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Showing papers by "University of Münster published in 1979"


Book ChapterDOI
TL;DR: In this article, second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems with constraints defined by closed convex cones are given, which are an immediate generalization of those known for the finite-dimensional case.
Abstract: Second-order necessary and sufficient optimality conditions are given for infinite-dimensional programming problems with constraints defined by closed convex cones. The necessary conditions are an immediate generalization of those known for the finite-dimensional case. However, this does not hold for the sufficient conditions as shown by a counterexample. Modified sufficient conditions are developed for the infinite-dimensional case.

256 citations



Journal ArticleDOI
TL;DR: In this article, X-ray photoelectron spectroscopy (XPS, ESCA) has been applied to sodium phosphate glasses with compositions between 15 and 50 mol% Na2O and for the purpose of comparison also to crystalline compounds containing oxygen and phosphorus.
Abstract: X-ray photoelectron spectroscopy (XPS, ESCA) has been applied to sodium phosphate glasses with compositions between 15 and 50 mol% Na2O and for the purpose of comparison also to crystalline compounds containing oxygen and phosphorus. From the measurements a discrimination between bridging and non-bridging oxygen atoms was possible. The method provides a quantitative technique for structural analysis of phosphate glasses.

199 citations


Journal ArticleDOI
01 Jul 1979
TL;DR: In this article, the analytic spread of an ideal I of a noetherian local ring (R, m) is shown to be of asymptotic nature, i.e. depends on the modules In/mIn = Un only for large n.
Abstract: In (3), corollary, p. 373) Burch gives the following inequality for the analytic spread l(I) of an ideal I of a noetherian local ring (R, m):In this paper we shall improve this by showing that the number min depth (R/In) may be replaced by the asymptotic value of depth (R/In) for large n (which exists) (see Section (2)). By its definition (see (6), def. 3)) the analytic spread is of asymptotic nature, i.e. depends on the modules In/mIn = Un only for large n. We shall prove a stronger result, Section (4), which also shows the asymptotic nature of l(I). This result might be interesting for itself, particularly as it is not of local nature. Once Section (4) is proved and once we know that depth (R/In) is asymptotically constant (which turns out to be an easy consequence of (1), (1)), our improved inequality is easily established: Indeed, replacing R by R/xR where x is regular with respect to almost all modules (R/In), we perform a change which affects only finitely many of the modules Un (see Section (8)).

192 citations


Journal ArticleDOI
TL;DR: In this article, the authors extended Aronson's and Weinberger's concept of asymptotic speed to the nonlinear integral equation t J g(u(t-s,x+y))k(s9\\y\\)dsdy, which is a spatial version of Kermack's and McKendrick's epidemic model.
Abstract: Recently Aronson [1] extended the concept of asymptotic speed which he and Weinberger [3], [4] had developed for nonlinear diffusion problems in population genetics, combustion and nerve propagation, to an epidemic model proposed by Kendall [11], [12] in 1957 (1965). In this model (which is a spatial version of Kermack's and McKendrick's epidemic model [13]) the aflfected individuals become immediately infectious and are removed at a constant rate. The model does not take into account that with most infectious diseases the affected individuals underlie an incubation period, before they become infective, and that they remain infective for a fixed period only. These features cannot be described by the equation considered by Aronson [1] which contains a derivative with respect to time and an integral with respect to space. It is therefore desirable to extend Aronson's and Weinberger's concept of asymptotic speed to the nonlinear integral equation t J g(u(t-s,x+y))k(s9\\y\\)dsdy

159 citations


Journal ArticleDOI
TL;DR: In this paper, a review of electron-photon angular correlations resulting from electron impact of atoms and molecules is given, and the theory of measurement of particle angular correlations is outlined in the following way.

148 citations


Journal ArticleDOI
TL;DR: In this paper, the authors use the concept of asymptotic speed to estimate the asymptic behavior of the solution of a nonlinear integral equation (with the nonlinearity not being monotone), which describes the development of a spatially distributed population.
Abstract: In this paper we use Aronson's and Weinberger's [1–4] concept of asymptotic speed to estimate the asymptotic behaviour of the solution of a nonlinear integral equation (with the nonlinearity not being monotone), which describes the development of a spatially distributed population.

133 citations


Journal ArticleDOI
TL;DR: In this paper, the authors give a general foundation for the theory of quadratic and hermitian forms over rings with involution, and show how to solve a number of important classification problems of linear algebra.

