LEGAL MECHANISM OF THE COURT FEE REFUND IN CASE OF TRIAL COMPLETION WITHOUT ADOPTION OF A JUDGEMENT IN CIVIL PROCEEDINGS

The peculiarities of the legal mechanism of returning the court fee in case of completion of civil cases without a court decision are analyzed, issues of these applications practical resolving are considered, as well as suggestions for improving the legal regulation in case of the closure of the proceedings or leaving the application without consideration are proposed. While analyzing examples of case law, it was established that the lack of legislative regulation of the procedure for confirming or denying the existence of grounds for the amount of court fees refund causes a lot of confusion and contradictory solutions to the judiciary in this regard. The position on the impossibility of equalization due to the different procedural nature of leaving without consideration of statements on procedural issues, such as: on providing evidence, on securing a claim, on dismissal of a judge, and leaving without considering a statement of claim as a civil procedural institute, regulated by Art. 257 of CPC of Ukraine are justified. It has been concluded that in case the court finds circumstances that are grounds for the application of the institute of leaving the application without consideration and provided for in Art. 257 of CPS of Ukraine, when considering applications on procedural issues, should apply such a special legal consequence as a return of the application without consideration. It has been established that returning an application on procedural issues without consideration and leaving an application without consideration are completely different legal categories. Return of applications on procedural issues without consideration due to its legal nature is a special basis for the application of the return of the application institute, and therefore the legal consequence of such an application would be considered not filed at all. In this connection, it has been proposed to enshrine in the legislation the provisions on the refund of the court fee in case of return without consideration of the application on procedural issues, for the submission of which such payment was paid.

ON THE INTERACTION OF A VISCOELASTIC CYLINDRICAL PIPE WITH INNER UNIFORM COATING AND INSERTS WITH A COMPLEX PROFILE

This work is devoted to the formulation and construction of an analytical solution to the problem of contact between a cylindrical viscoelastic aging pipe with an internal thin coating and an insert having a complex shape placed inside the pipe with an interference fit. In practice, the presence of such coatings is required, for example, to protect the main structure from aggressive external or internal environments, for its electrical insulation, etc. The manufacturing process of the inner coating determines its possible heterogeneity (dependence of properties on coordinates). An insert placed inside a pipe can have a complex profile that has a rapidly changing function. Taking these features into account is important when analyzing the stress-strain state of pipes with an internal coating. Using an approach based on the use of special basis functions and the type of solution, a representation for the contact stresses in the pipe in the region of the rigid insert is obtained. This approach makes it possible to distinguish functions that describe the properties of the inner coating and the shape of the outer profile of the insert in the form of separate terms and factors in the expression for the contact stresses in the insert region. Therefore, in order to achieve high accuracy when carrying out calculations, it is sufficient to restrict ourselves to a relatively small number of terms

Strong Solutions of the Incompressible Navier–Stokes–Voigt Model

This paper deals with an initial-boundary value problem for the Navier–Stokes–Voigt equations describing unsteady flows of an incompressible non-Newtonian fluid. We give the strong formulation of this problem as a nonlinear evolutionary equation in Sobolev spaces. Using the Faedo–Galerkin method with a special basis of eigenfunctions of the Stokes operator, we construct a global-in-time strong solution, which is unique in both two-dimensional and three-dimensional domains. We also study the long-time asymptotic behavior of the velocity field under the assumption that the external forces field is conservative.

From a reversible code to the quantum one: R-matrix

This research has been carried out in collaboration with D.Melnikov, A.Mironov, A.Morozov and An.Morozov. We study the relation between quantum programming and knot theory. The general idea is that knot theory provides a special basis for unitary matrices. We suggest to use R-matrices of knot theory as universal gates in quantum code. We also examine basic operations in reversible programming.

Rights as Process

This chapter focuses on the distance between rights as claims and rights in practice. To survey rights in the Progressive century, it proposes to define rights less as a thing and more as a process, to wit: “A right is a claim, made against a person or action of another, either a citizen or governmental officer, enforceable in a court of law.” Like other processes, a “right” has a beginning and an end. The beginning is the claim itself; the end, its anticipated enforcement. The chapter begins by briefly situating the Progressive era in a broader story of rights as defined above. It then discusses a handful of rights disputes in state and federal courts from the Progressive era forward, and the definition proposed is briefly applied to particular cases. The cases were not selected on any special basis; others would have served as well. They are discussed only to give the approach a trial run. The point is not to put things in boxes but to consider rights in a fresh way, both over this historical span and in general.

On Classification of Filiform Leibniz Algebras

In this work we prove that in classifying of filiform Leibniz algebras whose naturally graded algebra is a non-Lie algebra, it suffices to consider some special basis transformations. Moreover, we derive a criterion for two such Leibniz algebras to be isomorphic in terms of such transformations. The classification problem of filiform Leibniz algebras whose naturally graded algebra is non-Lie in an arbitrary dimension, is reduced to the investigation of the conditions obtained.

More on the Wilson $W_{tk}(v)$ Matrices

For integers $0\leq t\leq k\leq v-t$, let $X$ be a $v$-set, and let $W_{tk}(v)$ be a ${v \choose t}\times{v \choose k}$ inclusion matrix where rows and columns are indexed by $t$-subsets and $k$-subsets of $X$, respectively, and for row $T$ and column $K$, $W_{tk}(v)(T,K)=1$ if $T\subseteq K$ and zero otherwise. Since $W_{tk}(v)$ is a full rank matrix, by reordering the columns of $W_{tk}(v)$ we can write $W_{tk}(v) = (S|N)$, where $N$ denotes a set of independent columns of $W_{tk}(v)$. In this paper, first by classifying $t$-subsets and $k$-subsets, we present a new decomposition of $W_{tk}(v)$. Then by employing this decomposition, the Leibniz Triangle, and a known right inverse of $W_{tk}(v)$, we construct the inverse of $N$ and consequently special basis for the null space (known as the standard basis) of $W_{tk}(v)$.

Galerkin-Laguerre Spectral Solution of Self-Similar Boundary Layer Problems

In this work the Laguerre basis for the biharmonic equation introduced by Jie Shen is employed in the spectral solution of self-similar problems of the boundary layer theory. An original Petrov-Galerkin formulation of the Falkner-Skan equation is presented which is based on a judiciously chosen special basis function to capture the asymptotic behaviour of the unknown. A spectral method of remarkable simplicity is obtained for computing Falkner-Skan-Cooke boundary layer flows. The accuracy and efficiency of the Laguerre spectral approximation is illustrated by determining the linear stability of nonseparated and separated flows according to the Orr-Sommerfeld equation. The pentadiagonal matrices representing the derivative operators are explicitly provided in an Appendix to aid an immediate implementation of the spectral solution algorithms.