Lipschitz compact operators

We introduce the notion of Lipschitz compact (weakly compact, finite-rank, approximable) operators from a pointed metric space X into a Banach space E. We prove that every strongly Lipschitz p-nuclear operator is Lipschitz compact and every strongly Lipschitz p-integral operator is Lipschitz weakly compact. A theory of Lipschitz compact (weakly compact, finite-rank) operators which closely parallels the theory for linear operators is developed. In terms of the Lipschitz transpose map of a Lipschitz operator, we state Lipschitz versions of Schauder type theorems on the (weak) compactness of the adjoint of a (weakly) compact linear operator.

Robust Solutions of MultiObjective Linear Semi-Infinite Programs under Constraint Data Uncertainty

The multiobjective optimization model studied in this paper deals with simultaneous minimization of finitely many linear functions subject to an arbitrary number of uncertain linear constraints. We first provide a radius of robust feasibility guaranteeing the feasibility of the robust counterpart under affine data parametrization. We then establish dual characterizations of robust solutions of our model that are immunized against data uncertainty by way of characterizing corresponding solutions of robust counterpart of the model. Consequently, we present robust duality theorems relating the value of the robust model with the corresponding value of its dual problem.

An introduction to alysidal algebra (IV)

Purpose – Deontical impure systems are systems whose object set is formed by an s-impure set, whose elements are perceptuales significances (relative beings) of material and/or energetic objects (absolute beings) and whose relational set is freeways of relations, formed by sheaves of relations going in two-way directions and at least one of its relations has deontical properties such as permission, prohibition, obligation and faculty. The paper aims to discuss these issues. Design/methodology/approach – Mathematical and logical development of human society ethical and normative structure. Findings – Existence of relations with positive imperative modality (obligation) would constitute the skeleton of the system. Negative imperative modality (prohibition) would be the immunological system of protection of the system. Modality permission the muscular system, that gives the necessary flexibility. Four theorems have been formulated based on Gödel's theorem demonstrating the inconsistency or incompleteness of DISs. For each constructed systemic conception can happen to it one of the two following things: either some allowed responses are not produced or else some forbidden responses are produced. Responses prohibited by the system are defined as nonwished effects. Originality/value – This paper is a continuation of the four previous papers and is developed the theory of deontical impure systems.

Myth, Language, and Complex Ideologies

Ideologies use for their conservation and propagation persuasive methods of communication: rhetoric. Rhetoric is analyzed from the semiotic and logical-mathematical points of view. The following hypotheses are established: (1) language L is a self-explanatory system, mediated by a successive series of systems of cultural conventions, (2) connotative significances of an ideological advertising rhetoric must be known, and (3) the notion of ideological information is a neutral notion that does not imply the valuation of ideology or its conditions of veracity or falsification. Rhetorical figures like metonymy, metaphor, parable analogy, and allegory are defined as relations. Metaphor and parable are order relations. Operations of metonymic and metaphoric substitution are defined and several theorems derived from these operations have been deduced.

Reality, Systems and Impure Systems

Impure systems contain Objects and Subjects: Subjects are human beings. We can distinguish a person as an observer (subjectively outside the system) and that by definition is the Subject himself, and part of the system. In this case he acquires the category of object. Objects (relative beings) are significances, which are the consequence of perceptual beliefs on the part of the Subject about material or energetic objects (absolute beings) with certain characteristics.The IS (Impure System) approach is as follows: Objects are perceptual significances (relative beings) of material or energetic objects (absolute beings). The set of these objects will form an impure set of the first order. The existing relations between these relative objects will be of two classes: transactions of matter and/or energy and inferential relations. Transactions can have alethic modality: necessity, possibility, impossibility and contingency. Ontic existence of possibility entails that inferential relations have Deontic modality: obligation, permission, prohibition, faculty and analogy. We distinguished between theorems (natural laws) and norms (ethical, legislative and customary rules of conduct).

The Political Logic of Disintegration: Seven Lessons from the Soviet Collapse. CEPS Essay (No. 1), September 2012

In short, the European Union, as we know it, no longer exists. The very foundations on which it was built are eroding. Shared memories of the Second World War have faded away – half the 15- and 16-year-olds in German high schools do not know that Hitler was a dictator, while a third believe that he protected human rights. The collapse of the Soviet Union has stripped away the geopolitical rationale for European unity. The democratic welfare state that was at the heart of the post-war political consensus is under siege by, among other things, sheer demographics. And the prosperity that bolstered the European project’s political legitimacy is vanishing. More than six out of ten Europeans believe that the lives of today’s children will be more difficult than those of people from their own generation. Against this background, how unthinkable is the EU’s disintegration? Should Europeans make the mistake of taking the Union for granted? Should they assume that the Union would not collapse because it should not collapse? Here, Europe’s capacity to learn from the Soviet precedent could play a crucial part. For the very survival of the EU may depend on its leaders’ ability to manage a similar mix of political, economic and psychological factors that were in play in the process of the Soviet collapse. The game of disintegration is primarily a political one driven much more by the perceptions and misperceptions of the political actors than simply by the constellation of the structural factors – institutional and economic.

