Computer Algebra Systems (CAS), a powerful mathematical software currently available on hand held calculators, is becoming increasingly available to assist secondary students learn school mathematics. This study investigates how two teachers taught introductory differential calculus to their Year 11 classes using multiple representations in a CAS-supported curriculum. This thesis aims to explore the impact of the teaching on students’ understanding of the concept of derivative. / Understanding of the concept of derivative was gauged using an innovative Differentiation Competency Framework that was developed to describe understanding of the concept of derivative. It consists of eighteen competencies for formulation and interpretation of derivatives with, and without, translation between different representations. It clarified the objectives of the curriculum, purpose for using particular CAS activities, and also guided the construction of individual test items on the Differentiation Competency Test that enabled individual and class learning about the concept of derivative to be identified. / The Framework also helped identify each teacher’s privileging characteristics and facilitated analysis of the learning in relation to the teaching. / This study found that using multiple representations was important in developing understanding of the concept of derivative but that the graphical and the symbolic representations were the most useful and important to emphasize and link. / Analysis of the teaching actions showed that the teachers used CAS in ways that were consistent with their teaching approach and preferred use of representations and that a conceptual teaching method and student-centred style supported understanding of the concept of derivative. / Teaching is directly linked to learning and each class developed a different understanding of the concept of derivative that related to the combined effect of their teacher’s privileging characteristics: calculus content, teaching approach, and use of CAS. This study also shows that if a CAS-supported curriculum is to be successfully implemented, it needs to acquire institutional status including a corresponding change in assessment to legitimize new teaching practices.

Zugl.: Frankfurt (Main), Univ., Diplomarbeit, 2006

Thesis (PhD)--Macquarie University, Division of Economic and Financial Studies, Dept. of Statistics, 2008. / Bibliography: p. 73-77.

Univ., Diss.--Frankfurt (Main), 2003. / Literaturverz. S. [105] - 107.

Made available in DSpace on 2014-06-11T19:30:32Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-08-21Bitstream added on 2014-06-13T21:01:21Z : No. of bitstreams: 1 faria_fa_dr_ilha.pdf: 872755 bytes, checksum: d14b68025a60624f43ac43ae6b5e757e (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Já é conhecido da teoria de controle clássico, que a realimentação derivativa pode ser útil e em alguns casos, essencial para a obtenção do desempenho desejado. Além disso, existem problemas práticos em que a derivada dos estados é mais fácil de se obter do que os sinais dos estados. Por exemplo, nos seguintes problemas: controle de vibrações de sistemas mecânicos, sistemas de suspensão de automóveis, controle de vibrações em pontes suspensas e controle de vibrações na aterrissagem de aviões. O principal sensor usado nesses problemas é o acelerômetro. A partir do sinal do acelerômetro é possível obter com precisão a velocidade, mas não o deslocamento. Definindo o deslocamento e a velocidade como as variáveis de estado, então apenas os sinais da derivada dos estados estão disponíveis para a realimentação. A realimentação derivativa foi usada recentemente no projeto de sistemas lineares. Os procedimentos consideram o problema de alocação de pólos (ABDELAZIZ; VALÁŠEK, 2004, 2005) e o projeto de reguladores lineares quadráticos (DUAN; NI; KO, 2005). Infelizmente esses resultados não podem ser usados em sistemas incertos ou sujeitos à falhas estruturais. Para resolver esse caso, projetos baseados em DesigualdadesMatriciais Lineares (LMIs) foram propostos em (FARIA, 2005; ASSUNÇÃO et al., 2007e; FARIA; ASSUNÇÃO; TEIXEIRA, 2009a; CARDIM et al., 2008; FARIA et al., 2009c). LMIs podem ser facilmente resolvidas com softwares de otimização, tais como os pacotes “LMI control toolbox” e “SeDuMi” do MATLAB. Este trabalho aborda o projeto de controladores para sistemas descritores usando a realimentação da derivada dos estados. São apresentadas condições necessárias e suficientes baseadas em LMIs para a estabilidade assintótica de sistemas descritores. Como a estabilidade