28 research outputs found
On a new generalized inverse for matrices of an arbitrary index
No full text[EN] The purpose of this paper is to introduce a new generalized inverse, called DMP inverse, associated with a square complex matrix using its Drazin and Moore-Penrose inverses. DMP inverse extends the notion of core inverse, introduced by Baksalary and Trenkler for matrices of index at most 1 in (Baksalary and Trenkler (2010) [1]) to matrices of an arbitrary index. DMP inverses are analyzed from both algebraic as well as geometrical approaches establishing the equivalence between them. (C) 2013 Elsevier Inc. All rights reserved.This author was partially supported by Ministry of Education of Spain (Grant DGI MTM2010-18228).Malik, SB.; Thome, N. (2014). On a new generalized inverse for matrices of an arbitrary index. Applied Mathematics and Computation. 226:575-580. doi:10.1016/j.amc.2013.10.060S57558022
Notes on an Endogenous Growth Model with two Capital Stocks II: The Stochastic Case
No full textThis paper extends the class of stochastic AK growth models with a closed-form solution to the case where there are two capital goods in the model. To be precise, we consider the Uzawa-Lucas model of endogenous growth with human and physical capital. The extension holds, even if an external effect in the use of human capital in goods production occurs. Using the “guess and verify” method, we determine the value function of the social planner in the centralized economy and the value function of the representative agent in the decentralized case. We show that the introduction of income taxes on wages and of a subsidy on physical capital earnings is able to help the decentralized economy in reaching the social optimum, while keeping the policy maker’s budget balanced. Then the time series implications of the model’s solution are derived. In Appendix to the paper the uniqueness of the value functions is proved by using an alternative method.closed-form solution, value function, saddle path stability, endogenous growth
VAR Modeling for Dynamic Loadings Driving Volatility Strings
No full textThe implied volatility of an option as a function of strike price and time to maturity forms a volatility surface. Traders price according to the dynamics of this high dimensional surface. Recent developments that employ semiparametric models approximate the implied volatility surface (IVS) in a finite dimensional function space, allowing for a low dimensional factor representation of these dynamics. This paper presents an investigation into the stochastic properties of the factor loading time series using the vector autoregressive (VAR) framework and analyzes the dynamic relationship of these factors with economic indicators. Copyright The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected]., Oxford University Press.
Further properties on the core partial order and other matrix partial orders
No full textThis paper carries further the study of core partial order initiated by Baksalary and Trenkler [Core inverse of matrices, Linear Multilinear Algebra. 2010;58:681-697]. We have extensively studied the core partial order, and some new characterizations are obtained in this paper. In addition, simple expressions for the already known characterizations of the minus, the star (and one-sided star), the sharp (and one-sided sharp) and the diamond partial orders are also obtained by using a Hartwig-Spindelbck decomposition.This author was partially supported by Ministry of Education of Spain [grant number DGI MTM2010-18228] and by Universidad Nacional de La Pampa, Argentina, Facultad de Ingenieria [grant number Resol. No 049/11].Malik, SB.; Rueda, LC.; Thome, N. (2014). Further properties on the core partial order and other matrix partial orders. Linear and Multilinear Algebra. 