Negative Größen bei Diophant?

In this paper we champion Diophantus of Alexandria and Isabella Basmakova against Norbert Schappacher. In two publications ([46] and [47]) he puts forward inter alia two propositions: Questioning Diophantus' originality he considers affirmatively the possibility, that the Arithmetica are the joint work of a team of authors like Bourbaki. And he calls Basmakova's claim (in [5]), that Diophantus uses negative numbers, a "nonsense", reproaching her for her "thoughtlessness". First, we disprove Schappacher's Bourbaki thesis. Second, we investigate the semantic meaning and historical significance of Diophantus' keywords leipsis and mparxis. Next, we discuss Schappacher's epistemology of the history of mathematics and defend Basmakova's methods. Furthermore, we give 33 places where Diophantus uses negative quantities as intermediate results; they appear as differences a - b of positive rational numbers, the subtrahend b being bigger than the minuend a; they each represent the (negative) basis (pleyra) of a square number (tetragonos), which is afterwards computed by the formula (a - b)^2 = a^2 + b^2 - 2ab. Finally, we report how the topic "Diophantus and the negative numbers" has been dealt with by translators and commentators from Maximus Planudes onwards.

On Oseen Resolvent Estimates: A Negative Result

We consider the resolvent problem for the scalar Oseen equation in the whole space R^3. We show that for small values of the resolvent parameter it is impossible to obtain an L^2-estimate analogous to the one which is valid for the Stokes resolvent, even if the resolvent parameter has positive real part.

Time Discretization of the SST-generalized Navier-Stokes Equations: Positive and Negative Results

In the theory of the Navier-Stokes equations, the proofs of some basic known results, like for example the uniqueness of solutions to the stationary Navier-Stokes equations under smallness assumptions on the data or the stability of certain time discretization schemes, actually only use a small range of properties and are therefore valid in a more general context. This observation leads us to introduce the concept of SST spaces, a generalization of the functional setting for the Navier-Stokes equations. It allows us to prove (by means of counterexamples) that several uniqueness and stability conjectures that are still open in the case of the Navier-Stokes equations have a negative answer in the larger class of SST spaces, thereby showing that proof strategies used for a number of classical results are not sufficient to affirmatively answer these open questions. More precisely, in the larger class of SST spaces, non-uniqueness phenomena can be observed for the implicit Euler scheme, for two nonlinear versions of the Crank-Nicolson scheme, for the fractional step theta scheme, and for the SST-generalized stationary Navier-Stokes equations. As far as stability is concerned, a linear version of the Euler scheme, a nonlinear version of the Crank-Nicolson scheme, and the fractional step theta scheme turn out to be non-stable in the class of SST spaces. The positive results established in this thesis include the generalization of classical uniqueness and stability results to SST spaces, the uniqueness of solutions (under smallness assumptions) to two nonlinear versions of the Euler scheme, two nonlinear versions of the Crank-Nicolson scheme, and the fractional step theta scheme for general SST spaces, the second order convergence of a version of the Crank-Nicolson scheme, and a new proof of the first order convergence of the implicit Euler scheme for the Navier-Stokes equations. For each convergence result, we provide conditions on the data that guarantee the existence of nonstationary solutions satisfying the regularity assumptions needed for the corresponding convergence theorem. In the case of the Crank-Nicolson scheme, this involves a compatibility condition at the corner of the space-time cylinder, which can be satisfied via a suitable prescription of the initial acceleration.

An analysis of the anxiolytic effects of ethanol on consummatory successive negative contrast

The anxiolytic properties of ethanol (1 g/kg, 15% dose, i.p.) were studied in two experiments with rats involving incentive downshifts from a 32% to a 4% sucrose solution. In Experiment 1, alcohol administration before a downshift from 32% to 4% sucrose prevented the development of consummatory suppression (consummatory successive negative contrast, cSNC). In Experiment 2, ethanol prevented the attenuating effects of partial reinforcement (random sequence of 32% sucrose and nothing) on cSNC, causing a retardation of recovery from contrast. These effects of ethanol on cSNC are analogous to those described for the benzodiazepine anxiolytic chlordiazepoxide, suggesting that at least some of its anxiolytic effects are mediated by the same mechanisms. 

