bluuebunny/crossref_metadata_2025 huggingface dataset:
Über Glucosaminide
Authors: Zervas Leonidas , Konstas Stefanos
Published: June 2007

N‐Diphenylphosphoryl(DPP)–(X) und N‐Anisal‐O‐tetraacetyl‐β‐D‐glucosamin (VIII) werden mit Bromwasserstoff/Eisessig in die entsprechenden α‐1‐Bromverbindungen XII bzw. XIV übergeführt, die ihrerseits mit Hydroxyverbindungen, Alkoholen oder Zuckerderivaten, zu β‐Glucosaminiden (XV, XVII) umgesetzt werden. Anschließend werden die N‐Schutzgruppen entfernt, die DPP‐Gruppe durch katalytische Abhydrierung der Phenylgruppen (PtO2 als Katalysator), wobei gleichzeitig infolge der eintretenden sauren Reaktion auch die PN‐Bindung hydrolytisch gesprengt wird, die Anisalgruppe durch Zusatz von 1 Mol. starker wäßriger Säure. Die N‐DPP‐β‐Glucosaminide können ferner erst mit benzylalkoholischem Ammoniak zu N‐Dibenzylphosphoryl(DBP)‐β‐glucosaminiden umgeestert und dann katalytisch hydriert (Pd als Katalysator) werden, wobei wiederum nicht nur der Phosphorsäurerest entbenzyliert, sondern auch gleichzeitig die PN‐Bindung hydrolytisch gespalten wird.
Über Pentacarbonylmangan(—I)‐Verbindungen
Authors: Hieber Walter , Schropp Wilhelm
Published: June 2007

Salze des Mangancarbonylwasserstoffs mit komplexen Kationen können im Gegensatz zu denen des Kobaltcarbonylwasserstoffs und der Eisencarbonylwasserstoffe wegen der sehr schwachen Säurenatur des Carbonylhydrids nur in stark alkalischen Lösungen dargestellt werden. So führen Umsetzungen in wäßrigalkalischen Lösungen von Alkali‐pentacarbonylmanganaten mit Tri‐o‐phenanthrolin‐nickel(II)‐, ‐eisen(II)‐, wie auch mit Dibenzolchrom(I)‐ und Dicyclopentadienylkobalt(III)‐Salzen zu den entsprechenden unlöslichen Verbindungen [Ni(C12H8N2)3][Mn(CO)5]2, [Fe(C12H8N2)3][Mn(CO)5]2, [Cr(C6H6)2][Mn(CO)5] und [Co(C5H5)2][Mn(CO)5]. Bemerkenswert erscheint u. a. der leichte Redox‐Zerfall des [Cr(C6H6)2][Mn(CO)5] in Mangancarbonyl und Dibenzolchrom(0), während [Co(C5H5)2][Mn(CO)5] bei höherer Temperatur unzersetzt sublimiert werden kann. — Umsetzungen von Alkali‐pentacarbonylmanganaten mit Quecksilber(II)‐cyanid, Quecksilbersulfat oder Organoquecksilberbasen führen zur Bildung von Mangancarbonylquecksilber, [Mn(CO)5]2Hg. Die sehr stabile, unlösliche Verbindung, die in ihrem chemischen Verhalten dem Eisencarbonyl‐quecksilber sehr ähnlich ist, bildet mit Quecksilber(II)‐halogeniden praktisch undissoziierte Additionsverbindungen [Mn(CO)5]2Hg·HgX2 bzw. Mn(CO)5HgX (X = Cl, Br, J). — Die Infrarot‐Spektren der Verbindungen werden verglichen und diskutiert.
Zur Kenntnis der Reaktionen des Kobalttetracarbonyls mit verschiedenartigen Basen, VII. Reaktionen des Kobaltcarbonyls mit Verbindungen des 3‐wertigen Phosphors und seiner Homologen
Authors: Hieber Walter , Freyer Walter
Published: June 2007

In Fortführung der Versuche über phosphinhaltige Kobaltcarbonyle hat sich ergeben, daß der Reaktionsverlauf von der speziellen Art des Phosphins, d. h. den am Phosphor gebundenen organischen Resten, abhängt. So entstehen mit Triäthyl‐ und Tricyclohexyl‐phosphin bevorzugt (ca. 10°) die 2‐ionigen Verbindungen [Co(CO)3L2][Co(CO)4] (L = P(C2H5)3, P(C6H11)3); nur bei höherer Temperatur (ca. 35°) und in indifferenten Mitteln bildet sich das betr. echte Derivat des Kobaltcarbonyls [Co(CO)3L]2, das mit Triphenylphosphin auch schon bei tieferer Temperatur entsteht. Häufig liegen Gemische beider Verbindungstypen vor. — Mit Triphenyl‐arsin und ‐stibin sind die gleichfalls bei tieferer Temperatur (0°) gebildeten 2‐ionigen Verbindungen nur labil und wandeln sich spontan unter CO‐Abgabe in die echten Derivate um. — Ergänzende weitere Versuche wurden mit Mangancarbonyl und der 2‐zähligen Base Äthylen‐bis‐[diphenylphosphin] und mit Rheniumcarbonyl und Triphenylphosphin durchgeführt. Im letzteren Fall erhält man das diamagnetische Monosubstitutionsprodukt [Re(CO)4P(C6H5)3]2.
Untersuchungen über Stilbene, XXVI. Unsymmetrische Diaryl‐äthylene
Authors: Drefahl Günther , Ponsold Kurt
Published: June 2007

Darstellung und Eigenschaften von unsymmetrischen 1.2‐Diaryl‐äthylenen werden beschrieben.
Untersuchungen über Stilbene, XXVII. Stilbazole mit höheren aromatischen Ringsystemen
Authors: Drefahl Günther , Ponsold Kurt , Gerlach Eberhard
Published: June 2007

Darstellung und Eigenschaften von 1‐pyridyl‐ bzw. 1‐Chinolyl‐2‐aryl‐äthylenen werden beschrieben.
Untersuchungen über Stilbene, XXIX. Stilbenyl‐oxazole
Authors: Drefahl Günther , Engelmann Ulrich
Published: June 2007

Die Darstellung stilbenyl‐, α‐naphthyl‐ und phenylsubstituierter Oxazole wird beschrieben und das Ergebnis ihrer UV‐spektroskopischen Untersuchung diskutiert.
Untersuchungen über Stilbene, XXXI. Additionsreaktionen an α‐Nitro‐stilbene
Authors: Drefahl Günther , Ehrhardt Heinz
Published: June 2007

Die Bromwasserstoff‐, Hydroxylamin‐ und Ammoniak‐Addition an α‐Nitrostilbene wird beschrieben und durch sterische Zuordnung der Reaktionsprodukte der Additionsverlauf aufgeklärt.
Aminoalkohole, VII. Sterische Verhältnisse bei der Komplexbildung mit 2‐Amino‐cyclohexanolen
Authors: Drefahl Günther , Zimmermann Heinz , Gehrke Klaus
Published: June 2007