62(12):1629-1648. https://doi.org/10.1080/03081087.2013.839676S162916486212Mitra, S. K., & Bhimasankaram, P. (2010). MATRIX PARTIAL ORDERS, SHORTED OPERATORS AND APPLICATIONS. SERIES IN ALGEBRA. doi:10.1142/9789812838452Baksalary, J. K., & Hauke, J. (1990). A further algebraic version of Cochran’s theorem and matrix partial orderings. Linear Algebra and its Applications, 127, 157-169. doi:10.1016/0024-3795(90)90341-9Baksalary, O. M., & Trenkler, G. (2010). Core inverse of matrices. Linear and Multilinear Algebra, 58(6), 681-697. doi:10.1080/03081080902778222Baksalary, J. K., Baksalary, O. M., & Liu, X. (2003). Further properties of the star, left-star, right-star, and minus partial orderings. Linear Algebra and its Applications, 375, 83-94. doi:10.1016/s0024-3795(03)00609-8Groβ, J., Hauke, J., & Markiewicz, A. (1999). Partial orderings, preorderings, and the polar decomposition of matrices. Linear Algebra and its Applications, 289(1-3), 161-168. doi:10.1016/s0024-3795(98)10108-8Mosić, D., & Djordjević, D. S. (2012). Reverse order law for the group inverse in rings. Applied Mathematics and Computation, 219(5), 2526-2534. doi:10.1016/j.amc.2012.08.088Patrício, P., & Costa, A. (2009). On the Drazin index of regular elements. Open Mathematics, 7(2). doi:10.2478/s11533-009-0015-6Rakić, D. S., & Djordjević, D. S. (2012). Space pre-order and minus partial order for operators on Banach spaces. Aequationes mathematicae, 85(3), 429-448. doi:10.1007/s00010-012-0133-2Tošić, M., & Cvetković-Ilić, D. S. (2012). Invertibility of a linear combination of two matrices and partial orderings. Applied Mathematics and Computation, 218(9), 4651-4657. doi:10.1016/j.amc.2011.10.052Hartwig, R. E., & Spindelböck, K. (1983). Matrices for whichA∗andA†commute. Linear and Multilinear Algebra, 14(3), 241-256. doi:10.1080/03081088308817561Baksalary, O. M., Styan, G. P. H., & Trenkler, G. (2009). On a matrix decomposition of Hartwig and Spindelböck. Linear Algebra and its Applications, 430(10), 2798-2812. doi:10.1016/j.laa.2009.01.015Mielniczuk, J. (2011). Note on the core matrix partial ordering. Discussiones Mathematicae Probability and Statistics, 31(1-2), 71. doi:10.7151/dmps.1134Meyer, C. (2000). Matrix Analysis and Applied Linear Algebra. doi:10.1137/1.978089871951
Equalities of ideals associated with two projections in rings with involution
No full textIn this article we study various right ideals associated with two projections (self-adjoint idempotents) in a ring with involution. Results of O.M. Baksalary, G. Trenkler, R. Piziak, P.L. Odell and R. Hahn about orthogonal projectors (complex matrices which are Hermitian and idempotent) are considered in the setting of rings with involution. New proofs based on algebraic arguments, rather than finite-dimensional and rank theory, are given.The authors thank the anonymous reviewer for his\her useful suggestions, which helped to improve the original version of this article. The second author is supported by Grant No. 174007 of the Ministry of Science, Technology and Development, Republic of Serbia.Benítez López, J.; Cvetkovic-Ilic, D. (2013). Equalities of ideals associated with two projections in rings with involution. Linear and Multilinear Algebra. 61(10):1419-1435. doi:10.1080/03081087.2012.743026S141914356110Baksalary, O. M., & Trenkler, G. (2009). Column space equalities for orthogonal projectors. Applied Mathematics and Computation, 212(2), 519-529. doi:10.1016/j.amc.2009.02.042Benítez, J. (2008). Moore–Penrose inverses and commuting elements of C∗-algebras. Journal of Mathematical Analysis and Applications, 345(2), 766-770. doi:10.1016/j.jmaa.2008.04.062Green, J. A. (1951). On the Structure of Semigroups. The Annals of Mathematics, 54(1), 163. doi:10.2307/1969317Harte, R. (1992). On generalized inverses in C*-algebras. Studia Mathematica, 103(1), 71-77. doi:10.4064/sm-103-1-71-77Harte, R. (1993). Generalized inverses in C*-algebras II. Studia Mathematica, 106(2), 129-138. doi:10.4064/sm-106-2-129-138Koliha, J. J. (2000). Elements of C*-algebras commuting with their Moore-Penrose inverse. Studia Mathematica, 139(1), 81-90. doi:10.4064/sm-139-1-81-90Koliha, J. J., Cvetković-Ilić, D., & Deng, C. (2012). Generalized Drazin invertibility of combinations of idempotents. Linear Algebra and its Applications, 437(9), 2317-2324. doi:10.1016/j.laa.2012.06.005Koliha, J. J., & Rakočević, V. (2003). Invertibility of the Difference of Idempotents. Linear and Multilinear Algebra, 51(1), 97-110. doi:10.1080/030810802100023499Mary, X. (2011). On generalized inverses and Green’s relations. Linear Algebra and its Applications, 434(8), 1836-1844. doi:10.1016/j.laa.2010.11.045Von Neumann, J. (1936). On Regular Rings. Proceedings of the National Academy of Sciences, 22(12), 707-713. doi:10.1073/pnas.22.12.707Patrı́cio, P., & Puystjens, R. (2004). Drazin–Moore–Penrose invertibility in rings. Linear Algebra and its Applications, 389, 159-173. doi:10.1016/j.laa.2004.04.006Piziak, R., Odell, P. L., & Hahn, R. (1999). Constructing projections on sums and intersections. Computers & Mathematics with Applications, 37(1), 67-74. doi:10.1016/s0898-1221(98)00242-
