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    Optimal design for goodness-of-fit of the Michaelis-Menten enzyme kinetic function

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    We construct efficient designs for the Michaelis-Menten enzyme kinetic model capable of checking model assumption. An extended model, called EMAX model is also considered for this purpose. This model is widely used in pharmacokinetics and reduces to the Michaelis- Menten model for a specific choice of the parameter setting. Our strategy is to find efficient designs for estimating the parameters in the EMAX model and at the same time test the validity of the Michaelis-Menten model against the EMAX model by maximizing a minimum of the D- or D1-efficiencies taken over a range of values for the nonlinear parameters. In addition, we show that the designs obtained from maximizing the D-efficiencies are (i) efficient for estimating parameters in the EMAX model or the Michaelis-Menten model, (ii) efficient for testing the Michaelis-Menten model against the EMAX model and (iii) robust with respect to misspecification of the unknown parameters. --Chebyshev polynomials,EMAX model,goodness of fit test,locally D-optimal design,robust optimal design

    F. Michaelis, Nachfolger, Fabrikation: Neuheiten für Damenmode, Frankfurt-Main, Berlin, Gürtel, Pompadours, Jabots, Abt. S, Schweissblattfabrik, Kornsand & Co Frankfurt a. M.

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    F. MICHAELIS, NACHFOLGER, FABRIKATION: NEUHEITEN FÜR DAMENMODE, FRANKFURT-MAIN, BERLIN, GÜRTEL, POMPADOURS, JABOTS, ABT. S, SCHWEISSBLATTFABRIK, KORNSAND & CO FRANKFURT A. M. F. Michaelis, Nachfolger, Fabrikation: Neuheiten für Damenmode, Frankfurt-Main, Berlin, Gürtel, Pompadours, Jabots, Abt. S, Schweissblattfabrik, Kornsand & Co Frankfurt a. M. ( -

    F. Michaelis, Nachfolger, Fabrikation: Neuheiten für Damenmode, Frankfurt-Main, Berlin, Gürtel, Pompadours, Jabots, Abt. S, Schweissblattfabrik, Kornsand & Co Frankfurt a. M.

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    F. MICHAELIS, NACHFOLGER, FABRIKATION: NEUHEITEN FÜR DAMENMODE, FRANKFURT-MAIN, BERLIN, GÜRTEL, POMPADOURS, JABOTS, ABT. S, SCHWEISSBLATTFABRIK, KORNSAND & CO FRANKFURT A. M. F. Michaelis, Nachfolger, Fabrikation: Neuheiten für Damenmode, Frankfurt-Main, Berlin, Gürtel, Pompadours, Jabots, Abt. S, Schweissblattfabrik, Kornsand & Co Frankfurt a. M. ( -

    Das Tagebuch des Feldpredigers J. F. Seegebart und sein Brief an J. D. Michaelis

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    DAS TAGEBUCH DES FELDPREDIGERS J. F. SEEGEBART UND SEIN BRIEF AN J. D. MICHAELIS Das Tagebuch des Feldpredigers J. F. Seegebart und sein Brief an J. D. Michaelis ( - ) Cover ( - ) Titelseite ( - ) Dedication (i) Vorrede. (iii) Diarium bei dem Mars und Feldzuge nach Schlesien gehalten 1741 vom 14. Februar a. ej. ... (1) Diarium beym Feldzuge nach Schlesien vom 14. Februar 1741. (3) Martius. (Einmarsch in Schlesien.) (13) April. (29) Majus. (38) Junius. (46) Julius. (49) Augustus. (49) September. (56) Campagne im Jahre 1742. (60) Copia eines Schreibens [an den Professor J. D. Michaelis in Halle] aus Kuttenberg in Böhmen vom 24. Mai [1742]. (61

    Johannis Michaelis, SS. Theol. D. & Prof. Ord. ad D. Jacobi Gryphiswaldiæ Past. & Consist. Reg. Assessoris, Notæ Criticæ & Exegeticæ In Novum Testamentum

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    Præcipue quoad Hellenistica, Quas post beatum ejus obitum luci publicæ exposuit F. M. Petrus Michaelis, Past. Demmin. & Syn. Præpositus. Una cum Præfatione Joh. Fechtii, D.Die Vorlage enthält insgesamt 2 Werke. - Titelbl. in Rot- und Schwarzdr.Autopsie nach dem Exemplar der ULB HalleVorlageform des Erscheinungsvermerks: Rostochii & Lipsiæ. Apud Joh. Heinric. Rusworm. M DCC XXVIII. - Leipzig ist Messor

    Allium michaelis F. O. KHASS. & TOJIBAEV 2009, nov.sp.

