In this paper, we first consider the existence of and the general expression for the solution to the constrained inverse eigenproblem defined as follows: given a set of complex n-vectors {xi}i=1 and a set of complex numbers {λi}i=1, and an s-by-s real matrix C0, find an n-by-n real centrosymmetric matrix C such that the s-by-s leading principal submatrix of C is C0, and {xi}i=1 and {λi}i=1 are ...

We predict spatial solitons in photorefractive centrosymmetric media driven by the dc Kerr effect.

Second harmonic generation (SHG) is a well known non-linear optical phenomena which can be observed only in non-centrosymmetric crystals due to non-zero hyperpolarizability. In the current work we observed SHG from a Zn(II) complex which was originally thought to have crystallized in the centrosymmetric space group C2/c. This has been attributed to the unequal antiparallel packing of the metal ...

We present an extensive study of the Eulerian distribution on the set of centrosymmetric involutions, namely, involutions in Sn satisfying the property σ(i) + σ(n+ 1− i) = n+ 1 for every i = 1 . . . n. We find some combinatorial properties for the generating polynomial of such distribution, together with an explicit formula for its coefficients. Afterwards, we carry out an analogous study for t...

SUMMARY The structure of weighting coefficient matrices of Harmonic Differential Quadrature (HDQ) is found to be either centrosymmetric or skew centrosymmetric depending on the order of the corresponding derivatives. The properties of both matrices are briefly discussed in this paper. It is noted that the computational effort of the harmonic quadrature for some problems can be further reduced u...

The mol-ecule of the title compound, C(66)H(40)F(6)·CH(2)Cl(2), is centrosymmetric; the dihedral angle between the central fluorinated unit and the cyclo-penta-diene ring is 88.36 (7)°. The dihedral angles between the cyclo-penta-diene ring and the four surrounding phenyl rings are in the range 26.6 (1)-65.6 (1)°. Centrosymmetric cavities in the crystal structure are populated by disordered dic...

Tris(2- and 3-ureidobenzyl)amines with C(s) symmetry self-assemble in solution forming mixtures of regioisomeric capsular aggregates, one of which is chiral and the other centrosymmetric. Under certain conditions, a predominance of the centrosymmetric regioisomer is found before equilibrium, that is, a mixture close to the statistical ratio of the two species is reached. In the solid state, th...

When chiral compounds with low enantiomeric excess (ee, R:S=m:n) were absorbed into the void of crystalline sponge (CS), enantiomerically pure [(R)m(S)n] composites formed, changing centrosymmetric space group non-centrosymmetric one. The absolute configuration analyte was elucidated a reasonable Flack (Parsons) parameter value. This phenomenon is characteristic to “post-crystallization” in pre...

When chiral compounds with low enantiomeric excess (ee, R:S=m:n) were absorbed into the void of crystalline sponge (CS), enantiomerically pure [(R)m(S)n] composites formed, changing centrosymmetric space group non-centrosymmetric one. The absolute configuration analyte was elucidated a reasonable Flack (Parsons) parameter value. This phenomenon is characteristic to “post-crystallization” in pre...

5-nitrouracil is a polarizable molecule with permanent electric dipole moment. Its molecular properties caught the attention of physicists working on nonlinear optics or optoelectronics, but translation assets to crystalline solid has not been straightforward. This review compares all known crystal structures incorporating neutral ionic 5-nitrouracil, two species concomitantly, discussing effec...