On the Chern number of I-admissible filtrations of ideals

Let I be an m-primary ideal of a Noetherian local ring (R, m) of positive dimension. The coefficient e(1)(I) of the Hilbert polynomial of an I-admissible filtration I is called the Chern number of I. A formula for the Chern number has been derived involving the Euler characteristic of subcomplexes of a Koszul complex. Specific formulas for the Chern number have been given in local rings of dimension at most two. These have been used to provide new and unified proofs of several results about e(1)(I).

Bi-Lipschitz A-triviality of map germs and Newton filtrations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Materials, methods and systems for purification and/or seperation

Materials, methods and systems are provided for the purifn., filtration and​/or sepn. of certain mols. such as certain size biomols. Certain embodiments relate to supports contg. at least one polymethacrylate polymer engineered to have certain pore diams. and other properties, and which can be functionally adapted to for certain purifications, filtrations and​/or sepns. Biomols. are selected from a group consisting of: polynucleotide mols., oligonucleotide mols. including antisense oligonucleotide mols. such as antisense RNA and other oligonucleotide mols. that are inhibitory of gene function such as small interfering RNA (siRNA)​, polypeptides including proteinaceous infective agents such as prions, for example, the infectious agent for CJD, and infectious agents such as viruses and phage.

On the Rademacher maximal function

Tools known as maximal functions are frequently used in harmonic analysis when studying local behaviour of functions. Typically they measure the suprema of local averages of non-negative functions. It is essential that the size (more precisely, the L^p-norm) of the maximal function is comparable to the size of the original function. When dealing with families of operators between Banach spaces we are often forced to replace the uniform bound with the larger R-bound. Hence such a replacement is also needed in the maximal function for functions taking values in spaces of operators. More specifically, the suprema of norms of local averages (i.e. their uniform bound in the operator norm) has to be replaced by their R-bound. This procedure gives us the Rademacher maximal function, which was introduced by Hytönen, McIntosh and Portal in order to prove a certain vector-valued Carleson's embedding theorem. They noticed that the sizes of an operator-valued function and its Rademacher maximal function are comparable for many common range spaces, but not for all. Certain requirements on the type and cotype of the spaces involved are necessary for this comparability, henceforth referred to as the “RMF-property”. It was shown, that other objects and parameters appearing in the definition, such as the domain of functions and the exponent p of the norm, make no difference to this. After a short introduction to randomized norms and geometry in Banach spaces we study the Rademacher maximal function on Euclidean spaces. The requirements on the type and cotype are considered, providing examples of spaces without RMF. L^p-spaces are shown to have RMF not only for p greater or equal to 2 (when it is trivial) but also for 1 < p < 2. A dyadic version of Carleson's embedding theorem is proven for scalar- and operator-valued functions. As the analysis with dyadic cubes can be generalized to filtrations on sigma-finite measure spaces, we consider the Rademacher maximal function in this case as well. It turns out that the RMF-property is independent of the filtration and the underlying measure space and that it is enough to consider very simple ones known as Haar filtrations. Scalar- and operator-valued analogues of Carleson's embedding theorem are also provided. With the RMF-property proven independent of the underlying measure space, we can use probabilistic notions and formulate it for martingales. Following a similar result for UMD-spaces, a weak type inequality is shown to be (necessary and) sufficient for the RMF-property. The RMF-property is also studied using concave functions giving yet another proof of its independence from various parameters.

A maximal operator, Carleson's embedding, and tent spaces for vector-valued functions

This thesis is concerned with the area of vector-valued Harmonic Analysis, where the central theme is to determine how results from classical Harmonic Analysis generalize to functions with values in an infinite dimensional Banach space. The work consists of three articles and an introduction. The first article studies the Rademacher maximal function that was originally defined by T. Hytönen, A. McIntosh and P. Portal in 2008 in order to prove a vector-valued version of Carleson's embedding theorem. The boundedness of the corresponding maximal operator on Lebesgue-(Bochner) -spaces defines the RMF-property of the range space. It is shown that the RMF-property is equivalent to a weak type inequality, which does not depend for instance on the integrability exponent, hence providing more flexibility for the RMF-property. The second article, which is written in collaboration with T. Hytönen, studies a vector-valued Carleson's embedding theorem with respect to filtrations. An earlier proof of the dyadic version assumed that the range space satisfies a certain geometric type condition, which this article shows to be also necessary. The third article deals with a vector-valued generalizations of tent spaces, originally defined by R. R. Coifman, Y. Meyer and E. M. Stein in the 80's, and concerns especially the ones related to square functions. A natural assumption on the range space is then the UMD-property. The main result is an atomic decomposition for tent spaces with integrability exponent one. In order to suit the stochastic integrals appearing in the vector-valued formulation, the proof is based on a geometric lemma for cones and differs essentially from the classical proof. Vector-valued tent spaces have also found applications in functional calculi for bisectorial operators. In the introduction these three themes come together when studying paraproduct operators for vector-valued functions. The Rademacher maximal function and Carleson's embedding theorem were applied already by Hytönen, McIntosh and Portal in order to prove boundedness for the dyadic paraproduct operator on Lebesgue-Bochner -spaces assuming that the range space satisfies both UMD- and RMF-properties. Whether UMD implies RMF is thus an interesting question. Tent spaces, on the other hand, provide a method to study continuous time paraproduct operators, although the RMF-property is not yet understood in the framework of tent spaces.

