Class Of Exceptions Research Articles

Catullus 107: Removing the Hiatus and Other Textual Suggestions

In the first couplet quicquam is a fifteenth-century conjecture for the quid quid or quicquid of the tradition, and Ribbeck suggested quoi quid; cupidoque is a conjecture of the Aldine of 1502; O offers optigit, GR offer obtigit; Heinsius suggested insperati. In the second couplet there are various conjectures including Haupt's nobisque est. In the last couplet the tradition offers hac or me; there are numerous conjectures including Lachmann's hac res optandas and Guarinus' hac quid optandum. That the surviving MSS of Catullus depend on a single grossly corrupt archetype is notorious;2 the text of 107 is particularly bad and proportionately lacking in authority to persuade us of anomalies.3 The anomaly in line 1 is of course the purported between cupido and optanti. Proper consideration of the admissibility of this or of any other must begin with the plain fact that there is a rule against in Latin verse; the onus of proof, therefore, lies on those who would justify any individual exception or any class of exceptions to that rule. Catullus was not an Augustan elegist, but he was (in part) an elegist, and was not far removed from the Augustan era; if caesural was acceptable to the Augustans, it would admittedly strengthen the case for caesural in Catullus. Platnauer (1951: 57-58) lists three classes of in the Augustan elegists: (1) after the interjections o, heu, and a; (2) Greek hiatus before a quadrisyllabic word at the end of a hexameter, for example, in Maenalia I Atalanta; (3) at the caesura. So far as the first two classes of exception are

Generic 2 × 2 matrices in positive characteristic

Let R m ( K ) be the K -algebra generated by the generic 2 × 2 matrices y 1 , …, y m over a unitary commutative associative ring K . Our main result is that, with a small class of exceptions, for m a positive integer and p a prime, the kernel of the natural homomorphism R m (ℤ) → R m (ℤ p ) coincides with pR m (ℤ). The only exceptions are for m ≥ 5 and p = 2 when we give an explicit multilinear polynomial identity of degree 5 for the matrix algebra M 2 (ℤ 2 ) which does not follow from the spolynomial identities of M 2 (ℤ 2 ). This improves on Schelter's construction of a non-multilinear identity of this sort of degree 6, and Drensky and Tsiganchev's existence result for a multilinear identity such as we have found.

DEFINITE POSSESSIVES AND DISCOURSE NOVELTY

Standard wisdom holds that in order for a use of a definite description to be felicitous, its referent must be familiar', either because it was mentioned in previous discourse or because it is otherwise salient in the non-linguistic context. I show that a grammatically-defined class of demonstrably definite NPs containing definite possessors (e.g., that man's daughter) are routinely able to describe novel (unfamiliar) entities. I propose to account for this systematic class of exceptions to the standard familiarity requirement by providing a refined notion of familiarity, one that determines when a use of a possessed NP as a whole will count as familiar based (in part) on whether its possessor phrase counts as familiar.

Forbidden subgraphs, hamiltonicity and closure in claw-free graphs

We study the stability of some classes of graphs defined in terms of forbidden subgraphs under the closure operation introduced by the second author. Using these results, we prove that every 2-connected claw-free and P 7-free, or claw-free and Z 4-free, or claw-free and eiffel-free graph is either hamiltonian or belongs to a certain class of exceptions (all of them having connectivity 2).

On English sentence stress and the nature of metrical structure

This essay is concerned with a section of the suprasegmental phonology of English that has traditionally been called ‘sentence stress’: a domain that goes beyond the simple word and its accent, covering prominence relations within lexical compounds and syntactic phrases. Some almost commonplace assumptions are usually made about sentence stress in the phonological literature of English: first, that the distinction between compound stress and phrasal stress leads to a phonological contrast, so that in a compound noun likeblack boardthe left-hand constituent is the stronger one whereas in a phrase,black boardfor example, the right-hand one is. Second, that this prominence differentiation consists of a further contouring of the main stresses of the simple words involved so that word stress serves as input for sentence stress differentiation, as inGérman tèachervs.Gèrman téacher. Also frequently observed is a class of exceptions to this second assumption: thethìrteen méncases, where the primary stress of a word in isolation,thirtéen, gets shifted in certain contexts for rhythmic reasons.

On the Automorphism Groups of almost all Cayley Graphs

In spite of the difficulties which arise in constructing Cayley graphs with given regular automorphism group G , we conjecture that, unless G belongs to a known class of exceptions, almost all Cayley graphs of G have G for their full automorphism group . Here we prove this conjecture for nilpotent groups of odd order .

