text:
## Journal of Integral Equations and Applications

 Short Title: J. Integral Equations Appl. Publisher: Rocky Mountain Mathematics Consortium, Texas Tech University, Lubbock, TX ISSN: 0897-3962 Online: https://projecteuclid.org/all/euclid.jieahttp://rmmc.eas.asu.edu/jie/jie.html Predecessor: Journal of Integral Equations Comments: Indexed cover-to-cover
 Documents Indexed: 783 Publications (since 1988) References Indexed: 658 Publications with 13,438 References.
all top 5

### Latest Issues

 34, No. 2 (2022) 34, No. 1 (2022) 33, No. 4 (2021) 33, No. 3 (2021) 33, No. 2 (2021) 33, No. 1 (2021) 32, No. 4 (2020) 32, No. 3 (2020) 32, No. 2 (2020) 32, No. 1 (2020) 31, No. 4 (2019) 31, No. 3 (2019) 31, No. 2 (2019) 31, No. 1 (2019) 30, No. 4 (2018) 30, No. 3 (2018) 30, No. 2 (2018) 30, No. 1 (2018) 29, No. 4 (2017) 29, No. 3 (2017) 29, No. 2 (2017) 29, No. 1 (2017) 28, No. 4 (2016) 28, No. 3 (2016) 28, No. 2 (2016) 28, No. 1 (2016) 27, No. 4 (2015) 27, No. 3 (2015) 27, No. 2 (2015) 27, No. 1 (2015) 26, No. 4 (2014) 26, No. 3 (2014) 26, No. 2 (2014) 26, No. 1 (2014) 25, No. 4 (2013) 25, No. 3 (2013) 25, No. 2 (2013) 25, No. 1 (2013) 24, No. 4 (2012) 24, No. 3 (2012) 24, No. 2 (2012) 24, No. 1 (2012) 23, No. 4 (2011) 23, No. 3 (2011) 23, No. 2 (2011) 23, No. 1 (2011) 22, No. 4 (2010) 22, No. 3 (2010) 22, No. 2 (2010) 22, No. 1 (2010) 21, No. 4 (2009) 21, No. 3 (2009) 21, No. 2 (2009) 21, No. 1 (2009) 20, No. 4 (2008) 20, No. 3 (2008) 20, No. 2 (2008) 20, No. 1 (2008) 19, No. 4 (2007) 19, No. 3 (2007) 19, No. 2 (2007) 19, No. 1 (2007) 18, No. 4 (2006) 18, No. 3 (2006) 18, No. 2 (2006) 18, No. 1 (2006) 17, No. 4 (2005) 17, No. 3 (2005) 17, No. 2 (2005) 17, No. 1 (2005) 16, No. 4 (2004) 16, No. 3 (2004) 16, No. 2 (2004) 16, No. 1 (2004) 15, No. 4 (2003) 15, No. 3 (2003) 15, No. 2 (2003) 15, No. 1 (2003) 14, No. 4 (2002) 14, No. 3 (2002) 14, No. 2 (2002) 14, No. 1 (2002) 13, No. 4 (2001) 13, No. 3 (2001) 13, No. 2 (2001) 13, No. 1 (2001) 12, No. 4 (2000) 12, No. 3 (2000) 12, No. 2 (2000) 12, No. 1 (2000) 11, No. 4 (1999) 11, No. 3 (1999) 11, No. 2 (1999) 11, No. 1 (1999) 10, No. 4 (1998) 10, No. 3 (1998) 10, No. 2 (1998) 10, No. 1 (1998) 9, No. 4 (1997) 9, No. 3 (1997) ...and 32 more Volumes
all top 5

### Authors

 15 Xu, Yuesheng 12 Sloan, Ian Hugh 11 Atkinson, Kendall Eugene 10 Chandler-Wilde, Simon N. 10 O’Regan, Donal 9 Brunner, Hermann 9 Kress, Rainer 8 Chen, Zhongying 7 Desch, Wolfgang 7 Hansen, Olaf 7 Vainikko, Gennadi 6 Agarwal, Ravi P. 6 Appleby, John A. D. 6 Chapko, Roman 6 Lizama, Carlos 6 Prössdorf, Siegfried 6 Prüß, Jan Wilhelm 6 Väth, Martin 5 Anderssen, Robert Scott 5 Anselone, Philip M. 5 Appell, Jürgen M. 5 Baker, Christopher Thomas Hale 5 Cao, Yanzhao 5 Kulkarni, Rekha P. 5 McLean, William 5 Miller, Richard K. 5 Natroshvili, David 5 Roberts, Catherine Anne 5 Turi, Janos 5 Vecchio, Antonia 4 Arens, Tilo 4 Benchohra, Mouffak 4 Böttcher, Albrecht 4 Cakoni, Fioralba 4 Costarelli, Danilo 4 Crisci, Maria Rosaria 4 Domínguez, Víctor 4 Ezzinbi, Khalil 4 Haddar, Houssem 4 Herdman, Terry L. 4 Kirk, Colleen M. 4 Lanza de Cristoforis, Massimo 4 Liu, Zhenhai 4 Mastroianni, Giuseppe 4 Messaoudi, Salim A. 4 Mikhailov, Sergey E. 4 Mitina, Anna 4 Noren, Richard D. 4 Okrasiński, Wojciech 4 Pandey, Dwijendra Narain 4 Pani, Amiya Kumar 4 Pereverzev, Sergei V. 4 Potthast, Roland W. E. 4 Russo, Elvira 4 Saranen, Jukka 4 Sayas, Francisco-Javier 4 Silbermann, Bernd 4 Sinha, Rajen Kumar 4 Speck, Frank-Olme 4 Stephan, Ernst Peter 4 von Wolfersdorf, Lothar 4 Walter, Gilbert G. 3 Abbas, Said 3 Abbas, Syed 3 Al-Salman, Ahmad 3 Alvarez, Edgardo 3 Arias, Mariano R. 3 Bu, Shangquan 3 Burton, Theodore Allen 3 Pinheiro de Castro, Luís Filipe 3 Chang, Yong-Kui 3 Chen, Xiangling 3 Chudinovich, Igor Yuryevich 3 Constanda, Christian 3 de Hoog, Frank Robert 3 Diethelm, Kai 3 Eggermont, Paul P. B. 3 Elliott, David L. 3 Estrada, Ricardo 3 Feireisl, Eduard 3 Ford, Neville J. 3 Gal, Sorin Gheorghe 3 Ganesh, Mahadevan 3 Grigorieff, Rolf Dieter 3 Hannsgen, Kenneth B. 3 Heuer, Norbert 3 Hofmann, Bernd 3 Hrusa, William J. 3 Idczak, Dariusz 3 Ivanyshyn, Olha 3 Jiang, Ying 3 Kalitvin, Anatolij S. 3 Kaneko, Hideaki 3 Kilbas, Anatoliĭ Aleksandrovich 3 Kirane, Mokhtar 3 Kirsch, Andreas 3 Laurita, Concetta 3 Lin, Yanping 3 Liu, James Hetao 3 Martin, Paul Andrew ...and 833 more Authors
all top 5

### Fields

 524 Integral equations (45-XX) 283 Numerical analysis (65-XX) 175 Partial differential equations (35-XX) 152 Operator theory (47-XX) 90 Ordinary differential equations (34-XX) 51 Mechanics of deformable solids (74-XX) 34 Real functions (26-XX) 30 Optics, electromagnetic theory (78-XX) 26 Fluid mechanics (76-XX) 21 Probability theory and stochastic processes (60-XX) 20 Potential theory (31-XX) 20 Systems theory; control (93-XX) 18 Integral transforms, operational calculus (44-XX) 17 Harmonic analysis on Euclidean spaces (42-XX) 15 Functions of a complex variable (30-XX) 14 Approximations and expansions (41-XX) 14 Functional analysis (46-XX) 13 Biology and other natural sciences (92-XX) 11 Statistical mechanics, structure of matter (82-XX) 9 Information and communication theory, circuits (94-XX) 8 Abstract harmonic analysis (43-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 8 Global analysis, analysis on manifolds (58-XX) 8 Classical thermodynamics, heat transfer (80-XX) 7 Special functions (33-XX) 6 History and biography (01-XX) 5 General and overarching topics; collections (00-XX) 5 Measure and integration (28-XX) 5 Statistics (62-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Difference and functional equations (39-XX) 2 Computer science (68-XX) 2 Quantum theory (81-XX) 2 Operations research, mathematical programming (90-XX) 1 Algebraic topology (55-XX) 1 Mechanics of particles and systems (70-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX)

