The Calderón Brothers, a Happy Mathematical Relation

2014 ◽  
pp. 7-11
Author(s):  
Alexandra Bellow
Keyword(s):  
Mathematical Relation

scholarly journals Investigation on the Mathematical Relation Model of Structural Reliability and Structural Robustness

2021 ◽  
Vol 26 (2) ◽  
pp. 26
Author(s):  
Qi-Wen Jin ◽  
Zheng Liu ◽  
Shuan-Hai He
Keyword(s):  
Structural Damage ◽  
Structural Reliability ◽  
Relational Model ◽  
Engineering Practice ◽  
Variation Trend ◽  
Evaluation Indexes ◽  
Structural Robustness ◽  
Mathematical Relation ◽  
Relation Model ◽  
Random Variation

Structural reliability and structural robustness, from different research fields, are usually employed for the evaluative analysis of building and civil engineering structures. Structural reliability has been widely used for structural analysis and optimization design, while structural robustness is still in rapid development. Several dimensionless evaluation indexes have been defined for structural robustness so far, such as the structural reliability-based redundancy index. However, these different evaluation indexes are usually based on subjective definitions, and they are also difficult to put into engineering practice. The mathematical relational model between structural reliability and structural robustness has not been established yet. This paper is a quantitative study, focusing on the mathematical relation between structural reliability and structural robustness so as to further develop the theory of structural robustness. A strain energy evaluation index for structural robustness is introduced firstly by considering the energy principle. The mathematical relation model of structural reliability and structural robustness is then derived followed by a further comparative study on sensitivity, structural damage, and random variation factor. A cantilever beam and a truss beam are also presented as two case studies. In this study, a parabolic curve mathematical model between structural reliability and structural robustness is established. A significant variation trend for their sensitivities is also observed. The complex interaction mechanism of the joint effect of structural damage and random variation factor is also reflected. With consideration of the variation trend of the structural reliability index that is affected by different degrees of structural damage (mild impairment, moderate impairment, and severe impairment), a three-stage framework for structural life-cycle maintenance management is also proposed. This study can help us gain a better understanding of structural robustness and structural reliability. Some practical references are also provided for the better decision-making of maintenance and management departments.

Effects of a PFI refiner’s operational parameters on the swellability of recycled fiber

TAPPI Journal ◽  
2020 ◽  
Vol 19 (5) ◽  
pp. 239-246
Author(s):  
XIAONING SHEN ◽  
BO LI ◽  
WENXUAN MO ◽  
XIN-SHENG CHAI
Keyword(s):  
Water Retention ◽  
Fiber Quality ◽  
Operational Parameters ◽  
Fiber Morphology ◽  
Water Retention Value ◽  
Electron Microscopic ◽  
Mathematical Relation ◽  
Scanning Electron Microscopic ◽  
Recycled Fiber ◽  
Scanning Electron

This paper presents data on the effects of operational parameters (number of revolutions, linear pressure, and gap) of the PFI refiner on the swellability of recycled fiber, which was characterized by water retention value (WRV). The results showed that the increase of recycled fiber’s WRV was proportional to the number of revolutions and the linear pressure, but inversely proportional to the gap. The mathematical relation between these parameters and the fiber WRV could be described by an empirical model for gaps greater than 0.1 mm. Scanning electron microscopic images of fiber morphology showed that the basic framework of fibers could be maintained with the gap greater than 0.1 mm, but was destroyed with smaller gaps. This model provides a technical reference for quantitative control of refining treatment and an effective method for improving recycled fiber quality.

scholarly journals Lawful relation between perceptual bias and discriminability

2017 ◽  
Vol 114 (38) ◽  
pp. 10244-10249 ◽  
Author(s):  
Xue-Xin Wei ◽  
Alan A. Stocker
Keyword(s):  
Empirical Support ◽  
Human Perception ◽  
Perceptual Bias ◽  
Contextual Modulation ◽  
Mathematical Relation ◽  
Wide Range ◽  
Optimal Encoding ◽  
Stimulus Value ◽  
Sensory Encoding ◽  
Perceptual Changes

Perception of a stimulus can be characterized by two fundamental psychophysical measures: how well the stimulus can be discriminated from similar ones (discrimination threshold) and how strongly the perceived stimulus value deviates on average from the true stimulus value (perceptual bias). We demonstrate that perceptual bias and discriminability, as functions of the stimulus value, follow a surprisingly simple mathematical relation. The relation, which is derived from a theory combining optimal encoding and decoding, is well supported by a wide range of reported psychophysical data including perceptual changes induced by contextual modulation. The large empirical support indicates that the proposed relation may represent a psychophysical law in human perception. Our results imply that the computational processes of sensory encoding and perceptual decoding are matched and optimized based on identical assumptions about the statistical structure of the sensory environment.

scholarly journals Calculation of Differential Propagation Constant Determined by Plant Morphology Using Polarimetric Measurement

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Chufeng Hu ◽  
Nanjing Li
Keyword(s):  
Electromagnetic Wave ◽  
Measurement System ◽  
Random Distribution ◽  
Propagation Constant ◽  
Morphological Characteristics ◽  
Plant Morphology ◽  
Structural Features ◽  
Low Frequencies ◽  
Mathematical Relation ◽  
Power Profile

