LR property of non-well-formed scales

This article studies generated scales having exactly three different step sizes within the language of algebraic combinatorics on words. These scales and their corresponding step-patterns are called non well formed. We prove that they can be naturally inserted in the Christoffel tree of well-formed words. Our primary focus in this study is on the left- and right-Lyndon factorization of these words. We will characterize the non-well-formed words for which both factorizations coincide. We say that these words satisfy the LR property and show that the LR property is satisfied exactly for half of the non-well-formed words. These are symmetrically distributed in the extended Christoffel tree. Moreover, we find a surprising connection between the LR property and the Christoffel duality. Finally, we prove that there are infinitely many Christoffel–Lyndon words among the set of non-well-formed words and thus there are infinitely many generated scales having as step-pattern a Christoffel–Lyndon word.

Generadores ScalaCheck para property-based testing de programas Spark y Spark Streaming

En los últimos años hemos sido testigos de la expansión del paradigma big data a una velocidad vertiginosa. Los cambios en este campo, nos permiten ampliar las áreas a tratar; lo que a su vez implica una mayor complejidad de los sistemas software asociados a estas tareas, como sucede en sistemas de monitorización o en el Internet de las Cosas (Internet of Things). Asimismo, la necesidad de implementar programas cada vez robustos y eficientes, es decir, que permitan el cómputo de datos a mayor velocidad y de los se obtengan información relevante, ahorrando costes y tiempo, ha propiciado la necesidad cada vez mayor de herramientas que permitan evaluar estos programas. En este contexto, el presente proyecto se centra en extender la herramienta sscheck. Sscheck permite la generación de casos de prueba basados en propiedades de programas escritos en Spark y Spark Streaming. Estos lenguajes forman parte de un mismo marco de código abierto para la computación distribuida en clúster. Dado que las pruebas basadas en propiedades generan datos aleatorios, es difícil reproducir los problemas encontrados en una cierta sesion; por ello, la extensión se centrará en cargar y guardar casos de test en disco mediante el muestreo de datos desde colecciones mayores.

The Finite Embeddability Property for some noncommutative knotted varieties of RL and DRL.

Residuated lattices, although originally considered in the realm of algebra providing a general setting for studying ideals in ring theory, were later shown to form algebraic models for substructural logics. The latter are non-classical logics that include intuitionistic, relevance, many-valued, and linear logic, among others. Most of the important examples of substructural logics are obtained by adding structural rules to the basic logical calculus

Development of a Strengths-Based Model for Insurance Automobile, Property, and Casualty Claims Operations

ABSTRACT \ Employers know that to have a successful organization, they must have the right people in the right jobs. But how will they know whom to place where? The development of a model based upon an individual's personality traits and strengths, and how to best use them, is a good place to start. Employees working in positions in which their traits and strengths are maximized enjoy work more, are more efficient, and are less apt to be absent or to look for work elsewhere. It is a mutually beneficial process of selection for both employers and employees. This model illustrates the process in an automobile and property insurance claims operation through utilization of the Myers-Briggs Type Indicators and the StrengthsFinder Profiles.

[ Property act], 1787

Copy of act pertaining to taking of property for failure to pay taxes. Signed: Alexander Martin and John Sitgreaves.

Indenture acknowledging sale of property, Boston, 1753

Document acknowledges the sale of the late Samuel Clark's house and property to Alexander Hill. Samuel Clark's executor, James Clark, was required by law to sell the property to the highest bidder in order to pay the debts of the deceased.

Deed of sale of property, Hingham, Massachusetts, 1686

Deed acknowledging Sprague's sale of land in Hingham to Israel Fering. Signed by Sprague, Nathaniel Beale, Sr., and John Parsens, Jr.