CONTINUITY OF CONDITION SPECTRUM AND ITS LEVEL SET IN BANACH ALGEBRA

For 0 < � < 1 and a Banach algebra element a, this thesis aims to establish the results related to continuity of condition spectrum and its level set correspondence at (�; a). Here we propose a method of study to achieve the continuity. We first identify the Banach algebras at which the interior of the level set of condition spectrum is empty and then we obtain the continuity results. This thesis consists of four chapters. Chapter 1 contains all the prerequisites which are crucial for the development of the thesis. In particular, this chapter has a quick review of the basic properties of spectrum, condition spectrum, upper and lower hemicontiuous correspondences. We also concentrate on analytic vector valued maps and generalized maximum modulus theorem for them. For an element a in A, Chapter 2 has the results related to interior of the level of set of the condition spectrum of a. At first, we focus on

Stable U(IV) Complexes Form at High-Affinity Mineral Surface Sites

Uranium (U) poses a significant contamination hazard to soils, sediments, and groundwater due to its extensive use for energy production. Despite advances in modeling the risks of this toxic and radioactive element, lack of information about the mechanisms controlling U transport hinders further improvements, particularly in reducing environments where UIV predominates. Here we establish that mineral surfaces can stabilize the majority of U as adsorbed UIV species following reduction of UVI. Using X-ray absorption spectroscopy and electron imaging analysis, we find that at low surface loading, UIV forms inner-sphere complexes with two metal oxides, TiO2 (rutile) and Fe3O4 (magnetite) (at <1.3 U nm–2 and <0.037 U nm–2, respectively). The uraninite (UO2) form of UIV predominates only at higher surface loading. UIV–TiO2 complexes remain stable for at least 12 months, and UIV–Fe3O4 complexes remain stable for at least 4 months, under anoxic conditions. Adsorbed UIV results from UVI reduction by FeII or by the reduced electron shuttle AH2QDS, suggesting that both abiotic and biotic reduction pathways can produce stable UIV–mineral complexes in the subsurface. The observed control of high-affinity mineral surface sites on UIV speciation helps explain the presence of nonuraninite UIV in sediments and has important implications for U transport modeling

Computed Tomography With Intravenous Contrast Alone: The Role of Intra‐abdominal Fat on the Ability to Visualize the Normal Appendix in Children

Background Computed tomography ( CT ) with enteric contrast is frequently used to evaluate children with suspected appendicitis. The use of CT with intravenous ( IV ) contrast alone ( CT IV ) may be sufficient, however, particularly in patients with adequate intra‐abdominal fat ( IAF ). Objectives The authors aimed 1) to determine the ability of radiologists to visualize the normal (nondiseased) appendix with CT IV in children and to assess whether IAF adequacy affects this ability and 2) to assess the association between IAF adequacy and patient characteristics. Methods This was a retrospective 16‐center study using a preexisting database of abdominal CT scans. Children 3 to 18 years who had CT IV scan and measured weights and for whom appendectomy history was known from medical record review were included. The sample was chosen based on age to yield a sample with and without adequate IAF . Radiologists at each center reread their site's CT IV scans to assess appendix visualization and IAF adequacy. IAF was categorized as “adequate” if there was any amount of fat completely surrounding the cecum and “inadequate” if otherwise. Results A total of 280 patients were included, with mean age of 10.6 years (range = 3.1 to 17.9 years). All 280 had no history of prior appendectomy; therefore, each patient had a presumed normal appendix. A total of 102 patients (36.4%) had adequate IAF . The proportion of normal appendices visualized with CT IV was 72.9% (95% confidence interval [ CI ] = 67.2% to 78.0%); the proportions were 89% (95% CI  = 81.5% to 94.5%) and 63% (95% CI  = 56.0% to 70.6%) in those with and without adequate IAF (95% CI for difference of proportions = 16% to 36%). Greater weight and older age were strongly associated with IAF adequacy (p < 0.001), with weight appearing to be a stronger predictor, particularly in females. Although statistically associated, there was noted overlap in the weights and ages of those with and without adequate IAF . Conclusions Protocols using CT with IV contrast alone to visualize the appendix can reasonably include weight, age, or both as considerations for determining when this approach is appropriate. However, although IAF will more frequently be adequate in older, heavier patients, highly accurate prediction of IAF adequacy appears challenging solely based on age and weight. Resumen Tomografía Computarizada Únicamente con Contraste Intravenoso: El Papel de la Grasa Intrabadominal en la Capacidad para Visualizar el Apéndice Normal en los Niños Introduction La tomografía computarizada ( TC ) con contraste entérico es usada frecuentemente para evaluar a los niños con sospecha de apendicitis. El uso de la TC únicamente con contraste intravenoso ( TC IV ) puede ser suficiente, especialmente en pacientes con adecuada grasa intrabdominal ( GIA ). Objetivos 1) Determinar la capacidad de los radiólogos para visualizar el apéndice normal (sin enfermedad) con TC IV en niños, y valorar si la cantidad de GIA afecta a esta capacidad; y 2) valorar la asociación entre la idoneidad de la GIA y las características del paciente. Metodología Estudio retrospectivo de 16 hospitales que utilizó una base de datos prexistente de TC abdominales. Se incluyó a los niños entre 3 y 18 años que tenían una TC IV , una medida del peso e historia de apendectomía conocida por la revisión de la historia clínica. La muestra se eligió en base a la edad con el fin de conseguir una muestra con y sin GIA adecuada. Los radiólogos de cada centro releyeron las TC IV de sus centros para valorar la visualización del apéndice y la adecuación de la GIA . La GIA se clasificó como “adecuada” si había cualquier cantidad de grasa completamente alrededor del ciego e “inadecuada” si era de otra manera. Resultados Se incluyeron 280 pacientes, con una media de edad de 10,6 años (rango 3,1 a 17,9 años). Ninguno tenía historia previa de apendectomía; por lo tanto todos los pacientes tuvieron un apéndice presumiblemente normal. Ciento dos pacientes (36,4%) tuvieron GIA adecuada. El porcentaje de apéndices normales visualizados con TC IV fue de 72,9% ( IC 95% = 67,2% a 78,0%); la proporción fue 89% ( IC 95% = 81,5% a 94,5%), y 63% ( IC 95% = 56,0% a 70,6%) en aquéllos con y sin GIA adecuada ( IC 95% para la diferencia de proporciones = 16% a 36%). El mayor peso y la mayor edad se asociaron fuertemente con la adecuación de la GIA (p < 0,001), y el peso resultó ser el mayor factor predictivo, especialmente en mujeres. Aunque se asoció estadísticamente, se vio un solapamiento en los pesos y edades de aquéllos con y sin GIA adecuada. Conclusiones Los protocolos que usan la TC IV para visualizar el apéndice pueden razonablemente incluir el peso, la edad, o ambas como consideraciones para determinar cuándo esta aproximación es apropiada. Sin embargo, aunque la cantidad de GIA será frecuentemente más apropiada en los pacientes más mayores y de mayor peso, la predicción certera de adecuación de GIA es altamente desafiante si se basa sólo en la edad y el peso.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/99695/1/acem12185.pd

