The number of zeros of unilateral polynomials over coquaternions revisited

The literature on quaternionic polynomials and, in particular, on methods for finding and classifying their zero sets, is fast developing and reveals a growing interest in this subject. In contrast, polynomials defined over the algebra of coquaternions have received very little attention from researchers. One of the few exceptions is the very recent paper by Janovska and Opfer [Electron Trans Numer Anal. 2017;46:55-70], where, among other results, we can find a first attempt to prove that a unilateral coquaternionic polynomial of degree n has, at most, zeros. In this paper we present a full proof of this result, using a totally different and, from our point of view, much simpler approach. Also, we give a complete characterization of the zero sets of such polynomials and present a new result giving conditions which guarantee the existence of a special type of zeros. An algorithm to compute and classify all the zeros of a coquaternionic polynomial is proposed and several numerical examples are carefully constructed.Research at CMAT was financed by Portuguese Funds through FCT -Fundacao para a Ciencia e a Tecnologia, within the [project number UID/MAT/00013/2013]. Research at NIPE was carried out within the funding with COMPETE reference number POCI-01-0145-FEDER-006683 [project number UID/ECO/03182/2013], with the FCT/MEC's (Fundacao para a Ciencia e a Tecnologia, I.P.) financial support through national funding and by the ERDF through the Operational Programme on 'Competitiveness and Internationalization - COMPETE 2020' under the PT2020 Partnership Agreement

Analysis of ecological intensity of metallurgical production

Ferrous metallurgy is inherently a highly intensive field in terms of energy and raw materials. The impacts of high energy intensity are enormous: the necessary production of larger amount of energy related to high emissions of pollutants and greenhouse gases, associated with increasing negative impacts on the state of the environment and the health of inhabitants. The article suggests the possibility of using the method of structural analysis to calculate direct and complex ecological intensity and to use it as a basis to determine the ecological intensity of the individual metallurgical technologies. The processing of ecological structural model can significantly contribute to the identification of ecologically intensive final products and can improve the decision-making process in this area

Polynomials over quaternions and coquaternions: a unified approach

This paper aims to present, in a unified manner, results which are valid on both the algebras of quaternions and coquaternions and, simultaneously, call the attention to the main differences between these two algebras. The rings of one-sided polynomials over each of these algebras are studied and some important differences in what concerns the structure of the set of their zeros are remarked. Examples illustrating this different behavior of the zero-sets of quaternionic and coquaternionic polynomials are also presented.(undefined)info:eu-repo/semantics/publishedVersio

Database mirroring in fault-tolerant continuous technological process control

This paper describes the implementations of mirroring technology of the selected database systems – Microsoft SQL Server, MySQL and Caché. By simulating critical failures the systems behavior and their resilience against failure were tested. The aim was to determine whether the database mirroring is suitable to use in continuous metallurgical processes for ensuring the fault-tolerant solution at affordable cost. The present day database systems are characterized by high robustness and are resistant to sudden system failure. Database mirroring technologies are reliable and even low-budget projects can be provided with a decent fault-tolerant solution. The database system technologies available for low-budget projects are not suitable for use in real-time systems

Mathematica tools for quaternionic polynomials

In this paper we revisit the ring of (left) one-sided quaternionic polynomials with special focus on its zero structure. This area of research has attracted the attention of several authors and therefore it is natural to develop computational tools for working in this setting. The main contribution of this paper is a Mathematica collection of functions QPolynomial for solving polynomial problems that we frequently find in applications.(undefined)info:eu-repo/semantics/publishedVersio

Assessment of genetic diversity of selected tartary and common buckwheat accessions

Genetic diversity of plant genetic resources for food and agriculture is a unique and irreplaceable source for further crop genetic improvement. The aim of this paper was the field evaluation of buckwheat genetic resources in the Czech Republic. In the case of the 77 common buckwheat (Fagopyrum esculentum Moench.) genotypes, most had reddishgreen stems (80%), cordate leaves (82%), white flowers (87%), and grey ovate achenes (44% and 57%, respectively). Vegetative growth duration ranged from 104 to 131 days. The 1000 seed weight (TSW) varied from 18.6 to 33.2 g. In the 15 tartary buckwheat (Fagopyrum tataricum Gaertn.) genotypes, there were no remarkable differences in morphological traits. Vegetative growth duration was 101 to 148 days, and the TSW varied from 8.10 to 20.0 g. Similarity/dissimilarity dendograms were calculated using the results of the field evaluation. Principal component analysis was also performed. The dendrograms showed high diversity in the morphological and phenological characteristics evaluated. Performance of the buckwheat varieties, particularly, their developmental stages, depended highly on the weather conditions of the year. Only days to flowering seemed to be affected by variety. Because the evaluation was made according to the IPGRI buckwheat descriptors the characteristics are compatible with data from other gene banks.Para la mejora vegetal es imprescindible disponer de diversidad genética en los recursos fitogenéticos para la alimentación y la agricultura. El objetivo de este estudio fue la evaluación en campo de la morfología y fenología de 77 accesiones de alforfón de Tartaria (Fagopyrum tataricum Gaertn.) y 15 de trigo sarraceno (Fagopyrum esculentum Moench.) en las condiciones de Europa Central, en la República Checa. La mayoría de los genotipos del trigo sarraceno poseen pedúnculos de color rojo-verde (80%), hojas acorazonadas (82%), flores blancas (87%) y semillas de color gris y oblongas (44% y 57%, respectivamente); el ciclo vegetativo oscila entre 104 y 131 días y el peso de mil semillas (TSW) entre 18,6 y 33,2 g. En el caso del alforfón de Tartaria no se detectaron diferencias significativas en los caracteres morfológicos; el ciclo vegetativo oscila entre 101 y 148 días; y el TSW entre 8,10 y 20,0 g. En base a estos resultados se creó un dendrograma de similitud y disimilitud generado por un análisis de componentes principales. El dendrograma indica una gran diversidad en las características morfológicas y fenológicas. Las fases de desarrollo dependieron principalmente de las condiciones climáticas del año en variedades de trigo sarraceno. Solo el carácter «días hasta floración» parece afectado por la variedad. Debido a que la evaluación se hizo de acuerdo con los descriptores para trigo sarraceno del IPGRI, los resultados son compatibles con los datos de otros bancos de germoplasma

