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Showing papers by "University of Münster published in 1975"


Journal ArticleDOI
TL;DR: Two different mathematical models for PCP-data evaluation and the autoradiographic method yielded results agreeing within statistical error, suitable for asynchronous cell populations with a low fraction of S-phase cells, and for partially synchronized cells and high S- phase fractions as well.
Abstract: Mathematical models for the analysis of pulse-cytophotometric (PCP) data are described. With computer programs based on these models the fractions of cells in G1-, S- and(G2 + M)-phases are obtained. The methods are applied to PCP measurements of Ehrlich ascites tumor cells, human bone marrow cells and L-929-cells in culture. The results of the L-cell experiment are compared with autoradiographic results; for both methods the duration of the various phases has been calculated. Two different mathematical models for PCP-data evaluation and the autoradiographic method yielded results agreeing within statistical error. The application of the two models on different types of DNA-histograms is discussed: One model is suitable for asynchronous cell populations with a low fraction of S-phase cells, the other can be applied for partially synchronized cells and high S-phase fractions as well.

576 citations



Journal ArticleDOI
TL;DR: In this article, vertical impacts of 0.3-g cylindrical plastic projectiles into noncohesive quartz sand in which vertical and horizontal reference strate were employed by using layers of colored sand were performed at velocities of 5.9-6.9 km/sec.
Abstract: Results are presented for vertical impacts of 0.3-g cylindrical plastic projectiles into noncohesive quartz sand in which vertical and horizontal reference strate were employed by using layers of colored sand. The impacts were performed at velocities of 5.9-6.9 km/sec with a vertical gun ballistic range. The craters, 30-33 cm in diameter, reveal a radial decay of the ejecta mass per unit area with a power of -2.8 to -3.5. Material displaced from the upper 15% of the crater depth d is represented within the whole ejecta blanked, material from deeper than 28% of d is deposited inside 2 crater radii, and no material from deeper than 33% of d was ejected beyond the crater rim. Shock-metamorphosed particles (glassy agglutinates, cataclastic breccias, and comminuted quartz) amount to some 4% of the total displaced mass and indicate progressive zones of decay of shock intensity from a peak pressure of 300 kbar. The shock-metamorphosed particles and the shock-induced change in the grain size distribution of ejected samples have close analogies to the basic characteristics of the lunar regolith. Possible applications to regolith formation and to ejecta formations of large-scale impact craters are discussed.

305 citations


Journal ArticleDOI
TL;DR: The in vitro and in vivo effects of copper, zinc, cadmium, nickel, cobalt, and manganese on nitrate reductase, malate dehydro-genase, isocitrate dehydrogenase, and glucose-6-phosphate dehydrogenases of zinc-, copper- and non-resistant populations of Silene cucubalus were investigated.
Abstract: The in vitro and in vivo effects of copper, zinc, cadmium, nickel, cobalt, and manganese on nitrate reductase, malate dehydro-genase, isocitrate dehydrogenase, and glucose-6-phosphate dehydrogenase of zinc-, copper- and non-resistant populations of Silene cucubalus were investigated. During the in vitro experiments no resistant enzyme could be detected; enzymes of resistant and non-resistant ecotypes had a similar sensibility to all the metals. Nitrate reductase was the most sensitive enzyme. During the in vivo experiments remarkable differences were found. The nitrate reductase and the isocitrate dehydrogenase of the zinc-resistant population were activated when adding zinc to the culture medium, especially the nitrate reductase showed high activities at zinc concentrations where the nitrate reductase of the non-zinc-resistant populations was nearly completely inhibited. The zinc-resistant ecotype had a real need for zinc.