### Citations contained in zbMATH Open

606 Publications have been cited 4,226 times in 3,364 Documents Cited by Year
On integral equations of the first kind with logarithmic kernels. Zbl 0682.45001
Yan, Y.; Sloan, I. H.
1988
A survey of numerical methods for solving nonlinear integral equations. Zbl 0760.65118
Atkinson, Kendall E.
1992
Existence of mild solutions for fractional evolution equations. Zbl 1304.34013
Zhou, Yong; Zhang, Lu; Shen, Xiao Hui
2013
Numerical solution via Laplace transforms of a fractional order evolution equation. Zbl 1195.65122
McLean, William; Thomée, Vidar
2010
Characterization of boundary values of functions in Hardy spaces with applications in signal analysis. Zbl 1086.30035
Qian, Tao
2005
Numerical methods for hyperbolic and parabolic integro-differential equations. Zbl 0764.65086
Pani, A. K.; Thomée, V.; Wahlbin, L. B.
1992
Rate of approximation for multivariate sampling Kantorovich operators on some functions spaces. Zbl 1308.41017
Costarelli, Danilo; Vinti, Gianluca
2014
Analysis of direct boundary-domain integral equations for a mixed BVP with variable coefficient. I: Equivalence and invertibility. Zbl 1204.65139
Chkadua, O.; Mikhailov, S. E.; Natroshvili, D.
2009
The discrete multi-projection method for Fredholm integral equations of the second kind. Zbl 1138.65109
Chen, Zhongying; Long, Guangqing; Nelakanti, Gnaneshwar
2007
Traveling waves for a nonlocal dispersal SIR model with standard incidence. Zbl 1295.35170
Li, Wan-Tong; Yang, Fei-Ying
2014
Pseudospectra and singular values of large convolution operators. Zbl 0819.45002
Böttcher, Albrecht
1994
Order of approximation for sampling Kantorovich operators. Zbl 1308.41016
Costarelli, Danilo; Vinti, Gianluca
2014
Numerical solutions for weakly singular Hammerstein equations and their superconvergence. Zbl 0764.65085
Kaneko, Hideaki; Noren, Richard D.; Xu, Yuesheng
1992
Averaging in infinite dimensions. Zbl 0755.45012
Hale, Jack K.; Verduyn Lunel, Sjoerd M.
1990
Perturbation of linear abstract Volterra equations. Zbl 0824.45013
Corduneanu, C.
1990
Condition number estimates for combined potential boundary integral operators in acoustic scattering. Zbl 1167.35030
Chandler-Wilde, Simon N.; Graham, Ivan G.; Langdon, Stephen; Lindner, Marko
2009
Nonlinear integral equations for solving inverse boundary value problems for inclusions and cracks. Zbl 1139.45003
Ivanyshyn, Olha; Kress, Rainer
2006
Volterra equations which model explosion in a diffusive medium. Zbl 0804.45002
Roberts, Catherine A.; Lasseigne, D. Glenn; Olmstead, W. E.
1993
Real analytic dependence of simple and double layer potentials upon perturbation of the support and of the density. Zbl 1094.31001
Lanza de Cristoforis, Massimo; Rossi, Lucia
2004
Solution of Volterra integrodifferential equations with generalized Mittag-Leffler function in the Kernels. Zbl 1041.45011
Kilbas, Anatoly A.; Saigo, Megumi; Saxena, R. K.
2002
On integral equations arising in the first-passage problem for Brownian motion. Zbl 1044.60076
Peskir, Goran
2002
Rothe’s method for the heat equation and boundary integral equations. Zbl 0885.65101
Chapko, Roman; Kress, Rainer
1997
Three-point boundary value problems with solutions that change sign. Zbl 1055.34023
Infante, G.; Webb, J. R. L.
2003
Exact solution of a simple hypersingular integral equation. Zbl 0756.45003
Martin, P. A.
1992
Stability of continuous and discrete Volterra integro-differential equations by Liapunov approach. Zbl 0858.45008
Crisci, M. R.; Kolmanovskij, V. B.; Russo, E.; Vecchio, A.
1995
The Bedrosian identity and homogeneous semi-convolution equations. Zbl 1160.44004
Yu, Bo; Zhang, Haizhang
2008
A collocation method for solving nonlinear Volterra integro-differential equations of neutral type by sigmoidal functions. Zbl 1288.65185
Costarelli, Danilo; Spigler, Renato
2014
A Kac-Feynman integral equation for conditional Wiener integrals. Zbl 0751.45003
Park, Chull; Skoug, David
1991
An extension of the variational inequality approach for obtaining convergence rates in regularization of nonlinear ill-posed problems. Zbl 1206.47060
2010
$$L^p$$-approximation by truncated max-product sampling operators of Kantorovich-type based on Fejér kernel. Zbl 1371.41016
Coroianu, Lucian; Gal, Sorin G.
2017
Exponential stabilization of Volterra integral equations with singular kernels. Zbl 0673.45008
Desch, Wolfgang; Miller, Richard K.
1988
Solving Volterra integral equations of the second kind by sigmoidal functions approximation. Zbl 1285.65086
Costarelli, Danilo; Spigler, Renato
2013
The linear sampling method revisited. Zbl 1237.65118
Arens, Tilo; Lechleiter, Armin
2009
The discrete Galerkin method for nonlinear integral equations. Zbl 0664.65056
Atkinson, Kendall; Potra, Florian
1988
The modified quadrature method for logarithmic-kernel integral equations on closed curves. Zbl 0747.65100
Saranen, Jukka
1991
A discrete Galerkin method for first kind integral equations with a logarithmic kernel. Zbl 0676.65140
Atkinson, Kendall E.
1988
Singularity preserving Galerkin methods for weakly singular Fredholm integral equations. Zbl 0819.65139
Cao, Yanzhao; Xu, Yuesheng
1994
Existence, uniqueness and smoothness results for second-kind Volterra equations with weakly singular kernels. Zbl 0820.45003
Han, Weimin
1994
Integrable solutions of a functional-integral equation. Zbl 0755.45005
Emmanuele, Giovanni
1992
An iterative method for Tikhonov regularization with a general linear regularization operator. Zbl 1210.65092
Hochstenbach, Michiel E.; Reichel, Lothar
2010
Volterra integral equations and fractional calculus: do neighboring solutions intersect? Zbl 1238.45003
Diethelm, Kai; Ford, Neville J.
2012
On wave equations with boundary dissipation of memory type. Zbl 0858.35075
Propst, Georg; Prüss, Jan
1996
Fredholmness of singular integral operators with piecewise continuous coefficients on weighted Banach function spaces. Zbl 1044.45004
Karlovich, Alexei Yu.
2003
Fast methods for three-dimensional inverse obstacle scattering problems. Zbl 1138.65100
Harbrecht, Helmut; Hohage, Thorsten
2007
On necessary and sufficient conditions for exponential stability in linear Volterra integro-differential equations. Zbl 1088.45005
Appleby, John A. D.; Reynolds, David W.
2004
A nonlocal model for the exchange energy in ferromagnetic materials. Zbl 0762.45004
Rogers, Robert C.
1991
Integral equations for transmission problems in linear elasticity. Zbl 0694.73008
Costabel, M.; Stephan, E. P.
1990
A Nyström method for a class of integral equations on the real line with applications to scattering by diffraction gratings and rough surfaces. Zbl 1170.78365
Meier, A.; Arens, T.; Chandler-Wilde, S. N.; Kirsch, A.
2000
Nonlinear integral equation methods for the reconstruction of an acoustically sound-soft obstacle. Zbl 1135.65392
Ivanyshyn, Olha; Johansson, Tomas
2007
On pantograph integro-differential equations. Zbl 0816.45005
Iserles, Arieh; Liu, Yunkang
1994
General decay for a laminated beam with structural damping and memory: the case of non-equal wave speeds. Zbl 1407.35132
Li, Gang; Kong, Xiangyu; Liu, Wenjun
2018
Convergence estimates for solution of integral equations with GMRES. Zbl 0859.65137
Campbell, S. L.; Ipsen, I. C. F.; Kelley, C. T.; Meyer, C. D.; Xue, Z. Q.
1996
Wiener-Hopf-Hankel operators for some wedge diffraction problems with mixed boundary conditions. Zbl 0756.45005
Meister, E.; Speck, F.-O.; Teixeira, F. S.
1992
The regularizing Levenberg-Marquardt scheme is of optimal order. Zbl 1204.65059
Hanke, Martin
2010
Superconvergence of piecewise polynomial collocations for nonlinear weakly singular integral equations. Zbl 0910.65115
1997
Analysis of direct boundary-domain integral equations for a mixed BVP with variable coefficient. II: Solution regularity and asymptotics. Zbl 1194.65142
Chkadua, O.; Mikhailov, S. E.; Natroshvili, D.
2010
Existence, uniqueness and regularity of solutions to a class of third-kind Volterra integral equations. Zbl 1329.45001
Allaei, Sonia Seyed; Yang, Zhan-Wen; Brunner, Hermann
2015
Electromagnetic scattering from an orthotropic medium. Zbl 0980.78004
Potthast, Roland
1999
Deconvolution using Meyer wavelets. Zbl 0978.65122
Walter, Gilbert G.; Shen, Xiaoping
1999
A general method for solving plane crack problems. Zbl 0780.73012
Lu, Jianke
1993
On the theory of partial integral operators. Zbl 0747.45005
Kalitvin, A. S.; Zabrejko, P. P.
1991
Nonlinear integral equations on the half line. Zbl 0766.45001
Anselone, P. M.; Lee, J. W.
1992
On the use of Green’s function in sampling theory. Zbl 0917.41002
Annaby, M. H.; Zayed, A. I.
1998
Generation of nonlocal fractional dynamical systems by fractional differential equations. Zbl 1385.34009
Cong, N. D.; Tuan, H. T.
2017
Modified projection and the iterated modified projection methods for nonlinear integral equations. Zbl 1282.65170
Grammont, Laurence; Kulkarni, Rekha P.; Vasconcelos, Paulo B.
2013
Parabolic Volterra integrodifferential equations of convolution type. Zbl 0834.45012
Di Blasio, Gabriella
1994
Existence results for neutral integro-differential equations with unbounded delay. Zbl 1228.45019
Dos Santos, José Paulo C.; Henríquez, Hernán; Hernández, Eduardo
2011
Regularization of ill-posed linear equations by the non-stationary augmented Lagrangian method. Zbl 1203.90156
Frick, Klaus; Scherzer, Otmar
2010
On the generalized discrepancy principle for Tikhonov regularization in Hilbert scales. Zbl 1206.47015
Lu, S.; Pereverzev, S. V.; Shao, Y.; Tautenhahn, U.
2010
A real analyticity result for a nonlinear integral operator. Zbl 1278.47057
Lanza de Cristoforis, Massimo; Musolino, Paolo
2013
On the application of sequential and fixed-point methods to fractional differential equations of arbitrary order. Zbl 1335.34023
Tisdell, Christopher C.
2012
Surface integral formulation of the interior transmission problem. Zbl 1366.78019
2013
The discrete Petrov-Galerkin method for weakly singular integral equations. Zbl 0974.65122
Chen, Zhongying; Xu, Yuesheng; Zhao, Jiansheng
1999
A fully-discrete trigonometric collocation method. Zbl 0781.65094
McLean, W.; Prössdorf, Siegfried; Wendland, W. L.
1993
The direct method of fundamental solutions and the inverse Kirsch-Kress method for the reconstruction of elastic inclusions or cavities. Zbl 1166.74008
Alves, Carlos J. S.; Martins, Nuno F. M.
2009
The method of fundamental solutions for detection of cavities in EIT. Zbl 1189.78059
Borman, D.; Ingham, D. B.; Johansson, B. T.; Lesnic, D.
2009
A Nyström method for boundary integral equations on domains with a piecewise smooth boundary. Zbl 0780.65071
Jeon, Youngmok
1993
Discontinuous boundary-value problems: expansion and sampling theorems. Zbl 1089.34014
Annaby, M. H.; Freiling, G.; Zayed, A. I.
2004
Existence and approximations of solutions to some fractional order functional integral equations. Zbl 1189.26008
Muslim, M.; Nandakumaran, A. K.
2010
Superconvergence of the iterated hybrid collocation method for weakly singular Volterra integral equations. Zbl 1141.65091
Huang, Min; Xu, Yuesheng
2006
A numerical method for a nonlocal elliptic boundary value problem. Zbl 1149.65099
Cannon, J. R.; Galiffa, D. J.
2008
Approximate controllability of impulsive Riemann-Liouville fractional equations in Banach spaces. Zbl 1303.93041
Liu, Zhenhai; Bin, Maojun
2014
A fast wavelet collocation method for integral equations on polygons. Zbl 1104.65132
Wang, Yi; Xu, Yuesheng
2005
Upper and lower bounds for solutions of nonlinear Volterra convolution integral equations with power nonlinearity. Zbl 0982.45003
Karapetyants, Nikolai K.; Kilbas, Anatoly A.; Saigo, Megumi; Samko, Stefan G.
2000
Approximation methods and stability of singular integral equations for Freud exponential weights on the line. Zbl 1085.41020
Damelin, S. B.; Diethelm, K.
2004
Non-autonomous integrodifferential equations with non-local conditions. Zbl 1044.45002
Liu, James H.; Ezzinbi, Khalil
2003
On implicitly linear and iterated collocation methods for Hammerstein integral equations. Zbl 0749.65090
Brunner, Hermann
1991
An unconventional quadrature method for logarithmic-kernel integral equations on closed curves. Zbl 0760.65131
Sloan, Ian H.; Burn, B. J.
1992
Blow-up behavior of Hammerstein-type Volterra integral equations. Zbl 1261.45003
Brunner, H.; Yang, Z. W.
2012
The collocation method for solving the radiosity equation for unoccluded surfaces. Zbl 0914.65137
Atkinson, Kendall; Chandler, Graeme
1998
Higher accuracy methods for second-kind Volterra integral equations based on asymptotic expansions of iterated Galerkin methods. Zbl 0944.65140
Brunner, Hermann; Lin, Yanping; Zhang, Shuhua
1998
Variable coefficient transmission problems and singular integral operators on non-smooth manifolds. Zbl 1149.35027
Mitrea, Dorina; Mitrea, Marius; Shi, Qiang
2006
An integral equation for Maxwell’s equations in a layered medium with an application to the factorization method. Zbl 1136.78310
Kirsch, Andreas
2007
Recompression techniques for adaptive cross approximation. Zbl 1180.65162
Bebendorf, M.; Kunis, S.
2009
Collocation methods for second kind integral equations with non-compact operators. Zbl 0703.65090
Amini, S.; Sloan, I. H.
1990
Some properties of layer potentials and boundary integral operators for the wave equation. Zbl 1277.35082
Domínguez, Víctor; Sayas, Francisco-Javier
2013
Operator norms of powers of the Volterra operator. Zbl 0990.47041
Kershaw, D.
1999
On the characterization of self-regularization properties of a fully discrete projection method for Symm’s integral equation. Zbl 0982.65141
Pereverzev, Sergei V.; Prössdorf, Siegfried
2000
Phase transition problems in materials with memory. Zbl 0781.45009
Colli, Pierluigi; Grasselli, Maurizio
1993
Counterexamples for abstract linear Volterra equations. Zbl 0778.45013
Desch, Wolfgang; Prüss, Jan
1993
Multiple solutions for a binonlocal fractional $$p(x,\cdot)$$-Kirchhoff type problem. Zbl 1491.35428
Azroul, Elhoussine; Benkirane, Abdelmoujib; Shimi, Mohammed; Srati, Mohammed
2022
Integrodifferential equations of Volterra type with nonlocal and impulsive conditions. Zbl 07543124
2022
Solvability for generalized nonlinear functional integral equations in Banach spaces with applications. Zbl 1476.45011
Deep, Amar; Deepmala; Roshan, Jamal Rezaei
2021
Existence and continuity results for a nonlinear fractional Langevin equation with a weakly singular source. Zbl 07543109
