ORIGINAL_ARTICLE
On the two-wavelet localization operators on homogeneous spaces with relatively invariant measures
In the present paper, we introduce the two-wavelet localization operator for the square integrable representation of a homogeneous space with respect to a relatively invariant measure. We show that it is a bounded linear operator. We investigate some properties of the two-wavelet localization operator and show that it is a compact operator and is contained in a Schatten $p$-class.
http://wala.vru.ac.ir/article_29395_ef5554cee1c1583c3bc9f17d5bb7d85c.pdf
2017-12-01T11:23:20
2019-12-10T11:23:20
1
12
10.22072/wala.2017.61228.1109
homogenous space
square integrable representation
wavelet transform
localization operator
Schatten $p$-class operator
Fatemeh
Esmaeelzadeh
faride.esmaeelzadeh@yahoo.com
true
1
Department of Mathematics‎, ‎Bojnourd Branch‎, ‎Islamic Azad University‎, ‎Bojnourd‎, ‎Iran
Department of Mathematics‎, ‎Bojnourd Branch‎, ‎Islamic Azad University‎, ‎Bojnourd‎, ‎Iran
Department of Mathematics‎, ‎Bojnourd Branch‎, ‎Islamic Azad University‎, ‎Bojnourd‎, ‎Iran
LEAD_AUTHOR
Rajab Ali
Kamyabi-Gol
kamyabi@ferdowsi.um.ac.ir
true
2
Department of Mathematics‎, ‎Center of Excellency in Analysis on Algebraic Structures(CEAAS)‎, ‎Ferdowsi University Of Mashhad‎, Iran
Department of Mathematics‎, ‎Center of Excellency in Analysis on Algebraic Structures(CEAAS)‎, ‎Ferdowsi University Of Mashhad‎, Iran
Department of Mathematics‎, ‎Center of Excellency in Analysis on Algebraic Structures(CEAAS)‎, ‎Ferdowsi University Of Mashhad‎, Iran
AUTHOR
Reihaneh
Raisi Tousi
raisi@ferdowsi.um.ac.ir
true
3
‎Ferdowsi University Of Mashhad
‎Ferdowsi University Of Mashhad
‎Ferdowsi University Of Mashhad
AUTHOR
[1] S.T. Ali, J-P. Antoine and J-P. Gazeau,Coherent States, Wavelets and Their Generalizations, Springer-Verlag, New York, 2000.
1
[2] V. Catana, Two-wavelet localization operators on homogeneous spaces and their traces, Integral Equations Oper. Theory, 62 (2008), 351-363.
2
[3] V. Catana, Schatten-von Neumann norm inequalities for two- wavelet localization operators, J. Pseudo-Differ. Oper. Appl., 52 (2007), 265-277.
3
[4] F. Esmaeelzadeh, R.A. Kamyabi-Gol and R. Raisi Tousi, On the continuous wavelet transform on homogeneous spases, Int. J. Wavelets Multiresolut Inf. Process., 10(4) (2012), 1-18.
4
[5] F. Esmaeelzadeh, R. A. Kamyabi-Gol and R. Raisi Tousi, Localization operators on homogeneous spaces, Bull. Iran. Math. Soc., 39(3) (2013), 455-467.
5
[6] F. Esmaeelzadeh, R. A. Kamyabi-Gol and R. Raisi Tousi, Two-wavelet constants for square integrable representations of G/H, Wavel. Linear Algebra, 1 (2014), 63-73.
6
[7] J.M.G. Fell and R.S. Doran, Representation Of *-algebras, Locally Compact Groups, and Banach *-algebraic Bundles, Vol. 1, Academic Press, 1988.
7
[8] G.B. Folland, A Course in Abstract Harmonic Analysis, CRC Press, New York, 1995.
8
[9] H. Reiter and J. Stegeman, Classical Harmonic Analysis and Locally Compact Group, Claredon Press, 2000.
9
[10] K. Zhu, Operator Theory in Function Spaces, vol. 138, American Mathematical Society, 2007.
10
[11] M.W. Wong, Wavelet Transform and Localization Operators, Birkhauser Verlag, Basel-Boston-Berlin, 2002.
