On Some Fixed Point Results in E − Fuzzy Metric Spaces

In the existing literature, Banach contraction theorem as well as Meir-Keeler fixed point theorem were extended to fuzzy metric spaces. However, the existing extensions require strong additional assumptions. The purpose of this paper is to determine a class of fuzzy metric spaces in which both theorems remain true without the need of any additional condition. We demonstrate the wide validity of the new class.

Placement Inverse Source Problem under Partition Hyperbolic Equation

In this article, the inverse source problem is determined by the partition hyperbolic equation under the left end flux tension of the string, where the extra measurement is considered. The approximate solution is obtained in the form of splitting and applying the finite difference method (FDM). Moreover, this problem is ill-posed, dealing with instability of force after adding noise to the additional condition. To stabilize the solution, the regularization matrix is considered. Consequently, it is proved by error estimates between the regularized solution and the exact solution. The numerical results show that the method is efficient and stable.

Axisymmetric frictionless indentation of a rigid stamp into a semi-space with a surface energetic boundary

An axisymmetric problem for a frictionless contact of a rigid stamp with a semi-space in the presence of surface energy in the Steigmann–Ogden form is studied. The method of Boussinesq potentials is used to obtain integral representations of the stresses and the displacements. Using the Hankel transform, the problem is reduced to a single integral equation of the first kind on a contact interval with an additional condition. The integral equation is studied for solvability. It is shown that for the classic problem in the absence of surface effects and for the problem with the Gurtin–Murdoch surface energy without surface tension, the obtained equation represents a Cauchy singular integral equation. At the same time, for the Gurtin–Murdoch model with a non-zero surface tension and for the general Steigmann–Ogden model, the problem results in the integral equation of the first kind with a weakly singular or a continuous kernel, correspondingly. Hence, the contact problem is ill-posed in these cases. The integral equation of the first kind with an additional condition is solved approximately by using Gauss–Chebyshev quadrature for evaluation of the integrals. Numerical results for various values of the parameters are reported.

Constitutional amendments and revision of the Constitution of the Russian Federation: features of the 2020 procedure

The article discusses the issue of the procedure for changing the Constitution of the Russian Federation. Examples of norms of foreign constitutions are given, which constitutionalists recognize as rigid constitutions in the order of their amendment. The ways of changing the Constitution of the Russian Federation are considered: revision, adoption of amendments, amendment of Art. 65Identified problems such as the form of the amendment to the Constitution, the moment of entry into force of the amendment, the introduction by the Law of the Russian Federation on the amendment to the Constitution of the Russian Federation of 2020 a nationwide vote as an additional condition for the entry into force of the amendment, as well as additional powers of the Constitutional Court of the Russian Federation to verify compliance with Chapters 1, 2 and 9 of the Constitution of the Russian Federation of the provisions of the Law of the Russian Federation on the amendment to the Constitution of the Russian Federation that have not entered into force, as well as the procedure for the entry into force of Art. 1 of the Amendment Act. The critical notes are offered. In particular, the author comes to the conclusion that the approval of the constitutional amendment by the parliaments of the constituent entities of the Russian Federation is not a moment, but a condition for its entry into force, therefore, the law on the amendment cannot introduce additional conditions for the entry into force of constitutional amendments, since this leads to a violation requirements of Art. 136 of the Constitution, which cannot be amended by the federal parliament in the manner prescribed by chapter 9 of the Constitution.

Coincidence Point Results on Relation Theoretic F w , R g -Contractions and Applications

Motivated by the ideas of F -weak contractions and F , R g -contractions, the notion of F w , R g -contractions is introduced and studied in the present paper. The idea is to establish some interesting results for the existence and uniqueness of a coincidence point for these contractions. Further, using an additional condition of weakly compatible mappings, a common fixed-point theorem and a fixed-point result are proved for F w , R g -contractions in metric spaces equipped with a transitive binary relation. The results are elaborated by illustrative examples. Some consequences of these results are also deduced in ordered metric spaces and metric spaces endowed with graph. Finally, as an application, the existence of the solution of certain Voltera type integral equations is investigated.

Who Are the Compliant Correctional Clients? New Evidence on Protective Factors among Federal Supervised Releases

Protective factors facilitate success on community supervision, but relatively little is known about correctional clients who are highly compliant particularly in the federal system. Drawing on a near population of federal clients on supervised release in the Midwestern United States, the current study examined variables associated with compliant supervision status. One day on supervision contributed to a 1% reduction in the logged odds of supervision compliance. Clients with no drug history had 793% increased odds, clients with sustained remission had 620% increased odds, and clients with early remission had 458% increased odds of compliant supervision status relative to clients actively using drugs. Among the federal Post Conviction Risk Assessment (PCRA) indices, only PCRA Criminal History was significant as clients with less extensive criminal history were more likely to be compliant supervision clients. A one-unit change in PCRA Criminal History status was associated with 25% reduced odds of supervision compliance. Total conditions were inversely associated with compliant supervision status with each additional condition associated with a 19% reduced likelihood of compliant supervision status. None of the demographic variables was significantly associated with compliant supervision status. Implications of the findings for the protective factor paradigm in corrections are discussed.

Sign-changing solutions for Schrödinger system with critical growth

<abstract><p>We consider the following Schrödinger system</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \left\{ \begin{aligned} &amp;-\Delta u_j = \sum\limits_{i = 1}^k \beta_{ij}|u_i|^3|u_j|u_j+\lambda_j|u_j|^{q-2}u_j, \ \ \ \text{in}\, \, \Omega, \\ &amp;u_j = 0\quad\text{on}\, \, \partial\Omega, \, \, j = 1, \cdots, k \end{aligned} \right. \end{equation*} $\end{document} </tex-math></disp-formula></p> <p>where $ \Omega\subset\mathbb{R}^3 $ is a bounded domain with smooth boundary. Assume $ 5 &lt; q &lt; 6, \, \lambda_j &gt; 0, \, \beta_{jj} &gt; 0, \, j = 1, \cdots, k $, $ \beta_{ij} = \beta_{ji}, \, i\neq j, i, j = 1, \cdots, k $. Note that the nonlinear coupling terms are of critical Sobolev growth in dimension $ 3 $. We prove that under an additional condition on the coupling matrix the problem has infinitely many sign-changing solutions. The result is obtained by combining the method of invariant sets of descending flow with the approach of using approximation of systems of subcritical growth.</p></abstract>