The functional equation f(y − x) − g(xy) = h (1/x− 1/y) is solved for general solution. The result is then applied to show that the three functional equations f(xy) = f(x)+f(y), f(y−x)−f(xy) = f(1/x−1/y) and f(y−x)−f(x)−f(y) = f(1/x−1/y) are equivalent. Finally, twice differentiable solution functions of the functional equation f(y − x) − g1(x) − g2(y) = h (1/x− 1/y) are determined.

This paper introduces an exploration to permuting ability of a 2D torus under deterministic XY routing. The research is carried out for a number of communication models, namely, unidirectional uniaxial, bidirectional uniaxial, unidirectional biaxial, and bidirectional biaxial. Necessary and sufficient conditions of blocking occurrence in a 2D torus for uniaxial models are expressed mathematical...

Mutations in the Y linked testis determining gene SRY cause 46,XY sex reversal. However, only about 15% of cases of 46,XY sex reversal are accounted for by mutations in SRY. In this study we have investigated the possibility that mutations affecting the expression of SRY might cause some of the cases of sex reversal in which the coding sequence of SRY is normal. We have screened 2 kb of DNA imm...

the purpose of this paper is the generalization of structure factor for rods by polygon section in two dimensional phononic crystals. if we use the plane wave expansion method (pwe) for the propagation of acoustic waves in 2d phononic crystals, structure factor will be an important quantity. in order to confirm the obtained relations, we have calculated the band structure for xy and z vibration...

The proband was evaluated at 19 years of age because of primary amenorrhoea and, on chromosomal analysis, was found to have a 46,XY karyotype in 75% of her cells and 48,XY, +8, +21 in 25% of her cells. She appeared normal at birth and exhibited normal intellectual and physical development until puberty when secondary sexual differentiation failed. This young women showed none of the dysmorphic ...

We perform Monte Carlo simulations using the Wolff cluster algorithm of the XY model on both fixed and dynamical phi-cubed graphs (i.e. without and with coupling to two-dimensional quantum gravity). We compare the numerical results with the theoretical expectation that the phase transition remains of KT type when the XY model is coupled to gravity. We also examine whether the universality we di...

Six children, with severe deficiency of some or all of the immunoglobulins and minor somatic abnormalities, had chromosomal abnormalities: (1) 45,XY,t(13q/18q), (2) 46,XY,21ps +, (3) two brothers 46,XY (inv. 7) (4) 45,X,t(11p/10p)/46X,iXq,t(11p/10p) and, (5) in addendum, 45,XX,-18;46,XX, r18. The chromosome abnormalities were detected in B- as well as T-lymphocytes (as evidenced by using both P...

In this paper we prove that a finite partial commutative (idempotent commutative) Latin square can be embedded in a finite commutative (idempotent commutative) Latin square. These results are then used to show that the loop varieties defined by any non-empty subset of the identities {x(xy) = y, (yx)x = y} and the quasi-group varieties defined by any non-empty subset of {x” = x, x(xy) = y, (yx)x...

∀i, yi = [0, ..., 0 } {{ } j−1 , 1, 0, ..., 0 } {{ } c−j ] ⇒ xi W0 = x̄j W0, (1) where y i is the i-th row of the true cluster assignment matrix Y and x̄j is the mean of the data that belongs to class j. Denote X̄c = [x̄1, ..., x̄c]. Note that X̄c = XY Σ, where Σ ∈ Rc×c is a diagonal matrix with the i-th diagonal element as 1/ni, ni is the number of the data that belongs to class i. Then rank(X̄ c W0)...