162 citations


Journal ArticleDOI
TL;DR: Conclusions from formal histogenesis suggest that the signet ring cell type and the anaplastic (solid) type of early gastric cancer might start in the lower part of tubule necks, which could be the critical field of malignant transformation in the gastric mucosa.
Abstract: Summary Among 2003 gastric specimens from 301 patients, diagnosis for carcinoma was made in 45 cases. Examination of resection preparations revealed 36 cases of deep invasive stomach carcinoma and 9 cases of early gastric cancer confined to mucosa and/or submucosa. Carcinomatous proliferations limited to mucosa or submucosa are classified in three histologic types: intestinal (adeno), mucocellular (signet ring cell), and anaplastic (solid) type of early gastric cancer. Mixed types have been found combining the first and the second, or the second and the third type. One case presented a mixture of all three types. Possible precursor or initial stages of all three types were found in further 31 biopsies. Some of them were glandular lesions in superficial parts of the mucosa; this kind has been described previously as possible preneoplastic stage of the intestinal type of early gastric cancer. “Signet ring cell drippings” from lower parts of tubule necks were recorded as an initial form of the signet ring cell type. The process is interpreted as detaching of isolated signet ring cells from a gland neck zone in progressing atypical transformation. An early neoplastic stage of the anaplastic (solid) type of early gastric cancer is identified in the “gland neck dysplasia” located exclusively in the antrum between surface mucosa and antrum glands. This lesion appears rich in cells and stretched like a broad ribbon. Early gastric cancer of this third type will arise in the very same location. Conclusions from formal histogenesis suggest that the signet ring cell type and the anaplastic (solid) type of early gastric cancer might start in the lower part of tubule necks. In consequence, the neck region of gastric glands could be the critical field of malignant transformation in the gastric mucosa. Long-term follow-up studies will be needed to verify these observations and their interpretation.

103 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that for a sequence {an}n=la, n = 1, 2,,,... udth an --* aE A -~ -{c~(h) I c~ exists and is continuous on the right and strictly monotonic for h E (T o, T 1) } it holds that [P(Wn ~ 9Zan)] 1In ~ exp [c 0(h ) -ha], where the limit is equal to inf {exp [co(t ) -ta
Abstract: (i) ran(t) = S etW"dP ( c~ for all t E [0, T1),T 1 > O, (ii) ~n(t)/n -* Co(t) E R for all t E (To, Tx), 0 ~ T O ~ T1, where ~.(t)= in ran(t). Ther~ for auy sequence {an}n=la .... anE R , n = 1, 2 , , . . udth an --* aE A -~ -{c~(h) I c~ exists and is continuous on the right and strictly monotonic for h E (T o, T1) } it holds that [P(Wn ~ 9Zan)] 1In ~ exp [c0(h ) -ha], where the limit is equal to inf {exp [co(t ) -ta]}. t>0

99 citations


Journal ArticleDOI
TL;DR: A sequence of late replication patterns has been established in metaphase chromosomes of cultured human peripheral lymphocytes, in agreement with those obtained by the standard autoradiographic procedures, but are more accurate.
Abstract: The addition of thymidine (TdR) to cells growing in a medium containing 5-bromodeoxyuridine (BUdR) at the end of the first replication cycle results in the incorporation of TdR into the late replicating DNA regions. These sites can be visualized by staining the metaphase chromosomes with the fluorescent dye “33 258 Hoechst” or a “33 258 Hoechst” Giemsa procedure. A sequence of late replication patterns has been established in metaphase chromosomes of cultured human peripheral lymphocytes. The patterns are in agreement with those obtained by the standard autoradiographic procedures, but are more accurate. As is known from autoradiography, late replicating bands are in the position of G or Q bands. The “33 258 Hoechst” Giemsa staining procedure of chromosomes which have replicated in the presence of BUdR first and in TdR for the last 2 hrs of the S phase is preferable to the currently used Giemsa banding techniques: the method yields very well banded metaphases in all preparations examined, as the chromosome structure is not disrupted by the pretreatment. The bands are very distinct, even in the “difficult” chromosomes (e.g No. 4, 5, 8, and X). In female cells the late replicating X chromosome can be identified by its size and staining pattern. In addition to the replication asynchrony, the sequence of replication within both X chromosomes in female cells is not absolutely identical. The phenomenon of a phase difference in replication between the homologues is not a peculiarity of the X chromosome, but can be found in all autosomes as well as in homologous positions on the chromatids of individual chromosomes.

