No problem is ever permanently closed. The editor is always pleased to consider for publication new solutions or new insights o n p a s t p r oblems. (1) Determine the set of all c > 0 such that whenever (1) holds, then we have x + y + z xy + yz+ zx. The positive r eals c asked for are those satisfying c 4. From (1), we have xy < c and z = c ; xy x + y + xy. Substituting this value of z into th...

Let F be a field of characteristic zero or of a positive odd characteristic p. For a polynomial f ∈ F[x, y], we define a graph ΓF(xy, f) to be a bipartite graph with vertex partition P ∪L, P = F = L, and (p1, p2, p3) ∈ P is adjacent to [l1, l2, l3] ∈ L if and only if p2 + l2 = p1l1 and p3 + l3 = f(p1, l1). If f = xy, the graph ΓF(xy, xy ) has the length of a shortest cycle (the girth) equal to ...

The results of experimental hybridisation between some chromosome subraces belonging to the X0 and XY chromosome races of the brachypterous grasshopper P. sapporensis are presented. Pre-zygotic reproductive isolation mechanisms in experimental pairs were not confirmed. In crossings of XY-standard x X0-standard and XY-standard x X0-Naganuma chromosome subraces, a zygotic barrier has been found. ...

Given a graph G with vertex set V(G) and edge E(G), for the bijective function f(V(G))?{1,2,?,|V(G)|}, associated weight of an xy?E(G) under f is w(xy)=f(x)+f(y). If all edges have pairwise distinct weights, called edge-antimagic labeling. A path P in vertex-labeled said to be rainbow x?y if every two xy,x?y??E(P) it satisfies w(xy)?w(x?y?). The antimagic labeling there exists vertices x,y?V(G)...

BACKGROUND Prenatal deficit of androgens or androgen action results in atypical genitalia in individuals with XY disorders of sex development (XY,DSD). XY,DSD include mainly disorders of gonadal development and testosterone synthesis and action. Previously, most XY,DSD individuals were assigned to the female sex. Constructive genital surgery allowing heterosexual intercourse, gonadectomy, and h...

We consider Green's functions $G(z):=(H-z)^{-1}$ of Hermitian random band matrices $H$ on the $d$-dimensional lattice $(\mathbb Z/L\mathbb Z)^d$. The entries $h_{xy}=\bar h_{yx}$ are independent centered complex Gaussian variables with variances $s_{xy}=\mathbb E|h_{xy}|^2$. satisfy a banded profile so that $s_{xy}$ is negligible if $|x-y|$ exceeds width $W$. For any $n\in \mathbb N$, we constr...

XO/XY and XO/XY/XYY mosaic hermaphrodites were generated from crosses involving BALB/cWt males. The distribution of Y-bearing cells in the gonads of these mice was studied by in situ hybridisation using the Y-specific probe pY353B. XY cells were found to contribute to all cell lineages of the ovary including follicle cells. The proportion of XY follicle cells was not significantly different fro...