3,995 research outputs found
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 becomes strictly self-adjoint after multiplying by
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 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
-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 . 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 , 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
A symmetry classification for a class of (2+1)-nonlinear wave equation
In this paper, a symmetry classification of a -nonlinear wave equation
where is a smooth function on , using
Lie group method, is given. The basic infinitesimal method for calculating
symmetry groups is presented, and used to determine the general symmetry group
of this -nonlinear wave equation
Parameter estimation in pair hidden Markov models
This paper deals with parameter estimation in pair hidden Markov models
(pair-HMMs). We first provide a rigorous formalism for these models and discuss
possible definitions of likelihoods. The model being biologically motivated,
some restrictions with respect to the full parameter space naturally occur.
Existence of two different Information divergence rates is established and
divergence property (namely positivity at values different from the true one)
is shown under additional assumptions. This yields consistency for the
parameter in parametrization schemes for which the divergence property holds.
Simulations illustrate different cases which are not covered by our results.Comment: corrected typo
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