125 citations



Journal ArticleDOI
TL;DR: Fibronectin was detected by indirect immunofluorescence on primary cultures of rat hepatocytes maintained in the presence of fetal calf serum and isolated by immunoprecipitation and visualized by fluorography.

103 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the 7Li nuclear magnetic relaxation time T1 and of the broad line spectra over a wide temperature range for binary and ternary alkali silicate, alkali borate, and alkali phosphate glasses.


Journal ArticleDOI
TL;DR: Adsorptive endocytosis of lysosomal enzymes by fibroblasts and hepatocytes involves binding to cell surface receptors that recognize on lysOSomal enzymes a phosphorylated carbohydrate, most likely a mannose 6-phosphate residue.
Abstract: Adsorptive endocytosis of lysosomal enzymes by fibroblasts and hepatocytes involves binding to cell surface receptors that recognize on lysosomal enzymes a phosphorylated carbohydrate, most likely a mannose 6-phosphate residue [Kaplan et al. (1977) Proc. Natl Acad. Sci. U.S.A. 74, 2026–2030; Ullrich et al. (1978) Hoppe-Seyler's Z. Physiol. Chem. 359, 1591–1598]. Loss of α-N-acetylglucosaminidase endocytosis after treatment with endoglucosaminidase H indicated that the recognition site of α-N-acetylglucosaminidase is located on N-glycosidically linked oligosaccharides of the high mannose type. Acidic oligosacchrides with an average molecular weight of 2200 were liberated from α-N-acetylglucosaminidase by endoglucosaminidase H. These oligosaccharides were susceptible to degradation by alkaline phosphatase, α-mannosidase and β-N-acetylglucosaminidase. At the non-reducing terminal these oligosaccharides bear phosphorylated mannose and/or N-acetylglucosamine residues.

Journal ArticleDOI
TL;DR: The Teilkomplexe werden als submarine, abyssische bis bathyale Deckenergusse im Bereich ozeanischer Kruste gedeutet as discussed by the authors.
Abstract: Der mehrere Kilometer machtige, im wesentlichen aus ozeanischen Basalten aufgebaute Komplex von Nicoya, der den Sockel der zahlreichen pazifischen Halbinseln von Costa Rica und Panama bildet, wird biostratigraphisch zum ersten Mal in sechs, altersmasig sehr verschiedene Teilkomplexe (Subkomplexe) gegliedert (Abb. 33). Methodisch ist dies durch Extrapolation der markierenden Alterswerte moglich, wobei die in die Basalte eingeschlossenen sedimentaren Xenolithe aufgrund ihrer Mikrofauna ein Maximalalter, die normal lagernden hangenden Sedimente uber den Basalten ein Minimalalter des vulkanischen Ereignisses liefern. Damit wird bewiesen, das sich der Komplex, im Gegensatz zu den bisherigen Vorstellungen, sehr diskontinuierlich in der Zeit vom Oberjura bis in das Eozan gebildet hat. Die Teilkomplexe werden als submarine, abyssische bis bathyale Deckenergusse im Bereich ozeanischer Kruste gedeutet. Bei diesen Vorgangen wurden die inzwischen auf den liegenden Eruptiva abgelagerten Sedimente aufgearbeitet und in Form von Xenolithen innerhalb des sich neu bildenden Eruptionskorpers in eine vollig ortsfremde Umgebung verschleppt. Es wird angenommen, das sich die primare, also an einem mittelozeanischen Rucken gebildete, ozeanische Kruste erst im Liegenden dieser Teilkomplexe befindet. Abschliesend wird ein geotektonisches Modell (Abb. 34) vorgestellt, das im Einklang mit den vorliegenden Daten steht. Der Komplex von Nicoya wird als der nicht subduzierte Rest eines aseismischen Schwellensystems angesehen, der durch plate boundary jumping, also unter Verlagerung der Plattengrenze (Mittelamerika-Graben) nach W, an den sudzentralamerikanischen Inselbogen angefugt wurde.