11
ORIGINAL_ARTICLE
Characterizing sub-topical functions
In this paper, we first give a characterization of sub-topical functions with respect to their lower level sets and epigraph. Next, by using two different classes of elementary functions, we present a characterization of sub-topical functions with respect to their polar functions, and investigate the relation between polar functions and support sets of this class of functions. Finally, we obtain more results on the polar of sub-topical functions.
http://wala.vru.ac.ir/article_29393_0ee808b7959b2874e9dabf0d4972296f.pdf
2017-12-01T11:23:20
2019-12-10T11:23:20
13
23
10.22072/wala.2017.61257.1110
sub-topical function
elementary function
polar function
plus-co-radiant set
abstract convexity
Hassan
Bakhtiari
hbakhtiari@math.uk.ac.ir
true
1
Shahid Bahonar University of Kerman
Shahid Bahonar University of Kerman
Shahid Bahonar University of Kerman
AUTHOR
Hossein
Mohebi
hmohebi@uk.ac.ir
true
2
Shahid Bahonar University of Kerman
Shahid Bahonar University of Kerman
Shahid Bahonar University of Kerman
LEAD_AUTHOR
[1] H. Bakhtiari and H. Mohebi, Characterizing global maximizers of the difference of sub-topical functions, J. Appl. Math. Anal. Appl., 450(1) (2017), 63-76.
1
[2] A.R. Doagooei, Sub-topical functions and plus-co-radiant sets, Optimization, 65(1) (2016), 107-119, .
2
[3] S. Gaubert and J. Gunawardena, A Non-Linear Hierarchy for Discrete Event Dynamical Systems, In: Proceedings of the 4th Workshop on Discrete Event Systems Cagliari, Technical Report HPL-BRIMS-98-20, Hewlett-Packard Labs., Cambridge University Press, Cambridge, 1998.
3
[4] J. Gunawardena, An Introduction to Idempotency, Cambridge University Press, Cambridge, 1998.
4
[5] J. Gunawardena, From Max-Plus Algebra to Non-Expansive Mappings: A Non-Linear Theory for Discrete Event Systems. Theoretical Computer Science, Technical Report HPL-BRIMS-99-07, Hewlett-Packard Labs., Cambridge University Press, Cambridge, 1999.
5
[6] J. Gunawardena and M. Keane, On the Existence of Cycle Times for Some Nonexpansive Maps, Technical Report HPL-BRIMS-95-003, Hewlett-Packard Labs., Cambridge University Press, Cambridge, 1995.
6
[7] H. Mohebi, Topical functions and their properties in a class of ordered Banach spaces, Appl. Optim., 99 (2005), 343-361.
7
[8] H. Mohebi and M. Samet Abstract convexity of topical functions, J. Glob. Optim., 58(2) (2014), 365-375.
8
[9] A.M. Rubinov, Abstract Convexity and Global Optimization, Kluwer Academic Publishers, Dordrecht-Boston-London, 2000.
9
[10] A.M. Rubinov and I. Singer, Topical and sub-topical functions, downward sets and abstract convexity, Optimization, 50(5-6) (2001), 307-351.
10
[11] I. Singer, On radiant sets, downward sets, topical functions and sub-topical functions in lattice ordered groups, Optimization, 53(4) (2004), 393-428.
11
[12] C. Zalinescu, Convex Analysis in General Vector Spaces, World Scientific, London, 2002.
12
ORIGINAL_ARTICLE
Linear preservers of Miranda-Thompson majorization on MM;N
Miranda-Thompson majorization is a group-induced cone ordering on $\mathbb{R}^{n}$ induced by the group of generalized permutation with determinants equal to 1. In this paper, we generalize Miranda-Thompson majorization on the matrices. For $X$, $Y\in M_{m,n}$, $X$ is said to be Miranda-Thompson majorized by $Y$ (denoted by $X\prec_{mt}Y$) if there exists some $D\in \rm{Conv(G)}$ such that $X=DY$. Also, we characterize linear preservers of this concept on $M_{m,n}$.
