Three Portraits of S. Kovalevsky: Interpretation of S. Kovalevsky’s life and creativity in the works by P. Ja. Kochina, A. C. Leffler and A. Munro This research puts forward the hypothesis that S. Kovalevsky was an example of a multifaceted talent: an outstanding mathematician, writer and public figure simultaneously. As such, the basis of the phenomenon that is S. Kovalevsky is the ingenious synthesis of the various facets of creativity.  An attempt was made to achieve a better understanding of the multifaceted life and creativity of S. Kovalevsky though a comparative study of the perceptions of Kovalevsky put forward by the Swedish writer, A.C. Leffler (1892), and that of the Russian biographer, P. Ja. Kochina (1981), and that of the Canadian writer, A. Munro (2009), Nobel laureates in literature 2013. Similarities and differences in the interpretations and understanding of the life and creativity of S. Kovalevsky between the Swedish, Russian and Canadian authors were identified and an important part was to define which image of S. Kovalevsky appears in the analysis of the authors. Another essential component was to identify which image dominates, that of Kovalevsky as a mathematician, as a writer or as a public figure. A table, containing the results of a comparative analysis using the maximum number of identified, scientifically sound parameters, is also presented in the study for a clearer picture of the perception of S. Kovalevsky’s image presented by the three writers. Twenty-four such comparative parameters were identified. The article concludes with possible prospects for further research on the subject.

Abstract in English / In this dissertation we apply linear evolution equations to the Newtonian derivative, Caputo time fractional derivative and $-time fractional derivative. It is notable that the most utilized fractional order derivatives for modelling true life challenges are Riemann- Liouville and Caputo fractional derivatives, however these fractional derivatives have the same weakness of not satisfying the chain rule, which is one of the most important elements of the match asymptotic method [2, 3, 16]. Furthermore the classical bounded perturbation theorem associated with Riemann-Liouville and Caputo fractional derivatives has con rmed not to be in general truthful for these models, particularly for solution operators of evolution systems of a derivative with fractional parameter ' that is less than one (0 < ' < 1) [29]. To solve this problem, we introduce the derivative with new parameter, which is de ned as a local derivative but has a fractional order called $-derivative and apply this derivative to linear evolution equation and to support what we have done in the theory, we utilize application to population dynamics and we provide the numerical simulations for particular cases. / Mathematical Sciences / M.Sc. (Applied Mathematics)

<p>Anne Charlotte Leffler, Victoria Benedictsson and Frida Stéenhoff were all part of the Modern Breakthrough in Swedish literature. By utilizing Jürgen Habermas theoretical works on communicative action, and Nancy Fraser’s supplementary reading of his theory, this essay makes clear that the authors’ struggle for an understanding and a rethinking of social norms in their plays <em>Skådespelerskan </em>(1873), <em>Romeos Julia </em>(1888) and <em>Lejonets unge </em>(1896) can be read as a contribution to the public debate. Dialogue has a key function for female authors during the Modern Breakthrough. Women and mens’ possibilities to take part in conversation and argument as equals, requires the professional woman’s transgression and access to the privileges of both public (State) administration – “system”, and world of everyday life – “lifeworld”. As oppositional authors, Leffler, Benedictsson and Stéenhoff took advantage of the literary public domain, in this case the theatre. The theatre as public sphere had a more effective capacity to affect its audience than fiction. The plays were written and staged in a cultural period that, compared with the present one, in a greater sense influenced public opinion. The theatre was a powerful part of the public debate, and this debate involved parties from both on-stage and off-stage positions.</p><p>At the theatre Leffler, Benedictsson and Stéenhoff turned the private into politics. Their powerful contribution to the public debate were directed specifically towards the bourgeois audience. They carried on a controversy concerning the notion of the bourgeois family by showing scenarios that raised objection to its idealistic point of view. The bourgeois living room was exposed on stage. Conflicts related to the private sphere were brought up as a theme in a public sphere and by so means were incorporated into the public debate, which at that time was dominated by men. The plays mirrored the audience and the authors’ strategies were based upon the remodeling power inherent in conversation and argumentation. Thereby, the audience were confronted with an alternated reflection of themselves. This reflection should be read as a problematic representation of the writing of history. The alternate mirroring brought in itself forward an argument that emphasized why a new reflection was necessary.