Let SP be the set of upper strongly porous at 0 subsets of \mathbb{R}^{+} and let Î(SP) be the intersection of maximal ideals I\subseteq SP. Some characteristic properties of sets E \in Î(SP) are obtained. We also find a characteristic property of the intersection of all maximal ideals contained in a given set which is closed under subsets. It is shown that the ideal generated by the so-called completely strongly porous at 0 subsets of \mathbb{R}^{+} is a proper subideal of Î(SP). Earlier, completely strongly porous sets and some of their properties were studied in the paper V.Bilet, O.Dovgoshey (2013/2014)., Viktoriia Bilet, Oleksiy Dovgoshey, Jürgen Prestin., and Obsahuje seznam literatury
Let $q$ be a positive integer, $\chi $ denote any Dirichlet character $\mod q$. For any integer $m$ with $(m, q)=1$, we define a sum $C(\chi, k, m; q)$ analogous to high-dimensional Kloosterman sums as follows: $$ C(\chi, k, m; q)=\sum _{a_1=1}^{q}{}' \sum _{a_2=1}^{q}{}' \cdots \sum _{a_k=1}^{q}{}' \chi (a_1+a_2+\cdots +a_k+m\overline {a_1a_2\cdots a_k}), $$ where $a\cdot \overline {a}\equiv 1\bmod q$. The main purpose of this paper is to use elementary methods and properties of Gauss sums to study the computational problem of the absolute value $|C(\chi, k, m; q)|$, and give two interesting identities for it.
The Fibonacci Cube is an interconnection network that gets many desirable properties that are very important in the network design, network stability and applications. The extended Fibonacci Cube is a new network topology. The vulnerability value of a communication network shows the resistance of the network after the disruption of some centres or connection lines until the communication breakdown. In a network, as the number of centres belonging to sub networks changes, the vulnerability of the network also changes and requires greater degrees of stability or less vulnerability. If the communication network is modelled by graph G, the deterministic measures tend to provide a worst-case analysis of some aspects of overall disconnection process. Many graph theoretical parameters have been used in the past to describe the stability of communication networks. There are few parameters such as integrity, neighbour-integrity and tenacity number giving the vulnerability. Also, in the neighbour-integrity, if a station is destroyed, the adjacent stations will be betrayed so that the betrayed stations become useless to network as a whole.
In this paper we study the stability of the Extended Fibonacci Cube using the integrity and neighbour-integrity. We compared the obtained results with the results of the other network topologies. We saw that, for two graphs G1 and G2 that have same number of vertices if k(G1) > k(G2), then I(G1) > I(G2) and NI(G1)< NI(G2).
That early Buddhists were acquainted with the Homeric Hymns is vehemently suspected. That Homer’s epics were used by them has not been suspected. Buddhists of perhaps the third to fourth centuries clearly used two episodes, the Pyre of Patroclus and Odysseus’ Bow. Adaptations and variations lead to a suspicion that the stories, admired by Buddhist authors, were worked over more than once. That the Greek text of the original epics was used at that relatively late period has not been established.
Morphological examination of novel specimens of paruterinid cestodes from passerine birds from Brazil and Chile and of museum specimens from Paraguay revealed two new species: Anonchotaenia prolixa sp. n. from Elaenia albiceps chilensis Hellmayr from Chile, and Anonchotaenia vaslata sp. n. from Tyrannus melancholicus (Vieillot) (type host) and Myiodynastes maculatus (Statius Muller) from Paraguay. The generic diagnosis of Anonchotaenia Conn, 1900 is amended, prompted by the presence of the armed cirrus and the elongated cirrus sac of A. prolixa. Two species were redescribed: Anonchotaenia brasiliensis Fuhrmann, 1908 from Tachyphonus coronatus (Vieillot) and Thraupis cyanoptera (Vieillot) (new host records) from Brazil, and Thraupis sayaca (Linnaeus) and Volatinia jacarina (Linnaeus) from Paraguay (new host and geographic records); and Anonchotaenia macrocephala Fuhrmann, 1908 from Tachycineta leucorrhoa (Vieillot) (new host record) from Brazil, Tachycineta meyeni (Cabanis) from Chile (new host and geographic record) and Stelgidopteryx ruficollis (Vieillot) from Paraguay (new host and geographic record). Scanning electron microscopy of A. brasiliensis and A. macrocephala revealed less microthrix variation than has been reported for other cyclophyllidean taxa. Sequence data were generated for nuclear ssr- and lsr-DNA and mitochondrial rrnL and cox1 for A. prolixa, A. brasiliensis, and A. macrocephala. Maximum likelihood and Bayesian inference analyses supported each species as distinct, but revealed cryptic diversity among A. brasiliensis specimens from different host families. New host records of A. brasiliensis and A. macrocephala prompted a formal assessment of host specificity. Anonchotaenia prolixa was found to be oioxenous (HSS = 0), A. vaslata and A. macrocephala were found to be metastenoxenous (HSS = 3.000 and 3.302, respectively), whereas A. brasiliensis was found to be euryxenous (HSS = 5.876). Anonchotaenia brasiliensis has been found parasitising several species of different passerine families that participate in mixed-species foraging flocks in the Atlantic Forest. A diversity of species of other families join these flocks and are among the substantial number of South American passerine species yet to be examined for cestodes.