Intraoperative image-guided navigation system: development and applicability in 65 patients undergoing liver surgery

Background Image-guided systems have recently been introduced for their application in liver surgery.We aimed to identify and propose suitable indications for image-guided navigation systems in the domain of open oncologic liver surgery and,more specifically, in the setting of liver resection with and without microwave ablation. Method Retrospective analysis was conducted in patients undergoing liver resection with and without microwave ablation using an intraoperative image-guided stereotactic system during three stages of technological development (accuracy: 8.4 ± 4.4 mm in phase I and 8.4 ± 6.5 mm in phase II versus 4.5 ± 3.6 mm in phase III). It was evaluated, in which indications image-guided surgery was used according to the different stages of technical development. Results Between 2009 and 2013, 65 patients underwent image-guided surgical treatment, resection alone (n=38), ablation alone (n =11), or a combination thereof (n =16). With increasing accuracy of the system, image guidance was progressively used for atypical resections and combined microwave ablation and resection instead of formal liver resection (p<0.0001). Conclusion Clinical application of image guidance is feasible, while its efficacy is subject to accuracy. The concept of image guidance has been shown to be increasingly efficient for selected indications in liver surgery. While accuracy of available technology is increasing pertaining to technological advancements, more and more previously untreatable scenarios such as multiple small, bilobar lesions and so-called vanishing lesions come within reach.

Raw data of SCADCP (self-contained Acoustic Doppler Current Profiler) from three moorings in the Eastern Weddell Sea, 2005-2008

The success of any efforts to determine the effects of climate change on marine ecosystems depends on understanding in the first instance the natural variations, which contemporarily occur on the interannual and shorter time scales. Here we present results on the environmental controls of zooplankton distribution patterns and behaviour in the eastern Weddell Sea, Southern Ocean. Zooplankton abundance and vertical migration are derived from the mean volume backscattering strength (MVBS) and the vertical velocity measured by moored acoustic Doppler current profilers (ADCPs), which were deployed simultaneously at 64°S, 66.5°S and 69°S along the Greenwich Meridian from February, 2005, until March, 2008. While these time series span a period of full three years they resolve hourly changes. A highly persistent behavioural pattern found at all three mooring locations is the synchronous diel vertical migration (DVM) of two distinct groups of zooplankton that migrate between a deep residence depth during daytime and a shallow depth during nighttime. The DVM was closely coupled to the astronomical daylight cycles. However, while the DVM was symmetric around local noon, the annual modulation of the DVM was clearly asymmetric around winter solstice or summer solstice, respectively, at all three mooring sites. DVM at our observation sites persisted throughout winter, even at the highest latitude exposed to the polar night. Since the magnitude as well as the relative rate of change of illumination is minimal at this time, we propose that the ultimate causes of DVM separated from the light-mediated proximal cue that coordinates it. In all three years, a marked change in the migration behaviour occurred in late spring (late October/early November), when DVM ceased. The complete suspension of DVM after early November is possibly caused by the combination of two factors: (1) increased availability of food in the surface mixed layer provided by the phytoplankton spring bloom, and (2) vanishing diurnal enhancement of the threat from visually oriented predators when the illumination is quasi-continuous during the polar and subpolar summer. Zooplankton abundance in the water column, estimated as the mean MVBS in the depth range 50-300 m, was highest end of summer and lowest mid to end winter on the average annual cycle. However, zooplankton abundance varied several-fold between years and between locations. Based on satellite and in situ data of chlorophyll and sea ice as well as on hydrographic measurements, the interannual and spatial variations of zooplankton mean abundance can be explained by differences in the magnitude of the phytoplankton spring bloom, which develops during the seasonal sea ice retreat. Whereas the vernal ice melt appears necessary to stimulate the blooming of phytoplankton, it is not the determinator of the blooms magnitude, its areal extent and duration. A possible explanation for the limitation of the phytoplankton bloom in some years is top-down control. We hypothesise that the phytoplankton spring development can be curbed by grazing when the zooplankton had attained high abundance by growth during the preceding summer.

A note on the non-existence of multivalue A-stable methods of order greater than two /

Bibliography: leaf 3.

The Princeton colloquium; lectures on mathematics, delivered September 15 to 17, 1909, before members of the American Mathematical Society in connection with the summer meeting held at Princeton University, Princeton, N. J

Mode of access: Internet.

The Princeton Colloquium; lectures on mathematics, delivered September 15 to 17, 1909, before members of the American Mathematical Society in connection with the summer meeting held at Princeton University, Princeton, N.J.

Fundamental existence theorems, by G. A. Bliss.--Differential-geometric aspects of dynamics, by E. Kasner.

Irreducible cyclic presentations of the trivial group

We produce families of irreducible cyclic presentations of the trivial group. These families comprehensively answer questions about such presentations asked by Dunwoody and by Edjvet, Hammond, and Thomas. Our theorems are purely theoretical, but their derivation is based on practical computations. We explain how we chose the computations and how we deduced the theorems.

Forecasting with serially correlated regression models

In this article we investigate the asymptotic and finite-sample properties of predictors of regression models with autocorrelated errors. We prove new theorems associated with the predictive efficiency of generalized least squares (GLS) and incorrectly structured GLS predictors. We also establish the form associated with their predictive mean squared errors as well as the magnitude of these errors relative to each other and to those generated from the ordinary least squares (OLS) predictor. A large simulation study is used to evaluate the finite-sample performance of forecasts generated from models using different corrections for the serial correlation.

Utility functions on locally connected spaces

We investigate the role of local connectedness in utility theory and prove that any continuous total preorder on a locally connected separable space is continuously representable. This is a new simple criterion for the representability of continuous preferences, and is not a consequence of the standard theorems in utility theory that use conditions such as connectedness and separability, second countability, or path-connectedness. Finally we give applications to problems involving the existence of value functions in population ethics and to the problem of proving the existence of continuous utility functions in general equilibrium models with land as one of the commodities. (C) 2003 Elsevier B.V. All rights reserved.

The Debreu Gap Lemma and some generalizations

In this paper we study the Debreu Gap Lemma and its generalizations to totally ordered sets more general than (R, less than or equal to). We explain why it is important in economics to study utility functions which may not be real-valued and we build the foundations of a theory of continuity of such generalized utility functions. (C) 2004 Published by Elsevier B.V.