Nonlinear eigenvalue problems for higher order Lidstone boundary value problems

In this paper, we consider the Lidstone boundary value problem $y^{(2m)}(t) = \lambda a(t)f(y(t), \dots, y^{(2j)}(t), \dots y^{(2(m-1))}(t), 0 0$ and $a$ is nonnegative. Growth conditions are imposed on $f$ and inequalities involving an associated Green's function are employed which enable us to apply a well-known cone theoretic fixed point theorem. This in turn yields a $\lambda$ interval on which there exists a nontrivial solution in a cone for each $\lambda$ in that interval. The methods of the paper are known. The emphasis here is that $f$ depends upon higher order derivatives. Applications are made to problems that exhibit superlinear or sublinear type growth

Fully nonlinear boundary value problems with impulse

An impulsive boundary value problem with nonlinear boundary conditions for a second order ordinary differential equation is studied. In particular, sufficient conditions are provided so that a compression - expansion cone theoretic fixed point theorem can be applied to imply the existence of positive solutions. The nonlinear forcing term is assumed to satisfy usual sublinear or superlinear growth as $t\rightarrow\infty$ or $t\rightarrow 0^+$. The nonlinear impulse terms and the nonlinear boundary terms are assumed to satisfy the analogous asymptotic behavior

Method of the quasilinearization for nonlinear impulsive differential equations with linear boundary conditions

The method of quasilinearization for nonlinear impulsive differential equations with linear boundary conditions is studied. The boundary conditions include periodic boundary conditions. It is proved the convergence is quadratic

Functional Signatures of the Epiphytic Prokaryotic Microbiome of Agaves and Cacti.

Microbial symbionts account for survival, development, fitness and evolution of eukaryotic hosts. These microorganisms together with their host form a biological unit known as holobiont. Recent studies have revealed that the holobiont of agaves and cacti comprises a diverse and structured microbiome, which might be important for its adaptation to drylands. Here, we investigated the functional signatures of the prokaryotic communities of the soil and the episphere, that includes the rhizosphere and phyllosphere, associated with the cultivated Agave tequilana and the native and sympatric Agave salmiana, Opuntia robusta and Myrtillocactus geometrizans by mining shotgun metagenomic data. Consistent with previous phylogenetic profiling, we found that Proteobacteria, Actinobacteria and Firmicutes were the main represented phyla in the episphere of agaves and cacti, and that clustering of metagenomes correlated with the plant compartment. In native plants, genes related to aerobic anoxygenic phototrophy and photosynthesis were enriched in the phyllosphere and soil, while genes coding for biofilm formation and quorum sensing were enriched in both epiphytic communities. In the episphere of cultivated A. tequilana fewer genes were identified, but they belonged to similar pathways than those found in native plants. A. tequilana showed a depletion in several genes belonging to carbon metabolism, secondary metabolite biosynthesis and xenobiotic degradation suggesting that its lower microbial diversity might be linked to functional losses. However, this species also showed an enrichment in biofilm and quorum sensing in the epiphytic compartments, and evidence for nitrogen fixation in the rhizosphere. Aerobic anoxygenic phototrophic markers were represented by Rhizobiales (Methylobacterium) and Rhodospirillales (Belnapia) in the phyllosphere, while photosystem genes were widespread in Bacillales and Cyanobacteria. Nitrogen fixation and biofilm formation genes were mostly related to Proteobacteria. These analyses support the idea of niche differentiation in the rhizosphere and phyllosphere of agaves and cacti and shed light on the potential mechanisms by which epiphytic microbial communities survive and colonize plants of arid and semiarid ecosystems. This study establishes a guideline for testing the relevance of the identified functional traits on the microbial community and the plant fitness

Metatranscriptomic Sequencing of a Cyanobacterial Soil-Surface Consortium with and without a Diverse Underlying Soil Microbiome.

Soil surface consortia are easily observed and sampled, allowing examination of their interactions with soil microbiomes. Here, we present metatranscriptomic sequences from Dark Green 1 (DG1), a cyanobacterium-based soil surface consortium, in the presence and absence of an underlying soil microbiome and/or urea

Novel psychropiezophilic Oceanospirillales species Profundimonas piezophila gen. nov., sp. nov., isolated from the deep-sea environment of the Puerto Rico trench

