The hazards of symbolic definite integration (a continuing saga)

2015 ◽  
Vol 49 (1) ◽  
pp. 35-35
Author(s):  
Daniel Lichtblau
Keyword(s):  
Definite Integration

Stationary random vibration of a viscoelastic Timoshenko cantilever beam under diverse random processes

2019 ◽  
Vol 234 (4) ◽  
pp. 849-861
Author(s):  
Qingzhao Zhou ◽  
David He ◽  
Yaping Zhao
Keyword(s):  
White Noise ◽  
Cantilever Beam ◽  
Time Correlation ◽  
Random Excitation ◽  
Transverse Displacement ◽  
Mean Square ◽  
Concentrated Force ◽  
The Mean ◽  
Definite Integration ◽  
Band Limited

In this paper, the stochastic properties of a uniform Timoshenko cantilever beam are investigated systematically. Based on the external viscous damping and Kelvin–Voigt viscoelastic damping, the partial differential equations of the Timoshenko beam subjected to random excitation are derived. The applied load is the concentrated force, and the excitation related to includes the ideal white noise, the band-limited white noise, and the exponential noise. Expressions are obtained for the space–time correlation functions and the space–frequency power spectral density functions of the transverse displacement response. The evident improvement is that the infinite integral and the definite integration in the mean square responses are worked out by means of the residue integral method and the integration by partial fraction, and the exact solutions of the mean square response are obtained in the form of an infinite series finally. This improvement provides a basis for both the mode truncation and the modal cross-spectral densities whether which can be ignored. Providing the numerical example, the numerical results obtained show the effectiveness of the theoretical analysis.

The Effect of Friction at the Strip Footings’ Underside on the Expansion of Plastic Zones in Subgrade

2014 ◽  
Vol 1008-1009 ◽  
pp. 1227-1233
Author(s):  
Nian Chun Xu ◽  
Wen Jing Xia ◽  
Tong Qing Wu
Keyword(s):  
Critical Load ◽  
Bearing Capacity ◽  
Ultimate Bearing Capacity ◽  
Horizontal Direction ◽  
Strength Theory ◽  
Subgrade Soil ◽  
Plastic Zones ◽  
Definite Integration ◽  
Strip Footings ◽  
Two Sides

There exists horizontal friction besides vertically pressure at the foundations' underside. Considering the effect of friction on the expansion of plastic zones in subgrade is needed to accurately evaluate subgrade’s safety. A strip footing is chose as the research object. Assuming the distribution of friction at the strip footing’s underside is two symmetrical triangles. With the help of Flamant formula and via definite integration, the formulas of stress in subgrade induced by the friction are got. Setting the Coulomb-Mohr strength theory as the yielding criterion for the subgrade soil, through the comparison among the different friction angles in expansion characteristics of plastic zones, the research object is achieved. Two major conclusions as following: (1) the friction makes the plastic zones appear in advance, the initial critical load get smaller with the friction get bigger; (2) the plastic zones get broader in horizontal direction under the action of the friction, this makes the plastic zones in two sides beneath the footing run-through later and so enhances the subgrade’s ultimate bearing capacity.

scholarly journals New approach to the calculation of pistachio powder hysteresis

2016 ◽  
Vol 30 (2) ◽  
pp. 245-251 ◽  
Author(s):  
Hamid Tavakolipour ◽  
Mohsen Mokhtarian
Keyword(s):  
Goodness Of Fit ◽  
Capillary Condensation ◽  
Gravimetric Method ◽  
Sorption Isotherms ◽  
Moisture Sorption ◽  
Suitable Model ◽  
Moisture Sorption Isotherms ◽  
Different Temperatures ◽  
Definite Integration ◽  
Increasing Temperature

Abstract Moisture sorption isotherms for pistachio powder were determined by gravimetric method at temperatures of 15, 25, 35 and 40°C. A selected mathematical models were tested to determine the best suitable model to predict isotherm curve. The results show that Caurie model had the most satisfactory goodness of fit. Also, another purpose of this research was to introduce a new methodology to determine the amount of hysteresis at different temperatures by using best predictive model of isotherm curve based on definite integration method. The results demonstrated that maximum hysteresis is related to the multi-layer water (in the range of water activity 0.2-0.6) which corresponds to the capillary condensation region and this phenomenon decreases with increasing temperature.

Wave Propagation in Strings with Continuous and Concentrated Loads

1927 ◽  
Vol 23 (7) ◽  
pp. 768-778 ◽  
Author(s):  
Harold Jeffreys
Keyword(s):  
Wave Propagation ◽  
Finite Number ◽  
Degrees Of Freedom ◽  
Concentrated Loads ◽  
Definite Integration ◽  
Characteristic Features ◽  
Operational Methods

The motion of a light string loaded with equal masses at regular intervals has been discussed by operational methods. It is found that the system, though possessing only a. finite number of degrees of freedom, shows most of the characteristic features of dispersion. The operator e−σx/c that occurs in the discussion of uniform continuous strings is found to arise as the limit of an operator defined wholly in terms of definite integration, and its interpretation involves a theorem analogous to Taylor's theorem, but apparently more general. There is no phenomenon analogous to the conduction of heat. Any irregularity in the distribution of mass, however, produces strong internal reflexion of the shortest waves, and may provide a mechanism for conduction.

A critical approach proposal for training translation memory systems in translator education programs

FORUM ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 79-99
Author(s):  
Erika Nogueira de Andrade Stupiello ◽  
Marileide Dias Esqueda
Keyword(s):  
Memory Systems ◽  
Critical Approach ◽  
Education Programs ◽  
Translation Memory ◽  
Training Methodology ◽  
Fast Pace ◽  
Definite Integration ◽  
Undergraduate Programs ◽  
Translator Education

Abstract The fast pace of todays translation market and the definite integration of translation memory systems TMS in the translators workstation have created new demands in terms of technological skills expected from novice translators. Aiming to prepare future translators to meet market demands, many translation undergraduate programs in Brazil have included the training on translation memory systems in their curricula. Applying the action-research methodology, this paper reports on the training methodology used for TMS in translation classrooms at two Brazilian public universities. The collected data in both contexts suggest that TMS may affect both the composing of the final translation and the decision-making of trainee translators and the quality of their production if they do not reflectively challenge their choices and the suggested output.

scholarly journals Chaos Synchronization of Financial Chaotic System with External Perturbation

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Chengrong Xie ◽  
Yuhua Xu ◽  
Dongbing Tong
Keyword(s):  
Dynamical Systems ◽  
Lower Limit ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Scaling Function ◽  
External Perturbation ◽  
Projective Synchronization ◽  
Definite Integral ◽  
Function Projective Synchronization ◽  
Definite Integration

This paper investigates the problem of two kinds of function projective synchronization of financial chaotic system with definite integration scaling function, which are not fully considered in the existing research. Different from the previous methods, in this paper, the following two questions are investigated: (1) two kinds of the definite integration scaling function projective synchronization are given; (2) the upper and lower limit of the definite integral scaling function are the bound dynamical systems. Finally, illustrative example is provided to show the effectiveness of this method.

2. On Methods in Definite Integrals

1880 ◽  
Vol 10 ◽  
pp. 271-271
Author(s):  
Tait
Keyword(s):  
Infinite Series ◽  
Definite Integrals ◽  
Great Ease ◽  
Definite Integration ◽  
Image Position

This paper deals with various formulæ of definite integration which are, in general, put into forms in which they enable us with great ease to sum a number of infinite series. As a simple example of such a formula the following may be given:—From this it is easy to deduce innumerable results, of which the annexed are some of the more immediate.

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