Two new species of the feather mite family Pteronyssidae Oudemans, 1941 are described from the white-barred piculet, Picumnus cirratus Temminck from Brazil: Pterotrogus picumni sp. n. and Ramphastobius scutatus sp. n., representing the first mites described from this host. Pterotrogus picumni sp. n. can be readily distinguished from all previous species of the simplex group by having dorsal crest on femora I and II in both sexes. This is the first representative of the genus Pterotrogus Gaud, 1981 recorded on a host of the genus Picumnus Temminck. Ramphastobius scutatus sp. n. is unique among species of the genus by having in both sexes the prodorsal and scapular shields fused into a single propodonotal shield covering all prodorsum. An updated key to known species of the genus Ramphastobius Gaud, 1981 is presented.
The examination of the type series of Ophiotaenia gallardi (Johnston, 1911) (syn. Proteocephalus gallardi Johnston, 1911) revealed that it is a mixture of two species of different genera. Lectotype of Ophiotaenia gallardi is designated and the species is redescribed on the basis of it, conspecific paralectotypes and additional materials. The remaining part of the type series belongs to Vandiermenia gen. n. (Acanthotaeniinae), with V. beveridgei sp. n. as the type- and only species. The new genus differs from all other acanthotaeniine genera, i.e. Rostellotaenia Freze, 1963, Acanthotaenia von Linstow, 1903 and Kapsulotaenia Freze, 1963, by the presence of cortical uterine stem and paramuscular vitelline follicles, particular structure of the internal longitudinal musculature (absent laterally and more developed than in the three above-mentioned genera) and testes limited in two fields separated medially. Type series of Ophiotaenia mjobergi (Nybelin, 1917) (syn. Crepidobothrium mjobergi Nybelin, 1917), O. amphiboluri (Nybelin, 1917) (syn. Crepidobothrium amphiboluri Nybelin, 1917), O. striata (Johnston, 1914) (syn. Acanthotaenia striata Johnston, 1914) and O. longmani Johnston, 1916 are revised and compared with Ophiotaenia gallardi. Australotaenia hylae (Johnston, 1912) comb. n. is proposed for Ophiotaenia hylae Johnston, 1912. Australotaenia gen. n. differs from the remaining genera of the subfamily Acanthotaeniinae by (1) the Type 2 of the formation of the uterus (sensu de Chambrier et al. 2004) (all the other acanthotaeniines have the Type 1 of uterine development), (2) the cortical position of the uterine stem (all the other genera have medullary uterine stem) and (3) the morphology of the internal longitudinal musculature, which is composed of few well-developed bundles of fibres (in contrast to the other genera). The new genus also differs from Vandiermenia by eggs not in clusters, the presence of two testicular fields (versus one in Vandiermenia) and the structure of the longitudinal internal musculature with only 8-10 bundles (versus formed by numerous bundles and with the presence of secondary muscles in Vandiermenia). Ophiotaenia sp. sensu de Chambrier (2004), a parasite of Litoria moorei, is described as Australotaenia grobeli sp. n., which can be distinguished from Australotaenia hylae by the smaller number of testes (46-76 versus 74-106), greater cirrus-sac length/width of proglottis ratio (27-33% versus 17-19%) and the smaller ovary width / proglottis width ratio (55-63% versus 68-71%).
