Identification in residue analysis based on liquid chromatography with tandem mass spectrometry: Experimental evidence to update performance criteria
Mol, J.G.J. ; Zomer, P. ; Garcia Lopez, M. ; Fussell, R.J. ; Scholten, J. ; dr. Kok, A. ; Wolheim, A. ; Anastassiades, M. ; Lozano, A. ; Fernandez Alba, A. - \ 2015
Analytica Chimica Acta 873 (2015). - ISSN 0003-2670 - p. 1 - 13.
mycotoxin analysis - veterinary drugs - food - confirmation - extraction - pesticides - matrices
Liquid chromatography-tandem mass spectrometry (LC-MS/MS) is one of the most widely used techniques for identification (and quantification) of residues and contaminants across a number of different chemical domains. Although the same analytical technique is used, the parameters and criteria for identification vary depending on where in the world the analysis is performed and for what purpose (e.g. determination of pesticides, veterinary drugs, forensic toxicology, sports doping). The rationale for these differences is not clear and in most cases the criteria are essentially based on expert opinions rather than underpinned by experimental data. In the current study, the variability of the two key identification parameters, retention time and ion ratio, was assessed and compared against requirements set out in different legal and guidance documents. The study involved the analysis of 120 pesticides, representing various chemical classes, polarities, molecular weights, and detector response factors, in 21 different fruit and vegetable matrices of varying degrees of complexity. The samples were analysed non-fortified, and fortified at 10, 50 and 200µgkg(-1), in five laboratories using different LC-MS/MS instruments and conditions. In total, over 135,000 extracted-ion chromatograms were manually verified to provide an extensive data set for the assessment. The experimental data do not support relative tolerances for retention time, or different tolerances for ion ratios depending on relative abundance of the two product ions measured. Retention times in today's chromatographic systems are sufficiently stable to justify an absolute tolerance of ±0.1min. Ion ratios are stable as long as sufficient response is obtained for both product ions. Ion ratio deviations are typically within ±20% (relative), and within ±45% (relative) in case the response of product ions are close to the limit of detection. Ion ratio tolerances up to 50% did not result in false positives and reduced the false negative rate for pesticides with product ions in the low S/N range to
Spatially explicit fate modelling of nanomaterials in natural waters
Quik, J.T.K. ; Klein, J.J.M. de; Koelmans, A.A. - \ 2015
Water Research 80 (2015). - ISSN 0043-1354 - p. 200 - 208.
engineered nanomaterials - aquatic environments - nanoparticles - aggregation - systems - exposure - sedimentation - calibration - matrices - silver
Site specific exposure assessments for engineered nanoparticles (ENPs) require spatially explicit fate models, which however are not yet available. Here we present an ENP fate model (NanoDUFLOW) that links ENP specific process descriptions to a spatially explicit hydrological model. The link enables the realistic modelling of feedbacks between local flow conditions and ENP fate processes, such as homo- and heteroaggregation, resuspension and sedimentation. Spatially explicit simulations using five size classes of ENPs and five size classes of natural solids showed how ENP sediment contamination ‘hot spots’ and ENP speciation can be predicted as a function of place and time. For the catchment modelled, neglect of spatial heterogeneity caused relatively small differences in ENP retention. However, simplification of the number of size classes to one average class, resulted in up to 3.3 times lower values of retention compared to scenarios that used detailed size distributions. Local concentrations in sediment were underestimated up to 20 fold upon simplification of spatial heterogeneity or particle size distribution. We conclude that spatial heterogeneity should not be neglected when assessing the risks of ENPs.
Sire evaluation for total number born in pigs using a genomic reaction norms approach
Silva, F.F. ; Mulder, H.A. ; Knol, E.F. ; Lopes, M.S. ; Guimaraes, S.E.F. ; Lopes, P.S. ; Mathur, P.K. ; Viana, J.M.S. ; Bastiaansen, J.W.M. - \ 2014
Journal of Animal Science 92 (2014)9. - ISSN 0021-8812 - p. 3825 - 3834.
