Paleoripiphorus deploegi gen. n., sp. n. and Macrosiagon ebboi sp. n., described from two French Albo-Cenomanian ambers (mid Cretaceous), are the oldest definitely identified representatives of the Ripiphoridae: Ripiphorinae. They belong to or are closely related to extant genera of this coleopteran subfamily. Together with Myodites burmiticus Cockerell, 1917 from the Albian Burmese amber, they demonstrate that the group is distinctly older than suggested by the hitherto available fossil record. By inference after the biology of the extant Ripiphorinae, Macrosiagon ebboi may have been parasitic on wasps and Paleoripiphorus deploegi on bees, suggesting that Apoidea may have been present in the Lower Cretaceous.
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.
Effects of low-frequency electromagnetic fields (LF EMF) on the
activation of different tissue recovery processes have not yet
been fully understood. The detailed quantification of LF EMF
effects on the angiogenesis were analysed in our experiments by
using cultured human and mouse endothelial cells. Two types of
fields were used in the tests as follows: the LF EMF with
rectangular pulses, 340-microsecond mode at a frequency of
72 Hz and peak intensity 4 mT, and the LF EMF with sinusoidal
alternating waveform 5 000 Hz, amplitude-modulated by means
of a special interference spectrum mode set to a frequency linear
sweep from 1 to 100 Hz for 6 s and from 100 Hz to 1 Hz return
also for 6 s, swing period of 12 second. Basic parameters of
cultured cells measured after the LF EMF stimulus were viability
and proliferation acceleration. Both types of endothelial cells
(mouse and human ones) displayed significant changes in the
proliferation after the application of the LF EMF under conditions
of a rectangular pulse mode. Based on the results, another test
of the stimulation on a more complex endothelial-fibroblast
coculture model will be the future step of the investigation.
Many gregarious insects aggregate in naturally occurring refuges on their host plants. However, when refuges are filled, they may be forced to aggregate on exposed areas of the plant. This study examines the effects of refuge saturation on group size and defence against parasitism in larvae of Ammalo helops Cramer (Lepidoptera: Arctiidae) that form day-resting groups on the trunks of weeping laurel, Ficus benjamina L., in El Salvador. Population densities, group sizes and parasitism were recorded on eight trees for each of four generations in 1995 and 1996. When population densities were low, all larvae were located in small groups in naturally occurring structural refuges (rotted out holes, spaces between crossing branches and under aerial roots) on the host plant. In contrast, when population densities were high and structural refuges were full, many larvae formed significantly larger groups (density refuges) on the open trunk. Between 20 and 24% of late-instar larvae were parasitized and this was inversely dependent on the size of within tree populations, in spite of populations being fragmented among structural refuges. Similarly, in a study carried out at a different location on young trees without structural refuges, parasitism of larvae was inversely related to group size. Although parasitism rates decreased with increasing group size, most larvae preferentially selected the small naturally occurring refuges, where groups were restricted to low densities. If this behaviour is an adaptive trait, I speculate that parasitism (or some other unmeasured mortality factor) is lower in naturally occurring refuges than in large open groups.
The purpose of this paper is to introduce some new generalized double difference sequence spaces using summability with respect to a two valued measure and an Orlicz function in $2$-normed spaces which have unique non-linear structure and to examine some of their properties. This approach has not been used in any context before.
In this paper, following the methods of Connor \cite {connor}, we extend the idea of statistical convergence of a double sequence (studied by Muresaleen and Edely \cite {moe}) to $\mu $-statistical convergence and convergence in $\mu $-density using a two valued measure $\mu $. We also apply the same methods to extend the ideas of divergence and Cauchy criteria for double sequences. We then introduce a property of the measure $\mu $ called the (APO$_2$) condition, inspired by the (APO) condition of Connor \cite {jc}. We mainly investigate the interrelationships between the two types of convergence, divergence and Cauchy criteria and ultimately show that they become equivalent if and only if the measure $\mu $ has the condition (APO$_2$).