The dilemma of combining positive and negative items in scales

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Negative Fukui functions: new insights based on electronegativity equalization

The occurrence of negative values for Fukui functions was studied through the electronegativity equalization method. Using algebraic relations between Fukui functions and different other conceptual DFT quantities on the one hand and the hardness matrix on the other hand, expressions were obtained for Fukui functions for several archetypical small molecules. Based on EEM calculations for large molecular sets, no negative Fukui functions were found

Hemispheric asymmetries in recognition memory for negative and neutral words

Federmeier and Benjamin (2005) have suggested that semantic encoding for verbal information in the right hemisphere can be more effective when memory demands are higher. However, other studies (Kanske & Kotz, 2007) also suggest that visual word recognition differ in function of emotional valence. In this context, the present study was designed to evaluate the effects of retention level upon recognition memory processes for negative and neutral words. Sample consisted of 15 right-handed undergraduate portuguese students with normal or corrected to normal vision. Portuguese concrete negative and neutral words were selected in accordance to known linguistic capabilities of the right hemisphere. The participants were submitted to a visual half-field word presentation using a continuous recognition memory paradigm. Eye movements were continuously monitored with a Tobii T60 eye-tracker that showed no significant differences in fixations to negative and neutral words. Reaction times in word recognition suggest an overall advantage of negative words in comparison to the neutral words. Further analysis showed faster responses for negative words than for neutral words when were recognised at longer retention intervals for left-hemisphere encoding. Electrophysiological data through event related potentials revealed larger P2 amplitude over centro-posterior electrode sites for words studied in the left hemifield suggesting a priming effect for right-hemisphere encoding. Overall data suggest different hemispheric memory strategies for the semantic encoding of negative and neutral words.

Amygdala and ventromedial prefrontal cortex are inversely coupled during regulation of negative affect and predict the diurnal pattern of cortisol secretion among older adults

Among younger adults, the ability to willfully regulate negative affect, enabling effective responses to stressful experiences, engages regions of prefrontal cortex (PFC) and the amygdala. Because regions of PFC and the amygdala are known to influence the hypothalamic-pituitary-adrenal axis, here we test whether PFC and amygdala responses during emotion regulation predict the diurnal pattern of salivary cortisol secretion. We also test whether PFC and amygdala regions are engaged during emotion regulation in older (62- to 64-year-old) rather than younger individuals. We measured brain activity using functional magnetic resonance imaging as participants regulated (increased or decreased) their affective responses or attended to negative picture stimuli. We also collected saliva samples for 1 week at home for cortisol assay. Consistent with previous work in younger samples, increasing negative affect resulted in ventral lateral, dorsolateral, and dorsomedial regions of PFC and amygdala activation. In contrast to previous work, decreasing negative affect did not produce the predicted robust pattern of higher PFC and lower amygdala activation. Individuals demonstrating the predicted effect (decrease s attend in the amygdala), however, exhibited higher signal in ventromedial prefrontal cortex (VMPFC) for the same contrast. Furthermore, participants displaying higher VMPFC and lower amygdala signal when decreasing compared with the attention control condition evidenced steeper, more normative declines in cortisol over the course of the day. Individual differences yielded the predicted link between brain function while reducing negative affect in the laboratory and diurnal regulation of endocrine activity in the home environment.

Gaze fixations predict brain activation during the voluntary regulation of picture-induced negative affect

Recent studies have identified a distributed network of brain regions thought to support cognitive reappraisal processes underlying emotion regulation in response to affective images, including parieto-temporal regions and lateral/medial regions of prefrontal cortex (PFC). A number of these commonly activated regions are also known to underlie visuospatial attention and oculomotor control, which raises the possibility that people use attentional redeployment rather than, or in addition to, reappraisal as a strategy to regulate emotion. We predicted that a significant portion of the observed variance in brain activation during emotion regulation tasks would be associated with differences in how participants visually scan the images while regulating their emotions. We recorded brain activation using fMRI and quantified patterns of gaze fixation while participants increased or decreased their affective response to a set of affective images. fMRI results replicated previous findings on emotion regulation with regulation differences reflected in regions of PFC and the amygdala. In addition, our gaze fixation data revealed that when regulating, individuals changed their gaze patterns relative to a control condition. Furthermore, this variation in gaze fixation accounted for substantial amounts of variance in brain activation. These data point to the importance of controlling for gaze fixation in studies of emotion regulation that use visual stimuli.

