An indicator-based evolutionary multiobjective optimization algorithm (EMOA) is introduced which incorporates the contribution to the unary R2-indicator as the secondary selection criterion. First experiments indicate that the R2-EMOA accurately approximates the Pareto front of the considered continuous multiobjective optimization problems. Furthermore, decision makers’ preferences can be inclu...

Let m be a positive integer and let R1, R2 and B be three disjoint sets of points in the plane such that no three points of R1 ∪ R2 ∪ B lie on the same line and |B| = (m−1)|R1|+m|R2|. Put g = |R1∪R2|. Then there exists a subdivision X1∪X2∪· · ·∪Xg of the plane into g disjoint convex polygons such that (i) |Xi ∩ (R1 ∪ R2)| = 1 for all 1 ≤ i ≤ g; and (ii) |Xi ∩B| = m−1 if |Xi ∩R1| = 1, and |Xi ∩B...

We show that the cylinder Z(1) := B(1) × R2(n−1) embeds symplectically into B(R)× R2(n−2) if R > √ 3.

A braided n-path is a set of « paths ct(t) in R 3 (i = 1 , . . . , n) satisfying (1) c,(0 = (*,(>), MO, 0> ' i < * < r2, c ^ ) = P„ C/(r2) e { & , . . ,Ô„}(2) The paths do not intersect. Two braided «-paths are regarded as equivalent if and only if it is possible to deform the one configuration into the other respecting conditions (1) and (2) throughout the deformation; note that one does permi...

In this work, we study warm inflationary scenario based on a deformation of R2 gravity. We start considering Rp and assume p=2(1+?) with ??1 so that simply obtain inflation when setting ?=0. then derive the potential in Einstein frame consider dissipation parameter form ?=C1T C1 being coupling parameter. focus only strong regime which interaction between inflaton radiation fluid has been taken ...

For an algebraic number field k and a prime p, define the number p to be the maximal number d such that there exists a Galois extension of k whose Galois group is a free pro-p-group of rank d. The Leopoldt conjecture implies 1~ p ~ r2 +1, (r2 denotes the number of complex places of k). Some examples of k and p with 03C1 = r2 + 1 have been known so far. In this note, the invariant 03C1 is studie...