A class of well-posed parabolic final value problems

This paper focuses on parabolic final value problems, and well-posedness is proved for a large class of these. The clarification is obtained from Hilbert spaces that characterise data that give existence, uniqueness and stability of the solutions. The data space is the graph normed domain of an unbounded operator that maps final states to the corresponding initial states. It induces a new compatibility condition, depending crucially on the fact that analytic semigroups always are invertible in the class of closed operators. Lax--Milgram operators in vector distribution spaces constitute the main framework. The final value heat conduction problem on a smooth open set is also proved to be well posed, and non-zero Dirichlet data are shown to require an extended compatibility condition obtained by adding an improper Bochner integral.Comment: 16 pages. To appear in "Applied and numerical harmonic analysis"; a reference update. Conference contribution, based on arXiv:1707.02136, with some further development

Effect of screen-induced total-pressure distortion on axial-flow compressor stability

An experimental investigation was made to determine the effects of screen-induced total-pressure distortions on two J85-GE-13 turbojet engines. Results were compared to those from a previous program run with a third engine. All compressors were found to be sensitive to a critical angle of circumferential distortion equal to 60 deg., and they all adhered closely to the parallel compressor model. The sensitivity of compressor exit pressure to virtually any type of distortion pattern can be determined by defining stall lines for undistorted, hub radial distorted, and tip radial distorted inflows. The effect of multiple sectors of circumferential distortion is defined

Spectral Sensitivity in Ray-Finned Fishes: Diversity, Ecology and Shared Descent

A major goal of sensory ecology is to identify factors that underlie sensory-trait variation. One open question centers on why fishes show the greatest diversity among vertebrates in their capacity to detect color (i.e. spectral sensitivity). Over the past several decades, λmax values (photoreceptor class peak sensitivity) and chromacy (photoreceptor class number) have been cataloged for hundreds of fish species, yet the ecological basis of this diversity and the functional significance of high chromacy levels (e.g. tetra- and pentachromacy) remain unclear. In this study, we examined phylogenetic, physiological and ecological patterns of spectral sensitivity of ray-finned fishes (Actinoptergyii) via a meta-analysis of data compiled from 213 species. Across the fishes sampled, our results indicate that trichromacy is most common, ultraviolet λmax values are not found in monochromatic or dichromatic species, and increasing chromacy, including from tetra- to pentachromacy, significantly increases spectral sensitivity range. In an ecological analysis, multivariate phylogenetic latent liability modeling was performed to analyze correlations between chromacy and five hypothesized predictors (depth, habitat, diet, body coloration, body size). In a model not accounting for phylogenetic relatedness, each predictor with the exception of habitat significantly correlated with chromacy: a positive relationship in body color and negative relationships with body size, diet and depth. However, after phylogenetic correction, the only remaining correlated predictor was depth. The findings of this study indicate that phyletic heritage and depth are important factors in fish spectral sensitivity and impart caution about excluding phylogenetic comparative methods in studies of sensory trait variation

Understanding the evolution of native pinewoods in Scotland will benefit their future management and conservation

Scots pine (Pinus sylvestris L.) is a foundation species in Scottish highland forests and a national icon. Due to heavy exploitation, the current native pinewood coverage represents a small fraction of the postglacial maximum. To reverse this decline, various schemes have been initiated to promote planting of new and expansion of old pinewoods. This includes the designation of seed zones for control of the remaining genetic resources. The zoning was based mainly on biochemical similarity among pinewoods but, by definition, neutral molecular markers do not reflect local phenotypic adaptation. Environmental variation within Scotland is substantial and it is not yet clear to what extent this has shaped patterns of adaptive differentiation among Scottish populations. Systematic, rangewide common-environment trials can provide insights into the evolution of the native pinewoods, indicating how environment has influenced phenotypic variation and how variation is maintained. Careful design of such experiments can also provide data on the history and connectivity among populations, by molecular marker analysis. Together, phenotypic and molecular datasets from such trials can provide a robust basis for refining seed transfer guidelines for Scots pine in Scotland and should form the scientific basis for conservation action on this nationally important habitat