environment interaction - dairy-cattle - genetic-parameters - production traits - genotype - models - pedigree - matrices - merit - milk
In the era of genome-wide selection (GWS), genotype-by-environment (G×E) interactions can be studied using genomic information, thus enabling the estimation of SNP marker effects and the prediction of genomic estimated breeding values (GEBVs) for young candidates for selection in different environments. Although G×E studies in pigs are scarce, the use of artificial insemination has enabled the distribution of genetic material from sires across multiple environments. Given the relevance of reproductive traits such as the total number born (TNB) and the variation in environmental conditions encountered by commercial dams, understanding G×E interactions can be essential to choose the best sires for different environments. The present work proposes a two-step reaction norm approach for G×E analysis using genomic information. The first step provided estimates of environmental effects (herd-year-season - HYS), and the second step provided estimates of the intercept and slope for the TNB across different HYS levels, obtained from the first step, using a random regression model. In both steps, pedigree (A) and genomic (G) relationship matrices were considered. The genetic parameters (variance components, h2 and genetic correlations) were very similar when estimated using the A and G relationship matrices. The reaction norm graphs showed considerable differences in environmental sensitivity between sires, indicating a reranking of sires in terms of genetic merit across the HYS levels. Based on the G matrix analysis, SNP by environment interactions were observed. For some SNPs, the effects increased at increasing HYS levels, while for others, the effects decreased at increasing HYS levels or showed no changes between HYS levels. Cross-validation analysis demonstrated better performance of the genomic approach with respect to traditional pedigrees for both the G×E and standard models. The genomic reaction norm model resulted in an accuracy of GEBVs for “juvenile” boars varying from 0.14 to 0.44 across different HYS levels, while the accuracy of the standard genomic prediction model, without reaction norms, varied from 0.09 to 0.28. These results show that it is important and feasible to consider G×E interactions in evaluations of sires using genomic prediction models and that genomic information can increase the accuracy of selection across environments.
Rapid settling of nanoparticles due to heteroaggregration with suspended sediment
Velzeboer, I. ; Quik, J.T.K. ; Meent, D. van de; Koelmans, A.A. - \ 2014
Environmental Toxicology and Chemistry 33 (2014)8. - ISSN 0730-7268 - p. 1766 - 1773.
engineered nanomaterials - silver nanoparticles - aquatic environments - aggregation - exposure - water - particles - matrices - carbon - quantification
Sedimentation of engineered nanoparticles (ENPs) has been studied mainly in artificial media and stagnant systems mimicking natural waters. This neglects the role of turbulence and heteroaggregation with sediment. We studied the apparent sedimentation rates of selected ENPs (CeO2, PVP-Ag and SiO2-Ag) in agitated sediment-water systems resembling fresh, estuarine and marine waters. Experiments were designed to mimic low energy and periodically resuspended sediment water systems (14 days), followed by a long term aging, resuspension and settling phase (6 months), as would occur in receiving shallow lakes. ENPs in systems with periodical resuspension of sediment were removed with sedimentation rates between 0.14 and 0.50¿m/d. The sedimentation rates did not vary much among ENP type, salinity and aging time, which is attributed to the capture of ENPs in sediment flocks. The sedimentation rates were one to two orders of magnitude higher than those reported for aggregation-sedimentation in stagnant systems without suspended sediment. Heteroaggregation rates were estimated and ranged between 0.151 and 0.547 L/mg/d, which is up to 29 times higher than those reported for natural colloids under quiescent settling conditions. We conclude that rapid scavenging and sedimentation drives removal of ENPs from the water column
Development and validation of an LC-MS/MS method for the detection of phomopsin A in lupin and lupin-containing retail food samples from the Netherlands
Nijs, W.C.M. de; Pereboom-de Fauw, D.P.K.H. ; Dam, R.C.J. van; Rijk, T.C. de; Egmond, H.P. van; Mol, J.G.J. - \ 2013
Food Additives & Contaminants. Pt. A, Chemistry, Analysis, Control, Exposure & Risk Assessment 30 (2013)10. - ISSN 1944-0049 - p. 1819 - 1826.
