Generalizing Liouville-Type Problems For Differential 1-Forms From Lq Spaces To Non-Lq Spaces,
2016
CUNY Borough of Manhattan Community College
Generalizing Liouville-Type Problems For Differential 1-Forms From Lq Spaces To Non-Lq Spaces, Lina Wu, Ye Li
Publications and Research
We obtain Liouville-type results for closed and p-pseudo-coclosed differential 1-forms ! with energy of lim inf r!1 1 r2 R B(x0;r) j!jqdv < 1 (that is, 2-finite growth), which extends finite q-energy ( R M j!jqdv < 1) in Lq spaces to infinite q-energy ( R M j!jqdv = 1) in non-Lq spaces. In particular, we recapture mathematicians' vanishing results of Liouville- type theorem for ! with finite q-energy in Lq spaces. Our method in this paper provides a successful way to work on Liouville-type problems for differential forms with a variety of energy conditions in broad spaces.
On Crown-Free Set Families, Diffusion State Difference, And Non-Uniform Hypergraphs,
2016
University of South Carolina
On Crown-Free Set Families, Diffusion State Difference, And Non-Uniform Hypergraphs, Edward Lawrence Boehnlein
Theses and Dissertations
We present results in three different arenas of discrete mathematics. Let La(n, H) denote the cardinality of the largest family on the Boolean lattice that does not contain H as a subposet. Denote π(H) := limn→∞ La(n,H) (bn/ n2c) . A crown O2k for k ≥ 2 is a poset on 2 levels whose Hasse diagram is a cycle. Griggs and Lu (2009) showed π(O4k) = 1 for k ≥ 2. Lu (2014) proved π(O2k) = 1 for odd k ≥ 7. We prove that the maximum size of a O6 -free family, when restricted to the middle two levels …
Marquette University
Worldwide Cutaneous Malignant Melanoma Incidences Analyzed By Sex, Age, And Skin Type Over Time (1955–2007): Is Hpv Infection Of Androgenic Hair Follicular Melanocytes A Risk Factor For Developing Melanoma Exclusively In People Of European-Ancestry?, Stephen Merrill, Madhan Subramanian, Dianne E. Godar
Mathematics, Statistics and Computer Science Faculty Research and Publications
The cutaneous malignant melanoma (CMM) incidence has been increasing in an exponential manner in certain populations around the world for over 7 decades. To help illuminate the etiology, we performed worldwide temporal (1955–2007) CMM incidence analysis by sex, age (0–14, 15–29, 30–49, 50–69, 70–85+), and skin type on 6 continents using data from the International Agency for Research on Cancer. We observe an exponential increase in the CMM incidence over time and an increase of about 2 orders of magnitude between age groups 0–14 and 15–29 exclusively in European-ancestry populations around the world independent of skin type (I–III or III–IV). …
Cohomology Operations On Random Spaces,
2016
Wayne State University
Cohomology Operations On Random Spaces, Matthew John Zabka
Wayne State University Dissertations
Topology has recently received more attention from statisticians as some its tools have been applied to understanding the shape of data. In particular, a data set can generate a topological space, and this space’s topological structure can give us insight into some properties of the data. This framework has made it necessary to study random spaces generated by data. For example, without an understanding of the probabilistic properties of random spaces, one cannot conclude with any degree of confidence what the tools of topology tell us about a data set. While some results are known about the cohomological structure of …
Algorithmic Foundations Of Heuristic Search Using Higher-Order Polygon Inequalities,
2016
Nova Southeastern University
Algorithmic Foundations Of Heuristic Search Using Higher-Order Polygon Inequalities, Newton Henry Campbell Jr.
CCAC Theses and Dissertations
The shortest path problem in graphs is both a classic combinatorial optimization problem and a practical problem that admits many applications. Techniques for preprocessing a graph are useful for reducing shortest path query times. This dissertation studies the foundations of a class of algorithms that use preprocessed landmark information and the triangle inequality to guide A* search in graphs. A new heuristic is presented for solving shortest path queries that enables the use of higher order polygon inequalities. We demonstrate this capability by leveraging distance information from two landmarks when visiting a vertex as opposed to the common single landmark …
Pointwise Slant Submersions From Cosymplectic Manifolds,
2016
TÜBİTAK
Pointwise Slant Submersions From Cosymplectic Manifolds, Sezi̇n Aykurt Sepet, Mahmut Ergüt
Turkish Journal of Mathematics
In this paper, we characterize the pointwise slant submersions from cosymplectic manifolds onto Riemannian manifolds and give several examples.
On The Evolute Offsets Of Ruled Surfaces In Minkowski 3-Space,
2016
TÜBİTAK
On The Evolute Offsets Of Ruled Surfaces In Minkowski 3-Space, Dae Won Yoon
Turkish Journal of Mathematics
In this paper, we classify evolute offsets of a ruled surface in Minkowski 3-space $\Bbb L^3$ with constant Gaussian curvature and mean curvature. As a result, we investigate linear Weingarten evolute offsets of a ruled surface in $\Bbb L^3$.
