Boekbespreking: M.J. Beeson: Foundation of constructive mathematics. Rootselaar, B. van  \ 1986
Zentralblatt fur Mathematik (1986). 

Boekbespreking Foundation of constructive mathematics; Mathematical studies by M.J. Beeson Rootselaar, B. van  \ 1985
Zentralblatt fur Mathematik (1985). 

Boekbespreking Nearrings by G. Pilz Rootselaar, B. van  \ 1985
Mededelingen van het Wiskundig Genootschap 28 (1985).  p. 141  141. 

How to solve the system x?=Ax Rootselaar, B. van  \ 1985
American mathematical monthly 92 (1985).  p. 321  326. 

Output formulas for constant linear systems Rootselaar, B. van  \ 1984
Wageningen : LH  8 differentiaalvergelijkingen  intergraalvergelijkingen  differential equations  integral equations


Bernard Bolzano Gesamtausgabe 2B 3/1 Rootselaar, B. van; Lugt, A. van der  \ 1983
StuttgartBad Commstatt : Frommann Verlag  216 p. 

Einleitung Rootselaar, B. van  \ 1983
In: Bernard Bolzano Gesamtausgabe 2B 3/1 (1983) 1133, StuttgartBad Commstatt, Frommann Verlag (Holzboog) 

Disjunctive linear operators and partial multiplications in Riesz spaces Putten, B. van  \ 1980
Landbouwhogeschool Wageningen. Promotor(en): B. van Rootselaar.  Wageningen : Van Putten  101 functionaalanalyse  functional analysis
In dit proefschrift worden lineaire operatoren op Riesz ruimten bestudeerd, in het bijzonder disjunctieve lineaire operatoren. Enkele voorbeelden van niet orde begrensde disjunctieve lineaire operatoren van een Riesz ruimte op zichzelf worden gegeven, terwijl de orde begrensde disjunctieve lineaire operatoren in verband worden gebracht met een partieel gedefinieerde vermenigvuldigingsoperatie in de Riesz ruimte.
Hoofdstuk I geeft een inleiding in de theorie van Riesz ruimten. In hoofdstuk II worden enkele typen van convergentie bestudeerd in verband met lineaire operatoren. Disjunctieve lineaire operatoren worden in hoofdstuk III bestudeerd. In het bijzonder wordt aandacht geschonken aan disjunctieve lineaire functionalen en orde begrensde disjunctieve lineaire operatoren van een Archimedische Riesz ruimte met een sterke orde eenheid op zichzelf. In hoofdstuk IV worden Riesz ruimten bestudeerd die voorzien zijn van een vrij star gedefinieerde vermenigvuldigingsstructuur, de zogenaamde falgebra's. Enige overeenkomsten en verschillen tussen Riesz homomorfismen en ring homomorfismen worden aangegeven en een variant van de stelling van EllisPhelps wordt afgeleid. Met behulp van de in hoofdstuk V ontwikkelde theorie van inverteren en worteltrekken in regulator complete Φalgebra's wordt een generalisatie verkregen van bovengenoemde stelling. In hoofdstuk VI worden partiële vermenigvuldigingsoperaties op Archimedische Riesz ruimten met een zwakke orde eenheid axiomatisch ingevoerd. Op iedere Archimedische Riesz ruimte met sterke orde eenheid wordt tenslotte een intrinsieke partidle vermenigvuldiging aangegeven en in verband gebracht met de ruimte van alle orde begrensde disjunctieve lineaire operatoren van de Riesz ruimte op zichzelf. 

12 reviews in Mathematical en Zentralblatt fur Mathematik Rootselaar, B. van  \ 1979
Zentralblatt fur Mathematik (1979). 

Lineaire algebra Rootselaar, B. van  \ 1979
Groningen : Worters Noordhoff  ISBN 9789001763510 

Bernard Bolzano Rootselaar, B. van; Lugt, A. van der  \ 1979
In: Miscellanea Mathematica 1 + 2, Zweiter Teil 

Bernhard Bolzano, Miscellanea Mathematica 1+2 Rootselaar, B. van; Lugt, A. van der  \ 1977
Stuttgart : Unknown Publisher 

Dictionary of Scientific Biography XIV Rootselaar, B. van; Zermelo, E.F.F.  \ 1976
New york (1976).  ISSN 00287369  p. 613  616. 