mycotoxin analysis - leptostromiformis - extraction - maize - wheat - spectrometry - pesticides - matrices - fruits - seeds
Phomopsins (PHO) are mycotoxins produced by the fungus Diaporthe toxica (also referred to as Phomopsis leptostromiformis). Lupin is the most important host crop for this fungus and PHO are suspected as cause of lupinosis, a deadly liver disease, in sheep. Lupin is currently in use to replace genetically modified soy in many food products available on the European market. However, a validated method for analysis of PHO is not available until now. In this work, a dilute-and-shoot LC-MS/MS-based method was developed for the quantitative determination and identification of phomopsin A (PHO-A) in lupin and lupin-containing food. The method involved extraction by a mixture of acetonitrile/water/acetic acid (80/20/1 v/v), dilution of the sample in water, and direct injection of the crude extract after centrifugation. The method was validated at 5 and 25 µg PHO-A kg(-1) product. The average recovery and RSD obtained were 79% and 9%, respectively. The LOQ (the lowest level for which adequate recovery and RSD were demonstrated) was 5 µg PHO-A kg(-1). Identification of PHO-A was based on retention time and two transitions (789 > 226 and 789 > 323). Using the average of solvent standards from the sequence as a reference, retention times were all within ± 0.03 min and ion ratios were within ± 12%, which is compliant with European Union requirements. The LOD (S/N = 3 for the least sensitive transition) was 1 µg PHO-A kg(-1) product. Forty-two samples of lupin and lupin-containing food products were collected in 2011-2012 from grocery stores and internet shops in the Netherlands and analysed. In none of the samples was PHO-A detected
Determination of perfluorinated alkyl acid concnetrations in biological standard reference materials
Reiner, J.L. ; O'Connell, S.G. ; Butt, C.M. ; Kwadijk, C.J.A.F. - \ 2012
Analytical and Bioanalytical Chemistry 404 (2012)9. - ISSN 1618-2642 - p. 2683 - 2692.
marine food-web - perfluoroalkyl contaminants - perfluorooctane sulfonate - human plasma - great-lakes - water - samples - serum - environment - matrices
Standard reference materials (SRMs) are homogeneous, well-characterized materials used to validate measurements and improve the quality of analytical data. The National Institute of Standards and Technology (NIST) has a wide range of SRMs that have mass fraction values assigned for legacy pollutants. These SRMs can also serve as test materials for method development, method validation, and measurement for contaminants of emerging concern. Because inter-laboratory comparison studies have revealed substantial variability of measurements of perfluoroalkyl acids (PFAAs), future analytical measurements will benefit from determination of consensus values for PFAAs in SRMs to provide a means to demonstrate method-specific performance. To that end, NIST, in collaboration with other groups, has been measuring concentrations of PFAAs in a variety of SRMs. Here we report levels of PFAAs and perfluorooctane sulfonamide (PFOSA) determined in four biological SRMs: fish tissue (SRM 1946 Lake Superior Fish Tissue, SRM 1947 Lake Michigan Fish Tissue), bovine liver (SRM 1577c), and mussel tissue (SRM 2974a). We also report concentrations for three in-house quality-control materials: beluga whale liver, pygmy sperm whale liver, and white-sided dolphin liver. Measurements in SRMs show an array of PFAAs, with perfluorooctane sulfonate (PFOS) being the most frequently detected. Reference and information values are reported for PFAAs measured in these biological SRMs.
Multi-residue screening of veterinary drugs in egg, fish and meat using high-resolution liquid chromatography accurate mass time-of-flight mass spectrometry
Peters, R.J.B. ; Bolck, Y.J.C. ; Rutgers, P. ; Stolker, A.A.M. ; Nielen, M.W.F. - \ 2009
Journal of Chromatography. A, Including electrophoresis and other separation methods 1216 (2009)46. - ISSN 0021-9673 - p. 8206 - 8216.
growth-promoting agents - european decision - uplc-tof - performance - food - matrices - urine - antibiotics - validation - extraction
The last 2 years multi-compound methods are gaining ground as screening methods. In this study a high-resolution liquid chromatography combined with time-of-flight mass spectrometry (HRLC–ToF-MS) is tested for the screening of about 100 veterinary drugs in three matrices, meat, fish and egg. While the results are satisfactory for 70–90% of the veterinary drugs, a more efficient sample preparation or extract purification is required for quantitative analysis of all analytes in more difficult matrices like egg. The average mass measurement error of the ToF-MS for the veterinary drugs spiked at concentrations ranging from 4 to 400 µg/kg, is 3.0 ppm (median 2.5 ppm) with little difference between the three matrices, but slightly decreases with increasing concentration. The SigmaFit value, a new feature for isotope pattern matching, also decreases with increasing concentration and, in addition, shows an increase with increasing matrix complexity. While the average SigmaFit value is 0.04, the median is 0.01 indicating some high individual deviations. As with the mass measurement error, the highest deviations are found in those regions of the chromatogram where most compounds elute from the column, be it analytes or matrix compounds. The median repeatability of the method ranges from 8% to 15%, decreasing with increasing concentration, while the median reproducibility ranges from 15% to 20% with little difference between matrices and concentrations. The median accuracy is in between 70% and 100% with a few compounds showing higher values due to matrix interference. The squared regression coefficient is >0.99 for 92% of the compounds showing a good overall linearity for most compounds. The detection capability, CCß, is within 2 times the associated validation level for >90% of the compounds studied. By changing a few conditions in the analyses protocol and analysing a number of blank samples, it was determined that the method is robust as well as specific. Finally, an alternative validation strategy is proposed and tested for screening methods. While the results calculated for repeatability, within-lab reproducibility and CCß show a good comparison for the matrices meat and fish, and a reasonable comparison for the matrix egg, only 27 analyses are required to obtain these results versus 63 analysis in the traditional, 2002/657/EC, approach. This alternative is suggested as a cost-effective validation procedure for screening methods.
