Expanding solitons to the Hermitian curvature flow on complex Lie groups

We investigate the algebraic structure of complex Lie groups equipped with left-invariant metrics which are expanding semi-algebraic solitons to the Hermitian curvature flow (HCF). We show that the Lie algebras of such Lie groups decompose in the semidirect product of a reductive Lie subalgebra with their nilradicals. Furthermore, we give a structural result concerning expanding semi-algebraic solitons on complex Lie groups. It turns out that the restriction of the soliton metric to the nilradical is also an expanding algebraic soliton and we explain how to construct expanding solitons on complex Lie groups starting from expanding solitons on their nilradicals.Comment: 14 pages; section 4 extended; last version, to appear in Differential Geometry and its Application

A remark on the Bismut-Ricci form on 2-step nilmanifolds

In this note we observe that on a 2-step nilpotent Lie group equipped with a left-invariant SKT structure the (1,1)-part of the Bismut-Ricci form is seminegative definite. As application we give a simplified proof of the non-existence of invariant SKT static metrics on 2-step nilmanifolds and of the existence of a long time solution to the pluriclosed flow in 2-step nilmanifolds.Comment: 5 pages. Comments are welcom

recombinant pnpla3 protein shows triglyceride hydrolase activity and its i148m mutation results in loss of function

Abstract The patatin-like phospholipase domain containing 3 (PNPLA3, also called adiponutrin, ADPN) is a membrane-bound protein highly expressed in the liver. The genetic variant I148M (rs738409) was found to be associated with progression of chronic liver disease. We aimed to establish a protein purification protocol in a yeast system (Pichia pastoris) and to examine the human PNPLA3 enzymatic activity, substrate specificity and the I148M mutation effect. hPNPLA3 148I wild type and 148M mutant cDNA were cloned into P. pastoris expression vectors. Yeast cells were grown in 3 L fermentors. PNPLA3 protein was purified from membrane fractions by Ni-affinity chromatography. Enzymatic activity was assessed using radiolabeled substrates. Both 148I wild type and 148M mutant proteins are localized to the membrane. The wild type protein shows a predominant lipase activity with mild lysophosphatidic acid acyl transferase activity (LPAAT) and the I148M mutation results in a loss of function of both these activities. Our data show that PNPLA3 has a predominant lipase activity and I148M mutation results in a loss of function

PENGEMBANGAN DESAIN DIDAKTIS GEOMETRI DIMENSI TIGA DALAM KELAS INKLUSIF

Tujuan penelitian ini adalah mengembangkan desain pembelajaran geometri dimensi tiga yang dirancang peneliti untuk memberikan antisipasi didaktis pedagogis dan memperoleh deskripsi implementasi desain pembelajaran geometri dimensi tiga yang dirancang peneliti untuk memberikan antisipasi didaktis pedagogis dalam kelas inklusif di SMAN 1 Sukabumi. Penelitian ini merupakan penelitian kualitatif dengan jenis didactical design research. Subjek penelitian ini adalah siswa kelas XI IPS 1 SMAN 1 Sukabumi tahun ajaran 2015/2016 yang terdapat siswa tunanetra di dalamnya. Teknik pengumpulan data penelitian menggunakan tes kemampuan responden, pengembangan desain didaktis, observasi dan wawancara. Hasil penelitian menunjukkan desain pembelajaran geometri dimensi tiga yang dirancang peneliti dapat memberikan antisipasi didaktis pedagogis dan menciptakan situasi didaktis di kelas inklusif. ;--- The purpose of this research is to develop instructional design three-dimensional geometry which is designed to give didactical pedagogical anticipation and obtain a description of the implementation of instructional design three-dimensional geometry which is designed to give didactical pedagogical anticipation in inclusive classes at SMAN 1 Sukabumi. This study is a qualitative research with didactical design research. The subjects were students of class XI IPS SMAN 1 Sukabumi 1 academic year 2015/2016 contained a visual impairment student. The technique of data collection using the test the ability of respondents, didactical design development, observation and interview. The results showed that a three-dimensional geometry of instructional which is designed gave didactical pedagogical anticipation and didactical situation in inclusive class

ANALISIS KESULITAN BELAJAR SISWA TUNANETRA DI KELAS INKLUSIF PADA MATERI TRIGONOMETRI

The purpose of this study was to analyze the learning obstacles of blind students in an inclusive class at one of the high schools inSukabumi City as an inclusive schools. The method used is a qualitative method to analyze the learning difficulties of blind studentsin the inclusive class. The learning material that is focused on is trigonometry material which is quite abstract but quite applicable forall students in mathematics subjects. The analysis was carried out by observing the responses of blind students and other students inthe class simultaneously to the learning given to trigonometric material. The results show that learning obstacles of blind students ininclusive class include abstraction difficulties, inappropriate learning trajectory and lack of basic mathematical concepts

The anomaly flow on nilmanifolds

We study the Anomaly flow on 2-step nilmanifolds with respect to any Hermitian connection in the Gauduchon line. In the case of flat holomorphic bundle, the general solution to the Anomaly flow is given for any initial invariant Hermitian metric. The solutions depend on two constants K1 and K2, and we study the qualitative behaviour of the Anomaly flow in terms of their signs, as well as the convergence in Gromov–Hausdorff topology. The sign of K1 is related to the conformal invariant introduced by Fu, Wang and Wu. In the non-flat case, we find the general evolution equations of the Anomaly flow under certain initial assumptions. This allows us to detect non-flat solutions to the Hull-Strominger-Ivanov system on a concrete nilmanifold, which appear as stationary points of the Anomaly flow with respect to the Strominger-Bismut connection. © 2021, The Author(s), under exclusive licence to Springer Nature B.V