Nguyen Minh Dien
2021
Simulation of an integro-differential equation and application in estimation of ruin probability with mixed fractional Brownian motion. Zbl 07367836
Cai, Chunhao; Xiao, Weilin
2021
A method of solving a nonlinear boundary value problem for the Fredholm integro-differential equation. Zbl 1475.65220
Dzhumabaev, Dulat S.; Mynbayeva, Sandugash
2021
Two-point fractional boundary value problems. Zbl 1486.34063
Ferreira, Rui A. C.
2021
Solutions of Fredholm type integral equations via the classical Schauder fixed point theorem. Zbl 1480.45003
Ersoy, Merve Temizer
2021
A general and optimal stability result for a laminated beam. Zbl 1455.35144
Mukiawa, Soh Edwin; Apalara, Tijani A.; Messaoudi, Salim
2020
Regularization of a terminal value nonlinear diffusion equation with conformable time derivative. Zbl 1460.35385
van Au, Vo; Zhou, Yong; Can, Nguyen Huu; Tuan, Nguyen Tuy
2020
An optimized FD extrapolated scheme based on POD for the 2D integro-differential equation of parabolic type. Zbl 1454.65132
Luo, Zhendong
2020
Nonlocal elliptic variational-hemivariational inequalities. Zbl 1445.35310
Migórski, Stanisław; Nguyen, van Thien; Zeng, Shengda
2020
Analysis of boundary-domain integral equations based on a new parametrix for the mixed diffusion BVP with variable coefficient in an interior Lipschitz domain. Zbl 1447.35141
Mikhailov, S. E.; Portillo, C. F.
2020
Integral equations of the third kind in $$L^p$$ spaces. Zbl 1465.45001
Diogo, Teresa; Pedas, Arvet; Vainikko, Gennadi
2020
A subordination principle for subdiffusion equations with memory. Zbl 1460.35215
Ponce, Rodrigo
2020
Square-mean almost automorphic solution of a stochastic cellular neural network on time scales. Zbl 1460.34113
Dhama, Soniya; Abbas, Syed
2020
A fractional multiterm Gronwall lemma and its application to the stability of fractional integrodifferential systems. Zbl 1464.45022
Idczak, Dariusz
2020
On the existence, uniqueness and stability results for time-fractional parabolic integrodifferential equations. Zbl 1459.35367
Mahata, Shantiram; Sinha, Rajen Kumar
2020
Asymptotic expansion of iterated Galerkin solution of Fredholm integral equations of the second kind with Green’s kernel. Zbl 1465.45003
Rakshit, Gobinda; Rane, Akshay S.
2020
A well-posed surface currents and charges system for electromagnetism in dielectric media. Zbl 1469.78054
Ganesh, Mahadevan; Hawkins, Stuart; Jeznach, Cole; Volkov, Darko
2020
Nonlinear continuous Fornasini-Marchesini model of fractional order with nonzero initial conditions. Zbl 1448.35547
Idczak, Dariusz; Kamocki, Rafał; Majewski, Marek
2020
A stability result for an inverse problem with integrodifferential operator on a finite interval. Zbl 1464.45027
2020
An $$h$$-$$p$$ version of the Chebyshev spectral collocation method for Volterra integro-differential equations with vanishing delays. Zbl 1462.65097
Wang, Lina; Yi, Lijun; Jia, Hongli
2020
Mapping properties of weakly singular periodic volume potentials in Roumieu classes. Zbl 07282580
Dalla Riva, M.; Lanza De Cristoforis, M.; Musolino, P.
2020
On a class of noncompact weakly singular Volterra integral equations: theory and application to fractional differential equations with variable coefficient. Zbl 1464.45004
2020
Mixed impedance boundary value problems for the Laplace-Beltrami equation. Zbl 1454.35128
Castro, Luis; Duduchava, Roland; Speck, Frank-Olme
2020
Smooth solutions to mixed-order fractional differential systems with applications to stability analysis. Zbl 1420.34012
Gallegos, Javier A.; Aguila-Camacho, Norelys; Duarte-Mermoud, Manuel A.
2019
Fractional diffusion equation with distributed-order Caputo derivative. Zbl 1423.35427
2019
Embedded eigenvalues for the Neumann-Poincaré operator. Zbl 1436.31005
Li, Wei; Shipman, Stephen P.
2019
A doubly nonlocal Laplace operator and its connection to the classical Laplacian. Zbl 1429.35189
2019
Global attractivity for some classes of Riemann-Liouville fractional differential systems. Zbl 1431.34013
Tuan, H. T.; Czornik, Adam; Nieto, Juan J.; Niezabitowski, Michał
2019
Controllability of nonlinear impulsive integro-differential fractional time-invariant systems. Zbl 1440.45007
Huang, Yong; Liu, Zhenhai
2019
Fredholm-Choquet integral equations. Zbl 1444.45002
Gal, Sorin G.
2019
Volterra-Choquet integral equations. Zbl 1443.45002
Gal, Sorin G.
2019
A new class of Volterra-type integral equations from relativistic quantum physics. Zbl 1445.45005
Lienert, Matthias; Tumulka, Roderich
2019
Extrapolation methods for the numerical solution of nonlinear Fredholm integral equations. Zbl 1416.65013
Brezinski, Claude; Redivo-Zaglia, Michela
2019
Cordial Volterra integral operators in spaces $$L^p(0,T)$$. Zbl 1436.47015
2019
Uniqueness of solutions for weakly degenerate cordial Volterra integral equations. Zbl 1440.45002
Darbenas, Zymantas; Oliver, Marcel
2019
Well-posedness and stability for a viscoelastic wave equation with density and time-varying delay in $$\mathbb{R}^n$$. Zbl 1439.35058
Feng, Baowei; Yang, Xinguang; Su, Keqin
2019
Superconvergent product integration method for Hammerstein integral equations. Zbl 1416.65525
Allouch, C.; Sbibih, D.; Tahrichi, M.
2019
On some classes of elliptic systems with fractional boundary relaxation. Zbl 1421.35138
Prüss, Jan
2019
A hybrid collocation method for fractional initial value problems. Zbl 1416.65556
Wang, Linjun; Wang, Fang; Cao, Yanzhao
2019
$$L^p$$ bounds for a class of Marcinkiewicz integral operators. Zbl 1440.42047
2019
General decay for a laminated beam with structural damping and memory: the case of non-equal wave speeds. Zbl 1407.35132
Li, Gang; Kong, Xiangyu; Liu, Wenjun
2018
General and optimal decay in a memory-type Timoshenko system. Zbl 1394.35270
Messaoudi, Salim A.; Hassan, Jamilu Hashim
2018
Uniform exponential stability and applications to bounded solutions of integro-differential equations in Banach spaces. Zbl 06979944
Chang, Yong-Kui; Ponce, Rodrigo
2018
Exponential decay estimates of the eigenvalues for the Neumann-Poincaré operator on analytic boundaries in two dimensions. Zbl 1407.35147
Ando, Kazunori; Kang, Hyeonbae; Miyanishi, Yoshihisa
2018
A note on the well-posedness of terminal value problems for fractional differential equations. Zbl 1406.34009
Diethelm, Kai; Ford, Neville J.
2018
Solvability of linear boundary value problems for subdiffusion equations with memory. Zbl 1402.35304
Krasnoschok, Mykola; Pata, Vittorino; Vasylyeva, Nataliya
2018
Blow-up of solutions for semilinear fractional Schrödinger equations. Zbl 1393.35220
Fino, A. Z.; Dannawi, I.; Kirane, M.
2018
Split-step collocation methods for stochastic Volterra integral equations. Zbl 06873405
Xiao, Y.; Shi, J. N.; Yang, Z. W.
2018
Coupled Volterra integral equations with blowing up solutions. Zbl 1404.45010
Mydlarczyk, Wojciech
2018
Solution estimates for a system of nonlinear integral equations arising in optometry. Zbl 1395.45011
Okrasiński, Wojciech; Płociniczak, Łukasz
2018
Inverse scattering for shape and impedance revisited. Zbl 1402.35091
Kress, Rainer; Rundell, William
2018
Blow up of fractional reaction-diffusion systems with and without convection terms. Zbl 1390.35159
Pérez, Aroldo
2018
Existence of a mild solution for a neutral stochastic fractional integro-differential inclusion with a nonlocal condition. Zbl 1403.34055
Chadha, Alka; Bahuguna, D.; Pandey, Dwijendra N.
2018
On the numerical solution of the exterior elastodynamic problem by a boundary integral equation method. Zbl 1408.65093
Chapko, Roman; Mindrinos, Leonidas
2018
On a semi-linear system of nonlocal time and space reaction diffusion equations with exponential nonlinearities. Zbl 1393.35093
Ahmad, B.; Alsaedi, A.; Hnaien, D.; Kirane, M.
2018
Regularity properties of mild solutions for a class of Volterra equations with critical nonlinearities. Zbl 1404.45001
Abadias, Luciano; Alvarez, Edgardo; Lizama, Carlos
2018
On a Bohr-Neugebauer property for some almost automorphic abstract delay equations. Zbl 1406.34087
Benkhalti, Rachid; Es-Sebbar, Brahim; Ezzinbi, Khalil
2018
Energy decay rates for solutions of the Kirchhoff type wave equation with boundary damping and source terms. Zbl 1415.35177
Ha, Tae Gab
2018
$$L^p$$-approximation by truncated max-product sampling operators of Kantorovich-type based on Fejér kernel. Zbl 1371.41016
Coroianu, Lucian; Gal, Sorin G.
2017
Generation of nonlocal fractional dynamical systems by fractional differential equations. Zbl 1385.34009
Cong, N. D.; Tuan, H. T.
2017
Mathematical aspects of variational boundary integral equations for time dependent wave propagation. Zbl 1364.35187
Joly, Patrick; Rodríguez, Jerónimo
2017
A new and improved analysis of the time domain boundary integral operators for the acoustic wave equation. Zbl 1361.65075
Hassell, Matthew E.; Qiu, Tianyu; Sánchez-Vizuet, Tonatiuh; Sayas, Francisco-Javier
2017
Adaptive time domain boundary element methods with engineering applications. Zbl 1361.65073
Gimperlein, Heiko; Maischak, Matthias; Stephan, Ernst P.
2017
Runge-Kutta convolution quadrature and FEM-BEM coupling for the time-dependent linear Schrödinger equation. Zbl 1361.65076
Melenk, Jens Markus; Rieder, Alexander
2017
Global existence and asymptotic stability of mild solutions for stochastic evolution equations with nonlocal initial conditions. Zbl 1371.34086
Chen, Pengyu; Abdelmonem, Ahmed; Li, Yongxiang
2017
A modified volume integral equation for anisotropic elastic or conducting inhomogeneities: unconditional solvability by Neumann series. Zbl 1371.35054
Bonnet, Marc
2017
Central part interpolation schemes for integral equations with singularities. Zbl 1376.65158
Orav-Puurand, Kerli; Pedas, Arvet; Vainikko, Gennadi
2017
Regularized integral formulation of mixed Dirichlet-Neumann problems. Zbl 1387.35116
Akhmetgaliyev, Eldar; Bruno, Oscar P.
2017
Necessary Fredholm conditions for weighted singular integral operators with shifts and slowly oscillating data. Zbl 1376.45016
Karlovich, Alexei Yu.; Karlovich, Yuri I.; Lebre, Amarino B.
2017
Well-conditioned boundary integral equation formulations and Nyström discretizations for the solution of Helmholtz problems with impedance boundary conditions in two-dimensional Lipschitz domains. Zbl 1376.65146
Turc, Catalin; Boubendir, Yassine; Riahi, Mohamed Kamel
2017
Numerical approximation of first kind Volterra convolution integral equations with discontinuous kernels. Zbl 1361.65101
Davies, Penny J.; Duncan, Dugald B.
2017
Memory dependent growth in sublinear Volterra differential equations. Zbl 1384.45002
Appleby, John A. D.; Patterson, Denis D.
2017
$$L^p$$-solutions for a class of fractional integral equations. Zbl 1370.45007
Agarwal, Ravi P.; Asma; Lupulescu, Vasile; O’Regan, Donal
2017
Comparison between numerical methods applied to the damped wave equation. Zbl 1361.65077
Aimi, A.; Diligenti, M.; Guardasoni, C.
2017
Weak solutions for partial Pettis Hadamard fractional integral equations with random effects. Zbl 1384.45004
Abbas, Saïd; Albarakati, Wafaa; Benchohra, Mouffak; Zhou, Yong
2017
Well-posedness of fractional degenerate differential equations with infinite delay in vector-valued functional spaces. Zbl 1373.34115
Bu, Shangquan; Cai, Gang
2017
Recent progress in time domain boundary integral equations. Zbl 1359.00020
2017
Perturbed Hammerstein integral equations with sign-changing kernels and applications to nonlocal boundary value problems and elliptic PDEs. Zbl 1352.45006
Goodrich, Christopher S.
2016
Well-posed boundary integral equation formulations and Nyström discretizations for the solution of Helmholtz transmission problems in two-dimensional Lipschitz domains. Zbl 1416.65488
Domínguez, Víctor; Lyon, Mark; Turc, Catalin
2016
On some regular fractional Sturm-Liouville problems with generalized Dirichlet conditions. Zbl 1358.34035
Bensidhoum, Fatima-Zahra; Dib, Hacen
2016
Controllability of fractional integrodifferential equations with state-dependent delay. Zbl 1348.34131
Aissani, Khalida; Benchohra, Mouffak
2016
$$C^{\sigma,\alpha}$$ estimates for concave, non-local parabolic equations with critical drift. Zbl 1353.35083
Lara, Héctor Chang; Dávila, Gonzalo
2016
A collocation method solving integral equation models for image restoration. Zbl 1347.65197
Liu, Yuzhen; Shen, Lixin; Xu, Yuesheng; Yang, Hongqi
2016
The direct scattering problem of obliquely incident electromagnetic waves by a penetrable homogeneous cylinder. Zbl 1358.35182
Gintides, Drossos; Mindrinos, Leonidas
2016
Approximation of solutions to a delay equation with a random forcing term and non local conditions. Zbl 1355.34100
Chaudhary, Renu; Pandey, Dwijendra N.
2016
Existence of solutions and controllability for impulsive fractional order damped systems. Zbl 1356.34016
Liu, Zhenhai; Li, Xuemei
2016
Volterra integral equations on variable exponent Lebesgue spaces. Zbl 1334.45003
Castillo, R. E.; Ramos-Fernández, J. C.; Rojas, E. M.
2016
A mode III interface crack with surface strain gradient elasticity. Zbl 1381.74022
Wang, Xu; Schiavone, Peter
2016
Application of measure of noncompactness to Volterra equations of convolution type. Zbl 1355.45005
Alvarez, Edgardo; Lizama, Carlos
2016
Compositions of pseudo almost automorphic functions via measure theory and applications. Zbl 1361.43004
Fan, Zhenbin; Dong, Qixiang; Li, Gang
2016
Numerical methods for systems of nonlinear integro-parabolic equations of Volterra type. Zbl 1349.65269
Boglaev, Igor
2016
Boundary integral operator for the fractional Laplacian on the boundary of a bounded smooth domain. Zbl 1361.30063
Chang, Tongkeun
2016
Essential norm of a Volterra-type integral operator from Hardy spaces to some analytic function spaces. Zbl 1354.30048
Zhou, Jizhen; Zhu, Xiangling
2016
Approximate solution of Urysohn integral equations with non-smooth kernels. Zbl 1347.45004
Kulkarni, Rekha P.; Nidhin, T. J.
2016
Existence, uniqueness and regularity of solutions to a class of third-kind Volterra integral equations. Zbl 1329.45001
Allaei, Sonia Seyed; Yang, Zhan-Wen; Brunner, Hermann
2015
The oscillation of solutions of Volterra integral and integro-differential equations with highly oscillatory kernels. Zbl 1381.45009
Brunner, Hermann; Ma, Yunyun; Xu, Yuesheng
2015
Sharp control time for viscoelastic bodies. Zbl 1328.45013
Pandolfi, L.
2015
...and 506 more Documents
all top 5