nem sempre é suficiente, posteriormente... / From classical control theory, it is well-known that state-derivative feedback can be very useful, and even in some cases essential to achieve a desired performance. Moreover, there exist some practical problems where the state-derivative signals are easier to obtain than the state signals. For instance, in the following applications: suppression of vibration in mechanical systems, control of car wheel suspension systems, vibration control of bridge cables and vibration control of landing gear components. The main sensor used in these problems is the accelerometer. In this case, from the signals of the accelerometers it is possible to reconstruct the velocities with a good precision but not the displacements. Defining the velocities and displacement as the state variables, then one has available for feedback the state-derivative signals. Recent researches about state-derivative feedback design for linear systems have been presented. The procedures consider, for instance, the pole placement problem (ABDELAZIZ; VALÁŠEK, 2004, 2005), and the design of a Linear Quadratic Regulator (DUAN; NI; KO, 2005). Unfortunately these results are not applied to the control of uncertain systems or systems subject to structural failures. For this case, Linear Matrix Inequalities (LMIs) based designs were recently proposed in (FARIA, 2005; ASSUNÇÃO et al., 2007e; FARIA; ASSUNÇÃO; TEIXEIRA, 2009a; CARDIM et al., 2008; FARIA et al., 2009c). LMIs can be easily solved with optimization softwares, such as the packages “LMI control toolbox” and “SeDuMi” of MATLAB. This work focuses control designs for descriptor systems using the state-derivative feedback. Necessary and sufficient LMI-based conditions for asymptotically stability of descriptor systems are presented. As the stability of a control system is insufficient to obtain a suitable performance... (Complete abstract click electronic access below)

Uliginosina B é um derivado acilfloroglucinol natural, isolado de espécies de Hypericum nativas da América do Sul. Estudos prévios demonstraram que a uliginosina B apresenta efeitos do tipo antidepressivo e antinociceptivo em baixas doses (até 15 mg/kg, i.p. ou v.o.) e, em doses elevadas (90 mg/kg, i.p.), prejudica a coordenação motora. A atividade antidepressiva depende da ativação da neurotransmissão monoaminérgica e envolve a regulação da homeostase através do balanço de Na+. A atividade antinociceptiva é mediada por receptores opioides e dopaminérgicos da família D2. O efeito atáxico depende da ativação de receptores opioides e dopaminérgicos. Os efeitos parecem ser decorrentes da sua capacidade de inibir a recaptação de monoaminas (especialmente dopamina) com consequente ativação de receptores opioides e monoaminérgicos. O objetivo deste estudo foi aprofundar o conhecimento sobre o mecanismo de ação antinociceptiva de uliginosina B, investigando o envolvimento da neurotransmissão monoaminérgica, glutamatérgica e purinérgica. O tratamento com uliginosina B aumentou a disponibilidade intersticial de dopamina e seu metabólito, ácido homovanílico (HVA), no estriado de ratos; dados que reforçam o papel da neurotransmissão dopaminérgica nos efeitos da uliginosina B. O papel das outras monoaminas e da neurotransmissão glutamatérgica foi investigado nos efeitos antinociceptivo e atáxico induzidos por uliginosina B. A ataxia (90 mg/kg, i.p.) foi completamente prevenida pelo tratamento prévio com pCPA (inibidor da síntese de serotonina) e MK-801 (antagonista do receptor glutamatérgico NMDA), mas não foi afetada pelo prétratamento com prazosina ou ioimbina (antagonistas de receptores adrenérgicos α1 e α2, respectivamente). A atividade antinociceptiva (15 e 90 mg/kg, i.p.) foi reduzida significativamente pelo pré-tratamento com pCPA e MK-801 e aumentada pelo prétratamento com prazosina e ioimbina, apenas na dose mais elevada (90 mg/kg, i.p.). A importância da neurotransmissão monoaminérgica para o efeito antinociceptivo da uliginosina B foi confirmada através da análise isobolar. A associação de uliginosina B com amitriptilina (inibidor da recaptação de monoaminas) ou clonidina (agonista adrenérgico α2) apresentou interação aditiva – dados sugestivos de substâncias com mecanismos de ação mediados pelas mesmas vias – enquanto a associação com morfina (agonista opioide) apresentou interação sinérgica – dados indicativos de um possível uso clínico, como adjuvante opioide na farmacoterapia da dor. O efeito antinociceptivo de uliginosina B (15 mg/kg, i.p.) também foi prevenido pelo tratamento prévio com