Conforme observado por I. Moerdijk e G. Reyes em [63], os an´ eis **C** ∞ tˆ em sido estudados especialmente tendo em vista suas aplica¸ **c**˜ oes em Teoria de Singularidades e para construir toposes que sirvam de modelos para a Geometria Diferencial Sint´ etica. Neste trabalho, seguimos um caminho complementar, aprofundando nosso conhecimento sobre eles por um vi´ es mais puro, fazendo uso da Teoria das Categorias e os analisando a partir de pontos de vistas alg´ ebrico e l´ ogico-categorial. Iniciamos o trabalho apresentando uma sistematiza¸**c**˜ ao abrangente dos fatos fundamentais da teoria (equacional) dos an´ eis **C** ∞ , distribu´ıdos aqui e ali na literatura atual - a maioria sem demonstra¸ **c**˜ oes - mas que servem de base para a teoria. Na sequˆ encia, desenvolvemos alguns t´ opicos do que denominamos ´ Algebra Comutativa **C** ∞ , expandindo resultados parciais de [66] e [67]. Realizamos um estudo sistem´ atico dos an´ eis **C** ∞ von Neumann-regulares - na linha do estudo alg´ ebrico realizado em [2]- e apresentamos alguns resultados interessantes a seu respeito, juntamente com sua rela¸ **c**˜ ao (funtorial) com os espa¸ cos booleanos. Estudamos algumas no¸**c**˜ oes pertinentes ` a Teoria de Feixes para an´ eis **C** ∞ , tais como espa¸ cos (localmente) **C** ∞ −anelados e o s´ıtio de Zariski liso. Finalmente, descrevemos toposes classificantes para a teoria (alg´ ebrica) dos an´ eis **C** ∞ , a teoria (coerente) dos an´ eis locais **C** ∞ e a teoria (alg´ ebrica) dos an´ eis **C** ∞ von Neumann regulares.

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The objective **of** this article is to present a reflection on what we have called conceptual nexuses **of** the **algebraic** knowledge from the historic **and** **logical** movement **of** the concepts. A conceptual nexus is defined as a link between the historic **and** **logical** forms **of** understanding the concept, which do not necessarily coincide with the different languages that express the concept. This study, **of** a theoretical character, was carried out by taking as singular **some** episodes highlighted in the history **of** algebra **and** acknowledging in their particularities (manifestations **of** language, thought forms, etc.) the conceptual nexuses that configure **algebraic** thought: the relationship among variable magnitudes in general. It was assumed that the knowledge **of** the historic **and** **logical** movement **of** **algebraic** concepts **and** its theoretical thought forms generate implications for the constitution **of** algebra’s teaching object **and** for the organization **of** teaching, thus contributing to overcome epistemological impasses in the appropriation **of** knowledge both by those who teach **and** those who learn.

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Abstract It presents the organization **of** knowledge through its philosophical **and** historical suppositions. It approaches questions such as the significant modalities, among which are the Aristotle´s categories **and** predictables **and**, consequently, **and** consequently the prominence **of** meaning, the knowledge trees with its hierarchical **and** universal structures, aiming at thinking over the fixed references **of** knowledge in modern times, influencing the classification theory, as well as the controlled language constructions. The present work is divided into the organization **of** knowledge, on its classical philosophical suppositions, its application in Ancient Times **and** Middle-Ages besides the improvement **of** the languages built during Modern Ages. It makes **some** considerations about the organization **of** knowledge in the post-modern times, **and** points out to a change on the “tagging” **of** the collaborative knowledge beyond the indexation operated by the robots from the search engines.

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Neutrosophy is a new branch **of** philosophy which studies the origin **and** features **of** neutralities in the nature. Floren- tin Smarandache in 1980 firstly introduced the concept **of** neutrosophic logic where each proposition in neutrosophic logic is approximated to have the percentage **of** truth in a subset T, the percentage **of** indeterminacy in a subset I, **and** the percentage **of** falsity in a subset F so that this neutro- sophic logic is called an extension **of** fuzzy logic. In fact neutrosophic set is the generalization **of** classical sets, con- ventional fuzzy set 1 , intuitionistic fuzzy set 2 **and** in- terval valued fuzzy set 3 . This mathematical tool is used to handle problems like imprecise, indeterminacy **and** in- consistent data etc. By utilizing neutrosophic theory, Vasantha Kandasamy **and** Florentin Smarandache dig out neutrosophic **algebraic** structures in 11 . **Some** **of** them are neutrosophic fields, neutrosophic vector spaces, neu- trosophic groups, neutrosophic bigroups, neutrosophic N- groups, neutrosophic semigroups, neutrosophic bisemi- groups, neutrosophic N-semigroup, neutrosophic loops, neutrosophic biloops, neutrosophic N-loop, neutrosophic groupoids, **and** neutrosophic bigroupoids **and** so on. In this paper we have tried to develop the the generalization **of** neutrosophic ring **and** neutrosophic field in a **logical** manner. Firstly, preliminaries **and** basic concepts are given for neutrosophic **rings** **and** neutrosophic fields. Then we presented the newly defined notions **and** results in neutrosophic birings **and** neutrosophic N-**rings**,