Control of Strobilurin Fungicides in Wheat Using Direct Analysis in Real Time Accurate Time-of-Flight and Desorption Electrospray Ionization Linear Ion Trap Mass Spectrometry
Schurek, J. ; Vaclavik, L. ; Hooijerink, H. ; Lacina, O. ; Poustka, J. ; Sharman, M. ; Caldow, M. ; Nielen, M.W.F. ; Hajslova, J. - \ 2008
Analytical Chemistry 80 (2008)24. - ISSN 0003-2700 - p. 9567 - 9575.
liquid-chromatography - pesticide-residues - ambient conditions - food - azoxystrobin - vegetables - matrices - fruits - methyl - dart
Ambient mass spectrometry has been used for the analysis of strobilurin residues in wheat. The use of this novel, challenging technique, employing a direct analysis in a real time (DART) ion-source coupled with a time-of-flight mass spectrometer (TOF MS) and a desorption electrospray ionization (DESI) source coupled with a linear ion trap tandem MS (LIT MSn), permitted a direct screen of the occurrence of target fungicides in treated grains in less than 1 min. For quantification purpose by DART-TOF MS, an ethyl acetate extract had to be prepared. With the use of a prochloraz as an internal standard, the performance characteristics obtained by repeated analyses of extract, spiked at 50 ¿g kg¿1 with six strobilurins (azoxystrobin, picoxystrobin, dimoxystrobin, kresoxim-methyl, pyraclostrobin, and trifloxystrobin), were in the following range: recoveries 78¿92%, repeatability (RSD) 8¿15%, linearity (R2) 0.9900¿0.9978. The analysis of wheat with incurred strobilurin residues demonstrated good trueness of data generated by the DART-TOF MS method; the results were in a good agreement with those obtained by the conventional approach, i.e., by the QuEChERS sample handling procedure followed by identification/quantification employing high-performance liquid chromatography coupled with tandem mass spectrometry (LC¿MS/MS). Tandem mass spectrometry using DESI-LIT MSn provided a sufficient number of product ions for confirmation of the identity of azoxystrobin and pyraclostrobin in incurred wheat samples.
Ethical Matrix Manual
Mepham, B. ; Kaiser, M. ; Thorstensen, E. ; Tomkins, S. ; Millar, K. - \ 2006
The Hague : LEI, onderdeel van Wageningen UR - 45 p.
dierethiek - dierlijke productie - dierenwelzijn - matrices - animal ethics - animal production - animal welfare - matrices
The ethical matrix is a conceptual tool designed to help decision-makers (as individuals or working in groups) reach sound judgements or decisions about the ethical acceptability and/or optimal regulatory controls for existing or prospective technologies in the field of food and agriculture.
Sandwich immunoassays for the determination of peanut and hazelnut traces in foods
Kiening, M. ; Niessner, R. ; Baumgartner, S. ; Drs, E. ; Krska, R. ; Bremer, M.G.E.G. ; Tomkies, V. ; Reece, P. ; Danks, C. ; Immer, U. ; Wellner, M.G. - \ 2005
Journal of Agricultural and Food Chemistry 53 (2005)9. - ISSN 0021-8561 - p. 3321 - 3327.
