Integrating a Global Induction Mechanism into a Sequent Calculus

Most interesting proofs in mathematics contain an inductive argument which requires an extension of the LK-calculus to formalize. The most commonly used calculi for induction contain a separate rule or axiom which reduces the valid proof theoretic properties of the calculus. To the best of our knowledge, there are no such calculi which allow cut-elimination to a normal form with the subformula property, i.e. every formula occurring in the proof is a subformula of the end sequent. Proof schemata are a variant of LK-proofs able to simulate induction by linking proofs together. There exists a schematic normal form which has comparable proof theoretic behaviour to normal forms with the subformula property. However, a calculus for the construction of proof schemata does not exist. In this paper, we introduce a calculus for proof schemata and prove soundness and completeness with respect to a fragment of the inductive arguments formalizable in Peano arithmetic.Comment: 16 page

Factors affecting farmers’ adoption of natural farming technologies in New Albay, Maragusan, Compostela Valley, Philippines

In the Philippines, the sustainability of natural resources and the profitability of farming has become a major concern for smallholder farmers. To address these concerns, government agencies and the private sector are delivering workshops on natural farming technologies to farmers. Training includes the preparation of different concoctions such as indigenous micro-organisms (IMO), fermented fruit juice (FFJ) and fermented plant juice (FPJ), fish amino acid (FAA), oriental herbal juice (OHN) and calcium phosphate (Caphos). Other natural farm technologies include vermiculture. The products from the training are applied to the farmer’s own farms with any surplus products sold to other farmers. In Maragusan, Compostela Valley, Philippines, a group of smallholder farmers have successfully produced organic fertilizers as a result of the training provided to them. Initially, while training was provided to the group to facilitate the marketing of the fresh vegetable crops they produced, the skills learnt were readily transferable. This study discusses the development of the New Albay cluster and factors leading to its decline as a marketing cluster. This study will also explore the costs and returns associated with the application of organic fertilizer to vegetable crops in comparison to conventional farming practices. Results show that the cost of production arising from the use of natural farming technologies is lower than conventional farming

Social connections and smallholder vegetable farmers’ collaborative marketing strategy: The case of the small farmers association of Quirogpang in Davao City, the Philippines

In the Philippines, vegetable farmers generally have only small land holdings. Because of this, plus an apparent lack of financial capital, it is difficult for smallholder farmers to meet the large volume demands imposed by institutional buyers and wholesalers. The small volume and the large variation in quality puts smallholder farmers at a significant disadvantage when it comes to arranging transport and marketing. However, smallholder farmers can engage in collaborative cluster farming in order to meet the demands of the market and to bolster production volume. In the cluster, the farmers carry out production planning and marketing activities collectively. Utilizing the case study method and the 8-step clustering approach formulated by the Catholic Relief Services, this paper will present key success factors and several challenges faced by the Small Farmers Association of Quirogpang (SFAQ) in Marilog, Davao City, Philippines. At the same time, it will identify important institutional supports and strategies that may enhance the success of this and other clusters. The paper highlights key success factors such as the social connections shared by the cluster members and leadership. In this case, these commonalities exist because it is an area-based cluster which includes neighbours and relatives who all practice one religion and speak the same language or dialect

Estabilidad del rendimiento de algunos genotipos de habichuela en Honduras

Bean (Phaseolus vulgaris L.) cultivars are grown under diverse environmental conditions in Central America because of geography, multiple growing seasons and variable inputs. The regression of mean genotype yields onto mean environment yields may provide useful information for selecting beans with greater yield stability when grown under these conditions. The principal objective of this research was to test yield stability of bean cultivars and promising breeding lines across a range of environments representative of the bean growing regions of Honduras. In 1984, 25 cultivars/breeding lines of various origins were grown in 23 field trials in Honduras. The trials were conducted during two seasons and in three different departments. Stability was examined on the basis of mean square deviations (MSD) from regression, large rank order changes among mean seed yield of genotypes were evident when different seasons and departments were compared. A highly significant correlation of the regression slope (b) with mean genotype yield supported use of MSD to assess yield stability. Mean yield and MSD were not correlated. The two determinate cultivars in the trial had poor stability characteristics. Honduran varieties had greater yield and better stability characteristics than most entries in the trial. Black-seeded lines 'B-190', '3B-5-1' and '8325-7' had high mean yield and good stability characteristics. These results show the importance of testing for yield stability if a cultivar is to be released for use in different regions and seasons in Central American countries. Also high yield and stability, judged on the basis of MSD, can occur in the same genotype.Varias cultivares de habichuela (Phaseolus vulgaris L.) se sembraron en América Central en una variedad de condiciones ambientales debido a la geografía de las áreas de siembra y a las diversas estaciones de crecimiento a lo largo de todo el año. Las regresiones de los promedios de rendimiento de los genotipos y de los rendimientos medios por ambiente pueden proveer información valiosa para seleccionar líneas con una mejor estabilidad de rendimiento. El objetivo principal de esta investigación fue estudiar la estabilidad de rendimiento de cultivares y líneas de mejoramiento de habichuela con características prometedoras para autorizar su uso en tres áreas productoras de habichuela de Honduras. Los experimentos se sembraron durante dos épocas de siembra en tres departamentos del país. La estabilidad de rendimiento se determinó a partir de las desviaciones del cuadrado medio (MSD). De las regresiones se pudo observar grandes cambios en el orden de los genotipos cuando se compararon las épocas y los lugares de siembra. Una correlación altamente significativa entre la pendiente de regresión y el promedio de rendimiento por genotipo respalda el uso del método de las MSD para estudiar estabilidad de rendimiento. El promedio de rendimiento y las MSD no estuvieron correlacionados. Las dos cultivares determinadas incluidas en los exprerimentos presentaron características pobres de estabilidad. De las cuatro variedades de Honduras, dos de ellas tuvieron mejores rendimientos y estabilidad que la mayoría de las cultivares incluidas en los experimentos. Las líneas negras B-190, 3B-5-1 y 8325-7 presentaron buena estabilidad y excelentes promedios de rendimiento. Estos resultados muestran la importancia que tiene estudiar la estabilidad de rendimiento de una cultivar de frijol que se autoriza para sembrarse en diferentes regiones y estaciones de siembra de los países centroamericanos y también nos indica que y los altos rendimientos y la estabilidad medidos a base de las MSD pueden estar presentes en el mismo genotipo

