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 On the representation of elements of a von Neumann algebra in the form of finite sums of products of projections. III. Commutators in $C^*$-algebrasA. M. Bikchentaev 3 The test rank of a soluble product of free Abelian groupsCh. K. Gupta, E. I. Timoshenko 21 Conditions for instantaneous support shrinking and sharp estimates for the support of the solution of the Cauchy problem for a doubly non-linear parabolic equation with absorptionS. P. Degtyarev 37 Asymptotic behaviour of solutions of semilinear parabolic equationsYu. V. Egorov, V. A. Kondratiev 65 A priori estimates, existence and non-existence for quasilinear cooperative elliptic systemsH. Zou 83 Chromatic numbers of real and rational spaces with real or rational forbidden distancesA. M. Raigorodskii, I. M. Shitova 107 Codimension-two singularities in 3D affine control systems with a scalar controlA. O. Remizov 143