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Universidad Católica del Norte Apunte para un curso de Cálculo 1 (Primera Versión Experimental
Apunte para un curso de Cálculo 1 -Universidad Católica del Norte Programa de Aceleración Extracurricular -Enlace Escolar UCN 2014 a, respectivamente, entonces se debe asumir que tales objetos son diferentes, a menos que se diga explicitamente lo contrario. Debe entenderse que como letras, A y a son lo mismo, pero no como símbolos matemáticos. 7. El estudiante debe comprender que la mayor responsabilidad del éxito, su propio éxito, recae en él mismo. En tal sentido, es necesario que busque lograr su independencia en el estudio, esto es, debe tratar de no depender del profesor o el ayudante y ser capaz de usar bibliografía sin mayores problemas y jamás conformarse con lo estudiado del cuaderno o las guías de ejercicios dadas en la asignatura.
Diversity complex of plant species spread in Nasarawa State, Nigeria
2016
This research was carried out to assess the plant species diversity in Nasarawa State, Nigeria with a view to obtain an accurate database and inventory of the naturally occurring plant species in the state for reference and research purposes. This preliminary report covers a total of nine local government areas in the state. The work involved intensive survey and visits to the sample sites for this exercise. The diversity status of each plant and the distribution across the state were also determined using standard method. A total of number of 244 plant species belonging to 57 plant families were identified out of which the families, Asteraceae, Poaceae, Combretaceae, Euphorbiaceae, Moraceae and Papilionaceae were the most highly distributed across the entire study area. There was great extent of diversity in the distribution of plants across all the areas sampled with the highest in Wamba LGA. The most predominant food crop across the state was Sorgum spp. followed by Sesame indica...
According to the curricular documents, learning Mathematics in school aims to raise awareness of the nature of Mathematics as a problem-solving activity, based on a body of knowledge and procedures, but also as a dynamic discipline, closely linked to society through its relevance in everyday life and its role. in Natural Sciences, in Technologies and in Social Sciences. The major meaning of the current references in teachinglearning Mathematics is shifting the emphasis from teaching knowledge that has essentially remained the same from the old programs, on capacity building, where "using different strategies in solving problems" occupies a special place. This paper falls into this context; continuing the steps begun some time ago, a way to calculate the limits for four categories of strings is presented here, with the particularities and related examples.
1 - New Set Theory - Proof of the General Continuum Hypothesis
PLEASE DOWNLOAD PDF TO GET HYPERLINKS ON THE DOCUMENT. PLEASE CLICK ON "FOLLOW" TO GET THE LAST UPDATED VERSION. If there exists no bijection between two sets X and Y, either there exist no surjection from X to Y or there exist no injection from X to Y. This simple statement give rise to the bijectiveness relation, the injectiveness relation and the surjectiveness relation called ejectiveness set relations. X is either injective or bijective or surjective to Y. We write it as follows:(X →<Y):(X >↔<Y):(X >→ Y) = true A subpart of X is said to be a subjective subpart if it is injective to X and said otherwise to be an objective subpart if it is bijective to X. PWR&SUB«X» (PWR&OBJ«X») denotes the set of all the subjective (respectively objective) subparts of X. The ejectiveness set relations lead to the creation of two set operators: the ejectiveness minimum and the ejectiveness maximum denoted ┴ and ┬. We prove, once one set is infinite and the other at least of cardinal >1 , first XxY >↔< X ∪ Y >↔< X ┬ Y and second X → Y >↔< PWR«X» ┬ Y The ejectiveness set relations give rise also to a (natural) metric measuring the infiniteness of infinite sets, metric called in this paper the ordinal (and which does not correspond to the notion of ordinal used so far in the literature). When the ordinal becomes infinite, finite natural sequences can be further used to measure and compare the infiniteness of all the infinite sets of infinite ordinal. These natural sequences are called the magnitude of a given set. When the magnitude becomes infinite, finite 2-dimensional matrices, and thereafter k-dimensional matrices can be further used to measure and compare the infiniteness of all the infinite sets of infinite magniitude.
Optimal disturbance rejection control for nonlinear impulsive dynamical systems
Nonlinear Analysis: Theory, Methods & Applications, 2005
In this paper, we develop an optimality-based framework for addressing the problem of nonlinearnonquadratic hybrid control for disturbance rejection of nonlinear impulsive dynamical systems with bounded exogenous disturbances. Specifically, we transform a given nonlinear-nonquadratic hybrid performance criterion to account for system disturbances. As a consequence, the disturbance rejection problem is translated into an optimal hybrid control problem. Furthermore, the resulting optimal hybrid control law is shown to render the closed-loop nonlinear input-output map dissipative with respect to general supply rates. In addition, the Lyapunov function guaranteeing closed-loop stability is shown to be a solution to a steady-state hybrid Hamilton-Jacobi-Isaacs equation and thus guaranteeing optimality.
Irreversible thermodynamics in multiscale stochastic dynamical systems
Physical Review E, 2011
This work extends the results of the recently developed theory of a rather complete thermodynamic formalism for discrete-state, continuous-time Markov processes with and without detailed balance. We aim at investigating the question that whether and how the thermodynamic structure is invariant in a multiscale stochastic system. That is, whether the relations between thermodynamic functions of state and process variables remain unchanged when the system is viewed at different time scales and resolutions. Our results show that the dynamics on a fast time scale contribute an entropic term to the "internal energy function", u S (x), for the slow dynamics. Based on the conditional free energy u S (x), one can then treat the slow dynamics as if the fast dynamics is nonexistent. Furthermore, we show that the free energy, which characterizes the spontaneous organization in a system without detailed balance, is invariant with or without the fast dynamics: The fast dynamics is assumed to reach stationarity instantaneously on the slow time scale; they have no effect on the system's free energy. The same can not be said for the entropy and the internal energy, both of which contain the same contribution from the fast dynamics. We also investigate the consequences of time-scale separation in connection to the concepts of quasi-stationaryty and steady-adiabaticity introduced in the phenomenological steady-state thermodynamics.
Journal of Applied Probability, 2009
This work is concerned with the existence of an optimal control strategy for the long-run average continuous control problem of piecewise-deterministic Markov processes (PDMPs). In Costa and Dufour (2008), sufficient conditions were derived to ensure the existence of an optimal control by using the vanishing discount approach. These conditions were mainly expressed in terms of the relative difference of the α-discount value functions. The main goal of this paper is to derive tractable conditions directly related to the primitive data of the PDMP to ensure the existence of an optimal control. The present work can be seen as a continuation of the results derived in Costa and Dufour (2008). Our main assumptions are written in terms of some integro-differential inequalities related to the so-called expected growth condition, and geometric convergence of the post-jump location kernel associated to the PDMP. An example based on the capacity expansion problem is presented, illustrating the...