Während die beiden diastereomeren 2‐Amino‐cyclohexanole gegen methanolische Kobalt(II)‐chloridlösung praktisch gleiches Verhalten zeigen, lassen sich durch Einführung großer Substituenten bestimmte Konstellationen dieser Aminoalkohole mit unterschiedlichen komplexchemischen Eigenschaften stabilisieren.
Aminoalkohole, IX. Notiz zur stereochemischen Zuordnung der 3‐Amino‐camphanole‐(2) mittels Komplexbildung
Authors: Drefahl Günther , Zimmermann Heinz , Kurze Joachim
Published: June 2007

Auf Grund ihres unterschiedlichen komplexchemischen Verhaltens lassen sich die diastereomeren 3 endo‐Amino‐camphanole‐(2) schnell und eindeutig sterisch zuordnen.
Aminoalkohole, X. Addition von Jodisocyanat an unsymmetrische Olefine
Authors: Drefahl Günther , Ponsold Kurt
Published: June 2007

Der sterische Verlauf der Jodisocyanat‐Addition an Δ1‐Dihydro‐naphthalin und Inden wird untersucht, und Umwandlungsprodukte der Additionsverbindungen werden beschrieben.
Additionsreaktionen der NN‐Doppelbindung, IV. Zum Mechanismus der Phenylhydrazinsynthese nach E. Fischer
Authors: Huisgen Rolf , Lux Rudhard
Published: June 2007

Die Reduktion des Benzol‐diazosulfonats zu dem ebenfalls als Zwischenstufe bekannten Phenylhydrazin‐N‐sulfonat erfolgt vermutlich über eine Addition von Sulfit an die NN‐Doppelbindung. Kinetische Messungen der Bildung des p‐Nitrophenylhydrazin‐disulfonats aus p‐Nitrobenzol‐anti‐diazosulfonat sprechen gegen eine Radikalketten‐Addition, sind aber mit einer nucleophilen Anlagerung des Sulfits vereinbar.
Über Carbobromierung, III. Carbobromierung einiger Olefine und benzoider sowie nicht benzoider Aromaten
Authors: Treibs Wilhelm , Orttmann Harry
Published: June 2007

Ketten‐ und Ringolefine sowie benzoide Aromaten werden durch Oxalylbromid in Carbonsäurebromide übergeführt. Aus nichtbenzoiden Aromaten entstehen je nach den Reaktionsbedingungen Glyoxylsäure‐ oder unter CO‐Abspaltung Carbonsäurebromide. Der Reaktionsmechanismus der Carbobromierung und ‐chlorierung wird diskutiert.
Notiz zur Darstellung des Diphenochinons und einiger Derivate sowie des Stilbenchinons
Authors: König Karl‐Heinz , Schulze Werner , Möller Günther
Published: June 2007

Es werden verbesserte Darstellungsmethoden für die Synthese des Stilbenchinons, des Diphenochinons und einiger Derivate beschrieben.
Untersuchungen über 1‐Triphenylmethyl‐imidazole, II
Authors: Giesemann Heinz , Lettau Herbert , Mannsfeldt Hans‐Günter
Published: June 2007

Das beim Schmelzen des 1‐Triphenylmethyl‐4.5‐diphenyl‐imidazols entstehende Umlagerungsprodukt wurde als 2‐Triphenylmethyl‐4.5‐diphenyl‐imidazol erkannt. Bei der Reaktion zwischen 4.5‐Diphenyl‐imidazol‐silber und Triphenylchlormethan in siedendem absol. Toluol und Xylol entsteht teilweise, in Biphenyl bei 230° ausschließlich, das 2‐Triphenylmethyl‐4.5‐diphenyl‐imidazol. Das 1‐Triphenylmethyl‐4.5‐bis‐[p‐biphenylyl]‐imidazol lagert sich beim Erhitzen ebenfalls zur 2‐Triphenylmethyl‐Verbindung um. Eine Reihe von 1‐Triarylmethyl‐4.5‐diaryl‐imidazolen zersetzt sich beim Schmelzen zum Imidazol‐Derivat und nicht isolierbaren Reaktionsprodukten des Triarylmethyl‐Restes.
Untersuchungen über 1‐Triphenylmethyl‐imidazole, III
Authors: Giesemann Heinz , Oelschlägel Anneliese , Pfau Harald
Published: June 2007

Die Silbersalze von 2.4.5‐trisubstituierten Imidazol‐Derivaten reagieren mit Triphenylchlormethan infolge sterischer Hinderung nicht. 2‐Substituierte Imidazol‐Derivate lassen sich dagegen in 1‐Stellung tritylieren. Bei der Tritylierung des 2‐Phenyl‐imidazols entsteht das 2‐Phenyl‐4(5)‐triphenylmethyl‐imidazol als Nebenprodukt. Beim Erhitzen des 1‐Triphenylmethyl‐2‐phenyl‐imidazols auf die Schmelztemperatur lagert sich der Triphenylmethylrest ebenfalls in die 4(5)‐Stellung um. — 4(5)‐Phenyl‐ und 2.4(5)‐Diphenyl‐imidazol werden aus sterischen Gründen nur zu den 1.4‐Verbindungen trityliert. — Das Silbersalz des 2‐tert.‐Butyl‐imidazols reagiert mit Triphenylchlormethan unter Bildung des 2‐tert.‐Butyl‐4(5)‐triphenylmethyl‐imidazols, da die Substitution in 1‐Stellung infolge sterischer Hinderung nicht möglich ist.
Zur Kenntnis der Glykolate der Eisengruppe
Authors: Nast Reinhard , Rückemann Helmut
Published: June 2007

Es wird gezeigt, daß die seit langem bekannte Dismutation des Glyoxals zu Glykolsäure zur Darstellung von Schwermetallglykolaten verwendet werden kann. Sowohl die Hydroxyde als auch die Carbonate von Kobalt(II) und Nickel(II) werden von siedenden, wäßrigen Glyoxallösungen unter Bildung von Kobalt(II)‐glykolat bzw. Nickel(II)‐glykolat gelöst. Unter gleichen Bedingungen kann auch Eisen(III)‐hydroxyd in Eisen(II)‐glykolat übergeführt werden, wobei der Dismutation eine Reduktion von Eisen(III) durch Glyoxal vorausgeht. Der gemessene Paramagnetismus der festen Glykolate dieser Metalle zeigt, daß es sich um Anlagerungskomplexe handelt.
Äthinierungsreaktionen, XII. Äthinierung substituierter Anthrachinone
Authors: Ried Walter , Lukas Helmut
Published: June 2007

Die Äthinierungsreaktion wird an einer Reihe substituierter Anthrachinone untersucht, die Ergebnisse werden unter Zuhilfenahme der IR‐Spektren diskutiert und interpretiert.
Über Ferrocen‐pyrrol‐methinfarbstoffe
Authors: Treibs Alfred , Zimmer‐Galler Roswitha
Published: June 2007