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Management implies a strong relation between the process **and** the management system, which must react to the events that occur. )n the given context, the management system bears certain A) features, if in the presence **of** **some** information **of** minimum orientation from the human governor; it can carry out complex actions as a response to the events from the outward environment. )ntelligence can include the ability to accept certain abstract specifications **of** tasks in a general form **of** purposes/restrictions **and** the production **of** **some** reasonable actions that agree with the specifications. )n any real-time A) system there is a fundamental compromise between the action **and** the reasoning. Time is a precious resource that uses up if the system must create reasoning over the actions before their execution. This time consumption can limit the number **of** the desired alternative actions **and** in this way the reasoning task becomes much more difficult to realise. )n certain cases, the lack **of** success **of** an action can be the most unfavourable solution, while in other cases any **of** the actions can be better that total lack **of** it. The necessary time for reasoning can warn us over certain delays or disasters. The efficiency **of** a real-time A) system depends on its ability to allocate reasoning efforts in concordance with the process situations. The process **of** allocation is most **of** the time a difficult process due to countless overloads **of** information. The visible state **of** the process is huge **and** can contain incomplete, contradictory or uncertain information, which entails the use **of** **some** modules in the structure **of** the management system as **some** problem-solving ones. Furthermore, this information is often changing. )t is actually impossible for a real-time system based on symbolic A) techniques to completely process all the information at a given moment **and** to choose a convenient type **of** reasoning, **and** to also respect all real-time restrictions.

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Abstract. **Some** **aspects** **of** periodontitis pathogenesis in children. Shcherbina I.N., Kovach I.V., Dychko Ye.N., Taran O.M. Inflammatory processes in the tissues surrounding tooth root are frequent enough **and** develop as the direct complication **of** caries. As acute periodontitis is manifested with grinding toothache **and** violation **of** physio- **logical** act **of** chewing, symptoms **of** general intoxication, the continuous sluggish chronic periodontitis is harmful **and** dangerous to the organism as well. It forms the state **of** chronic dontogenetic intoxication **and** chroneosepsis with wrong functioning **of** **some** internal organs **and** body systems. The like complications can cause significant disturbance to the function **of** kidneys, liver, heart, joints **and** their treatment without ablating focus **of** inflammation is often in- effective; this must be taken into account by doctors-interns. However, scanning **of** the oral cavity by conservative means has its difficulties mostly because **of** ignoring pathogenesis **of** such inflammation. That is why activity **of** ferments **of** blood dehydrogenases from the periapical tissues **of** the teeth affected with the chronic periodontitis was studied. The level **of** succinate dehydrogenase **and** alpha-glycerophosphate degydrogenase **of** lymphocytes **of** 110 schoolchildren aged 13-17 years old was studied. The main group **of** examined individuals included those **of** infected with tuber- culousis – 50 individuals, **and** the control group (60 individuals) – clinically healthy ones without tuberculousis desease. All schoolchildren had 1 or 2 teeth affected with chronic periodontitis **of** the apical localization. The re- searchers found that a significant inhibition **of** activity **of** succinate dehydrogenase **and** alpha-glycerophosphate degydrogenase ferments occurs in the inflammatory periodontal tissues, which indicates to local immunity decline, **and** as a consequence, pathogenic bacteria activation. In people infected with tuberculousis these violations were more developed. Such features **of** periodontitis pathogenesis must be taken into account when providing a combined treatment.

