A set-theoretical point of view to study algebraic numbers has been introduced. We extend a result of Navarro-Bermudez concerning shift invariant measures in the Cantor space which are topologically equivalent to shift invariant measures which correspond to some algebraic integers. It is known that any transcendental numbers and rational numbers in the unit interval are not binomial. We proved that there are algebraic numbers of degree greater than two so that they are binomial numbers. Algebraic integers of degree 2 are proved not to be binomial numbers. A few compositive relations having to do with algebraic numbers on the unit interval have been studied; for instance, rationally related, integrally related, binomially related, B1-related relations. A formula between binomial numbers and binomial coefficients has been stated. A generalized algebraic equation related to topologically equivalent measures has also been stated.

This article discusses the development of two statistical methods to test the gene environment interaction effect of rare variants.

Article studies radial solutions of ∆u + K(r)f(u) = 0 on the exterior of the ball of radius R > 0 centered at the origin in ℝᶰ where f is odd with f < 0 on (0, β), f > 0 on (β, δ), f ≡ 0 for u > δ, and where the function K(r) is assumed to be positive and K(r) → 0 as r → ∞.

This article studies radial solutions of Δu + K(r)ƒ(u) = 0 on the exterior of the ball of radius R > 0 centered at the origin in ℝᴺ where ƒ is odd with ƒ < 0 on (0,ß), ƒ > 0 on (β, δ), ƒ ≡ 0 for u > δ, and where the function K(r) is assumed to be positive and K(r) → 0 as r → ∞.

This article studies radial solutions of Δu + K(r)ƒ(u) = 0 on the exterior of the ball of radius R > 0, BR, centered at the origin in ℝN with u = 0 on @BR where ƒ is odd with ƒ < 0 on (0; β), ƒ > 0 on (β;∞), f(u) ~ uᵖ with 0 < p < 1 for large u and K(r) ~ r⁻ᵅ for large r.

Article proving the existence of infinitely many radial solutions of ∆𝓊+𝐾(𝓇) ƒ (𝓊) = 0 on the exterior of the ball of radius R > 0, BR, centered at the origin in ℝᴺ with u = 0 on ∂BR and lim/r→∞ 𝓊(𝓇) = 0 where N > 2, f is odd with f < 0 on (0, β), f > 0 on (β, ∞), f is superlinear for large u, ƒ(𝓊) ∼ −1/(|𝓊|𝘲⁻¹𝓊) with 0 < q < 1 for small u, and 0 < 𝐾(𝓇) ≤ 𝐾₁/r∝ with 𝑁 + q(𝑁 − 2) < ∝ < 2(𝑁− 1) for large r.

Article proves the existence of an infinite number of radial solutions to ∆u+K(r)f(u) = 0 on ℝᶰ such that limᵣ →∞ u(r) = 0 with prescribed number of zeros on the exterior of the ball of radius R > 0 where f is odd with f < 0 on (0, β), f > 0 on (β, ∞) with f superlinear for large u, and K(r) ∼ r ⁻ᵅ with α > 2(N − 1).

This article proves the existence of an infinite number of radial solutions of Δu+K(r)ƒ(u) = 0, one with exactly n zeros for each nonnegative integer n on the exterior of the ball of radius R > 0, Bʀ, centered at the origin in ℝᴺ with u = 0 on ∂Bʀ and limᵣ→∞u(r) = 0 where N > 2, f is odd with ƒ < 0 on (0; β), ƒ > 0 on (β;∞), ƒ(u) ~ uᵖ with 0 < p < 1 for large u and K(r) ~ r-α with 0 < α < 2 for large r.

In this article, the author proves the existence of an infinite number of radial solutions of Δu+f(u)=0 on the exterior of the ball of radius R>0 centered at the origin and f is odd with f<0 on (0,β), f>0 on (β,δ), and f≡0 for u>δ. The primitive F(u)=∫u0f(t)dt has a "hilltop" at u=δ which allows one to use the shooting method and ODE techniques to prove the existence of solutions.

This article studies the spreading of a charged microdroplet using the lubrication approximation.

This article considers the analysis of the Betelu-Fontelos model of the spreading of a charged microdroplet on a at dielectric surface whose spreading is driven by surface tension and electrostatic repulsion.

This article describes the use of three members of the human NEET protein family (CISD1, mitoNEET; CISD2, NAF-1 or Miner 1; and CISD3, Miner2) as guides to conduct a phylogenetic analysis of eukaryotic NEET proteins and their evolution.

Article discusses IslandCafe, a proposed method for genomic island detection.

This article utilizes a recursive segmentation and cluster procedure presented as a genome-mining tool, GEMINI, to decipher genomic islands and understand their contributions to the evolution of virulence and antibiotic resistance in Pseudomonas aeruginosa.

This article explores the use of an information-entropy-based gene clustering method for genomic island detection in MRSA.

Poster presentation for the 2012 University Scholars Day at the University of North Texas discussing research on correlations between parent's education and children's test scores.

This article proves the existence of radial solutions of Δu + K(r)ƒ(u) = 0 on the exterior of the ball, of radius R, centered at the origin in ℝᴺ such that limᵣ→∞u(r) = 0 if R > 0 is sufficiently small.

This article proves the existence of an infinite number of radial solutions of Δ(u) + f(u) = 0 with prescribed number of zeros on the exterior of the ball of radius R > 0 centered at the origin in ℝᴺ where f is odd with f < 0 on (0, β), f > 0 on (β,∞) where β > 0.

This article proves the existence of an infinite number of radial solutions to Δu + K(r)ƒ(u) = 0 with a nonlinear boundary condition on the exterior of the ball of radius R centered at the origin in ℝᴺ.

This article discusses divergences of a sequence of functions and its set of subsequences.

This article uses yeast two-hybrid to demonstrate through vivo bimolecular fluorescence complementation (BiFC), direct coupling analysis (DCA), RNA-sequencing, ROS and iron imaging, and single and double shRNA lines with suppressed mNT, NAF-1 and mNT/NAF-1 expression, that mNT and NAF-1 directly interact in mammalian cells and could function in the same cellular pathway.

This article gives a common theoretical treatment for gradient and Newton type methods for general classes of problems.

Article addresses the question whether every Polish group that is not locally compact admits a Borel action on a standard Borel space whose associated orbit equivalence relation is not essentially countable. The authors e answer this question positively for the class of all Polish groups that embed in the isometry group of a locally compact metric space.

This article discusses how RNA-sequencing analysis was performed to assess how a glucose-supplemented diet and/or a hyl-2 mutation altered the transcriptome.