A set of m m positive integers { a 1 , a 2 , … , a m } \{a_1, a_2, \ldots , a_m\} is called a Diophantine m m -tuple if a i a j + 1 a_i a_j + 1 is a perfect square for all 1 ≤ i > j ≤ m 1 \le i > j \le m . Dujella proved that there is no Diophantine sextuple and that there are at most finitely many Diophantine quintuples. In particular, a folklore conjecture concerning Diophantine m m -tuples states that no Diophantine quintuple exists at all. We prove this conjecture.
A heat-sensitive adhesive, Tempfix(R), developed for scanning electron microscopy of powders and small particles, provides consistently high-quality secondary imaging with a variety of pollen grain morphologies and preparation protocols. Tempfix(R) was used successfully under all combinations of these conditions: (1) pollen air-dried from ETOH or artificially dried; (2) pollen transferred to naked or sputter-coated Tempfix(R); and (3) pollen transferred to solid (at room temperature) or tacky (40-43-degrees-C) Tempfix(R). In contrast to other adhesives, Tempfix(R): (1) does not react with the dehydration fluid ethanol; (2) permits control of depth of pollen penetration into the adhesive; (3) provides a high pollen retention rate with both air-dried and artificially dried preparations; and (4) has a smooth glassy background.
Six species of tardigrades were found to inhabit the fresh waters of hyporheic zones and springs in southeastern New York. The most abundant species was Thulinia ruffoi, a member of a genus that has not been found previously in North America. Tardigrades were scarce at most sites, typically constituting less than 1% of the invertebrate community. However, tardigrades made up 18% of invertebrates in springs and 5% in the hyporheic zone of the East Branch of Wappinger Creek. At the latter site, there was seasonal fluctuation in the abundance of tardigrades, with peak densities and oviposition occurring in the spring.
This is an extensively illustrated laboratory manual of transmission electron microscopy techniques for the technician, graduate student, or researcher. Chapters begin with a general discussion, move on to the chemicals and equipment required for the method being described and conclude with a step-by-step presentation of the method and instructions for the preparation of solutions. Notes at the end of each chapter warn of possible pitfalls and outline 'tricks of the trade'. The methods and techniques outlined have been tested for over ten years in clinical and research laboratory situations, and are entirely reliable. Practical Electron Microscopy covers fixation, dehydration and embedding, semi-thin and thin sectioning, the electron microscope, and photography. For this new edition, the chapters on photography and the electron microscope have been completely rewritten and two new chapters have been added, one on immuno electron microscopy using colloidal gold, and one dealing with such special techniques as retrieving specimens from paraffin and handling nasal brushings and blood samples. This manual will be an invaluable guide to anyone using electron microscopy on human and animal tissue and wishing to develop a routine that guarantees good and reproducible results.
In Florida, freshwater sponges grow abundantly in aquatic environments (i.e., ponds, streams, rivers, lakes, sinkhole ponds, and swamps), and their spicules are found in wet terrestrial environments (i.e., hydric soils). The isolation of spicules from surface soils and subsoils may be useful in understanding environmental change and in delineating terrestrial from aquatic systems. Therefore, objectives of this research were (1) to isolate and identify freshwater sponges spicules in selected Florida surface soils, (2) to study the distribution by depth of spicules in seven soils with various geneses and properties, and (3) to study the distribution of spicules across environments that range from dry terrestrial to aquatic. Small numbers (<1,000 spicules g(-1)) of spicules were found in the surface of well- and moderately well-drained soils. In the poorly and very poorly drained soils, spicule numbers were higher. In some soils, spicules also were isolated from beneath the surface, indicating that the original soil surface had been buried or that faunal pedoturbation had moved the spicules. Spicule counts from depths of 0-20 cm in three dry ponds were high and followed a trend, highest total spicule counts and organic matter (OM) amounts were in the center of the ponds. We conclude that the distribution of spicules in soils provides clues to the soil's genesis and the delineation of wet terrestrial areas.
Comparisons are made between specimens from areas on both sides of the Atlantic Ocean based on metric, meristic, and eidostic characters. In the Batillipedidae, the morphology of Batillipes tubernatis from Massachusetts, U.S.A. is compared with that of specimens from Britain, Germany, and Florida, U.S.A., and B. dicrocercus from Poland is compared with specimens from Massachusetts, Florida, and Italy; in the Halechiniscidae, Tanarctus heterodactylus from Delaware, U.S.A. is compared with specimens from North Carolina, U.S.A. and Brazil. All of the specimens considered here fall within the range of acceptable morphology for their respective species. Broad trans- and cis-oceanic distribution, therefore, seems to apply to these species and, by extension, perhaps to other meiofaunal species as well.