</p><p><em>Skådespelerskan</em>, <em>Romeos Julia </em>and <em>Lejonets unge</em> examine female artists in a bourgeois environment. Through the artist the structures that maintain bourgeois ideals are exposed and questioned, but first and foremost the artist show that communicative action between men and women was insufficient. The androcentric order did not acknowledge women and men as equals, in accordance with that, the possibility of conversation, in the sense of Habermas, came to nothing. Under such circumstances an understanding between men and women could not be reached. Love within the institution of marriage also suffered since it could not be founded in acknowledgement as long as the structure maintained. Saga and Adil, the main characters in <em>Lejonets unge</em>, personify, on the other hand, Stéenhoffs ideas of what is being needed to change the androcentric structure. They are citizens of the future.</p><p>My focus is on human action (in an Aristotelian sense) in the plays, the way characters stage themselves and bring the plot forward, shed light upon their possibilities and limitations in proportion to each other as men and women. My analysis thereby contrasts with the greater part of earlier research. I give prominence to the connection between psychological conflict and social position/role. In <em>Skådespelerskan</em>, <em>Romeos Julia</em> and <em>Lejonets unge</em> all of the characters’ psychological conflicts are based in gender issues, the consequences of being a man or woman in the 18th century, rather than explicit existential matters.</p>

Anne Charlotte Leffler, Victoria Benedictsson and Frida Stéenhoff were all part of the Modern Breakthrough in Swedish literature. By utilizing Jürgen Habermas theoretical works on communicative action, and Nancy Fraser’s supplementary reading of his theory, this essay makes clear that the authors’ struggle for an understanding and a rethinking of social norms in their plays Skådespelerskan (1873), Romeos Julia (1888) and Lejonets unge (1896) can be read as a contribution to the public debate. Dialogue has a key function for female authors during the Modern Breakthrough. Women and mens’ possibilities to take part in conversation and argument as equals, requires the professional woman’s transgression and access to the privileges of both public (State) administration – “system”, and world of everyday life – “lifeworld”. As oppositional authors, Leffler, Benedictsson and Stéenhoff took advantage of the literary public domain, in this case the theatre. The theatre as public sphere had a more effective capacity to affect its audience than fiction. The plays were written and staged in a cultural period that, compared with the present one, in a greater sense influenced public opinion. The theatre was a powerful part of the public debate, and this debate involved parties from both on-stage and off-stage positions. At the theatre Leffler, Benedictsson and Stéenhoff turned the private into politics. Their powerful contribution to the public debate were directed specifically towards the bourgeois audience. They carried on a controversy concerning the notion of the bourgeois family by showing scenarios that raised objection to its idealistic point of view. The bourgeois living room was exposed on stage. Conflicts related to the private sphere were brought up as a theme in a public sphere and by so means were incorporated into the public debate, which at that time was dominated by men. The plays mirrored the audience and the authors’ strategies were based upon the remodeling power inherent in conversation and argumentation. Thereby, the audience were confronted with an alternated reflection of themselves. This reflection should be read as a problematic representation of the writing of history. The alternate mirroring brought in itself forward an argument that emphasized why a new reflection was necessary. Skådespelerskan, Romeos Julia and Lejonets unge examine female artists in a bourgeois environment. Through the artist the structures that maintain bourgeois ideals are exposed and questioned, but first and foremost the artist show that communicative action between men and women was insufficient. The androcentric order did not acknowledge women and men as equals, in accordance with that, the possibility of conversation, in the sense of Habermas, came to nothing. Under such circumstances an understanding between men and women could not be reached. Love within the institution of marriage also suffered since it could not be founded in acknowledgement as long as the structure maintained. Saga and Adil, the main characters in Lejonets unge, personify, on the other hand, Stéenhoffs ideas of what is being needed to change the androcentric structure. They are citizens of the future. My focus is on human action (in an Aristotelian sense) in the plays, the way characters stage themselves and bring the plot forward, shed light upon their possibilities and limitations in proportion to each other as men and women. My analysis thereby contrasts with the greater part of earlier research. I give prominence to the connection between psychological conflict and social position/role. In Skådespelerskan, Romeos Julia and Lejonets unge all of the characters’ psychological conflicts are based in gender issues, the consequences of being a man or woman in the 18th century, rather than explicit existential matters.