DPCPX e ZM-241385 (antagonistas de receptores adenosinérgicos A1 e A2A, respectivamente). Este efeito esta relacionado, pelo menos em parte, com a capacidade da uliginosina B aumentar a hidrólise de AMP na medula espinhal e de ATP no córtex cerebral. A uliginosina B também inibiu in vitro a atividade da enzima Na+,K+-ATPase (isoformas α1 e α3). O conjunto de dados apresentados nesta tese evidencia a uliginosina B como um padrão estrutural multirreceptor promissor no desenvolvimento de fármacos com ação analgésica. Em suma, os efeitos antinociceptivo e atáxico induzidos pelo tratamento com uliginosina B são mediados pela ativação da neurotransmissão monoaminérgica, glutamatérgica, purinérgica e opióide, requisitadas com diferente grau de importância; e ainda envolvem o balaço iônico da Na+,K+-ATPase. / Uliginosin B is a natural acylphloroglucinol derivative obtained from Hypericum species native to South America. Previous studies have shown that uliginosin B presents antidepressant-like and antinociceptive effects at low doses (up to 15 mg/kg, i.p. or p.o.), and at high doses (90 mg/kg, i.p.) it impairs the motor coordination. The antidepressant-like activity seems to depend on the activation of monoaminergic neurotransmission and ionic balance of Na+. The antinociceptive effect is mediated by opioid and D2 dopamine receptors. The ataxic effect involves opioid and dopaminergic receptors activation. The uliginosin B effects appear to be a consequence of their ability to inhibit reuptake of monoamines (especially dopamine) with subsequent activation of opioid and monoaminergic receptors. The aim of this study was to deepen our knowledge about the mechanism of antinociceptive action of uliginosin B, investigating the involvement of monoaminergic, glutamatergic and purinergic neurotransmissions. Treatment with uliginosin B increased the interstitial availability of dopamine and its metabolite, homovanillic acid (HVA), in the striatum of rats; these data underscore the role of dopaminergic neurotransmission in the effects of uliginosin B. The role of other monoamines as well as the glutamatergic neurotransmission, were investigated in the antinociceptive and ataxic effects induced by uliginosin B. The ataxic effect (90 mg/kg, i.p.) was completely prevented by pre-treatment with pCPA (a serotonin synthesis inhibitor) and MK-801 (a NMDA glutamatergic receptor antagonist), but was not affected by pretreatment with prazosin or yohimbine (α1 and α2 adrenoceptor antagonists, respectively). The antinociceptive activity (15 and 90 mg/kg, i.p.) was significantly reduced by pretreatment with pCPA and MK-801 and increased by pretreatment with yohimbine and prazosin only at the highest dose (90 mg/kg, i.p.). The importance of monoaminergic neurotransmission for the uliginosin B antinociceptive effect was confirmed by isobolar analysis. The association between uliginosin B with amitriptyline (monoamine reuptake inhibitor) or clonidine (α2 adrenergic agonist) showed additive interaction - findings suggestive of substances with mechanisms of action mediated by the same pathways - while the association with morphine (opioid agonist) showed synergistic interaction - indicative of a possible clinical use as adjuvant to opioid pharmacotherapy of pain relief. The antinociceptive effect of uliginosin B (15 mg/kg, i.p.) was also prevented by pretreatment with DPCPX and ZM-241385 (A1 and A2A adenosinergic receptor antagonists, respectively). This effect is related, at least in part, to its ability of increases the AMP and ATP hydrolysis in the spinal cord and cerebral cortex synaptosomes, respectively. Moreover, uliginosin B inhibited the Na+,K+-ATPase activity (α1 and α3 isoforms) in vitro. The data set presented in this thesis pointed uliginosin B as a promising multirreceptor molecular pattern in the analgesic drug development. In summary, the antinociceptive and ataxic effects induced by uliginosin B were mediated by the activation of monoaminergic, glutamatergic, purinérgico and opioid neurotransmission and involves the ionic balance, required with different degree of importance.

Dans cette thèse, nous nous intéressons a la résolution de problèmes de contrôle optimal associés a des équations de diffusion et onde fractionnaires en temps et a données incomplètes, ou les dérivées sont prises au sens de Riemann-Liouville. / In this thesis, we are interested in the résolution of optimal control problems associated to fractional diffusion-wave equations in time with incomplete data, and where derivatives are understood in Riemann-Liouville sense.

