Mathematics Commons^™

Boundary Effects On The Locomotion Of Active Janus Particles, Marola W. Issa, Nicky R. Baumgartner

Undergraduate Research Posters 2018

Self-propelled or “active” micrometer scale particles are capable of supplying local mechanical work, necessary for microscale cargo delivery and useful in other applications within bioimaging and sensing. Research in the last decade has focused on developing, measuring, and manipulating the locomotion mechanisms of active particles in simple environments. However, many applications will be in complex environments with nearby boundaries or variations in physiochemical cues. This poster reports the directed motion of platinum coated polystyrene particles at infinite dilution in the presence of H2O2, which acts as a fuel to drive motion. A transport mechanism called “diffusiophoresis” drives motion of the …

Certain Strongly Clean Matrices Over Local Rings, Tuğçe Pekacar Çalci, Huanyin Chen

Turkish Journal of Mathematics

We are concerned about various strongly clean properties of a kind of matrix subrings $L_{(s)}(R)$ over a local ring $R$. Let $R$ be a local ring, and let $s\in C(R)$. We prove that $A\in L_{(s)}(R)$ is strongly clean if and only if $A$ or $I_2-A$ is invertible, or $A$ is similar to a diagonal matrix in $L_{(s)}(R)$. Furthermore, we prove that $A\in L_{(s)}(R)$ is quasipolar if and only if $A\in GL_2(R)$ or $A\in L_{(s)}(R)^{qnil}$, or $A$ is similar to a diagonal matrix $\left( \begin{array}{cc} \lambda&0\\ 0&\mu \end{array} \right)$ in $L_{(s)}(R)$, where $\lambda\in J(R)$, $\mu\in U(R)$ or $\lambda\in U(R)$, $\mu\in J(R)$, …

An Alternative Means For Observation-Based Cloud Size Distributions, Adam Stead

Undergraduate Research Posters 2018

Clouds are a poorly understood phenomenon that have a significant impact on climate and day-to-day weather. This research aims to measure cloud size distributions for shallow cumulus clouds from observational data. Clouds are sampled via a ceilometer, which indicates both the presence of cloudy air and the base height of the respective cloud. When combining this data with the recorded horizontal wind velocity, we can infer a cloud transect size distribution. After sufficient sampling, we can use an algorithm to deduce an approximate cloud area distribution for the specified time range and cloud field. Once the cloud size distributions are …

Symmetric Criticality In General Relativity, Charles G. Torre

Research Vignettes

In this worksheet I explore the local Lagrangian version of the Principle of Symmetric Criticality (PSC) due to Anderson, Fels, and Torre], which asserts the commutativity of the processes (i) of symmetry reduction (for finding group-invariant fields) and (ii) forming Euler-Lagrange equations. There are two obstructions to PSC, which I will call the Lie algebra obstruction and the isotropy obstruction. In this worksheet I will illustrate these obstructions in the General Theory of Relativity.

Hardy Space Theory And Endpoint Estimates For Multi-Parameter Singular Radon Transforms, Jiawei Shen

Wayne State University Dissertations

In [12], Christ, Nagel, Stein and Waigner studied the L p theories for the singular Radon Trans-

forms. Furthermore, B. Street in [68], and Stein and Street in [64–67] extended the theories of the

L p boundedness for multi-parameter singular integral operators, such as the Calderón Zygmund

operators and singular Radon transforms. In this dissertation, we will study the Hardy space H p

and its dual space associated with both the one-parameter and multi-parameter singular Radon

transforms, and consider the boundedness of the singular Radon transforms on such Hardy spaces

H p when 0 ≤ p ≤ 1.

Inspired by …

Determining Cloud Cover With Machine Learning, Sarah Sesek

Undergraduate Research Posters 2018

The cloud cover provided by boundary layer cumulus clouds is one of the greatest uncertainties in climate and weather prediction models. It is difficult with current technology to cheaply and accurately collect cloud cover data. The TSI (Total Sky Imager) provides a hemispheric field of view in order to maximize the area it can see. The farther away from the center of the image, the more angled the view of the the cloud is. Therefore, more of the side of the cloud is captured in addition to the cloud base. Machine learning is well suited to seeing through this bias. …

Advances In Processing, Mining, And Learning Complex Data: From Foundations To Real-World Applications, Jia Wu, Shirui Pan, Chuan Zhou, Gang Li, Wu He, Chengqi Zhang

Information Technology & Decision Sciences Faculty Publications

Processing, mining, and learning complex data refer to an advanced study area of data mining and knowledge discovery concerning the development and analysis of approaches for discovering patterns and learning models from data with a complex structure (e.g., multirelational data, XML data, text data, image data, time series, sequences, graphs, streaming data, and trees) [1–5]. These kinds of data are commonly encountered in many social, economic, scientific, and engineering applications. Complex data pose new challenges for current research in data mining and knowledge discovery as they require new methods for processing, mining, and learning them. Traditional …

Existence Of Solution For Some Two-Point Boundary Value Fractional Differential Equations, Kenneth Ifeanyi Isife

Turkish Journal of Mathematics

Using a fixed point theorem, we establish the existence of a solution for a class of boundary value fractional differential equation. Secondly, we will adopt the method of successive approximations to obtain an approximate solution to our problem. Furthermore, using the Laplace transform technique, an explicit solution to a particular case of our problem is obtained. Finally, some examples are given to illustrate our results.