Journal ArticleDOI
01 Jan 1979-Planta
TL;DR: Starch phosphorylase activity in extracts of spinach or pea leaves and of isolated chloroplasts was determined and separated by electrophoresis in polyacrylamide gels.
Abstract: Starch phosphorylase activity in extracts of spinach or pea leaves and of isolated chloroplasts was determined and separated by electrophoresis in polyacrylamide gels. In spinach leaf extracts, a specific activity of 16 nmol glucose 1-phosphate formed per min per mg protein was found, whereas a lower value (6 nmol per min per mg protein) was observed in preparations of isolated chloroplasts which were about 75% intact. In the spinach leaf extracts two forms of phosphorylase were found; chloroplast preparations almost exclusively contained one of these. In pea leaf extracts the specific activity was 10 nmol glucose 1-phosphate formed per min per mg protein. Three forms of phosphorylase contributed to this activity. Preparations of isolated chloroplasts with an intactness of about 85% exhibited a lower specific activity (5nmol per min per mg protein) and contained two of these three phosphorylase forms.

Journal ArticleDOI
TL;DR: The inhibitory effect of gangliosides is specific for high affinity uptake and not detectable on skin fibroblasts deficient in low-rho-lipoprotein receptor.
Abstract: The (high-affinity receptor)-mediated uptake of homologous low-density (low-rho) lipoproteins by cultured human arterial smooth muscle cells or human skin fibroblasts is controlled by the sialic acid content of low-rho lipoprotein particles This conclusion is derived from the following results 1 Gangliosides incubated with native low-rho lipoproteins associate with low-rho lipoprotein particles Low-rho lipoproteins modified by associated GLac1, GGtet1, and GGtet2b + GGtet3 gangliosides are internalized by arterial smooth muscle cells at a rate up to 80% lower than native low-rho lipoproteins or those preincubated with desialized gangliosides 2 The inhibitory effect of gangliosides is specific for high affinity uptake and not detectable on skin fibroblasts deficient in low-rho-lipoprotein receptor 3 Desialyzed low-rho lipoproteins are internalized by smooth muscle cells up to 100% faster than native low-rho lipoproteins, the enhancement of uptake corresponding to the degree of desialization

Journal ArticleDOI
TL;DR: In this paper, a new type of paramagnetic complexes is obtained from Co2(CO)8 or Mn2(Co)10 and 2,3-bis-(diphenylphosphino)maleic anhydride or its derivatives (PP).
Abstract: 2,3-Bis(diphenylphosphino)maleinsaure-anhydrid bzw. Derivate hiervon (PP) reagieren mit Co2(CO)8 und Mn2(CO)10 unter Spaltung der Metall-Metall-Bindung und Substitution von CO zu neuartigen paramagnetischen Komplexen der Formel (PP)Co(CO)3 (1 – 4) und (PP)Mn(CO)4(5). Bei normaler komplexchemischer Bindung der Elektronenpaardonoren enthalten die Valenzschalen des Co und Mn ein Elektron mehr, als der Kryptonschale entspricht. IR-, ESR- und Kristallstrukturuntersuchungen zeigen, das dieses ungepaarte Elektron auf den Phosphinliganden delokalisiert ist, der damit zu einem komplex gebundenen Radikalanion wird. Durch Oxidation von 1 bzw. 5 mit Iod werden ionische Iodide (6, 7) gebildet. Die Umsetzung des Phosphinliganden mit Fe2(CO)9 bzw. Co(CO)3NO fuhrt zu den elektroneutralen Komplexen (PP)Fe(CO)3(8) und (PP)Co(CO)NO (9). Synthesis, Properties, and Crystal Structures of Paramagnetic Carbonyl Derivatives of Cobalt and Manganese with 2,3-Bis(diphenylphosphino)maleic Anhydride and Related Phosphines as Ligands A new type of paramagnetic complexes is obtained from Co2(CO)8 or Mn2(CO)10 and 2,3-bis-(diphenylphosphino)maleic anhydride or its derivatives (PP). Their composition is (PP)Co(CO)3 (1–4) and (PP)Mn(CO)4(5). The valence shell of Co and Mn would contain one electron more than the crypton shell, if all donor atoms of the ligands contribute one electron pair in the normal way of carbonyl and phosphine complexes. It is shown by ESR, IR, and X-ray examinations, that this unpaired electron is delocalized on the phosphine ligand turning the latter to a complex-bonded radical anion. With iodine the paramagnetic complexes 1 or 5 are oxidized to cations forming iodides (6, 7). The reaction of Fe2(CO)9 and Co(CO)3NO with the phosphine ligand yields the electroneutral complexes (PP)Fe(CO)3(8) and (PP)Co(CO)NO (9).