Pyrrolaldehyde kondensieren mit Ferrocen, Ferrocenaldehyde mit Pyrrolderivaten zu Ferrocenyl‐pyrryl‐methinfarbstoffen.
Über Barbitursäure‐pyrrol‐methine
Authors: Treibs Alfred , Zimmer‐Galler Roswitha
Published: June 2007

Barbitursäure und ihre N‐Methylderivate kondensieren mit Pyrrolaldehyden und deren Vinylogen zu charakteristischen Methinderivaten.
Über halogen‐ und stickstoffhaltige Derivate aliphatischer Carbonsäuren, II. Indirekte Bromierung von Estern Anwendung auf Ester der Adipinsäure
Authors: Reinheckel Heinz
Published: June 2007

Die in der I. Mitteil. an Fettsäureestern beschriebene indirekte Bromierung von Estern wird auf Derivate der Adipinsäure übertragen. Mischungen von Adipinsäure‐monomethylester‐chlorid mit ‐dimethylester und von Adipinsäure‐dichlorid mit ‐dimethylester werden praktisch ebenso leicht bromiert wie Halbesterchlorid allein. Die Ausbeute an α‐Brom‐adipinsäure‐dimethylester (Veresterung der Gemische bei Aufarbeitung) ist bei Verwendung von Halbester‐chlorid am besten. Die „gemischte”︁ Bromierung des Diesters mit Buttersäure‐chlorid ist trotz schlechterer Ausbeute (im Vergleich zum Halbester‐chlorid) infolge ihrer Einfachheit zu empfehlen.
Über das Verhalten der Desbase aus 1.4.4‐Trimethyl‐piperidin
Authors: Lukeš Rudolf , Hofman Jiří
Published: June 2007

Das Hydrobromid dei aus 1.4.4‐Trimethyl‐piperidin (II) dargestellten Desbase 1‐Dimethylamino‐3.3‐dimethyl‐penten‐(4) (III) lieferte bei der Bromaddition das 1‐Dimethylamino‐3.3‐dimethyl‐4.5‐dibrom‐pentan‐hydrobromid (V) und die daraus freigesetzte Base cyclisierte sich anstatt zu einem Pyrrolidinderivat unerwartet zum 1.1.4.4‐Tetramethyl‐3‐brom‐piperidiniumbromid (VII). Weitere Umwandlungsprodukte dieser Stoffe werden beschrieben.
Zur Kenntnis des Lärchenharzes Die Diterpene Larixylacetat und Larixol
Authors: Wienhaus Heinrich , Pilz Wolfgang , Seibt Hermann , Dässler Hans‐Günther
Published: June 2007

Die IR‐spektroskopische Untersuchung eines neuen, aus dem Harz von Larix europaea D. C. gewonnenen Diterpenesters und des durch Verseifung erhaltenen Glykols wird beschrieben. Die Ergebnisse der Oxydation und der Dehydrierung des Alkohols werden diskutiert.
Zur Chemie der kondensierten Phosphate und Arsenate, XXXI. Über die Umsetzung von Phosphorsäure und phosphorsauren Salzen mit Acetylchlorid und Acetanhydrid
Authors: Grunze Ingrid , Thilo Erich , Grunze Herbert
Published: June 2007

Die primären Phosphate des Natriums und Kaliums lassen sich durch Acetanhydrid quantitativ in die entsprechenden Trimetaphosphate überführen. – Bei der Einwirkung von Acetylchlorid und Acetanhydrid auf Monophosphorsäure werden Acetylderivate von Polyphosphorsäuren gebildet.
Cyclisation homologer Sesquiterpensäuren, III. Über die säurekatalysierte Cyclisation der Homofarnesylsäure
Authors: Lucius Günther
Published: June 2007

Die Synthese der Homofarnesylsäure und ihre säurekatalysierte Cyclisation zu drei kristallisierten carbobicyclischen (±)‐Lactonen wird beschrieben.
Mittlere Ringe, XVI. Eigenschaften und Konfiguration der 1.4‐Benz‐lactame
Authors: Huisgen Rolf , Ugi Ivar
Published: June 2007

Aluminiumbromid ist dem Aluminiumchlorid als Kondensationsmittel bei der innermolekularen Friedel‐Crafts‐Acylierung von ω‐Phenyl‐fettsäurechloriden zu 1.2.3.4‐Benzo‐cycladien‐(1.3)‐onen‐(5) (I, n = 13–20) überlegen. – Durch Beckmann‐Umlagerung mit Benzolsulfochlorid und Pyridin werden aus den Oximen der Ringketone I die 1.4‐Benz‐lactame IV, n = 15–21 erhalten. Aus den UV‐ und IR‐Absorptionsspektren geht hervor, daß IV, n = 15–17 in festem Zustand (IV, n = 15–18 in Lösung) in der cis‐Amidkonfiguration vorliegen und daß ihre Acylanilid‐Mesomerie durch „mittlere Ring‐Effekte”︁ in unterschiedlichem Maße gestört ist. Ab IV, n = 18 (resp. n = 19) ist die Amidgruppe trans‐konfiguriert und weitgehend coplanar mit dem Benzolkern. Kinetische Messungen der Bromsubstitution der 1.4‐Benz‐lactame, die Basizitätskonstanten sowie die Umlagerungsgeschwindigkeiten der N‐Nitroso‐1.4‐benz‐lactame werden diskutiert.
Derivate der Zucker‐mercaptale, XXII. Alkylthio‐α‐D‐ribofuranoside und ihre Überführung in die Acetobrom‐D‐ribofuranose
Authors: Zinner Helmut , Koine Axel , Nimz Horst
Published: June 2007

Die Acetobrom‐D‐ribofuranose läßt sich in guter Ausbeute aus D‐Ribosemercaptalen über die Alkylthio‐α‐D‐ribofuranoside synthetisieren. Alkylthio‐α‐L‐arabopyranoside und Alkylthio‐β‐D‐xylopyranoside werden aus zugehörigen Acetobrom‐pentosen dargestellt.
Unmittelbare Cyanierung der Ferriciniumsalze
Authors: Nesmejanow A. N. , Perewalowa E. G. , Jurjewa L. P.
Published: June 2007

Ferriciniumsalze lassen sich auch in saurem Medium nur mit geringer Ausbeute cyanieren, besser mit flüss. Blausäure in Tetrahydrofuran. Das Ferrocen‐carbon‐säurenitril entsteht aber in 80‐proz. Ausb., wenn man das Ferriciniumsalz durch Ferrocen und FeCl3 ersetzt. Bei der gleichen Reaktion mit Alkylferrocen tritt die CN‐Gruppe in den substituierten Cyclopentadienyl‐Ring; sie sucht den unsubstituierten Ring auf, wenn man vom Monochlorferrocen oder Ferrocen‐carbonsäurenitril ausgeht.
Notiz über die Störung des Proazulen‐Nachweises mit Bromdampf‐Chloroform durch Hydrindene mit angularer Methylgruppe
Authors: Mayer Roland , Held Peter
Published: June 2007