97 citations


Journal ArticleDOI
TL;DR: Investigation of subacute necrotizing encephalomyelopathy in an infant with regressing psychomotor development revealed high glycogen levels in liver tissue and skeletal muscle, which contrast with decreased gluconeogenesis, which is suggested by the diminished pyruvate carboxylase activity.
Abstract: Grobe, H., v. Bassewitz, D. B., Dominick, H.-Chr. and Pfeiffer, R. A. (Departments of Paediatrics and of Medical Cell Biology, University of Munster, Munster, and Institute of Human Genetics, Medical School, Lubeck, BRD). Subacute necrotizing en-cephalomyelopathy. Clinical, ultrastructural, biochemical and therapeutic studies in an infant. Acta Paediatr Scand, 64: 755, 1975.–Subacute necrotizing encephalomyelopathy (SNE) has been observed in an infant with regressing psychomotor development. The concentrations of alanine, pyruvate and lactate were increased in the serum and blood as well as in the cerebrospinal fluid. Pyruvate carboxylase activity was reduced in the liver tissue. An inhibitor of thiamine-pyrophosphate-ATP-phosphotransferase was present in the urine. Thiamine treatment was followed by a decrease of serum alanine and blood pyruvate and lactate, but there was no clinical improvement during a period of 17 months. Ultrastructural investigations revealed high glycogen levels in liver tissue and skeletal muscle. These findings contrast with decreased gluconeogenesis, which is suggested by the diminished pyruvate carboxylase activity. Therefore it is concluded that reduced hepatic pyruvate carboxylase activity is not the primary cause of SNE.

86 citations


Journal ArticleDOI
TL;DR: Glycogen levels and the production of metabolic end products by the fresh water bivalve Anodonta cygena were determined under aerobic and anaerobic conditions and volatile fatty acids account for about 75% of the total accumulated end products.
Abstract: 1. Glycogen levels and the production of metabolic end products by the fresh water bivalveAnodonta cygena were determined under aerobic and anaerobic conditions. 2. The glycogen content accounts for 5–14% of the dry weight. After 30 hours of aerobic or anaerobic incubation no significant glycogen breakdown could be observed. 3. L-lactate and alanine seem to be only initial end products, whereas succinate increases continuously during the first 15 hours. 4. Anodonta cygnea also accumulates volatile fatty acids during anaerobiosis. After 30 hours of anoxia 30.1 and 46.0 μmol g−1 dry weight of acetate and propionate respectively are formed. In fact the volatile fatty acids account together for about 75% of the total accumulated end products.

74 citations


Journal ArticleDOI
TL;DR: In this paper, the synthesis of all Methyl Mono-, Di-, and Tri-O-benzyl-α-D-glucopyranosides is described.

71 citations


Journal ArticleDOI
TL;DR: In this paper, the Onsager-Machlup function of a nonlinear diffusion process is calculated directly as limit of finite dimensional probability densities using the Ito calculus.
Abstract: Using Ito stochastic differential equations to describe stochastic processes the Onsager-Machlup Function of a nonlinear diffusion process is calculated. It is shown that for two examples the Onsager-Machlup Function calculated directly as limit of finite dimensional probability densities agrees with the formula derived by using the Ito calculus but differs from a formula given by Graham who used the concept of Langevin equations.

Journal ArticleDOI
TL;DR: The pathway of carbohydrate degradation was investigated inArenicola marina by injecting 14C-Uglucose into the coelom of worms after 6 and 12 hours of anaerobiosis as discussed by the authors.
Abstract: The pathway of carbohydrate degradation was investigated inArenicola marina by injecting14C-U-glucose into the coelom of the worms After 6 and 12 hrs of anaerobiosis much of the radioactivity was found to be incorporated into succinate and propionate Large amounts of both labelled metabolites also appeared in the incubation water In addition, alanine accumulated radioactivity at a very high rate under aerobic as well as anaerobic conditions No labelled lactate was detected

