There are two conformationally similar mol-ecules in the asymmetric unit of he title compound, C18H18O4, in which the dihedral angles between the benzene rings are 23.54 (12) and 31.11 (12)°. In the crystal, C-H⋯π inter-actions (minimum H⋯ring centroid distance = 2.66 Å) link the mol-ecules into a layered structure extending down a.

In the title compound, C(22)H(23)BrN(4)O(4)S(2), the benzene rings bridged by the sulfonamide group are tilted relative to each other by 68.9 (1)° and the dihedral angle between the sulfur-bridged pyrimidine and benzene rings is 69.7 (1)°. The mol-ecular conformation is stabilized by a weak intra-molecular π-π stacking inter-action between the pyrimidine and the 4-methylbenzene rings [centroid-...

In tins article we study the possibility of designing storage rings with a reduced by two or more orders of magnitude with respect to existing rings, thus making the bunch length shorter by a factor of 10 or more . We will, with an appropriate design, show that this bunch length reduction can be achieved while simultaneously increasing the beam peak current. With this approach one can increase ...

In the title compound, C(11)H(10)ClN(3)S, the dihedral angle between the benzene and pyrimidine rings is 3.99 (4)°. In the crystal, inter-molecular N-H⋯N hydrogen bonds link the mol-ecules into ribbons of R(2) (2)(8) rings parallel to [100]. Weak C-H⋯S contacts connect adjacent ribbons into a two-dimensional undulating layer-like structure extending parallel to (110). The benzene and pyrimidine...

In the title compound, C40H30Cl2N2O4, the two benzene rings of the biphenyl unit are twisted with respect to each other, making a dihedral angle of 73.07 (4)°. The benzene rings of the benzamide groups form dihedral angles of 77.09 (5) and 55.48 (6)° with the central biphenyl moiety. In the crystal, mol-ecules are linked through N-H⋯O hydrogen bonds to form a fused R 2 (2)(38) ring motif which ...

There are two symmetry-independent mol-ecules in the asymmetric unit of the title compound, C(16)H(16)N(2)O, that differ in conformation. The dihedral angles between the benzene rings in the two mol-ecules are 44.35 (19) and 48.14 (17)°, but the rings twist in opposite directions. The acetamide groups make nearly equal dihedral angles of 25.4 (3) and 25.7 (3)° with the parent benzene rings. An ...

Motivated by the Poisson Dixmier-Moeglin equivalence problem, a systematic study of commutative unitary rings equipped with biderivation, namely binary operation that is derivation in each argument, here begun, an eye toward geometry corresponding B-varieties. Foundational results about extending biderivations to localisations, algebraic extensions and transcendental are established. Resolving ...

In this work, linearized multivariate skew polynomials over division rings are introduced. Such right linear the corresponding centralizer and generalize polynomial finite fields, group or differential rings. Their natural evaluation is connected to remainder-based of free polynomials. It shown that P-independent sets those given by linearly independent when partitioned into conjugacy classes. ...

Extending the Wedderburn-Artin theory of (classically) semisimple associative rings to realm topological with right linear topology, we show that abelian category left contramodules over such a ring is split (equivalently, semisimple) if and only discrete modules same semisimple). Our results in this direction complement those Iovanov-Mesyan-Reyes. An extension Bass perfect formulated as list c...

We introduce the notion of E-depth graded modules over polynomial rings to measure depth certain Ext modules. First, we characterize with (sufficiently) large as those whose partial general initial submodules preserve Hilbert function local cohomology supported at irrelevant maximal ideal, extending a result Herzog and Sbarra on sequentially Cohen-Macaulay Second, describe cone tables sufficien...