Hydrindene mit angularer Methylgruppe verfärben sich wie Proazulene mit Bromdampf in Chloroformlösung intensiv blauviolett und täuschen Azulenbildner vor.
Spontaneous navigational strategies and performance in the virtual town
Authors: Etchamendy Nicole , Bohbot Veronique D.
Published: June 2007

The 4‐on‐8 virtual maze provides evidence for variability in spontaneous strategy use during navigation. Functional magnetic resonance imaging (MRI) confirmed that these spatial and response strategies rely on the hippocampus and caudate nucleus memory systems, respectively. We asked whether the spontaneous use of a particular navigational strategy was associated with a particular ability to navigate in one's environment. We tested 30 young participants on the 4‐on‐8 virtual maze and we assessed their way finding ability in a virtual town. As expected, spatial learners performed well in the virtual town and the response learners, who never used external landmarks and relied purely on an egocentric strategy, performed poorly. Interestingly, a group who used the most efficient response strategy based on external landmarks in the 4‐on‐8 virtual maze, switched to the most efficient spatial strategy in the virtual town. Our data suggest that the best navigators are those who appropriately use spatial or response strategies depending on the demands of the task. © 2007 Wiley‐Liss, Inc.
Embeddings of resolvable mendelsohn triple systems
Authors: Bennett F. E. , Wei R.
Published: June 2007

In this article it is shown that any resolvable Mendelsohn triple system of order u can be embedded in a resolvable Mendelsohn triple system of order v iff v≥ 3u, except possibly for 71 values of (u,v). © 1993 John Wiley & Sons, Inc.
The structure of nilpotent steiner quadruple systems
Authors: Guelzow Andreas J.
Published: June 2007

Steiner quadruple systems can be coordinatized by SQS‐skeins. We investigate those Steiner quadruple systems that correspond to finite nilpotent SQS‐skeins. S. Klossek has given representation and construction theorems for finite distributive squags and Hall triple systems which were generalized by the author to the class of all finite nilpotent squags and their corresponding Steiner triple systems. In this article we present analogous theorems for nilpotent SQS‐skeins and Steiner quadruple systems. We also generalize the well‐known doubling constructions of Doyen/Vandensavel and Armanious. It is then possible to describe the structure of all nilpotent Steiner quadruple systems completely: the nilpotent Steiner quadruple systems are exactly those obtained from the trivial 2‐ (or 4‐) element Steiner quadruple system by repeated application of this generalized doubling construction. Moreover, we prove that the variety of semi‐boolean SQS‐skeins is not locally finite and contains non‐nilpotent SQS‐skeins. © 1993 John Wiley & Sons, Inc.
Disjoint skolem sequences and related disjoint structures
Authors: Baker C. , Shalaby N.
Published: June 2007

A Skolem sequence of order n is a sequence S = (s1, s2…, s2n) of 2n integers satisfying the following conditions: (1) for every k ∈ {1, 2,… n} there exist exactly two elements si,Sj such that Si = Sj = k; (2) If si = sj = k,i < j then j − i = k. In this article we show the existence of disjoint Skolem, disjoint hooked Skolem, and disjoint near‐Skolem sequences. Then we apply these concepts to the existence problems of disjoint cyclic Steiner and Mendelsohn triple systems and the existence of disjoint 1‐covering designs. © 1993 John Wiley & Sons, Inc.
Cyclically resolvable designs and triple whist tournaments
Authors: Anderson I. , Finizio N. J.
Published: June 2007

We construct cyclically resolvable (v, 4, 1) designs and cyclic triple whist tournaments TWh(v) for all v of the form 3p…p + 1, where the pi are primes ≡ 1 (mod 4), such that each P1 − 1 is divisible by the same power of 2. © 1993 John Wiley & Sons, Inc.
Linear spaces on 16 points
Authors: Heathcote Ghislaine
Published: June 2007

There are 398 nonisomorphic nontrivial linear spaces on 16 points having no lines of size two. In addition, there are 157,151 proper linear spaces on 17 points having one line of size five and 42 lines of size three. © 1993 John Wiley & Sons, Inc.
Extremal problems for triple systems
Authors: Lefmann Hanno , Phelps Kevin T. , Rödl Vojtěch
Published: June 2007

In this article Turán‐type problems for several triple systems arising from (k, k − 2)‐configurations [i.e. (k − 2) triples on k vertices] are considered. It will be shown that every Steiner triple system contains a (k, k − 2)‐configuration for some k < c log n/ log log n. Moreover, the Turán numbers of (k, k − 2)‐trees are determined asymptotically to be ((k − 3)/3).(n2) (1−o(1)). Finally, anti‐Pasch hypergraphs avoiding (5, 3) ‐and (6, 4)‐Configurations are considered. © 1993 John Wiley & Sons, Inc.
3‐(v, 4, 1) covering designs with chromatic numbers 2 and 3
Authors: Linek Václav , Mendelsohn Eric
Published: June 2007

A t‐(v, k, λ) covering design is a pair (X, B) where X is a v‐set and B is a collection of k‐sets in X, called blocks, such that every t element subset of X is contained in at least λ blocks of B. The covering number, Cλ(t, k, v), is the minimum number of blocks a t‐(v, k, λ) covering design may have. The chromatic number of (X, B) is the smallest m for which there exists a map φ: X → Zm such that ∣φ((β)∣ ≥2 for all β ∈ B, where φ(β) = {φ(x): x ∈ β}. The system (X, B) is equitably m‐chromatic if there is a proper coloring φ with minimal m for which the numbers ∣φ−1(c)∣ c ∈ Zm differ from each other by at most 1. In this article we show that minimum, (i.e., ∣B∣ = C λ (t, k, v)) equitably 3‐chromatic 3‐(v, 4, 1) covering designs exist for v ≡ 0 (mod 6), v ≥ 18 for v ≥ 1, 13 (mod 36), v ≡ 13 and for all numbers v = n, n + 1, where n ≡ 4, 8, 10 (mod 12), n ≥ 16; and n = 6.5a 13b 17c −4, a + b + c > 0, and n = 14, 62. We also show that minimum, equitably 2‐chromatic 3‐(v, 4, 1) covering designs exist for v ≡ 0, 5, 9 (mod 12), v ≥ 0, v = 2.5a 13b 17c + 1, a + b + c > 0, and v = 23. © 1993 John Wiley & Sons, Inc.
The intersection problem for m‐cycle systems
Authors: Billington Elizabeth J.
Published: June 2007

