Abstract Empirical evidence on the association between the shifting component of executive functioning and academic performance is equivocal. In two meta-analyses children's shifting ability is examined in relation to their performance in math ( k = 18, N = 2330) and reading ( k = 16, N = 2266). Shifting ability was significantly and equally associated with performance in both math ( r = .26, 95% CI = .15–.35) and reading ( r = .21, 95% CI = .11–.31). Intelligence was found to show stronger associations with math and reading performance than shifting ability. We conclude that the links between shifting ability, academic skills, and intelligence are domain-general.
In this paper, first we construct two subcategories (using symmetric representations and antisymmetric representations) of the category of relative Rota-Baxter operators on Leibniz algebras, and establish the relations with the categories of relative Rota-Baxter operators and relative averaging operators on Lie algebras. Then we show that there is a short exact sequence describing the relation between the controlling algebra of relative Rota-Baxter operators on a Leibniz algebra with respect to a symmetric (resp. antisymmetric) representation and the controlling algebra of the induced relative Rota-Baxter operators (resp. averaging operators) on the canonical Lie algebra associated to the Leibniz algebra. Finally, we show that there is a long exact sequence describing the relation between the cohomology groups of a relative Rota-Baxter operator on a Leibniz algebra with respect to a symmetric (resp. antisymmetric) representation and the cohomology groups of the induced relative Rota-Baxter operator (resp. averaging operator) on the canonical Lie algebra.
For the largest exceptional simple Lie superalgebra $F(4)$, having dimension $(24|16)$, we provide two explicit geometric realizations as supersymmetries, namely as the symmetry superalgebra of super-PDE systems of second and third order respectively.
Raj Mukhopadhyay, Binoy Sarkar, Arijit Barman
et al.
AbstractThis study evaluates the arsenic adsorption behavior of Fe‐exchanged smectite and phosphate‐bound kaolinite, in soil, tap water and double distilled water in the presence of competing anions such as silicate, phosphate, and sulfate, and at variable pH values. The maximum amounts of As adsorbed in soil are 620.6 and 607.6 µg g–1 at pH 5 by Fe‐exchanged smectite and phosphate‐bound kaolinite, respectively. The pH‐modified Freundlich equation fits well (R2 > 0.96) to the adsorption data, distinguishing the effect of pH on adsorption. The coefficients of pH‐value are 0.04 and 0.05 for phosphate‐bound kaolinite and Fe‐exchanged smectite, suggesting that low pH is suitable for the adsorption. The As adsorption is decreased in tap water at low pH compared to the soil due to the presence of iron (Fe2+/3+), sulfate, and bicarbonate in tap water. Among the competing anions in distilled water, phosphate is the most interfering anion for As adsorption. The competition coefficients of As‐phosphate binary adsorption derived from the Sheindorf equation are 3.93 and 0.56 for Fe‐exchanged smectite and phosphate‐bound kaolinite at pH 5. The Fe‐exchanged smectite can be used more effectively than phosphate‐bound kaolinite for As remediation in systems having low pH (pH ≈5) and high phosphate concentration.
Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to effectively include math in physics in a way that reaches most students remains unsolved. In this paper, we suggest that a fundamental issue has received insufficient exploration: the fact that in science, we don’t just use math, we make meaning with it in a different way than mathematicians do. In this reflective essay, we explore math as a language and consider the language of math in physics through the lens of cognitive linguistics. We begin by offering a number of examples that show how the use of math in physics differs from the use of math as typically found in math classes. We then explore basic concepts in cognitive semantics to show how humans make meaning with language in general. The critical elements are the roles of embodied cognition and interpretation in context. Then, we show how a theoretical framework commonly used in physics education research, resources, is coherent with and extends the ideas of cognitive semantics by connecting embodiment to phenomenological primitives and contextual interpretation to the dynamics of meaning-making with conceptual resources, epistemological resources, and affect. We present these ideas with illustrative case studies of students working on physics problems with math and demonstrate the dynamical nature of student reasoning with math in physics. We conclude with some thoughts about the implications for instruction.
We give a detailed explicit computation of weights of Kontsevich graphs which arise from connection and curvature terms within the globalization picture for the special case of symplectic manifolds. We will show how the weights for the curvature graphs can be explicitly expressed in terms of the hypergeometric function as well as by a much simpler formula combining it with the explicit expression for the weights of its underlined connection graphs. Moreover, we consider the case of a cotangent bundle, which will simplify the curvature expression significantly.
In this paper, we proposed a novel method using the elementary number theory to investigate the discrete nature of the screw dislocations in crystal lattices, simple cubic (SC) lattice and body centered cubic (BCC) lattice, by developing the algebraic description of the dislocations in the previous report (Hamada, Matsutani, Nakagawa, Saeki, Uesaka, Pacific J. Math.~for Industry {\bf{10}} (2018), 3). Using the method, we showed that the stress energy of the screw dislocations in the BCC lattice and the SC lattice are naturally described; the energy of the BCC lattice was expressed by the truncated Epstein-Hurwitz zeta function of the Eisenstein integers, whereas that of SC lattice is associated with the truncated Epstein-Hurwitz zeta function of the Gauss integers.