Branchiobdellids use anterior and posterior attachment sites to move in a leech-like fashion. The present study investigates the morphology of the adhesive organs in three species of branchiobdellids native to eastern North America: Bdellodrilus illuminatus, Cambarincola ingens, and Xironodrilus bashaviae. The anterior attachment organ is a glandular pad on the ventral surface of the peristomium. The posterior site is an adhesive disc formed from the terminal body segment The adhesive organs consist of epidermal support cells and two kinds of gland cells, and thus seem to represent a type of due-gland adhesive organ. One type of gland cell, the viscid cell, contains large (0.7-1.5 mu m), electron-dense, membrane-bounded, PAS+ granules that are released onto the attachment surface through pores in the cuticle. The perinuclear regions of the viscid cells are located subepidermally. Viscid granules are transported to the surface through elongated gland necks within which the central granular cytoplasm is delimited by a concentric sheath consisting of ER and longitudinally oriented microtubules. The second type of gland cell, the putative releasing cell, includes smaller (0.15-0.35 mu m) membrane-bounded granules. The perinuclear regions of the releasing cells are located among the viscid gland necks. At their apical ends, the releasing gland necks protrude into the cuticle, but pores were not observed. Both viscid and releasing cells are surrounded epically by epidermal support cells whose cuticle forms the attachment surface. Attachment at the anterior end appears primarily to involve chemical adhesion. The muscular structure of the posterior attachment disc suggests that suction, as well as adhesion, may be used here. Detailed similarities in adhesive-organ ultrastructure in several genera of branchiobdellids indicate homology of the adhesive organs within the Branchiobdellida.
Adenoplea nanus n. sp., belonging in the family Typhloplanidae, is the smallest member of the armata group, which also includes A. armata and A. paraproxenetes. The new species is distinguished from the two other members of the genus by its morphological features. The ease of rearing the species in the laboratory permitted investigation of its ecology.
Three new species of Bertrana, tiny orb-weavers, and three new species of Amazonepeira are described. Bertrana benuta comes from the coastal forest of southern Colombia, B. poa from the Ecuadorean Amazon region, and B. urahua from the Ecuadorean Andes. The new Amazonepeira, A. manaus, A. masaka, and A. beno all come from the Amazon region. Also, there are new Amazon records of the previously described A. herrera, and the male of Aculepeira carrara is matched to females belonging to Amazonepeira. The species differ in structures of the genitalia, which are illustrated.
Birefringent granules are visible in some specimens of Trichoplax adhaerens (phylum Placozoa) viewed under a microscope fitted with crossed polarizing filters. These granules lie in a ring around the periphery of the animal, just inside the edge. Their absence from specimens collected at other times and places hints at an extrinsic source, yet their orderly arrangement suggests that they are an integral part of the animal. Their composition, structure, relation to surrounding tissues, and possible function remain to be discovered.
Cyatholaimus cirolanae n. sp. is described from specimens collected externally from beneath the carapace of Cirolana polita off the Scotian Shelf and near-shore waters of Sable Island in the North Atlantic. The new species is included in Cyatholaimus because of its distally fused gubernaculum and the absence of pre-anal supplements. The new species differs from other members of the genus in the shape of the distal swelling of the gubernaculum which bears many small teeth. In this respect, the new species resembles Paracanthonchus heterodontus and P. longicaudatus. The new species occurred in 20-40% of the specimens of Cirolana polita examined. The nature of the association is unclear but Cirolana polita was the only species infected of 26 species of crustaceans examined, and worms were specific in their site preference, occurring consistently as clumps of about a dozen individuals between the third and fourth abdominal segments.
The platyhelminth worm Hydrolimax grisea is the only freshwater species of the Plagiostomidae in North America. Earlier, the species was reported from New Jersey south to North Carolina. The range is now known to include southern New England. Histological examination of several specimens revealed certain minor differences in pharynx morphology from an earlier description. The pharynx of New England specimens shows variation in the composition and arrangement of outer muscle layers, ciliation of the pharyngeal cavity, and the presence of a sphincter at the anterior tip.