Journal ArticleDOI
TL;DR: In this article, a 2,3-Bis(diphenylphosphino)maleic anhydride with the aid of diphenyl(trimethylsilyl)phosphine was synthesized.
Abstract: Derivate des 2,3-Dichlormaleinsaure-anhydrids, die als Heteroatom im Funfring S, C (als ) und N (als bzw )enthalten, wurden mit Diphenyl(trimethylsilyl)phosphin in die jeweiligen 2,3-Bis(diphenylphosphino)-Derivate (3–6) ubergefuhrt, die als zweizahnige Liganden zwei CO in den Carbonylen von Ni, Cr und Mo substituieren konnen (7–14) Die freien Liganden und ihre Metallcarbonyle sind intensiv farbig Die entsprechenden Absorptionsbanden zeigen einen betrachtlichen Einflus des Heteroatoms im Funfring an Weiterhin wurde die Solvatochromie der langwelligsten Absorptionsbande in den Metallcarbonylderivaten untersucht Zu Vergleichszwecken wurden ferner 2,3-Bis(diphenylamino)-N-methylmaleinimid (15) und zwei Diphenyl-phosphinoderivate (16, 18) des 3,4-Dichlor-5-methoxy-2(5H)-furanons erstmals dargestellt Die Zuordnung von vcc ist nunmehr in allen diesen Verbindungen moglich Ihre bis zu 120 cm−1 betragende Verschiebung und die Abhangigkeit der Farben der Verbindungen von der Ausdehnung des konjugierten Systems werden diskutiert Synthesis and Properties of Derivatives fo 2,3-Bis(diphenylphosphino)maleic Anhydride as a Contribution to the Problem of Colour, Conjugation, and complex Formation of this Class of Compounds Derivatives of 2,3-bis(diphenylphosphino)maleic anhydride containing S, C (as ) and N (as or ) as heteroatom within the ring system (3–6) are prepared from the corresponding 2,3-dichloro compounds with the aid of diphenyl(trimethylsilyl)phosphine These new compounds form chelate complexes of the type Ni(CO)2 L, Cr(CO)4-L (7–14) Ligands and complexes are strongly coloured The heteroatom of the maleic anhydride ring influences remarkably the corresponding absorption bands The solvatochromic effect on the low wave number absorption band of the metal(O) complexes is examined For comparison 2,3-bis(diphenylamino)-N-methylmaleimide (15) and two diphenylphosphino derivatives (16, 18) of 3,4-dichloro-5-methoxy-2(5H)-furanone are synthesized The vcc bands of the compounds are assigned The observed shifts (up to 120 cm−1) and the dependence of the colour on the size of the conjugated system are discussed

Journal ArticleDOI
TL;DR: The results demonstrate that these neurons found in the lateral part of the buccal ganglion of Helix pomatia fulfill the requirements of a model structure and can be used for comparative studies.

Journal ArticleDOI
TL;DR: In this paper, a systematic investigation has been conducted on room temperature reactions which proceed by simultaneous uptake and loss of electrons and ions by electronically conducting solids able to act as a host matrix.


Journal ArticleDOI
TL;DR: In this paper, a single focusing magnetic sector-field mass spectrometer was used to investigate the secondary ion emissions of clean silicon, oxygen-covered silicon, silicon oxide, silicon carbide and silicon nitride.

Journal ArticleDOI
TL;DR: In this article, the dihedral angles between the electron lone-pairs are found to vary from 45 to 180°, by means of these angles certain conformations can be assigned to 1-20.
Abstract: Die Konformationen der cyclischen N,N′-Dimethylhydrazine 1–10, der cyclischen bzw. bicyclischen Hydrazine 11–17 und der 1,1′-Bicycloamine 18–20 werden anhand ihrer Photoelektronenspektren analysiert. Die ermittelten Torsionswinkel zwischen den einsamen Elektronenpaaren liegen zwischen 45 und 180°. Mit ihrer Hilfe lassen sich 1–20 bestimmte Konformationen zuordnen. Die Befunde werden mit den Ergebnissen anderer Methoden verglichen. Conformational Analysis of Aliphatic Hydrazines by Photoelectron Spectroscopy, 2. Cyclic and Bicyclic Hydrazines The conformations of the cyclic N,N′-dimethylhydrazines 1–10, of the cyclic or bicyclic hydrazines 11–17, and of the 1,1′-bicycloamines 18–20 are analysed from their photoelectron spectra. The dihedral angles between the electron lone-pairs are found to vary from 45 to 180°. By means of these angles certain conformations can be assigned to 1–20. The results are discussed with reference to literature data.

Journal ArticleDOI
TL;DR: In this article, the RGM potentials were determined by directly unfolding the associated integral kernels of the generator coordinate method, which confirmed the concept of quasi-molecular rotational states which has been used to account for the backward angle anomaly observed in elastic α-40 Ca cross sections.