The diversity of deep-sea high-pressure-adapted (piezophilic) microbes in isolated monoculture remains low. In this study, a novel obligately psychropiezophilic bacterium was isolated from seawater collected from the Puerto Rico Trench at a depth of ~ 6,000 m. This isolate, designated YC-1, grew best in a nutrient rich marine medium with an optimal growth hydrostatic pressure of 50 MPa (range 20-70 MPa) at 8 °C. Under these conditions the maximum growth rate was extremely slow, 0.017 h-1, and the maximum yield was 3.51 × 107 cells ml-1. Cell size changed with pressure, shifting from 4.0-5.0 μm in length and 0.5-0.8 μm in width at 60 MPa, to 0.8-1.0 μm diameter coccoid cells under 20 MPa, the minimal pressure required for growth. YC-1 is a Gram-negative, non-flagellum forming, facultative anaerobic heterotroph. Its predominant cellular fatty acids are the monounsaturated fatty acids (MUFAs) C16:1 and C18:1. Unlike many other psychropiezophiles YC-1 does not synthesize any polyunsaturated fatty acids (PUFAs). Phylogenetic analysis placed YC-1 within the family of Oceanospirillaceae, closely related to the uncultured symbiont of the deep-sea whale bone-eating worms of the genus Osedax. In common with some other members of the Oceanospirillales, including those enriched during the Deepwater Horizon oil spill, YC-1 is capable of hydrocarbon utilization. Based on its characteristics, YC-1 appears to represent both a new genus and a new species which we name “Profundimonas piezophila” gen. nov., sp. nov

Expansion of Thaumarchaeota habitat range is correlated with horizontal transfer of ATPase operons.

Thaumarchaeota are responsible for a significant fraction of ammonia oxidation in the oceans and in soils that range from alkaline to acidic. However, the adaptive mechanisms underpinning their habitat expansion remain poorly understood. Here we show that expansion into acidic soils and the high pressures of the hadopelagic zone of the oceans is tightly linked to the acquisition of a variant of the energy-yielding ATPases via horizontal transfer. Whereas the ATPase genealogy of neutrophilic Thaumarchaeota is congruent with their organismal genealogy inferred from concatenated conserved proteins, a common clade of V-type ATPases unites phylogenetically distinct clades of acidophilic/acid-tolerant and piezophilic/piezotolerant species. A presumptive function of pumping cytoplasmic protons at low pH is consistent with the experimentally observed increased expression of the V-ATPase in an acid-tolerant thaumarchaeote at low pH. Consistently, heterologous expression of the thaumarchaeotal V-ATPase significantly increased the growth rate of E. coli at low pH. Its adaptive significance to growth in ocean trenches may relate to pressure-related changes in membrane structure in which this complex molecular machine must function. Together, our findings reveal that the habitat expansion of Thaumarchaeota is tightly correlated with extensive horizontal transfer of atp operons

VRCC-3D+: Qualitative spatial and temporal reasoning in 3 dimensions

Qualitative Spatial Reasoning (QSR) has varying applications in Geographic Information Systems (GIS), visual programming language semantics, and digital image analysis. Systems for spatial reasoning over a set of objects have evolved in both expressive power and complexity, but implementations or usages of these systems are not common. This is partially due to the computational complexity of the operations required by the reasoner to make informed decisions about its surroundings. These theoretical systems are designed to focus on certain criteria, including efficiency of computation, ease of human comprehension, and expressive power. Sadly, the implementation of these systems is frequently left as an exercise for the reader. Herein, a new QSR system, VRCC-3D+, is proposed that strives to maximize expressive power while minimizing the complexity of reasoning and computational cost of using the system. This system is an evolution of RCC-3D; the system and implementation are constantly being refined to handle the complexities of the reasoning being performed. The refinements contribute to the accuracy, correctness, and speed of the implementation. To improve the accuracy and correctness of the implementation, a way to dynamically change error tolerance in the system to more accurately reflect what the user sees is designed. A method that improves the speed of determining spatial relationships between objects by using composition tables and decision trees is introduced, and improvements to the system itself are recommended; by streamlining the relation set and enforcing strict rules for the precision of the predicates that determine the relationships between objects. A potential use case and prototype implementation is introduced to further motivate the need for implementations of QSR systems, and show that their use is not precluded by computational complexity. --Abstract, page iv

Eigenvalues of higher order Sturm-Liouville boundary value problems with derivatives in nonlinear terms

We shall consider the Sturm-Liouville boundary value problem y(m)(t)+λF(t,y(t),y′(t),…,y(q)(t))=0, t∈(0,1), y(k)(0)=0, 0≤k≤m−3, ζy(m−2)(0)−θy(m−1)(0)=0, ρy(m−2)(1)+δy(m−1)(1)=0 where m≥3, 1≤q≤m−2, and λ>0. It is noted that the boundary value problem considered has a derivative-dependent nonlinear term, which makes the investigation much more challenging. In this paper we shall develop a new technique to characterize the eigenvalues λ so that the boundary value problem has a positive solution. Explicit eigenvalue intervals are also established. Some examples are included to dwell upon the usefulness of the results obtained.Published versio

Positive operators and maximum principles for ordinary differential equations

We show an equivalence between a classical maximum principle in differential equations and positive operators on Banach Spaces. Then we shall exhibit many types of boundary value problems for which the maximum principle is valid. Finally, we shall present extended applications of the maximum principle that have arisen with the continued study of the qualitative properties of Green’s functions