Effects of changes in cell-count protocol on the histometric evaluation of a mixed epithelium have not been reported previously. Variations associated with numbers of cells per count were compared to that associated with numbers of counts per animal using histological preparations of six rat tracheas. The control consisted of 100 counts per animal, each from an epithelial length of 100 mu m. Fifteen additional data sets were created by deleting either counts per animal or cells per count. Thus, the 16 data sets contained either 100, 75, 50 or 25 counts per animal, with either 100%, 75%, 50% or 25% of the cells per 100 mu m. Cell tallies were comparable among the data sets. However, discernment between two cell types required at least 16 cells per count (approximately 75 mu m of epithelium). Discernment of near-neighbor cell occurrences required 300 counts (50 per subject) and 16 cells per count. Cell groups of the same type required 300 counts with 21 cells per count (approximately 100 mu m). The most subtle attribute was a bias against large cell groups, which was not significant with less than 450 counts (75 per subject) and 21 cells per count. We concluded that the sampling protocol for a mixed epithelium should reflect the amount of detail expected from the observations, because there is room for compromise to achieve expediency. Cell counts exhibited the most variation with changes in numbers of cells per count, and to a much lesser extent with changes in numbers of counts per subject.
Microscopy in round glass capillaries does not give an acceptable image of the contents because of strong distortions. Square, and generally right-angle, capillaries provide a higher quality image, but no access to the cell. Capillaries of elastomers combine good optical quality with access to the cell, and a great variety of manipulation through the capillary and by the capillary. Three properties are most important for capillary cell manipulation: (1) extensibility or elongation limit of a capillary, reaching 7-8 times and more, with latex, polyurethane and silicone; (2) transparency, which is sufficiently high for transmitted light microscopy in thin layers of elastomers; and (3) hardness, low in elastic materials, permits puncturing the capillary wall to reach the cell. Capillaries, owing to their softness and flexibility, may be flattened easily to improve observation. Cell manipulations, then, are possible with extensible capillaries: (1) elongation of the cell into a thin strand 7-8 times longer than cell diameter, thus separating cell structures; (2) excision of cell parts; (3) precise microscopy of the nucleus and organelles not masked by the cytoplasm; (4) microinjection; and (5) stimulation of contraction and relaxation of the cell.
Five specimens of Oochoristica ubelakeri n. sp. were recovered from the small intestine of 1 of 5 (20%) Agama atra knobeli from Namibia. Oochoristica ubelakeri n. sp. is most similar to O. theileri, originally described from the spiny agamid lizard, Agama hispida, in South Africa, but differs by having a much less muscular genital atrium, a lobed ovary, and an oval vitellarium. The new species may be differentiated readily from the two other species of Oochoristica from sub-Saharan African reptiles in that its testes occur in two clusters rather than one. In addition, O. ubelakeri n. sp. was found in 1 of 10 (10%) sand geckos, Chondrodactylus at angulifer, also from Namibia.
A new species of coccidian is described from Hemidactylus frenatus in Hawaii. Oocysts of Eimeria frenatus n. sp. were found in 5/72 (7%) lizards and are elongate, 24.4 x 16.8 (22.4-25.6 x 16.0-18.2) mu m, with a smooth, bilayered wall, Sporocysts are ellipsoid, 9.1 x 7.6 (8.2-9.8 x 6.8-8.0) mu m, and have a smooth, single-layered wall. In addition, oocysts of E. rochalamai were found in 6/72 (8%) individuals of E. frenatus; this represents a new host record.
The byssus attachment organ of zebra mussels (Dreissena polymorpha) was studied using scanning and transmission electron microscopy. We demonstrated that the byssus consisted of a root, a stem, threads, and attachment plaques. The root displayed two types of filaments, one with bilateral projections repeating every 60 nm and one without bilateral projections. Root filaments interdigitated with retractor muscle cells and inserted into the basal lamina of muscle cells. Filaments in different arrangements also were the dominant structural elements in the stem and threads. Stem filaments were clustered into tightly and loosely packed parallel bundles. Some of the tightly packed bundles displayed 350-nm periodic cross-bands. Longitudinally oriented thread filaments displayed a core averaging 7 nm and an electron-dense boundary. The stem, threads, and plaque were covered by a dense sheath. The plaque contained numerous vacuoles embedded in a filamentous mesh, and the attachment surface, except for the extreme edge, was electron-dense with numerous granular "attachment spots" applied to the inner face of the attachment surface. Bacteria were found frequently within the plaque vacuoles.
