The most massive stars in the Arches cluster

We study a sample composed of 28 of the brightest stars in the Arches cluster. We analyze K-band spectra obtained with the integral field spectrograph SINFONI on the VLT. Atmosphere models computed with the code CMFGEN are used to derive the effective temperatures, luminosities, stellar abundances, mass loss rates and wind terminal velocities. We find that the stars in our sample are either H-rich WN7-9 stars (WN7-9h) or O supergiants, two being classified as OIf+. All stars are 2-4 Myr old. There is marginal evidence for a younger age among the most massive stars. The WN7-9h stars reach luminosities as large as 2 x 1e6 Lsun, consistent with initial masses of ~ 120 Msun. They are still quite H-rich, but show both N enhancement and C depletion. They are thus identified as core H-burning objects showing products of the CNO equilibrium at their surface. Their progenitors are most likely supergiants of spectral types earlier than O4-6 and initial masses > 60 Msun. Their winds follow a well defined modified wind momentum - luminosity relation (WLR): this is a strong indication that they are radiatively driven. Stellar abundances tend to favor a slightly super solar metallicity, at least for the lightest metals. We note however that the evolutionary models seem to under-predict the degree of N enrichment.Comment: 19 pages, 15 figures. A&A accepte

Faces of Birkhoff Polytopes

The Birkhoff polytope B(n) is the convex hull of all (n x n) permutation matrices, i.e., matrices where precisely one entry in each row and column is one, and zeros at all other places. This is a widely studied polytope with various applications throughout mathematics. In this paper we study combinatorial types L of faces of a Birkhoff polytope. The Birkhoff dimension bd(L) of L is the smallest n such that B(n) has a face with combinatorial type L. By a result of Billera and Sarangarajan, a combinatorial type L of a d-dimensional face appears in some B(k) for k less or equal to 2d, so bd(L) is at most d. We will characterize those types whose Birkhoff dimension is at least 2d-3, and we prove that any type whose Birkhoff dimension is at least d is either a product or a wedge over some lower dimensional face. Further, we computationally classify all d-dimensional combinatorial types for d between 2 and 8.Comment: 29 page

The Farahat-Higman ring of wreath products and Hilbert schemes

We study the structure constants of the class algebra $R_Z(G_n)$ of the wreath products $G_n$ associated to an arbitrary finite group G with respect to the basis of conjugacy classes. We show that a suitable filtration on $R_Z(G_n)$ gives rise to the graded ring $\mathcal G_G(n)$ with non-negative integer structure constants independent of n (some of which are computed), which are then encoded in a Farahat-Higman ring $\mathcal G_G$. The real conjugacy classes of G come to play a distinguished role, and is treated in detail in the case when G is a subgroup of $SL_2(C)$. The above results provide new insight to the cohomology rings of Hilbert schemes of points on a quasi-projective surface.Comment: latex, abstract/introduction modified, to appear in Advances in Mat

Artinian algebras and Jordan type

The Jordan type of an element $\ell$ of the maximal ideal of an Artinian k-algebra A acting on an A-module M of k-dimension n, is the partition of n given by the Jordan block decomposition of the multiplication map $m_\ell$ on M. In general the Jordan type has more information than whether the pair $(\ell,M)$ is strong or weak Lefschetz. We develop basic properties of the Jordan type and their loci for modules over graded or local Artinian algebras. We as well study the relation of generic Jordan type of $A$ to the Hilbert function of $A$. We introduce and study a finer invariant, the Jordan degree type. In our last sections we give an overview of topics such as the Jordan types for Nagata idealizations, for modular tensor products, and for free extensions, including examples and some new results. We as well propose open problems.Comment: 53 pages. Added results, examples for Jordan degree type (Section 2.4) and Jordan type and initial ideal (Section 2.5

