Principle as a Means of Identifying a Legislative Gap (on the Example of Juvenile Justice)

The paper presents the principle as a research issue as a basis for identifying a legislative gap. In terms of research methodology, the paper uses an inductive and deductive method that plays the lion's role in shaping the final conclusion. Especially important is the legitimacy method, which broadly shows the importance of the principle in the development of law, for law and justice. The aim of the paper is to cover the issue with a new approach, in particular, the paper combines, on the one hand, a review of constitutional procedures for gaps in the legislation, analyzes of ways to correct gaps in the legislation, against which the principle can be considered The issue is covered by analyzing the importance of the norm-principle of juvenile justice – prioritizing the best interests and defining its role in identifying gaps in the legislation in juvenile justice. To illustrate this point, such a fundamental issue of juvenile justice as custodial bail and its relevance to the priority of best interests as a matter of principle is analyzed. The findings are based on a critical analysis of the functioning of the juvenile justice norm-principle with bail in conjunction with a discussion of the constitutional issues of detecting legislative gaps. The existence of the principle as the basis of any legislation is outlined and its mirror principle is shown, according to which it reflects the legislative gaps and shows the way to the harmonization of the legislation.

Explicit methods for the Hasse norm principle and applications to A n and S n extensions

Let K/k be an extension of number fields. We describe theoretical results and computational methods for calculating the obstruction to the Hasse norm principle for K/k and the defect of weak approximation for the norm one torus \[R_{K/k}^1{\mathbb{G}_m}\] . We apply our techniques to give explicit and computable formulae for the obstruction to the Hasse norm principle and the defect of weak approximation when the normal closure of K/k has symmetric or alternating Galois group.

On the Tits–Weiss conjecture and the Kneser–Tits conjecture for and (With an Appendix by R. M. Weiss)

We prove that the structure group of any Albert algebra over an arbitrary field is R-trivial. This implies the Tits–Weiss conjecture for Albert algebras and the Kneser–Tits conjecture for isotropic groups of type $\mathrm {E}_{7,1}^{78}, \mathrm {E}_{8,2}^{78}$ . As a further corollary, we show that some standard conjectures on the groups of R-equivalence classes in algebraic groups and the norm principle are true for strongly inner forms of type $^1\mathrm {E}_6$ .

Existence of Rost Varieties

This chapter proves that the norm varieties constructed in the previous chapter are indeed Rost varieties. In other words, it proves that Rost varieties exist. In doing so, the chapter also proves the Norm Principle, which is a theorem that supposes that 𝑘 is an 𝓁-special field of characteristic 0, and that 𝑋 is a norm variety for some nontrivial symbol ª. Then each element of ̅𝐻−1, −1(𝑋) is a Kummer element. In preparation for the proof of the Norm Principle, this chapter develops some basic facts about elements of ̅𝐻−1, −1(𝑋) supported on points 𝑥 with 𝑘(𝑥) : 𝑘=𝓁.

Degree Formulas

This chapter uses algebraic cobordism to establish some degree formulas. It presents δ‎ as a function from a class of smooth projective varieties over a field 𝑘 to some abelian group. Here, a degree formula for δ‎ is a formula relating δ‎(𝑋), δ‎(𝑌), and deg(𝑓) for any generically finite map 𝑓 : 𝑌 → 𝑋 in this class. The formula is usually δ‎(𝑌)=deg(𝑓)δ‎(𝑋). These degree formulas are used to prove that any norm variety over 𝑘 is a ν‎ n−1-variety. Using a standard result for the complex bordism ring 𝑀𝑈*, which uses a gluing argument of equivariant bordism theory, this chapter establishes Rost's DN (Degree and Norm Principle) Theorem for degrees, and defines the invariant η‎(𝑋/𝑆) of a pseudo-Galois cover.