Abstract We develop a diagrammatic categorification of the polynomial ring Z[x], based on geometrically defined graded algebra. This construction generalizes to some special functions, such as Chebyshev polynomials. Diagrammatic algebras featured in these categorifications lead first topological interpretations Bernstein-Gelfand-Gelfand reciprocity property.

In this paper, we introduce a novel approach for modeling surface reflection. We focus on using a family of probability distributions called Archimedean copulas as BRDF models. The Archimedean representation has an attractive property in that the multivariate distributions are characterized by their marginal distributions through a single univariate function only. It is shown that the proposed ...

Frobenius reciprocity asserts that induction from a subgroup and restriction to it are adjoint functors in categories of unitary [Formula: see text]-modules. In the 1980s, Guillemin Sternberg established parallel property Hamiltonian text]-spaces, which (as we show) unfortunately fails mirror situation where more than one text]-module “quantizes” given text]-space. This paper offers evidence is...

the purpose of this study is to investigate the relation between identity styles and commitment with quality of friendship among the students in third grade of high school. 400 participants from nineteen educational districts were chosen randomly. three quesnonnaires were used: identity style inventory, the quality of friendship, the reciprocity of friendship . the results indicated that inform...

Intellectual Property rights are valuable trading assets in regional and global economic regulation debates, and in particular in World Trade Organisation negotiations. Since the TRIPs agreement merely refers to a limited number of Intellectual Property categories, the scope of obligations in relation to the national and most favoured nation treatment principles is increasingly obscured. The re...

Starting from the constitutive properties that underpin the ideal memristor as originally defined by Leon Chua, we identify the conditions under which two memristors comply with the reciprocity theorem. In particular, we explore the minimal set of requirements for an ideal memristor and the physical implications of not complying with these criteria. Then, we show that reciprocity is satisfied w...

Let n, r be integers 1 and let V be a vector space of dimension n over C. Classically, we have natural commuting actions of the general linear group GL(V) and the symmetric group Sr on the tensor space V⊗r, and both actions satisfy the so-called Weyl reciprocity [W] (or the double centralizer property), which has been used by Schur and Weyl to link representations of Sr with representations of ...

The energy conservation of lossless network reflects a series of novel symmetry in S parameter. This paper presents the generalized modulus symmetry, spurious reciprocity, constant characteristic phase and determinant of the lossless block network. The perfect matching condition of block load network [Γl] and the invariable lossless property of S parameter of generalized block network are devel...