Comparison Of Software Packages For Detecting Differentially Expressed Genes From Single-Sample Rna-Seq Data,
2021
South Dakota State University
Comparison Of Software Packages For Detecting Differentially Expressed Genes From Single-Sample Rna-Seq Data, Rong Zhou
Electronic Theses and Dissertations
RNA-sequencing (RNA-seq) has rapidly become the tool in many genome-wide transcriptomic studies. It provides a way to understand the RNA environment of cells in different physiological or pathological states to determine how cells respond to these changes. RNA-seq provides quantitative information about the abundance of different RNA species present in a given sample. If the difference or change observed in the read counts or expression level between two experimental conditions is statistically significant, the gene is declared as differentially expressed. A large number of methods for detecting differentially expressed genes (DEGs) with RNA-seq have been developed, such as the methods …
Elementary College Geometry (2021 Ed.),
2021
CUNY New York City College of Technology
Elementary College Geometry (2021 Ed.), Henry Africk
Open Educational Resources
This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra. The emphasis is on applying basic geometric principles to the numerical solution of problems. For this purpose the number of theorems and definitions is kept small. Proofs are short and intuitive, mostly in the style of those found in a typical trigonometry or precalculus text. There is little attempt to teach theorem proving or formal methods of reasoning. However the topics …
The Siebeck-Marden-Northshield Theorem And The Real Roots Of The Symbolic Cubic Equation,
2021
Technological University Dublin
The Siebeck-Marden-Northshield Theorem And The Real Roots Of The Symbolic Cubic Equation, Emil Prodanov
Articles
The isolation intervals of the real roots of the symbolic monic cubic polynomial x 3 ` ax2 ` bx ` c are determined, in terms of the coefficients of the polynomial, by solving the Siebeck–Marden–Northshield triangle — the equilateral triangle that projects onto the three real roots of the cubic polynomial and whose inscribed circle projects onto an interval with endpoints equal to stationary points of the polynomial.
On Newton's Rule Of Signs,
2021
Technological University Dublin
On Newton's Rule Of Signs, Emil Prodanov
Articles
Analysing the cubic sectors of a real polynomial of degree n, a minor modification of Newton’s Rule of signs is proposed with which stricter upper limits on the number of real roots can be found. A new necessary condition for reality of the roots of a polynomial is also proposed. Relationship between the quadratic elements of the polynomial is established through its roots and those of its derivatives. Some aspects of polynomial discriminants are also discussed.
Fostering Mathematical Creativity Among Middle School Mathematics Teachers,
2021
Montclair State University
Fostering Mathematical Creativity Among Middle School Mathematics Teachers, Ceire H. Monahan
Theses, Dissertations and Culminating Projects
The purpose of this research was to understand in-service teachers’ experiences with and ideas about mathematical creativity after participating in a targeted professional development program. The professional development program encouraged participants to think creatively and foster students’ creativity. In this study I present the results from the main unit of analysis, 12 participants in a professional development program, along with a deep analysis of three exemplar teachers from each of the identified groups, adherence to traditional teaching practices (traditional), appreciation for teaching for creativity (creative but hesitant), and teaching for creativity (creative). The findings of this study highlight the combination …
Transitioning Secondary Mathematics Pedagogy Towards Reform-Oriented Practice Through Coteaching,
2021
Montclair State University
Transitioning Secondary Mathematics Pedagogy Towards Reform-Oriented Practice Through Coteaching, Jessica Tybursky Nuzzi
Theses, Dissertations and Culminating Projects
Reform standards in mathematics education have called for classrooms that are student-centered and that incorporate problem solving and reasoning for meaningful learning. After decades of reform efforts involving multiple stakeholders, research indicates that most classrooms remain teacher-centered and procedurally focused, due to the complexity of concerns and competing intentions that teachers face in their work. Coteaching, a commitment between two teachers to coplan, coenact, and coreflect on lessons, can serve as an ongoing, sustained, focused, integrated, reflective professional development structure that supports teachers towards growth. The theoretical constructs used to describe possible growth towards reform orientations in teaching secondary mathematics …
Combinatorial Models For Representations Of Simple And Affine Lie Algebras,
2021
University at Albany, State University of New York
Combinatorial Models For Representations Of Simple And Affine Lie Algebras, Adam Lee Schultze
Legacy Theses & Dissertations (2009 - 2024)
