Metaphorisms in programming

This paper introduces the metaphorism pattern of relational specification and addresses how specification following this pattern can be refined into recursive programs. Metaphorisms express input-output relationships which preserve relevant information while at the same time some intended optimization takes place. Text processing, sorting, representation changers, etc., are examples of metaphorisms. The kind of metaphorism refinement proposed in this paper is a strategy known as change of virtual data structure. It gives sufficient conditions for such implementations to be calculated using relation algebra and illustrates the strategy with the derivation of quicksort as example.

Factoriality and the pin-reutenauer procedure

We consider implicit signatures over finite semigroups determined by sets of pseudonatural numbers. We prove that, under relatively simple hypotheses on a pseudovariety V of semigroups, the finitely generated free algebra for the largest such signature is closed under taking factors within the free pro-V semigroup on the same set of generators. Furthermore, we show that the natural analogue of the Pin-Reutenauer descriptive procedure for the closure of a rational language in the free group with respect to the profinite topology holds for the pseudovariety of all finite semigroups. As an application, we establish that a pseudovariety enjoys this property if and only if it is full.

Faces em zona e índices harmônicos

Em uma zona cristalográfica podem ocorrer símbolos de faces, cujos índices de Miller, colocados em determinada ordem, formam aquilo que, em algebra, se conhece sob a designação de "série harmônica". Este trabalho mostra como tal possibilidade pode ser pesquisada.

7ª Contribuição ao estudo dos Flebotomus (Diptera: Psychodidae): descrição dos machos de 24 novas espécies