Let Im(v) denote the set of integers k for which a pair of m‐cycle systems of Kv, exist, on the same vertex set, having k common cycles. Let Jm(v) = {0, 1, 2,…, tv −2, tv} where tv = v(v − 1)/2m. In this article, if 2mn + x is an admissible order of an m‐cycle system, we investigate when Im(2mn + x) = Jm(2mn + x), for both m even and m odd. Results include Jm(2mn + 1) = Im(2mn + 1) for all n > 1 if m is even, and for all n > 2 if n is odd. Moreover, the intersection problem for even cycle systems is completely solved for an equivalence class x (mod 2m) once it is solved for the smallest in that equivalence class and for K2m+1. For odd cycle systems, results are similar, although generally the two smallest values in each equivalence class need to be solved. We also completely solve the intersection problem for m = 4, 6, 7, 8, and 9. (The cased m = 5 was done by C‐M. K. Fu in 1987.) © 1993 John Wiley & Sons, Inc.
Covering pairs by quintuples with index λ  0 (mod 4)
Authors: Assaf Ahmed M.
Published: June 2007

A (v, k. λ) covering design of order v, block size k, and index λ is a collection of k‐element subsets, called blocks, of a set V such that every 2‐subset of V occurs in at least λ blocks. The covering problem is to determine the minimum number of blocks, α(v, k, λ), in a covering design. It is well known that \documentclass{article}\pagestyle{empty}\begin{document}$ \alpha \left({\nu,\kappa,\lambda } \right) \ge \left\lceil {\frac{\nu}{\kappa}\left\lceil {\frac{{\nu - 1}}{{\kappa - 1}}\lambda} \right\rceil} \right\rceil = \phi \left({\nu,\kappa,\lambda} \right) $\end{document}, where [χ] is the smallest integer satisfying χ ≤ χ. It is shown here that α (v, 5, λ) = ϕ(v, 5, λ) + ϵ where λ ≡ 0 (mod 4) and e= 1 if λ (v−1)≡ 0(mod 4) and λv (v−1)/4 ≡ −1 (mod 5) and e= 0 otherwise With the possible exception of (v,λ) = (28, 4). © 1993 John Wiley & Sons, Inc.
Ternary codes of steiner triple systems
Authors: Key J. D.
Published: June 2007

The code over a finite field Fq of a design 𝒟 is the space spanned by the incidence vectors of the blocks. It is shown here that if 𝒟 is a Steiner triple system on v points, and if the integer d is such that 3d ≤ v < 3d+1, then the ternary code C of 𝒟 contains a subcode that can be shortened to the ternary generalized Reed‐Muller code ℛF3(2(d − 1),d) of length 3d. If v = 3d and d ≥ 2, then C⟂ ⊆ ℛF3(1,d)⊆ ℛ F3(2(d − 1),d) ⊆ C. © 1994 John Wiley & Sons, Inc.
Z‐cyclic triplewhist tournaments when the number of players involves primes of the form 8u + 5
Authors: Finizio Norman J.
Published: June 2007

When the number of players, v, in a whist tournament, Wh(v), is ≡ 1 (mod 4) the only instances of a Z‐cyclic triplewhist tournament, TWh(v), that appear in the literature are for v = 21,29,37. In this study we present Z‐cyclic TWh(v) for all v ∈ T = {v = 8u + 5: v is prime, 3 ≤ u ≤ 249}. Additionally, we establish (1) for all v ∈ T there exists a Z‐cyclic TWh(vn) for all n ≥ 1, and (2) if vi ∈ T, i = 1,…,n, there exists a Z‐cyclic TWh(v… v) for all ϵi ≥ 1. It is believed that these are the first instances of infinite classes of Z‐cyclic TWh(v), v ≡ 1 (mod 4). © 1994 John Wiley & Sons, Inc.
The bigraphical t‐wise balanced designs of index 1
Authors: Hoffman Dean G. , Kreher Donald L.
Published: June 2007

The t‐wise balanced designs of index 1 whose point set are the edges of Km,n, the complete bipartite graph, and that have the subgroup of all automorphisms that fix the two independent sets of Km,n as an automorphism group are studied. All such designs are found. © 1994 John Wiley & Sons, Inc.
On a conjecture of jungnickel and tonchev for quasi‐symmetric designs
Authors: Ionin Yury J. , Shrikhande Mohan S.
Published: June 2007

Jungnickel and Tonchev conjectured in [4] that if a quasi‐symmetric designDis ans‐fold quasi‐multiple of a symmetric (v,k,λ) design with (k,(s− 1)λ) = 1, thenDis a multiple. We prove this conjecture under any one of the conditions:s≤ 7,k− 1 is prime, or the designDis a 3‐design. It is shown that for any fixeds, the conjecture is true with at most finitely many exceptions. The unique quasi‐symmetric 3‐(22,7,4) design is characterized as the only quasi‐symmetric 3‐design, which as a 2‐design is ans‐fold quasi‐multiple withs≡ 1 (modk). © 1994 John Wiley & Sons, Inc.
On R*‐sequenceability and symmetric harmoniousness of groups
Authors: Wang Cheng‐De , Leonard Philip A.
Published: June 2007

We introduce a special harmoniousness called symmetric harmoniousness of groups and extend the R*‐sequenceability of abelian groups to nonabelian groups. We prove that the direct product of an R*‐sequenceable group of even order with a symmetric harmonious group of odd order is R*‐sequenceable. Examples of nonabelian R*‐sequenceable groups and nonabelian symmetric harmonious groups are given. It is shown that the nonabelian groups of order 3q (q prime) are symmetric harmonious. © 1994 John Wiley & Sons, Inc.
Resolvable BIBDs with block size 8 and index 7
Authors: Furino Steven , Greig Malcolm , Miao Ying , Yin Jianxing
Published: June 2007

The necessary conditions for the existence of a resolvable BIBD RB(k,λ; v) are λ(v − 1) = 0(mod k − 1) and v = 0(mod k). In this article, it is proved that these conditions are also sufficient for k = 8 and λ = 7, with at most 36 possible exceptions. © 1994 John Wiley & Sons, Inc.
The multiplier conjecture for elementary abelian groups
Authors: Weisheng Qiu
Published: June 2007

Applying the method that we presented in [19], in this article we prove: “Let G be an elementary abelian p‐group. Let n = dn1. If d(≠ p) is a prime not dividing n1, and the order w of d mod p satisfies \documentclass{article}\pagestyle{empty}\begin{document}$ w > \frac{{d^2}}{3} $\end{document}, then the Second Multiplier Theorem holds without the assumption n1 > λ, except that only one case is yet undecided: w ≤ d2, and \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{p - 1}}{{2w}} \ge 3 $\end{document}, and t is a quadratic residue mod p, and t is not congruent to \documentclass{article}\pagestyle{empty}\begin{document}$ x^{\frac{{p - 1}}{{2w}}j} $\end{document} (mod p) (1 ≤ j < 2w), where t is an integer meeting the conditions of Second Multiplier Theorem, and x is a primitive root of p.”. © 1994 John Wiley & Sons, Inc.
The automorphism group of a complete (q − 1)‐arc in PG(2,q)
Authors: Ali A. H. , Hirschfeld J. W. P. , Kaneta H.
Published: June 2007

The automorphism group of the set of 12 points associated with an apolar system of conics is determined. A complete (q − 1)‐arc for q = 13 can be obtained as a special case. The orbits of its automorphism group are also described. © 1994 John Wiley & Sons, Inc.
On the decomposition of λK into regular tournaments of order 5
Authors: Mahmoodi A. , Mathon R.
Published: June 2007