Generalized core inverses of matrices
No full text[EN] n this paper, we introduce two new generalized inverses of matrices, namely, the -core inverse and the (j, m)-core inverse. The -core inverse of a complex matrix extends the notions of the core inverse defined by Baksalary and Trenkler [1] and the core-EP inverse defined by Manjunatha Prasad and Mohana [10]. The (j, m)-core inverse of a complex matrix extends the notions of the core inverse and the DMP-inverse defined by Malik and Thome [9]. Moreover, the formulae and properties of these two new concepts are investigated by using matrix decompositions and matrix powers.This research is supported by the National Natural Science Foundation of China (NO. 11771076 and No. 11471186). The first author is grateful to China Scholarship Council for giving him a purse for his further study in Universitat Politecnica de Valencia, Spain.Xu, S.; Chen, J.; Benítez López, J.; Wang, D. (2019). Generalized core inverses of matrices. Miskolc Mathematical Notes (Online). 20(1):565-584. https://doi.org/10.18514/MMN.2019.2594S56558420
New matrix partial order based spectrally orthogonal matrix decomposition
No full text[EN] We investigate partial orders on the set of complex square matrices and introduce a new order relation based on spectrally orthogonal matrix decompositions. We also establish the relation of this concept with the known orders.The research of the first author was supported by the Grants [grant number RFBR-15-01-01132], [grant number MD-962.2014.1]. The second and third authors have been partially supported by Ministerio de Economia y Competitividad from Spain, DGI [grant number MTM2013-43678-P].Guterman, A.; Herrero Debón, A.; Thome, N. (2016). New matrix partial order based spectrally orthogonal matrix decomposition. Linear and Multilinear Algebra. 64(3):362-374. https://doi.org/10.1080/03081087.2015.1041365S362374643Meyer, C. (2000). Matrix Analysis and Applied Linear Algebra. doi:10.1137/1.9780898719512Mitra, S. K., & Bhimasankaram, P. (2010). MATRIX PARTIAL ORDERS, SHORTED OPERATORS AND APPLICATIONS. SERIES IN ALGEBRA. doi:10.1142/9789812838452Baksalary, O. M., & Trenkler, G. (2010). Core inverse of matrices. Linear and Multilinear Algebra, 58(6), 681-697. doi:10.1080/03081080902778222Baksalary, O. M., & Trenkler, G. (2014). On a generalized core inverse. Applied Mathematics and Computation, 236, 450-457. doi:10.1016/j.amc.2014.03.048Hernández, A., Lattanzi, M., Thome, N., & Urquiza, F. (2012). The star partial order and the eigenprojection at 0 on EP matrices. Applied Mathematics and Computation, 218(21), 10669-10678. doi:10.1016/j.amc.2012.04.034Hernández, A., Lattanzi, M., & Thome, N. (2013). On a partial order defined by the weighted Moore–Penrose inverse. Applied Mathematics and Computation, 219(14), 7310-7318. doi:10.1016/j.amc.2013.02.010Hernández, A., Lattanzi, M., & Thome, N. (2015). Weighted binary relations involving the Drazin inverse. Applied Mathematics and Computation, 253, 215-223. doi:10.1016/j.amc.2014.12.102Lebtahi, L., Patrício, P., & Thome, N. (2013). The diamond partial order in rings. Linear and Multilinear Algebra, 62(3), 386-395. doi:10.1080/03081087.2013.779272Malik, S. B., Rueda, L., & Thome, N. (2013). Further properties on the core partial order and other matrix partial orders. Linear and Multilinear Algebra, 62(12), 1629-1648. doi:10.1080/03081087.2013.839676Rakić, D. S., & Djordjević, D. S. (2012). Space pre-order and minus partial order for operators on Banach spaces. Aequationes mathematicae, 85(3), 429-448. doi:10.1007/s00010-012-0133-2Nambooripad, K. S. S. (1980). The natural partial order on a regular semigroup. Proceedings of the Edinburgh Mathematical Society, 23(3), 249-260. doi:10.1017/s0013091500003801Mitra, S. K. (1987). On group inverses and the sharp order. Linear Algebra and its Applications, 92, 17-37. doi:10.1016/0024-3795(87)90248-