### Cited by 3,597 Authors

 46 Costarelli, Danilo 41 O’Regan, Donal 37 Nelakanti, Gnaneshwar 36 Vinti, Gianluca 27 Qian, Tao 25 Chandler-Wilde, Simon N. 25 Xu, Yuesheng 23 Agarwal, Ravi P. 23 Kress, Rainer 22 Mikhailov, Sergey E. 22 Musolino, Paolo 22 Wendland, Wolfgang L. 21 Lanza de Cristoforis, Massimo 21 Sayas, Francisco-Javier 19 Vainikko, Gennadi 18 Böttcher, Albrecht 18 Brunner, Hermann 18 Pinheiro de Castro, Luís Filipe 18 Chapko, Roman 18 Huang, Jin 17 Kohr, Mirela 17 Natroshvili, David 17 Pedas, Arvet 17 Vecchio, Antonia 16 Appleby, John A. D. 16 Choi, Jae Gil 16 Dalla Riva, Matteo 16 Gil’, Michael Iosif 16 Pani, Amiya Kumar 15 Laurita, Concetta 15 Long, Guangqing 14 Chang, Seung Jun 14 Constanda, Christian 14 Pandey, Dwijendra Narain 14 Sbibih, Driss 14 Stephan, Ernst Peter 13 Sloan, Ian Hugh 13 Wang, Jinrong 12 Allouch, Chafik 12 Chen, Zhongying 12 Chudinovich, Igor Yuryevich 12 Diogo, Teresa 12 Hofmann, Bernd 12 Infante, Gennaro 12 Kulkarni, Rekha P. 12 Lesnic, Daniel 12 Reichel, Lothar 12 Silbermann, Bernd 12 Vlasov, Viktor Valentinovich 11 Al-saedi, Ahmed Eid Salem 11 Annaby, Mahmoud H. 11 Cai, Haotao 11 Cakoni, Fioralba 11 Chang, Yong-Kui 11 Dehghan Takht Fooladi, Mehdi 11 Ford, Neville J. 11 Goodrich, Christopher S. 11 Lee, Kuo-Ming 11 Li, Wan-Tong 11 Maleknejad, Khosrow 11 Nieto Roig, Juan Jose 11 Tan, Lihui 11 Xu, Da 11 Zhang, Bo 10 Ahmad, Bashir 10 Angeloni, Laura 10 Assari, Pouria 10 Chen, Qiuhui 10 Chepyzhov, Vladimir V. 10 Darwish, Mohamed Abdalla 10 De Bonis, Maria Carmela 10 Deng, Guantie 10 Jin, Qinian 10 Mastroianni, Giuseppe 10 Pandolfi, Luciano 10 Spence, Euan A. 10 Tahrichi, Mohamed 10 Tatar, Nasser-eddine 10 Yakubovich, Semyon B. 10 Yang, Feiying 10 Zhou, Yong 9 Al-Salman, Ahmad 9 Baker, Christopher Thomas Hale 9 Benchohra, Mouffak 9 Das, Payel 9 Gimperlein, Heiko 9 Haddar, Houssem 9 Johansson, B. Tomas 9 Kaltenbacher, Barbara 9 Kelley, Carl T. 9 Li, Hu 9 Lizama, Carlos 9 Mandal, Moumita 9 McLean, William 9 Prössdorf, Siegfried 9 Rautian, Nadegda Aleksandrovna 9 Salem, Hussein A. H. 9 Saranen, Jukka 9 Väth, Martin 9 Zweifel, Paul F. ...and 3,497 more Authors
all top 5

### Cited in 440 Journals

 243 Journal of Integral Equations and Applications 163 Journal of Computational and Applied Mathematics 128 Applied Mathematics and Computation 124 Journal of Mathematical Analysis and Applications 84 Applied Numerical Mathematics 67 Computers & Mathematics with Applications 59 Journal of Computational Physics 58 Applicable Analysis 57 Mathematical Methods in the Applied Sciences 47 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 45 Engineering Analysis with Boundary Elements 44 Advances in Difference Equations 43 Numerical Functional Analysis and Optimization 42 Inverse Problems 39 Advances in Computational Mathematics 38 Integral Equations and Operator Theory 38 Numerische Mathematik 37 Journal of Scientific Computing 32 Journal of Differential Equations 31 International Journal of Computer Mathematics 30 Mathematics of Computation 30 Computational and Applied Mathematics 29 Zeitschrift für Analysis und ihre Anwendungen 29 Numerical Algorithms 26 Fractional Calculus & Applied Analysis 25 Applied Mathematics Letters 24 BIT 23 ZAMP. Zeitschrift für angewandte Mathematik und Physik 22 Abstract and Applied Analysis 22 Inverse Problems in Science and Engineering 21 Journal of Inverse and Ill-Posed Problems 21 Mediterranean Journal of Mathematics 20 Numerical Methods for Partial Differential Equations 20 Complex Variables and Elliptic Equations 19 Computer Methods in Applied Mechanics and Engineering 18 Inverse Problems and Imaging 17 Proceedings of the American Mathematical Society 17 SIAM Journal on Scientific Computing 16 SIAM Journal on Mathematical Analysis 16 Integral Transforms and Special Functions 16 Nonlinear Analysis. Real World Applications 16 Journal of Applied Mathematics and Computing 15 Discrete and Continuous Dynamical Systems. Series B 15 Journal of Function Spaces 15 Nonlinear Analysis. Theory, Methods & Applications 14 Mathematics and Computers in Simulation 14 Results in Mathematics 14 Linear Algebra and its Applications 14 Journal of Mathematical Sciences (New York) 14 Journal of Inequalities and Applications 14 Journal of Fixed Point Theory and Applications 13 Journal of Mathematical Physics 13 Chaos, Solitons and Fractals 13 Journal of Approximation Theory 13 Mathematical and Computer Modelling 13 Communications in Nonlinear Science and Numerical Simulation 13 The ANZIAM Journal 13 Communications on Pure and Applied Analysis 12 Journal of Functional Analysis 12 SIAM Journal on Numerical Analysis 12 Journal of Complexity 12 Boundary Value Problems 12 Science China. Mathematics 11 Rocky Mountain Journal of Mathematics 11 Transactions of the American Mathematical Society 11 Journal de Mathématiques Pures et Appliquées. Neuvième Série 11 SIAM Journal on Applied Mathematics 11 Turkish Journal of Mathematics 11 Differential Equations 11 International Journal of Wavelets, Multiresolution and Information Processing 11 AIMS Mathematics 10 Wave Motion 10 Journal of Optimization Theory and Applications 10 Applications of Mathematics 10 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 10 Mathematical Problems in Engineering 10 Complex Analysis and Operator Theory 10 Evolution Equations and Control Theory 9 Mathematische Nachrichten 9 Applied Mathematical Modelling 9 Journal of Elasticity 9 Filomat 9 Discrete and Continuous Dynamical Systems 9 Positivity 9 Wuhan University Journal of Natural Sciences (WUJNS) 9 Journal of Evolution Equations 9 Fractional Differential Calculus 8 Ukrainian Mathematical Journal 8 Rendiconti del Circolo Matemàtico di Palermo. Serie II 8 Statistics & Probability Letters 8 Acta Applicandae Mathematicae 8 NoDEA. Nonlinear Differential Equations and Applications 8 Journal of Difference Equations and Applications 8 Doklady Mathematics 8 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 7 Archive for Rational Mechanics and Analysis 7 Journal of the Franklin Institute 7 Computing 7 Quarterly of Applied Mathematics 7 SIAM Journal on Control and Optimization ...and 340 more Journals
all top 5

### Cited in 51 Fields

 1,371 Numerical analysis (65-XX) 1,247 Integral equations (45-XX) 1,036 Partial differential equations (35-XX) 612 Operator theory (47-XX) 433 Ordinary differential equations (34-XX) 273 Mechanics of deformable solids (74-XX) 185 Real functions (26-XX) 177 Optics, electromagnetic theory (78-XX) 161 Approximations and expansions (41-XX) 146 Fluid mechanics (76-XX) 136 Probability theory and stochastic processes (60-XX) 135 Systems theory; control (93-XX) 133 Harmonic analysis on Euclidean spaces (42-XX) 123 Functional analysis (46-XX) 91 Functions of a complex variable (30-XX) 89 Information and communication theory, circuits (94-XX) 86 Calculus of variations and optimal control; optimization (49-XX) 85 Biology and other natural sciences (92-XX) 83 Potential theory (31-XX) 69 Integral transforms, operational calculus (44-XX) 66 Special functions (33-XX) 58 Classical thermodynamics, heat transfer (80-XX) 45 Statistical mechanics, structure of matter (82-XX) 42 Dynamical systems and ergodic theory (37-XX) 41 Difference and functional equations (39-XX) 38 Linear and multilinear algebra; matrix theory (15-XX) 35 Statistics (62-XX) 33 Measure and integration (28-XX) 28 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 25 Operations research, mathematical programming (90-XX) 24 Global analysis, analysis on manifolds (58-XX) 16 Computer science (68-XX) 15 Quantum theory (81-XX) 13 Abstract harmonic analysis (43-XX) 12 Several complex variables and analytic spaces (32-XX) 11 Geophysics (86-XX) 8 History and biography (01-XX) 7 Sequences, series, summability (40-XX) 6 General topology (54-XX) 5 General and overarching topics; collections (00-XX) 4 Number theory (11-XX) 3 Mathematical logic and foundations (03-XX) 3 Combinatorics (05-XX) 3 Mathematics education (97-XX) 2 Differential geometry (53-XX) 1 $$K$$-theory (19-XX) 1 Topological groups, Lie groups (22-XX) 1 Geometry (51-XX) 1 Mechanics of particles and systems (70-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX)


text:
Lemma 94.16.1. Up to a replacement as in Stacks, Remark 8.4.9 the functor

$\mathcal{P}\! \mathit{ic}_{X/B} \longrightarrow (\mathit{Sch}/S)_{fppf}$

defines a stack in groupoids over $(\mathit{Sch}/S)_{fppf}$.