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In this paper we raise firstly inadequacies **of** the analysis **of** the verb to shoot by Croft (1998). Subsequently, we assign to this verb alternative configurations **of** base **and** profile according to the causal structure model (Croft, 1991, 1998) **and** the action chain model (Langacker, 1999). That forms the basis **of** a cognitive-grammatical description **of** a subset **of** the readings **of** the German verbs schießen, abschießen, anschießen, erschießen, totschießen **and** niederschießen. It will be suggested that these senses can be attributed to a large extent to functions, which are applied to verbal bases **and** profiles, **and** extend or shift these segments. Qualia structure **of** the verbs' complements are also considered. **Aspects** **of** the generative lexicon theory (Pustejovsky, 1995) are included in this way into the cognitive semantic analysis. Differently than proposed by Pustejovsky (1995), however, we plead for ordered rules, which erase certain arguments **of** a verb under certain conditions, instead **of** classifying these items according to their possibility **of** being omitted.

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In RLF Wittgenstein keeps his Tractarian presupposition that there should be exactly one logic: “We must eventually reach the ultimate connection **of** the terms, the immediate connection which cannot be broken without destroying the propositional form as such.” (RLF 162 f.) This position is still connected with logicism in the sense that we can ind something which is logically fundamental: “Such rules, however, cannot be laid down until we have actually reached the ultimate analysis **of** the phenomena in question. This, as we all know, has not yet been achieved.” (RLF 171) But putting numbers “into the structure **of** the atomic propositions themselves” **and** assuming any kind **of** coordinate system within **logical** space allow a kind **of** formal interaction between the structured atomic propositions **and** the coordinates **of** the **logical** space. One consequence is that **some** complex expressions are not allowed. Can we maintain **logical** atomism in the long run? Can we maintain at least **some** **of** its **aspects**?

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The most practical **and** easiest way **of** diagnosing cryptosporidiosis is the detection **of** parasite oocysts in feces or other body fluids. Various techniques have been used to visualize these oocysts, such as Ziehl-Neelsen staining, modified, Kinyoun carbolfuchsin staining, modi- fied, **and** staining with safranin-methylene blue **and** meth- enamine silver. Concentration methods, such as formalin- ether sedimentation or Sheather’s sugar flotation method, increase considerably the sensitivity **of** oocyst detection. The oocysts **of** this protozoon can be visualized in histo- **logical** sections **of** intestinal mucosa obtained by biopsy **and** stained with hematoxylin-eosin as single cells or grouped on the mucosal surface, i.e., at the brush border **of** the intestinal epithelium. More recent techniques us- ing fluorescent dyes such as acridine orange **and** auramine carbolfuchsin provided results comparable to those ob- tained with the staining methods described above for di- arrheic feces, **and** are able to detect parasites even in formed feces. Immunoenzymatic techniques (ELISA) us- ing monoclonal antibodies have shown a high degree **of** sensitivity **and** specificity for the detection **of** oocysts in feces **and** contaminated water (Costa-Cruz et al. 1996, Hoxie et al. 1997, Guerrant 1997, Griffiths 1998). Serologi- cal tests for the detection **of** antibodies represent an alter- native to parasitological methods for the diagnosis **of** cryptosporidiosis. Immunoenzymatic assays (ELISA) us- ing crude extract **of** ruptured oocysts as antigen have shown good sensitivity, although **some** studies have dem- onstrated that immunoblotting is much more sensitive **and** specific for antibody detection. In these cases, IgA type responses are observed which are directed against anti- gens found on the surface **of** sporozoites, the infectious form **of** the parasite; such antibodies seem to exert a pro- tective effect against symptomatic infection (Mooss et al. 1998, Eisemberg et al. 2001). A specific PCR has been de- veloped **and** may represent a better option for the diagno- sis **of** this infection in the future (Griffiths 1998).

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most, at their boundaries. Most interestingly, Penrose tilings [49] — famous because **of** their mathematical properties, such as the lack **of** translational symmetry — waited ten years to be found as the ideal models for certain quasicrystals [35]. Kellendonk’s application consisted in the construction **of** a non-commutative space **and** the corresponding **C** ∗ -algebra from a tiling. Two other papers by Kellendonk would follow. In [24], Kellendonk takes a different approach to the same problem. This time, the definition **of** a multiplicative structure on the classes **of** portions **of** the tiling, consisting **of** a finite union **of** tiles under translation, yield an almost-groupoid from which a topological groupoid is built. The reason why only the local structure **of** the tiling (that is, how the tiling looks on finite patches) matters has to do with the local nature **of** the interactions in the solid. Subsequently, a group assigned to this topological groupoid is going to provide, in theory at least, **some** information on the solid modelled by the tiling. The almost-groupoid associated to the tiling is precisely the ancestor **of** the tiling semigroup, a concept that would only be formulated later by Mark V. Lawson [32] (see also Kellendonk **and** Lawson [26]).

