We construct large families of harmonic morphisms which are holomorphic with respect to Hermitian structures by finding heierarchies of Weierstrass-type representations. This enables us to find new examples of complex-valued harmonic mor-phisms from Euclidean spaces and spheres.

Adjacency and Laplacian matrices are popular structures to use as representations of shape graphs, because their sorted sets of eigenvalues (spectra) can be used as signatures for shape retrieval. Unfortunately, the descriptiveness of these spectra is limited, and handling graphs of different size remains a challenge. In this work, we propose a new framework in which the shapes (3D models in ou...

So far, topological band theory is discussed mainly for systems described by eigenvalue problems. Here, we develop a generalized problem (GEVP). Our analysis elucidates that non-Hermitian structures may emerge GEVP with Hermitian matrices. The above result verified analyzing two-dimensional toy model where symmetry-protected exceptional rings (SPERs) although the matrices involved are Hermitian...

The XX spin-chain with non-Hermitian diagonal boundary conditions is shown to be quasi-Hermitian for special values of the boundary parameters. This is proved by explicit construction of a new inner product employing a ”quasi-fermion” algebra in momentum space where creation and annihilation operators are not related via Hermitian conjugation. For a special example, when the boundary fields lie...

There is a known hyperkähler structure on any complexified Hermitian symmetric space G/K, whose construction relies identifying G/K with both (co)adjoint orbit and the cotangent bundle to compact Gu/K0. Via family of explicit diffeomorphisms, we show that almost all complex structures are equivalent one G/K; via related symplectic $T^{*}\left (G_{u}/K_{0}\right )$ . We highlight intermediate Kä...

Extended quantum mechanics using non-Hermitian (pseudo-Hermitian) Hamiltonians H = H is briefly reviewed. A few related mathematical experiments concerning supersymmetric regularizations, solvable simulations and large-N expansion techniques are summarized. We suggest that they could initiate a deeper study of non-localized structures (quasi-particles) and/or of their unstable and many-particle...

We show various vanishing theorems for the cohomology groups of compact hermitian man-ifolds for which the Bismut connection has (restricted) holonomy contained in SU (n) and classify all such manifolds of dimension four. In this way we provide necessary conditions for the existence of such structures on hermitian manifolds. Then we apply our results to solutions of the string equations and sho...

A bstract It is shown how extended supersymmetry realised directly on the (2 , 2) semichiral superfields of a symplectic sigma model gives rise to geometry doubled tangent bundle consisting two Yano F structures an almost para-hermitian manifold. Closure algebra and invariance action discussed in this framework integrability defined hold. The reduction usual (1 1) description identification wit...

Self-orthogonal codes have been of interest due to there rich algebraic structures and wide applications. Euclidean self-orthogonal codes have been quite well studied in literature. Here, we have focused on Hermitian self-orthogonal codes. Constructions of such codes have been given based on the well-known matrix-product construction for linear codes. Criterion for the underlying matrix and the...

The accurate segregation of DNA is essential for the faithful inheritance of genetic information. Segregation of the prototypical P1 plasmid par system requires two proteins, ParA and ParB, and a centromere. When bound to ATP, ParA mediates segregation by interacting with centromere-bound ParB, but when bound to ADP, ParA fulfils a different function: DNA-binding transcription autoregulation. T...