A photochemical strategy enabling tandem cyclization and dearomatization of ortho-sulfonamide-tethered alkylidenecyclopropanes via N-centered radicals has been developed under metal-free conditions. The reaction employs an organic fluorophore 1,2,3,5-tetrakis(carbazol-9-yl)-4,6-dicyanobenzene (4CzIPN) as a photocatalyst. This mild and operationally simple photocatalytic system demonstrates that the sulfonamidyl-radical-mediated intramolecular olefin amination effectively integrates radical ring opening with dearomatization pathways, thereby facilitating the synthesis of diverse fused seven-membered cyclic sulfonamides with a broad substrate scope, high regioselectivity, and excellent product diversity.

Fentanyl analogs, a major subclass of synthetic opioids, have emerged worldwide and pose serious public health threats owing to their widespread misuse. This study investigated the comparative in vitro metabolism of five fentanyl analogs with varying N-acyl side chain lengths (acetylfentanyl, fentanyl, butyrylfentanyl, valerylfentanyl, and crotonylfentanyl) to elucidate the relationship between drug structure and metabolism. Each analog (5 μmol/L) was incubated with human liver microsomes for 1 h, and after deproteinization, the samples were analyzed using liquid chromatography-high-resolution mass spectrometry. Elongation of the N-acyl side chain resulted in shorter half-lives and higher clearance values. Among the four analogs with N-acyl alkyl side chains, the formation of the nor-metabolites, the metabolites hydroxylated at the ethyl linker, and the metabolites hydroxylated at the piperidine ring increased with increasing side chain length, peaking with fentanyl or butyrylfentanyl, and then decreasing with valerylfentanyl, thereby exhibiting an overall inverted U-shaped trend. In contrast, the metabolites hydroxylated at the phenyl ring of the phenethyl group declined as the side chain lengthened, whereas the metabolites hydroxylated at the acyl side chain and the carboxylated metabolites increased. Crotonylfentanyl, featuring an N-acyl alkenyl side chain, deviated from the structure-metabolism relationship observed among the other analogs. These findings highlight distinct structure-dependent metabolic stabilities and biotransformation pathways among fentanyl analogs, providing valuable information for identifying diagnostic metabolites to confirm fentanyl analog use in humans.

Phase transition dynamics of HBDBA-MWCNT nanocomposites probed by temperature-dependent Raman spectroscopy.

Abstract We describe the lower algebraic K -theory of the integral group ring of both the pure and full braid groups of the real projective plane $$\mathbb {R}P^2$$ R P 2 with 3 strings, as well as that of the integral group ring of the mapping class group of $$\mathbb {R}P^2$$ R P 2 with 3 marked points. In addition, we give a general formula for the algebraic K -theory groups of the group ring of the mapping class group of non-orientable surfaces with k marked points, where $$k\ge 3$$ k ≥ 3 .

In-silico Exploration of Marine Algae-derived Compounds as the Potential Inhibitors of Polycomb Group Ring Finger 4 Protein

Purpose To describe the structure of a special sort of rings whose non-invertible elements are the sum of a nilpotent and a square-idempotent (which commute one another). Specifically, we consider in-depth and characterize in certain aspects the class of so-called strongly NUS-nil clean rings, that are those rings whose non-units are square-nil clean in the sense that they are a sum of a nilpotent and a square-idempotent that commutes with each other. This class of rings lies properly between the classes of strongly nil clean rings and strongly clean rings. Design/methodology/approach We develop an original method of proof based on polynomial expressions. Findings It is proved the valuable criterion that a ring R is strongly NUS-nil clean if, and only if, a4 - a2 ∈ Nil(R) for every a ∉ U(R). In particular, a ring R with only trivial idempotents is strongly NUS-nil clean if, and only if, R is a local ring with nil Jacobson radical. Some special matrix constructions and group ring extensions will provide us with new sources of examples of strongly NUS-nil clean rings. Originality/value We declare that the obtained by us results are absolutely original and do not duplicate other known results.

We show that the coordinate ring of a simply-connected simple algebraic group G G over the complex number field coincides with the Berenstein–Fomin–Zelevinsky cluster algebra and its upper cluster algebra, at least when G G is not of type F 4 F_4 .

UDC 512.5 We focus on recent promising trends in the application of the key concepts and approaches from the classical infinite-group theory to various branches of algebra, such as modules over group rings, infinite-dimensional linear groups, Leibniz algebras, other generalizations of the Lie algebras, and braces. The efficacy of these trends has been well-documented in a series of recent books from reputable publishers. In our article, we present a concise overview of these emerging trends. The analysis of the mutual influence of algebraic systems promotes deeper understanding of their individual and collective significance and illustrates the unity and diversity typical of contemporary mathematics. We believe that the subsequent development of investigations in this field would promote the appearance of new discoveries and innovations clarifying the fundamental role played by the groups, rings, algebras and other algebraic structures in modern mathematics.

Let G be a group and F an infinite field of characteristic p ≠ 2 . If either G is torsion, or p > 2 and G has only finitely many p -elements, we determine the conditions under which the symmetric units of the group ring FG , with respect to the classical involution, satisfy a bounded Engel identity.

Graduated orders over completed group rings and conductor formulæ

In this article, we investigate the Green ring of the small quantum group [Formula: see text], where [Formula: see text] is a root of unity of order [Formula: see text] and [Formula: see text] is even. We describe the structures of the Green rings by generators with relations.

In this paper, we show that all Coleman automorphisms of wreath products of some finite groups with trivial centers by any finite group are inner. In particular, the normalizer property holds for these groups.