An RTD[5,λ; v] is a decomposition of the complete symmetric directed multigraph, denoted by λK, into regular tournaments of order 5. In this article we show that an RTD[5,λ; v] exists if and only if (v−1)λ ≡ 0 (mod 2) and v(v−1)λ ≡ 0 (mod 10), except for the impossible case (v,λ) = (15,1). Furthermore, we show that for each v ≡ 1,5 (mod 20), v ≠ 5, there exists a B[5,2; v] which is not RT5‐directable. © 1994 John Wiley & Sons, Inc.
The preparata codes and a class of 4‐designs
Authors: Baartmans Alphonse H. , Bluskov Iliya , Tonchev Vladimir D.
Published: June 2007

An extension theorem for t‐designs is proved. As an application, a class of 4‐(4m + 1,5,2) designs is constructed by extending designs related to the 3‐designs formed by the minimum weight vectors in the Preparata code of length n = 4m, m ≥ 2. © 1994 John Wiley & Sons, Inc.
Incomplete perfect mendelsohn designs with block size 4 and holes of size 2 and 3
Authors: Bennett F. E. , Shen H. , Yin J.
Published: June 2007

Let v, k, and n be positive integers. An incomplete perfect Mendelsohn design, denoted by k‐IPMD(v, n), is a triple (X, Y, 𝔹) where X is a v‐set (of points), Y is an n‐subset of X, and 𝔹 is a collection of cyclically ordered k‐subsets of X (called blocks) such that every ordered pair (a, b) ∈ (X × X)\(Y × Y) appears t‐apart in exactly one block of 𝔹 and no ordered pair (a,b) ∈ Y × Y appears in any block of 𝔹 for any t, where 1 ≤ t ≤ k − 1. In this article, the necessary conditions for the existence of a 4‐IPMD(v, n), namely (v − n) (v − 3n − 1) ≡ 0 (mod 4) and v ≥ 3n + 1, are shown to be sufficient for the case n = 3. For the case n = 2, these conditions are sufficient except for v = 7 and with the possible exception of v = 14,15,18,19,22,23,26,27,30. The latter result provides a useful application to the problem relating to the packing of perfect Mendelsohn designs with block size 4. © 1994 John Wiley & Sons, Inc.
Sharply transitive 1‐factorizations of the complete graph with an invariant 1‐factor
Authors: Korchmáros Gábor
Published: June 2007

We give some simple characterizations of those n for which Kn has a sharply transitive 1‐factorization with an assigned automorphism group that acts sharply transitively on the vertex set and also fixes a 1‐factor. © 1994 John Wiley & Sons, Inc.
There are 526,915,620 nonisomorphic one‐factorizations of K12
Authors: Dinitz Jeffrey H. , Garnick David K. , McKay Brendan D.
Published: June 2007

We enumerate the nonisomorphic and the distinct one‐factorizations of K12. We also describe the algorithm used to obtain the result, and the methods we used to verify these numbers. © 1994 John Wiley & Sons, Inc.
5‐chromatic steiner triple systems
Authors: Fugère Jean , Haddad Lucien , Wehlau David
Published: June 2007

We show that, up to an automorphism, there is a unique independent set in PG(5,2) that meets every hyperplane in 4 points or more. Using this result, we show that PG(5,2) is a 5‐chromatic STS. Moreover, we construct a 5‐chromatic STS(v) for every admissible v ≥ 127. © 1994 John Wiley & Sons, Inc.
Hadamard matrices constructed from supplementary difference sets in the class ℋ︁1
Authors: Xia Ming‐Yuan , Xia Tian‐Bing
Published: June 2007

In this article we give the definition of the class ℋ︁1 and prove: (1) ℋ︁1(v) ≠ ϕ for v ∈ 𝒩 = 𝒩1 ∪ 𝒩2 ∪ 𝒩3 where

(2) there exists 2 − {2q2; q2 ± q, q2;q2 ± q} supplementary difference sets for q2 ∈ 𝒩; (3) there exists an Hadamard matrix of order 4v for v ∈ 𝒩; (4) if t is an order of T‐matrices, there exists an Hadamard matrix of order 4tv for v ∈ 𝒩. © 1994 John Wiley & Sons, Inc.
The spectrum for large sets of disjoint mendelsohn triple systems with any index
Authors: Kang Qing‐De , Lei Jian‐Guo , Chang Yan‐Xun
Published: June 2007

The spectrum for LMTS(v,1) has been obtained by Kang and Lei (Bulletin of the ICA, 1993). In this article, firstly, we give the spectrum for LMTS(v,3). Furthermore, by the existence of LMTS(v,1) and LMTS(v,3), the spectrum for LMTS(v,λ) is completed, that is v ≡ 2 (mod λ), v ≥ λ + 2, if λ ≢ 0(mod 3) then v ≢ 2 (mod 3) and if λ = 1 then v ≠ 6. © 1994 John Wiley & Sons, Inc.
The spectrum of self‐converse DTS
Authors: Kang Qingde , Chang Yanxun , Yang Guihua
Published: June 2007

A directed triple system, DTS(v) = (X,ℬ︁), is called self‐converse if it and its converse (X,ℬ︁−1) are isomorphic, where ℬ︁ = {(z,y,x);(x,y,z) ∈ ℬ︁}. In this article, the existence spectrum of self‐converse DTS(v) is given, which is v ≡ 0 or 1 (mod 3) and v ≠ 6. © 1994 John Wiley & Sons, Inc.
The existence of doubly near resolvable (v,3,2)‐BIBDs
Authors: Lamken E. R.
Published: June 2007

The existence of doubly near resolvable (v,2,1)‐BIBDs was established by Mullin and Wallis in 1975. In this article, we determine the spectrum of a second class of doubly near resolvable balanced incomplete block designs. We prove the existence of DNR(v,3,2)‐BIBDs for v ≡ 1 (mod 3), v ≥ 10 and v ∉ {34,70,85,88,115,124,133,142}. The main construction is a frame construction, and similar constructions can be used to prove the existence of doubly resolvable (v,3,2)‐BIBDs and a class of Kirkman squares with block size 3, KS3(v,2,4). © 1994 John Wiley & Sons, Inc.
Even cycle decompositions of complete graphs minus a 1‐factor
Authors: Alspach Brian , Marshall Susan
Published: June 2007

Some sufficient conditions are proven for the complete graph of even order with a 1‐factor removed to be decomposable into even length cycles. © 1994 John Wiley & Sons, Inc.
Embeddings of pure mendelsohn triple systems and pure directed triple systems
Authors: Hao Shen
Published: June 2007