Part I: Koskta-Foulkes polynomials are Lusztig's q-analogues of weight multiplicities for irreducible representations of semisimple Lie algebras. It has long been known that these polynomials can be written with all non-negative coefficients. A statistic on semistandard Young tableaux with partition content, called \textit{charge}, was used to give a combinatorial formula exhibiting this fact in type $A$. Defining a charge statistic beyond type $A$ has been a long-standing problem. In the first part of this thesis, we take a completely new approach based on the definition of Kostka-Foulkes polynomials as an alternating sum over Kostant partitions, which can be thought of …
Non-Academic Support Math Faculty Members Provide In Developmental Accelerated And Corequisite Support Courses In California Community Colleges,
2021
Illinois Mathematics and Science Academy
Non-Academic Support Math Faculty Members Provide In Developmental Accelerated And Corequisite Support Courses In California Community Colleges, David Vakil '92
Doctoral Dissertations
To guide practitioners of rapidly evolving developmental math reform in community colleges, this study surveyed California community college math faculty who taught accelerated developmental courses or corequisite support courses. The survey was conducted during the early implementation phase of both course types, during spring and fall 2018 terms. This study measured faculty’s self-reported provision of forms of non-academic support, frequency of implementation, and reasons faculty believed the support would help students succeed. The literature review guided grouping non-academic support into five forms: nurturing, helping students’ motivation, providing a growth mindset theory of intelligence, helping provide social integration, and helping to …
Integer-Valued Polynomials Satisfying The Lucas Property,
2021
TÜBİTAK
Integer-Valued Polynomials Satisfying The Lucas Property, Rattiya Meesa, Vichian Laohakosol, Tuangrat Chaichana
Turkish Journal of Mathematics
The classical theorem of Lucas states that the binomial polynomials, which form a basis for integer-valued polynomials, satisfy a congruence relation related to their integer parameters. We consider here three problems connected with this result in the setting of discrete valued structures. The first problem asks for the shapes of Lagrange-type interpolation polynomials which constitute a basis for integer-valued polynomials and satisfy the Lucas property; the result so obtained extends a 2001 result of Boulanger and Chabert. For the second problem, we show that the Carlitz polynomials, which form a basis for integer-valued polynomials in a function field, satisfy the …
Liftings And Covering Morphisms Of Crossed Modules In Group-Groupoids,
2021
TÜBİTAK
Liftings And Covering Morphisms Of Crossed Modules In Group-Groupoids, Serap Demi̇r Karakaş, Osman Mucuk
Turkish Journal of Mathematics
In this work we introduce lifting and covering of a crossed module in the category of group-groupoids; and then we prove the categorical equivalence of horizontal actions of a double group-groupoid and lifting crossed modules of corresponding crossed module in group-groupoids. These allow us to produce more examples of double group-groupoids.
A Short Note On Generic Initial Ideals,
2021
TÜBİTAK
A Short Note On Generic Initial Ideals, Beki̇r Daniş
Turkish Journal of Mathematics
The definition of a generic initial ideal includes the assumption $x_1>x_2> \cdots >x_n$. A natural question is how generic initial ideals change when we permute the variables. In the article [1, §2], it is shown that the generic initial ideals are permuted in the same way when the variables in the monomial order are permuted. We give a different proof of this theorem. Along the way, we study the Zariski open sets which play an essential role in the definition of a generic initial ideal and also prove a result on how the Zariski open set changes after a …
On The Analytical Development Of Incomplete Riemann-Liouville Fractional Calculus,
2021
TÜBİTAK
On The Analytical Development Of Incomplete Riemann-Liouville Fractional Calculus, Arran Fernandez, Ceren Ustaoğlu, Mehmet Ali̇ Özarslan
Turkish Journal of Mathematics
The theoretical development of fractional calculus includes the formulation of different definitions, the extension of properties from standard calculus, and the application of fractional operators to special functions. In two recent papers, incomplete versions of classical fractional operators were formulated in connection with special functions. Here, we develop the theory of incomplete fractional calculus more deeply, investigating further properties of these operators and answering some fundamental questions about how they work. By considering appropriate function spaces, we discover that incomplete fractional calculus may be used to analyse a wider class of functions than classical fractional calculus can consider. By using …
Certain Subclasses Of Spirallike Univalent Functions Related To Poisson Distribution Series,
2021
TÜBİTAK
Certain Subclasses Of Spirallike Univalent Functions Related To Poisson Distribution Series, Lakshminarayanan Vanitha, Chellakutti Ramachandran, Teodor Bulboaca
Turkish Journal of Mathematics
The aim of the present study is to find the essential properties for some subclasses of analytic functions which are related to Poisson distribution that are member of the classes of spiral-like univalent functions. Further, we studied inclusion relations for such subclasses, and also we determined some properties of an integral operator related to Poisson distribution series. Several corollaries and consequences of the main results are also considered.
