Measurements and geometry

The paper is aimed at demonstrating the points of contact between measurements and geometry, which is done by modelling the main elements of the measurement process by the elements of geometry. It is shown that the basic equation for measurements can be established from the expression of projective metric and represents its particular case. Commonly occurring groups of functional transformations of the measured value are listed. Nearly all of them are projective transformations, which have invariants and are useful if greater accuracy of measurements is desired. Some examples are given to demonstrate that real measurement transformations can be dealt with via fractional-linear approximations. It is shown that basic metrological and geometrical categories are related, and a concept of seeing a multitude of physical values as elements of an abstract geometric space is introduced. A system of units can be reasonably used as the basis of this space. Two tensors are introduced in the space. One of them (the affinor) describes the interactions within the physical object, the other (the metric tensor) establishes the summation rule on account of the random nature of components.

Some issues in creep-fatigue research

In the component operated at elevated temperatures, the life evaluation should be made in consideration of both creep and fatigue (creep-fatigue) such as the linear damage summation rule. However, the concept of creep-fatigue life evaluation has not spread well in the industry. In order to consider the reason, a series of past creep-fatigue research was surveyed, namely experimental methods, life evaluation procedures and strength design guidelines. As a result, it was revealed that the mechanism of creep-fatigue interaction has not been fully clarified yet, which results in obscuring the necessity of creep-fatigue life evaluation. The necessity of creep-fatigue life evaluation was reviewed and consequently it proved to be necessary in two cases. One is the case where the creep-fatigue interaction is significant for some kinds of material, loading modes and temperatures. The other is one where the amount of creep damage is almost the same as that of fatigue damage even though the creep-fatigue interaction is insignificant.

Obstructed View Factor Calculations for Multiple Obstructions in Closed Cavities

The inertial confinement fusion (ICF) program has been mainly concentrating on the indirect drive approach for the last three decades, due to relaxed requirements on driver-beam uniformity and reduced sensitivity to hydrodynamic instabilities. The optimal designs are important for maximum conversion of driving energy to X-rays, and finally, symmetrical irradiation of the capsule. The view factor (VF) evaluation is an important parameter providing significant radiation heat transport information in specific geometries. The present study is aimed at the VF calculations for closed cavities. The VF calculations include the case of energy transfer from one infinitesimal surface element of the enclosure to other similar infinitesimal surface elements of the cavity. Similarly, the obstructed VF is also calculated when multiple obstructions are present in the cavity. Two distinct computer programs are developed by programming in FORTRAN-90 to evaluate unobstructed VF and obstructed VF for a square geometry. The calculations are based on the crossed strings method, which is more reliable for simple geometries. The shadow effect method is used for the obstructed VF calculations. The results of the developed programs are benchmarked using the summation rule. In the case of no obstacles in the cavity, VF calculations solely obey the summation rule. However, in the presence of obstacles in the cavity, obstructed VF calculations showed the acceptable difference in comparison with the summation rule.

The Mellin transform and Euler-Maclaurin summation rule applied to system of n - independent harmonic oscillators

We confront the Mellin and the Euler-Maclaurin summation rule when used in order to calculate N independent harmonic oscillators thermodynamic potentials, and compare the approximate expressions with the exact ones for these quantities. The goal of this work is at least twofold: First, to compare the results obtained for the thermodynamic potentials of a system of N oscillators using the Mellin and the Euler-Maclaurin summation rule in order to have a discernment on which one is most appropriate for application to more complex systems with finite and infinite number of components. Second, to present to the reader the ideas of these techniques in a pedestrian way with the aim of providing one material with detailed calculation that can be useful like a basic reference to more deep calculation, in particular string theory and supergravity.

Cognitive Algebra Underlying High School Student´s Self-Efficacy Judgment to Solve Mathematical Problems in the Classroom or Online

<p>This study includes a sample of 112 high school students who provided self-efficacy<br />judgments to solve math problems. Thirty-six experimental conditions called scenarios were<br />created for this study by combining 4 factors regarding solving mathematical problems<br />(modality, degree of difficulty, structuring, and relevance of the task). Each scenario<br />described a hypothetical context that required the participant to imagine an activity to<br />reinforce the learning of math skills in the scenario. Thus, the experimental task was to read<br />each scenario and to judge how capable the participant felt to undertake each math task under<br />the hypothetical context. Results showed two levels of self-efficacy judgment among<br />participants. Students in the first level judged themselves as highly capable of performing<br />math activities, while those in the second level, judged themselves as moderate capable.<br />Regarding the first cluster factors regarding difficulty and the structure of the task had a<br />greater weight whereas in the second cluster task difficulty and task relevance factors<br />obtained the higher weight values. Finally, a cognitive summation rule used by participants to<br />integrate information from the different study factors was identified. Results implications on<br />education are discussed in this article.</p>

Spatial summation revealed in the earliest visual evoked component C1 and the effect of attention on its linearity

In natural scenes, multiple objects are usually presented simultaneously. How do specific areas of the brain respond to multiple objects based on their responses to each individual object? Previous functional magnetic resonance imaging (fMRI) studies have shown that the activity induced by a multiobject stimulus in the primary visual cortex (V1) can be predicted by the linear or nonlinear sum of the activities induced by its component objects. However, there has been little evidence from electroencephelogram (EEG) studies so far. Here we explored how V1 responded to multiple objects by comparing the EEG signals evoked by a three-grating stimulus with those evoked by its two components (the central grating and 2 flanking gratings). We focused on the earliest visual component C1 (onset latency of ∼50 ms) because it has been shown to reflect the feedforward responses of neurons in V1. We found that when the stimulus was unattended, the amplitude of the C1 evoked by the three-grating stimulus roughly equaled the sum of the amplitudes of the C1s evoked by its two components, regardless of the distances between these gratings. When the stimulus was attended, this linear spatial summation existed only when the three gratings were far apart from each other. When the three gratings were close to each other, the spatial summation became compressed. These results suggest that the earliest visual responses in V1 follow a linear summation rule when attention is not involved and that attention can affect the earliest interactions between multiple objects.

Development of Creep-Fatigue Evaluation Method for Modified 9Cr-1Mo Steel

This paper describes a creep–fatigue evaluation method for modified 9Cr-1Mo steel, which has been newly included in the 2012 edition of the Japan Society of Mechanical Engineers code for design and construction of fast reactors (JSME FRs code). In this method, creep and fatigue damages are evaluated on the basis of Miner's rule and the time fraction rule, respectively, and the linear summation rule is employed as the failure criterion. The conservativeness of this method without design factors was investigated using material test results, and it was shown that the time fraction approach can conservatively predict failure life if margins on the initial stress of relaxation and the stress relaxation rate are embedded. In addition, the conservatism of prediction tends to increase with time to failure. Comparison with the modified ductility exhaustion method, which is known to have good failure life predictability in material test results, shows that the time fraction approach predicts failure lives to be shorter in long-term strain hold conditions, where material test data are hardly obtained. These results confirm that the creep–fatigue evaluation method in the JSME FRs code has implicit conservatism in addition to explicit margins in the design procedures such as design factor.