tree nut allergy - dial telephone survey - elisa - prevalence - matrices - quantification - proteins - kits
People suffering from food allergies are dependent on accurate food labeling, as an avoidance diet is the only effective countermeasure. Even a small amount of allergenic protein can trigger severe reactions in highly sensitized patients. Therefore, sensitive and reliable tests are needed to detect potential cross-contamination. In this paper two fast sandwich immunoassays are described for the determination of peanut (Arachis hypogaea) and hazelnut (Corylus avellana) traces in complex food matrices. Mouse monoclonal antibodies were used as capture antibodies, and labeled rabbit polyclonal antibodies were used as detection antibodies in both assays. The assay time was 30 min in total, and cross-reactivities against a variety of fruits and seeds were found to be in the low 10-4% (ppm) level or in some cases not detectable. The recoveries in all tested food matrices ranged from 86 to 127%, and the limits of detection were in the range of 0.2-1.2 mg/kg (ppm) in food for both peanut and hazelnut, respectively
Preprocessing and exploratory analysis of chromatographic profiles of plant extracts
Hendriks, M.M.W.B. ; Cruz-Juarez, L. ; Bont, D. de; Hall, R.D. - \ 2005
Analytica Chimica Acta 545 (2005)1. - ISSN 0003-2670 - p. 53 - 64.
principal component analysis - least-squares algorithms - mass-spectrometry - herbal products - identification - metabolomics - matrices - choice
The characterization of herbal extracts to compare samples from different origin is important for robust production and quality control strategies. This characterization is now mainly performed by analysis of selected marker compounds. Metabolic fingerprinting of full metabolite profiles of plant extracts aims at a more rapid and thorough screening or classification of plant material. We will show that HPLC is an appropriate technique for metabolic fingerprinting of secondary metabolites, given that adequate preprocessing of raw profiles is performed. Additional variation, which results from sample preparation and changing measurement conditions, usually obscures the information of interest in these raw profiles. This paper illustrates the importance of preprocessing of chromatographic fingerprinting data. Different alignment methods are discussed as well as the influence of normalization. Weighted principal component analysis is introduced as a valuable alternative to autoscaling of data. LC-UV data on Willow (Salix sp.) extracts is used to evaluate these preprocessing methods and their influence on exploratory data analysis
|De bruikbaarheid van de matrix van Heaney
Staveren, W.A. van - \ 2004
Nederlands Tijdschrift voor Dietisten 59 (2004)8. - ISSN 0166-7203 - p. 207 - 208.
voedingsstoffen - voedingsstoffentekorten - gezondheid - voedingsonderzoek - matrices - nutrients - nutrient deficiencies - health - nutrition research - matrices
Professor Wija van Staveren (Wageningen Universiteit) stond in haar afscheidsrede stil bij de matrix van de Amerikaanse voedingsdeskundige Heany. Zij ging na of dit een goede aanvulling is op de hedendaagse aanpak om de relatie tussen voeding en gezondheid te onderzoeken en gaf haar visie op de toepasbaarheid hiervan voor wetenschap en beleid
|Over magische momenten in de ruimtelijke planvorming
Poel, K.R. de; Kranendonk, R.P. ; Eekhout, M.J.J. ; Geenen, J.J.N. - \ 2002
Groen : vakblad voor groen in stad en landschap 58 (2002)2. - ISSN 0166-3534 - p. 40 - 44.
ruimtelijke ordening - regionale planning - groene zones - ontwerp - kwaliteit - levensomstandigheden - sociaal welzijn - projecten - planning - innovatie adoptie - aspiraties - matrices - landschapsarchitectuur - physical planning - regional planning - green belts - design - quality - living conditions - social welfare - projects - planning - innovation adoption - aspirations - matrices
Het ontwikkelen van bijzondere kwaliteiten in planningsprocessen, de zogenoemde magische momenten. Het doel is om de leefruimte zodanig vorm te geven dat deze zo goed mogelijk zal voldoen aan de vragen die de toekomst stelt
|Wiskunde in Werking Dl. 1: vectoren en matrices toegepast
Gee, M. de - \ 2001
Utrecht : Epsilon (Epsilon uitgaven 48) - ISBN 9789050410632 - 288
wiskunde - vectoren - matrices - studieboeken - vectoranalyse - mathematics - vectors - matrices - textbooks - vector analysis
De eerste vier hoofdstukken van dit boek komen in licht gewijzigde vorm overeen met hoofdstukken uit Wiskunde in Werking (deel 28 in deze reeks). Het vijfde hoofdstuk is wat meer verdiepend. De klassieke basisstof uit de differentiaal- en integraalrekening en de lineaire algebra is verdeeld in betrekkelijk kleine eenheden, die de student zich door zelfstudie kan eigen maken. De docent speelt hierbij eerder een begeleidende dan een docerende rol. Bij deze zelfstudie wordt tevens veel aandacht besteed aan het bestuderen van concrete voorbeelden en oefeningen. De wiskundige technieken die worden aangedragen, worden direct ingebed in toepassingen, waardoor de verbinding tussen toepassing en wiskunde zeker zo belangrijk is als de wiskunde zelf.