The A. and his co-workers captured in trips in the hinterland of Brazil more tham 17.000 flebotomi from which 35 are new ones, 11 discribed by, him in previous papers. The A. found these insects in groups of species living in different habitats, some ones of them not yet known: ondoors, or outdoors attracted by light or animal baits, without Shannon’s trap, in great or small caves, in the jungle in tree’s holes, holes in stones, holes in the soil habited by animals like armadillos, pacas (Aguti paca), wild rats, cururú toad (Bufo sp.). He observed the life history of 13 species: Flebotomus longipalpis Lutz& Neiva, 1912, Flebotomus intermedius Lutz & Neiva, 1912, Flebotomus avellari Costa Lima, 1932, Flebotomus aragãoi costa Lima, 1932, Flebotomus lutzianus Costa Lima, 1932, Flebotomus limai fonseca, 1935, Flebotomus rickardi Costa Lima, 1936, Flebotomus dasipodogeton Castro, 1939, Flebotomus oswaldoi n. sp., Flebotomus villelai n. sp., Flebotomus triacanthus n. sp., Flebotomus longispinus n. sp. And flebotomus travassosi n. sp. He describes the male of 24 n. sp., explaining the differential diagnose of group or nearly allied species. He inclued F. rooti n. sp. And F. hirsutus n. sp. In the sub-genus Shannonomyia. The first one, very allied to F. davisi Root is different from it, for presenting in the dorsal side of the abdomen bristles and not scales and to have the median claspers longer than his inner appendage and F. hirsutus quite different from the others which show 3 spines on distal segment of the upper clasper and for being the only one who presents the bristles of inner appendage of median clasper longer than it. Only the females of F. amazonensis Root and f. chagasi Costa Lima, are known and then it is possible that they belong to one of the species of this sub-genus from whom only the male have been described. F. choti Floch & Abonnenc, captured also at Pará, F. triacanthus n. sp. F. trispinosus n. sp. And F. equatorialis n. sp. Are very related and to this group the A. proposes the same of Pressatia as sub-genus in honor to whom demonstrated the medical importance of the flebotomi, considering F. triacanthus as the type specie of this sub-genus. In this sub-genus the V papal joint is very long, longer than III + IV, the antennae with geniculated spines without posterior outgrowth. At the genitalia the basal segment of the upper clasper presents two types of bristles ou the inner face, arranged in tuft; the distal segment with 3 spines and 2 thin bristles something difficult to see one of them situated near the apical spine and the other on the base of tubercle where the median spine is articulated; the median clasper is unarmed and compressed; the inferior clasper is also unarmed and longer than de basal segment of the upper clasper; the pompeta is longer than the basal segment of the upper clasper. Following it is presented a key for the determination of the males of the four species of this sub-genus. F. micropygus n. sp., F. minasensis n. sp. e F. dandrophylus n. sp., f. shannoni, F. monticolus, F. pestanai, F. lanei and F. cayenensis constitute a group with many similars characters. F. micropygus is the only American species who present α smaller than β and for that reason and others is allied to. F. minuts and others related species, but presents two terminal spines on the distal segment of the upper clasper. F. micropygus and f. minasensis are quite different because they have very small genitalia, smaller than their heads. F. dendrophylus presents on the median clasper a naked area near the apex and for this and others characters is different from the others of the group. F. flaviscutellatus n. sp., F. oliverioi, F. intermedius and whithmani, are very allied but the first one can be very easily distinguished because it’s scutellum is light. Flebotomus barrettoi n. sp., F. coutinhoi n. sp., F. aragãoi, F. brasiliensis, F. lutzianus, F. texanus, F. pascalei, F. atroclavatus and F. tejeraae are very allied forming a natural group. The two last ones are not well known but the A. A. who have studied them described very long clipeus so long as the head and for that reason can be distinguished from all the others included the two new ones. F. coutinhoi is the only one who presents the apecis of the penis filaments twisted. F. barrettoi n. sp., can be distinguished from aragãoi, texamus and coutinhoi by the length of the penis filaments and from atrocavatus, tejeraae, lutzianus and brasiliensis by the arrangement of the spines of distal segment of the upper clasper. Flebotomus ubiquitalis n. sp., F. auraensis n. sp., F. affinis and F. microps e F. antunesi have many common characters. F. microps n. sp., can be distinguished from any one by the size of the eyes and the presence od well developed genae. This species and other new species are different from F. antunesi by the arrangement of the spines of the distal segment of the upper clasper of the latter. F. ubiquitalis n. sp. can be distinguished from others by the figure of the median clasper. F. auraensis n. sp. Can be distinguished from F. affinis n. sp. By the tuft hairs on the inner face of the basal segment and by arrangement of the spines of the sital segment of the upper clasper. Flebotomus brachipygus n. sp. Seemed to be F. rostrans, specie not well known, by the characters of the genitalia but can not be identified to her by the clypeus size and the palpi’s characters. Flebotomus costalimai, n. sp., f. tupynambai n. sp., and f. castroi Barreto & Coutinho, 1941, are very allied species and the A. proposes to included them the new sub-genus Castromyia, in honor to Dr. G. M. de Oliveira Castro, appointing like typespecies F. castroi with the V joint longer than III + IV; antennae with geniculated spines without posterior prolongation. Genitalia: the basal segment of the upper clasper with a tuft of hairs and the distal segment with 4 spines, one of them at the apex and near it a thin and straight bristle difficult to see; the median clasper with one spinous hair isolated...

RECASTING THE ELLIOTT CONJECTURE

Let A be a simple, unital, finite, and exact C*-algebra which absorbs the Jiang-Su algebra Z tensorially. We prove that the Cuntz semigroup of A admits a complete order embedding into an ordered semigroup which is obtained from the Elliott invariant in a functorial manner. We conjecture that this embedding is an isomor phism, and prove the conjecture in several cases. In these same cases - Z-stable algebras all - we prove that the Elliott conjecture in its strongest form is equivalent to a conjecture which appears much weaker. Outside the class of Z-stable C*-algebras, this weaker conjecture has no known counterexamples, and it is plausible that none exist. Thus, we reconcile the still intact principle of Elliott's classification conjecture -that K-theoretic invariants will classify separable and nuclear C*-algebras- with the recent appearance of counterexamples to its strongest concrete form.