On $Le$-Semigroups,
2016
TÜBİTAK
On $Le$-Semigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
We characterize the idempotent ideal elements of the $le$-semigroups in terms of semisimple elements and we prove, among others, that the ideal elements of an $le$-semigroup $S$ are prime (resp. weakly prime) if and only if they form a chain and $S$ is intraregular (resp. semisimple). The corresponding results on semigroups (without order) can be also obtained as an application of the results of this paper. The study of $poe$-semigroups plays an essential role in the theory of fuzzy semigroups and the theory of hypersemigroups.
Existence And Nonexistence Of Sign-Changing Solutions To Elliptic Critical Equations,
2016
TÜBİTAK
Existence And Nonexistence Of Sign-Changing Solutions To Elliptic Critical Equations, Mokhless Hammami, Houria Ismail
Turkish Journal of Mathematics
We consider the nonlinear equation $ -\Delta u = u ^{p-1}u -\varepsilon u \quad \mbox{in } \Omega , u =0 \quad \mbox{on } \partial \Omega ,$ where $\Omega $ is a smooth bounded domain in $\mathbb{R}^n$, $n \geq 4$, $ \varepsilon$ is a small positive parameter, and $p=(n+2)/(n-2)$. We study the existence of sign-changing solutions that concentrate at some points of the domain. We prove that this problem has no solutions with one positive and one negative bubble. Furthermore, for a family of solutions with exactly two positive bubbles and one negative bubble, we prove that the limits of the …
Uniqueness Of $P(F)$ And $P[F]$,
2016
TÜBİTAK
Uniqueness Of $P(F)$ And $P[F]$, Kuldeep Singh Charak, Banarsi Lal
Turkish Journal of Mathematics
Let $f$ be a nonconstant meromorphic function, $a (\not\equiv 0, \infty)$ be a meromorphic function satisfying $T(r,a) = o(T(r,f))$ as $r \rightarrow \infty$, and $p(z)$ be a polynomial of degree $n \geq 1$ with $p(0) = 0$. Let $P[f]$ be a nonconstant differential polynomial of $f$. Under certain essential conditions, we prove that $p(f) \equiv P[f]$, when $p(f)$ and $P[f]$ share $a$ with weight $l \geq 0$. Our result generalizes the results due to Zhang and L$\ddot{\text{u}}$, Banerjee and Majumdar, and Bhoosnurmath and Kabbur and answers a question asked by Zhang and L$\ddot{\text{u}}$.
Some Topological Properties Of The Spaces Of Almost Null Andalmost Convergent Double Sequences,
2016
TÜBİTAK
Some Topological Properties Of The Spaces Of Almost Null Andalmost Convergent Double Sequences, Medi̇ne Yeşi̇lkayagi̇l, Feyzi̇ Başar
Turkish Journal of Mathematics
Let $\mathcal{C}_{f_0}$ and $\mathcal{C}_{f}$ denote the spaces of almost null and almost convergent double sequences, respectively. We show that $\mathcal{C}_{f_0}$ and $\mathcal{C}_{f}$ are BDK-spaces, barreled and bornological, but they are not monotone and so not solid. Additionally, we establish that both of the spaces $\mathcal{C}_{f_0}$ and $\mathcal{C}_{f}$ include the space $\mathcal{BS}$ of bounded double series.
Generalizations Of 2-Absorbing Primaryideals Of Commutative Rings,
2016
TÜBİTAK
Generalizations Of 2-Absorbing Primaryideals Of Commutative Rings, Ayman Badawi, Ünsal Teki̇r, Emel Aslankarayi̇ği̇t Uğurlu, Gülşen Ulucak, Ece Yetki̇n Celi̇kel
Turkish Journal of Mathematics
ideals of $R$. In this paper, we extend the concept of 2-absorbing primary ideals to the context of $\phi $-2-absorbing primary ideals. Let $\phi :S(R)\rightarrow S(R)\cup \emptyset $ be a function. A proper ideal $I$ of $% R $ is said to be a $\phi $-2-absorbing primary ideal of $R$ if whenever $% a,b,c\in R$ with $abc\in I-\phi (I)$ implies $ab\in I$ or $ac\in \sqrt{I}$ or $bc\in \sqrt{I}$. A number of results concerning $\phi $-2-absorbing primary ideals are given.
Detection Of Coherent Structures In Flows,
2016
Montclair State University
Detection Of Coherent Structures In Flows, Klodiana Shkembi
Theses, Dissertations and Culminating Projects
In this work, we have developed an experimental flow tank that can produce realistic ocean-like flows, including multi-gyre flows. By generating controllable ocean-like flow fields, we can study the flows to gain a better understanding of ocean dynamics. In particular, we use particle image velocimetry and finite-time Lyapunov exponents to determine the location of the Lagrangian Coherent Structures that determine transport in complex fluid flows. This understanding is useful for designing control algorithms and for optimizing the use of autonomous vehicles operating in the stochastic and time-dependent ocean environment.
