Maximum curves and isolated points of entire functions

Given M(r; f) =maxjzj=r (jf(z)j) , curves belonging to the set of points M = fz : jf(z)j = M(jzj; f)g were de�ned by Hardy to be maximum curves. Clunie asked the question as to whether the set M could also contain isolated points. This paper shows that maximum curves consist of analytic arcs and determines a necessary condition for such curves to intersect. Given two entire functions f1(z) and f2(z), if the maximum curve of f1(z) is the real axis, conditions are found so that the real axis is also a maximum curve for the product function f1(z)f2(z). By means of these results an entire function of in�nite order is constructed for which the set M has an in�nite number of isolated points. A polynomial is also constructed with an isolated point.

Applications of Feller-Reuter-Riley transition functions

A Feller–Reuter–Riley function is a Markov transition function whose corresponding semigroup maps the set of the real-valued continuous functions vanishing at infinity into itself. The aim of this paper is to investigate applications of such functions in the dual problem, Markov branching processes, and the Williams-matrix. The remarkable property of a Feller–Reuter–Riley function is that it is a Feller minimal transition function with a stable q-matrix. By using this property we are able to prove that, in the theory of branching processes, the branching property is equivalent to the requirement that the corresponding transition function satisfies the Kolmogorov forward equations associated with a stable q-matrix. It follows that the probabilistic definition and the analytic definition for Markov branching processes are actually equivalent. Also, by using this property, together with the Resolvent Decomposition Theorem, a simple analytical proof of the Williams' existence theorem with respect to the Williams-matrix is obtained. The close link between the dual problem and the Feller–Reuter–Riley transition functions is revealed. It enables us to prove that a dual transition function must satisfy the Kolmogorov forward equations. A necessary and sufficient condition for a dual transition function satisfying the Kolmogorov backward equations is also provided.

Strong ergodicity of monotone transition functions

By revealing close links among strong ergodicity, monotone, and the Feller–Reuter–Riley (FRR) transition functions, we prove that a monotone ergodic transition function is strongly ergodic if and only if it is not FRR. An easy to check criterion for a Feller minimal monotone chain to be strongly ergodic is then obtained. We further prove that a non-minimal ergodic monotone chain is always strongly ergodic. The applications of our results are illustrated using birth-and-death processes and branching processes.

Feller transition functions, Resolvent Decomposition Theorems, and their application in unstable denumerable Markov processes

This paper surveys the recent progresses made in the field of unstable denumerable Markov processes. Emphases are laid upon methodology and applications. The important tools of Feller transition functions and Resolvent Decomposition Theorems are highlighted. Their applications particularly in unstable denumerable Markov processes with a single instantaneous state and Markov branching processes are illustrated.

Hemolymph Functions In Mytilus-Californianus - Cytochemistry Of Hemocytes And Their Responses To Foreign Implants And Hemolymph Factors In Phagocytosis

The hemocytes of Mytilus californianus are of three types: small and large basophils and large granular acidophils. The basophils contain lysosomal enzymes and phagocytose colloidal carbon. Agglutinins for yeast and human A Rh+ve erythrocytes are present in plasma, but are not needed for effective phagocytosis; in vitro both acidophilic and basophilic hemocytes rapidly phagocytose these particles. Plasma proteins, analyzed electrophoretically, are under strong homeostatic control. When Mya arenaria mantle is placed orthotopically on M. californianus mantle, the implant is invaded by host hemocytes in a manner consistent with that described in other published reports on molluscan graft rejection. Steady state is achieved by 26 days postimplant. Second- and third-set implants are rejected more rapidly than are first-set implants, but this is not a specific response. Third-set implants elicit a host cellular response that is more localized than the response to first-set implants. These data do not permit conclusions with respect to memory in these molluscan immune responses, but do imply a qualitative “improvement” in this quasi-immune response of M. californianus.

Consequences of a simulated rapid ocean acidification event for benthic ecosystem processes and functions

Whilst the biological consequences of long-term, gradual changes in acidity associated with the oceanic uptake of atmospheric carbon dioxide (CO2) are increasingly studied, the potential effects of rapid acidification associated with a failure of sub-seabed carbon storage infrastructure have received less attention. This study investigates the effects of severe short-term (8 days) exposure to acidified seawater on infaunal mediation of ecosystem processes (bioirrigation and sediment particle redistribution) and functioning (nutrient concentrations). Following acidification, individuals of Amphiura filiformis exhibited emergent behaviour typical of a stress response, which resulted in altered bioturbation, but limited changes in nutrient cycling. Under acidified conditions, A. filiformis moved to shallower depths within the sediment and the variability in occupancy depth reduced considerably. This study indicated that rapid acidification events may not be lethal to benthic invertebrates, but may result in behavioural changes that could have longer-term implications for species survival, ecosystem structure and functioning.

Cognitive inhibition and interference in dissociative indentity disorder: the effects of anxiety on specific executive functions:The effects of anxiety on specific executive functions

Using an experimentally based, computer-presented task, this study assessed cognitive inhibition and interference in individuals from the dissociative identity disorder (DID; n=12), generalized anxiety disorder (GAD; n=12) and non-clinical (n=12) populations. Participants were assessed in a neutral and emotionally negative (anxiety provoking) context, manipulated by experimental instructions and word stimuli. The DID sample displayed effective cognitive inhibition in the neutral but not the anxious context. The GAD sample displayed the opposite findings. However, the interaction between group and context failed to reach significance. There was no indication of an attentional bias to non-schema specific negative words in any sample. Results are discussed in terms of the potential benefit of weakened cognitive inhibition during anxious arousal in dissociative individuals.

Mouse Uterine Natural Killer Cell Functions During Early Pregnancy

Early pregnancy is characterized by complex interactions between blood vessels, leukocytes, and conceptus-derived trophoblasts within the gestational uterus. Uterine Natural Killer (uNK) cells become the most abundant leukocyte during decidualization and produce a wide array of angiogenic factors, yet little is known regarding their early pregnancy functions. To characterize the role(s) of uNK cells, whole mount in situ immunohistochemistry of live early implant sites was performed. A timecourse examination of murine early pregnancy (virgin, and gd4.5-9.5) implantation sites was performed. Comparison of Gd6.5, 8.5 and 9.5 implant sites from BALB/c+/+ controls (BALB/c) and BALB/c-Rag2-/-Il2rg-/- (alymphoid) identified anomalies that result from the absence of lymphocytes. In alymphoid decidua basalis, mesometrial angiogenesis was widespread but pruning of nascent vessels within alymphoid decidua basalis was deficient. As early gestation progressed, vessels of alymphoid decidua basalis showed no evidence for remodeling. Alymphoid implantation sites showed ~24h delay in uterine lumen closure and embryonic development. To determine if uNK cells would normalize the anomalies observed in alymphoid implantation sites, adoptive cell transfer of NK+ B- T- marrow to alymphoid mice was performed. All of the above anomalies were reversed by adoptive transfer of NK+B-T- marrow. My results suggest that uNK cells support vascular growth and development which ensures the decidua can support the growing conceptus early in pregnancy prior to formation and function of the placenta. Human decidual NK cells may fill similar roles and be important targets for strategies designed to correct intra-uterine growth restriction.