Existence and approximations of solutions to some fractional order functional integral equations

In this paper we shall study a fractional order functional integral equation. In the first part of the paper, we proved the existence and uniqueness of mile and global solutions in a Banach space. In the second part of the paper, we used the analytic semigroups theory oflinear operators and the fixed point method to establish the existence, uniqueness and convergence of approximate solutions of the given problem in a separable Hilbert space. We also proved the existence and convergence of Faedo-Galerkin approximate solution to the given problem. Finally, we give an example.

Dynamic changes in mitogen-activated protein kinase (MAPK) activities in the corpus luteum of the bonnet monkey (Macaca radiata) during development, induced luteolysis, and simulated early pregnancy: A role for p38 MAPK in the regulation of luteal function

Changes in MAPK activities were examined in the corpus luteum (CL) during luteolysis and pregnancy, employing GnRH antagonist (Cetrorelix)-induced luteolysis, stages of CL, and hCG treatment to mimic early pregnancy as model systems in the bonnet monkey. We hypothesized that MAPKs could serve to phosphorylate critical phosphoproteins to regulate luteal function. Analysis of several indices for structural (caspase-3 activity and DNA fragmentation) and functional (progesterone and steroidogenic acute regulatory protein expression) changes in the CL revealed that the decreased luteal function observed during Cetrorelix treatment and late luteal phase was associated with increased caspase-3 activity and DNA fragmentation. As expected, human chorionic gonadotropin treatment dramatically increased luteal function, but the indices for structural changes were only partially attenuated. All three MAPKs appeared to be constitutively active in the mid-luteal-phase CL, and activities of ERK-1/2 and p38-MAPK (p38), but not Jun N-terminal kinase (JNK)-1/2, decreased significantly (P < 0.05) within 12 - 24 h after Cetrorelix treatment. During the late luteal phase, in contrast to decreased ERK-1/2 and p38 activities, JNK-1/2 activities increased significantly (P < 0.05). Although human chorionic gonadotropin treatment increased ERK-1/2 and p38 activities, it decreased JNK-1/2 activities. The activation status of p38 was correlated with the phosphorylation status of an upstream activator, MAPK kinase-3/6 and the expression of MAPK activated protein kinase-3, a downstream target. Intraluteal administration of p38 kinase inhibitor (SB203580), but not MAPK kinase-1/2 inhibitor (PD98059), decreased the luteal function. Together, these data suggest an important role for p38 in the regulation of CL function in primates.

Climatic variability in Central Indian Himalaya during the last similar to 1800 years: Evidence from a high resolution speleothem record

Stable isotopes from a U/Th dated aragonite stalagmite from the Central Kumaun Himalaya provide evidence of variation in climatic conditions in the last similar to 1800 years. The delta O-18 and delta C-13 values vary from -4.3 parts per thousand to -7.6 parts per thousand and -3.4 parts per thousand to -9.1 parts per thousand respectively, although the stalagmite was not grown in isotopic equilibrium with cave drip water, a clear palaeoclimatic signal in stalagmite delta O-18 values is evident based on the regional climate data. The stalagmite showed a rapid growth rate during 830-910 AD, most likely the lower part of Medieval Warm Period (MWP), and 1600-1640 AD, the middle part of Little Ice Age (LIA). Two distinct phases of reduced precipitation are marked by a 2 parts per thousand shift in 8180 values towards the end of MWP (similar to 1080-1160 AD) and after its termination from similar to 1210 to 1440 AD. The LIA (similar to 1440-1880 AD) is represented by sub-tropical climate similar to modern conditions, whereas the post-LIA was comparatively drier. The Inter Tropical Convergence Zone (ITCZ) was located over the cave location during wetter/warmer conditions. When it shifted southward, precipitation over the study area decreased. A prominent drop in delta O-18 and delta C-13 values during the post-LIA period may also have been additionally influenced by anthropogenic activity in the area. (C) 2013 Elsevier Ltd and INQUA. All rights reserved.

Long-term effects of Macroternies termites, herbivores and annual early fire on woody undergrowth community in Sudanian woodland, Burkina Faso

Termites, herbivores and fire are recognized as major guilds that structure woody plant communities in African savanna and woodland ecosystems. An understanding of their interaction is crucial to design appropriate management regimes. The aim of this study was to evaluate the long-term impacts of herbivore, fire and termite activities on regeneration of trees. Permanent experimental quadrats were established in 1992 in the Sudanian woodland of Burkina Faso subjected to grazing by livestock and annual early fire and the control. Within the treatment quadrats, an inventory of the woody undergrowth community was conducted on termitaria occupied by Macrotermes subhyalinus, extended termitosphere (within 5 m radius from the mound base) and adjacent area (beyond 5 m from the mound base). Hierarchical analysis was performed to determine significant differences in species richness, abundance and diversity indices among vegetation patches within fire and herbivory treatments. Grazed quadrats had significantly (P < 0.001) more species and stem density of woody undergrowth than non-grazed quadrats but maintained similar level of species richness and stem density of woody undergrowth on termitaria. There were not significant differences (P>0.05) in species richness and stem density between burnt and unburnt quadrats. Termitaria supported a highly diverse woody undergrowth with higher stem density than either the extended termitosphere or rest of quadrats. The density of woody undergrowth was significantly related with mature trees of selected species on termitaria (R-2 = 0.593; P<0.001) than that on the extended termitosphere (R-2 = 0.333; P<0.001) and adjacent area (R-2 = 0.197; P<0.001). It can be concluded that termites facilitate the regeneration of woody species while grazing and annual early fire play a minor role in the regeneration of woody species. The current policy that prohibits grazing should be revised to accommodate the interests of livestock herders. (C) 2014 Elsevier GmbH. All rights reserved.