El teorema de Riemann-Roch y el morfismo de Gysin en geometría aritmética

Le th eor eme de Riemann-Roch originale a rme que pour tout morphisme propre f : Y ! X entre vari et es quasi-projectifs lisses sur un corps, et tout el ement a 2 K0(Y ) du groupe de Grothendieck des br es vectoriels on a ch(f!(a)) = f {u100000}Td(Tf ) ch(a) (cf. [BS58]). Ici ch est le caract ere de Chern, Td(Tf ) est la classe de Todd du br e tangent relative et f et f! sont les images directes de l'anneau de Chow et K0 respectivement. Apr es, Baum, Fulton et MacPherson ont d emontr e en [BFM75] le th eor eme de Riemann-Roch pour des morphismes localement intersection compl ete entre des sch emas alg ebriques (sch emas s epar es et localement de type ni sur un corps) projectifs et singuli eres. En [FG83] Fulton et Gillet ont d emontr e le th eor eme sans hypoth eses projectifs. L'extension a la th eorie K sup erieure pour des sch emas r eguli eres sur une base fut d emontr e par Gillet en [Gil81]. Le th eor eme de Riemann-Roch qu'il prouve est pour des morphismes projectifs entre des sch emas lisses et quasi-projectifs. Donc, dans le cas des sch emas sur un corps, le r esultat de Gillet n'inclus pas le th eor eme de [BFM75]. La plus grande g en eralisation du th eor eme de Riemann-Roch que je connais est [D eg14] et [HS15], o u D eglise et Holmstrom-Scholbach obtiennent ind ependamment le th eor eme de Riemann- Roch pour la K-th eorie sup erieure et les morphismes projectifs lic entre sch emas r eguli eres sur une base noetherienne de dimension nie... NOTA 520 8 El teorema de Riemann-Roch original de Grothendieck a rma que para todo mor smo propio f : Y ! X, entre variedades irreducibles quasiproyectivas lisas sobre un cuerpo, y todo elemento a 2 K0(Y ) del grupo de Grothendieck de brados vectoriales se satisface la relaci on ch(f!(a)) = f {u100000}Td(Tf ) ch(a) (cf. [BS58]). Recu erdese que ch denota el car acter de Chern, Td(Tf ) la clase de Todd del brado tangente relativo y f y f! las im agenes directas en el anillo de Chow y K0 respectivamente. M as tarde Baum, Fulton MacPherson probaron en [BFM75] el teorema de Riemann-Roch para mor smos localmente intersecci on completa entre esquemas algebraicos (es decir, esquemas separados localmente de tipo nito sobre cuerpo) proyectivos singulares. En [FG83] Fulton y Gillet probaron el teorema sin hip otesis proyectivas. La notable extensi on a la teor a K superior para esquemas regulares sobre una base fue probada por Gillet en [Gil81]. El teorema de Riemann-Roch all probado es para mor smos proyectivos entre esquemas lisos quasiproyectivos. Sin embargo, obs ervese que en el caso de esquemas sobre cuerpo el resultado de Gillet no recupera el teorema de [BFM75]. La mayor generalizaci on del teorema de Riemann-Roch que yo conozco es [D eg14] y [HS15] donde D eglise y Holmstrom-Scholbach obtuvieron independientemente el teorema de Riemann-Roch para teor a K superior y mor smos proyectivos lic entre esquemas regulares sobre una base noetheriana nito dimensional...

Propriété d'universalité de la fonction zêta de Riemann

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

A transatlantic case: the derivative action as a corporate governance tool

The derivative action as a minority shareholder protection device seems to be almost a dead-letter law in the British Isles as compared with the United States. Whether it can or should be revived through legislative reform and judicial interpretation presents us with important governance questions at first instance, but also raises questions regarding the importance of law, as distinct from non-legally enforceable norms, to the development of corporate governance systems, in particular regarding the director-shareholder relationship.

Propriété d'universalité de la fonction zêta de Riemann

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Targeting treatment resistant breast cancer stem cells with FKBPL and its peptide derivative, AD-01

FKBPL and its peptide derivative, AD-01, have already demonstrated well-established inhibitory effects on breast cancer growth and CD44 dependent anti-angiogenic activity1, 2, 3. Since breast cancer stem cells (BCSCs) are CD44 positive, we wanted to explore if AD-01 could specifically target BCSCs. FKBPL stable overexpression or AD-01 treatment were highly effective at reducing the BCSC population measured by inhibiting mammosphere forming efficiency (MFE) in cell lines and primary breast cancer samples from both solid breast tumours and pleural effusions. Flow cytometry, to assess the ESA+/CD44+/CD24- subpopulation, validated these results. The ability of AD-01 to inhibit the self-renewal capacity of BCSCs was confirmed across three generations of mammospheres, where mammospheres were completely eradicated by the third generation (p<0.001). Clonogenic assays suggested that AD-01 mediated BCSC differentiation, with a significant decrease in the number of holoclones and an associated increase in meroclones/paraclones. In support of this, the stem cell markers, Nanog and Oct4 were significantly reduced following AD-01 treatment, whilst transfection of FKBPL-targeted siRNAs led to an increase in these markers and in mammosphere forming potential, highlighting the endogenous role of FKBPL in stem cell signalling. The clinical relevance of this was confirmed using a publically available microarray data set (GSE7390), where, high FKBPL and low Nanog expression were independently associated with improved overall survival in breast cancer patients (log rank test p=0.03; hazard ratio=3.01). When AD-01 was combined with other agents, we observed synergistic activity with the Notch inhibitor, DAPT and AD-01 was also able to abrogate a chemo- and radiotherapy induced enrichment in BCSCs. Importantly, using ‘gold standard’ in vivo limiting dilution assays we demonstrated a delay in tumour initiation and reoccurrence in AD-01 treated xenografts. In summary, AD-01 appears to have dual anti-angiogenic and anti-BCSC activity which will be advantageous as this agent enters clinical trial.