Spin-to-Orbital Angular Momentum Conversion in Semiconductor Microcavities

We experimentally demonstrate a technique for the generation of optical beams carrying orbital angular momentum using a planar semiconductor microcavity. Despite being isotropic systems, the transverse electric - transverse magnetic (TE-TM) polarization splitting featured by semiconductor microcavities allows for the conversion of the circular polarization of an incoming laser beam into the orbital angular momentum of the transmitted light field. The process implies the formation of topological entities, a pair of optical half-vortices, in the intracavity field

Conformación de clúster de turismo como prueba piloto en el municipio de Nahuizalco

La conformación de un clúster turístico tiene como finalidad visible el agrupar un determinado sector de empresas que desarrollen un mercado turístico. En ese sentido, dichas empresas contribuirán a lograr una participación directa en el desarrollo de los mercados laborales, en la creación de instituciones e infraestructura especializada y en el incremento de los flujos de información, en donde el mayor intercambio de esta última genera el marco propicio para la innovación, la movilidad laboral y el enlace entre proveedores, productores y consumidores. Las empresas formantes del clúster cooperan para mejorar su competitividad, para alcanzar objetivos comunes y así fortalecer las economías de los lugares en desarrollo. En los últimos años del presente siglo, el tema de los clúster ha empezado a escucharse con más frecuencia y cada vez más fuerte, siendo esta una forma de explicar la ventaja competitiva que se adquiere por medio de la localización y el signo de cómo las comunidades o regiones pueden alcanzar mayores niveles de crecimiento y desarrollo económico, en función del aprovechamiento de los mercados.La presente investigación fue subvencionada por la Universidad Tecnológica de El Salvador. Las solicitudes de información, separatas y otros documentos relativos al presente estudio pueden hacerse a la dirección postal: calle Arce, 1020, Universidad Tecnológica de El Salvador, Facultad de Ciencias Empresarial o Vicerrectoría de Investigación, Dirección de Investigaciones calle Arce y 17ª avenida Norte, edificio José Martí, 2ª planta, o al correo electrónico: [email protected] Tecnológica de El Salvado

Referral of sexual violence against children: How do children and caregivers use a formal child protection mechanism in Harare, Zimbabwe?

Despite widespread expansion of policies to prevent and respond to violence over the past three decades, sexual violence against children remains common globally. Zimbabwe has expansive legal and policy frameworks to prevent, and formal services to respond to, sexual violence. Yet evidence is lacking about how children and caregivers use formal referral mechanisms. This study conducted secondary qualitative analysis of sexual violence cases [N=74] processed in Harare Magistrates Court and referred to Childline Zimbabwe, in October-November 2020, to examine which experiences children and/or their caregivers formally refer as sexual violence; how they perceive and manage these experiences; and how this relates to national policy contexts. Caregivers, particularly female, were central to reporting sexual violence. Data suggested that some forms of sexual violence were formally referred, including community sexual assault and abuse within families, however some adolescent girls faced blame and shame. There were gaps in reporting of sexual violence against boys, and sexual violence from dating partners or authority figures, with data suggesting that gendered stigma, shame, and fears of institutional authority, were barriers for reporting. Caregivers also reported consensual adolescent sexual relationships to police. These findings contribute to the limited evidence on forms of sexual violence that are and are not formally referred globally, and in sub-Saharan African settings. Existing policy frameworks in Zimbabwe can be strengthened around age of maturity, adolescent sexuality, sidelining of boy survivors, and the role of schools in child protection. Interventions should support caregivers’ efforts to report violence, while also addressing gendered blame and stigma, and stigmatisation of adolescent sexuality

Sub MeV Particles Detection and Identification in the MUNU detector ((1)ISN, IN2P3/CNRS-UJF, Grenoble, France, (2)Institut de Physique, Neuch\^atel, Switzerland, (3) INFN, Padova Italy, (4) Physik-Institut, Z\"{u}rich, Switzerland)

We report on the performance of a 1 m$^{3}$ TPC filled with CF$_{4}$ at 3 bar, immersed in liquid scintillator and viewed by photomultipliers. Particle detection, event identification and localization achieved by measuring both the current signal and the scintillation light are presented. Particular features of $\alpha$ particle detection are also discussed. Finally, the ${54}$Mn photopeak, reconstructed from the Compton scattering and recoil angle is shown.Comment: Latex, 19 pages, 20 figure