Some Epidemic models with fractional derivatives were proved to be well-defined, well-posed and more accurate [34, 51, 116], compared to models with the conventional derivative. An Ebola epidemic model with non-linear transmission is fully analyzed. The model is expressed with the conventional time derivative with a new parameter included, which happens to be fractional (that derivative is called the 􀀀derivative). We proved that the model is well-de ned and well-posed. Moreover, conditions for boundedness and dissipativity of the trajectories are established. Exploiting the generalized Routh-Hurwitz Criteria, existence and stability analysis of equilibrium points for the Ebola model are performed to show that they are strongly dependent on the non-linear transmission. In particular, conditions for existence and stability of a unique endemic equilibrium to the Ebola system are given. Numerical simulations are provided for particular expressions of the non-linear transmission, with model's parameters taking di erent values. The resulting simulations are in concordance with the usual threshold behavior. The results obtained here may be signi cant for the ght and prevention against Ebola haemorrhagic fever that has so far exterminated hundreds of families and is still a ecting many people in West-Africa and other parts of the world. The full comprehension and handling of the phenomenon of shattering, sometime happening during the process of polymer chain degradation [129, 142], remains unsolved when using the traditional evolution equations describing the degradation. This traditional model has been proved to be very hard to handle as it involves evolution of two intertwined quantities. Moreover, the explicit form of its solution is, in general, impossible to obtain. We explore the possibility of generalizing evolution equation modeling the polymer chain degradation and analyze the model with the conventional time derivative with a new parameter. We consider the general case where the breakup rate depends on the size of the chain breaking up. In the process, the alternative version of Sumudu integral transform is used to provide an explicit form of the general solution representing the evolution of polymer sizes distribution. In particular, we show that this evolution exhibits existence of complex periodic properties due to the presence of cosine and sine functions governing the solutions. Numerical simulations are performed for some particular cases and prove that the system describing the polymer chain degradation contains complex and simple harmonic poles whose e ects are given by these functions or a combination of them. This result may be crucial in the ongoing research to better handle and explain the phenomenon of shattering. Lastly, it has become a conjecture that power series like Mittag-Le er functions and their variants naturally govern solutions to most of generalized fractional evolution models such as kinetic, di usion or relaxation equations. The question is to say whether or not this is always true! Whence, three generalized evolution equations with an additional fractional parameter are solved analytically with conventional techniques. These are processes related to stationary state system, relaxation and di usion. In the analysis, we exploit the Sumudu transform to show that investigation on the stationary state system leads to results of invariability. However, unlike other models, the generalized di usion and relaxation models are proven not to be governed by Mittag-Le er functions or any of their variants, but rather by a parameterized exponential function, new in the literature, more accurate and easier to handle. Graphical representations are performed and also show how that parameter, called ; can be used to control the stationarity of such generalized models. / Mathematical Sciences / Ph. D. (Applied Mathematics)

La presente tesis doctoral, titulada "Contribution to the modelling of the light field distribution within Synechocystis sp. PCC 6803 cultures and its influence on cellular photosynthesis processes", engloba diversos trabajos cuyo objetivo es avanzar en la compresión de la distribución lumínica en cultivos de cianobacterias y en los efectos de la luz sobre los mecanismos fotosintéticos de dichos microorganismos. Se trata, en definitiva, de otro paso hacia la integración de modelos matemáticos sobre la fotosíntesis a nivel celular y a escala de cultivo. En primer lugar, para comprender cómo se comporta un cultivo de bacterias fotosintéticas, es fundamental predecir la distribución del campo de luz a lo largo del perfil del biorreactor, tanto a nivel de intensidad total, como respecto a su distribución de flujo de fotones. La distribución de longitudes de onda presente en el medio es importante puesto que muchos procesos de la fotosíntesis están regulados por ciertas longitudes de onda y, por tanto, están modulados por la distribución espectral - el color - de la luz. Aprovechando las propiedades inherentes ópticas