abstract: This thesis aims to investigate the capacity and bit error rate (BER) performance of multi-user diversity systems with random number of users and considers its application to cognitive radio systems. Ergodic capacity, normalized capacity, outage capacity, and average bit error rate metrics are studied. It has been found that the randomization of the number of users will reduce the ergodic capacity. A stochastic ordering framework is adopted to order user distributions, for example, Laplace transform ordering. The ergodic capacity under different user distributions will follow their corresponding Laplace transform order. The scaling law of ergodic capacity with mean number of users under Poisson and negative binomial user distributions are studied for large mean number of users and these two random distributions are ordered in Laplace transform ordering sense. The ergodic capacity per user is defined and is shown to increase when the total number of users is randomized, which is the opposite to the case of unnormalized ergodic capacity metric. Outage probability under slow fading is also considered and shown to decrease when the total number of users is randomized. The bit error rate (BER) in a general multi-user diversity system has a completely monotonic derivative, which implies that, according to the Jensen's inequality, the randomization of the total number of users will decrease the average BER performance. The special case of Poisson number of users and Rayleigh fading is studied. Combining with the knowledge of regular variation, the average BER is shown to achieve tightness in the Jensen's inequality. This is followed by the extension to the negative binomial number of users, for which the BER is derived and shown to be decreasing in the number of users. A single primary user cognitive radio system with multi-user diversity at the secondary users is proposed. Comparing to the general multi-user diversity system, there exists an interference constraint between secondary and primary users, which is independent of the secondary users' transmission. The secondary user with high- est transmitted SNR which also satisfies the interference constraint is selected to communicate. The active number of secondary users is a binomial random variable. This is then followed by a derivation of the scaling law of the ergodic capacity with mean number of users and the closed form expression of average BER under this situation. The ergodic capacity under binomial user distribution is shown to outperform the Poisson case. Monte-Carlo simulations are used to supplement our analytical results and compare the performance of different user distributions. / Dissertation/Thesis / M.S. Electrical Engineering 2012

L'utilisation d'aspects aléatoires a contribué de façon majeure aux dernières avancées dans le domaine de l'optimisation numérique; cela est dû en partie à la recrudescence de problèmes issus de l'apprentissage automatique (machine learning). Dans un tel contexte, les algorithmes classiques d'optimisation non linéaire, reposant sur des principes déterministes, se révèlent en effet bien moins performants que des variantes incorporant de l'aléatoire. Le coût de ces dernières est souvent inférieur à celui de leurs équivalents déterministes; en revanche, il peut s'avérer difficile de maintenir les propriétés théoriques d'un algorithme déterministe lorsque de l'aléatoire y est introduit. Effectuer une analyse de complexité d'une telle méthode est un procédé très répandu dans ce contexte. Cette technique permet déstimer la vitesse de convergence du schéma considéré et par là même d'établir une forme de convergence de celui-ci. Les récents travaux sur ce sujet, en particulier pour des problèmes d'optimisation non convexes, ont également contribué au développement de ces aspects dans le cadre déterministe, ceux-ci apportant en effet un éclairage nouveau sur le comportement des algorithmes. Dans cette thèse, on s'intéresse à l'amélioration pratique d'algorithmes d'optimisation sans dérivées à travers l'introduction d'aléatoire, ainsi qu'à l'impact numérique des analyses de complexité. L'étude se concentre essentiellement sur les méthodes de recherche directe, qui comptent parmi les principales catégories d'algorithmes sans dérivées; cependant, l'analyse sous-jacente est applicable à un large éventail de ces classes de méthodes. On propose des variantes probabilistes des propriétés requises pour assurer la convergence des algorithmes étudiés, en mettant en avant le gain en efficacité induit par ces variantes: un tel gain séxplique principalement par leur coût très faible en évaluations de fonction. Le cadre de base de notre analyse est celui de méthodes convergentes