Inequalities and equalities for l = 2 (Sylvester), l = 3 (Frobenius), and l > 3 matrices
No full textThis paper gives simple proofs of Sylvester (` = 2) and Frobenius
(` = 3) inequalities. Moreover, a new sufficient condition for the
equality of the Frobenius inequality is provided. In addition, an extension
for ` > 3 matrices and an application to generalized inverses
are provided.This paper has been partially supported by Ministerio de Economia y Competitividad (Grant DGI MTM2013-43678P and Red de Excelencia MTM2015-68805-REDT). The author thanks the referees for their valuable suggestions.Thome, N. (2016). Inequalities and equalities for l = 2 (Sylvester), l = 3 (Frobenius), and l > 3 matrices. Aequationes Mathematicae. 90(5):951-960. https://doi.org/10.1007/s00010-016-0412-4S951960905Baksalary J.K., Kala R.: The matrix equation AX − YB = C. Linear Algebra Appl. 25, 41–43 (1979)Baksalary O.M., Trenkler G.: On k-potent matrices.. Electr. J. Linear Algebra 26, 446–470 (2013)Ben-Israel, A., Greville T.N.E.: Generalized Inverses: Theory and Applications, 2nd edn. Wiley, New York (2003)Marsaglia G., Styan G.P.H.: Equalities and inequalities for ranks of matrices. Linear Multilinear Algebra 2, 269–292 (1974)Mosić D., Djordjević D.S.: Condition number of the W-weighted Drazin inverse. Appl. Math. Computat. 203(1), 308–318 (2008)Puntanen S., Styan G.P.H., Isotalo J.: Matrix Tricks for Linear Statistical Models. Springer, Berlin (2011)Tian Y., Styan G.P.H.: A new rank formula for idempotent matrices with applications. Comment. Math. Univ. Carolinae 43(2), 379–384 (2002)Wang G., Wei Y., Qiao S.: Generalized Inverses: Theory and Computations. Science Press, Beijing (2004
A weak group inverse for rectangular matrices
No full text[EN] In this paper, we extend the notion of weak group inverse to rectangular matrices (called WweightedWGinverse) by using the weighted core EP inverse recently investigated. This new generalized inverse also generalizes the well-known weighted group inverse given by Cline and Greville. In addition, we give several representations of the W-weighted WG inverse, and derive some characterizations and properties.First author was partially supported by UNRC (Grant PPI 18/C472) and CONICET (Grant PIP 112-201501-00433CO). Third author was partially supported by Ministerio de Economia, Industria y Competitividad of Spain (Grants DGI MTM2013-43678-P and Red de Excelencia MTM2017-90682-REDT).Ferreyra, DE.; Orquera, V.; Thome, N. (2019). A weak group inverse for rectangular matrices. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 113(4):3727-3740. https://doi.org/10.1007/s13398-019-00674-9S372737401134Ben-Israel, A., Greville, T.N.E.: Generalized Inverses: Theory and Applications, 2nd edn. Springer, New York (2003)Baksalary, O.M., Trenkler, G.: Core inverse of matrices. Linear Multilinear Algebra 58, 681–697 (2010)Baksalary, O.M., Trenkler, G.: On a generalized core inverse. Appl. Math. Comput. 236, 450–457 (2014)Bajodah, A.H.: Servo-constraint generalized inverse dynamics for robot manipulator control design. Int. J. Robot. Autom. 25, (2010). https://doi.org/10.2316/Journal.206.2016.1.206-3291Campbell, S.L., Meyer Jr., C.D.: Generalized Inverses of Linear transformations. SIAM, Philadelphia (2009)Cline, R.E., Greville, T.N.E.: A Drazin inverse for rectangular matrices. Linear Algebra Appl. 29, 53–62 (1980)Dajić, A., Koliha, J.J.: The weighted g-Drazin inverse for operators. J. Aust. Math. Soc. 2, 163–181 (2007)Doty, K.L., Melchiorri, C., Bonivento, C.: A theory of generalized inverses applied to robotics. Int. J. Rob. Res. 12, 1–19 (1993)Drazin, M.P.: Pseudo-inverses in associate rings and semirings. Am. Math. Mon. 65, 506–514 (1958)Ferreyra, D.E., Levis, F.E., Thome, N.: Revisiting of the core EP inverse and its extension to rectangular matrices. Quaest. Math. 41, 265–281 (2018)Ferreyra, D.E., Levis, F.E., Thome, N.: Maximal classes of matrices determining generalized inverses. Appl. Math. Comput. 