On quantification of weak sequential completeness

We consider several quantities related to weak sequential completeness of a Banach space and prove some of their properties in general and in $L$-embedded Banach spaces, improving in particular an inequality of G. Godefroy, N. Kalton and D. Li. We show some examples witnessing natural limits of our positive results, in particular, we construct a separable Banach space $X$ with the Schur property that cannot be renormed to have a certain quantitative form of weak sequential completeness, thus providing a partial answer to a question of G. Godefroy.Comment: 9 page

A note on the Mackey-star topology on a dual Banach space

[EN] By using a result in Kirk (Pac J Math 45:543 554, 1973), we show that there are separable Banach spaces such that their dual spaces, endowed with the Mackey-star topology, are not analytic. This solves a question raised in Kakol et al. (Descriptive topology in selected topics of functional analysis, Springer, 2011), and in Kakol and López-Pellicer (RACSAM 105:39 70, 2011).A. J. Guirao is Supported in part by MICINN and FEDER (Project MTM2008-05396), by Fundación Séneca (Project 08848/PI/08), by Generalitat Valenciana (GV/2010/036), and by Universitat Politècnica de València (project PAID-06-09-2829). V. Montesinos is Supported in part by Project MICINN MTM2011-22417, Generalitat Valenciana (GV/2010/036), and by Universitat Politècnica de València (Project PAID-06-09-2829).Guirao Sánchez, AJ.; Montesinos Santalucia, V. (2015). A note on the Mackey-star topology on a dual Banach space. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 109(2):417-418. https://doi.org/10.1007/s13398-014-0192-4S4174181092Fabian, M., Montesinos, V., Zizler, V.: On weak compactness in $$L_1$$ L 1 spaces. Rocky Mt. J. Math. 39, 1885–1893 (2009)Grothendieck, A.: Topological vector spaces, Translated from the French by Orlando Chaljub. Gordon and Breach Science publishers, New York (1973)Kąkol, J., López-Pellicer, M.: On realcompact topological vector spaces. RACSAM 105, 39–70 (2011)Kąkol, J., Kubiś, W., López-Pellicer, M.: Descriptive Topology in Selected Topics of Functional Analysis. In: Developments in Mathematics, vol. 24. Springer, New York (2011)Kirk, R.B.: A note on the Mackey topology for $$(C^b(X)^*, C^b(X))$$ ( C b ( X ) ∗ , C b ( X ) ) . Pac. J. Math. 45(2), 543–554 (1973)Köthe, G.: Topological vector spaces I, Translated by D.J.H. Garling, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band 159, 2nd edn. Springer, New York (1969)Schlüchtermann, G., Wheeler, R.F.: On strongly WCG Banach spaces. Math. Z. 199, 387–398 (1988

Towards Dynamic Contract Extension in Supplier Development

We consider supplier development within a supply chain consisting of a single manufacturer and a single supplier. Because investments in supplier development are usually relationship-specific, safeguard mechanisms against the hazards of partner opportunism have to be installed. Here, formal contracts are considered as the primary measure to safeguard investments. However, formal contracts entail certain risks, e.g., a lack of flexibility, particular in an ambiguous environment. We propose a receding horizon control scheme to mitigate possible contractual drawbacks while significantly enhancing the supplier development process and, thus, to increase the overall supply chain profit. Our findings are validated by a numerical case study

Towards dynamic contract extension in supplier development

We consider supplier development within a supply chain consisting of a single manufacturer and a single supplier. Because investments in supplier development are usually relationship-specific, safeguard mechanisms against the hazards of partner opportunism have to be installed. Here, formal contracts are considered as the primary measure to safeguard investments. However, formal contracts entail certain risks, e.g., a lack of flexibility, particular in an ambiguous environment. We propose a receding horizon control scheme to mitigate possible contractual drawbacks while significantly enhancing the supplier development process and, thus, to increase the overall supply chain profit. Our findings are validated by a numerical case study

The Top-Dog Index: A New Measurement for the Demand Consistency of the Size Distribution in Pre-Pack Orders for a Fashion Discounter with Many Small Branches

We propose the new Top-Dog-Index, a measure for the branch-dependent historic deviation of the supply data of apparel sizes from the sales data of a fashion discounter. A common approach is to estimate demand for sizes directly from the sales data. This approach may yield information for the demand for sizes if aggregated over all branches and products. However, as we will show in a real-world business case, this direct approach is in general not capable to provide information about each branch's individual demand for sizes: the supply per branch is so small that either the number of sales is statistically too small for a good estimate (early measurement) or there will be too much unsatisfied demand neglected in the sales data (late measurement). Moreover, in our real-world data we could not verify any of the demand distribution assumptions suggested in the literature. Our approach cannot estimate the demand for sizes directly. It can, however, individually measure for each branch the scarcest and the amplest sizes, aggregated over all products. This measurement can iteratively be used to adapt the size distributions in the pre-pack orders for the future. A real-world blind study shows the potential of this distribution free heuristic optimization approach: The gross yield measured in percent of gross value was almost one percentage point higher in the test-group branches than in the control-group branches.Comment: 22 pages, 15 figure

Quantitative Dunford-Pettis property

We investigate possible quantifications of the Dunford-Pettis property. We show, in particular, that the Dunford-Pettis property is automatically quantitative in a sense. Further, there are two incomparable mutually dual stronger versions of a quantitative Dunford-Pettis property. We prove that $L^1$ spaces and $C(K)$ spaces posses both of them. We also show that several natural measures of weak non-compactness are equal in $L^1$ spaces.Comment: 40 pages; the paper was shortened a bit, references were update

A systematic review and meta-analysis of the effects of clinical pathways on length of stay, hospital costs and patient outcomes

Background. To perform a systematic review about the effect of using clinical pathways on length of stay (LOS), hospital costs and patient outcomes. To provide a framework for local healthcare organisations considering the effectiveness of clinical pathways as a patient management strategy. Methods. As participants, we considered hospitalized children and adults of every age and indication whose treatment involved the management strategy "clinical pathways". We include only randomised controlled trials (RCT) and controlled clinical trials (CCT), not restricted by language or country of publication. Single measures of continuous and dichotomous study outcomes were extracted from each study. Separate analyses were done in order to compare effects of clinical pathways on length of stay (LOS), hospital costs and patient outcomes. A random effects meta-analysis was performed with untransformed and log transformed outcomes. Results. In total 17 trials met inclusion criteria, representing 4,070 patients. The quality of the included studies was moderate and studies reporting economic data can be described by a very limited scope of evaluation. In general, the majority of studies reporting economic data (LOS and hospital costs) showed a positive impact. Out of 16 reporting effects on LOS, 12 found significant shortening. Furthermore, in a subgroup-analysis, clinical pathways for invasive procedures showed a stronger LOS reduction (weighted mean difference (WMD) -2.5 days versus -0.8 days)). There was no evidence of differences in readmission to hospitals or in-hospital complications. The overall Odds Ratio (OR) for re-admission was 1.1 (95% CI: 0.57 to 2.08) and for in-hospital complications, the overall OR was 0.7 (95% CI: 0.49 to 1.0). Six studies examined costs, and four showed significantly lower costs for the pathway group. However, heterogeneity between studies reporting on LOS and cost effects was substantial. Conclusion. As a result of the relatively small number of studies meeting inclusion criteria, this evidence base is not conclusive enough to provide a replicable framework for all pathway strategies. Considering the clinical areas for implementation, clinical pathways seem to be effective especially for invasive care. When implementing clinical pathways, the decision makers need to consider the benefits and costs under different circumstances (e.g. market forces)