del cultivo, se desarrolló un modelo matemático basado en el concepto de campo auto-consistente. Este algoritmo, bautizado en la correspondiente publicación como Auto-consistent Field Approximation Algorithm (AFA), proporciona una predicción del campo lumínico, incluyendo la evolución espectral del mismo a lo largo del camino óptico, para cultivos aclimatados a distintos valores de radiación. Dicha investigación se publicó en la revista Algal Research mediante el artículo titulado "Light distribution and spectral composition within cultures of micro-algae: Quantitative modelling of the light field in photobioreactors", en el que se valida el algoritmo con datos experimentales de dos cepas de estudio de la cianobacteria Synechocystis. Si bien los resultados fueron satisfactorios, el empleo de la ley de Lambert-Beer con un valor constante de atenuación no permite modelizar la parte del campo de luz con menor intensidad, donde el coeficiente de atenuación deja de ser constante y el comportamiento se desvía del exponencial. Por ello, se decidió modelizar el campo de luz con una función que generaliza el caso exponencial mediante el uso de cálculo fraccionario. Se empleó una función de Mittag-Leffler que cumplía con los requisitos formales y ofrecía un ajuste de los datos mejor al obtenido mediante la ley de Lambert-Beer. Como un hallazgo notable, se determinó que el valor de dicho parámetro, que caracteriza la función de Mittag-Leffler, era el mismo para los datos empíricos de las dos cepas estudiadas. Este trabajo se publicó en la contribución llamada "Estimation of the light field inside photosynthetic microorganism cultures through Mittag-Leffler functions at depleted light conditions" en la revista Journal of Quantitative Spectroscopy & Radiative Transfer. Después se procedió a utilizar sendos trabajos de investigación para calcular el campo de luz en un cultivo de Synechocystis y relacionarlo con su productividad máxima. En concreto se ha estudiado, como indicador del rendimiento de la fotosíntesis, la producción de oxígeno y los mecanismos respiratorios asociados a distintas intensidades de luz. Esta investigación está en su fase final y se está ultimando la escritura del artículo para enviarlo a una revista científica próximamente. Dicho manuscrito se titula "Experimental characterisation of Synechocystis sp. PCC 6803 cultures productivity up on light conditions". Finalmente, se está desarrollando una cuarta contribución titulada "Individual pigment contribution to overall in vivo absorption in Synechocystis sp. PCC 6803 cells". Esta investigación estudia la cantidad de luz absorbida por los cromóforos de Synechocystis en función del tipo de iluminación utilizada y calcula la concentración de pigmentos presentes en la célula. / The present doctoral thesis, entitled "Contribution to the modelling of the light field distribution within Synechocystis sp PCC 6803 cultures and its influence on cellular photosynthesis processes", includes several works whose objective is to advance in the understanding of the light distribution in cyanobacterial cultures and in the effects of light on the photosynthetic mechanisms of these microorganisms. It is, ultimately, another step towards the integration of mathematical models on photosynthesis at the cellular level and at the scale of culture. First, to understand how a culture of photosynthetic bacteria behaves, it is essential to predict the distribution of the light field along the bioreactor profile, both at the level of total intensity and with respect to its photon flux distribution. The distribution of wavelengths present in the medium is important since many processes of photosynthesis are regulated by certain wavelengths and are therefore modulated by the spectral distribution - the colour - of the light. Taking advantage of the inherent optical properties of the culture, a mathematical model based on the self-consistent field concept was developed. This algorithm, named in the corresponding publication as Auto-consistent Field Approximation Algorithm (AFA), provides an estimation of the light field, including the spectral evolution thereof along the optical path-length, for acclimated cultures to different radiation values. This research was published in the journal Algal Research through the article entitled "Light distribution and spectral composition within cultures of micro-algae: Quantitative modelling of the light field in photobioreactors", in which the algorithm is validated with experimental data of two strains of study of the cyanobacterium Synechocystis. Although the results were satisfactory, the use of the Lambert-Beer Law with a constant attenuation value, cannot correctly model the part of the light field with less intensity, where the attenuation coefficient ceases to be constant and the behaviour deviates from the exponential. Therefore, it was decided to model the light field with a function that generalizes the exponential case through the use of fractional calculus. A Mittag-Leffler