au premier ordre, que nous appliquons à des problèmes sans ou avec contraintes linéaires. Les bonnes performances obtenues dans ce contexte nous incitent par la suite à prendre en compte des aspects d'ordre deux. A partir des propriétés de complexité des algorithmes sans dérivées, on développe de nouvelles méthodes qui exploitent de l'information du second ordre. L'analyse de ces procédures peut être réalisée sur un plan déterministe ou probabiliste: la deuxième solution nous permet d'étudier de nouveaux aspects aléatoires ainsi que leurs conséquences sur l'éfficacité et la robustesse des algorithmes considérés. / Randomization has had a major impact on the latest developments in the field of numerical optimization, partly due to the outbreak of machine learning applications. In this increasingly popular context, classical nonlinear programming algorithms have indeed been outperformed by variants relying on randomness. The cost of these variants is usually lower than for the traditional schemes, however theoretical guarantees may not be straightforward to carry out from the deterministic to the randomized setting. Complexity analysis is a useful tool in the latter case, as it helps in providing estimates on the convergence speed of a given scheme, which implies some form of convergence. Such a technique has also gained attention from the deterministic optimization community thanks to recent findings in the nonconvex case, as it brings supplementary indicators on the behavior of an algorithm. In this thesis, we investigate the practical enhancement of deterministic optimization algorithms through the introduction of random elements within those frameworks, as well as the numerical impact of their complexity results. We focus on direct-search methods, one of the main classes of derivative-free algorithms, yet our analysis applies to a wide range of derivative-free methods. We propose probabilistic variants on classical properties required to ensure convergence of the studied methods, then enlighten their practical efficiency induced by their lower consumption of function evaluations. Firstorder concerns form the basis of our analysis, which we apply to address unconstrained and linearly-constrained problems. The observed gains incite us to additionally take second-order considerations into account. Using complexity properties of derivative-free schemes, we develop several frameworks in which information of order two is exploited. Both a deterministic and a probabilistic analysis can be performed on these schemes. The latter is an opportunity to introduce supplementary probabilistic properties, together with their impact on numerical efficiency and robustness.

Uliginosina B é um derivado acilfloroglucinol natural, isolado de espécies de Hypericum nativas da América do Sul. Estudos prévios demonstraram que a uliginosina B apresenta efeitos do tipo antidepressivo e antinociceptivo em baixas doses (até 15 mg/kg, i.p. ou v.o.) e, em doses elevadas (90 mg/kg, i.p.), prejudica a coordenação motora. A atividade antidepressiva depende da ativação da neurotransmissão monoaminérgica e envolve a regulação da homeostase através do balanço de Na+. A atividade antinociceptiva é mediada por receptores opioides e dopaminérgicos da família D2. O efeito atáxico depende da ativação de receptores opioides e dopaminérgicos. Os efeitos parecem ser decorrentes da sua capacidade de inibir a recaptação de monoaminas (especialmente dopamina) com consequente ativação de receptores opioides e monoaminérgicos. O objetivo deste estudo foi aprofundar o conhecimento sobre o mecanismo de ação antinociceptiva de uliginosina B, investigando o envolvimento da neurotransmissão monoaminérgica, glutamatérgica e purinérgica. O tratamento com uliginosina B aumentou a disponibilidade intersticial de dopamina e seu metabólito, ácido homovanílico (HVA), no estriado de ratos; dados que reforçam o papel da neurotransmissão dopaminérgica nos efeitos da uliginosina B. O papel das outras monoaminas e da neurotransmissão glutamatérgica foi investigado nos efeitos antinociceptivo e atáxico induzidos por uliginosina B. A ataxia (90 mg/kg, i.p.) foi completamente prevenida pelo tratamento prévio com pCPA (inibidor da síntese de serotonina) e MK-801 (antagonista do receptor glutamatérgico NMDA), mas não foi afetada pelo prétratamento com prazosina ou ioimbina (antagonistas de receptores adrenérgicos α1 e α2, respectivamente). A atividade antinociceptiva (15 e 90 mg/kg, i.p.) foi reduzida significativamente pelo pré-tratamento com pCPA e MK-801 e aumentada pelo prétratamento com prazosina e ioimbina, apenas na dose mais elevada (90 mg/kg, i.p.). A importância da neurotransmissão monoaminérgica para o efeito