Proof. As usual, the hardest part is to show descent for objects. To see this let $\{ U_ i \to U\}$ be a covering of $(\mathit{Sch}/S)_{fppf}$. Let $\xi _ i = (U_ i, b_ i, \mathcal{L}_ i)$ be an object of $\mathcal{P}\! \mathit{ic}_{X/B}$ lying over $U_ i$, and let $\varphi _{ij} : \text{pr}_0^*\xi _ i \to \text{pr}_1^*\xi _ j$ be a descent datum. This implies in particular that the morphisms $b_ i$ are the restrictions of a morphism $b : U \to B$. Write $X_ U = U \times _{b, B} X$ and $X_ i = U_ i \times _{b_ i, B} X = U_ i \times _ U U \times _{b, B} X = U_ i \times _ U X_ U$. Observe that $\mathcal{L}_ i$ is an invertible $\mathcal{O}_{X_ i}$-module. Note that $\{ X_ i \to X_ U\}$ forms an fppf covering as well. Moreover, the descent datum $\varphi _{ij}$ translates into a descent datum on the invertible sheaves $\mathcal{L}_ i$ relative to the fppf covering $\{ X_ i \to X_ U\}$. Hence by Descent on Spaces, Proposition 73.4.1 we obtain a unique invertible sheaf $\mathcal{L}$ on $X_ U$ which recovers $\mathcal{L}_ i$ and the descent data over $X_ i$. The triple $(U, b, \mathcal{L})$ is therefore the object of $\mathcal{P}\! \mathit{ic}_{X/B}$ over $U$ we were looking for. Details omitted. $\square$

There are also:

• 1 comment(s) on Section 94.16: The Picard stack

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

format: plain


text:
# In hydrology, what's the difference between specific and total catchment area?

I am getting stuck on the concepts of Total Catchment Area (TCA) and Specific Catchment Area (SCA) as I try to learn more about TOPMODEL and hydrology modeling. What do these metrics mean in hydrology? The context I encounter these in is in calculating Topographic Wetness Index (TWI) values.

My understanding so far is that: TCA is basically equivalent to a watershed for any given pour point; SCA helps determine saturation and saturation excess flow and it is the ratio of a local catchment area for a pour point divided by the width of the contour where that pour point is. I'm especially uncertain about SCA because it's unclear to me how the width of the contour is involved in a catchment area (based on my conceptual framework of a watershed a/k/a catchment area being defined by a single pour point). So, maybe I also need "Flow Width" (a term I think I've seen used to describe that contour width used in SCA) to be explained in order to understand SCA.

To give some context to what I'm referring to, here's a passage which references both TCA and SCA:

"Upslope area is the total catchment area above a point or length of contour and the specific catchment area is the upslope area per width of contour or cell size, L (Moore et al., 1991). Specific catchment area is used to calculate saturation and saturation excess overland flow in hydrological models such as TOPMODEL (Beven and Kirkby, 1979) and, along with other topographic indices, to calculate erosion and landsliding in many other models. Upslope area is commonly used for mapping channels on the basis of threshold upslope areas for channel initiation.

J. Wainwright & M. Mulligan. Environmental Modelling: Finding Simplicity in Complexity. Oxford: Wiley. 2012. Ebook.

This was originally posted in GIS.SE where it was suggested it be moved here.

I will try to bring you some insights. In my opinion, SCA is poorly named.

Actually, the width is not involved in the catchment area which is given by TCA. SCA introduces a diffusive flow factor by considering flow width. It is a one dimensional value so it is not representative of an area and that's why it might be confusing. It gives us an idea of how concentrated are the incoming flow.

Besides this, I think you are also confused by the outlet concept which is often defined in GIS or in some conceptual definitions by a point. But actually, in order to compute a flow at an outlet you need flow velocity and a cross section. If this cross section area is assumed to be rectangular, it can be defined by the width and the height will vary according to the incoming flow. So when the outlet is considered as a point, it is more like a targeter of the outlet that has some dimensional characteristics.

So, for studies at the plot scale or the hillslope scale, the outlet is often defined by a line which is representative of the flow width at the downslope.

For grid based data, a pour point targets a representative area defined by the spatial resolution of your terrain data. If a point has no flow width, this area has one and the flow width is generally assumed to be the cell size as mentionned in your quote.

If you understand that, you may understand that the broader the width, the more diffuse will be the overland flow and therefore the less wet regarding the TWI or the less erosive. Of course, it remains resolution dependent.


text:
# Word Embeddings & Embedding Matrix

Word Embeddings are the core of applying the RNNs to Natural Language Processing Tasks. Embedding are used to convert words and sentences to ‘numbers’ which the computer can not only understand, but also use them for NLP tasks such as Man:Woman = King:? -> Queen.

### Word Representation

One Hot Representation

Vovabulary V = [a,aaron……,zulu, UNK]

The words are represented in a one hot representation based on the location they fall in the vocabulary. For example, the words with locations are (just an example, not actual): Man(5391), Woman(9853), King(4914), Queen (7157), Apple(456).

These worde are represented in One hot vectors as $O_{5391}$, $O_{9853}$, $O_{4914}$, $O_{7157}$, $O_{456}$

$O_{5391}$ = \left[ \eqalign{0\cr 0\cr 0\cr .\cr .\cr 1\cr .\cr .\cr .\cr .\cr .\cr .\cr 0\cr 0\cr .} \right] 1 is at the 5391st position.
$O_{9853}$ = \left[ \eqalign{0\cr 0\cr 0\cr .\cr .\cr .\cr .\cr .\cr .\cr 1\cr .\cr .\cr .\cr 0\cr .} \right] 1 is at the 9853rd position.

One of the shortcoming of this representation is that it considers each word equally,, and doesn’t generalize across words. For example, The sentence “I want a glass of orange juice” is learnt, but the algorithm cannot figure out a different but similar sentence “I want a glass of apple ?????”. It cannot learn on itself that apple and oranges are similar so the missing word in second sentence will also probably be “juice”. This is because the inner product between any oth the one hot vectors is zero (Eucledian Distance).

Featurized Representation: Word Embedding

For every word in a dictionary, we could learn a number accociated with each feature. For example for a feature “Gender”, the value for each word could be Man(-1), Woman(+1), King(-0.97), Queen(0.95), Apple(0.00), Orange(0.01) and so on. The same would be calculated for all the words and for all the features like Gender, Royal, Age, Food, size, cost, verb, noun, action…. etc.

If there are (say) 300 features, the first column would become a 300x1 dimension vector representing the word “Man”. This would be much different than a One hot encoded vector which was 10000x1 and all the values were 0 except one value which was the position of the word. For all the words, the embedding matrix would be a 300x10000 matrix.

The notation $e_{5391}$ for “Man” is used to represent the representation. Similarily, $e_{9853}$ is used to represent Woman.

In this representation notice that the vectors for “Orange” and “Apple” are quite similar (except, say, color feature). Most other features are same. This increases the odds of learning algorithm to learn that Apple and Oranges are similar things. This will enable the algorithm to generalize better among words.

Vizualizing word embeddings in a 2-D Space: t-SNE algorithm representation

Similar things are grouped together in the t-SNE representation

### Using Word Embeddings

Example: Named Entity Recognition

(1) Sally Johnson is an orange farmer (Training)
(2) Robert Lin is an apple farmer

In (1) the model is trained with Sally Johnson as a named entity. In (2), the algorithm sees that “apple” is similar to “orange”, thus Robert Lin must be similar to Sally Johnson and must be a named entity.

(3) Robert Lin is a durian cultivator

The model can identify from the Embedding matrix that “durian” is similar to “apple” and “cultivator” is similar to “farmer”

Typically the Embedding matrix are built from over 100Billion words and are quite large. Transfer learning is used in many named entity recognition example.

Steps

1. Learn word embeddings from large text corpus (1-100Bn words) or download pre-trained embeddings online
2. Transfer embeddings to new tasks with smaller training set (say 100k words).
3. Optional: Continue to finetune the word embeddings with new data

Relation to face recognition: Similar to facial recognition using a siamese network where encoding is learnt for a specific face and compared to the vector of a different face

For each of the 10000 word in vocabulary, a embedding vector $e_1$, $e_2$,….$e_{10,000}$ can be created.

### Properties of Word Embeddings

The word embeddings are good at detecting analogies, which are essentially how similar a vector is to another vector.

For example - How the embedding matrix learn the analogy Man:Woman $\approx$ King:Queen ?

Lets assume each of the word is represented by a 4 dimensional vector as shown in the table below

Man (say $e_{5391}$) = [ -1 0.01 0.03 0.09]

Similarily, vectors for Woman, King and Queen are also built in the same way.

Representing the vectors as $e_{Man}$,$e_{Woman}$,$e_{King}$ and $e_{Queen}$

$e_{Man}$ - $e_{Woman}$ $\approx$ \left[ \eqalign{-2\cr 0\cr 0\cr 0} \right]

$e_{King}$ - $e_{Queen}$ $\approx$ \left[ \eqalign{-2\cr 0\cr 0\cr 0} \right]

Thus, we can conclude that $e_{Man}$ - $e_{Woman}$ $\approx$ $e_{King}$ - $e_{Queen}$

We can change the above equation slightly so that if we need to find a word Man:Woman=King:??

$e_{Man}$ - $e_{Woman}$ $\approx$ $e_{King}$ - $e_{WORD}$ ,

or, $e_{WORD}$ $\approx$ $e_{King}$ - $e_{Man}$ + $e_{Woman}$

Mathematically speaking, To find word w: arg max(w) sim($e_w$, $e_{King}$ - $e_{Man}$ + $e_{Woman}$).

Sim is a similarity function - Cosine Similarity

#### Cosine Similarity

For calculation of sim($e_w$, $e_{King}$ - $e_{Man}$ + $e_{Woman}$), Cosine similarity is used which is defined as

sim(u,v) = $\frac {u^Tv}{||u||_2 ||v||_2}$

### Embedding Matrix

Assumption: Assume that the vocabulary contains 10000 words, and there are 300 features in the embedding matrix

Matrix E (Embedding Matrix): 300 x 10000

Matrix $O_j$: One hot vector representation of word j

The final vector $e_j$ = E.$O_j$ which is the embedding for word j

In practice, specialized functions are used to look for word embeddings

Source material from Andrew NG’s awesome course on Coursera. The material in the video has been written in a text form so that anyone who wishes to revise a certain topic can go through this without going through the entire video lectures.

