Pre-service Teachers’ Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers’ developing conceptions about (a) the nature of mathematical modeling in simulations of “real life” problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike other studies that have focused on single-topic and lesson-sized research sites, a course-sized research site was used in this study. Having been through several iterations over three teaching semesters, the 15-week long course was implemented with 25 pre-service secondary mathematics teachers. Findings revealed that pre-service teachers developed ideas about the nature of mathematical modeling involving what mathematical modeling is, the relationship between mathematical modeling and meaningful understanding, and the nature of mathematical modeling tasks. They also realized the changing roles of teachers during modeling implementations and diversity in students’ ways of thinking. The researchers’ conceptual development, on the other hand, involved realizing the critical aspect of the “teacher role” played by the instructor during modeling implementations, and the need for more experience of modeling implementations for pre-service teachers.     

A generalization of a theorem of Arrow,Barankin and Blackwell to a nonconvex case

The paper presents a generalization of a known density theorem of Arrow, Barankin, and Blackwell for properly efficient points defined as support points of sets with respect to monotonically increasing sublinear functions. This result is shown to hold for nonconvex sets of a partially ordered reflexive Banach space.     

On solitary wave diffraction by multiple,in-line vertical cylinders

The interaction of solitary waves with multiple, in-line vertical cylinders is investigated. The fixed cylinders are of constant circular cross section and extend from the seafloor to the free surface. In general, there are N of them lined in a row parallel to the incoming wave direction. Both the nonlinear, generalized Boussinesq and the Green–Naghdi shallow-water wave equations are used. A boundary-fitted curvilinear coordinate system is employed to facilitate the use of the finite-difference method on curved boundaries. The governing equations and boundary conditions are transformed from the physical plane onto the computational plane. These equations are then solved in time on the computational plane that contains a uniform grid and by use of the successive over-relaxation method and a second-order finite-difference method to determine the horizontal force and overturning moment on the cylinders. Resulting solitary wave forces from the nonlinear Green–Naghdi and the Boussinesq equations are presented, and the forces are compared with the experimental data when available.     

The statistical mechanics of spin-1 Ising model with AFM/AFM interactions on a bilayer Bethe lattice

The spin-1 Ising model is studied for the case of antiferromagnetic (AFM)/AFM interactions on the bilayer Bethe lattice by using the pairwise approach for several values of the coordination numbers q=3, 4 and 6 when the layers are linked with the external magnetic fields. The ground state (GS) phase diagrams, thermal variations of the order-parameters and the response functions are studied in detail to obtain the phase diagrams of the model. It was found that the system gives only one Néel temperature, T_N, for q=3. Two T_N's and first-order phase transition temperature, T_t, thus tricritical point, are found and the existence of two T_N's leads to the reentrant behavior when q=4 and 6 for some given system parameters.     

Synthesis, characterization and biological evaluation of a novel Cu(II) complex with the mixed ligands 2,6-pyridinedicarboxylic acid and 2-aminopyridine

A novel bridged binuclear Cu(II) complex with mixed ligands, di-μ-(2-aminopyridine(N,N′))-bis[(2,6-pyridinedicarboxylate)aquacopper(II)] tetrahydrate, formulated as [Cu(μ-ap)(dipic)(H₂O)]₂·4H₂O (1) (dipic = 2,6-pyridinedicarboxylate, ap = 2-aminopyridine), has been synthesized and characterized by elemental, spectral (IR and UV–Vis.), thermal analysis, magnetic measurements and single crystal X-ray diffraction analysis. The central Cu(II) ion resides on a centre of symmetry in a distorted square-pyramid coordination environment comprising of two N atoms, one from dipic and one from the ap ring, two carboxylate O atoms from dipic, and one O atom from water. Intermolecular N–HO and O–HO hydrogen bonds and π–π stacking interactions seem to be effective in the stabilization of the crystal structure. The free ligands and the complex were also evaluated for their antimicrobial and radical scavenging activities (DPPH = 1,1-diphenyl-2-picrylhydrazyl hydrate) using in vitro microdilution methods. Antimicrobial screening of the free ligands and their complex showed that the free ligands and the complex possess antifungal activity against Candida sp.     

