ion before(task(Si,Di), task(Sj,Dj)) :Si+Di #<= Sj. Conjunction between(X,Y,Z) :X #< Y, Y #< Z. Disjunction (but see below) neighbour(X,Y) :( X #= Y+1 ; Y #= X+1 ). Iteration not_among(X, L) :( foreach(Y,L),param(X) do X #\= Y ). Recursion not_among(X, []). not_among(X, [Y|Ys]) :X #\= Y, not_among(X, Ys). 11.4 Same Problem Different Model There are often many ways of modelling a problem. Consid...

ion before(task(Si,Di), task(Sj,Dj)) :Si+Di #<= Sj. Conjunction between(X,Y,Z) :X #< Y, Y #< Z. Disjunction (but see below) neighbour(X,Y) :( X #= Y+1 ; Y #= X+1 ). Iteration not_among(X, L) :( foreach(Y,L),param(X) do X #\= Y ). Recursion not_among(X, []). not_among(X, [Y|Ys]) :X #\= Y, not_among(X, Ys). 11.4 Same Problem Different Model There are often many ways of modelling a problem. Consid...

In this paper, a new method for estimating the linear regression coefficients approximation is presented based on Z-numbers. In this model, observations are real numbers, regression coefficients and dependent variables (y) have values ​​for Z-numbers. To estimate the coefficients of this model, we first convert the linear regression model based on Z-numbers into two fuzzy linear regression mode...

For a set S in a Banach space, we denote by dim(S) its covering dimension [1, p. 42]. Recall that, when S is a convex set, the covering dimension of S coincides with the algebraic dimension of S, this latter being understood as ∞ if it is not finite [1, p. 57]. Also, S and conv(S) will denote the closure and the convex hull of S, respectively. In [3], we proved what follows. dim({x ∈ X : Φ(x) =...

In this Article, we give a simple criterion for the regularity of a tri-linear mapping. We provide if f : X × Y × Z −→ W is a bounded tri-linear mapping and h : W −→ S is a bounded linear mapping, then f is regular if and only if hof is regular. We also shall give some necessary and sufficient conditions such that the fourth adjoint D^∗∗∗∗ of a tri-derivation D is again tri-derivation.

Throughout this paper only undirected simple graphs (without loops or multiple edges) are considered. Unless stated otherwise, we follow the book by Bollobás [2] for undefined terminology and definitions. LetG = G(m,n) = G(X,Y ) denote a bipartite graph with vertex classesX and Y such that |X| = m and |Y | = n. A complete bipartite subgraph with s vertices in the class X and t vertices in the c...

The Navy’s mine impact burial prediction model creates a time history of a cylindrical or a noncylindrical mine as it falls through air, water, and sediment. The output of the model is the predicted mine trajectory in air and water columns, burial depth/orientation in sediment, as well as height, area, and volume protruding. Model inputs consist of parameters of environment, mine characteristic...

From three-dimensional linearized hydrodynamic equations, it is found that the heat conductivity is proportional to (Lx/(L 2 yL 2 z)) , where Lx, Ly and Lz are the lengths of the system along the x, y and z directions, and we consider the case in which Lx ≫ Ly, Lz. The necessary condition for such a size dependence is derived as φ ≡ Lx/(n L 5/4 y L 5/4 z ) ≫ 1, where φ is the critical condition...

Let ξ := ξ(ω) (s×1) be a random vector defined on a probability space (Ω, S, P ); F, PF the distribution function and the probability measure corresponding to the random vector ξ. Let, moreover, g0(x, z), g1 0(y, z) be functions defined on Rn × Rs and Rn1 × Rs; fi(x, z), gi(y), i = 1, . . . , m functions defined on Rn × Rs and Rn1 ; h := h(z) (m × 1) a vector function defined on Rs, h ′ (z) = (...

In this paper we prove that the coordinate ring of the pinched Veronese (i.e k[X, XY, XY , Y , XZ, Y Z, XZ, Y Z, Z] ⊂ k[X, Y, Z]) is Koszul. The strategy of the proof is the following: we can consider a presentation S/I where S = k[X1, . . . , X9]. Using a distinguished weight ω, it’s enough to show that S/inωI is Koszul. We write inωI as J + H where J is generated by a Gröbner basis of quadric...