Using the a noncommutative version of Chevalley’s theorem due to Bergeron, Reutenauer, Rosas, and Zabrocki we compute the graded Frobenius series for their two sets of noncommutative harmonics with respect to the left action of the symmetric group (acting on variables). We use these results to derive the Frobenius series for the enveloping algebra of the derived free Lie algebra in n variables....

We analyze the distribution of eigenvalues quantum-mechanical rotating harmonic oscillator by means Frobenius method. A suitable ansatz leads to a three-term recurrence relation for expansion coefficients. Truncation series yields some particular and eigenfunctions in exact analytical form. The former can be organized such way that one obtains information about whole spectrum model.

In the field of computer vision, detection multiple objects with different scales within a single image is challenging. To target this problem, feature pyramids are basic component commonly found in multi-scale object detectors. construction standard pyramids, semantic features simply connected to rebuild new map, regardless whether these have positive effect output or not. order avoid introduc...

The annotated bibliography highlights work in the area of algorithmic test generation from formal speci cations with guaranteed fault coverage, i.e., fault model-driven test derivation. A fault model is understood as a triple, comprising a nite state speci cation, conformance relation and fault domain that is the set of possible implementations. The fault model can be specialized to Input/Outpu...

we give a new proof of the well known wedderburn's little theorem (1905) that a finite‎ ‎division ring is commutative‎. ‎we apply the concept of frobenius kernel in frobenius representation theorem in finite group‎ ‎theory to build a proof‎.

let $fneq1,3$ be a positive integer‎. ‎we prove that there exists a numerical semigroup $s$ with embedding dimension three such that $f$ is the frobenius number of $s$‎. ‎we also show that‎ ‎the same fact holds for affine semigroups in higher dimensional monoids‎.

Numerical difficulties are present in the particle finite element method even though it has been shown to be a powerful and effective approach to simulating fluid-structure interaction. To overcome problems of mass loss on the free surface and the added-mass effect, an improved fractional step method (FSM) that handles addedmass terms in a mathematically exact way is developed. A further benefi...

We discuss SPaRe: selective partial replication, a methodology for concurrent fault detection in finite state machine (FSMs). The proposed method is similar to duplication, wherein a replica of the circuit acts as a predictor that immediately detects errors by comparison to the original FSM. However, instead of duplicating the FSM, SPaRe selects a few prediction functions which only partially r...

A system of communicating finite state machines (SCFSM) is a usual design model of a complicated system composed of multiple communicating components. SCFSM testing usually depends on finite state machine (FSM) testing as an SCFSM can be converted to an equivalent FSM. SCFSM testing, however, should consider the properties of SCFSMs which are different from those of component FSMs. This paper p...

Multivariate time series (MTS) datasets are very common in various financial, multimedia, and hydrological fields. In this paper, a dimension-combination method is proposed to search similar sequences for MTS. Firstly, the similarity of single-dimension series is calculated; then the overall similarity of the MTS is obtained by synthesizing each of the single-dimension similarity based on weigh...