http://wala.vru.ac.ir/article_29392_451002d1ba46987bb96f23d9a78e8e6a.pdf
2017-12-01T11:23:20
2019-12-10T11:23:20
25
32
10.22072/wala.2017.61736.1113
Group-induced cone ordering
Linear preserver
Miranda-Thompson majorization
Ahmad
Mohammadhasani
a.mohammadhasani53@gmail.com
true
1
Department of Mathematics, Sirjan University of technology, Sirjan, Iran
Department of Mathematics, Sirjan University of technology, Sirjan, Iran
Department of Mathematics, Sirjan University of technology, Sirjan, Iran
LEAD_AUTHOR
Asma
Ilkhanizadeh Manesh
a.ilkhani@vru.ac.ir
true
2
Vali-e-Asr University of Rafsanjan
Vali-e-Asr University of Rafsanjan
Vali-e-Asr University of Rafsanjan
AUTHOR
[1] L.B. Beasley, S-G. Lee and Y-H Lee, A characterization of strong preservers of matrix majorization, Linear Algebra Appl., 367 (2003), 341-346,
1
[2] H. Chiang and C.K. Li, Generalized doubly stochastic matrices and linear preservers, Linear Multilinear Algebra, 53(1) (2005), 1-11.
2
[3] A. Giovagnoli and H.P. Wynn, G-majorization with applications to matrix orderings, Linear Algebra Appl., 67 (1985), 111-135.
3
[4] A.M. Hasani and M. Radjabalipour, On linear preservers of (right) matrix majorization, Linear Algebra Appl., 423 (2007), 255-261.
4
[5] A. Ilkhanizadeh Manesh, Right gut-Majorization on M_{n,m}, Electron. J. Linear Algebra, 31(1) (2016), 13-26.
5
[6] F. Khalooei, Linear preservers of two-sided matrix majorization, Wavel. Linear Algebra, 1 (2014), 43-50.
6
[7] M. Niezgoda, Cone orderings, group majorizations and similarly separable vectors, Linear Algebra Appl., 436 (2012), 579-594.
7
[8] A.W. Marshall, I. Olkin, and B.C. Arnold, Inequalities: Theory of Majorization and Its Applications, Springer, New York, 2011.
8
[9] M. Soleymani and A. Armandnejad, Linear preservers of even majorization on M_{n,m}, Linear Multilinear Algebra, 62(11) (2014), 1437-1449.
9
ORIGINAL_ARTICLE
Wilson wavelets for solving nonlinear stochastic integral equations
A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It\^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It\^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operational matrices of integration and stochastic integration, the problem under study is transformed to a system of nonlinear algebraic equations which can be simply solved to obtain an approximate solution for the main problem. Moreover, a new technique for computing nonlinear terms in such problems is presented. Furthermore, convergence of Wilson wavelets expansion is investigated. Several examples are presented to show the efficiency and accuracy of the proposed method.
http://wala.vru.ac.ir/article_29388_cab6f5111dc82287318b83ae253c9278.pdf
2017-12-01T11:23:20
2019-12-10T11:23:20
33
48
10.22072/wala.2017.59458.1106
Wilson wavelets
Nonlinear stochastic It^o-Volterra integral equation
Stochastic operational matrix
Bibi Khadijeh
Mousavi
khmosavi@gmail.com
true
1
Department of Pure Mathematica, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
Department of Pure Mathematica, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
Department of Pure Mathematica, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
AUTHOR
Ataollah
Askari Hemmat
askarihemmat@gmail.com
true
2
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
LEAD_AUTHOR
Mohammad Hossien
Heydari
heydari@stu.yazd.ac.ir
true
3
Shiraz University of Technology, Shiraz,
Shiraz University of Technology, Shiraz,
Shiraz University of Technology, Shiraz,
AUTHOR
[1] A. Abdulle and A. Blumenthal, Stabilized multilevel Monte Carlo method for stiff stochastic differential equations, J. Comput. Phys., 251 (2013), 445-460.
1
[2] E. Babolian and F. Fattahzadeh, Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration, Appl. Math. Comput., 188(1) (2007), 417-426.
2
[3] E. Babolian and A. Shahsavaran, Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets, J. Comput. Appl. Math., 225(1) (2009), 87-95.