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    <i>Allium michaelis</i> F. O. KHASS. & TOJIBAEV nov.sp. (sect. <i>Brevidentia</i> F. O. KHASS. & YENGAL.) <p>Bulbus solitarius ovatus 10-20 mm altus, 5-15 mm latus, tunicis brunneis coriaceis. Bulbulae paucae triangularia apice carinata. Caulis teres glaber striatus crassiusculus 10- 20 cm altus, 1,5-3 mm latus, usque ad medium glabris vaginis foliorum involutus. Folia in numero 2-3, 1- 2 mm lata semeteretia glabra flexuosa. Spatha recurvata persistens, pedicellis pluries breviora. Umbella hemisphaerica. Pedicelli subaequilongi 8-12 mm longi, ebracteolati. Perigonium campanulatum albido-viridulum apice violaceum, nervis viridibus. Tepala elliptico-ovata oblonga obtusa 3,5-4,5 mm longa, margine purpurascentibus, exteriora quam interiora breviora. Filamenta albida tepalis breviora, exteriora simplicia late basi denticulata, interiora tricuspidata, cuspidibus lateralibus ca. 1 mm longus. Antherae violaceae. Ovarium globosum purpureum. Capsula laevis 3- 4 mm in diam.</p> <p> Differt ab <i>A. haneltii</i> F. O. KHASS. & R. M. FRITSCH filamentis albis (nec violaceis), tricuspidatis (nec simplicibus), tepalis obtusatis (nec acutis) albido-viridulis (nec violaceis), caulis crassiusculis, foliis flexuosis, bulbulis apice carinatis.</p> <p>Habitat ad montium Kuramense (Asia Media Tian-Shan Occidentalis).</p> <p>Typus: Tien-Shan Occidentalis, montes Kuramensis, prope pagum Ujgursaj, N 40 54’54.1’’ E 71 03’ 27,2’’ h = 563m. s.l., 24.05.2009, Khassanov, Tojibaev, Keusgen (TASH).</p> <p>Species in honorem Prof. Dr. Michael Keusgen Marburgensis denominata est.</p> <p>Bulb solitary, ovate 10-20 mm long, 5-15 mm wide, outer tunics coriaceous, brownish. Bulblets several cymbiform keeled. Scape 10-20 cm long, 1,5-3 mm in diameter, lower half covered by smooth leaf sheaths. Leaves 2-3, 1- 2 mm thick, nearly terete, smooth, screwshaped. Spathe recurved, shorter than pedicels, persistent. Inflorescence semiglobose. Pedicels nearly equal, 8-12 mm long, without basal bracts. Flower cup shaped, whitishgreenish in the upper part violet with green nerve. Tepals elliptic ovate obtuse 3,5-4,5 mm long with purple margins, outer shorter than inner ones. Filaments whitish shorter than tepals, outer ones simple widely denticulate, inner ones tripartite with lateral cusps about 1 mm long. Anthers violet. Ovary globose purple. Capsule smooth, 3-4 mm in diameter.</p> <p> The junior author collected this species in March 2009 and it’s originality was clearly seen in the screw-shaped form of the leaves. This character is not rare in the subg. <i>Allium</i> and only Pamir-Alaian and Afghan small alliums show this character. For example, <i>A. ophiophyllum</i> VVED. (from South-western Pamir-Alai) has the same type of leaves, but this character is not stable, because within the studied populations of the above mentioned species some plants had somewhat curved leaves. Wendelbo (1971) also mentioned in the description of <i>A. spirophyllum</i> WENDELBO, that the leaves could be straight or screw- shaped. According to the purple ovary and cymbiform keeled leaves, the plants collected in 2009 could be allied to <i>A. haneltii</i>, which is growing in a distance of about 20 km closer to the main range on stony slopes. The bulblets of <i>A. haneltii</i> are attached to the middle of the bulb by the keel, and bulblets of <i>Allium michaelis</i> by the upper enlarged part (Figs 1-2). The scapes of the newly described species are clearly thick and tepals are larger and show another form (Figs. 3-4). Moreover, <i>Allium michaelis</i> is the only species of sect. <i>Brevidentia</i> having white filaments, which are shorter than the tepals. Such character has <i>A. hedgei</i> WENDELBO, growing in northern Afghanistan, but the structure and color of the filaments and bulblets are completely different. Usually, species of <i>Brevidentia</i> has strongly exserted filaments like in the case of the type species <i>A. brevidens</i> VVED. Morphologically, <i>Allium michaelis</i> and <i>A. haneltii</i> clearly belongs to sect. <i>Brevidentia</i>, but molecular data of the last taxon showed an outstanding position of Western Tian-Shanian species within subgen. <i>Allium</i> (FRIESEN et al. 2006).</p>Published as part of <i>Khassanov, F. O. & Tojibaev, K. Sh., 2009, One more new Allium L. species from the Fergan depression (Central Asia), pp. 1059-1062 in Linzer biologische Beiträge 41 (2)</i> on pages 1059-1060, DOI: <a href="http://zenodo.org/record/4523985">10.5281/zenodo.4523985</a&gt