Pro-form and metaphor—Pro-form and vocative

In their very interesting, well-argued and persuasive article 'A systematic approach to Russian obscene language' (RL 6/2, 1982, 232-249) F. Dreizin and T. Priestly write (236) that the mat nouns in the left-hand column of Table I (234) can only be used as PRO-nouns "with overt, explicit determinative adjectives". In other words, to use their own examples (omitting stress-marks), if you say (8) Vcera ja videl bljad you can only mean 'I saw a whore yesterday' but if you say (7) Vcera ja videl etu bljad' you can mean either 'I saw this whore yesterday', where bljad' is in its technical, i.e. literal sense, or 'I saw this person yesterday', where bljad is used as a PRO-noun, i.e. where bljad is almost indeed a pronoun, meaning 'human being', with some additional "colouring". This colouring can be of two types. The use of bljad hiere, instead of celoveka, can mean either we are in a for the sake of a better term "low demotic" mode, in which the entire discourse is coloured, that is to say that the use of bljad and other words of the same type simply signals "low demotic"; or the word bljad can mean, whether or not we are in "low demotic", roughly 'person, pejorative'. On p. 241 Dreizin and Priestly state that mat verbs, as PRO-verbs, are semantically void but "not totally void : they inevitably carry the feature of expressivity". From what I have just written it should be clear that a mat word (be it verb or noun) used as a pro-form (to introduce a blanket term covering all words prefixed with PRO-) may be no more than part of a text all of which is expressively marked or it may itself be an expressively marked item. To return to the use of mat nouns as pro-forms, Dreizin and Priestly state that there are exceptions to their rule that the mat nouns can only be used in this way with determinative adjectives. A class of exceptions is provided by mass-nouns: "in some cases, however, when mass-nouns are involved, the rule may be violated. For example, (14) V lagere kormili govnom. They served up shit in the (labour) camp', may (as in English) be understood in the non-technical sense." This is not in fact the case, for in the example govno is not used as a pro-form but is

Old English γ-metathesis and generative phonology

Postal (1968: 300) writes as follows:Bloomfield in effect noted the incompatibility of phenomena like … metathesis, dissimilation, etc., with the view of sound change as gradual drift in performance. Instead of admitting that these were counterexamples to the view, he simply appealed to terminology and declared that they were not sound change … But, since these types of changes are as systematic, regular, cross-lexical, etc., as other changes, this terminological attempt amounts to nothing more than the naming of a class of exceptions.

The generation of Sp( [formula omitted]2) by transvections

In 1955, in [2], Dieudonne, observing that each symplectic group Sp(V) is generated by its transvections, considered the problem of finding the minimal number of factors in the expression of elements 0 of Sp(V) as products of transvections in Sp(V).l The answer is in general residue cr, but with some classes of exceptions. Complications arise when the underlying field is 5, , and Dieudonne’s list of exceptions [2, p. 1641 for this case is incomplete. The difficulty occurs in 4.4” page 163 and seems to lie in the fact that, following the notation there, the plane T chosen orthogonal to c and d need not (in fact, cannot) be orthogonal to the revised “c” and ‘Id,” as is tacitly assumed. The proof in 4.4” fails and there is a class of exceptions of residue 5 in dimension 6 (see 3.3 below). This paper is devoted to completing the list of exceptions for ffs . Also mentioned are the minor corrections

