The pasting constructions for effect algebras

2014 ◽  
Vol 64 (5) ◽  
Author(s):  
Yongjan Xie ◽  
Yongming Li ◽  
Aili Yang

AbstractThe aim of this paper is to present several techniques of constructing a lattice-ordered effect algebra from a given family of lattice-ordered effect algebras, and to study the structure of finite lattice-ordered effect algebras. Firstly, we prove that any finite MV-effect algebra can be obtained by substituting the atoms of some Boolean algebra by linear MV-effect algebras. Then some conditions which can guarantee that the pasting of a family of effect algebras is an effect algebra are provided. At last, we prove that any finite lattice-ordered effect algebra E without atoms of type 2 can be obtained by substituting the atoms of some orthomodular lattice by linear MV-effect algebras. Furthermore, we give a way how to paste a lattice-ordered effect algebra from the family of MV-effect algebras.

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Biao Long Meng ◽  
Xiao Long Xin

We investigate relations of the two classes of filters in effect algebras (resp., MV-algebras). We prove that a lattice filter in a lattice ordered effect algebra (resp., MV-algebra) does not need to be an effect algebra filter (resp., MV-filter). In general, in MV-algebras, every MV-filter is also a lattice filter. Every lattice filter in a lattice ordered effect algebra is an effect algebra filter if and only if is an orthomodular lattice. Every lattice filter in an MV-algebra is an MV-filter if and only if is a Boolean algebra.


2016 ◽  
Vol 66 (2) ◽  
Author(s):  
Josef Niederle ◽  
Jan Paseka

AbstractA well known fact is that there is a finite orthomodular lattice with an order determining set of states which is not order embeddable into the standard quantum logic, the latticeWe show that a finite generalized effect algebra is order embeddable into the standard effect algebraAs an application we obtain an algorithm, which is based on the simplex algorithm, deciding whether such an order embedding exists and, if the answer is positive, constructing it.


2007 ◽  
Vol 83 (2) ◽  
pp. 181-216 ◽  
Author(s):  
Gejza Jenča

AbstractWe prove that every for every complete lattice-ordered effect algebra E there exists an orthomodular lattice O(E) and a surjective full morphism øE: O(E) → E which preserves blocks in both directions: the (pre)imageofa block is always a block. Moreover, there is a 0, 1-lattice embedding : E → O(E).


10.29007/71gb ◽  
2018 ◽  
Author(s):  
Gejza Jenča

The category of effect algebras is the Eilenberg-Moore category for themonad arising from the free-forgetful adjunction between categories of bounded posetsand orthomodular posets.In the category of effect algebras, an observable is a morphism whose domainis a Boolean algebra. The characterization of subsets of ranges of observables isan open problem.For an interval effect algebra E, a witness pair for a subset of S is an objectliving within E that "witnesses existence" of an observable whose rangeincludes S. We prove that there is an adjunction between the poset of allwitness pairs of E and the category of all partially inverted E-valuedobservables.


Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 164
Author(s):  
Songsong Dai

This paper studies rough approximation via join and meet on a complete orthomodular lattice. Different from Boolean algebra, the distributive law of join over meet does not hold in orthomodular lattices. Some properties of rough approximation rely on the distributive law. Furthermore, we study the relationship among the distributive law, rough approximation and orthomodular lattice-valued relation.


Author(s):  
Л. М. Берштейн

Работа посвящена двум медико-биологическим проблемам - семейному диабету (имея в виду наличие случаев сахарного диабета 2-го типа в семье, в том числе в разных поколениях), а также особенностям его связей с основными неинфекционными заболеваниями человека и приурочена к юбилею известнейшего отечественного специалиста (теоретика и врача) в области геронтологии и эндокринологии профессора В. М. Дильмана. Широко признанные труды Владимира Михайловича, основанные на оригинальных идеях и породившие важные практические следствия (включая применение антидиабетических бигуанидов в не использовавшихся до него областях, необходимость устранения метаболической иммунодепрессии, учета изменений с возрастом на уровне гипоталамического порога в различных гомеостатических системах и целого ряда других предложений), как представляется, в течение долгого времени будут питать интеллектуальным материалом и стимулировать к дальнейшему поиску его последователей и специалистов, которым еще предстоит окунуться в область, очерченную В. М. Дильманом и интересовавшую его в течение многих лет. The work discusses the two biomedical problems: family diabetes (bearing in mind the presence of cases of type 2 diabetes mellitus in the family, including its different generations) and the features of relationship of family diabetes with major non-communicable human diseases (NCDs). The paper is timed to the anniversary of the famous - in our country and abroad - expert in the field of gerontology and endocrinology, Professor V. M. Dilman. The widely recognized works of V. M. Dilman, based on original ideas and giving rise to important practical consequences (including the use of antidiabetic biguanides in areas not studied before him, the need to eliminate metabolic immunodepression, to take into account the changes with age at the level of the hypothalamic threshold in various homeostatic systems and a whole number of other essential proposals), which for a long time, as it seems, will stimulate the further scientific search of his followers and specialists, who have yet to get acquainted with the area that attracted Prof. Dilman and interested him for many years.


