L et I be an ideal, homogeneous with respect to the usual grading, in a polynomial ring R = k[x0, . . . , xn] in n+ 1 variables (over an algebraically closed field k). Denote the graded component of I of degree d by Id, and likewise the k-vector space of homogeneous forms of R of degree d by Rd. Since I is a graded R-module, we have k-linear maps μd,i : Id ⊗ Ri → Id+i given for each i and d by ...

We describe a quantitative phase imaging process using an x-ray laboratory-based source with an extremely broad bandwidth spectrum. The thickness of a homogeneous object can be retrieved by using separately spectrally weighted values for the attenuation coefficient and the decrement of the real part of the refractive index. This method is valid for a wide range of object types, including object...

the degree kirchhoff index of a connected graph $g$ is defined as‎ ‎the sum of the terms $d_i,d_j,r_{ij}$ over all pairs of vertices‎, ‎where $d_i$ is the‎ ‎degree of the $i$-th vertex‎, ‎and $r_{ij}$ the resistance distance between the $i$-th and‎ ‎$j$-th vertex of $g$‎. ‎bounds for the degree kirchhoff index of the line and para-line‎ ‎graphs are determined‎. ‎the special case of regular grap...

This paper proposes a systematic method to design hierarchical, decentralized, stabilizing controllers for homogeneous hierarchical dynamical networks. Based on LQR approach with a properly chosen performance index including global and local objectives with control input penalty, an obtained optimal LQR feedback gain gives the closed-loop system a prescribed desirable hierarchical structure. In...

We consider a shear flow of a scale invariant homogeneous Gaussian random velocity field which does not depend on the coordinates in the direction of the flow. We investigate a heat advection coming from a Gaussian random homogeneous source. We discuss a relaxation at large time of a temperature distribution determined by the forced advectiondiffusion equation. We represent the temperature corr...

in this paper we introduce two-wavelet constants for square integrable representations of homogeneous spaces. we establishthe orthogonality relations for square integrable representationsof homogeneous spaces which give rise to the existence of aunique self adjoint positive operator on the set of admissiblewavelets. finally, we show that this operator is a constant multiple of identity operator...

A scheme of double-negative left-handed atomic vapor medium based on dressed-state assisted simultaneous electric and magnetic resonances is suggested. In this mechanism, simultaneous electricand magnetic-dipole allowed transitions of atoms are driven by an optical wave by taking full advantage of both mixed-parity dressed-state assisted resonance and incoherent population pumping in a quantum-...

A wide variety of similarity indices for comparing two assemblages based on species incidence (i.e., presence/absence) data have been proposed in the literature. These indices are generally based on three simple incidence counts: the number of species shared by two assemblages and the number of species unique to each of them. We provide a new probabilistic derivation for any incidence-based ind...