Blood and urinary abnormalities induced during and after 24-hour continuous running: A case report

In this reported clinical case, a healthy and well-trained male subject [aged 37 years, maximal oxygen uptake (V[Combining Dot Above]O2max) 64 mL·kg·min] ran for 23 hours and 35 minutes covering 160 km (6.7 km/h average running speed). The analysis of hematological and biochemical parameters 3 days before the event, just after termination of exercise, and after 24 and 48 hours of recovery revealed important changes on muscle and liver function, and hemolysis. The analysis of urine sediments showed an increment of red and white blood cells filtrations, compatible with transient nephritis. After 48 hours, most of these alterations were recovered. Physicians and health professionals who monitor such athletic events should be aware that these athletes could exhibit transient symptoms compatible with severe pathologies and diseases, although the genesis of these blood and urinary abnormalities are attributable to transient physiological adaptations rather to pathological status.

ON APPROXIMATION METHODS FOR UNBOUNDED OPERATORS

Department of Mathematics, Cochin University of Science and Technology

Development of an air-scour control system for membrane bioreactors

The thesis involves the development and implementation of a new and robust control system based on permeability trends but at the same time capable of reducing aeration proportionally to permeate flux. Permeability was made a key parameter for directly comparing temporary changes in membrane performance. Transmembrane pressure and flux were gathered every 10 seconds and permeability values were automatically calculated; different mathematical algorithms were applied for the signal filtering of on-line data. Short term and long term permeability trends were compared once a day, and a control action was applied proportionally to the short term/long term permeability ratio without exceeding the aeration flow recommended by the membrane suppliers.

A further study of the recovery and purification of surfactin from fermentation broth by membrane filtration

Surfactin is a bacterial lipopeptide produced by Bacillus subtilis and is a powerful surfactant, having also antiviral, antibacterial and antitumor properties. The recovery and purification of surfactin from complex fermentation broths is a major obstacle to its commercialization; therefore, a two-step membrane filtration process was developed using a lab scale tangential flow filtration (TFF) unit with 10 kDa MWCO regenerated cellulose (RC) and polyethersulfone (PES)membranes at three different transmembrane pressure (TMP) of 1.5 bar, 2.0 bar and 2.5 bar. Two modes of filtrations were studied, with and without cleaning of membranes prior to UF-2. In a first step of ultrafiltration (UF-1), surfactin was retained effectively by membranes at above its critical micelle concentration (CMC); subsequently in UF-2, the retentate micelles were disrupted by addition of 50% (v/v) methanol solution to allow recovery of surfactin in the permeate. Main protein contaminants were effectively retained by the membrane in UF-2. Flux of permeates, rejection coefficient (R) of surfactin and proteinwere measured during the filtrations. Overall the three different TMPs applied have no significant effect in the filtrations and PES is the more suitable membrane to selectively separate surfactin from fermentation broth, achieving high recovery and level of purity. In addition this two-step UF process is scalable for larger volume of samples without affecting the original functionality of surfactin, although membranes permeability can be affected due to exposure to methanolic solution used in UF-2.

Utilização de colunas verticais de filtração em manta e areia como pré-tratamento de filtro lento

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Synthesis and characterisation of polyacrylonitrile and its derived carbon materials

