Transreal logical space of all propositions

Transreal numbers provide a total semantics containing classical truth values, dialetheaic, fuzzy and gap values. A paraconsistent Sheffer Stroke generalises all classical logics to a paraconsistent form. We introduce logical spaces of all possible worlds and all propositions. We operate on a proposition, in all possible worlds, at the same time. We define logical transformations, possibility and necessity relations, in proposition space, and give a criterion to determine whether a proposition is classical. We show that proofs, based on the conditional, infer gaps only from gaps and that negative and positive infinity operate as bottom and top values.

Biodiversity and resilience of ecosystem functions

Accelerating rates of environmental change and the continued loss of global biodiversity threaten functions and services delivered by ecosystems. Much ecosystem monitoring and management is focused on the provision of ecosystem functions and services under current environmental conditions, yet this could lead to inappropriate management guidance and undervaluation of the importance of biodiversity. The maintenance of ecosystem functions and services under substantial predicted future environmental change (i.e., their ‘resilience’) is crucial. Here we identify a range of mechanisms underpinning the resilience of ecosystem functions across three ecological scales. Although potentially less important in the short term, biodiversity, encompassing variation from within species to across landscapes, may be crucial for the longer-term resilience of ecosystem functions and the services that they underpin.

Declining resilience of ecosystem functions under biodiversity loss

The composition of species communities is changing rapidly through drivers such as habitat loss and climate change, with potentially serious consequences for the resilience of ecosystem functions on which humans depend. To assess such changes in resilience, we analyse trends in the frequency of species in Great Britain that provide key ecosystem functions-specifically decomposition, carbon sequestration, pollination, pest control and cultural values. For 4,424 species over four decades, there have been significant net declines among animal species that provide pollination, pest control and cultural values. Groups providing decomposition and carbon sequestration remain relatively stable, as fewer species are in decline and these are offset by large numbers of new arrivals into Great Britain. While there is general concern about degradation of a wide range of ecosystem functions, our results suggest actions should focus on particular functions for which there is evidence of substantial erosion of their resilience.

Non-homogeneous liver distribution of photosensitizer and its consequence for photodynamic therapy outcome

Background: Photodynamic therapy is mainly used for treatment of malignant lesions, and is based on selective location of a photosensitizer in the tumor tissue, followed by light at wavelengths matching the photosensitizer absorption spectrum. In molecular oxygen presence, reactive oxygen species are generated, inducing cells to die. One of the limitations of photodynamic therapy is the variability of photosensitizer concentration observed in systemically photosensitized tissues, mainly due to differences of the tissue architecture, cell lines, and pharmacokinetics. This study aim was to demonstrate the spatial distribution of a hematoporphyrin derivative, Photogem(R), in the healthy liver tissue of Wistar rats via fluorescence spectroscopy, and to understand its implications on photodynamic response. Methods: Fifteen male Wistar rats were intravenously photosensitized with 1.5 mg/kg body weight of Photogem(R). Laser-induced fluorescence spectroscopy at 532nm-excitation was performed on ex vivo liver slices. The influence of photosensitizer surface distribution detected by fluorescence and the induced depth of necrosis were investigated in five animals. Results: Photosensitizer distribution on rat liver showed to be greatly non-homogeneous. This may affect photodynamic therapy response as shown in the results of depth of necrosis. Conclusions: As a consequence of these results, this study suggests that photosensitizer surface spatial distribution should be taken into account in photodynamic therapy dosimetry, as this will help to better predict clinical results. (C) 2010 Elsevier B.V. All rights reserved.

Dependence of Response Functions and Orbital Functionals on Occupation Numbers

Explicitly orbital-dependent approximations to the exchange-correlation energy functional of density functional theory typically not only depend on the single-particle Kohn-Sham orbitals but also on their occupation numbers in the ground-state Slater determinant. The variational calculation of the corresponding exchange-correlation potentials with the optimized effective potential (OEP) method therefore also requires a variation of the occupation numbers with respect to a variation in the effective single-particle potential, which is usually not taken into account. Here it is shown under which circumstances this procedure is justified.

The Hilbert space of the Chern-Simons theory on a cylinder: a loop quantum gravity approach

As a laboratory for loop quantum gravity, we consider the canonical quantization of the three-dimensional Chern-Simons theory on a noncompact space with the topology of a cylinder. Working within the loop quantization formalism, we define at the quantum level the constraints appearing in the canonical approach and completely solve them, thus constructing a gauge and diffeomorphism invariant physical Hilbert space for the theory. This space turns out to be infinite dimensional, but separable.

On the Hamilton-Jacobi equation in the framework of generalized functions

In this work we study, in the framework of Colombeau`s generalized functions, the Hamilton-Jacobi equation with a given initial condition. We have obtained theorems on existence of solutions and in some cases uniqueness. Our technique is adapted from the classical method of characteristics with a wide use of generalized functions. We were led also to obtain some general results on invertibility and also on ordinary differential equations of such generalized functions. (C) 2011 Elsevier Inc. All rights reserved.

On isomorphism classes of C(2(m) circle plus [0, alpha]) spaces

We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces 2(m) circle plus [0, alpha], the topological sums of Cantor cubes 2(m), with m smaller than the first sequential cardinal, and intervals of ordinal numbers [0, alpha]. In particular, we prove that it is relatively consistent with ZFC that the only isomorphism classes of C(2(m) circle plus [0, alpha]) spaces with m >= N(0) and alpha >= omega(1) are the trivial ones. This result leads to some elementary questions on large cardinals.

ON CLOSED GEODESICS IN THE LEAF SPACE OF SINGULAR RIEMANNIAN FOLIATIONS

In this paper we prove the existence of closed geodesics in the leaf space of some classes of singular Riemannian foliations (s.r.f.), namely s.r.fs. that admit sections or have no horizontal conjugate points. We also investigate the shortening process with respect to Riemannian foliations.

THE FUNDAMENTAL GROUP OF THE SPACE OF MAPS FROM A SURFACE INTO THE PROJECTIVE PLANE

In this work we compute the fundamental group of each connected component of the function space of maps from it closed surface into the projective space

Stability of periodic travelling shallow-water waves determined by Newton`s equation

We study the existence and stability of periodic travelling-wave solutions for generalized Benjamin-Bona-Mahony and Camassa-Holm equations. To prove orbital stability, we use the abstract results of Grillakis-Shatah-Strauss and the Floquet theory for periodic eigenvalue problems.