3
[4] M.A. Berger and V.J. Mizel, Volterra equations with Ito integrals I, J. Integral Equations, 2(3) (1980), 187-245.
4
[5] K. Bittner, Wilson bases on the interval, Advances in Gabor Analysis, Birkhäuser Boston, (2003) 197-221.
5
[6] K. Bittner, Linear approximation and reproduction of polynomials by wilson bases, J. Fourier Anal. Appl., 8(1) (2002), 85-108.
6
[7] K. Bittner, Biorthogonal wilson Bases, Proc. SPIE Wavelet Applications in Signal and Image Processing VII, 3813 (1999), 410-421.
7
[8] Y. Cao, D. Gillespie and L. Petzod, Adaptive explicit-implicit tau-leaping method with automatic tau selection, J. Chem. Phys., 126(22) (2007), 1-9.
8
[9] C. Cattani and A. Kudreyko, Harmonic wavelet method towards solution of the Fredholm type integral equations of the second kind, Appl. Math. Comput., 215(12) (2010), 4164-4171.
9
[10] J.C. Cortes, L. Jodar and L. Villafuerte, Numerical solution of random differential equations: a mean square approach, Math. Comput. Modelling, 45(7-8) (2007), 757-765.
10
[11] I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992.
11
[12] I. Daubechies, S. Jaffard and J.L. Journe, A simple wilson orthonormal basis with exponential decay, SIAM J. Math. Anal., 22(2) (1991), 554--573.
12
[13] H.G. Feichtinger and T. Strohmer (eds.), Advances in Gabor analysis, Springer Science and Business Media, Davis, U.S.A, 2012.
13
[14] M.H. Heydari, M.R. Hooshandasl, F.M. Maalek Ghaini and C. Cattani, A computational method for solving stochastic It^{o} Volterra integral equations based on stochastic operational matrix for generalized hat basis functions, J. Comput. Phys., 270(1) (2014), 402-415.
14
[15] M.H. Heydari, M.R. Hooshmandasl, A. Shakiba and C. Cattani, Legendre wavelets Galerkin method for solving nonlinear stochastic integral equations, Nonlinear Dyn., 85(2) (2016), 1185-1202.
15
[16] M.H. Heydari, C. Cattani, M.R. Hooshandasl, F.M. Maalek Ghaini, An efficient computational method for solving nonlinear stochastic It^{o} integral equations: Application for stochastic problems in physics, J. Comput. Phys., 283 (2015), 148-168.
16
[17] M.H Heydari, M.R. Hooshmandasl and F. Mohammadi, Legendre wavelets method for solving fractional partial differential equations with Dirichlet boundary conditions, Appl. Math. Comput., 234 (2014), 267-276.
17
[18] M.H. Heydari, M.R. Hooshmandasl, F.M.M. Ghaini and F. Fereidouni, Two-dimensional Legendre wavelets for solving fractional poisson equation with Dirichlet boundary conditions, Eng. Anal. Bound. Elem., 37(11) (2013), 1331-1338.
18
[19] M.H. Heydari, M.R. Hooshmandasl and F.M. Maleak Ghaini, A good approximate solution for linear equation in a large interval using block pulse functions, J. Math. Ext., 7(1) (2013), 17-32.
19
[20] M.H. Heydari, M.R. Hooshmandasl, F.M. Maalek Ghaini and M. Li, Chebyshev wavelets method for solution of nonlinear fractional integro-differential equations in a large interval, Adv. Math. Phys., 2013 (2013), DOI. 10.1155/2013/482083.
20
[21] H. Holden, B. Oksendal, J. Uboe and T. Zhang, Stochastic Partial Differential Equations, second ed., Springer, New york, 1998.
21
[22] S.K. Kaushik and S. Panwar, An interplay between gabor and wilson frames, J. Funct. Spaces Appl., 2013 (2013), DOI. 10.1155/2013/610917.
22
[23] M. Khodabin, K. Malekinejad, M. Rostami and M. Nouri, Interpolation solution in generalized stochastic exponential population growth model, Appl. Math. Modelling, 36(3) (2012), 1023-1033.
