Teac 308: Teaching Mathematics In The Elementary School–A Peer Review Of Teaching Project Benchmark Portfolio,
2017
University of Nebraska - Lincoln
Teac 308: Teaching Mathematics In The Elementary School–A Peer Review Of Teaching Project Benchmark Portfolio, Amanda Thomas
UNL Faculty Course Portfolios
This portfolio outlines four aspects of the peer review of teaching project, which focused on TEAC 308: Teaching Mathematics in the Elementary School. The first aspect was the explicit articulation of student learning objectives drawn from the National Council of Teachers of Mathematics Principles to Actions: Ensuring Mathematical Success for All (2014). During this project, the nine objectives were aligned with instructional opportunities and assignments with those objectives. In addition to defining these objectives, the portfolio describes analysis of three components: student progress toward developing and demonstrating productive beliefs about aspects of teaching and learning mathematics, student progress across three …
Andoyer Equations For Noncollinear Planar Central Configurations,
2017
TÜBİTAK
Andoyer Equations For Noncollinear Planar Central Configurations, Antonio Carlos Fernandes, Luis Fernando Mello
Turkish Journal of Mathematics
In this article we obtain the Andoyer equations for noncollinear planar central configurations taking into account the center of mass of the system. We apply these equations to study two configurations. In the first one we prove that it is not possible to put a square central configuration and an equilateral triangle central configuration as a cocircular central configuration. In the second one we give the central configurations for the noncollinear planar $4$-body problem with one pair of equal positive masses and two null masses.
Cyclic Codes Over $\Mathbb{Z}_{4}+U\Mathbb{Z}_{4}+U^{2}\Mathbb{Z}_{4}$,
2017
TÜBİTAK
Cyclic Codes Over $\Mathbb{Z}_{4}+U\Mathbb{Z}_{4}+U^{2}\Mathbb{Z}_{4}$, Mehmet Özen, Nazmi̇ye Tuğba Özzai̇m, Nuh Aydin
Turkish Journal of Mathematics
In this paper, we study cyclic codes over the ring $R=\mathbb{Z}_{4}+u\mathbb{Z}_{4}+u^{2}\mathbb{Z}_{4}$,where $u^{3}=0$. We investigate Galois extensions of this ring and the ideal structure of these extensions.The results are then used to obtain facts about cyclic codes over $R$. We also determine the general form of the generator of a cyclic code and find its minimal spanning sets. Finally, we obtain many new linear codes over $\mathbb{Z}_4$ by considering Gray images of cyclic codes over $R$.
On Subdirectly Irreducible Regular Bands,
2017
TÜBİTAK
On Subdirectly Irreducible Regular Bands, Zheng-Pan Wang, Jing Leng, Hou-Yi Yu
Turkish Journal of Mathematics
Subdirectly irreducible regular bands whose structural semilattices are finite chains are characterized in terms of arefined semilattice of semigroups.
On Focal Curves Of Null Cartan Curves,
2017
TÜBİTAK
On Focal Curves Of Null Cartan Curves, Hakan Şi̇mşek
Turkish Journal of Mathematics
The focal curve, which is determined as the locus of centers of osculatingpseudo-spheres of a null Cartan curve, is investigated in Minkowski(n+2)-space $\mathcal{M}^{n+2}.$ Moreover, a curve called \textit{accelerationfocal curve }of a null Cartan curve is introduced by using a new family of functions.
On The Equivalence Of Alexandrov Curvature And Busemann Curvature,
2017
TÜBİTAK
On The Equivalence Of Alexandrov Curvature And Busemann Curvature, Shijie Gu
Turkish Journal of Mathematics
It is shown that the curvature bounded above (resp. below) in the sense of Alexandrov is equivalent to the curvature bounded above (resp. below) in the sense of Busemann if and only if the sum of adjacent average angles is at least (resp. at most) $\pi$.
