Steenrod operators, the Coulomb branch and the Frobenius twist

We observe a fundamental relationship between Steenrod operations and the Artin–Schreier morphism. We use Steenrod's construction, together with some new geometry related to the affine Grassmannian, to prove that the quantum Coulomb branch is a Frobenius-constant quantization. We also demonstrate the corresponding result for the $K$ -theoretic version of the quantum Coulomb branch. At the end of the paper, we investigate what our ideas produce on the categorical level. We find that they yield, after a little fiddling, a construction which corresponds, under the geometric Satake equivalence, to the Frobenius twist functor for representations of the Langlands dual group. We also describe the unfiddled answer, conditional on a conjectural ‘modular derived Satake’, and, though it is more complicated to state, it is in our opinion just as neat and even more compelling.

The motivic Satake equivalence

We refine the geometric Satake equivalence due to Ginzburg, Beilinson–Drinfeld, and Mirković–Vilonen to an equivalence between mixed Tate motives on the double quotient $$L^+ G {\backslash }LG / L^+ G$$ L + G \ L G / L + G and representations of Deligne’s modification of the Langlands dual group $${\widehat{G}}$$ G ^ .

Evaluation of the Therapeutic Effect of Magneto-Nanomicelles Based on Magneto-Thermal and Photo-Thermal Therapy

In this study, we investigated the hyperthermia efficiency of magnetic hyperthermia therapy (MHT), photo-thermal therapy (PTT), and the combination of both techniques by employing SPIO-based magneto-nanomicelles as the heating agents. Magneto-nanomicelles in aqueous suspension were exposed to 808-nm laser irradiation (PTT mode), alternating magnetic field (MHT mode), and both modalities (DUAL mode). All the three methods can offer effective temperature increases (above 20 °C). DUAL-mode resulted in an approximately 2-fold increase in heating efficiency (36 °C) compared with PTT or MHT alone. For in vivo experiments, a total of 24 Lewis carcinoma-bearing mice were randomly divided into four groups: the control group (no therapy), PTT, MHT, and DUAL group. In the three therapy groups, magneto-nanomicelles were injected into the tumor and the corresponding treatment measures were performed every other day for a total of three times each. MRI scans were used to calculate tumor volume after each treatment. One-way analysis of variance (ANOVA) was employed to compare the curative effect of different treatment groups. Compared with the control group, PTT, MHT, and DUAL groups all showed a significant inhibitory effect on tumor volume (P < 0.05). In the DUAL group, the mean tumor volume was smaller than that of the PTT or the MHT group. Our work demonstrated that hyperthermia using SPIO-based magnetonanomicelles has a remarkable suppressive effect in anticancer therapy. Moreover, the combined model of hyperthermia in vivo can achieve synthetic effects with shorter healing time by using the same magneto-nanomicelles.

Effect of a dual trigger on oocyte maturation in young women with decreased ovarian reserve for the purpose of elective oocyte cryopreservation

Objective: The aim of this study was to determine whether co-administration of a gonadotropin-releasing hormone (GnRH) agonist and human chorionic gonadotropin (hCG) for final oocyte maturation improved mature oocyte cryopreservation outcomes in young women with decreased ovarian reserve (DOR) compared with hCG alone.Methods: Between January 2016 and August 2019, controlled ovarian stimulation (COS) cycles in women (aged ≤35 years, anti-Müllerian hormone [AMH] <1.2 ng/mL) who underwent elective oocyte cryopreservation for fertility preservation were retrospectively analyzed.Results: A total of 76 COS cycles were triggered with a GnRH agonist and hCG (the dual group) or hCG alone (the hCG group). The mean age and serum AMH levels were comparable between the two groups. The duration of stimulation, total dose of follicle-stimulating hormone used, and total number of oocytes retrieved were similar. However, the number of mature oocytes retrieved and the oocyte maturation rate were significantly higher in the dual group than in the hCG group (p=0.010, p<0.001). After controlling for confounders, the dual-trigger method remained a significant factor related to the number of mature oocytes retrieved (p=0.016).Conclusion: We showed improved mature oocyte collection and maturation rate with the dual triggering of oocyte maturation in young women with DOR. A dual trigger appears to be more beneficial than hCG alone in terms of mature oocyte cryopreservation for young women with DOR.

The Tubby Torus as a Quotient Group

Let E be any metrizable nuclear locally convex space and E ^ the Pontryagin dual group of E. Then the topological group E ^ has the tubby torus (that is, the countably infinite product of copies of the circle group) as a quotient group if and only if E does not have the weak topology. This extends results in the literature related to the Banach–Mazur separable quotient problem.

GEOMETRY OF KOTTWITZ–VIEHMANN VARIETIES

We study basic geometric properties of Kottwitz–Viehmann varieties, which are certain generalizations of affine Springer fibers that encode orbital integrals of spherical Hecke functions. Based on the previous work of A. Bouthier and the author, we show that these varieties are equidimensional and give a precise formula for their dimension. Also we give a conjectural description of their number of irreducible components in terms of certain weight multiplicities of the Langlands dual group and we prove the conjecture in the case of unramified conjugacy class.

Dry Bulk Carrier Investment Selection through a Dual Group Decision Fusing Mechanism in the Green Supply Chain

Uncertain linguistic variables and scoring evaluations are two important evaluation mechanisms in the decision making field. Sustainability requirements for ship investment lead to the complexity of influence factors and the decision making process. The uncertain linguistic assessment features a large amount of ambiguity and subjectivity, while the scoring evaluation features high precision and distinct gradations. This paper constructs a criteria system in the green supply chain and proposes a dual group decision fusing mechanism for integrating the linguistic variable and scoring evaluation into a unified evaluation term. A hierarchical cloud of linguistic variable terms is constructed based on scoring via a reverse cloud generator, and then, the ship investment linguistic terms are transformed into prospect values. In addition, the consistency and investment selection performance are measured after aggregating the individual decision matrices for group decision making. The empirical research results on the selection of dry bulk carriers for investment show that dual group decision fusing mechanisms could effectively improve the consistency, decision making efficiency, and accuracy of dry bulk ship investment choices and reduce the cost of feedback adjustment for group decisions. In comparison with the trapezoidal fuzzy and fuzzy TOPSIS methods of group decision making, the proposed method performs better when there are a large number of alternatives.