Book ChapterDOI
TL;DR: In this article, the authors describe some recent aspects of the complex metabolism and degradation of phenolic constituents in higher plants, and the concept behind this field of research is the assumption that phenolic plant constituents are not metabolically inactive storage products simply accumulating during the whole life of a plant, but are subject to relatively rapid turnover and degradation.
Abstract: This chapter describes some recent aspects of the complex metabolism and degradation of phenolic constituents in higher plants. The concept behind this field of research is the assumption that phenolic plant constituents are not metabolically inactive storage products simply accumulating during the whole life of a plant, but are subject to relatively rapid turnover and degradation. This assumption is in contrast to previous ideas63, 76, 94and is based on a wide variety of experimental data3, 5, 6, 7, 26, 77, 94. These involve observations that various phenols or flavonoids found in seeds or young seedlings disappear completely upon germination3, 5, 36, 94. Certain phases of intensive growth are accompanied by substantial qualitative and/or quantitative changes in the spectrum of phenolics and these can only usually be interpreted by assuming catabolic processes to be involved. Various tracer studies5, 26have established the fact that both synthesis and turnover occur and that they occur simultaneously in the same plant. Phenol metabolism must be regarded, therefore, as a dynamic system involving steady-state concentrations of the various end products.


Journal ArticleDOI
TL;DR: In this article, the thermal intercalation of pyridine with 2H-TaS2 is associated with redox reactions involving guest layers and host molecules, and the reaction product is discussed in terms of a novel ionic bonding concept.

Journal ArticleDOI
TL;DR: The amount of OT-A necessary to completely inhibit protein synthesis in hepatoma tissue culture cells (HTC) is determined and its activity on DNA and RNA synthesis is tested and the capability of this amino acid for reversion of the mycotoxin action is tested.

Journal ArticleDOI
TL;DR: In this article, the cyclocarbonylation of vinyloxiranen to unsaturated δ-lactones has been verified and studied mechanistically by use of organometallic model reactions.
Abstract: Anhand metallorganischer Modellreaktionen wurde die Cyclocarbonylierung von Vinyloxiranen zu ungesattigten δ-Lactonen untersucht. Die photochemisch initiierte Komplexierung von Vinyloxiranen 1 (X = O) an Fe(CO)5 verlauft mehrstufig und fuhrt zu diastereomeren cis- bzw. trans-Ferralactonen 2. Vertreter beider Verbindungstypen (2k, 2 k′) wurden kristallographisch charakterisiert und chemisch bezuglich ihres Verhaltens gegenuber Nucleophilen und Elektrophilen studiert. Mit primaren Aminen bilden sich Ferralactame 7 unter Wanderung des Allylsystems sowie unter Konfigurationsumkehr an C-1 und C-4, was den exo-Angriff des Amins an C-4 des Allylsystems beweist. Bei Einwirkung von HO⊝ hingegen zerfallen Ferralactone zu CO⊝ und Dien-komplexen 10, wobei lediglich an C-1 eine Konfigurationsumkehr beobachtet wird. In diesem Fall greift HO⊝ somit an einer terminalen Carbonylgruppe an. Elektrophile bewirken die Spaltung der CO-O-Bindung unter Bildung von Allyl-Kationen (14, 16). Die Carbonylierung von Ferralactonen fuhrt in aprotischen Losungsmitteln in guten Ausbeuten zu ungesattigten S-Lactonen (12). Am Isoprenepoxid wurde gezeigt, das auch die homogenkatalytische Cyclocarbonylierung von Vinyloxiranen gute Ausbeuten an δ-Lactonen ergibt und dieses Verfahren fur Synthesen von Interesse ist. Organic Syntheses by Means of Transition Metal Complexes, 8 - Synthesis of Unsaturated δ-L-Lactones from Vinyloxiranes and Carbon Monoxide via Transition Metal Complexes The transition metal-assisted carbonylation of vinyloxiranes to unsaturated δ-lactones has been verified and studied mechanistically by use of organometallic model reactions. The light induced complexation of vinyloxiranes 1 by Fe(CO)5 was shown to be a multistep reaction in which diastereomeric cis-resp. trans- ferralactones 2 are formed. Complexes of both types (2k, 2k′) were characterized crystallographically and studied chemically concerning their reactions with nucleophiles and electrophiles. Reaction with primary amines gives ferralactames 7 by migration of the allyl group and inversion at C-1 as well as C-4 indicating an attack of amine at the exo-position of C-4. On the other hand the reaction with HO⊖ leads to the formation of CO⊝ and diene complexes 10 with inversion at C-1 only, indicating that the reaction has been initiated by attack of HO⊖ at a terminal carbonyl group. On electrophilic attack ferralactones form allyl cations (14, 16) by opening of the CO – O bond. Carbonylation of ferralactones with CO in aprotic solvents give good yields of unsaturated δ-lactones (12). In the case of isoprene epoxide it has been shown that homogeneous catalytic cyclocarbonylation of vinyloxiranes can be of synthetic use.