On The Zariski Topology Over An $L$-Module $M$,
2017
TÜBİTAK
On The Zariski Topology Over An $L$-Module $M$, Fethi̇ Çallialp, Gülşen Ulucak, Ünsal Teki̇r
Turkish Journal of Mathematics
Let $L$ be a multiplicative lattice and $M$ be an $L$-module. In this study, we present a topology said to be the Zariski topology over $\sigma (M),$ the collection of all prime elements of an $L$-module $M.$ We research some results on the Zariski topology over $\sigma (M).$ We show that the topology is a $T_{0}$-space and a $T_{1}$-space under some conditions. Some properties and results are studied for the topology over $\sigma (L)$, the collection of all prime elements of a multiplicative lattice $L.$
Value Distribution And Normality Of Meromorphic Functions Involving Partial Sharing Of Small Functions,
2017
TÜBİTAK
Value Distribution And Normality Of Meromorphic Functions Involving Partial Sharing Of Small Functions, Kuldeep Singh Charak, Shittal Sharma
Turkish Journal of Mathematics
In this paper, we generalize a value distribution result and use it to prove a normality criterion using partial sharing of small functions. Further in the sequel, various known normality criteria are improved and generalized on the domain $D:=\{z: z \lt R, 0\lt R\leq\infty \}$.
Existence And Global Attractivity Of Periodic Solutions In A Max-Type System Of Difference Equations,
2017
TÜBİTAK
Existence And Global Attractivity Of Periodic Solutions In A Max-Type System Of Difference Equations, Imane Dekkar, Nouressadat Touafek
Turkish Journal of Mathematics
We consider in this paper the following system of difference equations with maximum $$ \left\{ \begin{array}{lll} x(n+1)= & \max\{f_1(n,x(n)),g_1(n,y(n))\}& \\ & &, ~~ n=0,1,2, \ldots, \\ y(n+1)= & \max\{f_2(n,x(n)),g_2(n,y(n))\} & \\ \end{array} \right.$$ where $f_i, g_i$, $i=1,2$, are real-valued functions with periodic coefficients. We use the Banach fixed point theorem to get a sufficient condition under which this system admits a unique periodic solution. Moreover, we show that this periodic solution attracts all the solutions of the current system. Some examples are also given to illustrate our results.
$F$-Biminimal Immersions,
2017
TÜBİTAK
$F$-Biminimal Immersions, Fatma Gürler, Ci̇han Özgür
Turkish Journal of Mathematics
In the present paper, we define $f$-biminimal immersions. We consider $f$-biminimal curves in a Riemannian manifold and $f$-biminimal submanifolds of codimension $1$ in a Riemannian manifold, and we give examples of $f$-biminimal surfaces. Finally, we consider $f$-biminimal Legendre curves in Sasakian space forms and give an example.
Second Hankel Determinant For Certain Subclasses Ofbi-Univalent Functions,
2017
TÜBİTAK
Second Hankel Determinant For Certain Subclasses Ofbi-Univalent Functions, Murat Çağlar, Erhan Deni̇z, Hari Mohan Srivastava
Turkish Journal of Mathematics
In the present paper, we obtain the upper bounds for the second Hankel determinant for certain subclasses of analytic and bi-univalent functions. Moreover, several interesting applications of the results presented here are also discussed.
Canonical Involution On Double Jet Bundles,
2017
TÜBİTAK
Canonical Involution On Double Jet Bundles, Hülya Kadioğlu
Turkish Journal of Mathematics
In this study, we generalize double tangent bundles to double jet bundles. We present a secondary vector bundle structure on a 1-jet of a vector bundle. We show that the 1-jet of a vector bundle carries two vector bundle structures, namely primary and secondary structures. We also show that the manifold charts induced by primary and secondary structures belong to the same atlas. We prove that double jet bundles can be considered as a quotient of the second order jet bundle. We show that there exists a natural involution that interchanges between primary and secondary vector bundle structures on double …
Solvability Of Boundary Value Problems For Coupled Impulsive Differential Equations With One-Dimensional P-Laplacians,
2017
TÜBİTAK
Solvability Of Boundary Value Problems For Coupled Impulsive Differential Equations With One-Dimensional P-Laplacians, Yuji Liu
Turkish Journal of Mathematics
This paper is concerned with a boundary value problem of impulsive differential systems on the whole line with one-dimensional p-Laplacians. By constructing a weighted Banach space and defining a nonlinear operator, together with Schauder's fixed point theorem, sufficient conditions to guarantee the existence of at least one solution are established (Theorems 3.1-3.3). Two examples are given to illustrate the main results.
