Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.     

A Magnetic Nanoparticle-Based Time-Resolved Fluoroimmunoassay for Determination of the Cytokeratin 19 Fragment in Human Serum

A sensitive, rapid and novel measurement method for cytokeratin 19 fragment (CYFRA 21–1) in human serum by magnetic particle-based time-resolved fluoroimmunoassay (TRFIA) is described. Built on a sandwich-type immunoassay format, analytes in samples were captured by one monoclonal antibody coating onto the surface of magnetic beads and “sandwiched” by another monoclonal antibody labeled with europium chelates. The coefficient variations of the method were lower than 7 %, and the recoveries were in the range of 90–110 % for serum samples. The lower limit of quantitation of the present method for CYFRA 21–1 was 0.78 ng/ml. The correlation coefficient of CYFRA 21–1 values obtained by our novel TRFIA and CLIA was 0.980. The present novel TRFIA demonstrated high sensitivity, wider effective detection range and excellent reproducibility for determination of CYFRA 21–1 can be useful for early screening and prognosis evaluation of patients with non-small cell lung cancer.     

Microtextures Induced by Nanosecond Laser on Ni–Co Alloy Coatings

Ni–Co alloys have a wide range of applications in various fields owning to their excellent physical, chemical, and mechanical properties. In this paper, we prepare Ni–Co alloy coatings on 316L stain steel surfaces by electroplating. We present a novel approach utilizing a nanosecond laser to induce microtextures on Ni–Co alloy coatings. We study experimentally the effects of laser power and scanning rate on the surface morphologies of Ni–Co alloy coatings. The results indicate that the shape and size of induced microtextures can be controlled by the laser power and scanning rate. The size of grains increases with increase in the work current of the laser (WCL) at a certain scanning rate. With the WCL constant, the size of grains decreases with increase in scanning rate while their average height increases. It is a simple and easily-controlled method for the fabrication of microstructures on Ni–Co alloy coatings, which has promising applications in investigations of the properties of microtextured surfaces, such as friction, adhesion, and wetting.     

Scheduling with a due-window for acceptable lead-times

Due-dates are often determined during sales negotiations in two stages: (i) in the pre-sale stage, the customer provides a time interval (due-window) of his acceptable due-dates, (ii) in the second stage, the parties agree on the delivery penalties. Thus, the contract reflects penalties of both parts of the sales negotiations: earliness/tardiness penalties of the due-dates (as a function of the deviation from the agreed upon due-window), and earliness/tardiness penalties of the actual delivery times (as a function of the deviation from the due-dates). We model this setting of a two-stage negotiation on a single machine, and reduce the problem to a well-known setting of minimizing the weighted earliness/tardiness with a given (fixed) due-window. We adopt (and correct) a pseudo-polynomial dynamic programming algorithm for this NP-hard problem. The algorithm is extended to a setting of parallel identical machines, verifying that this case remains NP-hard in the ordinary sense. Moreover, an efficient greedy heuristic and a tight lower bound are introduced and tested. Extremely small optimality gaps are obtained in our numerical tests.