Author(s):  
Catherine W. Gathu ◽  
Jacob Shabani ◽  
Nancy Kunyiha ◽  
Riaz Ratansi

Background: Diabetes self-management education (DSME) is a key component of diabetes care aimed at delaying complications. Unlike usual care, DSME is a more structured educational approach provided by trained, certified diabetes educators (CDE). In Kenya, many diabetic patients are yet to receive this integral component of care. At the family medicine clinic of the Aga Khan University Hospital (AKUH), Nairobi, the case is no different; most patients lack education by CDE.Aim: This study sought to assess effects of DSME in comparison to usual diabetes care by family physicians.Setting: Family Medicine Clinic, AKUH, Nairobi.Methods: Non-blinded randomised clinical trial among sub-optimally controlled (glycated haemoglobin (HbA1c) ≥ 8%) type 2 diabetes patients. The intervention was DSME by CDE plus usual care versus usual care from family physicians. Primary outcome was mean difference in HbA1c after six months of follow-up. Secondary outcomes included blood pressure and body mass index.Results: A total of 220 diabetes patients were screened out of which 140 met the eligibility criteria and were randomised. Around 96 patients (69%) completed the study; 55 (79%) in the DSME group and 41 (59%) in the usual care group. The baseline mean age and HbA1c of all patients were 48.8 (standard deviation [SD]: 9.8) years and 9.9% (SD: 1.76%), respectively. After a 6-month follow-up, no significant difference was noted in the primary outcome (HbA1c) between the two groups, with a mean difference of 0.37 (95% confidence interval: -0.45 to 1.19; p = 0.37). DSME also made no remarkable change in any of the secondary outcome measures.Conclusion: From this study, short-term biomedical benefits of a structured educational approach seemed to be limited. This suggested that offering a short, intensified education programme might have limited additional benefit above and beyond the family physicians’ comprehensive approach in managing chronic conditions like diabetes.


2018 ◽  
Vol 1 (1) ◽  
pp. 69
Author(s):  
Citra Windani Mambang Sari ◽  
Fitri Nurul Khotimah ◽  
Sri Pratiwi Hartati

Diet is one of the main factors related to various diseases including Diabetes Mellitus (DM). High carbohydrate, fat, protein, and low fiber diets can increase the risk of type 2 DM occurrence, especially in the patient’s family as a risk group. Previous research on students with DM families in Central Java still had a high-calorie food consumption pattern. The diversity of population, culture, and age may affect the results. Therefore, this study aimed to describe the diet in the family of patients with type 2 DM in the working area of Puskemas (Community Health Center) Garuda Bandung.This research used a quantitative descriptive method by purposive sampling technique. The respondents in this study involved 46 people who were the children of type 2 DM patients in the working area of Puskesmas Garuda. Dietary data obtained from the food record sheet for 3 days and was calculated using Nutrisurvey software in kilocalories (kcal) as the unit of measurement then the results were categorized based on Consensus Perkeni 2015. Data analysis was using frequency distribution.The results showed that 39 (84.8%) respondents in the diet category less than body requirements, 37 (80.4%) respondents in the category of sufficient carbohydrate intake, 39 (84.6%) respondents in the category of excess fat intake, 45 (97.8%) respondents in the category of adequate protein intake, and 41 (89.1%) respondents in the category of less fiber.The conclusions from this study that almost all families of patients with type 2 DM in the work area of Puskesmas Garuda were in the diet category less than body requirement but with the excess fat intake and less fiber. Based on these results, the nurses in Puskesmas are expected to optimize the outreach programs by addressing families of DM patients to make the diet as an attempt to prevent the risk in the family of patients with type 2 DM.Key words: Diet, DM patients’ families, food record. Gambaran Diet pada Keluarga Pasien Diabetes Melitus Tipe 2AbstrakDiet adalah salah satu faktor utama yang berhubungan dengan berbagai penyakit termasuk Diabetes Melitus (DM). Diet tinggi karbohidrat, lemak, protein, serta rendah serat dapat meningkatkan risiko kejadian DM tipe 2 terutama pada keluarga pasien sebagai kelompok berisiko. Penelitian sebelumnya pada mahasiswa dengan keluarga DM di Jawa Tengah masih memiliki pola konsumsi makanan yang tinggi kalori. Perbedaan populasi, budaya, serta usia mungkin akan mempengaruhi hasil. Oleh karena itu, tujuan penelitian ini untuk menggambarkan diet pada keluarga pasien DM tipe 2 di wilayah kerja Puskemas Garuda Kota Bandung.Penelitian ini menggunakan metode deskriptif kuantitatif dengan teknik purposive sampling. Responden dalam penelitian ini berjumlah 46 orang yang merupakan anak kandung pasien DM tipe 2 di Wilayah Kerja Puskesmas Garuda. Data diet diperoleh melalui lembar food record selama 3 hari dihitung mengunakan software Nutrisurvey dengan hasil ukur dalam kilokalori (kcal) yang kemudian hasilnya dikategorikan berdasarkan Konsensus Perkeni 2015. Analisis data menggunakan distribusi frekuensi.Hasil penelitian menujukkan bahwa sebanyak 39 (84,8%) responden dalam kategori diet kurang dari kebutuhan, sebanyak 37 (80,4%) responden dalam kategori asupan karbohidrat cukup, sebanyak 39 (84,6%) responden dalam kategori asupan lemak berlebih, sebanyak 45 (97,8%) responden dalam kategori asupan protein cukup, dan 41 (89,1%) responden dalam kategori serat kurang.Simpulan dari penelitian ini bahwa hampir seluruh keluarga pasien DM tipe 2 di wilayah kerja Puskesmas Garuda berada pada kategori diet kurang dari kebutuhan tetapi dengan asupan lemak berlebih dan serat yang kurang. Berdasarkan hasil tersebut, maka perawat puskesmas diharapkan dapat mengoptimalkan program luar gedung dengan menyasar keluarga penderita DM untuk menjadikan diet sebagai upaya untuk mencegah risiko DM pada keluarga pasien DM tipe 2.Kata kunci : Diet, food record, keluarga pasien DM.


Author(s):  
Simin Saidi Goraghani ◽  
Rajab Ali Borzooei

 In this paper, by considering the notions of effect algebra and product effect algebra, we define the concept of effect module. Then we investigate some properties of effect modules, and we present some examples on them. Finally, we introduce some interesting topologies on effect modules.


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