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Regularity of local minimizers for perturbed variable exponent double phase functionals is discussed. We focus on show that minimizers for the functionals are locally bounded and locally Hölder continuous by using the De Giorgi iteration.

We consider the $L^{p}$ -regularity of the Szegö projection on the symmetrised polydisc $\\mathbb {G}_{n}$ . In the setting of the Hardy space corresponding to the distinguished boundary of the symmetrised polydisc, it is shown that this operator is $L^{p}$ -bounded for $p\\in (2-{1}/{n}, 2+{1}/{(n-1)})$ .

In this paper, we generalize the regularity to a symbolic 2‐plithogenic structure. We present the structure and elementary properties of regular symbolic 2‐plithogenic rings. We also found that the classical regular ring R is equivalent to the symbolic 2‐plithogenic ring 2 − SPR. In addition, we obtained several important results. The most important of these are as follows: U2−SPR⊆Reg2−SPR. U2−SPR∩Z2−SPR=∅. U2−SPR∩Id2−SPR=1. Id2−SPR∩N2−SPR=0. 2 − SPR is regular iff R is regular. We presented a rule for finding the element that satisfies the regularity condition for any element of the regular symbolic 2‐plithogenic field. The center of the regular symbolic 2‐plithogenic ring is also a regular.

We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of regularities are presented which shed light on the relations between seemingly different ideas and point to possible necessary conditions for local linear convergence of fundamental algorithms.

Let $\\alpha $ be a complex-valued $2$ -cocycle of a finite group $G.$ A new concept of strict $\\alpha $ -regularity is introduced and its basic properties are investigated. To illustrate the potential use of this concept, a new proof is offered to show that the number of orbits of G under its action on the set of complex-valued irreducible $\\alpha _N$ -characters of N equals the number of $\\alpha $ -regular conjugacy classes of G contained in $N,$ where N is a normal subgroup of $G.$

Let H be a subgroup of a finite group G and let $\\alpha $ be a complex-valued $2$ -cocycle of $G.$ Conditions are found to ensure there exists a nontrivial element of H that is $\\alpha $ -regular in $G.$ However, a new result is established allowing a prime by prime analysis of the Sylow subgroups of $C_G(x)$ to determine the $\\alpha $ -regularity of a given $x\\in G.$ In particular, this result implies that every $\\alpha _H$ -regular element of a normal Hall subgroup H is $\\alpha $ -regular in $G.$

This paper is devoted to the study of the normal (tangential) regularity of a closed set and the subdifferential (directional) regularity of its distance function in the context of Riemannian manifolds. The Clarke, Fréchet and proximal subdifferentials of the distance function from a closed subset in a Riemannian manifold are represented by corresponding normal cones of the set.

The supra topological topic is of great importance in preserving some topological properties under conditions weaker than topology and constructing a suitable framework to describe many real-life problems. Herein, we introduce the version of complete Hausdorffness and complete regularity on supra topological spaces and discuss their fundamental properties. We show the relationships between them with the help of examples. In general, we study them in terms of hereditary and topological properties and prove that they are closed under the finite product space. One of the issues we are interested in is showing the easiness and diversity of constructing examples that satisfy supra Ti spaces compared with their counterparts on general topology.

In view of the complex geological conditions and high drilling risk of TN Oilfield, analysising the influence of oil source, unconformity surface, fault properties and sandstone by strengthening the study of oil-rich regularity. The oil field has the characteristics of “near source reservoir, fault controlled reservoir, and enrichment of domi-nant facies”. The rolling development model of oil reservoirs has been established, which involves tapping the potential of fault zones and evaluating new traps, finely delineating the main sandstone in lithological reservoirs, optimal selection of favorable areas by matching the main sandstone with favorable traps, and achieving good development results.

In this paper, we determine the maximal subsemigroups of the singular part of endomorphism monoids of the star graphs Sn , for a given positive integer n, namely End(Sn ), wEnd(Sn ), and swEnd(Sn ), respectively. The monoid wEnd(Sn ) of all weak endomorphisms on Sn , the monoid End(Sn ) of all endomorphisms on Sn as well as the monoid swEnd(Sn ) of all strong weak endomorphisms on Sn is regular. We also determine the maximal regular submonoids of the singular part of wEnd(Sn ), End(Sn ), and swEnd(Sn ).