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...

Disorders of sex development (DSD) are congenital conditions characterized by atypical development of chromosomal, gonadal, and phenotypic sex. 46, XY DSD can result from disorders of testicular development or disorders of androgen synthesis/action. Prophylactic gonadectomy should be considered in patients with 46, XY DSD because of the increased risk of gonadal malignancy. We report two rare c...

the zero-divisor graph of a commutative ring r with respect to nilpotent elements is a simple undirected graph $gamma_n^*(r)$ with vertex set z_n(r)*, and two vertices x and y are adjacent if and only if xy is nilpotent and xy is nonzero, where z_n(r)={x in r: xy is nilpotent, for some y in r^*}. in this paper, we investigate the basic properties of $gamma_n^*(r)$. we discuss when it will be eu...

1.1. Geometry. A covariant derivative on a manifold M is an operator ∇XY on vector fields X and Y satisfying for any smooth function f : (i) ∇fXY = f∇XY ; and (ii) ∇X(fY ) = f∇XY + (∇Xf)Y . If g is a Riemannian metric on M , then there is associated with g a unique covariant derivative ∇ characterized by: (iii) ∇XY −∇YX = [X,Y ]; and (iv) ∇X ( g(Y,Z) ) = g(∇XY, Z) + g(Y,∇XZ). We define the Chri...

We investigate torque and also conventionally defined spin-Hall currents in two-dimensional (2D) spin-orbit coupled systems of spin-1/2 particles within the linear response Kubo formalism. We obtain some interesting relations between the conventional and torque spin-Hall conductivities for the generic effective Hamiltonian H0 = ǫ 0 k + A(k)σx − B(k)σy, where A(k) = η i ki + η A ijkikj + η A ijl...

The invaded cluster algorithm is used to study the XY model in two and three dimensions up to sizes 2000(2) and 120(3), respectively. A soft spin O(2) model, in the same universality class as the three-dimensional XY model, is also studied. The static critical properties of the model and the dynamical properties of the algorithm are reported. The results are K(c)=0.454 12(2) for the three-dimen...

and [[xy]z] + [[yz]x] + [[zx]y] = 0. Left multiplication in a Lie algebra is denoted by ad(x): ad(x)(y) = [x, y]. An associative algebra A becomes a Lie algebra A− under the product, [xy] = xy − yx. The first axiom implies that [xy] = −[yx] and the second (called the Jacobi identity) implies that x 7→ adx is a homomorphism of L into the Lie algebra (EndL)−, that is, ad [xy] = [adx, ad y]. Assum...

Sex reversal can occur in XY humans with only a single functional WT1 or SF1 allele or a duplication of the chromosome region containing WNT4. In contrast, XY mice with only a single functional Wt1, Sf1, or Wnt4 allele, or mice that over-express Wnt4 from a transgene, reportedly are not sex-reversed. Because genetic background plays a critical role in testis differentiation, particularly in C57...