R-matrix approach to integrable systems on time scales

A general unifying framework for integrable soliton-like systems on time scales is introduced. The $R$-matrix formalism is applied to the algebra of $\delta$-differential operators in terms of which one can construct infinite hierarchy of commuting vector fields. The theory is illustrated by two infinite-field integrable hierarchies on time scales which are difference counterparts of KP and mKP. The difference counterparts of AKNS and Kaup-Broer soliton systems are constructed as related finite-field restrictions.Comment: 21 page

Necessary optimality conditions for infinite horizon variational problems on time scales

We prove Euler-Lagrange type equations and transversality conditions for generalized infinite horizon problems of the calculus of variations on time scales. Here the Lagrangian depends on the independent variable, an unknown function and its nabla derivative, as well as a nabla indefinite integral that depends on the unknown function

Impacts of Land Abandonment on Vegetation: Successional Pathways in European Habitats

Changes in traditional agricultural systems in Europe in recent decades have led to widespread abandonment and colonization of various habitats by shrubs and trees. We combined several vegetation databases to test whether patterns of changes in plant diversity after land abandonment in different habitats followed similar pathways. The impacts of land abandonment and subsequent woody colonization on vegetation composition and plant traits were studied in five semi-natural open habitats and two arable habitats in six regions of Europe. For each habitat, vegetation surveys were carried out in different stages of succession using either permanent or non-permanent plots. Consecutive stages of succession were defined on a physiognomic basis from initial open stages to late woody stages. Changes in vegetation composition, species richness, numbers of species on Red Lists, plant strategy types, Ellenberg indicator values of the vegetation, Grime CSR strategy types and seven ecological traits were assessed for each stage of the successional pathway. Abandonment of agro-pastoral land-use and subsequent woody colonization were associated with changes in floristic composition. Plant richness varied according to the different habitats and stages of succession, but semi-natural habitats differed from arable fields in several ecological traits and vegetation responses. Nevertheless, succession occurred along broadly predictable pathways. Vegetation in abandoned arable fields was characterized by a decreasing importance of R-strategists, annuals, seed plants with overwintering green leaves, insect-pollinated plants with hemi-rosette morphology and plants thriving in nutrient-rich conditions, but an increase in species considered as endangered according to the Red Lists. Conversely, changes in plant traits with succession within the initially-open semi-natural habitats showed an increase in plants thriving in nutrient-rich conditions, stress-tolerant plants and plants with sexual and vegetative reproduction, but a sharp decrease in protected species. In conclusion, our study showed a set of similarities in responses of the vegetation in plant traits after land abandonment, but we also highlighted differences between arable fields and semi-natural habitats, emphasizing the importance of land-use legacy

I Blame Therefore it Was: Rape Myth Acceptance, Victim Blaming, and Memory Reconstruction

We examined the causal order of relationships between rape myth acceptance (RMA), victim blaming, and memory reconstruction. In Study 1, RMA-congruent memory (or alternatively, victim blaming) mediated the relationship between RMA and victim blaming (memory reconstruction). In Study 2, similar relationships emerged between RMA, victim blaming, and memory reconstruction. Although no mediation of RMA occurred in Study 2 independently, a mini meta-analysis of Studies 1 and 2 data replicated both patterns of mediation observed in Study 1. In Study 3, memory accuracy for neutral details of a rape scenario was unrelated to RMA. Manipulating memory to be more (vs. less) RMA congruent had no effect on victim blaming (Study 4), although manipulating perceived victim blameworthiness (Studies 5 and 6) produced RMA-congruent memory reconstruction when the victim was more (vs. less) blameworthy. The results suggest that, via victim blaming, RMA motivates a memory reconstruction process that explains and justifies victim blaming after the fact

Time-Fractional Optimal Control of Initial Value Problems on Time Scales

We investigate Optimal Control Problems (OCP) for fractional systems involving fractional-time derivatives on time scales. The fractional-time derivatives and integrals are considered, on time scales, in the Riemann--Liouville sense. By using the Banach fixed point theorem, sufficient conditions for existence and uniqueness of solution to initial value problems described by fractional order differential equations on time scales are known. Here we consider a fractional OCP with a performance index given as a delta-integral function of both state and control variables, with time evolving on an arbitrarily given time scale. Interpreting the Euler--Lagrange first order optimality condition with an adjoint problem, defined by means of right Riemann--Liouville fractional delta derivatives, we obtain an optimality system for the considered fractional OCP. For that, we first prove new fractional integration by parts formulas on time scales.Comment: This is a preprint of a paper accepted for publication as a book chapter with Springer International Publishing AG. Submitted 23/Jan/2019; revised 27-March-2019; accepted 12-April-2019. arXiv admin note: substantial text overlap with arXiv:1508.0075