Negative correlations between control performance and verbalizable knowledge: indicators for implicit learning in process control tasks?

Negative correlations between task performance in dynamic control tasks and verbalizable knowledge, as assessed by a post-task questionnaire, have been interpreted as dissociations that indicate two antagonistic modes of learning, one being “explicit”, the other “implicit”. This paper views the control tasks as finite-state automata and offers an alternative interpretation of these negative correlations. It is argued that “good controllers” observe fewer different state transitions and, consequently, can answer fewer post-task questions about system transitions than can “bad controllers”. Two experiments demonstrate the validity of the argument by showing the predicted negative relationship between control performance and the number of explored state transitions, and the predicted positive relationship between the number of explored state transitions and questionnaire scores. However, the experiments also elucidate important boundary conditions for the critical effects. We discuss the implications of these findings, and of other problems arising from the process control paradigm, for conclusions about implicit versus explicit learning processes.

Aging is associated with positive responding to neutral information but reduced recovery from negative information

Studies on aging and emotion suggest an increase in reported positive affect, a processing bias of positive over negative information, as well as increasingly adaptive regulation in response to negative events with advancing age. These findings imply that older individuals evaluate information differently, resulting in lowered reactivity to, and/or faster recovery from, negative information, while maintaining more positive responding to positive information. We examined this hypothesis in an ongoing study on Midlife in the US (MIDUS II) where emotional reactivity and recovery were assessed in a large number of respondents (N = 159) from a wide age range (36–84 years). We recorded eye-blink startle magnitudes and corrugator activity during and after the presentation of positive, neutral and negative pictures. The most robust age effect was found in response to neutral stimuli, where increasing age is associated with a decreased corrugator and eyeblink startle response to neutral stimuli. These data suggest that an age-related positivity effect does not essentially alter the response to emotion-laden information, but is reflected in a more positive interpretation of affectively ambiguous information. Furthermore, older women showed reduced corrugator recovery from negative pictures relative to the younger women and men, suggesting that an age-related prioritization of well-being is not necessarily reflected in adaptive regulation of negative affect.

Temperature sensitivity of the low-moisture-content limit to negative seed longevity-moisture content relationships in hermetic storage

Background and Aims The negative logarithmic relationship between orthodox seed longevity and moisture content in hermetic storage is subject to a low-moisture-content limit (m(c)), but is m(c) affected by temperature? Methods Red clover (Trifolium pratense) and alfalfa (Medicago sativa) seeds were stored hermetically at 12 moisture contents (2-15 %) and five temperatures (-20, 30, 40, 50 and 65 degrees C) for up to 14.5 years, and loss in viability was estimated. Key Results Viability did not change during 14.5 years hermetic storage at -20 degrees C with moisture contents from 2.2 to 14.9 % for red clover, or 2.0 to 12.0 % for alfalfa. Negative logarithmic relationships between longevity and moisture contents > m(c) were detected at 30-65 degrees C, with discontinuities at low moisture contents; m(c) varied between 4.0 and 5.4 % (red clover) or 4.2 and 5.5 % (alfalfa), depending upon storage temperature. Within the ranges investigated, a reduction in moisture content below m(c) at any one temperature had no effect on longevity. Estimates of m(c) were greater the cooler the temperature, the relationship (P < 0.01) being curvilinear. Above m(c), the estimates of C-H and C-Q (i.e. the temperature term of the seed viability equation) did not differ (P > 0.10) between species, whereas those of K-E and C-W did (P < 0.001). Conclusions The low-moisture-content limit to negative logarithmic relationships between seed longevity and moisture content in hermetic storage increased the cooler the storage temperature, by approx. 1.5 % over 35 degrees C (4.0-4.2 % at 65 degrees C to 5.4-5.5 % at 30-40 degrees C) in these species. Further reduction in moisture content was not damaging. The variation in m(c) implies greater sensitivity of longevity to temperature above, compared with below, m(c). This was confirmed (P < 0.005).