Learning with errors over group rings constructed by semi-direct product

The OBJECTIVE of the study was to analyze the long-term results of the use of modified aortic valve reimplantation in patients with aortic root and ascending aortic aneurysms. METHODS AND MATERIALS . From 2011 to 2024, 79 patients underwent surgery for ascending aortic aneurysm with aortic valve (AV) insufficiency using modified reimplantation of aortic valve (MRAV). The control groups were: 80 patients with Bentall procedure and 51 patients who underwent . RESULTS . The average age of patients in the MRAV group was 61 years (53-68). The average diameter of the aorta in the study group was 55 mm, in the Bentall group 54 mm and in the David group 60 mm. The average diameter of the AV fibrous ring in the study group was 24.7 before surgery and 22.5 after surgery, compared with the Bentall group, where the average diameter of the AV was 25.1 before surgery (p=0.189) and 21.9 after surgery (p=0.120). The average diameter of the AV in the David group was 23.1 before surgery (p=0.603) and 22.0 after surgery (p=0.213). In the long–term period, freedom from aortic regurgitation after 5 years was 79% for the David group and 92% for the MRAV group. After 10 years, this indicator decreased to 51.8% in the David group and 79.7% in the MRAV group. The survival rate of the compared groups after 5 years was 88.6% in the MRAV group with a slight decrease to 83% after 10 years; in the David group – 86.1% with a significant decrease to 54.4% after 10 years. In the Bentall group, the survival rate after 5 years was 88.5%. After 10 years, this indicator in this group had not changed. CONCLUSION . This study shows that the proposed technique can be performed with good immediate and long-term results. The technique is relatively simple and reproducible.

Abstract Let $${\mathcal {F}} \, = \, (\dots {\mathop {\rightarrow }\limits ^{\partial _{n+1}}} {\mathcal {F}}_n {\mathop {\rightarrow }\limits ^{\partial _n}} {\mathcal {F}}_{n-1}{\mathop {\rightarrow }\limits ^{\partial _{n-1}}} \dots \dots {\mathop {\rightarrow }\limits ^{\partial _1}} {\mathcal {F}}_0 \rightarrow {\mathfrak {R}} \rightarrow 0)$$ F = ( ⋯ → ∂ n + 1 F n → ∂ n F n - 1 → ∂ n - 1 ⋯ ⋯ → ∂ 1 F 0 → R → 0 ) be a free resolution over the group ring $${\mathfrak {R}}[\Phi ]$$ R [ Φ ] where $${\mathfrak {R}}$$ R is commutative and $$\Phi $$ Φ is finite. The $$n^{th}$$ n th syzygy $$\Omega _n^{{\mathfrak {R}}[\Phi ]}$$ Ω n R [ Φ ] is the stable class of $$\textrm{Im}(\partial _n)$$ Im ( ∂ n ) and has a tree structure with roots which do not extend infinitely downwards. We show that $$\Omega _3^{{\mathfrak {R}}[Q_{8p}]}$$ Ω 3 R [ Q 8 p ] has infinitely many isomorphically distinct modules at the minimal level when $$\,{\mathfrak {R}} = {\mathbb {Z}}[C_\infty ]$$ R = Z [ C ∞ ] is the integral group ring of the infinite cyclic group and $$Q_{8p}$$ Q 8 p is the quaternion group of order 8 p where $$p \ge 3$$ p ≥ 3 is prime. This poses severe difficulties in attempting to solve the D (2) problem of CTC Wall for the groups $$C_\infty \times Q_{8p}$$ C ∞ × Q 8 p

Homological properties of invariant rings of permutation groups

In this paper, we investigate the fixed submodules of modules over skew group rings. We give two applications, the first concerns the determination of a simple basis of the center of a skew group ring. In the second application, we characterize in terms of the structure groups all the mod-retractable skew group rings. More precisely, we prove that if [Formula: see text] is a group acting on a field [Formula: see text] with kernel [Formula: see text], then the skew group ring [Formula: see text] is mod-retractable if and only if [Formula: see text] is mod-retractable and [Formula: see text] is of finite index in [Formula: see text].

We employ a skew group ring of Z/2Z over U(sl₂) to construct modules over the universal Bannai–Ito algebra. Furthermore, we characterize the conditions under which the defining generators act as Leonard triples on these modules. As a combinatorial realization, we establish a surjective algebra homomorphism from the universal Bannai–Ito algebra to the Terwilliger algebra of an odd graph. This homomorphism provides a unified description of Leonard triples on all irreducible modules over the Terwilliger algebra.

In this paper, we introduce a new class of rings calling them 2-UNJ rings, which generalize the well-known 2-UJ, 2-UU and UNJ rings. Specifically, a ring [Formula: see text] is called 2-UNJ if, for every unit [Formula: see text] of [Formula: see text], the inclusion [Formula: see text] holds, where [Formula: see text] is the set of nilpotent elements and [Formula: see text] is the Jacobson radical of [Formula: see text]. We show that every 2-UJ, 2-UU or UNJ ring is 2-UNJ, but the converse does not necessarily hold, and we also provide counter-examples to demonstrate this explicitly. We, moreover, investigate the connections between these rings and other algebraic properties such as being potent, tripotent, regular and exchange rings, respectively. In particular, we thoroughly study some natural extensions, like matrix rings and Morita contexts, obtaining new characterizations that were not addressed in previous works. Furthermore, we establish conditions under which group rings satisfy the 2-UNJ property. These results not only provide a better understanding of the structure of 2-UNJ rings, but also pave the way for future intensive research in this area. In addition, our achievements considerably improve on recent results given by Tin, On 2-UNJ rings, Asian-European J. Math. 19 (2026) 2550105.

We develop general methods to compute the algebraic $K$-theory of crossed products by Bernoulli shifts on additive categories. From this we obtain a $K$-theory formula for regular group rings associated to wreath products of finite groups by groups satisfying the Farrell--Jones conjecture.