A locally compact quantum group of triangular matrices

We construct a one parameter deformation of the group of 2×2 upper triangular matrices with determinant 1 using the twisting construction. An interesting feature of this new example of a locally compact quantum group is that the Haar measure is deformed in a non-trivial way. Also, we give a complete description of the dual C∗-algebra and the dual comultiplication.Побудовано однопараметричну деформацію групи верхніх трикутних матриць розміру 2 × 2 із детермінантом 1 з використанням конструкції скруту. Цікавою рисою цього нового прикладу локально компактної квантової групи є нетривіальна деформація міри Хаара. Наведено також повний опис дуальної C*-алгебри та дуальної комультиплікації

HUBUNGAN ANTARA CURAH HUJAN, SUHU UDARA DAN KELEMBABAN DENGAN KEJADIAN DEMAM BERDARAH DENGUE DI KOTA MANADO TAHUN 2015-2020

Kasus demam berdarah dengue (DBD) masih tinggi di Manado. Kondisi lingkungan diduga berpengaruh pada angka kejadian DBD tersebut. Tujuan penelitian ini yaitu untuk mengetahui hubungan curah hujan, suhu udara, dan kelembaban dengan kejadian Demam Berdarah Dengue di Kota Manado tahun 2015-2020. Penelitian ini adalah studi korelasional menggunakan data kejadian DBD, curah hujan, suhu udara dan kelembaban di Manado dari Januari 2015 – Desember 2020. Hubungan faktor-faktor lingkungan ini dengan angka kejadian DBD dianalisis menggunakan grafik dan analisis korelasi Spearman. Hasil analisis menunjukkan adanya hubungan antara curah hujan (rho = 0,32; p = 0,006) dan suhu udara (rho = -0,41; p < 0,001) dengan angka kejadian DBD. Namun demikian, hubungan kelembaban dengan kejadian DBD tidak signifikan (rho = 0,12; p = 0,299). Penduduk Manado di daerah dengan curah hujan relatif tinggi dan suhu udara cenderung lebih rendah dari wilayah lain di Manado perlu meningkatkan kewaspadaan terhadap perjangkitan DBD. Penelitian ini memperlihatkan adanya hubungan antara faktor-faktor lingkungan tersebut dengan kejadian DBD di Manado. Kata Kunci: Kejadian DBD, Curah Hujan, Suhu Udara, Kelembaban ABSTRACTThe prevalence of dengue hemorrhagic fever (DHF) remains high in Manado. It has been suggested that certain environmental factors play a role in the number of cases. The objective of this study was to evaluate the relationship of precipitation, ambient temperature, and humidity with the prevalence of DHF in Manado. This was a correlational study using the data on rainfall rate, ambient temperature, and humidity in Manado recorded between January 2015 and December 2020 by the local department of meteorology and geophysics, as well as the information about DHF number of cases at the same period as published by the Health Department of Manado. The relationship between these environmental factors and DHF prevalence was analyzed using graphs and Spearman correlation. The results of the analysis showed a significant relationship between precipitation (rho = 0.32; p = 0.006) and air temperature (rho = -0.41; p < 0.001) with the prevalence of DHF. However, there was no significant relationship found between humidity and DHF prevalence (rho = 0.12; p = 0.299). Manado residents in areas with relatively high rainfall and air temperatures tend to be lower than other areas in Manado need to increase vigilance against DHF infection. This study shows a link between these environmental factors and the incidence of DHF in Manado. Keyword: DHF Prevalence, Precipitation, Ambient Temperature, Humidit

Stochasticity in the adaptive dynamics of evolution: The bare bones

First a population model with one single type of individuals is considered. Individuals reproduce asexually by splitting into two, with a population-size-dependent probability. Population extinction, growth and persistence are studied. Subsequently the results are extended to such a population with two competing morphs and are applied to a simple model, where morphs arise through mutation. The movement in the trait space of a monomorphic population and its possible branching into polymorphism are discussed. This is a first report. It purports to display the basic conceptual structure of a simple exact probabilistic formulation of adaptive dynamics