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Examples 3.7. A partially ordered set X is a split algebra for the downset monad if **and** only if X is completely distributive, in this case the map t : X → DX sends x ∈ X to the set {y ∈ X | y ≪ x} **of** all elements y ∈ Y which are totally below x (see [28, 17]). Similarly, a directed cocomplete partially ordered set X is a split algebra for I = (I, m, e) if **and** only if X is a domain (see Definition 2.5(4)); in this case the splitting t : X → IX is given by x 7→ {y ∈ X | y x}. Regarding the filter monad F = (F, m, e) on Top 0 , a continuous lattice X (equipped with the Scott topology) is a split algebra for F if **and** only if X is F-disconnected in the sense **of** [19]. Here, with α : F X → X denoting the algebra structure **of** X, for an open subset A ⊆ X we put µ(A) = {x ∈ X | α(f) = x for **some** f ∈ F X with A ∈ f}. Then X is F-disconnected precisely when µ(A) is open, for every open subset A ⊆ X; **and** in this case the map t : X → F X sends x ∈ X to the filter t(x) = {A ⊆ X | A open, x ∈ µ(A)}. The case **of** the prime filter monad is similar, with µ(A) now defined using only prime filters. In terms **of** partially ordered compact Hausdorff spaces, every split algebra for F 2 is a Priestley space, more precise, a Priestley

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For obtain optimal packing lattices we need to find spheres whose centers are points **of** a lattice 3 **and** that the intersection **of** any two spheres is only a point. For the determination **of** the radius **of** these spheres, note that fixed k > 0, the intersection **of** the compact set {x ∈ R n ; |x| ≤ k} with the lattice 3 is a finite set. Therefore the number t = min{|x|; x ∈ 3, x 6= 0} is well defined. Furthermore, ρ(3) = t/2 is the greatest radius such that it is possible to obtain a packing lattice. If B (ρ(3)) is the sphere with center in the origin **and** radius ρ(3) then the packing density **of** 3 is defined by

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responsible for actions he or she was not able to perform **of** his or her own free will. Accountability implies the capacity on the part **of** that person to act autonomously. Therefore, God creates in us a power to act **and** to choose a course **of** action, opting between two opposites. Furthermore, it is God who makes available the causes through which we operate, **and** it is He who removes any obstacles precluding those acts. However, these are at- tributed to us rather than to God. We appropriate these actions by our will **and** with the concurrence **of** external causes. The external causes condition our choice **of** one **of** the opposites. This is explained in the following way: we desire something when we form an idea **of** it. Then we accept it. **And** this acceptance or assent (ta sdiq) is not due to our choice. The corollary **of**

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A empresa vienense Österreichische Chemische Werke, dirigida pelos irmãos R. e O. Margulies, em 1904 procurou Haber, ainda Privatdozent (título equivalente à nossa Livre-docência) em Karlsruhe para uma orientação e quiçá um desenvolvimento poste- rior sobre a fixação do nitrogênio. Inicialmente, Haber indicou Ostwald (Haber desconhecia o que houvera em 1900, inclusive o pedido de patente), porém parece que ele não se interessou. Haber então, com seu assistente Gabriel van Oordt, partindo dos resulta- dos de Ramsay e Young, realizou o seguinte experimento: passou uma corrente muito lenta de amônia sobre pó de ferro aquecido a 1000 °**C** e separou a amônia não decomposta; passou, a seguir, os gases obtidos na decomposição (nitrogênio e hidrogênio) sobre o mesmo catalisador e obteve uma quantidade de amônia muito pró- xima da não decomposta. Isto significou que ele atingiu o estado de equilíbrio partindo das “duas pontas”, ou seja, pela decomposição e pela síntese,

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In general terms, **logical** pluralism is the claim that there is more than one adequate, coherent, or even, true logic. Note that, from a pure abstract point **of** view, this thesis may seem trivial today. It’s obvious that there are different pure logics. But **logical** pluralism is not exactly, or not only, about this. It amounts to acknowledge, for instance, that given a certain domain, there are at least two logics that formalize it in a fundamentally different way. **And** that, nonetheless, both are equally adequate for this task. There are many kinds **of** **logical** pluralism (Cf. BEALL, RESTAL, 2006 **and** SHAPIRO, 2014), but that’s not really relevant for the moment. In a schematic way, a pluralist logician claims that exists situations such that

