We study the dihedral multi-reference alignment problem of estimating orbit a signal from multiple noisy observations signal, acted on by random elements group. show that if group are drawn generic distribution, is uniquely determined second moment observations. This implies optimal estimation rate in high noise regime proportional to square variance noise. first result this type for over non-a...

Abstract Let G be a group and $$G_0 \subseteq G$$ G 0 ⊆ subset. A sequence over $$G_0$$ means finite of terms from , where the order elements is disregarded repetition allowed. product-one whose can ordered such that their product...

In the title compound, C(21)H(16)F(2)N(2), the dihedral angle between the fluoro-phenyl groups is 66.34 (8)°, and the dihedral angle between the envelope-configured pyrazole group (N/N/C/C/C) and the benzene ring is 11.50 (9)°. The dihedral angles between the benzene and the two fluoro-substituted phenyl groups are 77.7 (6) and 16.7 (5)°. Weak C-H⋯π interactions contribute to the stability of t...

Let Dn be the dihedral group of order 2n. For all integers r, s such that 1 ≤ r, s ≤ 2n, we give an explicit upper bound for the minimal size μDn (r, s) = min |A · B| of sumsets (product sets) A · B, where A and B range over all subsets of Dn of cardinality r and s respectively. It is shown by construction that μDn (r, s) is bounded above by the known value of μG (r, s), where G is any abelian ...

Given the discriminant dk of a quadratic field k, the number of cyclic relative extensions N\k of fixed odd prime degree p with dihedral absolute Galois group of order 2p , which share a common conductor /, is called the multiplicity of the dihedral discriminant d^ = f2^p~^d^ . In this paper, general formulas for multiplicities of dihedral discriminants are derived by analyzing the p-rank of th...

In the title compound, C16H10Cl2N4O4, the pyrazine rings make dihedral angles of 67.82 (9) and 75.91 (9)° with the benzene ring, while the dihedral angle between the pyrazine rings is 44.69 (10)°. The meth-oxy-carbonyl group makes a dihedral angle of 16.82 (8)° with the benzene ring to which it is attached. In the crystal, C-H⋯O hydrogen bonds link the mol-ecules, forming chains running along t...

The title compound, C16H13NO6, exhibits a biphenyl unit with a dihedral angle between the two aryl rings of 56.01 (5)°. The two ester groups vary slightly from planarity, with ar-yl-ester dihedral angles of 4.57 (5) and 16.73 (5)°. The nitro group is turned from the aromatic unit with an ar-yl-nitro dihedral angle of 48.66 (4)°. In the crystal, mol-ecules are connected by weak C-H⋯O inter-actio...

In the title compound, C(30)H(20)N(2)O(2), the orientation of the furyl group may induce a variety of coordination modes with this ligand. The dihedral angle between the two naphthyl rings is 79.25 (7)°. The furyl groups make dihedral angles of 62.0 (1) and 16.3 (2)° with the attached naphthyl groups. The dihedral angle between the two furyl rings is 49.3 (2)°.

In the title compound, C(23)H(18)O(3), the dihedral angle between the two naphthalene ring systems is 78.02 (3)°. The bridging carbonyl C-C(=O)-C plane makes a dihedral angle of 70.56 (5)° with the naphthalene ring system in the 2,7-dimeth-oxy-naphthalene moiety and a dihedral angle of 11.53 (5)° with the naphthalene ring system in the naphthoyl group. In the crystal, adjacent mol-ecules are li...