Sôbre alguns Phlebotomus e Brumptomyia da Colômbia (Diptera, Psychodidae)

The first case of Kala-azar in Colombia was discovered in Soledad, S. Vicente do Chucuri, Dept. Santander, by Gast-Galvis who viscerotomized a three year old girl deceased in December, 1943. In 1944, fifty-three Phlebotominae were collected in the chicken pen of the girl's house, two new species included. Mangabeira helped by A. Gast Galvis, Juan Antonio Montoya and E. Osorno Mesa, collected some Phlebotomus in that country. The geographical distribution of the species of Phlebotomus collected in Colombia (P. abonnenci, P. camposi, P. columbianus, P. dubitans, P. gasti, P. montoyai, P. saulensis, P. serranus, P. triramulus) and two species of Brumptomyia (B. beaupertuyi and b mesari), are included. our description of the male P. columbianus is based on some specimens found in association with females. However, doubts exist about such association of sexes. There is no correspondence between the length of the spicules and the ducts of spermathecae. Besides, the specimens were not obtained by raising. The following new species are described and compared with previously known ones: a) Phlebotomus gasti sp. n. differs from the other species by a protruding tubercle in the gubernaculum. It has also fewer setae in the tuft of the basistyle, a different length of the inferior gonapophyses, and a differently shaped clasper. b) Phlebotomus dubitans sp. n. differs from P. walkeri and P. deanei (according to personal information from O. Theodor, who examined the types, they are identical to P. williamsi and P. sericeus respectively), mainly because these species have the inferior gonapophyses larger than the basistyle and fewer setae in the basistyle. P. evandroi is separated by the shape of the claspers and by the tuft of setae of the basistyle. P. marajoensis is the closest relative to P. dubitans. There is a possibility of their being synonymous. On the other hand, they can be differentiated by the existence of three extra distal spines in P. marajoensis. There is also a difference in their palpal indexes: for marajoensis I - II - IV - III - V, and for dubitans I - IV (III - II) - V. We notice, too, that the inferior gonapophyses in P. marajoensis is a little shorter. P. marajoensis has a long seta in the basistyle (clearly shown in the original drawing), not found in the new species. c) Phlebotomus montoyai sp. n.: The closest relatives are P. noguchii, P. peruensis, P. pescei, P. quinquifer and P. rickardi. They differ from the new species by the number and length of the setae of the basistyle tuft which are more numerous and longer in the new species. The shapes of their claspers are also different. Other differences are: the basal portion of the basistyle in P. noguchii is very wide (in montoyai it is narrower); the intermediate spine of the dististyle is located on a protruding tubercle ( in the new species there is hardly a tubercle); the spicules are long, and the inferior gonapophyses is longer than the basistyle. P. quinquifer and P. rickardi have a shorter dististyle and narrower wings, with different venation. The main difference, however lies, in the M4, which ends almost at the level of the junction of M1 with M2 (in P. montoyai the M4 ends far behind). In P. peruensis and P. pescei the intermediary spine of the dististyle is closer to the distal spine than to the basal one, whereas in the new species it is situated between the two pairs. Their inferior gonapophyses is longer than the basistyle. d) Brumptomyia mesai sp. n. - Closest relatives are: B. hamatus, B. pentacanthus, B. beaupertuyi which are easily separated from the new species because the tufts of their basistyle have thin and differently shaped hairs. Also their claspers are shaped differently. B. avellari is also easily recognized on account of the twisted aspect of its clasper and because the basal tuft of the basistyle has few setae, B. brumpti tuft of setae arise directly from the basistyle; these setae are stronger than those of the new species. It has 8 blade-like setae located on the inner surface of the distal half, whereas the new species has only six setae. In B. brumpti, there are three median and two terminal spines in the dististyle; in the new species, there are two median and two terminal spines and one between them, which is closer to the two median spines. The comparison with B. galindoi is based in a specimen determined by Fairchild and deposited in the entomological collection of the "Faculdade de Higiene e Saúde Pública da Universidade de S. Paulo". The genitalia of the new species is much shorter, in galindoi the inferior gonapophyses is 0,8 mm long whereas in B. mesai it hardly reaches 0,6 mm. The shape of the clasper and the distribution of its setae are different. The sub-median lamellae, besides being longer in B. galindoi are also longer in comparison with the other parts of the genitalia. The gubernaculum of the new species is longer, thinner, and more pointed; in B. galindoi it is shorter and triangular. In the drawing published by Fairchild and Hertig 91947), the basistyle shows 8 blade-like setae on the distal half, whereas in the new species only six are found.

