Probate Law in Montana—Changes by the 1981 Legislature

1981 Probate Law Change

Combinatorics of Grassmannian Decompositions

This thesis studies several combinatorially defined families of subsets of the Grassmannian. We introduce and study a family of subsets called “basis shape loci” associated to transversal matroids. Additionally, we study the Deodhar and positroid decompositions of the Grassmannian. A basis shape locus takes as input data a zero/nonzero pattern in a matrix, which is equivalent to a specific presentation of a transversal matroid. The locus is defined to be the set of points in the Grassmannian which are the row spaces of matrices with the prescribed zero/nonzero pattern. We show that this locus depends only on the transversal matroid, not on the specific presentation. When a transversal matroid is a positroid, the closure of its basis shape locus is exactly the positroid variety labelled by the matroid. We give a sufficient, and conjecturally necessary, condition for when a transversal matroid is a positroid. Components in the Deodhar decomposition are indexed by Go-diagrams, certain fillings of Ferrers shapes with white stones, black stones, and pluses. Le-diagrams are a common combinatorial object indexing positroids; all Le-diagrams are Go-diagrams. We give a system of local flips on fillings of Ferrers shapes which may be used to turn arbitrary diagrams into Go-diagrams. When a Go-diagram is a Le-diagram, these flips are exactly the previously studied Le-moves. Using these local flips, we conjecture a combinatorial condition describing when one Deodhar component is contained in the closure of another within a Schubert cell. We define a variety containing and conjecturally equal to the closure of a Deodhar component and prove that this combinatorial criterion implies a containment of these varieties. We further show that there is no reasonable description of Go-diagrams in terms of forbidden subdiagrams by providing an injection from the set of valid Go- diagrams into the set of minimal forbidden subdiagrams. In lieu of such a description, we give an algorithmic characterization of Go-diagrams. Finally, we use the above results to prove several corollaries about Wilson loop cells, which arise in the study of scattering amplitudes in N=4 supersymmetric Yang-Mills theory. Notably, it was previously known that the matroid represented by a generic point in a Wilson loop cell is a positroid. We show that the closure of the Wilson loop cell agrees with the positroid variety labelled by this positroid

Partition Algebras and Kronecker Coefficients

Classical Schur-Weyl duality relates the representation theory of the general linear group to the representation theory of the symmetric group via their commuting actions on tensor space. With the goal of studying Kronecker products of symmetric group representations, the partition algebra is introduced as the commutator algebra of the diagonal action of the symmetric group on tensor space. An analysis of the representation theory of the partition offers results relating reduced Kronecker coefficients to Kronecker coefficients

Concerns of assuming linearity in the reconstruction of thermal maxima

Seasonal biases in proxy records are an outstanding issue in deciphering past climate evolution, and may contribute to the current discrepancy between models and proxy reconstructions during the Holocene, which is most pronounced in the northern extratropics. Bova et al. reported a method of transforming seasonal into mean annual temperatures (the SAT method) at low and mid-latitudes, and concluded that the thermal maxima during the Holocene and last interglacial (LIG) were mainly an artefact of a seasonal proxy response. We provide evidence that, in addition to this geographic mismatch, key assumptions of the SAT method are violated, and more importantly, that the method by construction removes thermal maxima. Thus, the main findings of Bova et al.4 probably reflect peculiarities of the SAT method instead of shedding light on the so-called Holocene conundrum

The Sedimentary Petrography, Depositional Environment and Tectonic Setting of the Aldwell Formation, Northern Olympic Peninsula, Washington

The upper Eocene Aldwell Formation crops out in an east-west trending band across the northern Olympic Peninsula, Washington. Petrographic analyses indicate that the Aldwell Formation has lithologically distinctive eastern and western portions. The rocks of the eastern Aldwell are basalt-rich lithic greywackes; their mean compositions are Qm-F-Lt: 5- 22-73 and polycrystalline quartz-volcanic rock fragments-total sedimentary rock fragments: 1-78-21. The rocks of the western Aldwell are chert-rich lithic arenites; their mean compositions are Qm-F-Lt: 27-19-54 and polycrystalline quartz-volcanic rock fragments-total sedimentary rock fragments: 66-11-23. Similarities in texture, composition, and alteration products suggest that the basalts of the Crescent seamount province as the likely source for the sediments of the eastern rocks. Since the basalts of the Crescent seamount province crop out both to the north (Metchosin Volcanics) and south (Crescent Formation) of the Aldwell Formation, no definite conclusions can be drawn regarding the provenance of the eastern Aldwell sediments. However, a northern source is inferred based on the restriction of abundant basaltic detritus to the eastern rocks and a southward transport direction for the olistostromal blocks in a conglomerate unit near Lake Aldwell. The provenance of the sediments in the western portion of the Aldwell Formation is speculative. A terrane located to the southwest of Vancouver Island during the late Eocene is proposed as the source of these sediments. The rocks in the eastern portion of the Aldwell Formation are predominantly thin-bedded, laminated siltstones with interbedded fine sands. The rocks in the western portion of the Aldwell Formation are thin-bedded siitstones with interbedded fine sands, commonly in thin lenses; coarse sandstone and conglomerate are also present. The eastern rocks are interpreted as having been deposited in an outer fan environment and the western rocks were deposited in a mid-fan environment, but the different lithologies indicate that deposition took place on two separate fans within the Juan de Fuca basin rather than in two areas of the same fan. A model for the tectonic setting of the Juan de Fuca basin and surrounding area during the deposition of the Aldwell Formation is proposed in which the Crescent seamount province, moving northeast on either the Kula or Farallon plate, converged against an allochthonous terrane then located near Vancouver Island, resulting in uplift and southerly transport of Aldwell sediments

I cambiamenti climatici: la sfida del XXI secolo

There is a large gap between the actions required to avoid a dangerous warming of the planet, and those already decided to contrast it. The more time passes, the more the pessimistic visions obtain valid motivations and reasons. In order to radically change in few decades an energetic system and a predatory attitude towards the planet’s resources, it is necessary to recognize the climate crisis as a systemic one, as a problem of justice and equity for the future generations. The climate science should help to understand the importance of this challenge, by emphasizing the consequences of today’s decisions for the future generations. To recover our reasons to deal with posterity, both as individuals and community, is a bigger endeavor. To understand the importance of the climate change requires not only more knowledge, but also the acceptance of the planetary limits, the redefinition of human expectations, and also a level of emotional understanding that is not sufficient today

Incidence of colorectal cancer and influence of dietary habits in fifteen European countries from 1971 to 2002

AbstractObjectiveThis study aimed to analyze the incidence of colorectal cancer in 15 European countries in recent decades and the relationship between the incidence found and changes in dietary habits.MethodsPearson's or Spearman's correlation coefficients were calculated by comparing incidence rates obtained from the International Agency for Research on Cancer for 1971-2002 with data on per capita consumption obtained from the Food and Agriculture Organization of the United Nations using 10-year delay intervals.ResultsIncidence rates increased in all countries except France in men and except Austria, Denmark, England and France in women. Of the dietary variables considered, there were marked increasing trends (linear regression coefficient, R ≥0.5) in red meat consumption in Germany (R = 0.9), Austria (R = 0.7), Finland (R = 0.8), Italy (R = 0.9), Poland (R = 0.5), Spain (R = 2.1), Sweden (R = 0.6), and the Netherlands (R = 0.7).ConclusionsChanges in dietary habits may be consistent with the observed trends in the incidence of colorectal cancer in the distinct European countries