Dictionary of Scientific Biography XIII Rootselaar, B. van; Turing, A.M.  \ 1976
New york (1976).  ISSN 00287369  p. 497  498. 

Annals of Systems Research Vol 5 Rootselaar, B. van  \ 1976
Unknown Publisher 

Analyse 2 en een half Rootselaar, B. van  \ 1976
Groningen : Tjeenk Willink  ISBN 9789001763527  220 p. 

A contribution to theory and practice of nonlinear parameter optimization Stol, P.T.  \ 1975
Landbouwhogeschool Wageningen. Promotor(en): B. van Rootselaar.  Wageningen : Pudoc  ISBN 9789022005620  197 testen  schatting  testing  estimation
Nonlinear parameter optimization in least squares was studied from a point of view of differential geometry. Properties of curvilinear coordinates, scale factors and curvature were investigated. Parameters of the condition function were expressed as functions of algorithm parameters to generalize the formulas. The analysis of the convergence process cumulated in the development of procedures that accelerate convergence. Scale factors were used as weights to the differential correction vector to improve the direction of search. A method to correct for curvature, called back projection method, was developed. Use was made of the tangent plane on which the path of search on the fitting surface was projected. Deviations from the original direction were corrected by optimizing the angle of deviation and the step factor. The correspondence between rate of convergence and curvature of the path of search was illustrated with an example. A small geodesic curvature at the starting point indicates fast convergence. Curvature properties of the parametric curves appeared to be of more influence than those of the fitting surface. To avoid heavy oscillation of intermediate parameter values a method was developed that required the intermediate points to be the foot of a perpendicular from the terminal point of intermediate observation vectors thus producing paths of controlled approach. Since condition functions may have a complicated structure in that they can be implicit functions, sequential functions or can consist of mathematical models involving alternative functions, it was treated how first derivatives can be calculated and programmed systematically for these functions. Methods introduced were made operational by means of a FORTRAN program. A description of the use of the subprograms and instructions to modify the main program to suit the various algorithms and procedures developed are given in the Appendices. 

