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The main purpose of this paper is to improve the bound of complexity of the well-known algorithms on polynomial ideals having complexities polynomial in dn, where d is the maximal degree of input polynomials and n is the number of variables. Instead of this bound, we present the more accurate bound max{S, Dn} where S is the size of the input polynomials in dense representation, and D is the arithmetic mean value of the degrees of input polynomials. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the little q-Schur algebra s(2,r) of type A1. The main purpose of this paper is to construct a monomial base of s(2,r). [ABSTRACT FROM AUTHOR]

In view of the support vectors of ε-SVR that are not distributed in the ε belt and only located on the outskirts of the ε belt, a novel algorithm to construct ε-SVR of a large-scale training sample set is proposed in this paper. It computes firstly the ε-SVR hyper-plane of a small training sample set and the distances d of all samples to the hyper-plane, then deletes the samples not in field ε ≤ d ≤ dmax and searches SVs gradually in the scope ε ≤ d ≤ dmax, and trains step-by-step the final ε-SVR. Finally, it analyzes the time complexity of the algorithm, and verifies its convergence in the theory and tests its efficiency by the simulation. [ABSTRACT FROM AUTHOR]

One of the main needs when dealing with multi-perspective specifications is to be able to have at our disposal, at intermediate stages of the development process, a merged view which properly reflects the knowledge of each participant in the elicitation tasks (and over which we can reason, even in the presence of disagreement and incompleteness). We show in this paper to what extent there can be many merged models, having all of them useful application. So there is not a unique operator which can be qualified as the best; on the contrary, there will be a suitable merging operator depending on the goal of the merging process. More concretely, we will propose a set of four composition operators: ∐max, ∐min, ∐maj and ∐maj+inc. They will be evaluated making use of a list of desired algebraic properties proposed by researchers on merging and which should be held by an ideal merging operator. This analysis can help us to compare the different operators, revealing the key features of each, and identifying weaknesses that may require further research. The conclusion drawn after this analysis points out that these properties are not useful enough to adequately characterize a merging operator. Therefore, new properties will be provided in order to complete the previous list and help to define better the behavior of the different merging operators. [ABSTRACT FROM AUTHOR]

In this paper we produce a finite algebra which generates a variety with a PSPACE-complete membership problem. We produce another finite algebra with a γ function that grows exponentially. The results are obtained via a modification of a construction of the algebra A(T) that was introduced by McKenzie in 1996. [ABSTRACT FROM AUTHOR]

This paper presents a fast algorithm for solving the n-queens problem. The basic idea of this algorithm is to use pre-computed solutions in 75% of the cases, while the remaining cases are solved by calling the Sosic's algorithm. The novelty of this algorithm is in the observation that these pre-computable cases exhibit a modular nature. In addition, the pre-computed solutions run 100 times faster than Sosic's algorithm in most cases. [ABSTRACT FROM AUTHOR]

The structural constants of an evolution algebra are given by a quadratic matrix. In this work we establish an equivalence between nil, right nilpotent evolution algebras and evolution algebras defined by upper triangular matrices. The classification of 2-dimensional complex evolution algebras is obtained. For an evolution algebra with a special form of the matrix, we describe all its isomorphisms and their compositions. We construct an algorithm running under Mathematica which decides if two finite dimensional evolution algebras are isomorphic. [ABSTRACT FROM AUTHOR]

Continuous-time quantum walks (CTQW) over finite group schemes is investigated, where it is shown that some properties of a CTQW over a group scheme defined on a finite group G induces a CTQW over group scheme defined on G/H, where H is a normal subgroup of G with prime index. This reduction can be helpful in analyzing CTQW on underlying graphs of group schemes. Even though this claim is proved for normal subgroups with prime index (using the Clifford's theorem from representation theory), it is checked in some examples that for other normal subgroups or even non-normal subgroups, the result is also true! It means that CTQW over the graph on G, starting from any arbitrary vertex, is isomorphic to the CTQW over the quotient graph on G/H if we take the sum of the amplitudes corresponding to the vertices belonging to the same cosets. [ABSTRACT FROM AUTHOR]

