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Combining the sharp isoperimetric inequality established by Z. Balogh and A. Kristály [Math. Ann., in press, doi:10.1007/s00208-022-02380-1] with an anisotropic symmetrization argument, we establish sharp Morrey–Sobolev inequalities on n -dimensional Finsler manifolds having nonnegative n -Ricci curvature. A byproduct of this method is a Hardy–Sobolev-type inequality in the same geometric setting. As applications, by using variational arguments, we guarantee the existence/multiplicity of solutions for certain eigenvalue problems and elliptic PDEs involving the Finsler–Laplace operator. Our results are also new in the Riemannian setting. [ABSTRACT FROM AUTHOR]

Abstract: Phillips type polyethylene stabilised with combinations of 700 ppm phenolic antioxidant and different amounts of various phosphorous stabilisers (sterically hindered aryl phosphite [Hostanox PAR 24], phosphonite [Sandostab P-EPQ], and aryl–alkyl phosphine [PEPFINE]) was processed by six consecutive extrusions. The polymer was characterised by FT-IR spectroscopy, rheological (melt flow index, creep compliance), colour and oxidation induction time measurements. Films were prepared by blowing and their mechanical strength was determined by Elmendorf and dart drop tests. The consumption of the antioxidants was compared to the characteristics of the polymer and to the strength of the films. The consumption rate of both the phenolic and the phosphorous antioxidants is reduced in their combinations compared to single antioxidants. The chemical structure of the polymer is modified considerably in the first extrusion even at high antioxidant levels. The mechanism of stabilisation is determined by the type of the antioxidant(s) in further processing steps. The phenolic antioxidant does not prevent the formation of long chain branches. The phosphonite and the phosphine hinder efficiently hydrogen abstraction from the polymer chain and long chain branching. Their efficiency is similar, but the phosphonite is consumed fast, while the phosphine oxidises slowly. The investigated phosphite is less reactive; the contribution of the phenolic antioxidant to the inhibition reactions is significant in phenol/phosphite combinations, therefore long chain branching increases continuously with increasing number of processing steps. [Copyright &y& Elsevier]

Abstract: The role of a phenolic and three phosphorous (phosphite, phosphonite and phosphine) antioxidants in the melt stabilisation of polyethylene was studied in a Phillips type polyethylene by multiple extrusions. The polyethylene was stabilised with a single antioxidant at 700 ppm and with phenolic/phosphorous antioxidant combinations containing 700 ppm of each component. The functional groups (methyl, vinyl, vinylidene, trans-vinylene and carbonyl) of polyethylene and the residual amount of phosphorous antioxidants were analysed quantitatively by FT-IR methods developed in our laboratory. The rheological characteristics, the colour and the residual thermo-oxidative stability of the polymer were determined and compared. Blown films were prepared and their mechanical strength measured by the Elmendorf and Dart-drop tests. The comparison of the different characteristics revealed that the chemical reactions taking place during the first processing of the nascent polymer powder, as well as the chemical composition of the antioxidants determine the reactions taking place in further processing operations. The changes in the characteristics of stabilised polyethylene during processing are controlled by the phosphorous stabiliser. The effect and final result depend on the chemical structure of the given antioxidant. The phenolic antioxidant itself does not hinder the formation of long chain branches. It reduces the rate of oxidation of the various phosphorous stabilisers, but does not modify the mechanism of stabilisation of the phosphonite and the phosphine. The reactions of the phosphite are significantly modified by the presence of a phenolic antioxidant. [Copyright &y& Elsevier]

Aims: TP53 alterations have a significant prognostic effect in myeloid neoplasms. Our objective was to investigate the TP53 gene mutation status, p53 protein expression and their relationship in dysplasia‐related myeloid neoplasms with varying levels of myeloblast counts. Methods and results: A total of 76 bone marrow biopsy samples with different blast counts were analysed. Total and strong (3+) p53 expression was determined. Dual immunohistochemical staining was performed to determine the cell population associated with p53 expression. NGS analysis was performed using the Accel‐Amplicon Comprehensive TP53 panel. Both p53 expression and TP53 VAF showed a significant correlation with the myeloblast ratio (P < 0.0001); however, p53 expression was also present in other cell lineages. The VAF value exhibited a significant correlation with p53 expression. A high specificity (0.9800) was observed for TP53 mutation using the ≥ 10% strong (3+) p53 cut‐off value, although the sensitivity (0.4231) was low. Conclusions: Strong (3+) p53 expression using a ≥ 10% cut‐off value accurately predicts TP53 mutation but does not reveal the allelic state. The p53 expression is significantly influenced by myeloblast count, and histological interpretation should consider the presence of intermixed non‐neoplastic marrow cells with varying physiological p53 expression. [ABSTRACT FROM AUTHOR]

Given a complete non-compact Riemannian manifold (M, g) with certain curvature restrictions, we introduce an expansion condition concerning a group of isometries G of (M, g) that characterizes the coerciveness of G in the sense of Skrzypczak and Tintarev (Arch Math 101(3): 259–268, 2013). Furthermore, under these conditions, compact Sobolev-type embeddings à la Berestycki-Lions are proved for the full range of admissible parameters (Sobolev, Moser-Trudinger and Morrey). We also consider the case of non-compact Randers-type Finsler manifolds with finite reversibility constant inheriting similar embedding properties as their Riemannian companions; sharpness of such constructions are shown by means of the Funk model. As an application, a quasilinear PDE on Randers spaces is studied by using the above compact embeddings and variational arguments. [ABSTRACT FROM AUTHOR]

Abstract: Polyethylene (PE) compounds were prepared with five primary antioxidants and five application stabilizers, pelletized and extruded to pipes under industrial conditions. The pipes were stored in water at 80 °C for one year. Samples were taken at various intervals and a range of properties were determined from the functional group (methyl, vinyl, t-vinylene) content of the polymer to the crack propagation rate of the pipe. The results showed that chemical reactions take place both during extrusion and soaking. The chain structure of the polymer is modified only during processing, but not during storage, at least in the time scale of the study. The direction and extent of changes are determined mainly by the type of the application stabilizer, but primary antioxidants also influence them to some extent. Soaking modifies the physical, but not the chemical structure of the polymer. On the other hand, the chemical reactions of the additives determine color and stabilizer loss thus the residual stability of the pipes. The chemical structure of the polymer has a larger effect on final properties, on the rate of slow crack propagation and failure, than the physical structure of the pipes. As a consequence, the application stabilizer plays an important role in the determination of pipe performance. [Copyright &y& Elsevier]

Abstract: Different aspects of the melt stabilising effect of various antioxidant packages were studied in a Phillips type polyethylene in the work described in this series of papers. The polymer was stabilised with various combinations of a phenolic antioxidant with phosphite, phosphonite, and phosphine type secondary antioxidants and processed by multiple extrusions followed by film blowing. After determining the role of the antioxidants in the melt stabilisation process and the effect of antioxidant consumption on polymer properties the correlation of the rheological characteristics of polymer with the tear and impact strengths of films is discussed in this paper. The Elmendorf tear strength of films measured in transverse direction, which is sensitive to long chain branching, correlates closely with viscous compliance determined by creep recovery experiments and the ratio of melt flow indices measured at high and low loads. The relationships are independent of the type and amount of antioxidant added. This makes possible the prediction of the effect of various antioxidant packages on film properties on the basis of rheological measurements. The correlation between the dart drop impact strength of the films and the rheological characteristics of the polymer is less reliable. [Copyright &y& Elsevier]