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 Hugo Leiva Advances in Linear Algebra & Matrix Theory (ALAMT) , 2015, DOI: 10.4236/alamt.2015.54016 Abstract: In this paper, we find two formulas for the solutions of the following linear equation  , where is a real matrix. This system has been well studied since the 1970s. It is known and simple proven that there is a solution for all if, and only if, the rows of A are linearly independent, and the minimum norm solution is given by the Moore-Penrose inverse formula, which is often denoted by ; in this case, this solution is given by . Using this formula, Cramer’s Rule and Burgstahler’s Theorem (Theorem 2), we prove the following representation for this solution  , where are the row vectors of the matrix A. To the best of our knowledge and looking in to many Linear Algebra books, there is not formula for this solution depending on determinants. Of course, this formula coincides with the one given by Cramer’s Rule when .
 Applied Mathematics (AM) , 2010, DOI: 10.4236/am.2010.14033 Abstract: In this paper we characterize a broad class of semilinear surjective operators given by the following formula where Z are Hilbert spaces, and is a suitable nonlinear function. First, we give a necessary and sufficient condition for the linear operator to be surjective. Second, we prove the following statement: If and is a Lipschitz function with a Lipschitz constant small enough, then and for all the equation admits the following solution .We use these results to prove the exact controllability of the following semilinear evolution equation , , where , are Hilbert spaces, is the infinitesimal generator of strongly continuous semigroup in the control function belong to and is a suitable function. As a particular case we consider the semilinear damped wave equation, the model of vibrating plate equation, the integrodifferential wave equation with Delay, etc.
 Applied Mathematics (AM) , 2016, DOI: 10.4236/am.2016.715147 Abstract: For many control systems in real life, impulses and delays are intrinsic phenomena that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbations of a system do not destroy its controllability. There are many practical examples of impulsive control systems with delays, such as a chemical reactor system, a financial system with two state variables, the amount of money in a market and the savings rate of a central bank, and the growth of a population diffusing throughout its habitat modeled by a reaction-diffusion equation. In this paper we apply the Rothe’s Fixed Point Theorem to prove the interior approximate controllability of the following Benjamin Bona-Mohany(BBM) type equation with impulses and delay where and are constants, Ω is a domain in , ω is an open non-empty subset of Ω , denotes the characteristic function of the set ω , the distributed control , are continuous functions and the nonlinear functions are smooth enough functions satisfying some additional conditions.
 Advances in Linear Algebra & Matrix Theory (ALAMT) , 2018, DOI: 10.4236/alamt.2018.81002 Abstract: In this paper, we study the existence of solutions for the semilinear equation , where A is a , , and is a nonlinear continuous function. Assuming that the Moore-Penrose inverse AT(AAT)-1？exists (A denotes the transposed matrix of A) which is true whenever the determinant of the matrix AAT is different than zero, and the following condition on the nonlinear term satisfied . We prove that the semilinear equation has solutions for all . Moreover, these solutions can be found from the following fixed point relation .
 Gonzalo Leiva Bifurcaciones , 2005, Abstract: Gonzalo Leiva comenta, revisa y documenta el trabajo visual de Samuel Shats titulado 'Tierra Baldia' desde una perspectiva urbana.
 Carlos Leiva Tecnología en Marcha , 2005, Abstract: El presente artículo se ocupa de describir y comparar el aprendizaje y las teorías del conocimiento conductivas y cognoscitivas. La rese a histórica se inicia con los postulados de Platón y Aristóteles. Los temas tratados en este artículo son: el conductismo como una expresión de la teoría asociacionista, cuyo progenitor es precisamente A ristóteles, luego se analiza el procesamiento de información el cual es la corriente que desplazó al conductismo y que actualmente se mantiene a la vanguardia. Después se presenta la corriente organicista que enfoca la construcción activa de los conceptos por parte del sujeto y finalmente se presentan las conclusiones del artículo.