Cuntz-Li algebras from a-adic numbers

The a-adic numbers are those groups that arise as Hausdorff completions of noncyclic subgroups of the rational numbers. We give a crossed product construction of (stabilized) Cuntz-Li algebras coming from the a-adic numbers and investigate the structure of the associated algebras. In particular, these algebras are in many cases Kirchberg algebras in the UCT class. Moreover, we prove an a-adic duality theorem, which links a Cuntz-Li algebra with a corresponding dynamical system on the real numbers. The paper also contains an appendix where a nonabelian version of the "subgroup of dual group theorem" is given in the setting of coactions.Comment: 41 pages; revised versio

Dualities for maximal coactions

We present a new construction of crossed-product duality for maximal coactions that uses Fischer's work on maximalizations. Given a group $G$ and a coaction $(A,\delta)$ we define a generalized fixed-point algebra as a certain subalgebra of $M(A\rtimes_{\delta} G \rtimes_{\widehat{\delta}} G)$, and recover the coaction via this double crossed product. Our goal is to formulate this duality in a category-theoretic context, and one advantage of our construction is that it breaks down into parts that are easy to handle in this regard. We first explain this for the category of nondegenerate *-homomorphisms, and then analogously for the category of $C^*$-correspondences. Also, we outline partial results for the "outer" category, studied previously by the authors.Comment: Minor revisio

Rigidity theory for C∗C^*-dynamical systems and the "Pedersen Rigidity Problem", II

This is a follow-up to a paper with the same title and by the same authors. In that paper, all groups were assumed to be abelian, and we are now aiming to generalize the results to nonabelian groups. The motivating point is Pedersen's theorem, which does hold for an arbitrary locally compact group $G$, saying that two actions $(A,\alpha)$ and $(B,\beta)$ of $G$ are outer conjugate if and only if the dual coactions $(A\rtimes_{\alpha}G,\widehat\alpha)$ and $(B\rtimes_{\beta}G,\widehat\beta)$ of $G$ are conjugate via an isomorphism that maps the image of $A$ onto the image of $B$ (inside the multiplier algebras of the respective crossed products). We do not know of any examples of a pair of non-outer-conjugate actions such that their dual coactions are conjugate, and our interest is therefore exploring the necessity of latter condition involving the images, and we have decided to use the term "Pedersen rigid" for cases where this condition is indeed redundant. There is also a related problem, concerning the possibility of a so-called equivariant coaction having a unique generalized fixed-point algebra, that we call "fixed-point rigidity". In particular, if the dual coaction of an action is fixed-point rigid, then the action itself is Pedersen rigid, and no example of non-fixed-point-rigid coaction is known.Comment: Minor revision. To appear in Internat. J. Mat

HPV infection and immunochemical detection of cell-cycle markers in verrucous carcinoma of the penis

Penile verrucous carcinoma is a rare disease and little is known of its aetiology or pathogenesis. In this study we examined cell-cycle proteins expression and correlation with human papillomavirus infection in a series of 15 pure penile verrucous carcinomas from a single centre. Of 148 penile tumours, 15 (10%) were diagnosed as pure verrucous carcinomas. The expression of the cell-cycle-associated proteins p53, p21, RB, p16INK4A and Ki67 were examined by immunohistochemistry. Human papillomavirus infection was determined by polymerase chain reaction to identify a wide range of virus types. The expression of p16INK4A and Ki67 was significantly lower in verrucous carcinoma than in usual type squamous cell carcinoma, whereas the expression of p53, p21 and RB was not significantly different. p53 showed basal expression in contrast to usual type squamous cell carcinoma. Human papillomavirus infection was present in only 3 out of 13 verrucous carcinomas. Unique low-risk, high-risk and mixed viral infections were observed in each of the three cases. In conclusion, lower levels of p16INK4A and Ki67 expressions differentiate penile verrucous carcinoma from usual type squamous cell carcinoma. The low Ki67 index reflects the slow-growing nature of verrucous tumours. The low level of p16INK4A expression and human papillomavirus detection suggests that penile verrucous carcinoma pathogenesis is unrelated to human papillomavirus infection and the oncogenes and tumour suppressor genes classically altered by virus infection.Peer reviewedFinal Accepted Versio

Strong Pedersen rigidity for coactions of compact groups

We prove a version of Pedersen's outer conjugacy theorem for coactions of compact groups, which characterizes outer conjugate coactions of a compact group in terms of properties of the dual actions. In fact, we show that every isomorphism of a dual action comes from a unique outer conjugacy of a coaction, which in this context should be called strong Pedersen rigidity. We promote this to a category equivalence.Comment: 13 pages. Minor revision, with numerous wording changes but the same theorems. To appear in IJ

Cost-Effective Solutions for Lithium-Ion Battery Manufacturing: Comparative Analysis of Olefine and Rubber-Based Alternative Binders for High-Energy Ni-Rich NCM Cathodes

Promoting safer and more cost-effective lithium-ion battery manufacturing practices, while also advancing recycling initiatives, is intrinsically tied to reducing reliance on fluorinated polymers like polyvinylidene difluoride (PVDF) as binders and minimizing the use of hazardous and expensive solvents such as N-methyl pyrrolidone (NMP). In pursuit of this objective, olefin- and rubber-based polymers have been investigated as promising alternatives for binder materials in high-energy Ni-rich LiNixCoyMnzO2 (NCM, x≥0.8) cathodes for lithium-ion batteries (LIBs). Alternative binders such as polyisobutylene (PIB), poly(styrene-butadiene-styrene) (SBS), nitrile butadiene rubber (NBR), and its hydrogenated version (HNBR) offer versatile solutions. These polymers can be dissolved in industrial solvents, such as toluene, and have been further processed into homogeneous cathode slurries, thus facilitating the manufacturing of high-energy Ni-rich NCM cathodes for lithium-ion batteries. The evaluation of NCM811 cathodes obtained from PIB, SBS, NBR, and HNBR has involved a thorough assessment of their physical and chemical properties, electrochemical performance, and production expenses, compared with NCM811 cathodes based on PVDF. Notably, cathodes employing PIB and HNBR have exhibited outstanding qualities, showcasing high specific capacity and remarkable electrochemical stability akin to PVDF-based counterparts. Furthermore, the alternative binders′ superior adhesion, elasticity, and thermal stability have facilitated obtaining uniform and mechanically stable cathode films. Furthermore, using toluene, with its low vapor pressure, has significantly reduced energy costs associated with drying processes, thereby enhancing the overall cost-effectiveness of the NCM811 cathodes

In-water synthesis of isocyanides under micellar conditions

An in-water dehydration of N-formamides to afford isocyanides using micellar conditions at room temperature is reported. This method allows for the preparation of aliphatic isocyanides in an environmental friendly manner. The replacement of undesirable components such as phosphorous oxychloride, triethyl amine and dichloromethane (the classical combination used for the dehydration of N-formamides), by p-toluen sulphonyl chloride, sodium hydrogen carbonate and water makes this transformation really sustainable and safe