1,047,617 research outputs found

    Generalised Stretched Littlewood-Richardson Coefficients

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    The Littlewood-Richardson (LR) coefficient counts among many other things the LR tableaux of a given shape and a given content. We prove, that the number of LR tableaux weakly increases if one adds to the shape and the content the shape and the content of another LR tableau. We also investigate the behaviour of the number of LR tableaux, if one repeatedly adds to the shape another shape with either fixed or arbitrary content. This is a generalisation of the stretched LR coefficients, where one repeatedly adds the same shape and content to itself.Comment: 15 pages, rewritten with more results and examples (compared with v1), final version to appear at Journal of Combinatorial Theory

    Strigolactones spatially influence lateral root development through the cytokinin signaling network

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    Strigolactones are important rhizosphere signals that act as phytohormones and have multiple functions, including modulation of lateral root (LR) development. Here, we show that treatment with the strigolactone analog GR24 did not affect LR initiation, but negatively influenced LR priming and emergence, the latter especially near the root-shoot junction. The cytokinin module ARABIDOPSIS HISTIDINE KINASE3 (AHK3)/ARABIDOPSIS RESPONSE REGULATOR1 (ARR1)/ARR12 was found to interact with the GR24-dependent reduction in LR development, because mutants in this pathway rendered LR development insensitive to GR24. Additionally, pharmacological analyses, mutant analyses, and gene expression analyses indicated that the affected polar auxin transport stream in mutants of the AHK3/ARR1/ARR12 module could be the underlying cause. Altogether, the data reveal that the GR24 effect on LR development depends on the hormonal landscape that results from the intimate connection with auxins and cytokinins, two main players in LR development

    The benefits of the orthogonal LSM models

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    In the last few decades both the volume of high-quality observing data on variable stars and common access to them have boomed; however the standard used methods of data processing and interpretation have lagged behind this progress. The most popular method of data treatment remains for many decades Linear Regression (LR) based on the principles of Least Squares Method (LSM) or linearized LSM. Unfortunately, we have to state that the method of linear regression is not as a rule used accordingly namely in the evaluation of uncertainties of the LR parameters and estimates of the uncertainty of the LR predictions. We present the matrix version of basic relations of LR and the true estimate of the uncertainty of the LR predictions. We define properties of the orthogonal LR models and show how to transform general LR models into orthogonal ones. We give relations for orthogonal models for common polynomial series.Comment: 5 pages, 2 figures, submitted to Odessa Astronomical Publications, vol. 20, 200

    Analysis of margin classification systems for assessing the risk of local recurrence after soft tissue sarcoma resection

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    Purpose: To compare the ability of margin classification systems to determine local recurrence (LR) risk after soft tissue sarcoma (STS) resection. Methods: Two thousand two hundred seventeen patients with nonmetastatic extremity and truncal STS treated with surgical resection and multidisciplinary consideration of perioperative radiotherapy were retrospectively reviewed. Margins were coded by residual tumor (R) classification (in which microscopic tumor at inked margin defines R1), the R+1mm classification (in which microscopic tumor within 1 mm of ink defines R1), and the Toronto Margin Context Classification (TMCC; in which positive margins are separated into planned close but positive at critical structures, positive after whoops re-excision, and inadvertent positive margins). Multivariate competing risk regression models were created. Results: By R classification, LR rates at 10-year follow-up were 8%, 21%, and 44% in R0, R1, and R2, respectively. R+1mm classification resulted in increased R1 margins (726 v 278, P < .001), but led to decreased LR for R1 margins without changing R0 LR; for R0, the 10-year LR rate was 8% (range, 7% to 10%); for R1, the 10-year LR rate was 12% (10% to 15%) . The TMCC also showed various LR rates among its tiers (P < .001). LR rates for positive margins on critical structures were not different from R0 at 10 years (11% v 8%, P = .18), whereas inadvertent positive margins had high LR (5-year, 28% [95% CI, 19% to 37%]; 10-year, 35% [95% CI, 25% to 46%]; P < .001). Conclusion: The R classification identified three distinct risk levels for LR in STS. An R+1mm classification reduced LR differences between R1 and R0, suggesting that a negative but < 1-mm margin may be adequate with multidisciplinary treatment. The TMCC provides additional stratification of positive margins that may aid in surgical planning and patient education

    On Local Relaxation Methods and Their Application to Convection-Diffusion Equations

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    This paper discusses local relaxation (LR) methods which can be regarded as generalizations of the successive overrelaxation (SOR) method. The difference is that within an LR method the relaxation factor is allowed to vary from equation to equation. A number of existing methods are found to be in fact special LR methods. Moreover, based on SOR theory, a new LR method is developed. The performance of LR methods is illustrated by applying them to central difference approximations of convection-diffusion equations. It is found that equations with small diffusion coefficients can be handled without difficulty. For equations with strongly varying coefficients, and for nonlinear equations, a properly selected LR method can be significantly more efficient than the optimum SOR method. As a special example, a 16 Ɨ 16 driven cavity problem for a Reynolds number of 10^6 can be solved in just a few seconds on a modern computer.

    Monotonicity and Inequalities for Ratio of the Generalized Logarithmic Means

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    Let c > b > a > 0 be real numbers. Then the function f(r) = Lr(a,b)/Lr(a,c) is strictly decreasing on (āˆ’āˆž,āˆž), where Lr(a, b) denotes the generalized (extended) logarithmic mean of two positive numbers a and b
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