333, 42–52 (2018)Gigola, S., Lebtahi, L., Thome, N.: The inverse eigenvalue problem for a Hermitian reflexive matrix and the optimization problem. J. Comput. Appl. Math. 291, 449–457 (2016)Hartwig, R.E.: The weighted ∗ -core-nilpotent decomposition. Linear Algebra Appl. 211, 101–111 (1994)Kirkland, S.J., Neumann, M.: Group inverses of M-matrices and their applications. Chapman and Hall/CRC, London (2013)Malik, S., Thome, N.: On a new generalized inverse for matrices of an arbitrary index. Appl. Math. Comput. 226, 575–580 (2014)Male s ˇ ević, B., Obradović, R., Banjac, B., Jovović, I., Makragić, M.: Application of polynomial texture mapping in process of digitalization of cultural heritage. arXiv:1312.6935 (2013). Accessed 14 June 2018Manjunatha Prasad, K., Mohana, K.S.: Core EP inverse. Linear Multilinear Algebra 62, 792–802 (2014)Mehdipour, M., Salemi, A.: On a new generalized inverse of matrices. Linear Multilinear Algebra 66, 1046–1053 (2018)Meng, L.S.: The DMP inverse for rectangular matrices. Filomat 31, 6015–6019 (2017)Mosić, D.: The CMP inverse for rectangular matrices. Aequaetiones Math. 92, 649–659 (2018)Penrose, R.: A generalized inverse for matrices. Proc. Cambrid. Philos. Soc. 51, 406–413 (1955)Soleimani, F., Stanimirović, P.S., Soleymani, F.: Some matrix iterations for computing generalized inverses and balancing chemical equations. Algorithms 8, 982–998 (2015)Xiao, G.Z., Shen, B.Z., Wu, C.K., Wong, C.S.: Some spectral techniques in coding theory. Discrete Math. 87, 181–186 (1991)Wang, H.: Core-EP decomposition and its applications. Linear Algebra Appl. 508, 289–300 (2016)Wang, H., Chen, J.: Weak group inverse. Open Math. 16, 1218–1232 (2018)Wei, Y.: A characterization for the W -weighted Drazin inverse and a Crammer rule for the W -weighted Drazin inverse solution. Appl. Math. Comput. 125, 303–310 (2002
Characterization and Evaluation of Detoxification Functions of a Nontumorigenic Immortalized Porcine Hepatocyte Cell Line (HepLiu)
No full text Primary porcine hepatocytes (PPH) are currently used in research and therapeutic applications as the biological component of extracorporeal liver assist devices to overcome the shortage of human hepatocytes. However, their finite life span and typically rapid loss of functions limit their utility. An immortalized, nontumorigenic, highly differentiated porcine hepatocyte cell line was developed in our laboratory to resolve these disadvantages. PPH were transfected with simian virus 40 (SV40) T antigen under the control of the SV40 early promoter. From the established 69 clones, 23 clones displaying hepatocyte-like morphology were screened for diazepam metabolism. One clone, HepLiu D63, has been maintained in culture for > 2 years, through more than 60 passages and 240 divisions. Albumin protein, present in early passages, was lost at later passages, but albumin transcript still was detectable in later passages. Carbamoyl phosphate synthetase, a gateway enzyme of the urea cycle, was consistently detectable in HepLiu cells. Cytokeratin 18, a characteristic marker of primary hepatocytes, was detected by both immunofluorescent staining and Western blot in HepLiu cells. Furthermore, maintenance of P450 functions in HepLiu cells was evidenced by diazepam and 7-ethoxycoumarin metabolites measured by HPLC. Phase II conjugative function was measured as acetaminophen glucuronidation. P450 dealkylase was demonstrated microscopically by the conversion of a nonfluorescent substrate to a fluorescent product. Both Northern blot analysis and immunofluorescent staining showed SV40 T antigen expression in the nuclei of HepLiu cells. No tumor formation occurred when HepLiu cells were injected into severe combined immunodeficient (SCID) mice nor was the TA1 (a tumor marker) mRNA expressed, even in later passages. This immortalized, nontumorigenic, highly functional cell line may provide a valuable tool for drug/toxicological studies, liver biologic regulation studies, and artificial liver support systems. </jats:p