Using AMMI, factorial regression and partial least squares regression models for interpreting genotype x environment interaction.
Vargas, M. ; Crossa, J. ; Eeuwijk, F.A. van; Ramirez, M.E. ; Sayre, K. - \ 1999
Crop Science 39 (1999)4. - ISSN 0011-183X - p. 955 - 967.
trials - matrices
Partial least squares (PLS) and factorial regression (FR) are statistical models that incorporate external environmental and/or cultivar variables for studying and interpreting genotype × environment interaction (GEl). The Additive Main effect and Multiplicative Interaction (AMMI) model uses only the phenotypic response variable of interest; however, if information on external environmental (or genotypic) variables is available, this can be regressed on the environmental (or genotypic) scores estimated from AMMI and superimposed on the AMMI biplot. The objectives of this study with two wheat [Triticum turgidum (L.) var. durum] field trials were (i) to compare the results of PLS, FR, and AMMI on the basis of external environmental (and cultivar) variables, (ii) to examine whether procedures based PLS, FR, and AMMI identify the same or a different subset of cultivar and/or environmental covariables that influence GEI for grain yield, and (iii) to find multiple FR models that include environmental and cultivar covariables and their cross products that explain a large proportion of GEI with relatively few degrees of freedom. Results for the first trial showed that AMMI, PLS, and FR identified similar cultivar and environmental variables that explained a large proportion of the cultivar × year interaction. Results for the second wheat trial showed good correspondence between PLS and FR for 23 environmental covariables. For both trials, PLS and FR complement each other and the AMMI and PLS biplots offered similar interpretations of the GEl. The FR analysis can be used to confirm these results and to obtain even more parsimonious descriptions of the GEL
Het ontwikkelen, optimaliseren en beperkt valideren van voorbehandelings-, extractie-, en opwerkingsvoorschriften ten behoeve van het bepalen van organische verbindingen in de vaste matrices : grond, waterbodem en bouwstoffen voor de in project V24/104 ontwikkelde GCMS - voorschriften (project 105 fase 3)
Traag, W.A. - \ 1998
Wageningen etc. : RIKILT-DLO [etc.] (Rapport / Rijks-Kwaliteitsinstituut voor Land- en Tuinbouwprodukten 98.016)
organische verbindingen - analytische methoden - bodem - sediment - bouwmaterialen - matrices - gc-ms - waterbodems - organic compounds - analytical methods - soil - sediment - building materials - matrices - gc-ms - water bottoms
|Het ontwikkelen, optimaliseren en beperkt valideren van voorbehandelings-, extractie-, en opwerkingsvoorschriften ten behoeve van het bepalen van organische verbindingen in de vaste matrices; grond, waterbodem en bouwstoffen voor de in project V24/104 ontwikkelde GCMS-voorschriften. (Project 105 fase 3)
Traag, W.A. ; Zuidema, T. ; Leeuwen, M. van; Gaalen, F.R. van; Harmsen, J. - \ 1998
Wageningen : DLO-Rijks-Kwaliteitsinstituut voor land- en tuinbouwprodukten (RIKILT-DLO) (Rapport RIKILT-DLO 98.016) - 23 p.
organic compounds - analytical methods - soil - building materials - matrices - water bottoms
|Optimaliseringstechnieken: principes en toepassingen. Derde geheel herziene druk.
Hendriks, T.H.B. ; Beek, P. van; Leijster, W. de - \ 1991
Houten : Bohn Stafleu van Loghum - ISBN 9789031312412 - 348
optimalisatie - programmeren - matrices - lineair programmeren - operationeel onderzoek - transport - verkeer - wiskundige modellen - dynamisch programmeren - markov-processen - computer software - computerwiskunde - lineaire algebra - vectorruimten - veeltermen - logistiek - queuing theory - niet-lineair programmeren - optimization - programming - matrices - linear programming - operations research - transport - traffic - mathematical models - dynamic programming - markov processes - computer software - computational mathematics - linear algebra - vector spaces - polynomials - logistics - queuing theory - nonlinear programming