Journal ArticleDOI
TL;DR: Seeds of Moringa peregrina (Moringaceae), on treatment with myrosinase, produce 2-propyl, 2-butyl and 2-methylpropyl isothiocyanate in addition to 5,5-dimethyl-oxazolidine-2-thione, all new to the family but known as natural derivatives from other sources.

Journal ArticleDOI
TL;DR: In this paper, the authors used agents for reductive cleavage of disulfide crosslinks and suitable proteolytic enzymes to achieve DNA-proportional uptake of fluorochromes.
Abstract: Methods are given for the preparation and staining of human spermatozoa for flow cytometric DNA measurements. Using agents for the reductive cleavage of disulfide crosslinks and suitable proteolytic enzymes an effective decondensation of the sperm chromatin and a DNA-proportional uptake of fluorochromes is achieved. Thus reliable and precise measurements of the relative DNA content of human spermatozoa are possible and the two subpopulations of haploid spermatozoa can be distinguished according to the difference in their DNA content.

Journal ArticleDOI
TL;DR: In this paper, it is shown that besides the HOMO-LUMO energy difference, the diene 1,4 distance plays an important part for the rate of reaction.
Abstract: Die Reaktivitat von Cyclopentadien und cis-fixierten Di-exo-methylenverbindungen in Diels-Alder-Reaktionen wird im Rahmen des Grenzorbitalmodells untersucht. Es wird gezeigt, das neben der Energiedifferenz der dominanten Grenzorbitalwechselwirkung auch der Dien-1,4-Abstand eine wichtige Funktion besitzt. Je kurzer dieser ist, umso reaktiver ist das Dien. Dies zeigt die Kinetik der Umsetzung von Tetracyanethylen und Maleinsaureanhydrid mit Cyclopentadien und den Di-exo-methylenverbindungen 2–6, deren 1,4-Abstand auf Grund von Kraftfeldrechnungen bekannt ist. Zwischen 1,4-Abstand des Diens und log k2 der Cycloaddition besteht ein linearer Zusammenhang, der sich theoretisch begrunden last. Significance of Diene-1,4-Distance on the Reactivity in Diels-Alder Reactions The reactivity of cyclopentadiene and di-exo-methylene compounds in Diels-Alder reactions is investigated using the frontier molecular orbital method. It is shown that besides the HOMO-LUMO energy difference the diene 1,4-distance plays an important part for the rate of reaction. The shorter this distance is the higher becomes the reactivity. Experimentally this is shown by the rates of reaction of tetracyanoethylene and maleic anhydride with cyclopentadiene and di-exo-methylene compounds 2–6. The 1,4-distance of the latter is known from force field calculations. 1,4-Distance and log k2 exhibit a linear relationship which is supported by theoretical considerations.

