Two new philometrid nematodes, Philometra overstreeti sp. n. and Philometroides paralichthydis sp. n., are described from female specimens collected from the southern flounder Paralichthys lethostigma Jordan et Gilbert (Paralichthyidae, Pleuronectiformes) in estuaries of South Carolina, USA. P. overstreeti is characterized by the presence of eight large, equal in size cephalic papillae, the absence of caudal projections, the body length of gravid females (14.10-27.06 mm) and the location in the host (among teeth). P. paralichthydis from the host's fins and the buccal cavity differs from its congeners mainly in possessing longitudinal cuticular ornamentations in addition to transverse ones or individual rounded bosses. It is the first species of Philometroides reported from flatfishes (Pleuronectiformes). A re-examination of type specimens of Margolisianum bulbosum Blaylock et Overstreet, 1999 showed that, in fact, nematodes belonging to two different species (now described to be new to science) and genera were confused in the original description of this taxon and in the diagnosis of Margolisianum. Since the male holotype of M. bulbosum cannot be identified to genus, Margolisianum bulbosum is a species inquirenda and a species incertae sedis. Consequently, Margolisianum becomes a genus inquirendus.
Protogyrodactylus ethiopicus sp. n. and P. kritskyi sp. n. are described from the gills of Gerres nigri Günther (Gerreidae, Perciformes) captured from the estuary of the Sine-Saloum River (Senegal, West Africa). These new species differ from previously described species within the genus by a mid- or dextro-ventral vaginal opening (dextral in all other species). They are part of a morphological species group within Protogyrodactylus Johnston et Tiegs, 1922 that has the tip of the superficial root of the ventral anchor resembling a hook and two anterior projections on the anterior margin of the ventral bar. Protogyrodactylus ethiopicus differs from the remaining species in this group mainly by the morphology of the base of the male copulatory organ (MCO), which is disk-shaped, and the shape of the anterior projections of the ventral bar (round in the new species and relatively elongate in the other species of the group). The other new species, P. kritskyi, differs from all others in the same morphological group in having a MCO with a greatly expanded base that bears a heel-like subterminal sclerotization.
Two new species of rhabdochonid nematodes are described from the intestine of freshwater fishes in Chiang Mai Province, northern Thailand: Rhabdochona (Rhabdochona) pseudomysti sp. n. from the catfish Pseudomystus siamensis (Regan) (Bagridae, Siluriformes) in the Fang Brook, a tributary of the Kok River (the Mekong River basin), Fang District and Rhabdochona (Globochona) thaiensis sp. n. from the cyprinid Mystacoleucus marginatus (Valenciennes) (Cyprinidae, Cypriniformes) in the Ping River (the Chao Phraya River basin), Muang District. Rhabdochona pseudomysti is mainly characterized by simple, leaf-like oval deirids (a unique feature among Rhabdochona spp.), a prostom with 14 anterior teeth, the presence of basal prostomal teeth, the length ratio of the muscular and glandular portions of oesophagus (1:2.1-2.6), an unusually long left spicule (1.10-1.22 mm), length ratio of spicules (1:11.5-14.7), arrangement of genital papillae, and conspicuously elevated vulval lips. Rhabdochona thaiensis differs from other representatives of the subgenus Globochona Moravec, 1972 possessing caudal projections on the tail tip in that it has only 2 claw-shaped projections located ventrally on the tail tip of both males and females; the species is mainly characterized by the presence of distinct pseudolabia, 8 anterior prostomal teeth, absence of basal teeth, bifurcated deirids, length ratio of the muscular and glandular portions of oesophagus (1:11.3-11.9), conspicuously short (135-141 µm) left spicule, arrangement of genital papillae, and somewhat elevated vulval lips. Fully developed eggs of R. pseudomysti and R. thaiensis remain unknown. These are the first nominal species of Rhabdochona reported from Thailand.
Two new species of the syringophilid mites (Acari: Syringophilidae) are described from quills of passeriform birds. Syringophilopsis faini sp. n. is described from Sylvia curruca (L.) (Sylviidae) and Syringophiloidus carpodaci sp. n. is described from Carpodacus erythrinus (Pall.) (Fringillidae). Characters are detailed that differentiate Syringophilopsis faini from three species of a new "turdus" group, and Syringophiloidus carpodaci from S. minor.