Written on February 18, 2018
]


text:
### T-0.1, r. 2 - Regulation respecting the Québec sales tax

350.51.1R2. The prescribed information for the purposes of the first paragraph of section 350.51.1 of the Act is the following where the person referred to in that section is a registrant:
(1)  the information required under subparagraphs 1 to 3 of the first paragraph of section 350.51R7.2;
(2)  the information required under subparagraphs 2 to 4 of the first paragraph of section 350.51R5;
(3)  the registration number assigned to the person pursuant to subsection 1 or 1.5 of section 241 of the Excise Tax Act (R.S.C. 1985, c. E-15);
(4)  the registration number assigned to the person pursuant to section 415 or 415.0.6 of the Act;
(5)  a row of 42 equal signs (=) immediately preceding the information required under subparagraphs 6 to 13;
(6)  the information required under subparagraphs 8 to 10 of the first paragraph of section 350.51R5;
(7)  mention that the document is an original invoice, a reprinted invoice, a revised invoice, a credit note or that the person has received payment, as the case may be;
(8)  the information required under subparagraphs 12 to 14 of the first paragraph of section 350.51R5;
(9)  the number of the device referred to in section 350.52.1 of the Act assigned by the Minister to the person at the time the device is activated;
(10)  a sequential number, based on one or more series, identifying the invoice and linked by a dash to the information required under subparagraph 9;
(11)  the information required under paragraphs 1 and 2 of section 350.51.1R1;
(12)  a row of 4 to 42 special characters; and
(13)  a row of 42 equal signs (=) immediately following the information required under subparagraphs 5 to 12.
The information required under subparagraphs 5 to 13 of the first paragraph are generated in that order by the device referred to in section 350.52.1 of the Act.
O.C. 586-2015, s. 7; O.C. 321-2017, s. 11.
350.51.1R2. The prescribed information for the purposes of the first paragraph of section 350.51.1 of the Act is the following where the person referred to in that section is a registrant:
(1)  the information required under subparagraphs 1 to 3 of the first paragraph of section 350.51R7.2;
(2)  the information required under subparagraphs 2 to 4 of the first paragraph of section 350.51R5;
(3)  the registration number assigned to the person pursuant to subsection 241(1) of the Excise Tax Act (R.S.C. 1985, c. E-15);
(4)  the registration number assigned to the person pursuant to section 415 of the Act;
(5)  a row of 42 equal signs (=) immediately preceding the information required under subparagraphs 6 to 13;
(6)  the information required under subparagraphs 8 to 10 of the first paragraph of section 350.51R5;
(7)  mention that the document is an original invoice, a reprinted invoice, a revised invoice, a credit note or that the person has received payment, as the case may be;
(8)  the information required under subparagraphs 12 to 14 of the first paragraph of section 350.51R5;
(9)  the number of the device referred to in section 350.52.1 of the Act assigned by the Minister to the person at the time the device is activated;
(10)  a sequential number, based on one or more series, identifying the invoice and linked by a dash to the information required under subparagraph 9;
(11)  the information required under paragraphs 1 and 2 of section 350.51.1R1;
(12)  a row of 4 to 42 special characters; and
(13)  a row of 42 equal signs (=) immediately following the information required under subparagraphs 5 to 12.
The information required under subparagraphs 5 to 13 of the first paragraph are generated in that order by the device referred to in section 350.52.1 of the Act.
O.C. 586-2015, s. 7.


text:
# Do spaces in \cite make a difference?

I just found the hard way that it matters.

For example,

\cite{aref, bref}

is different from

\cite{aref,bref}

Notice the space after the comma in first one. If it does matter, this looks real silly to me.

I just need to verify if this is the case.

Just to add, I am using Miktex and Texmaker

This is how it's looking now:

\cite{jiang2006research,datta2006distributed,bandyopadhyay2006clustering}

Before it was:

\cite{jiang2006research, datta2006distributed, bandyopadhyay2006clustering}

Here is a full example of code which fails:

\documentclass[twoside,11pt]{article}

\usepackage{jair, theapa, rawfonts}

\begin{document}

\begin{abstract}
Abstracts will go here.

\end{abstract}

\section{Introduction}
\label{Introduction}

\subsection{Thesis Background}

As expected, most of the work involved combination of the disciplines of \textit{Data Mining} and \textit{Computer Networks} \cite{jiang2006research, datta2006distributed, bandyopadhyay2006clustering}.

\vskip 0.2in
\bibliographystyle{theapa}
\bibliography{refs}

\end{document}

refs.bib looks as follows:

@article{bandyopadhyay2006clustering,
title={Clustering distributed data streams in peer-to-peer environments},
author={Bandyopadhyay, S. and Giannella, C. and Maulik, U. and Kargupta, H. and Liu, K. and Datta, S.},
journal={Information Sciences},
volume={176},
number={14},
pages={1952--1985},
year={2006},
publisher={Elsevier}
}

@article{datta2006distributed,
title={Distributed data mining in peer-to-peer networks},
author={Datta, S. and Bhaduri, K. and Giannella, C. and Wolff, R. and Kargupta, H.},
journal={Internet Computing, IEEE},
volume={10},
number={4},
pages={18--26},
year={2006},
publisher={IEEE}
}

@article{jiang2006research,
title={Research issues in data stream association rule mining},
author={Jiang, N. and Gruenwald, L.},
journal={ACM Sigmod Record},
volume={35},
number={1},
pages={14--19},
year={2006},
publisher={ACM}
}

@book{datta2008probabilistic,
title={Probabilistic approximate algorithms for distributed data mining in peer-to-peer networks},
author={Datta, S.},
year={2008},
publisher={ProQuest}
}

-
Can you please give the code that you found the hard way ? –  Harish Kumar Oct 28 '12 at 23:51
Oh!. This won't help. Can you please give a code from \doumentclass...\end{document} like I gave in the answer? Also include those packages which are suspects!. If they are not standard packages (i.e., not found on CTAN), you may give their link also. –  Harish Kumar Oct 28 '12 at 23:58
Dear @Shamim Hafiz, where can we find jair and theapa? They don't look standard. –  Harish Kumar Oct 29 '12 at 8:14
@ShamimHafiz You are using a very old package theapa.sty that redefines \cite in a wrong way. There are more recent packages that provide APA citation style. –  egreg Oct 29 '12 at 8:44
@ShamimHafiz I don't know about JAIR; but the file they provide is from 1993 and is written in ugly LaTeX. However it's not responsible for the failure of \cite with spaces in its argument. –  egreg Oct 29 '12 at 22:50

Trust your own eyes ;-)

\documentclass[
12pt,a4paper]{scrartcl}
\usepackage{filecontents}
\begin{filecontents*}{\jobname.bib}

@ARTICLE{mwe2012,
author = {Smith, A. and Johnson, B. and Willians, C.},
title = {The three most common surnames in the United States of America},
journal = {Review of Useless Knowledge},
year = {2012},
volume = {8},
number = {1},
pages = {290--290}
}

@ARTICLE{mwe2011,
author = {Miller, J. and Brown, D.},
title = {Most used surnames in fake passports},
journal = {Journal of Nosense Ranks},
year = {2011},
volume = {5},
number = {3},
pages = {1--130},
pmid = {1234567},
url = {http://www.mwe.com/mwe2011},
doi = {http://dx.doi.org/10.1016/jnr.2011.01.01},
}
\end{filecontents*}
%----------------------------------------------------------------------

\begin{document}

\section{First section}
nonumy eirmod tempor invidunt~\cite{mwe2011,mwe2012}.

\noindent nonumy eirmod tempor invidunt~\cite{mwe2011,   mwe2012}.

\bibliographystyle{unsrt}
\bibliography{\jobname}

\end{document}

Update:

From the comments above, it seems you want to use APA style citations. The following code illustrates the solution (where I used apacite package)

\documentclass{article}
\usepackage[a4paper,margin=2cm]{geometry}
\usepackage{apacite} %% for APA style
\usepackage{filecontents}
\begin{filecontents*}{\jobname.bib}
title={Clustering distributed data streams in peer-to-peer environments},
author={Bandyopadhyay, S. and Giannella, C. and Maulik, U. and Kargupta, H. and Liu, K. and Datta, S.},
journal={Information Sciences},
volume={176},
number={14},
pages={1952--1985},
year={2006},
publisher={Elsevier}
}

@article{datta2006distributed,
title={Distributed data mining in peer-to-peer networks},
author={Datta, S. and Bhaduri, K. and Giannella, C. and Wolff, R. and Kargupta, H.},
journal={Internet Computing, IEEE},
volume={10},
number={4},
pages={18--26},
year={2006},
publisher={IEEE}
}

@article{jiang2006research,
title={Research issues in data stream association rule mining},
author={Jiang, N. and Gruenwald, L.},
journal={ACM Sigmod Record},
volume={35},
number={1},
pages={14--19},
year={2006},
publisher={ACM}
}

@book{datta2008probabilistic,
title={Probabilistic approximate algorithms for distributed data mining in peer-to-peer networks},
author={Datta, S.},
year={2008},
publisher={ProQuest}
}
\end{filecontents*}
%----------------------------------------------------------------------

\begin{document}

\section{First section}
tempor invidunt~\cite{jiang2006research,datta2008probabilistic}.

\noindent
tempor invidunt~\cite{jiang2006research,   datta2006distributed}.

\bibliographystyle{apacite}
\bibliography{\jobname}

\end{document}

And your code (with apacite) will be

\documentclass{article}
\usepackage{apacite} %% for APA style
\usepackage{jair,rawfonts}
\usepackage{filecontents}
\begin{filecontents*}{\jobname.bib}
title={Clustering distributed data streams in peer-to-peer environments},
author={Bandyopadhyay, S. and Giannella, C. and Maulik, U. and Kargupta, H. and Liu, K. and Datta, S.},
journal={Information Sciences},
volume={176},
number={14},
pages={1952--1985},
year={2006},
publisher={Elsevier}
}

@article{datta2006distributed,
title={Distributed data mining in peer-to-peer networks},
author={Datta, S. and Bhaduri, K. and Giannella, C. and Wolff, R. and Kargupta, H.},
journal={Internet Computing, IEEE},
volume={10},
number={4},
pages={18--26},
year={2006},
publisher={IEEE}
}

@article{jiang2006research,
title={Research issues in data stream association rule mining},
author={Jiang, N. and Gruenwald, L.},
journal={ACM Sigmod Record},
volume={35},
number={1},
pages={14--19},
year={2006},
publisher={ACM}
}

@book{datta2008probabilistic,
title={Probabilistic approximate algorithms for distributed data mining in peer-to-peer networks},
author={Datta, S.},
year={2008},
publisher={ProQuest}
}
\end{filecontents*}
%----------------------------------------------------------------------
\begin{document}

\begin{abstract}
Abstracts will go here.

\end{abstract}

\section{Introduction}
\label{Introduction}

\subsection{Thesis Background}

As expected, most of the work involved combination of the disciplines of \textit{Data Mining} and \textit{Computer Networks} \cite{jiang2006research,         datta2006distributed,                                          bandyopadhyay2006clustering}.

\vskip 0.2in

\bibliographystyle{apacite}
\bibliography{\jobname}

\end{document}

Compile and see for yourself. Don't use theapa.bst and theapa.sty They are old. Instead use apacite.

-
Hey, I want to read these journals regularly !!!11 ;-D –  Speravir Oct 29 '12 at 0:21
@Speravir: :-). I picked up[ those in this site only. Liked them very much and using them ;-) –  Harish Kumar Oct 29 '12 at 0:26
Thanks for the code update. Here is the link that you requested: "www.cs.cmu.edu/afs/cs/project/jair/pub/information/.../jair.sty " You would need to actually google it and it's not a raw link which would open up straightway. –  Shamim Hafiz Oct 29 '12 at 17:21
@ShamimHafiz: See the update. Don't use theapa. –  Harish Kumar Oct 29 '12 at 22:47
@HarishKumar: Thanks for the update and advice. egreg mentioned that, jair.sty is too old. Do you have any suggestion for it's alternative. As for a bit of humor, if I try to Google jair style, I get an alternate suggestion for hairstyle :P. The concerning part is, the phrase jair style might be outdated. –  Shamim Hafiz Oct 29 '12 at 23:45


text:
# How do I auto mount my partition?

I've a partition on /dev/sda2 of 279 GB Ext4 filesystem, but I'm not able to auto mount it on login.

