The following note develops theorems which enable one to schedule operations on a single-stage production system so a s to minimize certain functions o r optimizers. It is shown that the maximum tardiness of job completion is minimized by ordering the jobs according to the date the job is due to be completed. The s u m of times until eachjob is completed may be minimized under various conditions. If all jobs can be completed by their due dates, a weighted s u m of completion times can be minimized, subject to all jobs being completed by their due dates. This is done by scheduling l a s t the jobs with the l a r g e s t ratio of p r o c e s sing time to weighting factor among those jobs which will be completed on time i f scheduled l a s t ; the next to l a s t job is scheduled by applying the s a m e rule to the remaining jobs, and so forth, until the complete ordering is obtained.In the process of production scheduling there are so many factors that must be taken into consideration that the determination of a best schedule is impossible without a very precise meaning of the word "best." We shall discuss some fairly simple criteria which might be used as a means of judging whether or not a schedule is good. We shall also show how the choice of an optimizer will affect the characteristics of best schedules, in certain special cases.We shall be concerned with single-stage production and with optimizers such that there is never any advantage in delaying the completion of any operation, unless the completion of at least one other operation is moved forward. It is not difficult to see that a schedule is then completely determined by the ordering of the objects to be processed; that is, an optimal solution subject to a given ordering is obtained by performing each operation as soon as possible, consistent with the ordering. SECTION 1In most of the scheduling with which we will be concerned, we establish sufficient conditions that an ordering will be a "best" ordering in some sense of the word. We wish now to establish a sufficient condition that we shall use repeatedly. ment can be expressed as a function f over the set of all schedules. Since the schedule is assumed to be completely determined by the ordering, then f can be considered as a function of the ordering or as a function over the set of permutations of the n objects to be processed.We wish to find a permutation n , where n is the order ( r l , r2,. . . , nn), which minimizes the value of f.
The accurate detection of DNA sequences is essential for a variety of post human genome projects including detection of specific gene variants for medical diagnostics and pharmacogenomics. A specific DNA sequence detection assay based on surface-enhanced resonance Raman scattering (SERRS) and an amplification refractory mutation system (ARMS) is reported. Initially, generation of PCR products was achieved by using specifically designed allele-specific SERRS active primers. Detection by SERRS of the PCR products confirmed the presence of the sequence tested for by the allele-specific oligonucleotides. This lead directly to the multiplex genotyping of human DNA samples for the deltaF508 mutational status of the cystic fibrosis transmembrane conductance regulator gene using SERRS active primers in an ARMS assay. Removal of the unincorporated primers allowed fast and accurate analysis of the three genotypes possible in this system in a multiplex format without any separation of amplicons. The results indicate that SERRS can be used in modern genetic analysis and offers an opportunity for the development of novel assays. This is the first demonstration of the use of SERRS in multiplex genotyping and shows potential advantages over fluorescence as a detection technique with considerable promise for future development.
Sensitive and fast analytical methods for the identification of specific DNA sequences and fragments are a prerequisite to exploit the advantages of the new understanding of DNA with the completion of the human genome map. The most frequently used analytical methods employ fluorescence spectroscopy to detect a labeled nucleic-acid probe. [1, 2] Detection of the fluorophore confirms the presence of a specific base sequence. The main disadvantage of this method for an oligomer mixture is identification of differently labeled sequences due to the inherently broad fluorescent signals. Differentiation is possible by using fluorophores with very different emission profiles [3] or by time-resolved fluorescence detection instead. [4] However, these methods require special fluorophores and complex equipment that still cannot easily composition of the polymer sheets depends on the type of polymers used and the presence or absence of a capping layer. The patterns used here resulted in polymer films that can be classified either as materials or as macromolecules. More familiar systems that combine macroscopic and molecular dimensions are liposomes, SAMs, and Langmuir ± Blodgett films. [22] The smallest patterns that can now be formed by mCP are approximately 0.01 mm 2 ; the two-dimensional polymers derived from these patterns will have M r % 100 MDa and would begin to approach the molecular weight of very large soluble polymers such as polyacrylamide (20 MDa) [23] and lphage DNA (32 MDa). [24] This study represents a first step towards the fabrication (rather than synthesis) of polymers with well-defined nanosize shapes and dimensions. The combination of (nano)lithographic techniques and surface chemistry will allow the fabrication of a wide range of different shapes and chemical functionalities for these macromolecules.
Mitoxantrone is an anticancer agent for which it is important to know the concentration in blood during therapy. Current methods of analysis are cumbersome, requiring a pretreatment stage. A method based on surface-enhanced resonance Raman scattering (SERRS) has been developed using a flow cell and silver colloid as the SERRS substrate. It is simple, sensitive, fast, and reliable. Both blood plasma and serum can be analyzed directly, but fresh serum is preferred here due to reduced fluorescence in the clinical samples available. Fluorescence is reduced further by the dilution of the serum in the flow cell and by quenching by the silver of surface-adsorbed material. The effectiveness of the latter process is dependent on the contact time between the serum and the silver. The linear range encompasses the range of concentrations detected previously in patient samples using HPLC methods. In a comparative study of a series of samples taken from a patient at different times, there is good agreement between the results obtained by HPLC and SERRS with no significant difference between them at the 95% limit. The limit of detection in serum using the final optimized procedure for SERRS was 4.0 x 10(-11) M (0.02 ng/mL) mitoxantrone. The ease with which the SERRS analysis can be carried out makes it the preferred choice of technique for mitoxantrone analysis.
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