23
[24] M. Khodabin, K. Malekinejad, M. Rostami and M. Nouri, Numerical approach for solving stochastic Volterra-Fredholm integral equations by stochastic operational matrix, Comput. Math. Appl., 64(6) (2012), 1903-1913.
24
[25] M. Khodabin, K. Malekinejad, M. Rostami and M. Nouri, Numerical solution of stochastic differential equations by second order Runge- Kutta methods, Appl. Math. Modelling, 53 (2011), 1910-1920.
25
[26] P.E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer, Berlin, 1999.
26
[27] J.J. Levin and J.A. Nohel, On a system of integro-differential equations occurring in reactor dynamics, J. Math. Mech., 9 (1960), 347-368.
27
[28] K. Maleknejad, M. Khodabin and M. Rostami, Numerical solutions of stochastic Volterra integral equations by a stochastic operational matrix based on block pulse functions, Math. Comput. Modelling, 55(3-4) (2012), 791-800.
28
[29] K. Maleknejad, M. Khodabin and M. Rostami, A numerical method for solving m-dimensional stochastic Ito-Volterra integral equations by stochastic operational matrix, Comput. Math. Appl., 63(1) (2012), 133-143.
29
[30] J.J. Levin and J.A. Nohel, On a system of integro differential equations occurring in reactor dynamics, J. Math. Mech., 9(3) (1960), 347-36.
30
[31] F. Mohammadi, A Chebyshev wavelet operational method for solving stochastic Volterra-Fredholm integral equations, Int. J. Appl. Math. Res., 4(2) (2015), 217-227.
31
[32] F. Mohammadi, A wavelet-based computational method for solving stochastic It^{o}-Volterra integral equations, J. Comput. Phys., 298(1) (2015), 254-265.
32
[33] B.KH. Mousavi, A. Askari hemmat and M. H. Heydari, An application of Wilson system in numerical solution of Fredholm integral equations, PJAA, 2 (2017), 61-72.
33
[34] B. Oksendal, Stochastic Differential Equations, fifth ed. in: An introduction with Applications, Springer, New York, 1998.
34
[35] E. Platen and N. Bruti-Liberati, Numerical Solution of Stochastic Differential Equations with Jumps in Finance, Springer, Berlin, 2010.
35
[36] S. Yousefi and A. Banifatemi, Numerical solution of Fredholm integral equations by using CAS wavelets, Appl. Math. Comput., 183(1) (2006), 458-463.
36
ORIGINAL_ARTICLE
Some results on Haar wavelets matrix through linear algebra
Can we characterize the wavelets through linear transformation? the answer for this question is certainly YES. In this paper we have characterized the Haar wavelet matrix by their linear transformation and proved some theorems on properties of Haar wavelet matrix such as Trace, eigenvalue and eigenvector and diagonalization of a matrix.
http://wala.vru.ac.ir/article_29498_344e26e2a5021349b589b01c71d47239.pdf
2017-12-01T11:23:20
2019-12-10T11:23:20
49
59
10.22072/wala.2018.53432.1093
Linear transformation
Haar wavelets matrix
Eigenvalues and vectors
Siddu
Shiralasetti
shiralashettisc@gmail.com
true
1
Pavate nagar
Pavate nagar
Pavate nagar
LEAD_AUTHOR
Kumbinarasaiah
S
kumbinarasaiah@gmail.com
true
2
Pavate nagar
Pavate nagar
Pavate nagar
AUTHOR
[1] J. Astola and L. Yaroslavsky, Advances in Signal Transforms:Theory and Applications, Hindawi Publishing Corporation, 2007.
1
[2] P. Chang and P. Piau, Haar wavelet matrices designation in numerical solution of ordinary differential equations, Int. J. Appl. Math., 38 (2008), 3-11.
2
[3] C.F. Chen and C.H. Hsiao, Haar wavelet method for solving lumped and distributed-parameter systems, IEE Proc., Control Theory Appl., 144 (1997), 87-94.
3
[4] C. Capilla, Application of the haar wavelet transform to detect microseismic signal arrivals, Journal of Applied Geophysics, 59 (2006), 36-46.
