematic case is that the only equation of state found to be distinguished by admitting extra $n$-dimensional conserved integrals, apart from mass, momentum, energy, angular momentum and Galilean momentum (which are admitted for all equations of state), is the well-known polytropic equation of state with dimension-dependent exponent $\gamma=1+2/n$. In the vorticity case, no distinguished equations of state are found to arise, and here the main result of the classification is that, in all even dimensions $n\geq 2$, a generalized version of Kelvin's two-dimensional circulation theorem is obtained for a general equation of state.Comment: 24 pages; published version with misprints correcte

Byudjet tashkilotlarida byudjet mablag’laridan foydalanishning nazorat tizimini takomillashtirish masalalari

Ushbu maqolada davlat byudjetidan byudjet tashkilotlariga mablag‘ ajratish va moliyalashtirish jarayonida samarali moliyaviy nazorat tizimini ta’minlash masalalari tadqiq etilgan

Four dimensional Lie symmetry algebras and fourth order ordinary differential equations

Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is described.Comment: 12 page