Extensions Of The Matrix-Valued$\ Q-$Sturm-Liouville Operators,
2021
TÜBİTAK
Extensions Of The Matrix-Valued$\ Q-$Sturm-Liouville Operators, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna
Turkish Journal of Mathematics
In this paper, we investigate the matrix-valued$\ q-$Sturm--Liouville problems. We establish an existence and uniqueness result. Later, we introduce the corresponding maximal and minimal operators for this system. Moreover, we give a criterion under which these operators are self-adjoint. Finally, we characterize extensions (maximal dissipative, maximal accumulative, and self-adjoint) of the minimal symmetric operator.
Statistically Multiplicative Convergence On Locally Solid Riesz Algebras,
2021
TÜBİTAK
Statistically Multiplicative Convergence On Locally Solid Riesz Algebras, Abdullah Aydin, Mi̇kai̇l Et
Turkish Journal of Mathematics
In this paper, we introduce the statistically multiplicative convergent sequences in locally solid Riesz algebras with respect to algebra multiplication and solid topology. We study this concept and the notion of $st_m$-bounded sequences, and also, we prove some relations between this convergence and the other convergences such as the order convergence and the statistical convergence in topological spaces. Also, we give some results related to semiprime $f$-algebras.
Generalized Stevi\'C-Sharma Type Operators From Hardy Spaces Into $N$Th Weighted Type Spaces,
2021
TÜBİTAK
Generalized Stevi\'C-Sharma Type Operators From Hardy Spaces Into $N$Th Weighted Type Spaces, Ebrahim Abbasi, Yongmin Liu, Mostafa Hassanlou
Turkish Journal of Mathematics
In this paper, some characterizations for boundedness, essential norm and compactness of generalized Stevic-Sharma type operators from Hardy spaces into $n$th weighted type spaces are given.
On B-Generalized Skew Derivations In Banach Algebras,
2021
TÜBİTAK
On B-Generalized Skew Derivations In Banach Algebras, Abdul Nadim Khan
Turkish Journal of Mathematics
} Let $\mathscr{A}$ be a Banach algebra over $\mathbb{R}$ or $\mathbb{C}$. In this paper, we describe the behavior of recently defined $b$-generalized skew derivations which satisfy certain differential identities on some specific subsets of $\mathscr{A}$.
Fundamental Group Of Galois Covers Of Degree 5 Surfaces,
2021
TÜBİTAK
Fundamental Group Of Galois Covers Of Degree 5 Surfaces, Meirav Amram, Cheng Gong, Mina Teicher, Wan-Yuan Xu
Turkish Journal of Mathematics
Let $X$ be an algebraic surface of degree $5$, which is considered a branch cover of $\mathbb{CP}^2$ with respect to a generic projection. The surface has a natural Galois cover with Galois group $S_5$. In this paper, we deal with the fundamental groups of Galois covers of degree $5$ surfaces that degenerate to nice plane arrangements; each of them is a union of five planes such that no three planes meet in a line.
Logarithmic Dimension And Bases In Whitney Spaces,
2021
TÜBİTAK
Logarithmic Dimension And Bases In Whitney Spaces, Alexander Goncharov, Yasemi̇n Şengül Tezel
Turkish Journal of Mathematics
We give a formula for the logarithmic dimension of the generalized Cantor-type set $K$. In the case when the logarithmic dimension of $K$ is smaller than $1$, we construct a Faber basis in the space of Whitney functions $\mathcal{E}(K)$.
B-Property Of Sublattices In Vector Lattices,
2021
TÜBİTAK
B-Property Of Sublattices In Vector Lattices, Ömer Şafak Alpay, Svetlana Gorokhova
Turkish Journal of Mathematics
We study $b$-property of a sublattice (or an order ideal) $F$ of a vector lattice $E$. In particular, $b$-property of $E$ in $E^\delta$, the Dedekind completion of $E$, $b$-property of $E$ in $E^u$, the universal completion of $E$, and $b$-property of $E$ in $\hat{E}(\hat{\tau})$, the completion of $E$.