Temperature dependence of binary and ternary recombination of H3+ ions with electron

We study binary and the recently discovered process of ternary He-assisted recombination of H3+ ions with electrons in a low temperature afterglow plasma. The experiments are carried out over a broad range of pressures and temperatures of an afterglow plasma in a helium buffer gas. Binary and He-assisted ternary recombination are observed and the corresponding recombination rate coefficients are extracted for temperatures from 77 K to 330 K. We describe the observed ternary recombination as a two-step mechanism: First, a rotationally-excited long-lived neutral molecule H3* is formed in electron-H3+ collisions. Second, the H3* molecule collides with a helium atom that leads to the formation of a very long-lived Rydberg state with high orbital momentum. We present calculations of the lifetimes of H3* and of the ternary recombination rate coefficients for para and ortho-H3+. The calculations show a large difference between the ternary recombination rate coefficients of ortho- and para-H3+ at temperatures below 300 K. The measured binary and ternary rate coefficients are in reasonable agreement with the calculated values.Comment: 15 page

Behavioral types in programming languages

A recent trend in programming language research is to use behav- ioral type theory to ensure various correctness properties of large- scale, communication-intensive systems. Behavioral types encompass concepts such as interfaces, communication protocols, contracts, and choreography. The successful application of behavioral types requires a solid understanding of several practical aspects, from their represen- tation in a concrete programming language, to their integration with other programming constructs such as methods and functions, to de- sign and monitoring methodologies that take behaviors into account. This survey provides an overview of the state of the art of these aspects, which we summarize as the pragmatics of behavioral types

Cultural Sensitivity: A Requirement When Developing Food Safety Interventions

Extension materials that are sensitive to changing demographics and culture increase relevance and compliance with food safety practices. Produce safety extension materials were developed for U.S. Virgin Islands (USVI) produce growers to help with compliance with a new food safety rule. We developed employee training materials based on a needs assessment and behavioral change was evaluated six months after dissemination. The original materials were not seen as culturally appropriate but after modifications, improvements in food safety practices and behavior changes were observed. These results suggest that extension educators should seek feedback from target populations about potential interventions before implementation

Binary pattern tile set synthesis is NP-hard

In the field of algorithmic self-assembly, a long-standing unproven conjecture has been that of the NP-hardness of binary pattern tile set synthesis (2-PATS). The $k$-PATS problem is that of designing a tile assembly system with the smallest number of tile types which will self-assemble an input pattern of $k$ colors. Of both theoretical and practical significance, $k$-PATS has been studied in a series of papers which have shown $k$-PATS to be NP-hard for $k = 60$, $k = 29$, and then $k = 11$. In this paper, we close the fundamental conjecture that 2-PATS is NP-hard, concluding this line of study. While most of our proof relies on standard mathematical proof techniques, one crucial lemma makes use of a computer-assisted proof, which is a relatively novel but increasingly utilized paradigm for deriving proofs for complex mathematical problems. This tool is especially powerful for attacking combinatorial problems, as exemplified by the proof of the four color theorem by Appel and Haken (simplified later by Robertson, Sanders, Seymour, and Thomas) or the recent important advance on the Erd\H{o}s discrepancy problem by Konev and Lisitsa using computer programs. We utilize a massively parallel algorithm and thus turn an otherwise intractable portion of our proof into a program which requires approximately a year of computation time, bringing the use of computer-assisted proofs to a new scale. We fully detail the algorithm employed by our code, and make the code freely available online

On the nature of symbolic execution

In this paper, we provide a formal definition of symbolic execution in terms of a symbolic transition system and prove its correctness with respect to an operational semantics which models the execution on concrete values. We first introduce such a formal model for a basic programming language with a statically fixed number of programming variables. This model is extended to a programming language with recursive procedures which are called by a call-by-value parameter mechanism. Finally, we show how to extend this latter model of symbolic execution to arrays and object-oriented languages which feature dynamically allocated variables