4
[5] M.D. Choi, Completely positive linear maps on complex matrices, Linear Algebra Appl., 10 (1975), 285-290.
5
[6] I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992.
6
[7] J. Eisenfeld, Block diagonalization and eigenvalues, Linear Algebra Appl., 15 (1976), 205-215.
7
[8] G. Hariharan and K. Kannan, An overview of haar wavelet method for solving differential and integral equations, World Applied Sciences Journal, 23(12) (2013), 01-14.
8
[9] M.H. Heydaria and F.M. Maalek Ghainia, Legendre wavelets method for numerical solution of time-fractional heat equation, Wavel. Linear Algebra, 1 (2014), 19-31.
9
[10] R.D. HILL, Linear transformations which preserve hermitian matrices, Linear Algebra Appl., 6 (1973), 257-262.
10
[11] C.H. Hsiao, Haar wavelet approach to linear stiff systems, Math. Comput. Simul., 64 (2004), 561-567.
11
[12] I. Aziz and S.U. Islam, New algorithms for the numerical solution of nonlinear fredholm and volterra integral equations using Haar wavelets, J. Comput. Appl. Math., 239 (2013), 333-345.
12
[13] R. Jiwari, A Haar wavelet quasilinearization approach for numerical simulation of burger's equation, Comput. Phys. Commun., 183 (2012), 2413-2423.
13
[14] R. Jiwari, A hybrid numerical scheme for the numerical solution of the Burger's Equation, Comput. Phys. Commun., 188 (2015), 59-67.
14
[15] K. Nouri, Application of shannon wavelet for solving boundary value problems of fractional differential equations, Wavel. Linear Algebra, 1 (2014), 33-42.
15
[16] U. Lepik, Numerical solution of evolution equations by the Haar wavelet method, Appl. Math. Comput., 185 (2007), 695-704.
16
[17] U. Lepik, Numerical solution of differential equations using Haar wavelets, Math. Comput. Simul., 68 (2005), 127-143.
17
[18] U. Lepik, H. Hein, Haar Wavelets With Applications, Springer International publishing, 2014.
18
[19] M. Marcus, Linear transformations on matrices, Journal of research of the notional bureau of standards-B. Mathematical sciences, 75B (1971), 107-113.
19
[20] J. K. Merikoski, P.H. George and S.H. Wolkowicz, Bounds for ratios of eigenvalues using traces, Linear Algebra Appl., 55 (1983), 105-124.
20
[21] A. Mohammed, M. Balarabe and A.T. Imam, Rhotrix linear transformation, Advances in Linear Algebra and Matrix Theory, 2 (2012), 43-47.
21
[22] R.K. Mallik, The inverse of a tridiagonal matrix, Linear Algebra Appl., 325 (2001), 109-139.
22
[23] U. Saeed and M. Rehman, Haar wavelet quasilinearization technique for fractional nonlinear differential equations, Appl. Math. Comput., 220 (2013), 630-648.
23
[24] S.C. Shiralashetti and A.B. Deshi, An effective Haar wavelet collocation method for the numerical solution of multiterm fractional differential equation, Nonlinear Dyn., 83 (2016), 293-303.
24
[25] S.C. Shiralashetti, A.B. Deshi and P.B. Mutalik Desai, Haar wavelet collocation method for the numerical solution of singular initial value problems, Ain Shams Engineering Journal, 7 (2016), 663-670.
25
[26] S.C. Shiralashetti, L.M. Angadi, A.B. Deshi and M.H. Kantli, Haar wavelet method for the numerical solution of Klein-Gordan equations, Asian-Eur. J. Math., 9(1), (2016) 1-14.
26
[27] S.C. Shiralashetti, M.H. Kantli and A.B. Deshi, Haar wavelet based numerical solution of nonlinear differential equations arising in fluid dynamics, International Journal of Computational Materials Science and Engineering, 5(2) (2016), 1-13.
27
[28] S.C. Shiralashetti, L.M. Angadi, A.B. Deshi and M.H. Kantli, Haar wavelet method for the numerical solution of Benjamin-Bona-Mahony equations, Journal of Information and Computing Sciences, 11(2) (2016), 136-145.
