Тhe effect of Cr substitution for Fe on ferroelectric and magnetic properties of PbFe0.5Nb0.5O3, PbFe0.5Sb0.5O3 and BiFeO3 multiferroics

Проведены диэлектрические и мессбауэровские исследования сегнетоэлектрических и магнитных фазовых переходов в твердых растворах PbFe0.5-xCrxNb0.5O3, BiFe1-xCrxO3, PbFe0.5-xCrxSb0.5O3. Во всех этих системах замещение железа хромом разрушает как сегнетоэлектрический, так и магнитный дальний порядок.PbFe0.5-xCrxNb0.5O3, BiFe1-xCrxO3, PbFe0.5-xCrxSb0.5O3 solid solutions have been carried out. In all the systems studied Cr substitution for Fe destroys both ferroelectric and magnetic long-range order.Работа выполнена при поддержке Российского Фонда Фундаментальных Исследований (грант 16-52-0072 Бел_a) и Белорусского Республиканского Фонда Фундаментальных Исследований (грант T16R-079)

Group representation base vector expansions (for representations of S characterized by single-hook or by two-rowed Young tableaux)

In this thesis the base vectors for irreducible representations of the sy_tetric group n, for the two particular cases(a) Representations characterized by the partition [n-k.1 kI - so called single-hook representations;.(b) Representations characterized by the partition Cn-m,m] - so called double-row representations,are given explicitly as linear combinations of determinantal functions.Chapters I, II and III with the corresponding Tables I, II and III. give expansions for the base vectors of [n-k.1kI Chapter I has type I expansions with (k+1)-rowed determinants having k variables. Chapter II describes type II, expansions in terms of k-rowed determinants with k variables. Chapter III has type III expansions with %k+1) -rowed determinants with k+1 variables, described however in terms of the states missing from the determinants. Chapter IV gives a very simple expansion of the base vectors for Cn-m,m] in terms of m-fold products of type I two-rowed determinants with one variable.'A1Z Tables go- up to the value n=10. The Introduction brings detailed examples illustrating the various types of expansion.</p