Two new gonad-infecting species of Philometra Costa, 1845 (Philometridae), P. brevicollis sp. n. and P. mira sp. n., are described from the ovary of the brownstripe red snapper, Lutjanus vitta (Quoy et Gaimard) (Lutjanidae, Perciformes), from the South Pacific Ocean off the coast of New Caledonia. Based on light and scanning electron microscopy examination, these new nematodes are compared with all other gonad-infecting species of Philometra. The former species (males and mature and gravid females available) mainly differs from its congeners in the length of males (5.39-5.92 mm), equally long spicules (279-312 µm), and the gubernaculum (151-168 µm), in that the distal end of the gubernaculum bears dorsolateral transverse lamella-like structures, and in the structure of the male caudal end. The latter species (only males available) is characterized by the length of males (3.47-3.66 mm), equally long spicules (96-105 µm), and the gubernaculum (78-84 µm), the absence of a dorsal reflected barb or lamella-like structures on the distal end of gubernaculum, and by the structure of the male caudal end. Judging from the occurrence in the host, P. brevicollis is the main philometrid parasitizing the gonads of L. vitta, in which it can reproduce, whereas this fish probably serves as only the paradefinitive host for P. mira. Both P. brevicollis and P. mira are the first nominal species of Philometra described from fishes of the family Lutjanidae.
Two new nematode species, Paragendria papuanensis sp. n. (Quimperiidae) and Rhabdochona papuanensis sp. n. (Rhabdochonidae), are described from the intestine of freshwater fishes Glossamia gjellerupi (Weber et Beaufort) (Apogonidae) and Melanotaenia affinis (Weber) (Melanotaeniidae), respectively, from the Sogeram River (Ramu River basin), Madang Province, northern Papua New Guinea. The former species is characterized mainly by the absence of oesophageal teeth, the presence of conspicuously inflated papillae of the last two subventral pairs, a gubernaculum, spicules 69-75 µm long, eggs measuring 57-66 × 39-45 µm, and by a small body (male and female 3.2-3.7 and 5.8 mm long, respectively). Paragendria is considered a valid genus, to which P. aori (Khan et Yaseen, 1969) comb. n., P. guptai (Gupta et Masoodi, 2000) comb. n., P. hanumanthai (Gupta et Jaiswal, 1988) comb. n. and P. vermae (Gupta et Masoodi, 2000) comb. n. are newly transferred. Rhabdochona papuanensis differs from all congeners mainly in having hammer-shaped deirids and from individual species also in other characters. Both findings represent the first records of species of Paragendria and Rhabdochona from the Australian zoogeographical region and the first records of the representatives of these genera from fishes of the families Apogonidae and Melanotaeniidae, respectively.
Two new nematodes, Paraseuratoides ophisterni gen. et sp. n. (Seuratoidea: Quimperiidae) and Philometra ophisterni sp. n. (Dracunculoidea: Philometridae) are described based on specimens recovered from the intestine and mesentery, respectively, of the swamp-eel Ophisternon aenigmaticum Rosen et Greenwood (Synbranchiformes: Synbranchidae) from a canal of the Papaloapan River in Tlacotalpan, State of Veracruz, Mexico. The genus Paraseuratoides is most similar to Paraseuratum Johnston et Mawson, 1940, differing from it mainly in the absence of a bulbous inflation on the anterior end of the oesophagus and in the structure of the mouth (presence of 6 spines in addition to 6 oesophageal teeth). Neoquimperia Wang, Zhao, Wang et Zhang, 1979 and Wuinema Yu et Wang, 1992 are synonymised with Ezonema Boyce, 1971 and Paragendria Baylis, 1939, respectively, and Haplonema hamulatum Moulton, 1931 is considered a junior synonym of Ichthyobronema conoura Gnedina et Savina, 1930. Philometra ophisterni (only females) is mainly characterised by minute cephalic papillae, a greatly developed anterior oesophageal bulb separated from the cylindrical part of the oesophagus, anterior extension of the oesophageal gland anterior to the nerve ring, and by the character of large caudal projections. This is the first Philometra species recorded from inland fishes in Mexico.