Informatiesystemen en het besturen van ondernemingen Nielen, G.C.J.F.  \ 1969
Wageningen University. Promotor(en): B. van Rootselaar; M. Euwe.  Alphen aan de Rijn : Samsom  119 bedrijfsvoering  leiderschap  organisaties  computers  minicomputers  microcomputers  gegevensverwerking  plantenecologie  theorie  bestuur  bedrijfseconomie  machines  management  leadership  organizations  computers  minicomputers  microcomputers  data processing  plant ecology  theory  administration  business management  machines
In a complex management environment, the events to be controlled cannot be comprehended within a reasonable time. The different aspects of the events, however, may be grouped into modules, which can be controlled as one unit. This type of control is influenced by the dependence of modules. This dependence may result where the controlling of one aspect limits the choice in another aspect. If these limitations exist within one module, the control is not impaired; if they exist from module to module, the modules are dependent ('bound foreign aspects' are not controlled by us, but they limit the choice in the control of our module). Decision making for a module demands data, both for the 'indigenous' aspects of the module and for its bound foreign aspects. The data take the following form: 'reports' describe the situation to depart from, 'orientations' the decisions from the modules that limit our choice, 'extrapolations' the most probable outcome of uncontrolled aspects. These three types of data are combined and evaluated to form 'predictions' which describe the course of events as accurately as possible. For every module there also is a 'statute' containing the rules (prescribed or discretionary) that govern the actions of the controlling unit of the module. The statute and predictions are combined to yield a 'decision' that is published as a plan insofar as it implies limitations elsewhere. After some delay, necessary for the dependent modules to react to this plan (for them an orientation) the decision is executed or implemented (to be executed by others). The 'term' of a module is the average time needed to initiate the execution of a decision with respect to the aspects in that module. A close relationship must exist between the term of a module and the time needed to change the initial situation to the desired situation. This relationship is used to determine the allowable term of a module and hence, depending also on the kind of aspects, its size. The formation of modules leads to a management structure that is subject to a number of efficiency criteria: viz. economy, completeness, consistency and 'power' (the number of aspects that are controlled within a given time). The enhancement of the 'power' of a management unit ought to be considered as the primary objective of measures to change the structure or to accellerate the data processing. Structural measures consist of lodging new aspects in modules or of joining and splitting existing modules into new ones. It appears necessary to continually reorganise a management structure. A management structure is not homogeneous; there are 'lower' and 'higher' modules. The latter comprise those aspects which cause numerous limitations and are therefore considered important. Important aspects usually are concurrent with a long term of the module: this is not always the case. The relations between management units are determined by the relative superiority of their decisions: superior meaning 'close to reality, workable' rather than 'close to an ideal'. Units that frequently publish superior decisions become dominant in the structure; the control of higher modules must be realised by dominant units. The prescribed part of the statute of a module originates with a number of dominant modules; not with one 'boss'. In this concept of a management structure there is no place for notions like 'span of control', 'vertical hierarchy', 'staff and line functions' etc. In our idea, a structure appears as a dynamic, pyramidical form in which a number of modules exist with multiple connections of different kinds for the exchange of information. The term of a module is partly determined by the information technique employed in and between the management units. Fast processing of data leads to bigger modules, more power, a better approximation of completeness and perhaps to more economic control. These results can only be reached if the better information technique is supplemented by the appropriate structural changes. Data processing is an ubiquitous activity: it appears useful to define some of its concepts in detail. First we introduce an information system as being a set of data with a corresponding separation function to divide sets of data into three subsets: useful within the system; useful outside the system, useless. We then recognize 'observations' (data to be appended to the system) 'messages' (data to be released by the system) and 'experience' (data retained by the system at a given moment). Observations contain information, if the experience is changed as a result of the processing of that observation. Within the set 'experience' we recognize the subset 'procedures'; it is the description of all functions that can be applied in the system. Part of the procedures  the construction  cannot be changed without altering the system; the remaining part of the procedures  the instructions  can be modified within the system. Some procedures are described exactly; they are programs. Other procedures are described insufficiently, or not at all; some are even indescribable as yet. Computers can execute all data processing, including modification of instructions, provided the procedures are nothing but programs. The abstract formulation of the concept information system leads to the mathematical descriptions of system, subsystem, union of systems, and intersection of systems. An algebra of systems can now be developed for stationary systems (no modification). An interesting kind of information system is the control system, that contains in its experience a realised model of a module of aspects. The observations of a control system concern the indigenous and bound foreign aspects of the module, the messages give rise to the fixing of the indigenous aspects. The definition of module (assuming the simultaneous control of all aspects) implies that control systems cannot have a union and cannot be split. Subsystems of control systems, however, can be integrated into a union of systems. The information technique as it exists in a management structure can be improved in several ways. Qualitative improvement can be made' by the application of refined models, by a decrease in the delays that render predictions useless and by an increase in the consistency of reporting. Quantitative improvement can be made by an increase in data processing speed. Fast information techniques can result from three measures: standardization, integration, mechanization; these measures are sometimes interchangeable and, moreover, partly interdependent. Standardization is the effort to use identical components in different systems; integration is the development of systems that comprise a number of (sub)systems; mechanization is our word for the application of computers in information systems. Each of these measures has advantages and disadvantages, not necessarily all systems must be standardized, integrated and mechanised. The concept 'total system' is not useful. Integration appears efficient where systems serve dependent modules and have common components (files or procedures). The time needed to develop an integrated system, however, can be too long with a view to the rapidly changing demands. (In the next decade this is the case.) Computers offer the opportunity to design systems with intricate procedures and yet a short response time. Through the use of remote and multiple input/ output equipment and a central memory the consistency of the data can be insured. An integrated, mechanised information system for a management structure (MIB) can supply the reports, the orientations, the extrapolations and the analyses of tentative decisions for a number of control systems. The human element in such a system demands that the computer element responds immediately to tentative decisions. A constraint of this nature suggest a random access memory organisation: one possibility is to employ the chain addressing method. The specifications of the computer for a MIB are such that we may expect these systems in the near future. 

Met wiskundige zekerheid Rootselaar, B. van  \ 1963
Wageningen : Unknown Publisher  14 wiskunde  mathematische logica  verzamelingenleer  mathematics  mathematical logic  set theory
Rede Wageningen
