Abstract: Previous studies focused on the comparison of the optimal output levels of regret- averse firms under uncertainty and firms under certainty. This paper extends the theory by further investigating the effects of regret-aversion on production. We compare the optimal output levels of regret-averse firms with purely risk- averse firms under uncertainty and firms under certainty. We first show that the linear-regret firms will surely produce more than their purely risk-averse counterparts and surely produce less than firms under certainty. Thereafter, we give sufficient conditions to ensure the regret-averse firms to produce more than the purely risk-averse counterparts and study the comparative statics of the optimal production. We also develop properties of regret-aversion on production.

Resumen: Estudios previos se focalizaron en la comparación de los niveles óptimos de producción de empresas aversas al arrepentimiento bajo certidumbre e incerti- dumbre. Aquí se extiende la teoría al comparar los niveles óptimos de producción de empresas aversas al arrepentimiento con aquellas aversas al riesgo (con certidumbre e incertidumbre). Mostramos que empresas con arrepentimiento lineal producirán más que las empresas aversas al riesgo y menos que con certidumbre. Desarrollamos las propiedades de la aversión al arrepentimiento en la producción utilizando un modelo binario. Los resultados encontrados pueden ser de utilidad para las decisiones de producción.

ABSTRACT BACKGROUND: Osteosarcoma is the most prevalent malignant bone tumor in children and adolescents. Lung metastases are associated with poor prognosis. OBJECTIVE: The aim here was to explore the prevalence of and risk and prognostic factors for lung metastases in high-grade osteosarcoma patients. DESIGN AND SETTING: Retrospective cohort study based on the Surveillance, Epidemiology and End Results (SEER) database in the United States. METHODS: Data on 1,408 high-grade osteosarcoma patients registered in the SEER database between 2010 and 2015 were extracted. From these, all patients with high-grade osteosarcoma and initial lung metastasis were selected for analysis on risk and prognostic factors for lung metastases. Overall survival was estimated. RESULTS: There were 238 patients (16.90%) with lung metastases at diagnosis. Axial location, tumor size > 10 cm (odds ratio, OR 3.19; 95% confidence interval, CI: 1.58-6.45), higher N stage (OR 4.84; 95% CI: 1.94-12.13) and presence of bone metastases (OR 8.73; 95% CI: 4.37-17.48) or brain metastases (OR 25.63; 95% CI: 1.55-422.86) were significantly associated with lung metastases. Younger age and surgical treatment (hazard ratio, HR 0.46; 95% CI: 0.30-0.71) favored survival. Median survival was prolonged through primary tumor surgery. CONCLUSIONS: The factors revealed here may guide lung metastasis screening and prophylactic treatment for osteosarcoma patients. A primary tumor in an axial location, greater primary tumor size, higher lymph node stage and presence of bone or brain metastases were significantly correlated with lung metastases. The elderly group (≥ 60 years) showed significant correlation with poor overall survival. For improved survival among high-grade osteosarcoma patients with lung metastases, aggressive surgery on the primary tumor site should be encouraged.

In this paper, the notions of SPN-compactness, countable SPNcompactness and the SPN-Lindelöf property are introduced in L-topological spaces by means of strongly preclosed L-sets. In an L-space, an Lset having the SPN-Lindelöf property is SPN-compact if and only if it is countably SPN-compact. (Countable) SPN-compactness implies (countable) N-compactness, the SPN-Lindelöf property implies the N-Lindelöf property, but each inverse is not true. Every L-set with finite support is SPN-compact. The intersection of an (a countable) SPN-compact L-set and a strongly preclosed L-set is (countably) SPNcompact. The strong preirresolute image of an (a countable) SPNcompact L-set is (countably) SPN-compact. Moreover SPN-compactness can be characterized by nets