Limit laws for Random matrices and free products

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

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Residual separability of subgroups in free products with amalgamated subgroup of finite index

Sibirskii matematicheskii zhurnal ◽

10.33048/smzh.2019.60.212 ◽

2018 ◽

Vol 60 (2) ◽

pp. 411-418

Author(s):

A. A. Kryazheva

Keyword(s):

Finite Index ◽

Free Products ◽

Amalgamated Subgroup

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Gluten-Free Dry Mixtures with Rice and Amaranth for Children over Three Years Old with Gluten Intolerance

Food Industry ◽

10.29141/2500-1922-2020-5-1-3 ◽

2020 ◽

Vol 5 (1) ◽

pp. 23-31

Author(s):

Sergey Urubkov ◽

Svetlana Khovanskaya ◽

Ekaterina Pyrieva ◽

Olga Georgieva ◽

Stanislav Smirnov

Keyword(s):

Celiac Disease ◽

Treatment Effectiveness ◽

Raw Materials ◽

Calculated Data ◽

Limited Range ◽

Gluten Free ◽

Fruit And Vegetable ◽

Organoleptic Evaluation ◽

Free Products ◽

Wide Range

Diet therapy is one of the main approaches to the treatment of a wide range of diseases of the digestive system. The treatment effectiveness of celiac disease depends on how strictly the patient adheres to a gluten-free diet. It is often disrupted due to the limited range of recommended foods and dishes, especially for children who are particularly sensitive to dietary restrictions. In this case, the development of new types of specialized gluten-free products is relevant, allowing to expand the diet both in terms of nutritional value and taste diversity. This study concerns the recipe developments of dry gluten-free mixtures using rice and amaranth with the inclusion of fruit and vegetable and berry raw materials intended for the nutrition of children over three years old suffering from celiac disease. When developing the recipes, researchers used various combinations of rice and amaranth flour, as well as fruit and vegetable powders. The rice flour composition varied in the range from 15 to 75%; amaranth – from 15 to 45%; fruit and vegetable and berry powders – up to 10%. The finished product was gluten-free cookies, muffins, pancakes made of rice and amaranth. Organoleptic evaluation showed that the studied samples of gluten-free cookies have high quality characteristics, have a pleasant taste and aroma. According to the calculated data, specialized gluten-free dry mixtures intended for children over three years with celiac disease can serve as an important source of: vegetable carbohydrates – from 26.81 to 55.19 g / 100g of finished products; protein – from 4.06 to 11.82 g/100g of finished products; dietary fiber – from 3.82 to 6.36 g/100g of finished products; and energy – from 158.12 to 333.96 kcal/100g of finished products) The developed recipess of gluten-free products can help to provide children with an adequate amount of nutrients and energy.

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