Spectral and evolution problems. Proceedings 19th Crimean by Kopachevsky N.D., Orlov I.V. (eds.)

By Kopachevsky N.D., Orlov I.V. (eds.)

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B ⊂ A∗M следует из равенства a1 , g + ˜ ⊂ A∗ . m⊥ = a, g1 + n⊥ , справедливого для всех пар {a, a1 } ∈ AM . Отсюда получаем B M ⊥ Установим обратное включение. Пусть пара {a, a1 } ∈ J( B). Это означает, что для всех пар {g + m⊥ , g1 + n⊥ } ∈ B выполняется равенство a1 , g + m⊥ − a, g1 + n⊥ = 0. 109] и M = M (замыкание в сильной топологии), получим, что пара {a, a1 } ∈ M × M . Поэтому a1 , g = a, g1 для всех пар {g, g1 } ∈ A∗ . Равенство A = A = J(⊥ (A∗ )) влечет {a, a1 } ∈ A. 109] {a, a1 } ∈ AM .

We present a formula for calculating the number of ordinal values and lattice sizes of special type of partially ordered sets (small and full crowns), proposed a method for estimating the size of partially ordered sets by using the principle of consistency. е. пары P, = P, где P — непустое конечное множество (носитель P), а — порядок (рефлексивное, антисимметричное и транзитивное бинарное отношение) на нём. у. множеств обозначим P(n).

TSm , при этом в подматрице TSt по столбцам записаны все характеристические векторы классов эквивалентности ∼t , t ∈ {1, 2, . . , m}. Нетрудно видеть, что HS = TS · TSт . Очевидно, что матрица PS = mE − HS является матрицей попарных расстояний Хэмминга системы точек S, поскольку её ij-й элемент равен |{t ∈ {1, 2, . . , m} | (˜ si )t = (˜ sj )t }|, i ∈ {1, 2, . . , q}, j ∈ {1, 2, . . , q}. При t ∈ {1, 2, . . , m}, r ∈ {0, 1, . . , p(t)} на множестве {1, 2, . . , q} введём отношение эквивалентности ∼tr : (˜ si )t < atr , (˜ sj )t < atr , (˜ si )t ≥ atr , (˜ sj )t ≥ atr , i ∼tr j ⇔ (значения (˜ si )t , (˜ sj )t находятся по одну сторону от порога atr ).

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