Level sets of (p,e-p)outer generalized pseudo spectrum

Let A be a complex Banach algebra with unit e. Let p be a non trivial idempotent element in A and ε>0. For a∈A, it is proved that the interior of the level set of (p,e−p)−ε pseudo spectrum of a is empty in the unbounded component of (p,e−p) resolvent set of a. An example is constructed to show that the condition ‘unbounded component’ can not be dropped. Further, it is proved this ‘unbounded component’ can be dropped in the case when A is B(X) where X is a complex uniformly convex Banach space. That is, if T∈B(X) then interior of the level set of (p,I−p)−ε pseudo spectrum is empty in (p,I−p) resolvent set of T

Level sets of the condition spectrum

For 0 < ε ≤ 1 and an element a of a complex unital Banach algebra A, we prove the following two topological properties about the level sets of the condition spectrum. (1) If ε = 1, then the 1-level set of the condition spectrum of a has an empty interior unless a is a scalar multiple of the unity. (2) If 0 < ε < 1, then the ε-level set of the condition spectrum of a has an empty interior in the unbounded component of the resolvent set of a. Further, we show that, if the Banach space X is complex uniformly convex or if X* is complex uniformly convex, then, for any operator T acting on X, the level set of the ε-condition spectrum of T has an empty interior

On some fixed point theorems in Banach spaces

In this paper, some fixed point theorems are proved for multi-mappings as well as a pair of mappings. These extend certain known results due to Kirk, Browder, Kanna, Ćirić and Rhoades

Software defined networking challenges and future direction: A case study of implementing SDN features on OpenStack private cloud

Cloud computing provides services on demand instantly, such as access to network infrastructure consisting of computing hardware, operating systems, network storage, database and applications. Network usage and demands are growing at a very fast rate and to meet the current requirements, there is a need for automatic infrastructure scaling. Traditional networks are difficult to automate because of the distributed nature of their decision making process for switching or routing which are collocated on the same device. Managing complex environments using traditional networks is time-consuming and expensive, especially in the case of generating virtual machines, migration and network configuration. To mitigate the challenges, network operations require efficient, flexible, agile and scalable software defined networks (SDN). This paper discuss various issues in SDN and suggests how to mitigate the network management related issues. A private cloud prototype test bed was setup to implement the SDN on the OpenStack platform to test and evaluate the various network performances provided by the various configurations

Predicting functional associations from metabolism using bi-partite network algorithms

<p>Abstract</p> <p>Background</p> <p>Metabolic reconstructions contain detailed information about metabolic enzymes and their reactants and products. These networks can be used to infer functional associations between metabolic enzymes. Many methods are based on the number of metabolites shared by two enzymes, or the shortest path between two enzymes. Metabolite sharing can miss associations between non-consecutive enzymes in a serial pathway, and shortest-path algorithms are sensitive to high-degree metabolites such as water and ATP that create connections between enzymes with little functional similarity.</p> <p>Results</p> <p>We present new, fast methods to infer functional associations in metabolic networks. A local method, the degree-corrected Poisson score, is based only on the metabolites shared by two enzymes, but uses the known metabolite degree distribution. A global method, based on graph diffusion kernels, predicts associations between enzymes that do not share metabolites. Both methods are robust to high-degree metabolites. They out-perform previous methods in predicting shared Gene Ontology (GO) annotations and in predicting experimentally observed synthetic lethal genetic interactions. Including cellular compartment information improves GO annotation predictions but degrades synthetic lethal interaction prediction. These new methods perform nearly as well as computationally demanding methods based on flux balance analysis.</p> <p>Conclusions</p> <p>We present fast, accurate methods to predict functional associations from metabolic networks. Biological significance is demonstrated by identifying enzymes whose strong metabolic correlations are missed by conventional annotations in GO, most often enzymes involved in transport vs. synthesis of the same metabolite or other enzyme pairs that share a metabolite but are separated by conventional pathway boundaries. More generally, the methods described here may be valuable for analyzing other types of networks with long-tailed degree distributions and high-degree hubs.</p