We prove that computing a geometric minimum-dilation graph on a given set of points in the plane, using not more than a given number of edges, is an NP-hard problem, no matter if edge crossings are allowed or forbidden. We also show that the problem remains NP-hard even when a minimum-dilation tour or path is sought; not even an FPTAS exists in this case. [ABSTRACT FROM AUTHOR]

We introduce some new types of "small" subsets of a group: sparse, k-sparse, thin, k-thin, almost thin subsets. We study the interrelations between these types and apply the obtained results to the Stone–Čech compactification βG of a discrete group G. [ABSTRACT FROM AUTHOR]

We describe irreducible representations and character formulas of the Renner monoids for reductive monoids, which generalize the Munn–Solomon representation theory of rook monoids to any Renner monoids. The type map and polytope associated with reductive monoids play a crucial role in our work. It turns out that the irreducible representations of certain parabolic subgroups of the Weyl groups determine the complete set of irreducible representations of the Renner monoids. An analogue of the Munn–Solomon formula for calculating the character of the Renner monoids, in terms of the characters of the parabolic subgroups, is shown. [ABSTRACT FROM AUTHOR]

We use the algorithms Bottomup and Topdown to study the finitistic dimensions of a class of extension algebras: the trivially twisted extensions of monomial algebras. A hybrid algorithm for determination of the finitistic dimension of the aforementioned extension is presented, and in particular, conditions for construction of such extensions that have relatively larger finitistic dimension are investigated. [ABSTRACT FROM AUTHOR]

The trace algebra Cnd over a field of characteristic 0 is generated by all traces of products of d generic n × n matrices, n, d ≥ 2. Minimal sets of generators of Cnd are known for n = 2 and 3 for any d and for n = 4 and 5 and d = 2. The explicit defining relations between the generators are found for n = 2 and any d and for n = 3, d = 2 only. Defining relations of minimal degree for n = 3 and any d are also known. The minimal degree of the defining relations of any homogeneous minimal generating set of C42 is equal to 12. Starting with the generating set given recently by Drensky and Sadikova, we have determined all relations of degree ≤ 14. For this purpose we have developed further algorithms based on representation theory of the general linear group and easy computer calculations with standard functions of Maple. [ABSTRACT FROM AUTHOR]

We prove some no-go theorems on the existence of a Fock representation of the *-Lie algebra generated by $B_k^n (t) =\int_0^t b_s^{\dagger^n} b_s^k ds$, where $b_s^\dagger$, bs are the Hida white noise densities. In particular we prove the nonexistence of such a representation for any *-Lie algebra containing $b_s^3$. This drastic difference with the quadratic case proves the necessity of investigating different renormalization rules for the case of higher powers of white noise. [ABSTRACT FROM AUTHOR]

We study the connection between *-representations of algebras associated with graphs, locally-scalar graph representations and the problem about the spectrum of a sum of two Hermitian operators. For algebras associated with Dynkin graphs we give an explicit description of the parameters for which there are irreducible representations and an algorithm for constructing these representations. [ABSTRACT FROM AUTHOR]

In this article, we explicitly calculated the values of the representations of the Hecke algebra $\mathcal {H}$, associated with a Gelfand–Graev character of GL4(q), at some of the standard basis elements. [ABSTRACT FROM AUTHOR]

The members of the class C6 in Aschbacher's structure theorem for subgroups of the general linear group GL(d,q) are the normalizers of certain absolutely irreducible, symplectic-type r-groups, where r is a prime, d a power of r and q ≡ 1 (mod r). For a prime r > 2 and d = r, we present a constructive one-sided Monte Carlo algorithm to recognize whether or not a given subgroup G of GL(r,q) contains a normal extra-special r-group of order r3 and exponent r. In the former case the algorithm returns a homomorphism from G into SL(2,r) with kernel being the extra-special r-group times the center. [ABSTRACT FROM AUTHOR]

The embedding diagrams of representations of the N=2 superconformal algebra with central charge c=3 are given. Some non-unitary representations possess subsingular vectors that are systematically described. The structure of the embedding diagrams is largely defined by the spectral flow symmetry. As an additional consistency check the action of the spectral flow on the characters is calculated. [ABSTRACT FROM AUTHOR]