scholarly journals Generalized Hermite Reduction, Creative Telescoping and Definite Integration of D-Finite Functions

2018 ◽  
Author(s):  
Alin Bostan ◽  
Frédéric Chyzak ◽  
Pierre Lairez ◽  
Bruno Salvy
Keyword(s):  
Definite Integration ◽  
Creative Telescoping

scholarly journals Efficient rational creative telescoping

2021 ◽  
Author(s):  
Mark Giesbrecht ◽  
Hui Huang ◽  
George Labahn ◽  
Eugene Zima
Keyword(s):  
Creative Telescoping

scholarly journals THE NON-COMMUTATIVE A-POLYNOMIAL OF TWIST KNOTS

2010 ◽  
Vol 19 (12) ◽  
pp. 1571-1595 ◽  
Author(s):  
STAVROS GAROUFALIDIS ◽  
XINYU SUN
Keyword(s):  
Difference Equation ◽  
Recursion Relation ◽  
Jones Polynomial ◽  
Minimal Order ◽  
Quantum Topology ◽  
And Topology ◽  
Jones Polynomials ◽  
Creative Telescoping ◽  
Colored Jones Polynomials ◽  
Telescoping Method

The purpose of the paper is two-fold: to introduce a multivariable creative telescoping method, and to apply it in a problem of Quantum Topology: namely the computation of the non-commutative A-polynomial of twist knots. Our multivariable creative telescoping method allows us to compute linear recursions for sums of the form [Formula: see text] given a recursion relation for [Formula: see text] and the hypergeometric kernel c(n, k). As an application of our method, we explicitly compute the non-commutative A-polynomial for twist knots with -15 and 15 crossings. The non-commutative A-polynomial of a knot encodes the monic, linear, minimal order q-difference equation satisfied by the sequence of colored Jones polynomials of the knot. Its specialization to q = 1 is conjectured to be the better-known A-polynomial of a knot, which encodes important information about the geometry and topology of the knot complement. Unlike the case of the Jones polynomial, which is easily computable for knots with 50 crossings, the A-polynomial is harder to compute and already unknown for some knots with 12 crossings.

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 Reduction-based creative telescoping for fuchsian D-finite functions

2018 ◽  
Vol 85 ◽  
pp. 108-127 ◽  
Author(s):  
Shaoshi Chen ◽  
Mark van Hoeij ◽  
Manuel Kauers ◽  
Christoph Koutschan
Keyword(s):  
Creative Telescoping

scholarly journals Some open problems related to creative telescoping

2017 ◽  
Vol 30 (1) ◽  
pp. 154-172 ◽  
Author(s):  
Shaoshi Chen ◽  
Manuel Kauers
Keyword(s):  
Open Problems ◽  
Creative Telescoping
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