On the Diophantine equation (nk)=(ml)+d\binom{n}{k}=\binom{m}{l}+d

By finding all integral points on certain elliptic and hyperelliptic curves we completely solve the Diophantine equation $\binom{n}{k}=\binom{m}{l}+d$ for $-3\leq d\leq 3$ and $(k,l)\in\{(2,3),\; (2,4),\;(2,5),\; (2,6),\; (2,8),\; (3,4),\; (3,6),\; (4,6), \; (4,8)\}.$ Moreover, we present some other observations of computational and theoretical nature concerning the title equation

Holistic Teaching Practices through a Growth Mindset Lens: A Case Study Examination of ELA High School Classrooms

A prevalent issue that exists in education is students who demonstrate a defeated or fixed mindset—that is, when students view their intelligence and academic abilities as something that is inherent and cannot be changed overtime. Most of the research on growth mindset takes place in math classrooms, as the literature suggests that math is more frequently viewed as a subject area in which students have fixed mindsets. Additionally, most of the research on growth mindsets involves the use of quantitative research methods as opposed to the use of qualitative methods. Furthermore, there is a lack of research that examines teaching practices holistically in terms of how teachers may implicitly or explicitly portray growth or fixed mindset messages to students through their approach towards classroom organization, instruction, and evaluation and assessment. Therefore, this study sought to examine holistic teaching practices through a growth mindset lens to determine those general and discipline specific practices that may perpetuate growth mindset messages to students in high school English Language Arts classrooms. A case study design has been utilized in which four ELA high school teachers have been observed to determine how growth mindset messages may be perpetuated to students. A framework was developed outlining general and discipline-specific practices that may convey growth mindset messages to students in high school ELA classrooms. Limitations and directions for future research are also discussed

Estudio mineralógico de los granates de la Unidad de Fuente Piedra (Sierra Nevada, Cordilleras Béticas)

The Fuente Piedra Unit Includes garnet-bearing metape- liks. The mineralogical sIcibdy of garnets reveals a shift to the alniandine end of the Al-Sp-Pyr. series in imreasing con- ditions of metamorphism.

Bacterial Cellulose: A sustainable source to develop value-added products - A review

In recent decades, worldwide economic and environmental issues have prompted research scientists to re-direct their interests to bio-based resources, which are sustainable in nature. In this context, microbial polysaccharides, such as bacterial cellulose (BC), also known as microbial cellulose (MC), are some of the upcoming and emergent resources and have potential application in various bio- and non-bio-based sectors of the modern world. Many researchers have already established novel BC/MC production methods, and many new studies have been published on lab-scale and large-scale production aspects of BC/MC to date. To further expand the novel use of this sustainable source, significant progress toward the development of BC/MC has appeared in recent years. Specifically, there have been many publications and/or research reports on the valorization of BC/MC in the food, paper, materials, biomedical, pharmaceutical, and cosmeceutical industries, among others. This review will address the novel application aspects of BC/MC today, with the aim of demonstrating the importance of this sustainable and novel source in the development of value-added products