The Monomial Conjecture and Order Ideals

In this article first we prove that a special case of the order ideal conjecture, originating from the work of Evans and Griffith in equicharacteristic, implies the monomial conjecture due to M. Hochster. We derive a necessary and sufficient condition for the validity of this special case in terms certain syzygis of canonical modules of normal domains possessing free summands. We also prove some special cases of this observation

Effect of external electric field on the charge density waves in one dimensional Hubbard superlattices

We have studied the ground state of the one dimensional Hubbard superlattice structures with different unit cell sizes in the presence of electric field. Self consistent Hartree-Fock approximation calculation is done in the weak to intermediate interaction regime. Studying the charge gap at the Fermi level and the charge density structure factor, we get an idea how the charge modulation on the superlattice is governed by the competition between the electronic correlation and the external electric field.Comment: 6 pages, 8 figures. accepted in Journal of Physics: Condensed Matte

Ceramics in gas turbine: Powder and process characterization

Some of the intrinsic properties of various forms of Si3N4 and SiC are listed and limitations of such materials' availability are pointed out. The essential features/parameters to characterize a batch of powder are discussed including the standard techniques for such characterization. In process characterization, parameters in sintering, reaction sintering, and hot pressing processes are discussed including the factors responsible for strength limitations in ceramic bodies. Significant improvements in material properties can be achieved by reducing or eliminating the strength limiting factors with consistent powder and process characterization along with process control

Laser assisted deposition

Applications of laser-based processing techniques to solar cell metallization are discussed. Laser-assisted thermal or photolytic maskless deposition from organometallic vapors or solutions may provide a viable alternative to photovoltaic metallization systems currently in use. High power, defocused excimer lasers may be used in conjunction with masks as an alternative to direct laser writing to provide higher throughput. Repeated pulsing with excimer lasers may eliminate the need for secondary plating techniques for metal film buildup. A comparison between the thermal and photochemical deposition processes is made

State-of-the-art of SiAlON materials

Research presented includes work on phase relations, crystal structure, synthesis, fabrication, and properties of various SiAlONs. The essential features of compositions, fabrication methods, and microstructure are reviewed. High temperature flexure strength, creep, fracture toughness, oxidation, and thermal shock resistance are discussed. These data are compared to those for some currently produced silicon nitride ceramics to assess the potential SiAlON materials for use in advanced gas turbine engines

The Monomial Conjecture and order ideals II

Let $I$ be an ideal of height $d$ in a regular local ring $(R,m,k=R/m)$ of dimension $n$ and let $\Omega$ denote the canonical module of $R/I$. In this paper we first prove the equivalence of the following: the non-vanishing of the edge homomorphism \eta_d: \ext{R}{n-d}{k,\Omega} \rightarrow \ext{R}{n}{k,R}, the validity of the order ideal conjecture for regular local rings, and the validity of the monomial conjecture for all local rings. Next we prove several special cases of the order ideal conjecture/monomial conjecture.Comment: 16 page

Signature of strong atom-cavity interaction on critical coupling

We study a critically coupled cavity doped with resonant atoms with metamaterial slabs as mirrors. We show how resonant atom-cavity interaction can lead to a splitting of the critical coupling dip. The results are explained in terms of the frequency and lifetime splitting of the coupled system.Comment: 8 pages, 5 figure