Journal ArticleDOI
TL;DR: In this paper, the isotope effect for self-diffusion in cobalt was measured at seven temperatures in the range 1451 to 1745 K by means of the standard radio-tracer method using lathe sectioning in the paramagnetic and sputter sectioning of the ferromagnetic region.
Abstract: Self-diffusion in cobalt is investigated from 896 to 1745 K by means of the standard radio-tracer method using lathe sectioning in the paramagnetic and sputter sectioning in the ferromagnetic region. The diffusion coefficients vary between about 10−17 cm2 s−1 and 10−9 cm2 s−1; their temperature dependence can be described by DT = 0.55 exp (−2.99 eV/kT) cm2 s−1. In contrast to iron no influence of the magnetic order−disorder transition on the diffusivity is observed within the experimental accuracy. The isotope effect for self-diffusion is measured at seven temperatures in the range 1451 to 1745 K. Its magnitude and its decrease with increasing temperature indicate that diffusion occurs mainly via monovacancies with an increasing but small contribution of divacancies with increasing temperature. In Kobalt wird die Selbstdiffusion mit radioaktiven Isotopen von 896 bis 1745 K untersucht, wobei die Schichtenteilung im paramagnetischen Bereich mit Hilfe der Drehbank und im ferromagnetischen Bereich mit einer Zerstaubungs-Methode durchgefuhrt wurde. Die Diffusionskoeffizienten variieren zwischen 10−17 und 10−9 cm2 s−1 und ihre Temperaturabhangigkeit kann durch DT = 0,55 exp (−2,99 eV/kT) cm2 s−1 beschrieben werden. Im Gegensatz zum Eisen wurde kein Einflus des magnetischen Ordnungs–Unordnungs-Ubergangs auf die Diffusion innerhalb der experimentellen Genauigkeit gefunden. Der Isotopieeffekt der Selbstdiffusion wurde bei sieben Temperaturen im Bereich 1451 bis 1745 K gemessen. Seine Grose und seine Abnahme mit zunehmender Temperatur weisen darauf hin, das die Diffusion vorwiegend uber Leerstellen erfolgt und das mit zunehmender Temperatur ein zunehmender, jedoch kleiner Anteil von Doppelleerstellen beigemischt ist.

Journal ArticleDOI
TL;DR: Paramyosin of 5-HT treated catch muscles is phosphorylated 2 to 4 times better than paramyos in of ACh treated or untreated catch muscles, andCytoplasmatic protein kinases show a higher affinity towards paramYosin as a phosphoryl acceptor thanprotein kinases associated with paramyOSin.
Abstract: 1. InMytilus edulis two proteins of the contractile apparatus can be phosphorylated by cyclic AMP dependent protein kinases: a 295,000 d protein of unknown function, and paramyosin. 2. Paramyosin isolated from thick filaments by the selective extraction method contains the 106,000 d monomer only, whereas paramyosin extracted from ethanol ether dried powder contains equal amounts of the 108,000 d, and the 106,000 d monomers, and traces of the 104,000 d monomer. 3. Paramyosin isolated from ethanol ether dried powder incorporates up to four times the amount of32P than paramyosin isolated by the selective extraction method. 4. Cytoplasmatic protein kinases show a higher affinity towards paramyosin as a phosphoryl acceptor than protein kinases associated with paramyosin. 5. Paramyosin of 5-HT treated catch muscles is phosphorylated 2 to 4 times better than paramyosin of ACh treated or untreated catch muscles.

Journal ArticleDOI
TL;DR: The ultrastructure of the freshwater flagellateTetraselmis cordiformis Stein (Chlorophyceae) was investigated and the general morphology could be described as typical prasinophycean (PrasinophyCEae sensuChristensen) and the organism shares all generic characteristics of Platymonas West.
Abstract: The ultrastructure of the freshwater flagellateTetraselmis cordiformis Stein (Chlorophyceae) was investigated. The general morphology could be described as typical prasinophycean (Prasinophyceae sensu Christensen) and the organism shares all generic characteristics ofPlatymonas West. The flagellar apparatus has been examined in detail. The four flagella emerge from an apical trough in the theca and are arranged in a zig-zag row. They are covered by three types of scales. Four cruciate flagellar roots of compound type are present. One part is microtubular (4-2-4-2 system) and the other prominent part is fibrillar with distinctive cross striations. The four roots are short and terminate at the bottom of the apical through, where they attach the flagellar apparatus to the theca. The four-stranded root shows no changes in root tubule configuration. In addition to the cruciate root system there are two massive rhizoplasts. The rhizoplasts exhibit different striation patterns along their length. Taxonomic implications and flagellar root system structure as it relates to current theories of evolution in green algae are discussed.

Journal ArticleDOI
H. Maurer1
TL;DR: In this article, the results of [9] were applied to obtain upper and lower bounds for the directional derivative of the extremal value function as well as necessary and sufficient conditions for the existence of such a derivative.
Abstract: This paper deals with optimal control problems subject to differentiable perturbations in the objective function and constraints. The results of [9] are applied to obtain upper and lower bounds for the directional derivative of the extremal value function as well as necessary and sufficient conditions for the existence of the directional derivative. In particular, the results show the close connection between the multipliers of the Minimum Principle and the sensitivity of the optimal value with respect to perturbations.