General mathematical theories usually originate from the investigation of particular problems and notions which could not be handled by available tools and methods. The Fučík spectrum and the p-Laplacian are typical examples in the field of nonlinear analysis. The systematic study of these notions during the last four decades led to several interesting and surprising results and revealed deep relationship between the linear and the nonlinear structures. This paper does not provide a complete survey. We focus on some pioneering works and present some contributions of the author. From this point of view the list of references is by no means exhaustive.
In this paper we study two operations of merging components in a chain graph, which appear to be elementary operations yielding an equivalent graph in the respective sense. At first, we recall basic results on the operation of {\em feasible merging} components, which is related to classic LWF (Lauritzen, Wermuth and Frydenberg) Markov equivalence of chain graphs. These results are used to get a graphical characterisation of {\em factorisation equivalence} of classic chain graphs. As another example of the use of this operation, we derive some important invariants of LWF Markov equivalence of chain graphs. Last, we recall analogous basic results on the operation of {\em legal merging} components. This operation is related to the so-called {\em strong equivalence} of chain graphs, which includes both classic LWF equivalence and alternative AMP (Andersson, Madigan and Perlman) Markov equivalence.
Let $G=(V(G),E(G))$ be a graph. Gould and Hynds (1999) showed a well-known characterization of $G$ by its line graph $L(G)$ that has a 2-factor. In this paper, by defining two operations, we present a characterization for a graph $G$ to have a 2-factor in its line graph $L(G).$ A graph $G$ is called $N^{2}$-locally connected if for every vertex $x\in V(G),$ $G[\{y\in V(G)\; 1\leq {\rm dist}_{G}(x,y)\leq 2\}]$ is connected. By applying the new characterization, we prove that every claw-free graph in which every edge lies on a cycle of length at most five and in which every vertex of degree two that lies on a triangle has two $N^{2}$-locally connected adjacent neighbors, has a $2$-factor. This result generalizes the previous results in papers: Li, Liu (1995) and Tian, Xiong, Niu (2012), and is the best possible.
A subset of the plane is called a two point set if it intersects any line in exactly two points. We give constructions of two point sets possessing some additional properties. Among these properties we consider: being a Hamel base, belonging to some $\sigma $-ideal, being (completely) nonmeasurable with respect to different $\sigma $-ideals, being a $\kappa $-covering. We also give examples of properties that are not satisfied by any two point set: being Luzin, Sierpiński and Bernstein set. We also consider natural generalizations of two point sets, namely: partial two point sets and $n$ point sets for $n=3,4,\ldots , \aleph _0,$ $\aleph _1.$ We obtain consistent results connecting partial two point sets and some combinatorial properties (e.g. being an m.a.d. family).
We give some explicit values of the constants $C_{1}$ and $C_{2}$ in the inequality $C_{1}/{\sin (\frac{\pi }{p})}\le \left| P\right| _{p}\le C_{2}/{\sin (\frac{\pi }{p})}$ where $\left| P\right| _{p}$ denotes the norm of the Bergman projection on the $L^{p}$ space.
Gravid females of two species of philometrid nematodes (Philometridae) were collected from marine perciform fishes in Japanese waters, mainly from the southern Sea of Japan. Based on light microscopy and scanning electron microscopy examinations, the previously described but poorly known species Philometra cryptocentri Yamaguti, 1961 is redescribed from specimens recovered from the abdominal cavity of Acanthogobius flavimanus (Temminck et Schlegel), Pterogobius elapoides (Günther) and P. zonoleucus Jordan et Snyder (all Gobiidae) (all new host records); the number (14) and arrangement of cephalic papillae in this species are described for the first time. The new species, Philometroides branchiostegi sp. n. from head tissues of Branchiostegus japonicus (Houttuyn) (Malacanthidae), based on a single specimen, is mainly characterized by the embossment of the entire body except for the cephalic end, presence of four submedian pairs of large cephalic papillae of external circle and two small lateral single papillae of internal circle, pair of large papilla-like caudal projections, the oesophagus with a distinct anterior inflation, by a markedly small body (length about 18 mm) and the larvae 306-465 µm long.