Related papers: Forms of Nice Functions
We consider an ordinary nonlinear differential equation with generalized coefficients as an equation in differentials in algebra of new generalized functions. Then the solution of such equation will be a new generalized function. In the…
The classical Hamilton equations of motion yield a structure sufficiently general to handle an almost arbitrary set of ordinary differential equations. Employing elementary algebraic methods, it is possible within the Hamiltonian structure…
One of the main virtues of trees is to represent formal solutions of various functional equations which can be cast in the form of fixed point problems. Basic examples include differential equations and functional (Lagrange) inversion in…
Formulas for the solutions of initial value problems for ordinary differential equations with singular $\delta^{(n)}$-like driving terms are derived in the framework of an algebra of generalized functions (of Colombeau type) over a field of…
Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of…
A new approach to the problem of group classification is applied to the class of first-order non-linear equations of the form $u_a u_a=F(t,u,u_t)$. It allowed complete solution of the group classification problem for a class of equations…
Under certain conditions, we obtain sharp bounds on some functionals defined in the coefficient space of starlike functions. It has been found that the functionals are closely associated with certain coefficient problems, which are of…
Ultrafunctions are a particular class of functions defined on a non-Archimedean field. They provide generalized solutions to functional equations which do not have any solutions among the real functions or the distributions. In this paper…
The aim of the work is to construct new polynomial systems, which are solutions to certain functional equations which generalize the second-order differential equations satisfied by the so called classical orthogonal polynomial families of…
We prove a uniqueness theorem for a large class of functional equations in the plane, which resembles in form a classical result of Aczel. It is also shown that functional equations in this class are overdetermined in the sense of Paneah.…
Inspired by prior work of Bruinier and Ono and Mertens and Rolen, we study class polynomials for non-holomorphic modular functions arising from modular forms of negative weight. In particular, we give general conditions for the…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…
Many studies have investigated students' epistemological framing when solving physics problems. Framing supports students' problem solving as they decide what knowledge to employ and the necessary steps to solve the problem. Students may…
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
We consider maps between commutative groups and their functional degrees. These degrees are defined based on a simple idea -- the functional degree should decrease if a discrete derivative is taken. We show that the maps of finite…
We study certain classes of equations for $F_q$-linear functions, which are the natural function field counterparts of linear ordinary differential equations. It is shown that, in contrast to both classical and $p$-adic cases, formal power…
Classes of algebraic structures that are defined by equational laws are called varieties or equational classes. A variety is finitely generated if it is defined by the laws that hold in some fixed finite algebra. We show that every…
Estimation of linear and quadratic functionals over different classes of univalent functions is one of the classical problems in geometric function theory. In this paper we solve the problem over some classes of so-called non-linear…
Based on an original classification of differential equations by types of regular Lie group actions, we offer a systematic procedure for describing partial differential equations with prescribed symmetry groups. Using a new powerful…