Some binuclear complexes of iron and cobalt with isocyanide ligands

Whereas Co₂(CO)₈ and RNC (R= Me, Et, and Cy) react to give mixtures of [(RNC)₅Co] [Co(CO)₄] and the covalent, carbonyl-bridged [(RNC)_mCo₂(CO)_8?m] derivatives (m = 1–3), [(π-dienyl)Fe(CO)₂]₂ give only [(π-dienyl)₂Fe₂(CO)_4?n(CNR)_n] complexes (dienyl = C₅H₅, MeC₅H₄ and C₉H₇; n = 1–2) that exist in solution as mixtures of cis- and trans-CO- and RNC-bridged tautomers with the μ-RNC species decreasing in importance as the bulk of R increases.     

Exceptional congruences for the coefficients of certain eta-product newforms

Let F(z)=∑_n=1^∞a(n)qⁿ denote the unique weight 16 normalized cuspidal eigenform on . In the early 1970s, Serre and Swinnerton-Dyer conjectured that

     

Parity of the Partition Function in Arithmetic Progressions, II

Let p(n) denote the ordinary partition function. Subbarao conjecturedthat in every arithmetic progression r (mod t) there are infinitelymany integers N = r (mod t) for which p(N) is even, and infinitelymany integers M = r (mod t) for which p(M) is odd. We provethe conjecture for every arithmetic progression whose modulusis a power of 2. 2000 Mathematics Subject Classification 11P83.     

Classification for forecasting and stock control: a case study

Different stock keeping units (SKUs) are associated with different underlying demand structures, which in turn require different methods for forecasting and stock control. Consequently, there is a need to categorize SKUs and apply the most appropriate methods in each category. The way this task is performed has significant implications in terms of stock and customer satisfaction. Therefore, categorization rules constitute a vital element of intelligent inventory management systems. Very little work has been conducted in this area and, from the limited research to date, it is not clear how managers should classify demand patterns for forecasting and inventory management. A previous research project was concerned with the development of a theoretically coherent demand categorization scheme for forecasting only. In this paper, the stock control implications of such an approach are assessed by experimentation on an inventory system developed by a UK-based software manufacturer. The experimental database consists of the individual demand histories of almost 16?000 SKUs. The empirical results from this study demonstrate considerable scope for improving real-world systems.     

Identification of candidate biomarkers in ovarian cancer serum by depletion of highly abundant proteins and differential in‐gel electrophoresis

Ovarian cancer is the fifth leading cause of cancer death for women in the US, yet survival rates are over 90% when it is diagnosed at an early stage, highlighting the need for biomarkers for early detection. To enhance the discovery of tumor‐specific proteins that could represent novel serum biomarkers for ovarian cancer, we depleted serum of highly abundant proteins which can mask the detection of proteins present in serum at low concentrations. Three commercial immunoaffinity columns were used in parallel to deplete the highly abundant proteins in serum from 60 patients with serous ovarian carcinoma and 60 non‐cancer controls. Medium and low abundance serum proteins from each serum pool were then evaluated by the quantitative proteomic technique of differential in‐gel electrophoresis. The number of protein spots that were elevated in ovarian cancer sera by at least twofold ranged from 36 to 248, depending upon the depletion and separation methods. From the 33 spots picked for MS analysis, nine different proteins were identified, including the novel candidate ovarian cancer biomarkers leucine‐rich α2 glycoprotein‐1 and ficolin 3. Western blotting validated the relative increases in serum protein levels for three of the proteins identified, demonstrating the utility of this approach for the identification of novel serum biomarkers for ovarian cancer.     

Formation of seasonal groups and application of seasonal indices

Estimating seasonal variations in demand is a challenging task faced by many organisations. There may be many stock-keeping units (SKUs) to forecast, but often data histories are short, with very few complete seasonal cycles. It has been suggested in the literature that group seasonal indices (GSI) methods should be used to take advantage of information on similar SKUs. This paper addresses two research questions: (1) how should groups be formed in order to use the GSI methods? and (2) when should the GSI methods and the individual seasonal indices (ISI) method be used? Theoretical results are presented, showing that seasonal grouping and forecasting may be unified, based on a Mean Square Error criterion, and K-means clustering. A heuristic K-means method is presented, which is competitive with the Average Linkage method. It offers a viable alternative to a company's own grouping method or may be used with confidence if a company lacks a grouping method. The paper gives empirical findings that confirm earlier theoretical results that greater accuracy may be obtained by employing a rule that assigns the GSI method to some SKUs and the ISI method to the remainder.     

On the categorization of demand patterns

The categorization of alternative demand patterns facilitates the selection of a forecasting method and it is an essential element of many inventory control software packages. The common practice in the inventory control software industry is to arbitrarily categorize those demand patterns and then proceed to select an estimation procedure and optimize the forecast parameters. Alternatively, forecasting methods can be directly compared, based on some theoretically quantified error measure, for the purpose of establishing regions of superior performance and then define the demand patterns based on the results. It is this approach that is discussed in this paper and its application is demonstrated by considering EWMA, Croston's method and an alternative to Croston's estimator developed by the first two authors of this paper. Comparison results are based on a theoretical analysis of the mean square error due to its mathematically tractable nature. The categorization rules proposed are expressed in terms of the average inter-demand interval and the squared coefficient of variation of demand sizes. The validity of the results is tested on 3000 real-intermittent demand data series coming from the automotive industry.