28
[29] S.C. Shiralashetti, L.M. Angadi, M.H. Kantli and A.B. Deshi, Numerical solution of parabolic partial differential equations using adaptive gird Haar wavelet collocation method, Asian-Eur. J. Math., 10(1) (2017), 1-11.
29
[30] S.C. Shiralashetti, A.B. Deshi, S.S. Naregal and B. Veeresh, Wavelet series solutions of the nonlinear emden-flower type equations, International Journal of Scientific and Innovative Mathematical Research, 3(2) (2015), 558-567.
30
[31] S.C. Shiralashetti, P.B. Mutalik Desai and A. B. Deshi, A comparative study of finite element method and Haar wavelet collocation method for the numerical solution of nonlinear ordinary differential equations, International Journal of Modern Mathematical Sciences, 13(3) (2015), 228-250.
31
[32] S.U. Islam, I. Aziz, A. Fhaid and A. Shah, A numerical assessment of parabolic partial differential equations using Haar and legendre wavelets, Appl. Math. Modelling, 37 (2013), 9455-9481.
32
[33] S.U. Islam, I. Aziz, and A.S. Al-Fhaid, An improved method based on Haar wavelets for numerical solution of nonlinear integral and Integro-differential equations of first and higher orders, J. Comput. Appl. Math., 260 (2014), 449-469.
33
[34] G. Strang, Linear Algebra and Its Applications, Cengage Learning, (2005).
34
ORIGINAL_ARTICLE
Projection Inequalities and Their Linear Preservers
This paper introduces an inequality on vectors in $\mathbb{R}^n$ which compares vectors in $\mathbb{R}^n$ based on the $p$-norm of their projections on $\mathbb{R}^k$ ($k\leq n$). For $p>0$, we say $x$ is $d$-projectionally less than or equal to $y$ with respect to $p$-norm if $\sum_{i=1}^k\vert x_i\vert^p$ is less than or equal to $ \sum_{i=1}^k\vert y_i\vert^p$, for every $d\leq k\leq n$. For a relation $\sim$ on a set $X$, we say a map $f:X \rightarrow X$ is a preserver of that relation, if $x\sim y$ implies $f(x)\sim f(y)$, for every $x,y\in X$. All the linear maps that preserve $d$-projectional equality and inequality are characterized in this paper.
http://wala.vru.ac.ir/article_29391_0c3c85a7a89bc6f8ac60bfcc89b198b0.pdf
2017-12-01T11:23:20
2019-12-10T11:23:20
61
67
10.22072/wala.2017.63024.1115
projectional inequality
Linear preserver
inequality of vectors
Mina
Jamshidi
m.jamshidi@kgut.ac.ir
true
1
Graduate University of Advanced Technology, Kerman, Iran.
Graduate University of Advanced Technology, Kerman, Iran.
Graduate University of Advanced Technology, Kerman, Iran.
LEAD_AUTHOR
Farzad
Fatehi
f.fatehi@sussex.ac.uk
true
2
University of Sussex, Brighton, United Kingdom.
University of Sussex, Brighton, United Kingdom.
University of Sussex, Brighton, United Kingdom.
AUTHOR
[1] T. Ando, Majorization, doubly stochastic matrices and comparison of eigenvalues, Linear Algebra Appl., 118 (1989), 163-248.
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[2] A. Armandnejad, S. Mohtashami and M. Jamshidi, On linear preservers of g-tridiagonal majorization on R^n, Linear Algebra Appl., 459 (2014), 145-153.
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[3] A. Armandnejad and M. Jamshidi, Multiplicative isomorphisma at invertible matrices, Miskolc Math. Notes, 15(2) (2014), 287-292.
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[4] G. Bennet, Majorization versus power majorization, Anal. Math., 12(4) (1986), 283-286.
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[5] A. Armandnejad and A. Salemi, The structure of linear preservers of gs-majorization, Bull. Iran. Math. Soc., 32(2) (2006), 31-42.
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[6] G. Dahl, Matrix majorization, Linear Algebra Appl., 288 (1999), 53-73.
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[7] A.W. Marshall and Ingram Olkin, Inequalities: Theory of Majorization and Its Applications, Academic Press, 1979.
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