sMany theories of structure from motion divide the process into twosparts which are solved using different assumptions. Smoothness of thesvelocity field is often assumed to solve the motion correspondencesproblem, and then rigidity is used to recover the 3D structure. Wesprove results showing that, in a statistical sense, smoothness of thesvelocity field follows from rigidity of the motion.

The Hochschild-Kostant-Rosenberg theorem, which relates the Hochschild homology of an algebra to its modules of differential $n$-forms, can be considered a benchmark for smoothness of an algebra. This notion is used here in the search for a conception of smoothness formulated in the context of codifferential categories, both commutative and noncommutative. Since it is desirable to adapt such a conception to the noncommutative context, the theory of this domain is developed considerably; a significant result in this direction establishes a connection between noncommutative codifferential categories and commutative ones. This investigation necessitates, then, both the formulation of a notion of smoothness for $T$-algebras in codifferential categories and an adaptation of the Hochschild-Kostant-Rosenberg theorem to a wide variety of contexts which includes noncommutative ones. The former consideration fosters both the notion of a smooth monad, and a formulation of Andr\'e-Quillen homology in codifferential categories; the latter engenders a highly adaptable version of the Hochschild-Kostant-Rosenberg theorem. Specifically, it is shown that for any algebra modality there exists a corresponding Hochschild-Kostant-Rosenberg theorem. This includes a version of the theorem for the free associative algebra monad, the conclusion of which is satisfied by noncommutative smooth algebras.

<p>Two methods for the measurement of micro-scale stressvariations of press felt surfaces were developed. The methodswere based on a thin plastic film that was coated with anopaque stress-sensitive layer (Cronapress conversion film). Thefilm was compressed between a felt and a smooth surface. Uponapplication of load the opaque layer became partiallytransparent at the locations where load was applied by thesurface fibres of the felt. The degree of transparency was afunction of the locally applied stress. The spatial resolutionof the method was 6.3 µm, which means that even details ofthe order of the diameter of a batt fibre diameter can beresolved.</p><p>Parameters characterising the stress variations were used toquantitatively describe the extent of the stress variations,the size of the contact areas and the distance between them.The applicability of these contact characterisation parameterswas evaluated in laboratory wet pressing experiments and inpilot paper machine trials for two sets of specially designedpress felts. In general, the dewatering result was mainlyinfluenced by the diameter of the felt surface batt fibres andby the web grammage. For a specific pulp type and operatingconditions a multivariate model was formulated based on themeasured web dryness, web grammage and each contactcharacterisation parameter. The model was able to describe thedewatering capability of the different felts tested. Contactcharacterisation parameters related to contact properties (e.g.contact area ratio) gave the best prediction for low grammagewebs, while parameters related to flow properties (e.g. size ofopenings) gave the best prediction for high grammage webs.</p><p>Furthermore it was found that at a certain web grammage, thesurface batt fibre diameter did not have an influence on thedewatering result. This grammage was termed "transitiongrammage". Below the transition grammage a fine surface gavesignificantly better dewatering, while the opposite trend wasobserved above the transition grammage. Based on these results,a modified dewatering hypothesis was formulated. Thishypothesis links the non-uniform compression of the wet webwith different dewatering situations for low and high grammagewebs.</p><p><b>Keywords</b>Press felts, Roughness, Smoothness, SurfaceStructure, Uniformity, Wet pressing, Batt fibre, Base weave,Stress variations, Micro-scale.</p>

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Existing research suggests that market misvaluations affect corporate investment, often leading to suboptimal investment. I examine whether earnings smoothness reduces the impact of market valuations on corporate investment and in turn enhances investment efficiency. I find that earnings smoothness has a strong negative effect on the sensitivity of corporate investment to stock prices. Further analyses indicate that this negative effect is driven by both innate and discretionary components of earnings smoothness and is more pronounced for firms operating in more volatile business environments. I complement these findings by demonstrating that firms with smoother earnings have lower over- (under-)investment and higher future operating performance. Collectively, the evidence suggests that earnings smoothness improves corporate investment efficiency by reducing the impact of market valuations on investment.