I've added the partition entry /dev/sda /home ext4 defaults 0 0 in /etc/fstabt still it does not auto mount.

I've even tried to edit the mount options from disks (please see the below screenshot), yet no results.

The udisks command works well but the problem is that, it asks a admin password for standard user.

So my question is how do I auto mount this partition or at least grant read write permission to standard user so that they can mount this partition using udisks command.

Thanks to dschinn1001 I was able to automount my partition by editing the entry in fstab.

First I fount the UUID using sudo blkid

Then edit the fstab file using sudo /etc/fstab

Add the entry in the following format

[Device] [Mount Point] [File System Type] [Options] [Dump] [Pass]

Mount Point will be the location where you want to mount your partition
File System Type will be displayed when you run blkid command
Options Add the options you need. See options in Fstab for more details.
Dump This value will be zero most cases. See Fstab for more details.
Pass This value will be zero most cases. See Fstab for more details.

So finally this is how my entry looks like.

UUID=fe9ab5ba-35ed-49c5-b1d3-9bfc02060867 /media/mount ext4 auto,user,rw,exec 0 0

Save the file and restart your PC.

In the options I've mentioned

auto which means auto mount
user which means grant standard users to mount partition
exec Permit the execution of binaries from the filesystem

-

partition entry is not quite correct ( /home is in /dev/sda2 ? ) :

you wrote:

/dev/sda /home ext4 defaults 0 0

( if you write like that then you should replace /dev/sda with:

UUID=number-of-device

you can determine UUID-number with command: sudo blkid)

but it could look like this too ( in older Linux-Versions):

/dev/sda /mnt/ext4 defaults 0 0

or like this:

/dev/sda /media/ext4 defaults 0 0

more is explained here :

https://help.ubuntu.com/community/AutomaticallyMountPartitions

https://help.ubuntu.com/community/Fstab

https://help.ubuntu.com/community/UsingUUID

-

By /etc/fstabt I assume you meant /etc/fstab. The problem with your mount spec is probably that you want to mount a partition, where /dev/sda refers to the entire disk.

/dev/sda2 /home ext4 defaults 0 0

(as an example). List available partitions using sudo fdisk -l. As dschinn1001 mentions, a UUID is more desirable than a disk/partition number. The corresponding entry in my own fstab runs:

UUID=xxx /home ext4 defaults 0 2

Worth mentioning, /home is where your user accounts live. You have been running apparently with /home sourced from somewhere else. Once you get /home mounting properly from a new partition at boot time, the old home directory will be buried.

-


text:
Recognitions:
Gold Member

## The relation between angular and linear momentum

In the image above the line ABCDE represents the trajectory of a point mass, in inertial motion. Point S is in inertial motion also. As we know, in inertial motion equal distances are covered in equal intervals of time.

All of the consecutive triangles (SAB, SBC, etc) have the same area, as they have the same base and same height. This implies that equal areas are swept out in equal intervals of time.

The image below reproduces Newton's demonstration that Kepler's law of areas follows from the laws of motion.

A point mass is traveling along the curvilinear trajectory BCDE
Point S represents the common center of mass of two point masses that attract each other. It follows from the third law that point S is in inertial motion. The force upon the traveling point mass is at all times towards point S.

Without any force the point mass would proceed to point c. At point B the point mass receives an impulse towards S. The resulting motion is the vector sum of the original velocity and the added velocity component. This algorithm is repeated over the length of the curve.

The consecutive triangles all have the same area. In the limit of infinitisimal time increments the segments produce the curve.

I think these geometric demonstrations illustrate that angular momentum is a compound entity, reducible to elements. The elements of angular momentum are Newton's laws of motion.
Attached Thumbnails

 PhysOrg.com physics news on PhysOrg.com >> Is there an invisible tug-of-war behind bad hearts and power outages?>> Penetrating the quantum nature of magnetism>> Rethinking the universe: Groundbreaking theory proposed in 1997 suggests a 'multiverse'
 Cleonis, I replied in the other thread because the OP in this post seems a little bit different from what we were talking about there. You may be correct that our disagreement is just about definitions. Anyways -- I agree with you about the interpretation of the angular momentum laws as theorems. That is a nice way of putting it. However, force laws being an axiom and angular momentum laws being theorems does not imply they are dependent, mathematically speaking. For example, you wouldn't say calculus is really dependent on the axioms of set theory. In most cases in calculus, you don't care at all about set theory, even though strictly speaking they are obviously dependent. What I really meant was that angular momentum and linear momentum are linearly independent, in the sense that $$( r \times (mv) ) \cdot (mv) = 0$$.

 Quote by mordechai9 What I really meant was that angular momentum and linear momentum are linearly independent, in the sense that $$( r \times (mv) ) \cdot (mv) = 0$$.
Isn't it the definitions that are linearly independent? The cross product gives us the norm to an imaginary surface where v is the actual path of a massive particle.

Recognitions:
Gold Member

## The relation between angular and linear momentum

 Quote by mordechai9 I agree with you about the interpretation of the angular momentum laws as theorems. That is a nice way of putting it. However, force laws being an axiom and angular momentum laws being theorems does not imply they are dependent, mathematically speaking. For example, you wouldn't say calculus is really dependent on the axioms of set theory. In most cases in calculus, you don't care at all about set theory, even though strictly speaking they are obviously dependent. What I really meant was that angular momentum and linear momentum are linearly independent, in the sense that $$( r \times (mv) ) \cdot (mv) = 0$$.

OK, we agree as to the status of angular momentum as a theorem of the laws of motion.

For completeness: when I refer to laws of motion I think of a modernized formulation of them. This modernized formulation is designed to be logically equivalent with the traditional formulation, but more suited to the purpose.

1. When an object is in inertial motion it covers equal distances in equal intervals of time (This law asserts uniformity of space and time.)
2. F=m*a (to define the concept of force)
3. When two objects interact (attracting or repelling each other) then their common center of mass remains in inertial motion. (Once again asserting uniformity of space and time.)

(This version of the 3rd law is exclusively about dynamics. Newton's formulation of the 3rd law attempts so cover statics also, which is a superfluous attempt.)

(Pressed for time now, I'll post some more comment tomorrow.)

Recognitions:
Gold Member
 Quote by mordechai9 I agree with you about the interpretation of the angular momentum laws as theorems. That is a nice way of putting it. However, force laws being an axiom and angular momentum laws being theorems does not imply they are dependent, mathematically speaking. For example, you wouldn't say calculus is really dependent on the axioms of set theory. In most cases in calculus, you don't care at all about set theory, even though strictly speaking they are obviously dependent. What I really meant was that angular momentum and linear momentum are linearly independent, in the sense that $$( r \times (mv) ) \cdot (mv) = 0$$.

I'd like to take a closer look at the comparison with calculus. The first post of this thread presents a diagram that shows Newton's derivation of Kepler's second law. Newton uses a precursor of differential calculus. His derivation rests on taking the limit of infinitisimal time increments. Whereas Newton had to take the limit explicitly in all his proofs, today we can expect everyone to be familiar with differential calculus, allowing more complicated problems to be addressed.

(Yet another comparison: levels of computer language. The very first computers were programmed in machine language, then assembler languages were developed, then third generation languages. Each language level is dependent on services rendered by the level below it. Using the higher level environment is much more efficient use of programmer man-hours.)

In physics computations angular momentum is used in situation where it gives an efficiency advantage. Still, if a phenomenon can be accounted for in terms of angular momentum it can also be accounted for in terms of instantaneous linear momentum of two or more interacting objects. This is always valid, since angular momentum is reducible, with the laws of motion as elements.

In physics I distinguish between what matters for efficiency advantage and what matters for understanding at gut level. What is best for computational efficiency is not necessarily suitable for gut level understanding.

In the case of gyroscopic precession the computation that uses the angular momentum of the spinning top and the vector cross product you readily get the correct prediction of the motion, but it doesn't illuminate why the spinning top tends to precess.

Interestingly, understanding why the vector cross product arises in the first place is in fact accessible. That is what I demonstrated in the thread about how a rolling hoops remain upright.

 Tags angular momentum, linear momentum

 Similar discussions for: The relation between angular and linear momentum Thread Forum Replies Introductory Physics Homework 1 Advanced Physics Homework 3 Advanced Physics Homework 0 Classical Physics 18 Introductory Physics Homework 1


text:
Some events of a probability experiment can occur simultaneously and some events cannot occur simultaneously.

For example, consider the experiment of throwing die. Let us define the event A as getting an odd number and the event B as getting an event number and the third event C as getting a multiple of 3. The outcomes of the three events can be listed as follows:
A = {1, 3, 5} B = {2, 4, 6} and C = {3, 6}
Events A and C have the outcome 3 as common, while B and C have the outcome 6 in common. The events A and B do not share any common outcomes. Suppose the outcome turns out to be 3, we conclude that both the events A and C have occurred. And for the outcome 6, we say that both the events B and C have occurred. But there is no possibility of saying that both the events A and B have occurred. A and B are hence the mutually exclusive events. This against events A and C or the events B and C are not mutually exclusive and hence mutually inclusive events.

## Mutually Exclusive Events Definition

Two events are called mutually exclusive events if they cannot occur at the same.  This means they do not share common outcomes.As we saw above when you throw a die, the events of getting an odd number and getting an even number are mutually exclusive.  Similarly when you toss a coin the events of getting a Head and getting the Tail are mutually exclusive.

An event and its complement are mutually exclusive.

A number of events E1, E2, E,3 .........En are called mutually exclusive if the occurrence of one event denies the occurrence of other events. if these events together form the sample space, then they are called mutually exclusive and exhaustive.

When a fair die is thrown, the events of getting 1, 2, 3, 4 , 5 and 6 are all mutually exclusive and exhaustive events.

In fact, the sample space for any experiment consists of mutually exclusive simple events.

The event A ∩ B is a null set when A and B are mutually exclusive. Hence P(A ∩ B) = 0.Thus the probability of either A or B occurs is the sum of their probabilities.

Addition law for the union of two mutually exclusive events
P(A or B) = P(A) + P(B).

## Mutually Exclusive Events Examples

1. In a multiple choice question, getting the answer correct and getting the wrong answer are mutually exclusive events.

2. At a political rally, there are 25 Republicans, 30 Democrats and 10 independents. If a person is selected at random find the probability that she or he is a Republican or a Democrat.
As the person chosen cannot be both Republican and Democrat, we can use the addition rule for Mutually exclusive events here.
P( Republican or Democrat) = P(Republican) + P(Democrat)
= $\frac{25}{65}$ + $\frac{30}{65}$ = $\frac{55}{65}$ = $\frac{11}{13}$.

3. For an online degree program, the available instructors for various subjects are as follows:
 Subject Number of Instructors Math 10 Physics 6 Chemistry 5 Biology 5 Statistics 4

If an instructor is selected as the Lead, find the probability that the person selected teaches either Math or Stats assuming that each person teaches only one subject. Since each person teaches only one subject, we can apply the addition rule for mutually exclusive events here.
P(Math or Stats) = P(Math) + P(Stats)
= $\frac{10}{30}$ + $\frac{4}{30}$ = $\frac{14}{30}$ = $\frac{7}{15}$.

4. Identify whether the given events are mutually exclusive or not.
(a) Selecting a student who is either a sophomore or doing Math major.
(b) Selecting a student who is either a sophomore or a Freshman.
(a) These events are not mutually exclusive, as a sophomore doing Math major can be picked.
(b) These two events are mutually exclusive as a student cannot be both a sophomore and a Freshman.

### Compound Events

 Inclusion Exclusion Examples Compound Event Dependent Events Types of Events Sample Spaces Vector Space Sample Variance of the Sample Means Sampling Distribution of Sample Mean Population and Sampling Binomial Distribution Sample Problems Hypothesis Testing Sample Problems Compounded Interest
 Calculate Sample Mean Calculate Sample Size sample covariance calculator


text:
# The Icosidodecahedron

A semi-regular polyhedron with two triangles and two pentagons alternating around each vertex.

The icosidodecahedron is one of the thirteen archimedian solids. It can be created by slicing suitable sections off the vertices of either a dodecahedron or an icosahedron and thus may be inscribed in either solid.