A Discretization of the Hadamard fractional derivative

We present a new discretization for the Hadamard fractional derivative, that simplifies the computations. We then apply the method to solve a fractional differential equation and a fractional variational problem with dependence on the Hadamard fractional derivative.

Riemann-Hilbert problems for poly-Hardy space on the unit ball

In this paper, we focus on a Riemann–Hilbert boundary value problem (BVP) with a constant coefficients for the poly-Hardy space on the real unit ball in higher dimensions. We first discuss the boundary behaviour of functions in the poly-Hardy class. Then we construct the Schwarz kernel and the higher order Schwarz operator to study Riemann–Hilbert BVPs over the unit ball for the poly- Hardy class. Finally, we obtain explicit integral expressions for their solutions. As a special case, monogenic signals as elements in the Hardy space over the unit sphere will be reconstructed in the case of boundary data given in terms of functions having values in a Clifford subalgebra. Such monogenic signals represent the generalization of analytic signals as elements of the Hardy space over the unit circle of the complex plane.

Recovery of palladium from a spent automobile catalyst leaching solution by a thiodiglycolamide derivative

In the sequence of previous research on the development of novel liquid-liquid amidetype compounds to efficiently and selectively extract platinum-group metals (PGMs) from concentrated hydrochloric acid media, a specific thiodiglycolamide derivative – N,N’-dimethyl-N,N’-dicyclohexylthiodiglycolamide (DMDCHTDGA) – has been applied for the recovery of palladium(II) from a spent automobile catalyst leaching solution, containing palladium(II) and rhodium(III) as PGMs. The results obtained are rather promising, since the DMDCHTDGA behavior towards the two PGMs is similar to that observed for hydrochloric acid aqueous media studied before, simulating the real leaching phases. Within eleven metal elements co-existing in solution, the majority in high fold-excesses, only aluminum(III) and cerium(III) interfere in the palladium(II) liquid-liquid extraction process, requiring further optimization.

Anti-Metastatic Properties of a Marine Bacterial Exopolysaccharide-Based Derivative Designed to Mimic Glycosaminoglycans

Osteosarcoma is the most frequent malignant primary bone tumor characterized by a high potency to form lung metastases. In this study, the effect of three oversulfated low molecular weight marine bacterial exopolysaccharides (OS-EPS) with different molecular weights (4, 8 and 15 kDa) were first evaluated in vitro on human and murine osteosarcoma cell lines. Different biological activities were studied: cell proliferation, cell adhesion and migration, matrix metalloproteinase expression. This in vitro study showed that only the OS-EPS 15 kDa derivative could inhibit the invasiveness of osteosarcoma cells with an inhibition rate close to 90%. Moreover, this derivative was potent to inhibit both migration and invasiveness of osteosarcoma cell lines; had no significant effect on their cell cycle; and increased slightly the expression of MMP-9, and more highly the expression of its physiological specific tissue inhibitor TIMP-1. Then, the in vivo experiments showed that the OS-EPS 15 kDa derivative had no effect on the primary osteosarcoma tumor induced by osteosarcoma cell lines but was very efficient to inhibit the establishment of lung metastases in vivo. These results can help to better understand the mechanisms of GAGs and GAG-like derivatives in the biology of the tumor cells and their interactions with the bone environment to develop new therapeutic strategies.

A Caputo fractional derivative of a function with respect to another function

In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor’s Theorem, Fermat’s Theorem, etc., are studied. Also, a numerical method to deal with such operators, consisting in approximating the fractional derivative by a sum that depends on the first-order derivative, is presented. Relying on examples, we show the efficiency and applicability of the method. Finally, an application of the fractional derivative, by considering a Population Growth Model, and showing that we can model more accurately the process using different kernels for the fractional operator is provided.

Fractional differential equations with dependence on the Caputo-Katugampola derivative

In this paper we present a new type of fractional operator, the Caputo–Katugampola derivative. The Caputo and the Caputo–Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a fractional Cauchy type problem, with dependence on the Caputo–Katugampola derivative, is proven. A decomposition formula for the Caputo–Katugampola derivative is obtained. This formula allows us to provide a simple numerical procedure to solve the fractional differential equation.