The morphology of vegetation greatly impacts propagation of polarized electromagnetic wave. In order to validate this phenomenon, the mathematical relation between the differential propagation constant of forest vegetation and of its polarized echo is quantitatively derived by using backscattering power profile. The fluctuation of differential propagation constant with frequency is analyzed by combining the morphological characteristics of vegetation. The accurate copolarized data of 3–10 GHz frequency-domain of small trees are obtained by indoor wideband polarimetric measurement system. The results show that morphological characteristics of vegetation at different frequencies can be obtained by the differential propagation constant of polarized electromagnetic wave. At low frequencies, the plants with structural features presented oriented distribution. However, the plants show random distribution of the echoes at higher frequencies, which is mainly from the canopy. The research provides important information to choose the coherence models employed in the parameters retrieval of vegetations.

scholarly journals Accelerated method for the determination of freeze-thaw resistance of concrete

2015 ◽  
Vol 1 ◽  
pp. 170 ◽  
Author(s):  
Sergey Nikolskiy ◽  
Olga Pertseva
Keyword(s):  
High Efficiency ◽  
Reference Method ◽  
Mean Value ◽  
Nondestructive Method ◽  
National Standard ◽  
Labor Input ◽  
Standard Specification ◽  
Freeze Thaw ◽  
Mathematical Relation

<p class="R-AbstractKeywords"><span lang="EN-US">Main purpose of this research is to create the new reference method of determining the freeze-thaw resistance of concrete that is characterized by small labor input, high efficiency and a wide application scope. The offered method is based on measurement of long strength by nondestructive method. During this research, the theoretical analysis of concrete's specimen dependence on freeze-thaw resistance and energy, which is emitted by a specimen during destruction, has been carried out.  Freeze-thaw resistance of a specimen is calculated as the mathematical relation of these energies, and the freeze-thaw resistance of concrete is calculated as an arithmetic mean value across specimens. </span></p><p class="R-AbstractKeywords"><span lang="EN-US">To prove the method correctness it was realized on 10 concrete specimens. Age of specimens cosolidation is 88 days. Speciments of concrete mortar were prepared using a mix of portland cement 400 (12,3%), sand of dimentions 0.6-5 mm (24,7%), granite macadam of dimentions 5-20 mm (55,4%) and water (7,4%). Freeze-thaw resistance such mortar was determed earlier by method, approved national standard specification, it was equal 105 cycles. According dimentions by new offered method freeze-thaw resistance such mortar is equal 107 cycles and its confidence interval is equal 5,4 (probability P = 0,95). Therefore, spread of results could be casual and the offered method is correct.</span></p>

scholarly journals STUDY, DESIGN AND SIMULATION OF A PROGRAM FOR NUMERICAL EVALUATION OF VEHICLES’ FUEL CONSUMPTION DUE TO DRAG FORCE; CASE OF LIGHT VEHICLES.

2020 ◽  
Vol 7 (1) ◽  
pp. 1-11
Author(s):  
Mbelle Samuel Bisong ◽  
Paune Felix ◽  
Lokoue D. Romaric Brandon ◽  
Pierre Kisito Talla
Keyword(s):  
Mathematical Model ◽  
Computer Program ◽  
Fuel Consumption ◽  
Drag Force ◽  
Numerical Evaluation ◽  
Construction Companies ◽  
Mathematical Relation ◽  
Basic Equations ◽  
Valid Information

Nowadays, vehicles are being abandoned by their users due to their high fuel consumption which had not been studied by the user from the start. Thus, the need to study the fuel consumption of vehicles due to one of the factors which greatly affects it; drag force, so as to produce information which vehicle users can have before purchasing their vehicles. With regards to this, this work is focused on the development of a computer program able to evaluate the fuel consumption of light vehicles. To achieve this, the basic equations of consumption are used to arrive at a mathematical relation between drag force and fuel consumption. This mathematical model is further implemented on the analytical software Matlab in order to produce the various consumption curves of the vehicles case study. A simulator which takes into consideration a vehicle’s engine data in order to produce specific consumption curves and provide valid information on the fuel consumption of the vehicle is developed from this mathematical model. It can be used in automotive construction companies and also by any individual.

Improvement of Surface Layer Formation Technology for Articles Produced by Layer-by-Layer Laser Sintering

2013 ◽  
Vol 379 ◽  
pp. 56-59 ◽  
Author(s):  
N.A. Saprykina ◽  
A.A. Saprykin
Keyword(s):  
Surface Layer ◽  
Powder Material ◽  
Copper Powder ◽  
Manufacturing Process ◽  
Laser Sintering ◽  
Layer By Layer ◽  
Layer Formation ◽  
Mathematical Relation ◽  
Surface Layer Formation

Mathematical relation between roughness of the surface layer of the sintered article and layer-by-layer laser sintering modes obtained from experiments conducted using copper powder material PMS-1. Authors suggest that split manufacturing process of an article and its inner part must be split to roughing, semi-finishing and finishing modes.

Sign in / Sign up

Export Citation Format

Share Document