Synthesis of new phosphorus ylides: Spectroscopic and X‐ray structural studies

Stable phosphoranes, Ar₃P = CHCOR (R = C₆H₅, C₆H₄NO₂, C₆H₄OCH₃, CH₃, OCH₂C₆H₅; Ar = p‐tolyl or phenyl), have been C‐acylated by acetic anhydride to obtain new types of phosphorus ylides. Synthesis and characterization of six phosphorus ylides of the type Ar₃PC(COCH₃)(COR) are reported. The reaction of {(p‐tolyl)₃PCHCOC₆H₅} ( I ), {(p‐ tolyl)₃PCHCOC₆H₄NO₂} ( II ), {Ph₃PCHCOC₆H₄NO₂} ( III ), {Ph₃PCHCOC₆H₄OCH₃} ( IV ), {(p‐tolyl)₃PCHCOCH₃} ( V ), and {Ph₃PCHCOOCH₂C₆H₅} ( VI ) with acetic anhydride in dry chloroform as solvent gives (p‐tolyl)₃PC(COMe)(COC₆H₅), α‐acetyl‐α‐benzoylmethy‐lenetriphenylphosphorane ( 1 ), {(p‐tolyl)₃PC(COMe) (COC₆H₄NO₂)} ( 2 ), {Ph₃PC(COMe)(COC₆H₄NO₂)} ( 3 ), {Ph₃PC(COMe)(COC₆H₄OCH₃)} ( 4 ), {(p‐tolyl)₃ PC(COCH₃)₂} ( 5 ), and {Ph₃PC(COMe)(COOCH₂ C₆H₅)} ( 6 ). Single crystal X‐ray analyses for ylides 2 , 5 , and 6 reveal the monoclinic ( 2, 5 ) and triclinic ( 6 ) crystal systems. Characterization of the obtained compounds was also performed by elemental analysis, IR, ¹H, ³¹P, and ¹³C NMR. The geometries of these compounds have been investigated using density functional theory (DFT). In addition, electronic parameters of these compounds such as HOMO and LUMO energy, Mulliken partial charge, and dipole moment were obtained. In this paper, the reactivity of these ylides is discussed in regard to the aforementioned data. © 2010 Wiley Periodicals, Inc. Heteroatom Chem 21:475–485, 2010; View this article online at wileyonlinelibrary.com . DOI 10.1002/hc.20633     

On the fundamental equations of piezoelasticity of quasicrystal media

The three-dimensional fundamental equations of elasticity of quasicrystals with extension to quasi-static electric effect are expresses in both differential and variational invariant forms for a regular region of quasicrystal material. The principle of conservation of energy is stated for the regular region and the constitutive relations are obtained for the piezoelasticity of material. A theorem is proved for the uniqueness in solutions of the fundamental equations by means of the energy argument. The sufficient boundary and initial conditions are enumerated for the uniqueness. Hamilton’s principle is stated for the regular region and a three-field variational principle is obtained under some constraint conditions. The constraint conditions, which are generally undesirable in computation, are removed by applying an involutory transformation. Then, a unified variational principle is obtained for the regular region, with one or more fixed internal surface of discontinuity. The variational principle operating on all the field variables generates all the fundamental equations of piezoelasticity of quasicrystals under the symmetry conditions of the phonon stress tensor and the initial conditions. The resulting equations, which are expressible in any system of coordinates and may be used through simultaneous approximation upon all the field variables in a direct method of solutions, pave the way to the study of important dislocation, fracture and interface problems of both elasticity and piezoelasticity of quasicrystal materials.     

Chemical Analysis of Hydroxyapatite Artificial Bone Powders by Energy Dispersive X-Ray Fluorescence Spectrometry(EDXRF)

Stoichiometric hydroxyapatite (HA) nanoparticles were synthesized by a wet chemical method. Calcium nitrate tetra hydrate used as calcium source and dibasic ammonium phosphate used as phosphorous source. Calcium nitrate tetra hydrate and dibasic ammonium phosphate solutions were prepared by dissolving the salts in distilled water. Stoichiometric hydroxyapatite nanoparticles used by artificial bone powders and synthesized by a wet chemical method were analyzed using EDXRF method.The concentrations of K, Ca, Ti, V, Cr, Fe, Ni, Cu, Sr and Pb for artificial bone powders have been determined. Besides, Calcium contents were evaluated according to the agitation time and temperature in the production process.     

The Bethe lattice treatment of sound attenuation for a spin- 3/2 Ising model

The sound attenuation phenomena is investigated for a spin- 3/2 Ising model on the Bethe lattice in terms of the recursion relations by using the Onsager theory of irreversible thermodynamics. The dependencies of sound attenuation on the temperature (T$T$), frequency (w$w$), Onsager coefficient (γ$\gamma$) and external magnetic field (H$H$) near the second-order (_Tc)$\left(T_c\right)$ and first-order (_Tt)$\left(T_t\right)$ phase transition temperatures are examined for given coordination numbers q$q$ on the Bethe lattice. It is assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process, thus two relaxation times are obtained and which are used to obtain an expression for the sound attenuation coefficient (α)$\left(\alpha \right)$. Our investigations revealed that only one peak is obtained near _Tt$T_t$ and three peaks are found near _Tc$T_c$ when the Onsager coefficient is varied at a given constant frequency for q=3$q=3$. Fixing the Onsager coefficient and varying the frequency always leads to two peaks for q=3,4$q=3,4$ and 6 near _Tc$T_c$. The sound attenuation peaks are observed near _Tt$T_t$ at lower values of external magnetic field, but as it increases the sound attenuation peaks decrease and eventually disappear.     

TiO2 embedded hydrothermally synthesized carbon composite as interlayer for lithium-sulfur batteries

Journal of Solid State Electrochemistry - Lithium-sulfur battery chemistry is one of the best alternatives to meet the demand of future electric vehicles providing high theoretical capacity and...