DEMAND DRIVERS FOR FRESH-CUT FLOWERS AND THEIR SUBSTITUTES: AN APPLICATION OF HOUSEHOLD EXPENDITURE ALLOCATION MODELS

Flowers are purchased for a variety of reasons ranging from expressions of love or sympathy to satisfying environmental and beautification goals. Unlike many foods where some of the attributes can be quantitatively measured such as grams of fat in meats and milligrams of cholesterol in fluid milk, these aesthetically pleasing products present an array of attributes that are closely tied to the buyers reasons for making the purchase. Clearly the attributes are fundamentally different since the goal associated with the purchase depends on the buyers objectives. This also implies that the demand for such products should be much more closely tied to the characteristics for the buyers and the reasons for buying. Flowers are not absolutely essential for survival and; hence, one may find a given share of the population as non-buyers or infrequent buyers. That is, there is considerable latitude with the decision to purchase or not, and again, this wider range of choices is closely tied to the demographics and occasions or periods. Knowing the latitude with the decision to purchase and the perceptions of the characteristics for products are essential to understanding the demand. Purchasing of fresh-cut flowers, potted plants, and dry/artificial flowers should be substitutable to some degree even though physically they are fundamentally different products. Yet these products have many similar attributes when considering the purpose for use. They can be used to express thanks, reflect emotions, project beauty, and show environmental concerns. Hence, even with the physical differences, consumers may easily change their buying behaviors among these types of flower products. Expenditure patterns are tied to many things, including incomes, purposes, occasions, information and perceptions, and product availability (i.e., outlets). These levels of expenditures depend on market penetration (number of buyers), frequency of transaction among buyers, and prevailing prices. Hence, anything that influences consumer entry into the marketing via more (or fewer) buyers and/or increased frequency of transactions must be measured to have a fuller grasp of the demand for flower products. Understanding demand for flowers is useful to help the flower industry to be proactive in addressing demand issues. Actionable variables such as generic and brand promotion programs, and innovative selling methods are important factors likely to influence the future direction of the industry. Hence, it is important to have a complete definitive understanding of the demand drivers for fresh-cut flowers and their substitutes including the relative importance of entry and transactions. To measure factors influencing the demand for flowers such as prices, seasonality, and demographic variables, the demand for flowers in the different forms was estimated using the Almost Ideal Demand System (AIDS) to examine household behaviors in the U.S. flower industry. The model for fresh-cut, potted plants, and dry/artificial flowers explicitly accounted for differences in outlets, purposes, purchasing occasions, growth, income demographics, and prices. These variables were incorporated into the likelihood specification of the AIDS model, including the weight prices often referred to as the Stone Index. Note that Stone Index was not used, rather the parameters included in the weighting were part of the likelihood specification. The actual estimation was completed using the maximum likelihood function that also accounted for possible correlation in the equation residuals. The actual estimation was completed using the maximum likelihood function that also accounted for possible correlation in the equation residuals. Since flowers were made up of a wide range of varieties, references to quantities purchased had little meaning. The AIDS model was in terms of expenditures and prices and not directly the quantities. Yet an explicit demand function can be derived from the model if one can identify a meaningful quantity measure. Instead of quantities demanded the total transactions on flowers were used as a surrogate for quantities. Hence, demand is in terms of transactions per household with the transaction defined as household buyers (b) times monthly frequency (f) of purchases per household; Then, these transactions were expressed on a per household base. Given the complexity and nonlinear nature of the AIDS model, the full meaning of the coefficients cannot be seen by simply observing the coefficient values. To fully gain insight into what can be learned from the estimates, simulations and sensitivity analyses are needed. That is, using the estimated models show the responses to simulated changes in the model variables. Calculating the demand elasticities for the own prices, cross prices and expenditures can be useful for indicating both the allocations of the budget shares among the three flower types; fresh-cut flowers, potted flowering plants, and dry/artificial flowers. However, the distribution properties for each estimated elasticity depend on the distribution properties of each coefficient and actual variable values in the model. It is extremely difficult to calculate each elasticity distribution because of the nonlinear nature of the AIDS model. A useful approach to get around this problem is a bootstrap resampling approach. An application of the bootstrapping is to resample with replacement and re-estimate the elasticity over and over again and determine the distribution properties from the range of estimates. Each simulation procedure measured demand changes by adjusting one or more variables relative to the mean value of all other variables in the demand model. For illustration purposes, each continuous variable was adjusted from 50 percent of the mean level to 150 percent of the mean using increments of 10 percent. Once demand models are known their use can be extended beyond identifying what causes demand changes. They can be useful for making longer term projections and/or forecasts. In other to make projections, both the time span and some expectation about changes in each demand variable must be made. In many circumstances it is nearly impossible to know what future values of specific demand variables will be. Whereas, some variables such as the number of households and income growth can be approximated with some degree of confidence. Furthermore, temporal demand changes were captured with the proxy measure using the time variables where the time represents existing periods and can be extended out to future months. Hence, simply changing the time variables for those future periods is straight forward. Using this time line and placing a set of growth assumptions on total expenditures provide one mechanism for projecting into future periods. These are projections instead of forecast since the projections are based on a set of assumed conditions such as absolute and relative prices, outlet selection, and purpose. Even with these conditions, the projections provide considerable insight into the underlying forces embedded in the AIDS model parameters. As a result, a fresh-cut share as gift-giving was higher relative to that for self-use, while potted shares and dry/artificial shares were slightly higher for self-uses compared to gifts-giving. Monthly shares and expenditures on fresh-cut flowers and dry/artificial flowers from florists were higher than through supermarkets, while shares and expenditures on potted flowering plants from supermarkets were higher than through florists. From the projections, the fresh-cut flower industry would benefit from an overall growth in consumer spending on flower products, while both the potted flower industry and the dry/artificial flower industry lost their shares as total incomes increased for the long-run period. Demand system models provided a picture of the consumer side of the market and attempted to provide the empirical insight into what drive changes in the purchasing behavior. Demand can be assumed completely exogenous to an industry and the industry just accepts the pattern of change. The AIDS model as suggested in this research provides insight into where changes could occur and what the relative category position would appear to be in the absence of any stimulations or adjustment within the flower industry. Yet the same pattern may point to areas needing attention by various sectors within the flower industry. For example, how much gain could be realized by changing the fall drop in seasonal patterns? Who should be targeted? What is the potential gain from price competitiveness versus specific demand enhancement programs? Surprising there are few if any definitive analyses of the broad demand for flowers and this analysis should give the industry a better perspective on the demand for fresh-cut flowers relative to the other goods.Demand and Price Analysis,