    Neolinycus michaelis Heinrich 1971

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    Neolinycus michaelis Heinrich, 1971 (Figures 17–21) Neolinycus michaelis Heinrich, 1971: 1025 (descr.); Tereshkin 2009: 1458, 1579 (descr., fig.). Neolinycus michaelis michaelis Heinrich 1972: 210 (distr., neallotype designation); Heinrich 1977: 280 (descr., distr.); Carlson 1979: 542 (cat., distr., syn.); Yu and Horstmann 1997: 677 (cat.); Schmidt and Schmidt 2011: 86 (cat.); Yu et al. 2016 (cat.). Neolinycus michaelis georgianus Heinrich, 1972: 210 (descr.); Heinrich 1977: 281 (descr., distr., key); Carlson 1979: 542 (cat., distr., syn.); Yu and Horstmann 1997: 677 (cat.); Schmidt and Schmidt 2011: 86 (cat.); Yu et al. 2016 (cat.). Synonymised under the nominate subspecies by Carlson (1979: 542). Neolinycus michaelis arkansae Heinrich, 1977: 282 (descr.); Yu and Horstmann 1997: 677 (cat.); Schmidt and Schmidt 2011: 86 (cat.); Yu et al. 2016 (cat.). Hereby regarded as a synonym of the nominate subspecies. Original type series Holotype ♀ of L. michaelis michaelis, by original designation (ZSM); holotype ♀ of L. michaelis georgianus, by original designation (ZSM); holotype ♂ L. michaelis arkansae, by original designation in (ZSM); paratype: 1♂ L. michaelis arkansae (ZSM). Type locality United States of America, Mississippi, Lafayette Co., Water Valley (L. michaelis michaelis); Georgia, Monroe Co., Forsyth (L. michaelis georgianus); Arkansas, Garaland Co. (L. michaelis arkansae). Type specimens examined (Figures 17–19) Holotype of L. michaelis michaelis: ‘[White Label] Water Valley/Lafayette Co./Mississ. U.S.A. / 5.–10. VIII 70. // Neolinycus / michaelis ♀ /det. Heinrich Hein. // [Red Type] Holotype // [Pink Label] Zoologische Staatssammlung/München/Type-No.: ZSM-Hym-00443’ (images examined). Holotype of L. michaelis georgianus: ‘[White Label] Forsyth, Monroe Co./ Georgia, U.S.A. / 7.–27. VIII 19 71 [originally 1969, then overwritten “71”]/[White Label] Neolinycus / ♀ michaelis /georgianus /det. Heinrich Hein. // michaelis /georgianus/72 det. G. Heinrich Hei. // [Red Type] Holotype // [Pink Label] Zoologische Staatssammlung/ München/Type-No.: ZSM-Hym-00444’ (ZSM) (images examined). Holotype L. michaelis arkansae: ‘[White Label] Arkansas, USA /Garland Co./ 12-17. May 72 // [White Lable] Neolinycus / michaelis /arkansae ♂ /det. Heinr. Heinr. //’ [Red Type] Holotype // [Pink Label] Zoologische Staatssammlung/München/Type-No.: ZSM-Hym-00445” (ZSM) (examined). Material examined UNITED STATES OF AMERICA, FLORIDA: USA, FL, Alachua Co., Gainsville, Pierce’s Homestead, S 9-T10S-R18E, Malaise Trap, 01 November 1974, leg. W.H. Pierce, 1♀ (FSCA); idem, 03 November 1973, 1♂ (FSCA); idem, 09 May 1974 1♀ (FSCA); Alachua Co., San Felasco Hammock, Insect Flight Trap, 22 April 1977, leg. G.B. Fairchild & H.V. Weems, 1♀ (FSCA); Gainsville, Doyle Conner Building, Malaise Trap, 03 September 1973, leg. E. E. Grissell, 1♀ (FSCA); idem, 06 November 1973, 1♀ (FSCA); idem, 24 October 1973, 1♀ (FSCA); idem, 21–25 April 1975, 1♀ (FSCA); Baker Co., Glen St. Mary, Rural Yard / Mxd Woods, Malaise trap, 30 November 2006, leg. E. Zoll & S. Fullerton, 1♀ (UCFC); idem, 16 November 2006, 1♀ (UCFC); idem, 05 April 2007, 1♂ (UCFC); Clay Co., Gold Head State Park, Ravine Hardwoods, 20 March 1995, leg. C. Porter & L. Strange, 19♂♂ & 1♀ (FSCA) (wrongly identified as Cyclolabus carolinensis by Porter); idem, 05 May 1995, 1♂ (FSCA); idem, 07 October 1996, 1♂ (FSCA); idem, 15February–12 March 1997, 3♂♂ (FSCA); idem, 15 March–02 April 1997, 3♂♂ & 1♀ (FSCA); idem, 1–15 May 1997, 2♂♂ (FSCA); idem, June 1997, 