Stability of Einstein metrics on symmetric spaces of compact type

We prove the linear stability with respect to the Einstein-Hilbert action of the symmetric spaces $${\text {SU}}(n)$$ SU ( n ) , $$n\ge 3$$ n ≥ 3 , and $$E_6/F_4$$ E 6 / F 4 . Combined with earlier results, this resolves the stability problem for irreducible symmetric spaces of compact type.

Equivariant harmonic maps depend real analytically on the representation

We consider harmonic maps into symmetric spaces of non-compact type that are equivariant for representations that induce a free and proper action on the symmetric space. We show that under suitable non-degeneracy conditions such equivariant harmonic maps depend in a real analytic fashion on the representation they are associated to. The main tool in the proof is the construction of a family of deformation maps which are used to transform equivariant harmonic maps into maps mapping into a fixed target space so that a real analytic version of the results in [4] can be applied.

Nodal curves and polarizations with good properties

In this paper we deal with polarizations on a nodal curve C with smooth components. Our aim is to study and characterize a class of polarizations, which we call “good”, for which depth one sheaves on C reflect some properties that hold for vector bundles on smooth curves. We will concentrate, in particular, on the relation between the $${{\underline{w}}}$$ w ̲ -stability of $${\mathcal {O}}_C$$ O C and the goodness of $${{\underline{w}}}$$ w ̲ . We prove that these two concepts agree when C is of compact type and we conjecture that the same should hold for all nodal curves.

Influence of Fibrosis Amount and Patterns on Ventricular Arrhythmogenesis and Pumping Efficacy: Computational Study

Myocardial fibrosis is an integral component of most forms of heart failure. Clinical and computational studies have reported that spatial fibrosis pattern and fibrosis amount play a significant role in ventricular arrhythmogenicity. This study investigated the effect of the spatial distribution of fibrosis and fibrosis amount on the electrophysiology and mechanical performance of the human ventricles. Seventy-five fibrosis distributions comprising diffuse, patchy, and compact fibrosis types that contain 10–50% fibrosis amount were generated. The spatial fibrosis distribution was quantified using the fibrosis entropy (FE) metric. Electrical simulations under reentry conditions induced using the S1–S2 protocol were conducted to investigate the fibrosis arrhythmogenicity. We also performed mechanical simulations to examine the influence of the fibrosis amount and the spatial distribution of fibrosis on the pumping efficacy of the LV. We observed that the mean FE of the compact type is the largest among the three types. The electrical simulation results revealed that the ventricular arrhythmogenicity of diffuse fibrosis depends on the fibrosis amount and marginally on the spatial distribution of fibrosis. Meanwhile, the ventricular arrhythmogenicity of the compact and patchy fibrosis pattern is more reliant on the spatial distribution of fibrosis than on the fibrosis amount. The average number of phase singularities (PSs) in the compact fibrosis pattern was the highest among the three patterns of fibrosis. The diffuse type of fibrosis has the lowest average number of PSs than that in the patchy and compact fibrosis. The reduction in the stroke volume (SV) showed high influence from the electrical instabilities induced by the fibrosis amount and pattern. The compact fibrosis exhibited the lowest SV among the three patterns except in the 40% fibrosis amount. In conclusion, the fibrosis pattern is as crucial as the fibrosis amount for sustaining and aggravating ventricular arrhythmogenesis.

Macedonian Architecture From 19th Century in The Village of Leshok, Republic of Macedonia

INTRODUCTION: The old rural architecture in Macedonia is insufficiently studied and in many villages is in the process of extinction, especially in Western Macedonia where there are many villages whose inhabitants have emigrated. OBJECTIVES: The objective of this research is the folk architecture of the house in the village of Leshok, near Tetovo, and getting acquainted with the other types of objects that are part of the rural-economic yard and are inextricably linked to the daily work, life and customs of the peasant from this region. MATERIAL AND METHODS: For analysis of the traditional architecture of the houses in the village of Leshok from the late 19th and early 20th centuries, 10 typical houses with different structure and location are chosen, which are identified and displayed by the Google Earth search engine. RESULTS: The basic characteristics of the architecture of the village house in Leshok are explained, where the economic yard together with the economic objects are included. The functional solutions of the foundations of houses from the end of the 19th and the beginning of the 20th century are shown, the constructions used in the house of Leshok are described, as well as the materials that were used for their construction. In the end we get acquainted with the interior and the design of the premises in the old Macedonian house. CONCLUSION: Leshok belongs to the group of mountain villages of compact type. The configuration of the terrain, the dead riverbed, dictated the way of construction, where the houses are placed one above the other and each has a clear view of the valley. In that way, the basic architectural features of the Leshok house are formed. It is a typical mountain house built of stone and wood, on two floors and with an open veranda.

Assessment of the Efficiency, Environmental and Economic Effects of Compact Type On-Site Wastewater Treatment Plants—Results from Random Testing

This study presents the results of random testing of selected on-site wastewater treatment plants (WWTPs) constructed in Poland in Masovia Voivodship in the years 2011–2016. The vast majority of tested on-site WWTPs were compact (container) type treatment plants, based on low rate activated sludge (AS), sequencing batch reactors (SBR), or a hybrid (activated sludge supported with biological film, AS + BF) method. Compact type plans are becoming more and more popular in single households in Poland, due to the option of co-financing. According to certificates provided by producers and distributors, container on-site wastewater treatment plants are efficient in BOD5 removal, with the expected removal rate being over 80%. The aim of this study was (1) to analyze BOD5 in effluents sampled from randomly selected on-site WWTPs, (2) to evaluate predicted and real environmental effects of the implementation of on-site WWTPs in selected communes within Masovia Voivodship, and (3) to calculate unit environmental and economic effects of container on-site WWTPs in three different technologies. Results of this study show that in most cases, there is a gap between the declared and the real BOD5 removal efficiency. There is also a difference between the performance of different container type technologies. The lowest real environmental effect was obtained for AS technology, and the highest for the hybrid one. The predicted environmental effect has only been almost achieved in the case of hybrid systems. Based on net present value (NPV) benefits, technologies can be set up as follows: AS > SBR > AS + BF, making the AS method the most effective technology from the point of view of the economy.