There is an algorithm which computes the minimal number of generators of the ideal of a reduced curve C in affine n-space over an algebraically closed field K, provided C is not a local complete intersection. The existence of such an algorithm follows from the fact that given d ∈ N, there exists d ∈ N, such that if a is a height n−1 radical ideal inK[X1, . . . ,Xn], generated by polynomials of ...

In knowledge mining, current trend is witnessing the emergence of a growing number of works towards defining “concise and lossless” representations. One main motivation behind is: tagging a unified framework for drastically reducing large sized sets of association rules. In this context, generic bases of association rules – whose backbone is the conjunction of the concepts of minimal generator ...

A definition of atomic codeword for a group code is presented. Some properties of atomic codewords of group codes are investigated. Using these properties, it is shown that every minimal tail-biting trellis for a group code over a finite abelian group can be constructed from its characteristic generators, which extends the work of Koetter and Vardy who treated the case of a linear code over a f...

We address two aspects of finitely generated modules of finite projective dimension over local rings and their connection in between: embeddability and grade of order ideals of minimal generators of syzygies. We provide a solution of the embeddability problem and prove important reductions and special cases of the order ideal conjecture. In particular we derive that in any local ring R of mixed...

A new family of word-oriented linear feedback shift registers named σ−LFSRs is presented and analyzed in this paper. σ−LFSRs are constructed by few fundamental instructions so that they have high efficiency. Comparing with the theory of classical LFSRs, we research on the basic properties of σ−LFSRs, such as minimal polynomial, state graph, coordinate sequence, and the properties of primitive σ...

Abstract In this paper, we first construct thermofield double states for bosonic string theory in the light-cone gauge. We then obtain a coherent-thermal state and thermal-coherent state. use covariance matrix approach to calculate circuit complexity of states. approach, generate optimal geodesics by horizontal generator, using length minimal group manifold.

Quasi-polycyclic (QP for short) codes over a finite chain ring R are generalization of quasi-cyclic codes, and these can be viewed as an R[x]-submodule $${\mathcal {R}}_m^{\ell }$$ , where {R}}_m:= R[x]/\langle f\rangle $$ f is monic polynomial degree m R. If factors uniquely into coprime basic irreducibles, then their algebraic structure allow us to characterize the generator polynomials minim...

Modeling of wind power plant (WPP) is a crucial issue in system studies. In this paper, new model WPP for steady state (i.e. load flow) studies proposed. Similar to the previous T-circuit based models, it also developed on equivalent induction generator. However, unlike mathematical formulation shorter and less complicated. Moreover, derivation present work much simpler. Only minimal operations...

UNLABELLED The objective of this manuscript was to report a case of a patient with extruded pulse generator 3 years after implantation of a spinal cord stimulator system.With the increasing incidence of chronic pain, spinal cord stimulation (SCS) is becoming more commonly utilized by pain physicians. SCS is a generally safe intervention with minimal adverse effects; however, there are risks of ...

The use of Generative Adversarial Networks (GANs) has led to significant advancements in the field compositional image synthesis. In particular, recent progress focused on achieving synthesis at semantic part level. However, enhance performance this level, existing approaches literature tend prioritize over efficiency, utilizing separate local generators for each part. This approach leads a lin...