Homogenization Of Stokes Systems With Periodic Coefficients,
2016
University of Kentucky
Homogenization Of Stokes Systems With Periodic Coefficients, Shu Gu
Theses and Dissertations--Mathematics
In this dissertation we study the quantitative theory in homogenization of Stokes systems. We study uniform regularity estimates for a family of Stokes systems with rapidly oscillating periodic coefficients. We establish interior Lipschitz estimates for the velocity and L∞ estimates for the pressure as well as Liouville property for solutions in ℝd. We are able to obtain the boundary W{1,p} estimates in a bounded C1 domain for any 1 < p < ∞. We also study the convergence rates in L2 and H1 of Dirichlet and Neumann problems for Stokes systems with rapidly oscillating periodic coefficients, without any regularity assumptions on the coefficients.
Tabulating Pseudoprimes And Tabulating Liars,
2016
Illinois Wesleyan University
Tabulating Pseudoprimes And Tabulating Liars, Andrew Shallue
Scholarship
This paper explores the asymptotic complexity of two problems related to the Miller-Rabin-Selfridge primality test. The first problem is to tabulate strong pseudoprimes to a single fixed base $a$. It is now proven that tabulating up to $x$ requires $O(x)$ arithmetic operations and $O(x\log{x})$ bits of space. The second problem is to find all strong liars and witnesses, given a fixed odd composite $n$. This appears to be unstudied, and a randomized algorithm is presented that requires an expected $O((\log{n})^2 + |S(n)|)$ operations (here $S(n)$ is the set of strong liars). Although interesting in their own right, a notable application …
A Coin Vibrational Motor Swimming At Low Reynolds Number,
2016
University of Rochester
A Coin Vibrational Motor Swimming At Low Reynolds Number, Alice C. Quillen, Hesam Askari, Douglas H. Kelley, Tamar Friedmann, Patrick W. Oakes
Mathematics Sciences: Faculty Publications
Low-cost coin vibrational motors, used in haptic feedback, exhibit rotational internal motion inside a rigid case. Because the motor case motion exhibits rotational symmetry, when placed into a fluid such as glycerin, the motor does not swim even though its oscillatory motions induce steady streaming in the fluid. However, a piece of rubber foam stuck to the curved case and giving the motor neutral buoyancy also breaks the rotational symmetry allowing it to swim. We measured a 1 cm diameter coin vibrational motor swimming in glycerin at a speed of a body length in 3 seconds or at 3 mm/s. …
Alexander And Writhe Polynomials For Virtual Knots,
2016
Loyola Marymount University
Alexander And Writhe Polynomials For Virtual Knots, Blake Mellor
Mathematics, Statistics and Data Science Faculty Works
We give a new interpretation of the Alexander polynomial Δ0 for virtual knots due to Sawollek and Silver and Williams, and use it to show that, for any virtual knot, Δ0 determines the writhe polynomial of Cheng and Gao (equivalently, Kauffman's affine index polynomial). We also use it to define a second-order writhe polynomial, and give some applications.
Generalized Local And Nonlocal Master Equations For Some Stochastic Processes,
2016
Loyola Marymount University
Generalized Local And Nonlocal Master Equations For Some Stochastic Processes, Yanping Ma
Mathematics, Statistics and Data Science Faculty Works
In this paper, we present a study on generalized local and nonlocal equations for some stochastic processes. By considering the net flux change in a region determined by the transition probability, we derive the master equation to describe the evolution of the probability density function. Some examples, such as classical Fokker-Planck equations, models for Lévy process, and stochastic coagulation equations, are provided as illustrations. A particular application is a consistent derivation of coupled dynamical systems for spatially inhomogeneous stochastic coagulation processes.
A Characteristic Averaging Property Of The Catenary,
2016
Lehigh University
A Characteristic Averaging Property Of The Catenary, Vincent Coll, Jeff Dodd
Research, Publications & Creative Work
It is well-known that the catenary is characterized by an extremal centroidal condition: It is the shape of the curve whose centroid is the lowest among all curves having a prescribed length and specified endpoints. Here, we establish a broad characteristic averaging property of the centenary that yields two new centroidal characterizations.
Restricted Lie Algebras With Maximal 0-Pim,
2016
University of South Alabama
Restricted Lie Algebras With Maximal 0-Pim, Jorg Feldvoss, Salvatore Siciliano, Thomas Weigel
University Faculty and Staff Publications
In this paper it is shown that the projective cover of the trivial irreducible module of a finite-dimensional solvable restricted Lie algebra is induced from the one dimensional trivial module of a maximal torus. As a consequence, the number of the isomorphism classes of irreducible modules with a fixed p-character for a finite-dimensional solvable restricted Lie algebra L is bounded above by p MT(L), where MT(L) denotes the maximal dimension of a torus in L. Finally, it is proved that in characteristic p > 3 the projective cover of the trivial irreducible L-module is induced …
