1,452 research outputs found
n-Ary quasigroups of order 4
We characterize the set of all N-ary quasigroups of order 4: every N-ary
quasigroup of order 4 is permutably reducible or semilinear. Permutable
reducibility means that an N-ary quasigroup can be represented as a composition
of K-ary and (N-K+1)-ary quasigroups for some K from 2 to N-1, where the order
of arguments in the representation can differ from the original order. The set
of semilinear N-ary quasigroups has a characterization in terms of Boolean
functions. Keywords: Latin hypercube, n-ary quasigroup, reducibilityComment: 10pp. V2: revise
On reducibility of n-ary quasigroups
An -ary operation is called an -ary quasigroup of order
if in the equation knowledge of any elements
of , ..., uniquely specifies the remaining one. is permutably
reducible if
where
and are -ary and -ary quasigroups, is a permutation, and
. An -ary quasigroup is called a retract of if it can be
obtained from or one of its inverses by fixing arguments. We prove
that if the maximum arity of a permutably irreducible retract of an -ary
quasigroup belongs to , then is permutably reducible.
Keywords: n-ary quasigroups, retracts, reducibility, distance 2 MDS codes,
latin hypercubesComment: 13 pages; presented at ACCT'2004 v2: revised; bibliography updated; 2
appendixe
Hypodynamic and hypokinetic condition of skeletal muscles
Data are presented in regard to the effect of unilateral brachial amputation on the physiological characteristics of two functionally different muscles, the brachial muscle (flexor of the brachium) and the medial head of the brachial triceps muscle (extensor of the brachium), which in rats represents a separate muscle. Hypokinesia and hypodynamia were studied
3D discrete element modeling of concrete: study of the rolling resistance effects on the macroscopic constitutive behavior
The Discrete Element Method (DEM) is appropriate for modeling granular materials [14] but also cohesive materials as concrete when submitted to a severe loading such an impact leading to fractures or fragmentation in the continuum [1, 5, 6, 8]. Contrarily to granular materials, the macroscopic constitutive behavior of a cohesive material is not directly linked to contact interactions between the rigid Discrete Elements (DE) and interaction laws are then defined between DE surrounding each DE. Spherical DE are used because the contact detection is easy to implement and the computation time is reduced in comparison with the use of 3D DE with a more complex shape. The element size is variable and the assembly is disordered to prevent preferential cleavage planes. The purpose of this paper is to highlight the influence of DE rotations on the macroscopic non-linear quasi-static behavior of concrete. Classically, the interactions between DE are modeled by spring-like interactions based on displacements and rotation velocities of DE are only controlled by tangential forces perpendicular to the line linking the two sphere centroids. The disadvantage of this modeling with only spring-like interactions based on displacements is that excessive rolling occurs under shear, therefore the macroscopic behavior of concrete is too brittle. To overcome this problem a non linear Moment Transfer Law (MTL) is introduced to add a rolling resistance to elements. This solution has no influence on the calculation cost and allows a more accurate macroscopic representation of concrete behavior. The identification process of material parameters is given and simulations of tests performed on concrete samples are shown
Vector Ambiguity and Freeness Problems in SL (2, ℤ).
We study the vector ambiguity problem and the vector freeness problem in SL(2,Z). Given a finitely generated n×n matrix semigroup S and an n-dimensional vector x, the vector ambiguity problem is to decide whether for every target vector y=Mx, where M∈S, M is unique. We also consider the vector freeness problem which is to show that every matrix M which is transforming x to Mx has a unique factorization with respect to the generator of S. We show that both problems are NP-complete in SL(2,Z), which is the set of 2×2 integer matrices with determinant 1. Moreover, we generalize the vector ambiguity problem and extend to the finite and k-vector ambiguity problems where we consider the degree of vector ambiguity of matrix semigroups
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