Related papers: A combinatorial characterisation of embedded polar…
In this paper we propose a definition of regularity suited for polar spaces of infinite rank and we investigate to which extent properties of regular polar spaces of finite rank can be generalized to polar spaces of infinite rank.
Optical vector beam generation based on the superposition technique [Phys. Rev. Lett. 107(5), 053601 (2011)] has attracted significant interest in both fundamental and applied optics due to its simplicity and cost-effectiveness. In this…
(Electric) polarization tensors describe part of the leading order term of asymptotic voltage perturbations caused by low volume fraction inhomogeneities of the electrical properties of a medium. They depend on the geometry of the support…
The sedenion compounding fields and their quantum interplays can be presented by analogy with the octonionic electromagnetic, gravitational, strong and weak interactions. In sedenion fields which are associated with electromagnetic,…
In the first part of this article, we study linear cones over totally ordered fields. We show that for each such cone there uniquely exists a universal vector space (called its spanned vector space) into which it embeds as a generating…
Spatial solitons can exist in various kinds of nonlinear optical resonators with and without amplification. In the past years different types of these localized structures such as vortices, bright, dark solitons and phase solitons have been…
The motivation of this work is to define cohomology classes in the space of knots that are both easy to find and to evaluate, by reducing the problem to simple linear algebra. We achieve this goal by defining a combinatorial graded cochain…
The generation of pulsed polarization entangled photon pair has been realized using type-I phase matching in the spontaneous parametirc downconversion process in a space cascaded two-crystal geometry. The optical axes of the crystal are…
Partial combinatory algebras are algebraic structures that serve as generalized models of computation. In this paper, we study embeddings of pcas. In particular, we systematize the embeddings between relativizations of Kleene's models, of…
Efficient technique of manipulation with phase prefactors in electronic Fock spaces is developed. Its power is demonstrated on example of both relatively simple classic configuration interaction matrix element evaluation and essentially…
Models with Hilbert space fragmentation are characterized by (exponentially) many dynamically disconnected subspaces, not associated with conventional symmetries but captured by nontrivial Krylov subspaces. These subspaces usually exhibit a…
The uniform structure on a differential space defined by a family of generators is considered.
Binary neutron star mergers can form short-lived magnetar-like remnants whose magnetically dominated polar towers reach $B\sim10^{15}$--$10^{16}\,\mathrm{G}$, but the microphysical composition of these outflows remains poorly understood.…
Polar commutative n-complex numbers of the form u=x_0+h_1x_1+h_2x_2+...+h_{n-1}x_{n-1} are introduced in n dimensions, the variables x_0,...,x_{n-1} being real numbers. The polar n-complex number can be represented, in an even number of…
We classify the epimorphisms of the buildings ${BC}_l(K,K_0,\sigma,L, q_0)$, where l is at least two, of pseudo-quadratic form type. This completes the classification of epimorphisms of irreducible spherical Moufang buildings of rank at…
In this article we give a computational study of combinatorics of the discriminantal arrangements. The discriminantal arrangements are parametrized by two positive integers n and k such that n>k. The intersection lattice of the…
In this paper, we study structure theorems of algebras of symmetric functions. Based on a certain relation on elementary symmetric polynomials generating such algebras, we consider perturbation in the algebras. In particular, we understand…
The past decade has seen an increase of star formation studies made at the molecular cloud scale, motivated mostly by the deployment of a wealth of sensitive infrared telescopes and instruments. Embedded clusters, long recognised as the…
We investigate the structure of graded commutative exponential functors. We give applications of these structure results, including computations of the homology of the symmetric groups and of extensions in the category of strict polynomial…
The number of Borel orbits in polarizations (the symmetric variety $SL(n)/S(GL(p)\times GL(q))$) is analyzed, various (bivariate) generating functions are found. Relations to lattice path combinatorics are explored.