Carbon is a versatile material which is composed of different allotropes, and also come in with different structures. Carbon nanofibres (CNFs) is one dimensional carbon nanomaterials, which have exhibited superior mechanical properties, great specific area, good electrical conductivity, good biocompatibility, and ease of modification. In addition to the lower cost associated to compare with carbon nanotubes (CNTs), CNFs have been attracted in numerous applications, such as reinforcement materials, filtrations, Li-ion battery, supercapacitor as well as tissue engineering, just to list a few. Therefore, it is a great deal to understand the relationship between the fabrication conditions and the characteristics of the resulted CNFs. In this project, electrospun PAN NFs were used as precursor material to fabricate carbon nanofibres. In order to produce CNFs with good morphology, the processing parameters of PAN nanofibres by electrospinning was optimized toward to the morphology at solution concentration of 12 wt%. The optimized processing parameters at given concentration were 16 kV, 14 cm and 1.5 mL/h, which led to the formation of PAN NFs with average fibre diameter of approximately 260 nm. Along with the effect of processing parameter study, the effect of concentration on the morphology was also carried out at optimized processing parameters. It was found that by increasing concentration of PAN solution from 2 to 16%, the resulted PAN transformed from beads only, to beaded fibres and finally to smooth fibres. With further increasing concentration the morphology of smooth fibres remain with increase in the fibre diameter. Electrospun PAN NFs with average fibre of 306 nm was selected to be converted into CNFs by using standard heating procedures, stabilisation in air at 280 °C and carbonization in N2. The effect of carbonization temperature ranging from 500 to 1000 °C was investigated, by using SEM, FTIR, Raman, and Impedance spectroscopy. With increasing carbonization temperature from 500 to 1000 °C, the diameter of NFs was decreased from 260 to 187, associated with loss of almost all functional groups of NFs. It was indicated by Raman results, that the graphitic crystallite size was increased from 2.62 to 5.24 nm, and the activation energy obtained for this growth was 7570 J/mol. Furthermore, impedance results (i.e. Cole-Cole plot) revealed that the electrical characteristic of CNFs transitioned from being insulating to electrically conducting in nature, suggested by the different electrical circuits extracted from Cole-Cole plots with carbonization temperature from 500 to 800 °C. The carbonization on PAN NFs with diameter of ~431nm was carried out by using novel route, microwave plasma enhance chemical vapour deposition (MPECVD) process. To compare with carbonized PAN NFs by using conventional route, MPECVD was not only able to facilitate carbonization process, but more interestingly can form carbon nanowalls (CNWs) grown on the surfaces of carbonized PAN NFs. Suggested by the unique morphology, the potential applications for the resulted carbon fibrous hybrid materials are supercapacitor electrode material, filtrations, and etc., The method developed in this project required one step less, compared with other literature. Therefore, using MPECVD on stabilised PAN NFs is proposed as economical, and straightforward approach towards mass production of carbon fibrous hybrid materials containing CNWs.

Biomassaperäisen liuoksen fraktiointi membraanisuodatuksella

Työn tavoitteena oli hiilihydraattien ja aminohappojen talteenotto biomassaperäisistä liuoksista erilaisina fraktioina ultra- ja nanosuodattamalla niitä erilaisilla membraaneilla. Työ tehtiin selvitystyönä Senson Oy:lle syystalven 2015 ja kevään 2016 välisenä aikana. Teoriaosassa perehdyttiin nanosuodatukseen ja sen erilaisiin sovelluksiin teollisuudessa, sekä lyhyesti muihin paineavusteisiin membraanisuodatusprosesseihin. Teoriaosassa myös keskityttiin erityisesti nanosuodatuksessa käytettyihin membraaneihin sekä niiden likaantumismekanismeihin. Kokeellisessa osassa keskityttiin hiilihydraattien ja aminohappojen talteenottoon kolmesta biomassaperäisestä liuoksesta. Tutkimuksen osa-alueita olivat ultrasuodatus, ultrasuodatuksen konsentraatin kirkastaminen sekä ultrasuodatuksen permeaatin fraktiointi nanosuodatuksella. Tutkimuksessa kiinnitettiin myös erityistä huomiota suodatuskalvojen likaantumiseen ja peseytyvyyteen sekä kalvojen käytettävyyteen pesujen jälkeen. Ultrasuodatuksessa kaikkien kolmen liuoksen kohdalla tutkittavien hiilihydraattien saanto permeaattiin oli hyvä, noin 90 %. Ultrasuodatuksissa käytettyjen membraanien osalta ei myöskään ollut havaittavissa merkittävää likaantumista. Ultrasuodatuksen konsentraattien kirkastamiskokeissa sameutta aiheuttavat komponentit saatiin poistettua kaikista liuoksista yli 94 %:in tehokkuudella. Nanosuodatuksissa monosakkaridit saatiin erotettua suuremmista hiilihydraattikomponenteista joko täysin tai lähes täysin (97 - 100 %). Nanosuodatuksissa käytettyjen membraanien osalta huomattavaa likaantumista oli havaittavissa vain membraanilla 2. Tulosten perusteella nanosuodatuksen voidaan sanoa olevan tehokas tapa erottaa pienet monosakkaridit suuremmista hiilihydraattiyhdisteistä.