Journal ArticleDOI
TL;DR: Chitin synthesis inLocusta migratoria has been examined by following the incorporation of labelled N-acetylglucosamine into chitin at different stages of the larvaladult moulting cycle from 4 days before to 8 days after ecdysis.
Abstract: 1. Chitin synthesis inLocusta migratoria has been examined by following the incorporation of labelled N-acetylglucosamine into chitin at different stages of the larvaladult moulting cycle from 4 days before to 8 days after ecdysis. With glucose high incorporation rates were measured only during the first 2 days after ecdysis. Acetylglucosamine was incorporated intensively before this period (5 to 7 times higher than glucose). After ecdysis the rate of aminosugar incorporation increases rapidly up to the level of maximum incorporation of glucose and remains at this level for one week. 2. During the days prior to imaginal ecdysis the precursors for chitin synthesis originate almost exclusively from the decomposition of the chitin of the larval cuticle. 3. A few minutes after injection of labelled glucose, acetylglucosamine, or UDP-acetylglucosamine into 24 hour adult locusts, radioactivity is detectable in all chitin precursors. These compounds are found mainly in the integument and in the hemolymph, and to a lesser extent also in the fat body. 4. Preparations of the abdominal integument incorporate chitin precursorsin vitro; under these conditions glucose is the preferred precursor.

Journal ArticleDOI
TL;DR: In this article, the frequency dependence of the admittance of insulators or high resistivity semiconductors provided with two ohmic contacts is calculated for a trap free sample and a sample with one trap level.
Abstract: The frequency dependence of the admittance of insulators or high resistivity semiconductors provided with two ohmic contacts is calculated for a trap free sample and a sample with one trap level. In the first case only a transit time effect occurs causing periodical oscillations of the conductance and the capacitance with decreasing amplitudes at frequencies ω ≫ T−1, T being the transit time. If traps are present an additional frequency dependence of the admittance due to the capture and emission of carriers occurs. For suitable energy levels the trap relaxation and the transit time effect can be separated. The low frequency value of the conductance and the voltage dependence of the low frequency value of the capacitance yield the trap concentration or the energy level, respectively, and the capture cross section of the trap. Thus a new, simple and accurate method for the determination of the capture cross section of deep levels is obtained. Der Frequenzgang der Admittanz eines Isolators bzw. hochohmigen Halbleiters mit ohmschen Kontakten wird fur den trapfreien und trapbehafteten Fall berechnet. Im trapfreien Fall tritt nur ein reiner Laufzeiteffekt auf, Leitwert und Kapazitat zeigen fur Frequenzen ωT ≫ 1 (T Laufzeit) periodische Schwankungen abnehmender Amplitude. Im trapbehafteten Fall tritt zusatzlich zum Laufzeiteffekt eine Traprelaxation im Frequenzgang der Admittanz auf. Bei geeigneter Lage der Storstelle konnen diese beiden Effekte voneinander getrennt werden. Der Wert des Leitwertes und die Spannungs-abhangigkeit des Niederfrequenzwertes der Kapazitat liefern die Konzentration, bzw. die energetische Lage und den Wirkungsquerschnitt der Storstelle, so das man auf diese Weise ein neues, einfaches und genaues Verfahren besitzt, den Wirkungsquerschnitt tiefer Storstellen zu bestimmen.

Journal ArticleDOI
TL;DR: The structure of non-stoichiometric titanium disulfide (Ti1.023S2) was refined from single crystal X-ray data as discussed by the authors, and it was shown that the additional cations are inserted in the z = 1 2 plane.

Journal ArticleDOI
TL;DR: In this article, a general method for the conformational analysis of aliphatic hydrazines from their photoelectron spectra is established and applied to the acyclic compounds 2, 9-20.
Abstract: Ein allgemeines Verfahren zur Konformationsanalyse aliphatischer Hydrazine anhand ihrer Photoelektronenspektren wird entwickelt und auf die acyclischen Verbindungen 2, 9–20 angewendet. Das Verfahren grundet sich auf eine direkte Korrelation des Torsionswinkels ϕ zwischen den beiden einsamen Elektronenpaaren mit der aus dem Photoelektronenspektrum ermittelten Aufspaltung Δϵ der beiden n-Orbitale. Quantenchemische Modellrechnungen nach der MINDO/2-Methode fuhren zu der Beziehung Δϵ = A cosϕ + B, deren Koeffizienten mithilfe von Verbindungen bekannter Konformation zu A = 2.20 eV und B = –0.15 eV bestimmt werden. Bei 2, 9–20 werden nur geringfugige Anderungen von Δϵ mit der Substitution beobachtet, sie besitzen demnach samtlich die gauche-Konformation. Conformational Analysis of Aliphatic Hydrazines by Photoelectron Spectroscopy, 1. Acyclic Hydrazines A general method for the conformational analysis of aliphatic hydrazines from their photoelectron spectra is established and applied to the acyclic compounds 2, 9–20. The method is based on a direct correlation of the dihedral angle ϕ between the two electron lone-pairs with the split Δϵ of the n-orbitals obtained from the photoelectron spectra. Quantum chemical calculations by the MINDO/2 procedure suggest the relation Δϵ = A cosϕ + B. For the coefficients the values A = 2.20 eV and B = –0.15 eV are determined from compounds of known conformations. For 2, 9–20 only minor effects of the substituents on Δϵ have been observed, therefore these compounds all exist in the gauche conformation.