Transversal Lightlikesubmanifolds Of Metallic Semi-Riemannian Manifolds, Feyza Esra Erdoğan

Turkish Journal of Mathematics

The main purpose of the present paper is to study the geometry of transversal lightlike submanifolds and radical transversal lightlike submanifolds of metallic semi-Riemannian manifolds. We investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these manifolds to be a metric connection. We also obtain characterization of transversal lightlike submanifolds of metallic semi-Riemannian manifolds. Finally, we give two examples.

On Rectifying Curves In Euclidean 3-Space, Sharief Deshmukh, Bang-Yen Chen, Sana Hamoud Alshammari

Turkish Journal of Mathematics

First, we study rectifying curves via the dilation of unit speed curves on the unit sphere $S^{2}$ in the Euclidean space $\mathbb E^3$. Then we obtain a necessary and sufficient condition for which the centrode $d(s)$ of a unit speed curve $\alpha(s)$ in $\mathbb E^3$ is a rectifying curve to improve a main result of \cite{cd05}. Finally, we prove that if a unit speed curve $\alpha(s)$ in $\mathbb E^3$ is neither a planar curve nor a helix, then its dilated centrode $\beta(s)=\rho(s) d(s)$, with dilation factor ${\rho}$, is always a rectifying curve, where $\rho$ is the radius of curvature of …

A New Approach To $H$-Supplemented Modules Via Homomorphisms, Ali Reza Moniri Hamzekolaee, Abdullah Harmanci, Yahya Talebi, Burcu Üngör

Turkish Journal of Mathematics

The class of $H$-supplemented modules, which is a nice generalization of that of lifting modules, has been studied extensively in the last decade. As the concept of homomorphisms plays an important role in module theory, we are interested in $H$-supplemented modules relative to homomorphisms. Let $R$ be a ring, $M$ a right $R$-module, and $S=$ End$_{R}(M)$. We say that $M$ is endomorphism $H$-supplemented (briefly, $E$-$H$-supplemented) provided that for every $f\in S$ there exists a direct summand $D$ of $M$ such that $Imf+X=M$ if and only if $D+X=M$ for every submodule $X$ of $M$. In this paper, we deal with the …

Parametric Nondifferentiable Multiobjective Fractional Programmingunder $(B,\Psi ,\Phi ,\Rho )$-Univexity, Tadeusz Antczak, Ram Verma

Turkish Journal of Mathematics

In this paper, we are concerned with optimality conditions and duality results for nondifferentiable multiobjective fractional programming problems. Parametric necessary optimality conditions are established for such vector optimization problems in which each component of the involved functions is locally Lipschitz. Further, under the introduced concept of nondifferentiable $(b,\Psi ,\Phi ,\rho )$-univexity, the parametric sufficient optimality conditions are established for a new class of nonconvex multiobjective fractional programming problems. Furthermore, for the considered multiobjective fractional programming problem, its parametric vector dual problem in the sense of Schaible is defined. Then several duality theorems are also established under $(b,\Psi ,\Phi ,\rho )$% …

On $H$-Antimagicness Of Cartesian Product Of Graphs, Martin Baca, Andrea Semanicova-Fenovcikova, Muhammad Awais Umar, Des Welyyanti

Turkish Journal of Mathematics

A graph $G=(V(G),E(G))$ admits an $H$-covering if every edge in $E$ belongs to a~subgraph of $G$ isomorphic to $H$. A graph $G$ admitting an $H$-covering is called {\it $(a,d)$-$H$-antimagic} if there is a bijection $f:V(G)\cup E(G) \to \{1,2,\dots, V(G) + E(G) \}$ such that, for all subgraphs $H'$ of $G$ isomorphic to $H$, the $H$-weights, $wt_f(H')= \sum_{v\in V(H')} f(v) + \sum_{e\in E(H')} f(e),$ constitute an arithmetic progression with the initial term $a$ and the common difference $d$. In this paper we provide some sufficient conditions for the Cartesian product of graphs to be $H$-antimagic. We use partitions subsets of integers …

Worst-Case Large Deviations Upper Bounds For I.I.D. Sequencesunder Ambiguity, Mustafa Ç. Pinar

Turkish Journal of Mathematics

An introductory study of large deviations upper bounds from a worst-case perspective under parameter uncertainty (referred to as ambiguity) of the underlying distributions is given. Borrowing ideas from robust optimization, suitable sets of ambiguity are defined for imprecise parameters of underlying distributions. Both univariate and multivariate i.i.d. sequences of random variables are considered. The resulting optimization problems are challenging min‒max (or max‒min) problems that admit some simplifications and some explicit results, mostly in the case of the normal probability law.