Generalized Convolution Product For An Integral Transform On A Wiener Space,
2017
TÜBİTAK
Generalized Convolution Product For An Integral Transform On A Wiener Space, Byoung Soo Kim, Il Yoo
Turkish Journal of Mathematics
We introduce a generalized convolution product $(F*G)_{\vec\alpha,\vec\beta}$ for integral transform ${\mathcal F}_{\gamma,\eta}$ for functionals defined on $K[0,T]$, the space of complex valued continuous functions on $[0,T]$ that vanish at zero. We study some interesting properties of our generalized convolution product and establish various relationships that exist among the generalized convolution product, the integral transform, and the first variation for functionals defined on $K[0,T]$. We also discuss the associativity of the generalized convolution product.
P-Subordination Chains And P-Valence Integral Operators,
2017
TÜBİTAK
P-Subordination Chains And P-Valence Integral Operators, Erhan Deni̇z, Hali̇t Orhan, Murat Çağlar
Turkish Journal of Mathematics
In the present investigation we obtain some sufficient conditions for the analyticity and the $p$-valence of an integral operator in the unit disk $\mathbb{D}$. Using these conditions we give some applications for a few different integral operators. The significant relationships and relevance to other results are also given. A number of known univalent conditions would follow upon specializing the parameters involved in our main results.
New Recurrences For Euler's Partition Function,
2017
TÜBİTAK
New Recurrences For Euler's Partition Function, Mircea Merca
Turkish Journal of Mathematics
In this paper, the author invokes some consequences of the bisectional pentagonal number theorem to derive two linear recurrence relations for Euler's partition function $p(n)$. As a corollary of these results, we obtain an efficient method to compute the parity of Euler's partition function $p(n)$ that requires only the parity of $p(k)$ with $k \leq n/4$.
Stability Analysis Of Nonlinear Fractional Differential Order Systems With Caputo And Riemann--Liouville Derivatives,
2017
TÜBİTAK
Stability Analysis Of Nonlinear Fractional Differential Order Systems With Caputo And Riemann--Liouville Derivatives, Javad Alidousti, Reza Khoshsiar Ghaziani, Ali Bayati Eshkaftaki
Turkish Journal of Mathematics
In this paper we establish stability theorems for nonlinear fractional orders systems (FDEs) with Caputo and Riemann--Liouville derivatives. In particular, we derive conditions for $ {\bf \cal{F}}$-stability of nonlinear FDEs. By numerical simulations, we verify numerically our theoretical results on a test example.
Chaos-Related Properties On The Product Of Semiflows,
2017
TÜBİTAK
Chaos-Related Properties On The Product Of Semiflows, Alica Miller, Chad Money
Turkish Journal of Mathematics
In this paper we generalize some results about the chaos-related properties on the product of two semiflows, which appeared in the lite\-rature in the last few years, to the case of the most general possible acting monoids. In order to do that we introduce some new notions, namely the notions of a directional, psp and sip monoid, and the notion of a strongly transitive semiflow. In particular, we obtain a sufficient condition for the Devaney chaoticity of a product, which works for the (very large) class of the psp acting monoids.
Dissipative Operator And Its Cayley Transform,
2017
TÜBİTAK
Dissipative Operator And Its Cayley Transform, Eki̇n Uğurlu, Kenan Taş
Turkish Journal of Mathematics
In this paper, we investigate the spectral properties of the maximaldissipative extension of the minimal symmetric differential operatorgenerated by a second order differential expression and dissipative andeigenparameter dependent boundary conditions. For this purpose we use thecharacteristic function of the maximal dissipative operator and inverseoperator. This investigation is done by the characteristic function of theCayley transform of the maximal dissipative operator, which is a completelynonunitary contraction belonging to the class $C_{0}.$ Using Solomyak'smethod we also introduce the self-adjoint dilation of the maximal dissipativeoperator and incoming/outgoing eigenfunctions of the dilation. Moreover, weinvestigate other properties of the Cayley transform of the maximaldissipative operator.
Corrigendum: On Density Theorems For Rings Of Krull Type With Zero Divisors,
2017
TÜBİTAK
Corrigendum: On Density Theorems For Rings Of Krull Type With Zero Divisors, Başak Ay Saylam
Turkish Journal of Mathematics
This corrigendum is written to correct some parts of the paper "On density theorems for rings of Krull type with zero divisors". The proofs of Proposition 2.4 and Proposition 4.3 are incorrect and the current note makes the appropriate corrections.
