Algebra

Use of spreadsheets in a beginning algebra course was investigated mainly with regard to their potential to promote generalization of patterns. Less is known about their use in promoting understanding and learning of transformational activities. The overall purpose of this paper is to consider the conceptual aspects of learning a transformational skill (use of the distributive law to produce equivalent algebraic expressions) in a learning sequence composed of both spreadsheets and paper-and-pencil activities. We conducted a sequence of classroom activities in several classes, and analyzed the students’ work on a spreadsheet activity and on an assessment activity by both qualitative and quantitative methods. The findings indicate both encouraging benefits and some potential sources of difficulties caused by the use of spreadsheets at initial stages of learning symbolic transformations.

Abstract. Let k be a field and let F⊂ k [x1,..., xn] be a finite set of monomials whose exponents lie on a positive hyperplane. We give necessary conditions for the normality of both the Rees algebra R [Ft] and the subring k [F]. If the monomials in F have the same ...

The algebra of qualified relations proposed by Ceri and Pelagatti supports pruning of distributed database queries, minimizing the number of sites involved in evaluation. Domain interval typing in the framework of formal type inference subsumes this approach, pruning not only unsatisfiable subqueries involving fragmentation predicates, but also unsatisfiable subqueries mentioning any relation attribute

INTISARI Dalam tesis ini dianalisa mengenai model matematika peningkatan enzim hati akibat mono-infeksi HIV. Model ini dibangun atas dasar asumsi infeksi HIV hanya menyebabkan replikasi virus terjadi hanya pada sel CD4+, dan tidak terjadi pada sel hepatosit. Selain itu, tingginya enzim hati (alanine aminotransferase) merupakan indikator kuat dalam menentukan tingkat kerusakan hati. Model HIV dalam hati ini adalah pengembangan dari model infeksi viral HIV ke sel CD4+ yang diteliti oleh Perelson (1994), yang kemudian dimodifikasi oleh Nampala (2013) dengan penambahan model sel CTLs dalam tubuh. Berbeda dengan apa yang dilakukan dengan peneliti sebelumnya, dalam tesis ini dilakukan suatu koreksi syarat eksistensi ekuilibrium endemik dan dilakukan metode baru dalam menentukan kestabilan lokal dan global titik ekuilibrium bebas penyakit (infeksi). Analisis bifurkasi dilakukan disekitar untuk mengetahui kestabilan titik ekuilibrium endemik. Hasil dari penelitian ini adalah titik ekuilibrium bebas infeksi dan titik ekuilibrium endemik keduanya tidak stabil ketika Hal ini mengindikasikan bahwa HIV dengan berjalannya waktu mampu menyebabkan kerusakan hati yang ekstrim tanpa gejala lazim dalam waktu cukup singkat. Hasil simulasi numerik memberikan hubungan menarik antara peningkatan enzim hati, virus, sel CD4+, dan sel hepatosit. Kata kunci : Level alanine aminotransferase (ALT), HIV, endemik, bifurkasi. ABSTRACT In this thesis, we analyse the mathematical model of liver enzyme elevation due to mono-infection with HIV. This model is built on the assumption of HIV infection only causes viral replication only on CD4+ cells, and it doesn't occur in hepatocytes cell. In addition, high liver enzymes (alanine aminotransferase or ALT) is a strong indicator in determining the extent of liver damage. Models of HIV in the heart is the development of models viral infection of HIV to CD4+ cells were examined by Perelson (1994), and then modified by Nampala (2013) models with the addition of model CTLs cells in the body. In contrast to what is done by the previous researcher, in this thesis we do a correction of conditions existence of endemic equilibrium and perform a new method to determine the local and global stability of the disease-free equilibrium point (infection). Bifurcation analyse around for determine the stability of the endemic equilibrium point. The results of this research is the point of the infection-free equilibrium and endemic equilibrium point which is unstable when both. This indicates that HIV as time goes capable of causing extreme damage to the liver in short time. Numerical simulation results provide an interesting relationship between liver enzymes, viruses, CD4+ cells, and hepatocyte cells.

Asphalt is a small component in the flexible pavement. As a binder, it is commonly needed 4 %-10 % of total mixtures of the mix design. In the mixed design have to consider the technical aspect and another aspects including to obtain material easly on the site. There for, it is necessary to study the alternative material (asphalt) when asphalt not ready in the market any time. This study to compare both the asphalt Pertamina Pen 60/70 products with the asphalt Esso Pen 60/70 products base on the Bina Marga specifications. In order to have the best result, it is necessary to study in the laboratory to know Marshall characteristic and Structural Values (modulus elastisity and material strengthening coefficiens) on both of the asphalt Pertamina Pen 60/70 products with the asphalt Esso Pen 60/70 products on the asphalt optimum content. By using the VIM as a Marshall convensional 6 % find the asphalt optimum content value, based on it ± 0,5 % the VIM-PRD value on the 2 x 400 blow was determined. From the individual test result as well as in mixed result show that the stability value of the asphalt Pertamina Pen 60/70 products (906 kg) is lower than the stability value of asphalt Esso Pen 60/70 products (989 kg). Beside that, the Voids in Mix (VIM) as well as the PRD value indicate that the result for the asphalt Pertamina Pen 60/70 products is lower than the VIM value of the asphalt Esso Pen 60/70 products. Which caused impervious layer and the air can not filled in the mixing to result in oksidation and to be damage the asphalt. The result study show that Voids in Mineral Aggregate (VMA) Marshall value of the Pertamina Pen 60/70 products is lower than the VMA value of the asphalt Esso Pen 60/70 products. But for PRD value is invertion result. The Voids in Filled with Bitumen (VFB) Marshall as well as PRD value show that the asphalt Pertamina Pen 60/70 products bigger than the VFB value of the asphalt Esso Pen 60/70 products. The result study concerning the characteristics of both asphalt trade fulfill the requirement of Bina Marga specifications.

Faculty members should determine the factors that contribute to poor performance of both teachers and students through regular monitoring and evaluation of the teaching and learning process. Teaching styles seem to vary as much as learning styles. Matching teaching style to learning style is not a panacea that solves all classroom conflicts. Other factors such as classroom climate, previous background, motivation, and gender will of course greatly influence the amount and quality of learning that takes place. Still, for math teachers, being self reflective and explicit about the role of learning styles can make teaching more rewarding and enhance student learning at the same time. Hence, it is deemed necessary to assess the students' learning styles and teachers' teaching styles. This research was conducted to identify and assess teaching and learning styles and its effect on performance of freshman engineering students of TIP Manila in algebra during the first semester of s...

We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural embeddings of the classical groups, inductive systems of representations with totally bounded weight multiplicities are classified. An analogue of the Steinberg tensor product theorem for arbitrary indecomposable inductive systems for such embeddings is proved.

We use a recent result concerning the eigenvalues of a generic (non-Hermitian) complex perturbation of a bounded Hermitian sequence of matrices to prove that the asymptotic spectrum of the product of Toeplitz sequences, whose symbols have a real-valued essentially bounded product h, is described by the function h in the “Szegö way”. Then, using Mergelyan’s theorem, we extend the result

In this article properties of the $(b, c)$-inverse, the inverse along an element, the outer inverse with prescribed range and null space $A^{(2)}_{T, S}$ and the Moore-Penrose inverse will be studied in the contexts of Banach spaces operators, Banach algebras and $C^*$-algebras. The main properties to be considered are the continuity, the differentiability and the openness of the sets of all invertible elements defined by all the aforementioned outer inverses but the Moore-Penrose inverse. The relationship between the $(b, c)$-inverse and the outer inverse $A^{(2)}_{T, S}$ will be also characterized