It is proved in this article that the necessary and sufficient conditions for the embedding of a λ‐fold pure Mendelsohn triple system of order v in λ‐fold pure Mendelsohn triple of order u are λu(u − 1) ≡ 0 (mod 3) and u ⩾ 2v + 1. Similar results for the embeddings of pure directed triple systems are also obtained. © 1995 John Wiley & Sons, Inc.
On a class of small 2‐designs over gf(q)
Authors: Miyakawa Masashi , Munemasa Akihiro , Yoshiara Satoshi
Published: June 2007

A 2 − (v,k,λ;q) design is a pair (V, B) of a v‐dimensional vector space V over GF(q) and a collection B of k‐dimensional subspaces of V such that each 2‐dimensional subspace of V is contained in exactly λ members of B. Assuming transitivity of their automorphism groups on the nonzero vectors of V, we give a classification of nontrivial such designs for v = 7, q = 2,3 with small λ, together with the nonexistence proof of those designs for v ⩽ 6. © 1995 John Wiley & Sons, Inc.
More cyclic triplewhist tournaments
Authors: Anderson I. , Finizio N. J.
Published: June 2007

We extend the set of values of n for which it is known that a Z‐cyclic triple whist tournament for 4n players exists by proving that if there exists such a tournament for q + 1 players, where q ≡ 3 (mod 4) is prime, then there exists such a tournament for qpa11…pann + 1 players, whenever the pi are primes ≡ 5 (mod 8). © 1995 John Wiley & Sons, Inc.
Zero‐sum block designs and graph labelings
Authors: Tuza Zsolt
Published: June 2007

Proving a conjecture of Aigner and Triesch, we show that every graph G = (V,E) without isolated vertices and isolated edges admits an edge labeling ξ: E → {0,1}m with binary vectors of length m = [log2 n] + 1 such that the sums.

CALLING STATEMENT :

(taken modulo 2 componentwise) are mutually distinct, provided that n is sufficiently large. The proof combines probabilistic arguments with explicitly constructed Steiner systems. © 1995 John Wiley & Sons, Inc.
A representation theorem and Z‐cyclic whist tournaments
Authors: Finizio Norman J.
Published: June 2007

Let E denote the group of units (i.e., the reduce set of residues) in the ring Z. Here we consider q,p to be primes, q ≡ 3 (mod 4), q ⩾ 7, p ≡ 1 (mod 4). Let W denote a common primitive root of 3, q, and p2. If H denotes the (normal) subgroup of E that is generated by {−1, W}, we show that the factor group E/H is cyclic by demonstrating the existence of an element x in E such that the coset xH has order equal to |E/H|. This order is given by gcd(pn−1(p − 1),q − 1). This representation of E/H is exploited via an appropriate construction to produce Z‐cyclic whist tournaments for 3qpn players. Consequently these results extend those of an early study of Wh(3qpn) that was restricted to gcd(pn−1(p − 1),q − 1) = 2. © 1995 John Wiley & Sons, Inc.
Large sets of 3‐designs from psl(2, q), with block sizes 4 and 5
Authors: Cusack C. A. , Graham S. W. , Kreher D. L.
Published: June 2007

We determine the distribution of 3−(q + 1,k,λ) designs, with k ϵ {4,5}, among the orbits of k‐element subsets under the action of PSL(2,q), for q ϵ 3 (mod 4), on the projective line. As a consequence, we give necessary and sufficient conditions for the existence of a uniformly‐PSL(2,q) large set of 3−(q + 1,k,λ) designs, with k ϵ {4,5} and q ≡ 3 (mod 4). © 1995 John Wiley & Sons, Inc.
On simple radical difference families
Authors: Buratti Marco
Published: June 2007

For q a prime power and k odd (even), we define a (q,k,1) difference family to be radical if each base block is a coset of the kth roots of unity in the multiplicative group of GF(q) (the union of a coset of the (k − 1)th roots of unity in the multiplicative group of GF(q) with zero). Such a family will be denoted by RDF. The main result on this subject is a theorem dated 1972 by R.M. Wilson; it is a sufficient condition for the existence of a (q,k, 1)‐RDF for any k. We improve this result by replacing Wilson's condition with another sufficient but weaker condition, which is proved to be necessary at least for k ⩽ 7. As a consequence, we get new difference families and hence new Steiner 2‐designs. © 1995 John Wiley & Sons, Inc.
A unique arithmetic labeling of hexagonal lattices
Authors: Chang Gerard J. , Hwang F. K. , Wright P. E. , Griggs J. R.
Published: June 2007

Consider an r‐layer hexagon consisting of 3r2 + 3r + 1 hexagonal cells. Can one label the cells by the set Nr = {0,1,…, 3r2 + 3r} such that each line of adjacent cells are labeled by numbers forming an arithmetic progression modulo (3r2 + 3r + 1) (in proper ordering)? We show that for each r there exists such a labeling unique up to equivalence. We also study some other related issues. © 1995 John Wiley & Sons, Inc.
Bounds on orthogonal arrays and resilient functions
Authors: Bierbrauer Jürgen
Published: June 2007

The only known general bounds on the parameters of orthogonal arrays are those given by Rao in 1947 [J. Roy. Statist. Soc. 9 (1947), 128–139] for general OAγ(t,k,v) and by Bush [Ann. Math. Stat. 23, (1952), 426–434] [3] in 1952 for the special case γ = 1. We present an algebraic method based on characters of homocyclic groups which yields the Rao bounds, the Bush bound in case t ⩾ v, and more importantly a new explicit bound which for large values of t (the strength of the array) is much better than the Rao bound. In the case of binary orthogonal arrays where all rows are distinct this bound was previously proved by Friedman [Proc. 33rd IEEE Symp. on Foundations of Comput. Sci., (1992), 314–319] in a different setting. We also note an application to resilient functions. © 1995 John Wiley & Sons, inc.
Virtually balanced incomplete block designs for v = 22, k = 8, and λ = 4
Authors: Hedayat A. S. , Stufken J. , Zhang W. G.
Published: June 2007

When basic necessary conditions for the existence of a balanced incomplete block design are satisfied, the design may still not exist or it may not be known whether it exists. In either case, other designs may be considered for the same parameters. In this article we introduce a class of alternative designs, which we will call virtually balanced incomplete block designs. From a statistical point of view these designs provide efficient alternatives to balanced incomplete block designs, and from a combinatorial point of view they offer challenging new questions. © 1995 John Wiley & Sons, Inc.
On orthogonal double covers of kn and a conjecture of chung and west
Authors: Gronau H.‐D. O. F. , Mullin R. C. , Schellenberg P. J.
Published: June 2007