2♂♂ (FSCA); idem, July 1997, 2♂♂ & 1♀ (FSCA); idem, Ravine-mixed woods, 15 May 1996, 14♂♂ & 1♀ (FSCA); idem, 05–26 April 1996, 7♂♂ (FSCA); idem, 02 April–15 May 1997, 13♂♂ & 4♀♀ (FSCA); Collier Co., Naples, Tr.17, 10 March 1988, leg. Belmont, 11♂♂ & 1♀ (FSCA); idem, 29 June 1987, 5♂♂ (FSCA); idem, 31 May 1987 2♂♂ & 1♀ (FSCA); idem, 22 July 1987, 3♂♂ & 1♀ (FSCA); idem, 02 August 1987, 1♂ (FSCA); idem, 24 May 1987, 5♂♂ (FSCA); Columbia & Baker Co. Line, Osceola Nat. For., Jct. Rt. 90, Malaise Trap, 29 March–13 April 1977, leg. J.R. Wiley, 1♂ (FSCA); Gadsen Co., Quincy, NFREC, 28 July 1989, leg. Gupta, 1♂ (FSCA); Lake Co., Green Swamp, W. M. Dist., 08 May 1987, leg. Nigg., 1♂ (FSCA); idem, 28 August 1987, 1♀ (FSCA); GEORGIA: Athens, Bot. Garden M.Tr., 05 May 1983, leg. Gupta, 1♂ (FSCA); idem, 05 June1983, leg. Gupta, 2♂♂ (FSCA). Updated distribution (Figure 21) UNITED STATES OF AMERICA: Arkansas (Heinrich 1977), Florida (new state record), Georgia (Heinrich 1972), Louisiana (Heinrich 1972), Mississippi (Heinrich 1971), Tennessee (Heinrich 1977). Host Unknown. Male The first description of a male was provided by Heinrich (1972, p. 210), who referred to the specimen as the neallotype. Comments Heinrich (1971, p. 1025) described the genus Neolinycus and the species N. michaelis based on a single female from Mississippi (Figure 17). The same author, a year later, described a new subspecies, Neolinycus michaelis georgianus Heinrich, 1972, based on a female from Georgia that was ‘Chromatically strikingly different, particularly by color of mesoscutum and pleuron’ (Figure 18) (Heinrich 1972, p. 210). According to Heinrich (1972), N. michaelis georgianus differs from the nominotypical subspecies by the following characters: black mesoscutum (orange in michaelis); longitudinal white lines running across the mesoscutum (small and reduced in michaelis); mostly orange pleura (mostly white in michaelis); white prescutellar carinae (orange in michaelis). In the same work, he also described the male of N. michaelis michaelis for the first time, acknowledging the presence of slight infuscation of the metasoma on tergites 2–5, and the different colouration of the mesoscutum, with the lateral lobes black and the median lobe orange. Later on, Heinrich (1977, p. 282) proposed another new subspecies, Neolinycus michaelis arkansae, this time based on two male specimens from Arkansas (Figure 19), that differ from the other two subspecies by: the entirely black mesoscutum (character revised below); the black bands on metasoma covering more than half of 2–5 tergites; the mostly white mesopleuron; prescutellar carinae not white marked. The differences among all these subspecies are summarised in Table 1. Carlson (1979, p. 542) synonymised N. michaelis georgianus without providing any evidence or comments for the new proposed treatment and failed to list N. michaelis arkansae in his catalogue of Ichneumoninae of North America. It is not clear whether Yu et al. (2016) reocrded Carlson’s (1979) treatment and considered the subspecies georgianus to be a synonym. Reading Heinrich (1972, 1977), it is pretty clear that the author’s subspecies hypotheses are mostly based on two factors: colour pattern and distribution. After studying the type specimens of the different subspecies, we realised that the ‘entire mesoscutum black’ that Heinrich (1977, p. 282) listed among the characters important for the separation of N. michaelis arkansae from the other two subspecies is incorrect: two reduced white stripes are clearly present on the mesoscutum, and the pin simply obscures part of them (Figure 