Real rank zero algebras have the corona factorization property

The purpose of this short note is to prove that a stable separable C*-algebra with real rank zero has the so-called corona factorization property, that is, all the full multiplier projections are properly in finite. Enroute to our result, we consider conditions under which a real rank zero C*-algebra admits an injection of the compact operators (a question already considered in [21]).

Chain conditions for Leavitt path algebras

In this paper, results known about the artinian and noetherian conditions for the Leavitt path algebras of graphs with finitely many vertices are extended to all row-finite graphs. In our first main result, necessary and sufficient conditions on a row-finite graph E are given so that the corresponding (not necessarily unital) Leavitt path K-algebra L(E) is semisimple. These are precisely the algebras L(E)for which every corner is left (equivalently, right)artinian. They are also precisely the algebras L(E) for which every finitely generated left (equivalently, right) L(E)-module is artinian. In our second main result, we give necessary and sufficient conditions for every corner of L(E) to be left (equivalently, right) noetherian. They also turn out to be precisely those algebras L(E) for which every finitely generated left(equivalently, right) L(E)-module is noetherian. In both situations, isomorphisms between these algebras and appropriate direct sums of matrix rings over K or K[x, x−1] are provided. Likewise, in both situations, equivalent graph theoretic conditions on E are presented.

A relative double commutant theorem for hereditary sub-C*-algebras

We prove a double commutant theorem for hereditary subalgebras of a large class of C*-algebras, partially resolving a problem posed by Pedersen[8]. Double commutant theorems originated with von Neumann, whose seminal result evolved into an entire field now called von Neumann algebra theory. Voiculescu proved a C*-algebraic double commutant theorem for separable subalgebras of the Calkin algebra. We prove a similar result for hereditary subalgebras which holds for arbitrary corona C*-algebras. (It is not clear how generally Voiculescu's double commutant theorem holds.)

Strongly non-degenerate Lie algebras

Let A be a semiprime 2 and 3-torsion free non-commutative associative algebra. We show that the Lie algebra Der(A) of(associative) derivations of A is strongly non-degenerate, which is a strong form of semiprimeness for Lie algebras, under some additional restrictions on the center of A. This result follows from a description of the quadratic annihilator of a general Lie algebra inside appropriate Lie overalgebras. Similar results are obtained for an associative algebra A with involution and the Lie algebra SDer(A) of involution preserving derivations of A

Weighted limits in simplicial homotopy theory

We extend the theory of Quillen adjunctions by combining ideas of homotopical algebra and of enriched category theory. Our results describe how the formulas for homotopy colimits of Bousfield and Kan arise from general formulas describing the derived functor of the weighted colimit functor.

On two examples by Iyama and Yoshino

In a recent paper Iyama and Yoshino consider two interesting examples of isolated singularities over which it is possible to classify the indecomposable maximal Cohen-Macaulay modules in terms of linear algebra data. In this paper we present two new approaches to these examples. In the first approach we give a relation with cluster categories. In the second approach we use Orlov's result on the graded singularity category. We obtain some new results on the singularity category of isolated singularities which may be interesting in their own right.

Homotopy exponents for large H-Spaces

We show that H-spaces with finitely generated cohomology, as an algebra or as an algebra over the Steenrod algebra, have homotopy exponents at all primes. This provides a positive answer to a question of Stanley.

Localization of algebras over coloured operads

We give sufficient conditions for homotopical localization functors to preserve algebras over coloured operads in monoidal model categories. Our approach encompasses a number of previous results about preservation of structures under localizations, such as loop spaces or infinite loop spaces, and provides new results of the same kind. For instance, under suitable assumptions, homotopical localizations preserve ring spectra (in the strict sense, not only up to homotopy), modules over ring spectra, and algebras over commutative ring spectra, as well as ring maps, module maps, and algebra maps. It is principally the treatment of module spectra and their maps that led us to the use of coloured operads (also called enriched multicategories) in this context.

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defined by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincaré-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.