A collection 𝔾 = {G1, G2,…,Gn} of spanning subgraphs of Kn is called an orthogonal double cover if (i) every edge of Kn belongs to exactly two of the Gi's and (ii) any two distinct Gi's intersect in exactly one edge. Chung and West conjectured that there exists an orthogonal double cover of Kn, for all n, in which each Gi has maximum degree 2, and proved this result for n in six of the residue classes modulo 12. In another context, Ganter and Gronau showed that for n ≡ 1 mod 3, n ≠ 10, there exists an orthogonal double cover of Kn in which each Gi consists of an isolated vertex and the vertex disjoint union of K3's (actually these orthogonal double covers result from the solution of the directed version of the problem, which reduces to the undirected case when the orientation of the arcs is ignored). Clearly the covers of Ganter and Gronau satisfy the Chung‐West requirement. In this article, the configurations of Ganter and Gronau are generalized to include the cases n ≡ 0,2 mod 3, and the results are used to provide a unified solution of the Chung‐West problem. For n ≠ 5 mod 6, all the spanning subgraphs in the collection 𝔾 are isomorphic to each other; however, this is not the case when n ≡ 5 mod 6. In addition to solving the Chung‐West problem, we also go on to show that for n ≡ 2 mod 3 and n > 287, there exists an orthogonal double cover of Kn in which each spanning subgraph Gi consists of the vertex‐disjoint union of an isolated vertex, and quadrilateral, and (n−5)/3 triangles. Of the 96 cases with 2 ⩽ n ⩽ 287, 65 cases are resolved and 31 remain open. © 1995 John Wiley & Sons, Inc.
Some simple and automorphism‐free 2‐(15,5,4) designs
Authors: Nowzari‐Dalini A. , Torabi R. , Khosrovshahi G. B.
Published: June 2007

A variation of “trading signed design” algorithm is utilized to produce some 104 simple and aotomorphism‐free 2‐(15,5,4) designs. © 1995 John Wiley & Sons, Inc.
Note on large sets of infinite steiner systems
Authors: Cameron Peter J.
Published: June 2007

Large sets of Steiner systems S(t,k,n) exist for all finite t and k with t < k and all infinite n. The vector space analogues exist over a field F for all finite t and k with t < k provided that either v or F is infinite, and n ⩾ 2k − t + 1. This inequality is best possible. © 1995 John Wiley & Sons, Inc.
On r*‐sequenceability and symmetric harmoniousness of groups. II
Authors: Wang Cheng‐De , Leonard Philip A.
Published: June 2007

In this paper we investigate symmetric harmoniousness of groups and connections of this concept to the R*‐sequenceability of groups. We prove that, under suitable assumptions, the direct product of a symmetric harmonious group with a group that is R*‐sequenceable is R*‐sequenceable; we discuss the symmetric harmoniousness of abelian and of nilpotent groups; we also prove that, for a fixed odd prime p, all but possibly finitely many of the nonabelian groups of order pq (q prime, q ≡ 1 (mod p)) are symmetric harmonious. © 1995 John Wiley & Sons, Inc.
Completions of Convexly Ordered Valuation Rings
Authors: Mathews Larry
Published: June 2007

We prove that every convexly ordered valuation ring has a unique completion as a uniform space, which furthermore is a convexly ordered valuation ring. In addition, we give a model theoretic characterisation of complete convexly ordered valuation rings, and give a necessary and sufficient condition for the completion of a convexly ordered valuation ring to be a real closed ring.

Mathematics Subject Classification: 03C60, 13L05, 54E15.
The Prime Spectrum of an MV‐Algebra
Authors: Belluce L. P. , Nola Antonio Di , Sessa Salvatore
Published: June 2007

In this paper we show that the prime ideal space of an MV‐algebra is the disjoint union of prime ideal spaces of suitable local MV‐algebras. Some special classes of algebras are defined and their spaces are investigated. The space of minimal prime ideals is studied as well.

Mathematics Subject Classification: 03B50, 06D99.
Cofinal Indiscernibles and some Applications to New Foundations
Authors: Körner Friederike
Published: June 2007

We prove a theorem about models with indiscernibles that are cofinal in a given linear order. We apply this theorem to obtain new independence results for Quine's set theory New Foundations, thus solving two open problems in this field.

Mathematics Subject Classification: 03C55, 03B15, 03B60, 03E70.
An Extension Principle for Fuzzy Logics
Authors: Gerla Giangiacomo
Published: June 2007

Let S be a set, P(S) the class of all subsets of S and F(S) the class of all fuzzy subsets of S. In this paper an “extension principle” for closure operators and, in particular, for deduction systems is proposed and examined. Namely we propose a way to extend any closure operator J defined in P(S) into a fuzzy closure operator J* defined in F(S). This enables us to give the notion of canonical extension of a deduction system and to give interesting examples of fuzzy logics. In particular, the canonical extension of the classical propositional calculus is defined and it is showed its connection with possibility and necessity measures. Also, the canonical extension of first order logic enables us to extend some basic notions of programming logic, namely to define the fuzzy Herbrand models of a fuzzy program. Finally, we show that the extension principle enables us to obtain fuzzy logics related to fuzzy subalgebra theory and graded consequence relation theory.

Mathematics Subject Classification: 03B52.
Reflection of Long Game Formulas
Authors: Heikkilä Heikki , Väänänen Jouko
Published: June 2007

We study game formulas the truth of which is determined by a semantical game of uncountable length. The main theme is the study of principles stating reflection of these formulas in various admissible sets. This investigation leads to two weak forms of strict‐II11 reflection (or ∑1‐compactness). We show that admissible sets such as H(ω2) and Lω2 which fail to have strict‐II11 reflection, may or may not, depending on set‐theoretic hypotheses satisfy one or both of these weaker forms.

Mathematics Subject Classification: 03C70, 03C75.
A Conjecture Concerning the Spectrum of a Sentence
Authors: Ash Christopher J.
Published: June 2007

We give a plausible‐sounding conjecture involving the number of n‐equivalence classes of structures of size m which would imply that the complement of a spectrum is also a spectrum.

Mathematics Subject Classification: 03B10, 03D15, 68Q15.
On Solvable Congruences in Finitely Decidable Varieties
Authors: Valeriote Matthew A.
Published: June 2007

In this paper we establish the (1, 2)‐ and (2, 1)‐transfer principles for finitely decidable locally finite varieties, where a class of structures is finitely decidable if the first order theory of its finite members is recursive. The transfer principles deal with the local structure of finite algebras and have strong global consequences.

Mathematics Subject Classification: 08A05, 03C13, 08B05, 08B10.
Maximum Schemes in Arithmetic
Authors: Fernández‐Margarit A. , Pérez‐Jiménez M. J.
Published: June 2007

In this paper we deal with some new axiom schemes for Peano's Arithmetic that can substitute the classical induction, least‐element, collection and strong collection schemes in the description ofPA.

Mathematics Subject Classification: 03F30, 03H15.
A New Proof that “Krull implies Zorn”
Authors: Banaschewski Bernhard
Published: June 2007

In the present note we give a direct deduction of the Axiom of Choice from the Maximal Ideal Theorem for commutative rings with unit.

Mathematics Subject Classification: 03E25, 04A25, 13A15.
The Hauptsatz for Stratified Comprehension: A Semantic Proof
Authors: Crabbé Marcel
Published: June 2007

We prove the cut‐elimination theorem, Gentzen's Hauptsatz, for the system for stratified comprehension, i. e. Quine's NF minus extensionality.

Mathematics Subject Classification: 03B15, 03F05.