[EN] The Ph.D. thesis "Weighted Banach Spaces of harmonic functions" presented here, treats several topics of functional analysis such as weights, composition operators, Fréchet and Gâteaux differentiability of the norm and isomorphism classes. The work is divided into four chapters that are preceded by one in which we introduce the notation and the well-known properties that we use in the proofs in the rest of the chapters. In the first chapter we study Banach spaces of harmonic functions on open sets of R^d endowed with weighted supremun norms. We define the harmonic associated weight, we explain its properties, we compare it with the holomorphic associated weight introduced by Bierstedt, Bonet and Taskinen, and we find differences and conditions under which they are exactly the same and conditions under which they are equivalent. The second chapter is devoted to the analysis of composition operators with holomorphic symbol between weighted Banach spaces of pluriharmonic functions. We characterize the continuity, the compactness and the essential norm of composition operators among these spaces in terms of their weights, thus extending the results of Bonet, Taskinen, Lindström, Wolf, Contreras, Montes and others for composition operators between spaces of holomorphic functions. We prove that for each value of the interval [0,1] there is a composition operator between weighted spaces of harmonic functions such that its essential norm attains this value. Most of the contents of Chapters 1 and 2 have been published by E. Jordá and the author in [48]. The third chapter is related with the study of Gâteaux and Fréchet differentiability of the norm. The \v{S}mulyan criterion states that the norm of a real Banach space X is Gâteaux differentiable at x\inX if and only if there exists x^* in the unit ball of the dual of X weak^* exposed by x and the norm is Fréchet differentiable at x if and only if x^* is weak^* strongly exposed in the unit ball of the dual of X by x. We show that in this criterion the unit ball of the dual of X can be replaced by a smaller convenient set, and we apply this extended criterion to characterize the points of Gâteaux and Fréchet differentiability of the norm of some spaces of harmonic functions and continuous functions with vector values. Starting from these results we get an easy proof of the theorem about the Gâteaux differentiability of the norm for spaces of compact linear operators announced by Heinrich and published without proof. Moreover, these results allow us to obtain applications to classical Banach spaces as the space H^\infty of bounded holomorphic functions in the disc and the algebra A(\overline{\D}) of continuous functions on \overline{\D} which are holomorphic on \D. The content of this chapter has been included by E. Jordá and the author in [47]. Finally, in the forth chapter we show that for any open set U of R^d and weight v on U, the space hv0(U) of harmonic functions such that multiplied by the weight vanishes at the boundary on U is almost isometric to a closed subspace of c0, extending a theorem due to Bonet and Wolf for the spaces of holomorphic functions Hv0(U) on open sets U of C^d. Likewise, we also study the geometry of these weighted spaces inspired by a work of Boyd and Rueda, examining topics such as the v-boundary and v-peak points and we give the conditions that provide examples where hv0(U) cannot be isometric to c0. For a balanced open set U of R^d, some geometrical conditions in U and convexity in the weight v ensure that hv0(U) is not rotund. These results have been published by E. Jordá and the author [46]. / [ES] La presente memoria, "Espacios de Banach ponderados de funciones armónicas ", trata diversos tópicos del análisis funcional, como son las funciones peso, los operadores de composición, la diferenciabilidad Fréchet y Gâteaux de la norma y las clases de isomorfismos. El trabajo está dividido en cuatro capítulos precedidos de uno inicial en el que introducimos la notación y las propiedades conocidas que usamos en las demostraciones del resto de capítulos. En el primer capítulo estudiamos espacios de Banach de funciones armónicas en conjuntos abiertos de R^d dotados de normas del supremo ponderadas. Definimos el peso asociado armónico, explicamos sus propiedades, lo comparamos con el peso asociado holomorfo introducido por Bierstedt, Bonet y Taskinen, y encontramos diferencias y condiciones para que sean exactamente iguales y condiciones para que sean equivalentes. El capítulo segundo