About Projections of Solutions for Fuzzy Differential Equations

In this paper we propose the concept of fuzzy projections on subspaces of , obtained from Zadeh's extension of canonical projections in , and we study some of the main properties of such projections. Furthermore, we will review some properties of fuzzy projection solution of fuzzy differential equations. As we will see, the concept of fuzzy projection can be interesting for the graphical representation of fuzzy solutions

The impact of surgical delay on resectability of colorectal cancer: An international prospective cohort study

AIM: The SARS-CoV-2 pandemic has provided a unique opportunity to explore the impact of surgical delays on cancer resectability. This study aimed to compare resectability for colorectal cancer patients undergoing delayed versus non-delayed surgery. METHODS: This was an international prospective cohort study of consecutive colorectal cancer patients with a decision for curative surgery (January-April 2020). Surgical delay was defined as an operation taking place more than 4 weeks after treatment decision, in a patient who did not receive neoadjuvant therapy. A subgroup analysis explored the effects of delay in elective patients only. The impact of longer delays was explored in a sensitivity analysis. The primary outcome was complete resection, defined as curative resection with an R0 margin. RESULTS: Overall, 5453 patients from 304 hospitals in 47 countries were included, of whom 6.6% (358/5453) did not receive their planned operation. Of the 4304 operated patients without neoadjuvant therapy, 40.5% (1744/4304) were delayed beyond 4 weeks. Delayed patients were more likely to be older, men, more comorbid, have higher body mass index and have rectal cancer and early stage disease. Delayed patients had higher unadjusted rates of complete resection (93.7% vs. 91.9%, P = 0.032) and lower rates of emergency surgery (4.5% vs. 22.5%, P < 0.001). After adjustment, delay was not associated with a lower rate of complete resection (OR 1.18, 95% CI 0.90-1.55, P = 0.224), which was consistent in elective patients only (OR 0.94, 95% CI 0.69-1.27, P = 0.672). Longer delays were not associated with poorer outcomes. CONCLUSION: One in 15 colorectal cancer patients did not receive their planned operation during the first wave of COVID-19. Surgical delay did not appear to compromise resectability, raising the hypothesis that any reduction in long-term survival attributable to delays is likely to be due to micro-metastatic disease

Normas Vectoriais Hermiticas com Valores em Algebras de Yoshida #beta#-Regulares

In this dissertation we make generalizations of some usual results in Metric Spaces to V-Metric Spaces. A V-Metric Space is a space where a 'Metric' - V-Metric or Vectorial Metric - was defined and with range in partially ordered linear space. We will be specially dealing with V-Metric Spaces, the vectorial metrics of which are induced by a vectorial norms and also, specifically with norms which are associated with mappings that we have the defined and named Vectorial Inner-Products. In the first chapter and extremely relevant generalization is made: we extend to a nonfinite dimensional space the notion of Regular Yosida Space, we have adopted for these spaces the designation of '#beta#-Regular Yosida Spaces' (#beta#-denotes the set of all hipermaximal bands in a Yosida Space). We present a new version of the Yosida Theorem II', which establishes a one-one Riesz Homomorphism of a #beta#-Regular Yosida Spaces in the Space B(#beta#) the elements of which are real bounded mappings defined on #beta#. We also prove that if the space is a Dedekind Complete the homomorphism is a mapping onto B(#beta#). This fact allows us to define a 'Product' operation in the Yosida Space turning in into an algebra (Yosida Algebra). Among the several results proved in the considered algebras we namely remark the following: if Y is a Dedekind Complete #beta#-Regular Yosida Algebra and also norm complete then the norm defined in Y is necessarily the following: ??? In chapter three besides several results concerning series convergence and families summability of elements in a V-Metric Space, we prove an important representation Theorem for elements in vectorially normed spaces. This theorem is an indispensable tool in the proofs of many subsquent results. In chapter four we define the concept of Vectorial Inner-Product and it is shown how we can use the vectorial inner-product to define a vectorial norm. We given a necessary and sufficient condition for a vectorial norm to be hermitian and generalize some 'classic' results in the inner-product spaces namely. Bessel's Inequality, Parseval's Formula and some properties related with a complete ortonormal related with a complete orthonormal sets. In chapter five we establish conditions such that, being #epsilon#_1, #epsilon#_2 V-Metric Spaces, we may define a vectorial norma in L(#epsilon#_1,#epsilon#_2), the elements of which are bounded linear operators with domain #epsilon#_1 and renga in #epsilon#_2. It is also made a generalization of the Hahn-Banach Theorem as well as given some important consequences of it. We finish this chapter with a Fixed Point Theorem. In the chapter six the emphasis is mainly on the study of the bounded linear operators in V-Metric Spaces. We probe among other things the following inclusions: ??? This chapter finishes with a Representation Theorem for bounded linear operators on a complete vectorial Inner-Product space. In chapter seven it is made an approach to the study of the Best Approximation Problem in V-Metric Space. Being G nonempty compact subset of a V-Metric Space #epsilon# and given #mu# (element of)#epsilon#\g, establish a sufficient condition that proves the exisyence of a best approximation of #mu# in G. We finish our dissertation with a brief introduction to the study of differentiation in V-Metric Spaces (p-differentiation). This notion of differentiation coincides with a Frechet differentiation when p is an ordinary norm. With this notion it is possible to generalize in a V-Metric Spaces some usual properties in Banach spaces related with Frechet differentiationAvailable from Fundacao para a Ciencia e a Tecnologia, Servico de Informacao e Documentacao, Av. D. Carlos I, 126, 1200 Lisboa / FCT - Fundação para o Ciência e a TecnologiaSIGLEPTPortuga

The impact of surgical delay on resectability of colorectal cancer: An international prospective cohort study

The SARS-CoV-2 pandemic has provided a unique opportunity to explore the impact of surgical delays on cancer resectability. This study aimed to compare resectability for colorectal cancer patients undergoing delayed versus non-delayed surgery

The impact of surgical delay on resectability of colorectal cancer: An international prospective cohort study

AimThe SARS-CoV-2 pandemic has provided a unique opportunity to explore the impact of surgical delays on cancer resectability. This study aimed to compare resectability for colorectal cancer patients undergoing delayed versus non-delayed surgery.MethodsThis was an international prospective cohort study of consecutive colorectal cancer patients with a decision for curative surgery (January-April 2020). Surgical delay was defined as an operation taking place more than 4 weeks after treatment decision, in a patient who did not receive neoadjuvant therapy. A subgroup analysis explored the effects of delay in elective patients only. The impact of longer delays was explored in a sensitivity analysis. The primary outcome was complete resection, defined as curative resection with an R0 margin.ResultsOverall, 5453 patients from 304 hospitals in 47 countries were included, of whom 6.6% (358/5453) did not receive their planned operation. Of the 4304 operated patients without neoadjuvant therapy, 40.5% (1744/4304) were delayed beyond 4 weeks. Delayed patients were more likely to be older, men, more comorbid, have higher body mass index and have rectal cancer and early stage disease. Delayed patients had higher unadjusted rates of complete resection (93.7% vs. 91.9%, P = 0.032) and lower rates of emergency surgery (4.5% vs. 22.5%, P ConclusionOne in 15 colorectal cancer patients did not receive their planned operation during the first wave of COVID-19. Surgical delay did not appear to compromise resectability, raising the hypothesis that any reduction in long-term survival attributable to delays is likely to be due to micro-metastatic disease