A Comparative Study Of Gauss‒Laguerre Quadrature And An Open Type Mixed Quadrature By Evaluating Some Improper Integrals, Pritikanta Patra, Debasish Das, Rajani Ballav Dash

Turkish Journal of Mathematics

An open type mixed quadrature rule is constructed blending the anti-Gauss 3-point rule with Steffensen's 4-point rule. The analytical convergence of the mixed rule is studied. An adaptive integration scheme is designed based on the mixed quadrature rule. A comparative study of the mixed quadrature rule and the Gauss‒Laguerre quadrature rule is given by evaluating several improper integrals of the form $\int\limits_{0}^{\infty}e^{-x}f(x)dx$. The advantage of implementing mixed quadrature rule in developing an efficient adaptive integration scheme is shown by evaluating some improper integrals.

Various Centroids And Some Characterizations Of Catenary Rotation Hypersurfaces, Dong-Soo Kim, Young Ho Kim, Dae Won Yoon

Turkish Journal of Mathematics

We study positive $C^1$ functions $z=f(x), x=(x_1,\cdots, x_n)$ defined on the $n$-dimensional Euclidean space $ \mathbb R^{n}$. For $x=(x_1,\cdots, x_n)$ with nonzero numbers $x_1, \cdots, x_n$, we consider the rectangular domain $I(x)=I(x_1)\times \cdots \times I(x_n)\subset \mathbb R^{n}$, where $I(x_i)= [0, x_i]$ if $x_i>0$ and $I(x_i)= [x_i,0]$ if $x_i

On The Dimension Of Vertex Labeling Of $K$-Uniform Dcsl Of An Even Cycle, Nageswara Rao Karrey, Germina Kizhekekunnel Augustine

Turkish Journal of Mathematics

In this paper, we discuss the lower bound for the dcsl index $ \delta_k $ of a $k$-uniform dcsl of even cycle $ C_{2n},\ n\geq 2 $, in terms of the dimension of a poset and prove that $dim({\mathscr{F}})\leq \delta_k(C_{2n}) $, where ${\mathscr{F}}$ is the range of any $k$-uniform dcsl $ f $ of $ C_{2n},\ n\geq 2 $.

A Study Of The Tubular Surfaces Constructed By Thespherical Indicatrices In Euclidean $3-$Space, Fatma Ateş, Erdem Kocakuşakli, İsmai̇l Gök, Yusuf Yayli

Turkish Journal of Mathematics

A basic goal of this paper is to investigate the tubular surface constructed by the spherical indicatrices of any spatial curve in the Euclidean $3-$ space. This kind of tubular surface is designed for the alternative moving frame $\{N,C,W\}$ in conjunction with finding a relationship between the tubular surfaces and their special curves, such as geodesic curves, asymptotic curves, and minimal curves. The minimal curve $\gamma $ on a surface is defined by the property that its fundamental coefficients satisfy Eq. (3.7) along the curve $\gamma $. At the end of this article, we exemplify these curves on the tubular …

Second Hankel Determinant For Certain Subclasses Of Bi-Univalent Functions Involving Chebyshev Polynomials, Hali̇t Orhan, Evri̇m Toklu, Ekrem Kadioğlu

Turkish Journal of Mathematics

In this paper our purpose is to find the upper bound estimate for the second Hankel determinant $ a_{2}a_{4}-a_{3}^{2} $ for functions defined by convolution belonging to the class $\mathcal{N}_{\sigma}^{\mu,\delta}(\lambda,t)$ by using Chebyshev polynomials.

Existence Of Maximal Ideals In Leavitt Path Algebras, Songül Esi̇n, Müge Kanuni̇ Er

Turkish Journal of Mathematics

Let $E$ be an arbitrary directed graph and let $L$ be the Leavitt path algebra of the graph $E$ over a field $K$. The necessary and sufficient conditions are given to assure the existence of a maximal ideal in $L$ and also the necessary and sufficient conditions on the graph that assure that every ideal is contained in a maximal ideal are given. It is shown that if a maximal ideal $M$ of $L$ is nongraded, then the largest graded ideal in $M$, namely $gr(M)$, is also maximal among the graded ideals of $L$. Moreover, if $L$ has a unique …