for a finite field $mathbb{f}_q$, the bivariate skew polynomial ring $mathbb{f}_q[x,y;rho,theta]$ has been used to study codes cite{xh}. in this paper, we give some characterizations of the ring $r[x,y;rho,theta]$, where $r$ is a commutative ring. we investigate 2-d skew $(lambda_1,lambda_2)$-constacyclic codes in the ring $r[x,y;rho,theta]/langle x^l-lambda_1,y^s-lambda_2rangle_{mathit{l}}.$ a...

In this paper, some results of Singh, Gopalakrishna and Kulkarni (1970s) have been extended to higher order derivatives. It has been shown that, if $sumlimits_{a}Theta(a, f)=2$ holds for a meromorphic function $f(z)$ of finite order, then for any positive integer $k,$ $T(r, f)sim T(r, f^{(k)}), rrightarrowinfty$ if $Theta(infty, f)=1$ and $T(r, f)sim (k+1)T(r, f^{(k)}), rrightarrowinfty$ if $Th...

Objective: In this research, a new approach termed as “evolutionary-based brain map” is presented as a diagnostic tool to classify schizophrenic and control subjects by distinguishing their electroencephalogram (EEG) features.Methods: Particle swarm optimization (PSO) is employed to find discriminative frequency bands from different EEG channels. By deploying the energy of those selected fr...

In a scenario where data-storage qubits are kept in isolation as far possible, with minimal measurements and controls, noise mitigation can still be done using additional probes, corrections applied only when needed. Motivated by the case of solid-state qubits, we consider dephasing arising from two-state fluctuator, described random telegraph process, probe which is also qubit, so-called spect...

The Wiskott-Aldrich syndrome (WAS) is one of several human immunodeficiency diseases inherited as an X-linked trait. The location of WAS on the X chromosome is unknown. We have studied 10 kindreds segregating for WAS for linkage with cloned, polymorphic DNA markers and have demonstrated significant linkage between WAS and two loci, DXS14 and DXS7, that map to the proximal short arm of the X chr...

Any covering Y ! X of a hyperbolic Riemann surface X of-nite area determines an inclusion of Teichm uller spaces Teich(X) ,! Teich(Y). We show this map is an isometry for the Teichm uller metric if the covering is amenable, and contracting otherwise. In particular , we establish jjjj < 1 for classical Poincar e series (Kra's `Theta conjecture'). The appendix develops the theory of geometric lim...

The moduli space Sg of smooth spin curves parameterizes pairs [C, η], where [C] ∈ Mg is a curve of genus g and η ∈ Pic(C) is a theta-characteristic. The finite forgetful map π : Sg → Mg has degree 22g and Sg is a disjoint union of two connected components S+ g and S− g of relative degrees 2g−1(2g +1) and 2g−1(2g − 1) corresponding to even and odd theta-characteristics respectively. A compactifi...

PURPOSE To map the gene for autosomal dominant cataracts (ADC) in an American white family of European descent. METHODS Ophthalmic examinations and linkage analyses using a variety of polymorphisms were performed; two-point lod scores calculated. RESULTS Affected individuals (14 studied) exhibited variable expressivity of embryonal nuclear opacities based on morphology, location within the ...

The moduli space Sg of smooth spin curves parameterizes pairs [C, η], where [C] ∈ Mg is a curve of genus g and η ∈ Pic(C) is a theta-characteristic. The finite forgetful map π : Sg → Mg has degree 22g and Sg is a disjoint union of two connected components S+ g and S− g of relative degrees 2g−1(2g +1) and 2g−1(2g − 1) corresponding to even and odd theta-characteristics respectively. A compactifi...