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As então chamadas “terras ítria e céria” foram estudadas entre os anos de 1839 e 1843 por Carl G. Mosander (1797- 1858), que mostrou não serem substâncias simples e sim mis- turas bastante complexas. Mosander conseguiu isolar da céria, em 1839, as substâncias simples dos elementos cério e lantânio, e da ítria, em 1843, as dos elementos ítrio, térbio e érbio. Em 1878, Jean Charles G. de Marignac (1817-1894) isolou o itérbio e, em 1880, o gadolínio. Em 1879, Boisbaudran isolou o samário e, em 1886, o disprósio. Também em 1879, Cleve evi- denciou a existência do hólmio e do tálio, e Nilson descobriu o escândio. Outros pesquisadores também conseguiram isolar no- vos elementos. Em 1885, confirmando suspeitas de outros pes- quisadores de que o didímio era uma mistura de elementos, o Barão Auer von Welsbach (1858-1929), químico austríaco, iso- lou o praseodímio (“didímio verde”) e o neodímio (“novo didímio”) a partir do didímio (do grego: “gêmeo”); posterior- mente (1907), em colaboração com Georges Urbain (1872-) e **C**. James, isolou o lutécio a partir da ítria. Em 1901, Eugène A. Demarçay (1852-1904) caracterizou a existência do európio 7,54 .

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Because **of** its various forms **of** transmission, he- patitis remains circulating in the population. The most common forms **of** infection are sexual, pa- renteral **and** vertical [10]. However, other forms **of** transmission such as use **of** manicure tools, crack pipe **and** tools to inhale cocaine have been associa- ted with hepatitis [11]. The incidence may be even higher than those reported in various regions **of** the country as often hepatitis is only diagnosed after clinical suspicion. The delay in diagnosis may con- tribute to a poor prognosis, with the presence **of** complications such as liver cirrhosis, hepatocellular carcinoma cell **and** even death.

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This paper describes **some** morphological **aspects** **of** Cylicocyclus brevicapsulatus (Ihle, 1920) (Nematoda: Cyathostominae) from Equus caballus in Brazil. The worms were studied using an optical microscope (measurements **and** illustrations) **and** a scanning electron microscope for a more detailed examination **of** the external morphology. The buccal capsule is very short, with a very thin wall, **and** the dorsal gutter is absent. Other morphological **aspects** are described including measurement **of** the spicules **and** gubernaculum.

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ABSTRACT - (Development **and** **some** histochemical **aspects** **of** foliar glandular trichomes **of** Stevia rebaudiana (Bert.) Bert. - Asteraceae). The ten-celled biseriate glandular trichome **of** Stevia rebaudiana (Bert.) Bert.-Asteraceae, found on both leaf surfaces, originates from a single protruding, protodermal cell undergoing an anticlinal division. A subsequent series **of** periclinal divisions, occurring in acropetal sequence, leads to the formation **of** the trichome, composed **of** five pairs **of** cells, one pair **of** basal cells, another **of** stalk cells **and** three pairs **of** secretory head cells. Developing, still two-celled glandular trichomes already occur on leaf primordia **of** the second pair (these primordia measuring, in **some** cases, ca. 0.30 mm in length), **and** most **of** the glandular trichomes are at the mature phase on very young, expanding leaves, for example on those **of** the sixth pair. The secretory material released by the head cells is stored in the trichome cavity (subcuticular space). Basic histochemical tests reveal that such material is lipophilic (mainly) **and** hydrophilic in nature.

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This work is financed by the ERDF – European Regional Development Fund through the Operational Programme for Competitiveness **and** Internationalisation – COMPETE 2020 Pro- gramme **and** by National Funds through the Portuguese funding agency, FCT – Fundação para a Ciência e a Tecnologia within project POCI-01-0145-FEDER-016692. We also gratefully ac- knowledge partial financial assistance by Portuguese funds through CIDMA (Center for Research **and** Development in Mathematics **and** Applications), **and** the Portuguese Foundation for Sci- ence **and** Technology (“FCT – Fundação para a Ciência e a Tecnologia”), within the project UID/MAT/04106/2013. Finally, Renato Neves **and** Pedro Nora are supported by FCT grants SFRH/BD/52234/2013 **and** SFRH/BD/95757/2013, respectively.

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