Evaluación de la diversidad génetica en alforfón de Tartaria y trigo sarraceno

Genetic diversity of plant genetic resources for food and agriculture is a unique and irreplaceable source for further crop genetic improvement. The aim of this paper was the field evaluation of buckwheat genetic resources in the Czech Republic. In the case of the 77 common buckwheat (Fagopyrum esculentum Moench.) genotypes, most had reddishgreen stems (80%), cordate leaves (82%), white flowers (87%), and grey ovate achenes (44% and 57%, respectively). Vegetative growth duration ranged from 104 to 131 days. The 1000 seed weight (TSW) varied from 18.6 to 33.2 g. In the 15 tartary buckwheat (Fagopyrum tataricum Gaertn.) genotypes, there were no remarkable differences in morphological traits. Vegetative growth duration was 101 to 148 days, and the TSW varied from 8.10 to 20.0 g. Similarity/dissimilarity dendograms were calculated using the results of the field evaluation. Principal component analysis was also performed. The dendrograms showed high diversity in the morphological and phenological characteristics evaluated. Performance of the buckwheat varieties, particularly, their developmental stages, depended highly on the weather conditions of the year. Only days to flowering seemed to be affected by variety. Because the evaluation was made according to the IPGRI buckwheat descriptors the characteristics are compatible with data from other gene banks.Para la mejora vegetal es imprescindible disponer de diversidad genética en los recursos fitogenéticos para la alimentación y la agricultura. El objetivo de este estudio fue la evaluación en campo de la morfología y fenología de 77 accesiones de alforfón de Tartaria (Fagopyrum tataricum Gaertn.) y 15 de trigo sarraceno (Fagopyrum esculentum Moench.) en las condiciones de Europa Central, en la República Checa. La mayoría de los genotipos del trigo sarraceno poseen pedúnculos de color rojo-verde (80%), hojas acorazonadas (82%), flores blancas (87%) y semillas de color gris y oblongas (44% y 57%, respectivamente); el ciclo vegetativo oscila entre 104 y 131 días y el peso de mil semillas (TSW) entre 18,6 y 33,2 g. En el caso del alforfón de Tartaria no se detectaron diferencias significativas en los caracteres morfológicos; el ciclo vegetativo oscila entre 101 y 148 días; y el TSW entre 8,10 y 20,0 g. En base a estos resultados se creó un dendrograma de similitud y disimilitud generado por un análisis de componentes principales. El dendrograma indica una gran diversidad en las características morfológicas y fenológicas. Las fases de desarrollo dependieron principalmente de las condiciones climáticas del año en variedades de trigo sarraceno. Solo el carácter "días hasta floración" parece afectado por la variedad. Debido a que la evaluación se hizo de acuerdo con los descriptores para trigo sarraceno del IPGRI, los resultados son compatibles con los datos de otros bancos de germoplasma

Achieving high strength and low Young’s modulus by controlling the beta stabilizers content in Ti-Nb-Ta-Zr-O alloys

High strength and low Young’s modulus is the desired combination of mechanical properties for the endoprostheses material. Metastable beta titanium alloys are promising materials for this application. In this study, four Ti-xNb-6Ta-7Zr-0.7O (wt.%) alloys were prepared where Nb content ranged from 26 to 35 wt. %. All alloys contained pure beta phase. The high oxygen content causes high microhardness (330 HV), hence also the strength, while decreasing content of Nb leads to lower electrons per atom (e/a) ratio. The e/a ratio affects the Young’s modulus which is highest (76 GPa) in Ti-35Nb-6Ta-7Zr-0.7O alloy with e/a=4.31 and the lowest (64 GPa) in Ti-26Nb-6Ta-7Zr-0.7O with e/a=4.24. Such evolution of Young’s modulus is in accordance with existing literature data, however, in comparison with other works, the Ti-26Nb-6Ta-7Zr-0.7O alloy shows double microhardness when compared to alloys with similar Young’s modulus. Therefore, the approach of using controlled oxygen content for alloy design is very promising for development of biocompatible metastable beta Ti alloy for endoprostheses production