function was used that fulfilled the formal requirements and offered a better data fit than that obtained with the Lambert-Beer law. As a remarkable finding, it was determined that the value of this parameter, which characterises the Mittag-Leffler function, was the same for the empirical data of both studied strains. This work was published in the contribution called "Estimation of the light field in photosynthetic microorganism cultures through Mittag-Leffler functions at depleted light conditions" in the journal Journal of Quantitative Spectroscopy & Radiative Transfer. Thereafter we proceeded to use both research works to calculate the light field within Synechocystis cultures and relate it to its maximum productivity. Specifically, it has been studied, as an indicator of the performance of photosynthesis, the production of oxygen and the associated respiratory mechanisms under different light intensities. This research is in its final phase and the writing of the article is being finalised to submit it to a scientific journal soon. This manuscript is entitled "Experimental characterization of Synechocystis sp. PCC 6803 cultures productivity up on light conditions". Finally, a fourth contribution entitled "Individual pigment contribution to overall in vivo absorption in Synechocystis sp. PCC 6803 cells" is under development. This research studies the amount of light absorbed by Synechocystis chromophores according to the type of employed illumination and calculates the concentration of pigments present in the cell. / La present tesi doctoral, titulada "Contribution to the modelling of the light field distribution within Synechocystis sp. PCC 6803 cultures and its influence on cellular photosynthesis processes", engloba diversos treballs l'objectiu dels quals és avançar en la compressió de la distribució lumínica en cultius de cianobacteris i en els efectes de la llum sobre els mecanismes fotosintètics d'aquests microorganismes. Llavors, es tracta en definitiva d'un altre pas cap a la integració de models matemàtics sobre la fotosíntesi a nivell cel·lular i a escala de cultiu. En primer lloc, per a comprendre com es comporta un cultiu de bacteris fotosintètics, és fonamental predir la distribució del camp de llum al llarg del perfil del bioreactor, tant a nivell d'intensitat total, com pel que fa a la seua distribució de flux de fotons. La distribució de longituds d'ona present en el medi és important ja que molts processos de la fotosíntesi estan regulats per certes longituds d'ona i, per tant, estan modulats per la distribució espectral - el color - de la llum. Aprofitant les propietats inherents òptiques del cultiu, es va desenvolupar un model matemàtic basat en el concepte de camp auto-consistent. Aquest algoritme, batejat en la corresponent publicació com Auto-consistent Field Approximation Algorithm (AFA), proporciona una predicció del camp lumínic, incloent l'evolució espectral del mateix al llarg del camí òptic, per a cultius aclimatats a diferents valors de radiació. Aquesta investigació es va publicar a la revista Algal Research mitjançant l'article titulat "Light distribution and espectral composition within cultures of micro-algae: Quantitative modelling of the light field in photobioreactors", en què es valida l'algoritme amb dades experimentals de dues soques d'estudi de la cianobacteri Synechocystis. Si bé els resultats van ser satisfactoris, l'ús de la llei de Lambert-Beer amb un valor constant d'atenuació no permet modelitzar la part del camp de llum amb menys intensitat, on el coeficient d'atenuació deixa de ser constant i el comportament es desvia del exponencial. Per això, es va decidir modelitzar el camp de llum amb una funció que generalitza el cas exponencial mitjançant l'ús de càlcul fraccionari. Es va emprar una funció de Mittag-Leffler que complia amb els requisits formals i oferia un ajust de les dades millor a l'obtingut mitjançant la llei de Lambert-Beer. Com una troballa notable, es va determinar que el valor d'aquest paràmetre, que caracteritza la funció de Mittag-Leffler, era el mateix per a les dades empíriques de les dues soques estudiades. Aquest treball es va publicar en la contribució anomenada "Estimation of the light field inside Photosynthetic microorganisme cultures through Mittag-Leffler functions at depleted light conditions" a la revista Journal of Quantitative Spectroscopy & Radiative Transfer. Després, es va procedir a utilitzar sengles treballs d'investigació per calcular el camp de llum en un cultiu de Synechocystis i relacionar-lo amb la seua productivitat màxima. En concret s'ha estudiat, com a indicador del rendiment de la fotosíntesi, la producció d'oxigen i els mecanismes respiratoris associats a diferents intensitats de llum. Aquesta investigació està en la seua fase final i s'està ultimant l'escriptura de l'article per enviar-lo a una revista científica pròximament. Dit manuscrit es titula "Experimental characterisation of Synechocystis sp. PCC 6803 cultures productivity up on light conditions". Finalment, s'està desenvolupant una quarta contribució titulada "Individual pigment contribution to overall in vivo absorption in Synechocystis sp. PCC 6803 cells". Aquesta recerca estudia la quantitat de llum absorbida pels cromòfors de Synechocystis en funció del tipus d'il·luminació utilitzada i calcula la concentració de pigments presents en la cèl·lula. / Fuente Herraiz, D. (2018). Contribution to the modelling of the light field distribution within Synechocystis sp. PCC 6803 cultures and its influence on cellular photosynthesis processes [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/106362 / TESIS

