Abstract C 11 H 14 N 2 S , monoclinic, I 2/ a (no. 15), = 11.4278(8) Å, b 8.5816(6) c 25.1115(18) β 95.173(6)°, V 2452.6(3) Å 3 Z 8, R gt ( F ) 0.0416, wR ref 0.1169, T 293 K.

Abstract C 36 H Cd 3 I 2 N 4 O 8 , orthorhombic, Pbca (no. 61), a = 18.909(4) Å, b 16.149(3) c 26.050(5) V 7955(3) Å Z 8, R gt ( F ) 0.0439, wR ref 0.0752, T 293(2) K.

The generating set of Z n is determined completely for n 8, with the exception of the (46,6,1) design. Some general results are presented for larger values of n.

We classify the (finite and infinite) virtually cyclic subgroups of the pure braid groups PnpRP2q of the projective plane. The maximal finite subgroups of PnpRP2q are isomorphic to the quaternion group of order 8 if n 3, and to Z4 if n ¥ 4. Further, for all n ¥ 3, up to isomorphism, the following groups are the infinite virtually cyclic subgroups of PnpRP2q: Z, Z2 Z and the amalgamated product ...

Several recent works have discussed tree structured sparse coding [8, 10, 7, 3], where N data points in R written as the d × N matrix X are approximately decomposed into the product of matrices WZ . HereW is a d×K dictionary matrix, and Z is a K×N matrix of coefficients. In tree structured sparse coding, the rows of Z correspond to nodes on a tree, and the columns of Z are encouraged to be nonz...

Let f∗(z) = ∞ ∑ j=0 aj z j be a convergent series in which {aj}j=0 are known real numbers. In this paper, by referring to Osler’s lemma [8], we obtain explicit forms of the two bivariate series ∞ ∑ j=0 an j+m r j cos(α+ j)θ and ∞ ∑ j=0 an j+m r j sin(α+ j)θ, where r, θ are real variables, α ∈ R, n ∈ N and m ∈ {0, 1, . . . , n − 1}. With some illustrative examples, we also show how to obtain the...

‎Let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial‎ ‎of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$‎. ‎In this paper we obtain some new results about the dependence of $|p(Rz)|$ on $|p(rz)| $ for $r^2leq rRleq k^2$‎, ‎$k^2 leq rRleq R^2$ and for $Rleq r leq k$‎. ‎Our results refine and generalize certain well-known polynomial inequalities‎.

For δ ≥ 1 and n ≥ 1, we examine the simplicial complex of graphs on n vertices in which each vertex has degree at most δ; we identify a given graph with its edge set and admit one loop at each vertex. δ = 1 yields the matching complex, and it is known that there is 3-torsion in degree d of the homology of this complex whenever n−4 3 ≤ d ≤ n−6 2 . We establish similar bounds for δ ≥ 2. Specifica...