Journal ArticleDOI
TL;DR: Arginine can be estimated spectrophotometrically by the oxidation of NADH usingoctopine dehydrogenase using octopine dehydrationrogenase and is applicable to the estimation of arginine in the presence of mono- and disubstituted guanidino compounds.

Journal ArticleDOI
TL;DR: In this paper, the ternary chalcogenides were obtained by the reaction of TiS 2 and NbS 2 in alkali halide melts with H 2 S, in a flow reactor system at 800−1000 °C.
Abstract: Layered ternary Sulfides, A 0.5 TiS 2 and A 0.5 .5NbS 2 (with A = Li, Na, K, Rb, Cs), were obtained by the reaction of TiS 2 and NbS 2 in alkali halide melts with H 2 S, in a flow reactor system at 800−1000 °C. On contact with water the ternary compounds give the hydrated phases, A 0.5 (H 2 O) y [TiS 2 ] and A 0.5 (H 2 O) y [NbS 2 ], with polyelectrolyte character. TaS 2 , under similar conditions, in an inert gas atmosphere yields layered tantalum sulfides A 0.3 TaS 2 . Redox reactions of transition metal complexes soluble in the halide melts are supposed to be responsible for the formation of the ternary chalcogenides.

Journal ArticleDOI
TL;DR: In this paper, the elastic and inelastic scattering of α-particles from 40, 44, 48Ca has been studied at Eα = 100 MeV between ≁ lab = 16-166°.


Journal ArticleDOI
TL;DR: Octopine dehydrogenase was purified 120-fold from adductor muscle of the fresh water bivalve Anodonta cygnea L. by gel filtration on Sephadex G-100 and chromatography on DEAE-SephadeX A 50 and hydroxylapatite.
Abstract: 1. Octopine dehydrogenase was purified 120-fold from adductor muscle of the fresh water bivalveAnodonta cygnea L. by gel filtration on Sephadex G-100 and chromatography on DEAE-Sephadex A 50 and hydroxylapatite. 2. In comparison to the purified enzyme from marine species the final preparation of the octopine dehydrogenase fromAnodonta showed similarK m (1.0 mM for arginine, 0.4 mM for pyruvate, 1.2 mM for octopine) and pH values (6.3 and 10.1 respectively) and a similar molecular weight (40 000 Dalton). 3. During electrophoresis on standard polyacrylamide gels octopine dehydrogenase showed a multiple band pattern which is due to isoenzymes. 4. Alanine, lactate and succinate had no effect on the enzyme activity. Octopine, however, inhibited it strongly (Fig. 4) 5. Thede-novo synthesis of octopine in isolated adductor muscles from14C-pyruvate was not significantly different under aerobic or anaerobic conditions.

Journal ArticleDOI
TL;DR: The spin polarization of photoelectrons emitted by thallium atoms exposed to circularly polarized light has been measured between 1400 and 1700 AA{ as mentioned in this paper, which is explained on the basis of Fano's resonance theory.
Abstract: The spin polarization of photoelectrons emitted by thallium atoms exposed to circularly polarized light has been measured between 1400 and 1700 \AA{}. The polarization curve shows a pronounced structure which is determined by the autoionization resonances. The results are explained on the basis of Fano's resonance theory.

Journal ArticleDOI
TL;DR: Calculations show that there is no difference in edge resolution at 100 keV to be expected, in agreement with experiment, and the influence of beam broadening increases relative to the chromatic error with increasing energy.