Movement rules in functional perspective

MOVEMENT RULES IN FUNCTIONAL PERSPECTIVE Ronald W. Langacker University of California, San Diego This paper offers a functional explanation for the existence and for the special properties of movement rules in natural languages. A survey of reasonably wellestablished movement transformations in English reveals certain asymmetries in the classes of such rules encountered empirically and in their formal properties. It is argued that the special formal properties of backing rules correlate with their function , which is different from the function of raising, lowering, and fronting rules. The latter three types can be given a uniform functional characterization in terms of the notion Objective content', a notion that has figured prominently, though implicitly, in the history of generative grammar. This notion is discussed in preliminary terms, as is that of relative 'prominence', whose syntactic relevance has been clearly established . The hypothesis is advanced that raising, lowering, and fronting rules all serve the function of increasing the prominence of objective content in surface structure. This hypothesis accounts for the asymmetries noted in regard to the movement rules of English, and it also provides a motivated explanation for the fact that backing rules are upward bounded. Movement rules are shown to be only one facet of a broad conspiracy to ensure the surface prominence of objective content. This conspiracy is further explored in the context of information theory and generative semantics. During the briefhistory oftransformational grammar, the concerns ofthis school of linguistic thought have broadened dramatically. The perspective of Chomsky 1957 and other early transformational works was narrowly syntactic and formalistic , though one can hardly deny the insightful character of this research. Today, however, generative grammarians are concerned with phonological, intonational, lexical, semantic, contextual, and functional matters to such an extent that syntactic questions per se have largely been overshadowed. Indeed, in view of what we have learned in the last few years, it is difficult to conceive of any further substantial progress in syntactic theory and description being made in isolation from these other domains. Functional studies are particularly fascinating, because they offer some hope of explaining 'why' languages have certain properties, and 'why' somehow seems a more exciting question than 'what'. A simple and familiar example showing the relevance of functional considerations to syntactic analysis is provided by complement clauses headed by the subordinator that. It is well known that the complementizer that may normally be deleted when it heads an object complement clause, or a subject complement clause which has been extraposed:1 (1)My daughter believes (that) I'm too old to play rugby. (2)It is apparent (that) he has never played rugby before. 1 As the following examples show, that occasionally cannot be deleted in extraposed complement clauses: *It is well known the complementizer that may normally be deleted. *It has been established the Ziegenfluss hypothesis is false. *It has been shown conclusively mice are prolific breeders. This class of exceptions is probably semantically based. 630 MOVEMENT RULES IN FUNCTIONAL PERSPECTIVE631 However, that-deletion is not permitted in non-extraposed subject clauses : (3)That he has never played rugby before is apparent. (4)*He has never played rugby before is apparent. Viewed in purely syntactic terms, the non-deletability of that in 3 is surprising and must be treated as exceptional in some fashion—hardly a satisfying state of affairs. On the other hand, a functional perspective enables us to begin to explain why English should observe this restriction. If /Aai-deletion were permitted in nonextraposed subject complement clauses, the resulting surface structures, such as 4, would present the language user with certain processing difficulties ; in this instance, the listener would naturally hypothesize (mistakenly) that He has never ... initiates the main clause, since nothing would signal its subordinate status until later in the sentence. The retention of that in sentence-initial complement clauses enables the listener to avoid this processing error; but in sentences like 1-2, where the previous context {My daughter believes, It is apparent) makes it clear that a following clause will be subordinate, that is in a sense superfluous and thus may be omitted.2 This functional explanation does not necessarily make the irregularity go away, but somehow we feel better knowing that it...

Some Properties of Generalized Concave Functions

This paper examines properties and interrelations of several concepts of generalized concavity. It shows that the class of functions that are both “generalized concave” and “generalized convex” is closely related to the class of monotone functions of a single variable. After excluding a certain small class of exceptions, the paper shows that, for arbitrary (perhaps not differentiable) functions, concave implies pseudoconcave, pseudoconcave implies strictly quasiconcave, and strictly quasiconcave implies quasiconcave. Several results characterizing the extreme values of generalized concave functions are given.

Caesar's cursus and the intervals between Offices

The puzzle of C. Julius Caesar's date of birth and cursus honorum has never been satisfactorily solved. The facts can be stated quite simply. All but two of the sources referring to his age imply 100 B.C. as the date of his birth, and the date of his quaestorship agrees with this; yet he held the senior magistracies two years earlier than, according to what we know of the normal cursus, that date would allow. Are nearly all the sources wrong (as Mommsen thought) ? Or did Caesar at some time get a special dispensation, which no one has bothered to mention (as the majority opinion would now hold) ? Or is there another explanation of a more general kind, fitting Caesar into a class of exceptions (as Afzelius proposed) ?

On Minimax Statistical Decision Procedures and their Admissibility

This paper is concerned with the problem of making a decision on the basis of a sequence of observations on a random variable. Two loss functions, each depending on the distribution of the random variable, the number of observations taken, and the decision made, are assumed given. Minimax problems can be stated for weighted sums of the two loss functions, or for either one subject to an upper bound on the expectation of the other. Under suitable conditions it is shown that solutions of the first type of problem provide solutions for all problems of the latter types, and that admissibility for a problem of the first type implies admissibility for problems of the latter types. Two examples are given: Estimation of the mean of a random variable which is (1) normal with known variance, (2) rectangular with known range. The resulting minimax estimates are, with a small class of exceptions, proved admissible among the class of all procedures with continuous risk functions. The two loss functions are in each case the number of observations, and an arbitrary nondecreasing function of the absolute error of estimate. Extensions to a function of the number of observations for the first loss function are indicated, and two examples are given for the normal case where the sample size can or must be randomised among more than a consecutive pair of integers.

RE-DEDICATION OF SCIENCE IN GERMANY

THE first victims of Nazi anti-Semitism in Germany were news or persons of Jewish descent in official positions, for example at the universities ; with a small class of exceptions, they were dismissed by a decree issued within six weeks of Hitler's final accession to power. The great chemist Fritz Haber, director of the Kaiser Wilhelm Institut fur Physikalische chemie in Berlin-Dahlem, though by birth a Jew, did not himself fall under the decree, but a number of junior members of his staff did. Haber decided to resign in protest against this decree, and a few months later (in the summer of 1933) he left Germany. In his absence false accusations were levelled against him which rendered a return dangerous. He became an exile and died in exile on January 29, 1934 (see Nature, 133, 349 ; 1934).