está dedicado al análisis de los operadores de composición con símbolo holomorfo entre espacios de Banach ponderados de funciones pluriarmónicas. Caracterizamos la continuidad, la compacidad y la norma esencial de operadores de composición entre estos espacios en términos de los pesos, extendiendo los resultados de Bonet, Taskinen, Lindström, Wolf, Contreras, Montes y otros para operadores de composición entre espacios de funciones holomorfas. Probamos que para todo valor del intervalo [0,1] existe un operador de composición sobre espacios ponderados de funciones armónicas tal que su norma esencial alcanza dicho valor. La mayoría de los contenidos de los capítulos 1 y 2 han sido publicados por E. Jordá y la autora en [48]. El capítulo tercero está relacionado con el estudio de la diferenciabilidad Gâteaux y Fréchet de la norma. El criterio de \v{S}mulyan establece que la norma de un espacio de Banach real X es Gâteaux diferenciable en x\in X si y sólo si existe x^* en la bola unidad del dual de X débil expuesto por x y la norma es Fréchet diferenciable en x si y sólo si x^*es débil fuertemente expuesto en la bola unidad del dual de X por x. Mostramos que en este criterio la bola del dual de X puede ser reemplazada por un conjunto conveniente más pequeño, y aplicamos este criterio extendido para caracterizar los puntos de diferenciabilidad Gâteaux y Fréchet de la norma de algunos espacios de funciones armónicas y continuas con valores vectoriales. A partir de estos resultados conseguimos una prueba sencilla del teorema sobre la diferenciabilidad Gâteaux de la norma de espacios de operadores lineales compactos enunciado por Heinrich y publicado sin la prueba. Además, éstos nos permiten obtener aplicaciones para espacios de Banach clásicos como H^\infty de funciones holomorfas acotadas en el disco y A(\overline{\D}) de funciones continuas en \overline{\D} que son holomorfas en \D. Los contenidos de este capítulo han sido incluidos por E. Jordá y la autora en [47]. Finalmente, en el capítulo cuarto mostramos que para cualquier abierto U contenido en R^d y cualquier peso v en U, el espacio hv0(U), de funciones armónicas tales que multiplicadas por el peso desaparecen en el infinito de U, es casi isométrico a un subespacio cerrado de c0, extendiendo un teorema debido a Bonet y Wolf para los espacios de funciones holomorfas Hv0(U) en abiertos U de C^d. Así mismo, inspirados por un trabajo de Boyd y Rueda también estudiamos la geometría de estos espacios ponderados examinando tópicos como la v-frontera y los puntos v-peak y damos las condiciones que proporcionan ejemplos donde hv0(U) no puede ser isométrico a c0. Para un conjunto abierto equilibrado U de R^d, algunas condiciones geométricas en U y sobre convexidad en el peso v aseguran que hv0(U) no es rotundo. Estos resultados han sido publicados por E. Jordá y la autora en [46]. / [CAT] La present memòria, "Espais de Banach ponderats de funcions harmòniques", tracta diversos tòpics de l'anàlisi funcional, com són les funcions pes, els operadors de composició, la diferenciabilitat Fréchet i Gâteaux de la norma i les clases d'isomorfismes. El treball està dividit en quatre capítols precedits d'un d'inicial en què introduïm la notació i les propietats conegudes que fem servir en les demostracions de la resta de capítols. En el primer capítol estudiem espais de Banach de funcions harmòniques en conjunts oberts de R^d dotats de normes del suprem ponderades. Definim el pes associat harmònic, expliquem les seues propietats, el comparem amb el pes associat holomorf introduït per Bierstedt, Bonet i Taskinen, i trobem diferències i condicions perquè siguen exactament iguals i condicions perquè siguen equivalents. El capítol segon està dedicat a l'anàlisi dels operadors de composició amb símbol holomorf entre espais de Banach ponderats de funcions pluriharmòniques. Caracteritzem la continuïtat, la compacitat i la norma essencial d'operadors de composició entre aquests espais en termes dels pesos, estenent els resultats de Bonet, Taskinen, Lindström, Wolf, Contreras, Montes i altres per a operadors de composició entre espais de funcions holomorfes. Provem que per a tot valor de l'interval [0,1] hi ha un operador de composició sobre espais ponderats de funcions harmòniques tal que la seua norma essencial arriba aquest valor. La majoria dels continguts dels capítols 1 i 2 han estat publicats per E. Jordá i l'autora en [48]. El capítol tercer està relacionat amb l'estudi de la diferenciabilitat Gâteaux y Fréchet de la norma. El