19a). The character has been revised in Table 1. Moreover, we have also analysed several specimens of Neolinycus from Florida and Georgia, and the same specimens that Porter (2003) examined and wrongly identified as Cyclolabus carolinenesis Heinrich, 1962. Because of this new material, we provide here three lines of evidence that, when analysed together, falsify the subspecies concepts proposed by Heinrich and that support both Carlson’s (1979) synonymisation and the establishment of a further new junior synonym N. michaelis michaelis = N. michaelis arkansae. The first evidence derives from the observation of specimens that have a colour pattern halfway between the purportedly different subspecies. For instance, a male specimen from Florida has tergites 2–5 of the metasoma infuscate (condition considered diagnostic for N. michaelis michaelis) but associated with a complete black mesoscutum with well-developed longitudinal white lines (condition considered diagnostic for N. michaelis georgianus) (Figure 20a–b). Nine male specimens have very reduced longitudinal white lines on the mesoscutum that are partially red (median lobe) and partially black (lateral lobes) (typical of males of N. michaelis michaelis) but with black bands covering more than half of tergites 2–5 (typical of N. michaelis arkansae) (Figure 20c–d). Eight other females fitting the colour pattern expected for the latter subspecies were collected among male specimens with colour pattern halfway between N. michaelis georgianus and N. michaelis arkansae. The second line of evidence is composed of specimens collected in the ‘wrong range’ – that is, the range expected/ascertained/assumed to be that of the other subspecies. This is the case for four males that correspond to the holotype of N. michaelis arkansae and were collected in Georgia, which is the typical range of N. michaelis georgianus. The third line of evidence is composed of specimens well matching with the colour pattern expected for two different subspecies but collected together in the same location. This is the case for a female that agrees chromatically with the definition of N. michaelis michaelis by having an orange mesoscutum with very reduced white longitudinal stripes but was collected in Florida among specimens matching the colour pattern of N. michaelis georgianus (Figures 20e–f). From all the above evidence, it is clear that a continuum in colour pattern and distribution exists, and the subspecies cannot be unequivocally differentiated based either on consistent morphological traits or on clear distributional patterns. Therefore, we hereby regard for the first time N. michaelis arkansae as a junior synonym of N. michaelis michaelis and confirm the synonymisation by Carlson (1979) of N. michaelis georgianus with N. michaelis michaelis. Heinrich (1971, p. 1025) reported Michael Horan as the collector of the type for N. michaelis. There is no collector information on the labels (Figure 17c). Heinrich (1972, p. 210) reported F. Naumann as the collector of the type for N. michaelis georgianus. There is no collector information on the labels (Figure 18c).Published as part of Dal Pos, Davide, Heilman, Victoria & Welter-Schultes, Francisco, 2022, Platylabini (Hymenoptera: Ichneumonidae: Ichneumoninae) of the south-eastern United States: new distributional data, taxonomic notes, illustrated keys, and an annotated catalogue of the genera and species, pp. 1869-1938 in Journal of Natural History 56 on pages 1896-1903, DOI: 10.1080/00222933.2022.2134061, http://zenodo.org/record/739761
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