This paper deals with bases in a finite–dimensional Hilbert space. Such a space can be realized as a subspace of the representation space of SU2 corresponding to an irreducible representation of SU2. The representation theory of SU2 is reconsidered via the use of two truncated deformed oscillators. This leads to replace the familiar scheme {j2, jz} by a scheme {j2, vra}, where the two–parameter...

Let V be a finite dimensional representation of a p-group, G, over a field, k, of characteristic p. We show that there exists a choice of basis and monomial order for which the ring of invariants, k[V ]G, has a finite SAGBI basis. We describe two algorithms for constructing a generating set for k[V ]G. We use these methods to analyse k[2V3]3 where U3 is the p-Sylow subgroup of GL3(Fp) and 2V3 i...

Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of data dimensions makes solutions and TT-ranks of TT decomposition inconsistent. To alleviate this problem, we propose a permutation symmetric network structu...

Dextrous manipulation based on techniques for non-linear dimension reduction and manifold learning is an upcoming field of research and offers promising opportunities. Still, many problems remain unsolved and researchers are seeking for new representations that combine efficient learning of examples and robust generalisation to unseen situations. Here, we propose a manifold representation of ha...

Numerical modeling was carried out to investigate the responses of suction bucket foundations under vertical cyclic loading. Numerical results were compared with centrifuge experiment results. Before the capacity of the model suction bucket to resist cyclic loading could be investigated, the static pullout capacities had to be determined. The buckets with different aspect ratio are investigated...

‎‎A natural generalization of two dimensional cyclic code ($T{TDC}$) is two dimensional skew cyclic code‎. ‎It is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $R_n:=F[x,y;rho,theta]/_l$‎. ‎In this paper we characterize the left ideals of the ring $R_n$ with two methods and find the generator matrix for two dimensional s...

Let q : Ĉ → Ĉ be any quadratic polynomial and r : C2 ∗ C3 → PSL(2,C) be any faithful discrete representation of the free product of finite cyclic groups C2 and C3 (of orders 2 and 3) having connected regular set. We show how the actions of q and r can be combined, using quasiconformal surgery, to construct a 2 : 2 holomorphic correspondence z → w, defined by an algebraic relation p(z,w) = 0.

The (reduced) Burau representation Vn of the braid group Bn is obtained from the action of Bn on the homology of an infinite cyclic cover of the disc with n punctures. In this paper, we calculate H∗(Bn;Vn). Our topological calculation has the following arithmetic interpretation (which also has different algebraic proofs): the expected number of points on a random superelliptic curve of a fixed ...

From the homotopy groups of two cubic spherical 3-manifolds we construct the iso-morphic groups of deck transformations acting on the 3-sphere. These groups become the cyclic group of order eight and the quaternion group respectively. By reduction of representations from the orthogonal group to the identity representation of these subgroups we provide two subgroup-periodic bases for the harmoni...

In this paper, we tackle the challenges of multilabel classification by developing a general conditional dependency network model. The proposed model is a cyclic directed graphical model, which provides an intuitive representation for the dependencies among multiple label variables, and a well integrated framework for efficient model training using binary classifiers and label predictions using...