criteri de \v{S}mulyan estableix que la norma d'un espai de Banach real X és Gâteaux diferenciable en x\inX si i només si existeix x^* a la bola unitat del dual de X feble exposat per x i la norma és Fréchet diferenciable en x si i només si x^* és feble fortament exposat a la bola unitat del dual de X per x. Mostrem que en aquest criteri la bola del dual de X pot ser substituïda per un conjunt convenient més petit, i apliquem aquest criteri estès per caracteritzar els punts de diferenciabilitat Gâteaux i Fréchet de la norma d'alguns espais de funcions harmòniques i contínues amb valors vectorials. A partir d'aquests resultats aconseguim una prova senzilla del teorema sobre la diferenciabilitat Gâteaux de la norma d'espais d'operadors lineals compactes enunciat per Heinrich i publicat sense la prova. A més, aquests ens permeten obtenir aplicacions per a espais de Banach clàssics com l'espai H^\infty de funcions holomorfes acotades en el disc i l'àlgebra A(\overline{\D}) de funcions contínues en \overline{\D} que són holomorfes en \D. Els continguts d'aquest capítol han estat inclosos per E. Jordá i l'autora en [47]. Finalment, en el capítol quart mostrem que per a qualsevol conjunt obert U de R^d i qualsevol pes v en U, l'espai hv0(U), de funcions harmòniques tals que multiplicades pel pes desapareixen en el infinit d'U, és gairebé isomètric a un subespai tancat de c0, estenent un teorema degut a Bonet y Wolf per als espais de funcions holomorfes Hv0(U) en oberts U de C^d. Així mateix, inspirats per un treball de Boyd i Rueda també estudiem la geometria d'aquests espais ponderats examinant tòpics com la v-frontera i els punts v-peak i donem les condicions que proporcionen exemples on hv0(U) no pot ser isomètric a c0. Per a un conjunt obert equilibrat U de R^d, algunes condicions geomètriques en U i sobre convexitat en el pes v asseguren que hv0(U) no és rotund. Aquests resultats han estat publicats per E. Jordá i l'autora en [46]. / Zarco García, AM. (2015). Weighted Banach spaces of harmonic functions [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/56461 / TESIS

Two methods for the measurement of micro-scale stressvariations of press felt surfaces were developed. The methodswere based on a thin plastic film that was coated with anopaque stress-sensitive layer (Cronapress conversion film). Thefilm was compressed between a felt and a smooth surface. Uponapplication of load the opaque layer became partiallytransparent at the locations where load was applied by thesurface fibres of the felt. The degree of transparency was afunction of the locally applied stress. The spatial resolutionof the method was 6.3 µm, which means that even details ofthe order of the diameter of a batt fibre diameter can beresolved. Parameters characterising the stress variations were used toquantitatively describe the extent of the stress variations,the size of the contact areas and the distance between them.The applicability of these contact characterisation parameterswas evaluated in laboratory wet pressing experiments and inpilot paper machine trials for two sets of specially designedpress felts. In general, the dewatering result was mainlyinfluenced by the diameter of the felt surface batt fibres andby the web grammage. For a specific pulp type and operatingconditions a multivariate model was formulated based on themeasured web dryness, web grammage and each contactcharacterisation parameter. The model was able to describe thedewatering capability of the different felts tested. Contactcharacterisation parameters related to contact properties (e.g.contact area ratio) gave the best prediction for low grammagewebs, while parameters related to flow properties (e.g. size ofopenings) gave the best prediction for high grammage webs. Furthermore it was found that at a certain web grammage, thesurface batt fibre diameter did not have an influence on thedewatering result. This grammage was termed "transitiongrammage". Below the transition grammage a fine surface gavesignificantly better dewatering, while the opposite trend wasobserved above the transition grammage. Based on these results,a modified dewatering hypothesis was formulated. Thishypothesis links the non-uniform compression of the wet webwith different dewatering situations for low and high grammagewebs. KeywordsPress felts, Roughness, Smoothness, SurfaceStructure, Uniformity, Wet pressing, Batt fibre, Base weave,Stress variations, Micro-scale. / <p>QCR 20161026</p>

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