 VertexSymbol WythoffSymbol No. ofVertices No. ofEdges {3}Faces {5}Faces SymmetryGroup Dual Polyhedron 3.5.3.5 2 | 3 5 30 60 20 12 A5×C2 RhombicTriacontahedron

Edge ratios:

• e/rho = 2tan(18^@)=2sqrt((5-2sqrt(5))/5)
• e/R = (sqrt(5)-1)/2
• e/(e_12) = (1+sqrt(5))/4
• e/(e_20) = 1/2

where e is the edge length, rho is the inter-radius, R is the circum-radius, e_12 is the edge of the circumscribing dodecahedron, and e_20 is the edge of the circumscribing icosahedron.


text:
# Topology and music

A new paper appeared on the arXiv this week applying some simple topological ideas to the analysis of musical modes.  This contains some simple ideas about fundamental groups and so on and I was thinking it might make a project for a musically-oriented student in my MASS course.  There have been several papers of this sort recently: the earliest that I’m aware of is Rachel Hall’s article in Science five years ago. (Dr Hall is a professor at Saint Joseph’s University in Philadelphia and before that was a student in the Geometric Functional Analysis group at Penn State.)

A mode is a seven-note scale.  The familiar major scale of Western music (C,D,E,F,G,A,B) is a mode (Ionian mode), but one can obtain different modes by starting from a different note (e.g. Aeolian mode, A,B,C,D,E,F,G) or by using a different starting scale, or both. The authors analyze a mode into two chords: the seventh chord made by notes I, III, V, and VII of the scale, and the triad made by notes II, IV and VI.  For instance, Ionian mode is a major seventh (CEGB) plus a minor triad (DFA); Aeolian mode is a minor seventh (ACEG) plus a diminished triad (BDF).   Spaces of chords are natural examples of configuration spaces (selections of $$n$$ distinct points from the space of notes, with order irrelevant) so this allows the representation of a mode as a subspace of a product of two configuration spaces.

I’m not really competent to judge the music theory here (as a guitarist, I’m usually sticking with two or three of the innumerable possible scales that the authors identify), but it is a fascinating point (this is also what I got out of Rachel Hall’s paper) that music is full of natural examples of configuration spaces, including knots and Möbius bands and other topological exotica.

#### References

Bergomi, Mattia G., and Alessandro Portaluri. Modes in Modern Music from a Topological Viewpoint. ArXiv e-print, September 3, 2013. http://arxiv.org/abs/1309.0687.

Budney, Ryan, and William Sethares. Topology of Musical Data. ArXiv e-print, July 4, 2013. http://arxiv.org/abs/1307.1201.

Callender, Clifton, Ian Quinn, and Dmitri Tymoczko. “Generalized Voice-Leading Spaces.” Science 320, no. 5874 (April 18, 2008): 346–348. doi:10.1126/science.1153021.

Hall, Rachel Wells. “Geometrical Music Theory.” Science 320, no. 5874 (April 18, 2008): 328–329. doi:10.1126/science.1155463.


text:
# Integer compositions with quadratic sum constraint

A statistical question I'm studying has led me to the following counting problem: Let $\lambda_j := \binom{j}{2}$. For integers $1 \le q \le n$ and $1 \le b \le \lambda_n$, determine $X[n,q,b]=$ the number of compositions $(i_1,\dots,i_q)$ of $n$ (i.e. $\sum i_j = n$ and $\min_j i_j \ge 1$) such that $\sum_{j=1}^q \lambda_{i_j} = b$.

I can calculate $X[n,q,b]$ by means of the recursion $$X[n,q,b] = \sum_{r=1}^q \binom{q}{r} X[n-q,r,b+q-n]$$ with base cases \begin{align} X[n,n,b] &= \mathbf{1}\{b=0\}\\ X[n,1,b] &= \mathbf{1}\{b=\lambda_n\}\\ X[n,q,b] &= 0,\,q>n\text{ or }b>\lambda_{n-q+1}. \end{align}

At each level $n$ of the recursion there are $O(n^3)$ terms to compute, and each one takes $O(n)$ time, so this trying to solve for $X$ in this way becomes prohibitively slow for large $n$.

I'm wondering if there is a way to speed this computation up, particularly if there is any sort of asymptotic (in $n$) approximation possible. The reason I think there might be is that normalizing the sequence $\{X[n,q,b]\}_{b=1}^{\lambda_n}$ by its sum $\binom{n-1}{q-1}$ and smoothing the resulting density a bit shows it to have a nice form that looks something like a gamma density, except with a heavier tail. It would be interesting to understand why. Anyways, any pointers to related literature would be appreciated.

• So a generating function is $\sum_{n\ge 1\atop b\ge1} X(n,q,b)x^ny^b=\Big(\sum_{i=1}^{\infty}x^iy^{(\!{i\atop 2})}\Big)^q.$ – Pietro Majer Feb 18 '17 at 0:44
• $\sum_j \lambda_{i_j} = b$ here is equivalent to $\sum_j i_j^2=2b+n$. – Max Alekseyev Feb 18 '17 at 18:17
• In fact, $X[n,q,b]$ can be computed in $O(bnq^2)$ time. – Max Alekseyev Feb 18 '17 at 19:57
• @MaxAlekseyev That's right. Since $b$ and $q$ are as large as $O(n^2)$ and $n$, respectively, the whole thing ends up taking at least $O(n^5)$ (there is also the need to use BigNums, so the complexity is actually higher). – jth Feb 19 '17 at 13:24


text:
replaceString

A Workflow Engine function that replaces a string or regular expression in a field with a specified string.

This function is available for event, alert, enrichment, and Situation workflows.

Arguments

Workflow Engine function replaceString takes the following arguments:

Name

Required

Type

Description

field

Yes

String

Field to replace text in.

replace

Yes

String

Original string to replace. This value is treated as a regex. Do not include leading or trailing delimiters.

with

No

String

New string you want to use instead. If you leave this field blank, replaces the original string with a blank space.

Example

The following example demonstrates typical use of Workflow Engine function replaceString.

Some systems abbreviate "database" as "d.b." or "D.B.". If you had a class field that contains the value "A D.B. has failed", and you wanted to replace the abbreviation with "database", set the following:

• field: class

• replace: d\.b\.

• with: database

The UI translates your settings to the following JSON:

{"field":"class","replace":"d\\.b\\.","with":"database"}

The function replaces any occurrences of "d.b." and "D.B.", so the resulting value reads "A database has failed".


text:
Coordinates - February 2005, Stage 2&3

Problems

Arrangements

Stage: 2 Challenge Level:

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Fred the Class Robot

Stage: 2 Challenge Level:

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

Cartesian Isometric

Stage: 2 Challenge Level:

The graph below is an oblique coordinate system based on 60 degree angles. It was drawn on isometric paper. What kinds of triangles do these points form?

Ten Hidden Squares

Stage: 2 Challenge Level:

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

Eight Hidden Squares

Stage: 2 and 3 Challenge Level:

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

Isosceles Triangles

Stage: 3 Challenge Level:

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Lost

Stage: 3 Challenge Level:

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

Square Coordinates

Stage: 3 Challenge Level:

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?


text:
Mathematics Prelims

June 13, 2009

Change of Basis

Filed under: Algebra,Linear Algebra — cjohnson @ 4:19 pm

In any non-trivial vector space there will be several possible bases we could pick.  In $\mathbb{R}^3$, for instance, we could use $\{ [1, 0, 0]^T, [0, 1, 0]^T, [0, 0, 1]^T \}$ or $\{ [1, 2, 0]^T, [3, 0, 1]^T, [4, 2, -1]^T \}$.  This first basis is known as the standard basis, and in general for an $n$-dimensional vector space over $\mathcal{F}$, we’ll refer to $\{ [1, 0, 0, ..., 0]^T, [0, 1, 0, ..., 0]^T, ..., [0, ..., 0, 1]^T \}$ as the standard basis, and will let $e_i$ denote the vector with a 1 in the $i$-th position, and zeros elsewhere.

When we write down a vector like $[1, 2, 3]^T$ we implicitly mean that these are the coordinates to use with the vectors in the standard basis; these are the coefficients we multiply the $e_i$ basis vectors by to get describe our vector.

$\displaystyle \left[ \begin{array}{c} 1 \\ 2 \\ 3 \end{array} \right] = 1 \left[ \begin{array}{c} 1 \\ 0 \\ 0 \end{array} \right]+ 2 \left[ \begin{array}{c} 0 \\ 1 \\ 0 \end{array} \right] + 3 \left[ \begin{array}{c} 0 \\ 0 \\ 1 \end{array} \right]$

But how would we find the appropriate coordinates if we were to use $\{ [1, 2, 0]^T, [3, 0, 1]^T, [4, 2, -1]^T \}$ as our basis?  Let’s suppose our coefficients are $\alpha_1, \alpha_2, \alpha_3$.  Then what we want to do is find the values of the $\alpha_i$ such that

$\displaystyle \alpha_1 \left[ \begin{array}{c} 1 \\ 2 \\ 0 \end{array} \right] + \alpha_2 \left[\begin{array}{c}3 \\ 0 \\ 1\end{array}\right] + \alpha_3\left[\begin{array}{c}4 \\ 2 \\ -1\end{array}\right] = \left[ \begin{array}{c} 1 \\ 2 \\ 3 \end{array}\right]$

So what we have is a system of equations:

$\displaystyle \left[ \begin{array}{ccc} 1 & 3 & 4 \\ 2 & 0 & 2 \\ 0 & 1 & -1 \end{array} \right] \left[ \begin{array}{c} \alpha_1 \\ \alpha_2 \\ \alpha_3 \end{array} \right]= \left[ \begin{array}{c} 1 \\ 2 \\ 3 \end{array} \right]$

Notice that since the columns of this matrix form a basis for $\mathbb{R}^3$, the matrix is invertible, and so we can easily solve for the $\alpha_i$.

$\displaystyle \left[ \begin{array}{c} \alpha_1 \\ \alpha_2 \\ \alpha_3 \end{array} \right] = \left[ \begin{array}{ccc} 1 & 3 & 4 \\ 2 & 0 & 2 \\ 0 & 1 & -1 \end{array} \right]^{-1} \left[ \begin{array}{c} 1 \\ 2 \\ 3 \end{array} \right] = \left[ \begin{array}{c} 5/2 \\ 3/2 \\ -3/2\end{array} \right]$

In general, if we have a basis $A = \{ a_1, ..., a_n \}$, we will write

$\displaystyle \left[ \begin{array}{c} \alpha_1 \\ \vdots \\ \alpha_n \end{array} \right]_A$

to mean that the $\alpha_i$ are the coefficients of the $a_i$ vectors in our $A$ basis, and will let $_AI$ be the matrix converts the coordinates for the standard basis to coordinates in our $A$ basis.  Likewise, $I_A$ will be the matrix which converts coordinates from the $A$ basis to coordinates with the standard basis.

Generalizing on the argument above we see that we can calculate $I_A$ by simply using our basis vectors as our columns.  For $_AI$ we take the inverse of this matrix.

$\displaystyle I_A = \left[ \, \left. a_1 \, \right| \, \left. a_2 \, \right| \, \left. \cdots \, \right| \, a_n \, \right]$

$\displaystyle _AI = \left[ \, \left. a_1 \, \right| \, \left. a_2 \, \right| \, \left. \cdots \, \right| \, a_n \, \right]^{-1}$

Now suppose we have two bases, $A = \{ a_1, ..., a_n \}$ and $B = \{ b_1, ..., b_n \}$.  The matrix which will take coordinates with respect to the $A$ basis and convert them into coordinates for the $B$ basis is denoted $_BI_A$.  One way to calculate $_BI_A$ is to convert our $A$-coordinates into standard coordinates, and then convert those into $B$-coordinates:

$\displaystyle _BI_A = _BI \, I_A$

Alternatively, we could note that

$\displaystyle [ a_i ]_B = _BI_A [ a_i ]$

$\displaystyle \, = _BI_A \left[ \begin{array}{c} 0 \\ \vdots \\ 0 \\ 1 \\ 0 \\ \vdots \\ 0 \end{array} \right]_A$ (with the 1 in the $i$-th spot)

$\displaystyle \, = \left(_BI_A\right)_{*i}$ (recall $M_{*i}$ is the notation I use for the $i$-th column of $M$)

So the $i$-th column of $_BI_A$ is simply $i$-th vector from our $A$ basis, but in $B$-coordinates.