Furthering the understanding of silicate-substitution in α-tricalcium phosphate : an X-ray diffraction, X-ray fluorescence and solid-state nuclear magnetic resonance study

High-purity (SupT) and reagent-grade (ST), stoichiometric and silicate-containing α-tricalcium phosphate (α-TCP: ST0/SupT0 and Si-TCP x = 0.10: ST10/SupT10) were prepared by solid-state reaction based on the substitution mechanism Ca3(PO4)(2-x)(SiO4)x. Samples were determined to be phase pure by X-ray diffraction (XRD), and Rietveld analysis performed on the XRD data confirmed inclusion of Si in the α-TCP structure as determined by increases in unit cell parameters; particularly marked increases in the b-axis and β-angle were observed. X-ray fluorescence (XRF) confirmed the presence of expected levels of Si in Si-TCP compositions as well as significant levels of impurities (Mg, Al and Fe) present in all ST samples; SupT samples showed both expected levels of Si and a high degree of purity. Phosphorus (31P) magic-angle-spinning solid-state nuclear magnetic resonance (MAS NMR) measurements revealed that the high-purity reagents used in the synthesis of SupT0 can resolve the 12 expected peaks in the 31P spectrum of α-TCP compared to the low-purity ST0 that showed significant spectral line broadening; line broadening was also observed with the inclusion of Si which is indicative of induced structural disorder. Silicon (29Si) MAS NMR was also performed on both Si-TCP samples which revealed Q0 species of Si with additional Si Q1/Q2 species that may indicate a potential charge-balancing mechanism involving the inclusion of disilicate groups; additional Q4 Si species were also observed, but only for ST10. Heating and cooling rates were briefly investigated by 31P MAS NMR which showed no significant line broadening other than that associated with the emergence of β-TCP which was only realised with the reagent-grade sample ST0. This study provides an insight into the structural effects of Si-substitution in α-TCP and could provide a basis for understanding how substitution affects the physicochemical properties of the material

Algebraic construction of the Darboux matrix revisited

We present algebraic construction of Darboux matrices for 1+1-dimensional integrable systems of nonlinear partial differential equations with a special stress on the nonisospectral case. We discuss different approaches to the Darboux-Backlund transformation, based on different lambda-dependencies of the Darboux matrix: polynomial, sum of partial fractions, or the transfer matrix form. We derive symmetric N-soliton formulas in the general case. The matrix spectral parameter and dressing actions in loop groups are also discussed. We describe reductions to twisted loop groups, unitary reductions, the matrix Lax pair for the KdV equation and reductions of chiral models (harmonic maps) to SU(n) and to Grassmann spaces. We show that in the KdV case the nilpotent Darboux matrix generates the binary Darboux transformation. The paper is intended as a review of known results (usually presented in a novel context) but some new results are included as well, e.g., general compact formulas for N-soliton surfaces and linear and bilinear constraints on the nonisospectral Lax pair matrices which are preserved by Darboux transformations.Comment: Review paper (61 pages). To be published in the Special Issue "Nonlinearity and Geometry: Connections with Integrability" of J. Phys. A: Math. Theor. (2009), devoted to the subject of the Second Workshop on Nonlinearity and Geometry ("Darboux Days"), Bedlewo, Poland (April 2008

Hostile and Benevolent Sexism: The Differential Roles of Human Supremacy Beliefs, Women’s Connection to Nature, and the Dehumanization of Women

Scholars have long argued that sexism is partly rooted in dominance motives over animals and nature, with women being perceived as more animal-like and more closely connected to nature than men. Yet systematic research investigating these associations is currently lacking. Five studies (total N=2,409) consistently show that stronger beliefs in human supremacy over animals and nature were related to heightened hostile and benevolent sexism. Furthermore, perceiving women as more closely connected to nature than men was particularly associated with higher benevolent sexism, whereas subtle dehumanization of women was uniquely associated with higher hostile sexism. Blatant dehumanization predicted both types of sexism. Studies 3 and 4 highlight the roles of social dominance orientation and benevolent beliefs about nature underpinning these associations, while Study 5 demonstrates the implications for individuals’ acceptance of rape myths and policies restricting pregnant women’s freedom. Taken together, our findings reveal the psychological connections between gender relations and human-animal relations