Let G be a finite group with integral group ring Λ = Z[G]. The syzygies Ωr(Z) are the stable classes of the intermediate modules in a free Λ-resolution of the trivial module. They are of significance in the cohomology theory of G via the ‘co-represention theorem’ Hr(G,N) = HomDer(Ωr(Z), N). We describe the Ωr(Z) explicitly for the dihedral groups D4n+2, so allowing the construction of free reso...

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

How can one justify the secession of a territory from a liberal-democratic state of the kind currently prevalent in North America and Western Europe? The question does not primarily concern a mutually agreed secession, such as that of Norway from the United Kingdoms of Norway and Sweden in 1905. If the government and legislature of the ‘parent state’ freely agree to a secession of a part of its...

In this paper a non-diagonal regulator, based on the QFT method, is synthesized for an uncertain MIMO plant whose output and control signals are subjected to hard time-domain constraints. This procedure includes the design of a non-diagonal pre-controller based on a new simple approach, followed by the sequential design of a diagonal QFT controller. We present a new formulation for the latter s...

We compute liftings of the Nichols algebra of a Yetter-Drinfeld module of Cartan type B 2 subject to the small restriction that the diagonal elements of the braiding matrix are primitive nth roots of 1 with odd n = 5. As well, we compute the lift-ings of a Nichols algebra of Cartan type A 2 if the diagonal elements of the braiding matrix are cube roots of 1; this case was not completely covered...

In this paper we study the Cartan matrix associated to Ext-projective stratifying system induced by a basic and τ-rigid object M in mod(A) means of g-vectors indecomposable direct summands M. particular show that group module can be calculated directly using these vectors. Moreover characterise systems coming from modules have diagonal matrix.

The practical visual data do not necessarily lie in linear subspaces, so deep convolutional subspace clustering network is proposed to segment the into multiple categories accurately. original contains stacked encoder module, decoder module and self-expression module. We firstly alter i.e., add a new k-block diagonal regularizer weights of It means that $$\ell _1$$ or _2$$ abandoned. directly p...

In order to reduce the memory access time for a Single-Instruction Multiple-Data stream (SIMD) computer with pq processing elements attached to a host computer, a multiaccess memory system is proposed in this paper. The proposed memory system supports simultaneous access to pq data elements within a 4-directional block (p q), a row (1 pq), a column (pq 1), a forward-diagonal, and a backward-dia...

We compute liftings of the Nichols algebra of a Yetter-Drinfeld module of Cartan type B2 subject to the small restriction that the diagonal elements of the braiding matrix are primitive nth roots of 1 with odd n 6= 5. As well, we compute the liftings of a Nichols algebra of Cartan type A2 if the diagonal elements of the braiding matrix are cube roots of 1; this case was not completely covered i...

B. Magajna and J. Schweizer showed in 1997 and 1999, respectively, that C*-algebras of compact operators can be characterized by the property that every norm-closed (and coinciding with its biorthogonal complement, resp.) submodule of every Hilbert C*-module over them is automatically an orthogonal summand. We find out further generic properties of the category of Hilbert C*-modules over C*-alg...