Search results for "MATHEMATICS"
showing 10 items of 22031 documents
Optimal Spectral Wavelengths for Discriminating Orchard Species Using Multivariate Statistical Techniques
2019
Sustainable management of orchard fields requires detailed information about the tree types, which is a main component of precision agriculture programs. To this end, hyperspectral imagery can play a major role in orchard tree species mapping. Efficient use of hyperspectral data in combination with field measurements requires the development of optimized band selection strategies to separate tree species. In this study, field spectroscopy (350 to 2500 nm) was performed through scanning 165 spectral leaf samples of dominant orchard tree species (almond, walnut, and grape) in Chaharmahal va Bakhtiyari province, Iran. Two multivariable methods were employed to identify the optimum wavelengths:…
Benson group additivity values of phosphines and phosphine oxides: Fast and accurate computational thermochemistry of organophosphorus species
2018
Composite quantum chemical methods W1X-1 and CBS-QB3 are used to calculate the gas phase standard enthalpy of formation, entropy, and heat capacity of 38 phosphines and phosphine oxides for which reliable experimental thermochemical information is limited or simply nonexistent. For alkyl phosphines and phosphine oxides, the W1X-1, and CBS-QB3 results are mutually consistent and in excellent agreement with available G3X values and empirical data. In the case of aryl-substituted species, different computational methods show more variation, with G3X enthalpies being furthest from experimental values. The calculated thermochemical data are subsequently used to determine Benson group additivity …
Extremal Irregular Digraphs
2018
A digraph is called irregular if its distinct vertices have distinct degree pairs. An irregular digraph is called minimal (maximal) if the removal of any arc (addition of any new arc) results in a non-irregular digraph. It is easily seen that the minimum sizes among irregular n-vertex whether digraphs or oriented graphs are the same and are asymptotic to (√2/3) n3/2; maximum sizes, however, are asymptotic to n2 and n2/2, respectively. Let s stand for the sum of initial positive integers, s = 1, 3, 6, . . . . An oriented graph Hs and a digraph Fs, both large (in terms of the size), minimal irregular, and on any such s vertices, s ≥ 21, are constructed in [Large minimal irregular digraphs, Op…
Mathematical and Coding Lessons Based on Creative Origami Activities
2019
AbstractThis paper considers how creativity and creative activities can be encouraged in regular mathematical classes by combining different teaching approaches and academic disciplines. We combined origami and paper folding with fractals and their mathematical properties as well as with coding in Scratch in order to facilitate learning mathematics and computer science. We conducted a case study experiment in a Serbian school with 15 high school students and applied different strategies for learning profound mathematical and coding concepts such as fractals dimension and recursion. The goal of the study was to employ creative activities and examine students’ activities during this process i…
Developing Primary School Students’ Formal Geometric Definitions Knowledge by Connecting Origami and Technology
2019
In this paper, we present opportunities with the uses of origami and technology, in our case GeoGebra, in teaching formal geometric definitions for fifth-grade primary school students (11-12yrs). Applying origami in mathematical lessons is becoming to be recognized as a valuable tool for improving students’ mathematical knowledge. In previous studies, we developed origami and technology activities for high-school mathematics, but we wanted to explore if such approach would work in primary school as well. For this reason, we chose a flat origami model оf the crane and we used this model to introduce students to basic geometrical notions and definitions, such as points, lines, intersections o…
Osculating spheres to a family of curves.
2021
The authors study the extrinsic conformal geometry of space forms involving pencils of circles or spheres. They consider curves orthogonal to a foliation of an open set of a 3-sphere by spheres and prove that the osculating spheres to the curves at points of a leaf form a pencil. They first prove the analogous result in a lower-dimensional case, that is, foliations of the 2-dimensional sphere and their orthogonal foliations. The 3-dimensional result, that is, the result for a foliation of (an open subset of) the 3-dimensional sphere by 2-dimensional spheres, is obtained using the de Sitter space, which is a model for the set of oriented spheres of the 3-dimensional sphere.
Biharmonic obstacle problem: guaranteed and computable error bounds for approximate solutions
2020
The paper is concerned with a free boundary problem generated by the biharmonic operator and an obstacle. The main goal is to deduce a fully guaranteed upper bound of the difference between the exact minimizer u and any function (approximation) from the corresponding energy class (which consists of the functions in $H^2$ satisfying the prescribed boundary conditions and the restrictions stipulated by the obstacle). For this purpose we use the duality method of the calculus of variations and general type error identities earlier derived for a wide class of convex variational problems. By this method, we define a combined primal--dual measure of error. It contains four terms of different natu…
Quantitative Approximation Properties for the Fractional Heat Equation
2017
In this note we analyse \emph{quantitative} approximation properties of a certain class of \emph{nonlocal} equations: Viewing the fractional heat equation as a model problem, which involves both \emph{local} and \emph{nonlocal} pseudodifferential operators, we study quantitative approximation properties of solutions to it. First, relying on Runge type arguments, we give an alternative proof of certain \emph{qualitative} approximation results from \cite{DSV16}. Using propagation of smallness arguments, we then provide bounds on the \emph{cost} of approximate controllability and thus quantify the approximation properties of solutions to the fractional heat equation. Finally, we discuss genera…
Intrinsic Lipschitz Graphs and Vertical β-Numbers in the Heisenberg Group
2016
The purpose of this paper is to introduce and study some basic concepts of quantitative rectifiability in the first Heisenberg group $\mathbb{H}$. In particular, we aim to demonstrate that new phenomena arise compared to the Euclidean theory, founded by G. David and S. Semmes in the 90's. The theory in $\mathbb{H}$ has an apparent connection to certain nonlinear PDEs, which do not play a role with similar questions in $\mathbb{R}^{3}$. Our main object of study are the intrinsic Lipschitz graphs in $\mathbb{H}$, introduced by B. Franchi, R. Serapioni and F. Serra Cassano in 2006. We claim that these $3$-dimensional sets in $\mathbb{H}$, if any, deserve to be called quantitatively $3$-rectifi…
Equivalence of viscosity and weak solutions for the normalized $p(x)$-Laplacian
2018
We show that viscosity solutions to the normalized $p(x)$-Laplace equation coincide with distributional weak solutions to the strong $p(x)$-Laplace equation when $p$ is Lipschitz and $\inf p>1$. This yields $C^{1,\alpha}$ regularity for the viscosity solutions of the normalized $p(x)$-Laplace equation. As an additional application, we prove a Rad\'o-type removability theorem.