antinociceptivo da uliginosina B foi confirmada através da análise isobolar. A associação de uliginosina B com amitriptilina (inibidor da recaptação de monoaminas) ou clonidina (agonista adrenérgico α2) apresentou interação aditiva – dados sugestivos de substâncias com mecanismos de ação mediados pelas mesmas vias – enquanto a associação com morfina (agonista opioide) apresentou interação sinérgica – dados indicativos de um possível uso clínico, como adjuvante opioide na farmacoterapia da dor. O efeito antinociceptivo de uliginosina B (15 mg/kg, i.p.) também foi prevenido pelo tratamento prévio com DPCPX e ZM-241385 (antagonistas de receptores adenosinérgicos A1 e A2A, respectivamente). Este efeito esta relacionado, pelo menos em parte, com a capacidade da uliginosina B aumentar a hidrólise de AMP na medula espinhal e de ATP no córtex cerebral. A uliginosina B também inibiu in vitro a atividade da enzima Na+,K+-ATPase (isoformas α1 e α3). O conjunto de dados apresentados nesta tese evidencia a uliginosina B como um padrão estrutural multirreceptor promissor no desenvolvimento de fármacos com ação analgésica. Em suma, os efeitos antinociceptivo e atáxico induzidos pelo tratamento com uliginosina B são mediados pela ativação da neurotransmissão monoaminérgica, glutamatérgica, purinérgica e opióide, requisitadas com diferente grau de importância; e ainda envolvem o balaço iônico da Na+,K+-ATPase. / Uliginosin B is a natural acylphloroglucinol derivative obtained from Hypericum species native to South America. Previous studies have shown that uliginosin B presents antidepressant-like and antinociceptive effects at low doses (up to 15 mg/kg, i.p. or p.o.), and at high doses (90 mg/kg, i.p.) it impairs the motor coordination. The antidepressant-like activity seems to depend on the activation of monoaminergic neurotransmission and ionic balance of Na+. The antinociceptive effect is mediated by opioid and D2 dopamine receptors. The ataxic effect involves opioid and dopaminergic receptors activation. The uliginosin B effects appear to be a consequence of their ability to inhibit reuptake of monoamines (especially dopamine) with subsequent activation of opioid and monoaminergic receptors. The aim of this study was to deepen our knowledge about the mechanism of antinociceptive action of uliginosin B, investigating the involvement of monoaminergic, glutamatergic and purinergic neurotransmissions. Treatment with uliginosin B increased the interstitial availability of dopamine and its metabolite, homovanillic acid (HVA), in the striatum of rats; these data underscore the role of dopaminergic neurotransmission in the effects of uliginosin B. The role of other monoamines as well as the glutamatergic neurotransmission, were investigated in the antinociceptive and ataxic effects induced by uliginosin B. The ataxic effect (90 mg/kg, i.p.) was completely prevented by pre-treatment with pCPA (a serotonin synthesis inhibitor) and MK-801 (a NMDA glutamatergic receptor antagonist), but was not affected by pretreatment with prazosin or yohimbine (α1 and α2 adrenoceptor antagonists, respectively). The antinociceptive activity (15 and 90 mg/kg, i.p.) was significantly reduced by pretreatment with pCPA and MK-801 and increased by pretreatment with yohimbine and prazosin only at the highest dose (90 mg/kg, i.p.). The importance of monoaminergic neurotransmission for the uliginosin B antinociceptive effect was confirmed by isobolar analysis. The association between uliginosin B with amitriptyline (monoamine reuptake inhibitor) or clonidine (α2 adrenergic agonist) showed additive interaction - findings suggestive of substances with mechanisms of action mediated by the same pathways - while the association with morphine (opioid agonist) showed synergistic interaction - indicative of a possible clinical use as adjuvant to opioid pharmacotherapy of pain relief. The antinociceptive effect of uliginosin B (15 mg/kg, i.p.) was also prevented by pretreatment with DPCPX and ZM-241385 (A1 and A2A adenosinergic receptor antagonists, respectively). This effect is related, at least in part, to its ability of increases the AMP and ATP hydrolysis in the spinal cord and cerebral cortex synaptosomes, respectively. Moreover, uliginosin B inhibited the Na+,K+-ATPase activity (α1 and α3 isoforms) in vitro. The data set presented in this thesis pointed uliginosin B as a promising multirreceptor molecular pattern in the analgesic drug development. In summary, the antinociceptive and ataxic effects induced by uliginosin B were mediated by the activation of monoaminergic, glutamatergic, purinérgico and opioid neurotransmission and involves the ionic balance, required with different degree of importance.