A Minimal Poset Resolution of Stable Ideals

We use the theory of poset resolutions to construct the minimal free resolution of an arbitrary stable monomial ideal in the polynomial ring whose coefficients are from a field. This resolution is recovered by utilizing a poset of Eliahou-Kervaire admissible symbols associated to a stable ideal. The structure of the poset under consideration is quite rich and in related analysis, we exhibit a regular CW complex which supports a minimal cellular resolution of a stable monomial ideal.Comment: 25 pages, 2 figure

LANDSAT 3 return beam vidicon response artifacts: A report on RBV photographic product characteristics and quality coding system

Analysis of large volumes of LANDSAT 3 RBV digital data that were converted to photographic form led to the firm identification of several visible artifacts (objects or structures not normally present, but producted by an external agency or action) in the imagery. These artifacts were identified, categorized, and traced directly to specific sensor response characteristics. None of these artifacts is easily removed and all cases remain under active study of possible future enhancement. The seven generic categories of sensor response artifacts identified to date include: (1) shading and stairsteps; (2) corners out of focus; (3) missing reseaus; (4) reseau distortion and data distortion; (5) black vertical line; (6) grain effect; and (7) faceplate contamination. An additional category under study, but not yet determined to be caused by sensor response, is a geometric anomaly. Examples of affected imagery are presented to assist in distinguishing between image content and innate defects caused by the sensor system

The Betti poset in monomial resolutions

Let $P$ be a finite partially ordered set with unique minimal element $\hat{0}$. We study the Betti poset of $P$, created by deleting elements $q\in P$ for which the open interval $(\hat{0}, q)$ is acyclic. Using basic simplicial topology, we demonstrate an isomorphism in homology between open intervals of the form $(\hat{0},p)\subset P$ and corresponding open intervals in the Betti poset. Our motivating application is that the Betti poset of a monomial ideal's lcm-lattice encodes both its $\mathbb{Z}^{d}$-graded Betti numbers and the structure of its minimal free resolution. In the case of rigid monomial ideals, we use the data of the Betti poset to explicitly construct the minimal free resolution. Subsequently, we introduce the notion of rigid deformation, a generalization of Bayer, Peeva, and Sturmfels' generic deformation

Spaceborne sensors (1983-2000 AD): A forecast of technology

A technical review and forecast of space technology as it applies to spaceborne sensors for future NASA missions is presented. A format for categorization of sensor systems covering the entire electromagnetic spectrum, including particles and fields is developed. Major generic sensor systems are related to their subsystems, components, and to basic research and development. General supporting technologies such as cryogenics, optical design, and data processing electronics are addressed where appropriate. The dependence of many classes of instruments on common components, basic R&D and support technologies is also illustrated. A forecast of important system designs and instrument and component performance parameters is provided for the 1983-2000 AD time frame. Some insight into the scientific and applications capabilities and goals of the sensor systems is also given