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Mathematics has got roots in Finland in the last quarter of the 19th century and came to flourish in the first quarter of the next century. In the first quarter of the 20th century, mathematicians were involved in teaching mathematics at schools and writing school textbooks. This involvement decreased and came to an end by the launching of the ‘New Math’ project. Mathematics education for elite was of positive affect to higher education, and this has changed by the spread of education, the decrease of mathematics teaching hours at schools and the changes in school mathematical curricula. The impact of curriculum changes is evident in Finnish students’ performance in the IEA comparative studies, PISA and IMO.

Mathematics has got roots in Finland in the last quarter of the 19th century and came to flourish in the first quarter of the next century. In the first quarter of the 20th century, mathematicians were involved in teaching mathematics at schools and writing school textbooks. This involvement decreased and came to an end by the launching of the ‘New Math’ project. Mathematics education for elite was of positive affect to higher education, and this has changed by the spread of education, the decrease of mathematics teaching hours at schools and the changes in school mathematical curricula. The impact of curriculum changes is evident in Finnish students’ performance in the IEA comparative studies, PISA and IMO.

Notre objectif dans cette thèse est l'étude des équations différentielles non linéaires comportant des dérivées fractionnaires en temps et/ou en espace. Nous nous sommes intéressés dans un premier temps à l'étude de deux systèmes non linéaires d'équations différentielles fractionnaires en temps et/ou en espace, puis à l'étude d'une équation différentielle fractionnaire en temps. Plus exactement pour la première partie, les questions concernant l'existence globale et le comportement asymptotique des solutions d'un système non linéaire d'équations différentielles comportant des dérivées fractionnaires en temps et en espace sont élucidées. Les techniques utilisées reposent sur des estimations obtenues pour les solutions fondamentales et la comparaison de certaines inégalités fractionnaires. Toujours dans la première partie, l'étude d'un système non linéaire d'équations de réaction-diffusion avec des dérivées fractionnaires en espace est abordée. L'existence locale et l'unicité des solutions sont prouvées à l'aide du théorème du point fixe de Banach. Nous montrons que les solutions sont bornées et analysons leur comportement à l'infini. La deuxième partie est consacrée à l'étude d'une équation différentielle fractionnaire non linéaire. Sous certaines conditions sur la donnée initiale, nous montrons que la solution est globale alors que sous d'autres, elle explose en temps fini. Dans ce dernier cas, nous donnons son profil ainsi que des estimations bilatérales du temps d'explosion. Alors que pour la solution globale nous étudions son comportement asymptotique. / Our objective in this thesis is the study of nonlinear differential equations involving fractional derivatives in time and/or in space. First, we are interested in the study of two nonlinear time and/or space fractional systems. Our second interest is devoted to the analysis of a time fractional differential equation. More exactly for the first part, the question concerning the global existence and the asymptotic behavior of a nonlinear system of differential equations involving time and space fractional derivatives is addressed. The used techniques rest on estimates obtained for the fundamental solutions and the comparison of some fractional inequalities. In addition, we study a nonlinear system of reaction-diffusion equations with space fractional derivatives. The local existence and the uniqueness of the solutions are proved using the Banach fixed point theorem. We show that the solutions are bounded and analyze their large time behavior. The second part is dedicated to the study of a nonlinear time fractional differential equation. Under some conditions on the initial data, we show that the solution is global while under others, it blows-up in a finite time. In this case, we give its profile as well as bilateral estimates of the blow-up time. While for the global solution we study its asymptotic behavior.