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.     

On the existence of $$\kappa $$-existentially closed groups

Using explicit constructions of the Weierstrass mock modular form and Eisenstein series coefficients, we obtain closed formulas for the generating functions of values of shifted convolution L-functions associated to certain elliptic curves. These identities provide a surprising relation between weight 2 newforms and shifted convolution L-values when the underlying elliptic curve has modular degree 1 with conductor N such that \(\text {genus}(X_0(N)) = 1\).     

Measurement and optimization of responsiveness in supply chain networks with queueing structures

In this paper we consider supply chains with multiple stages of serial or network structure. The supply chains are endogenous in the sense that they involve queues because each order’s lead-time is dependent on the orders already in the system. We define supply chain responsiveness as the probability of fulfilling customer orders within a promised lead-time and study the problems of measuring and optimizing supply chain responsiveness using queueing network models. We first consider a single-server multi-stage serial supply chain and find a closed form expression for the fulfilment time distribution. For the multi-server multi-stage problem, the closed form evaluation of the fulfilment time distribution becomes intractable due to the dependency of the lead-times in different stages. We circumvent this difficulty by proposing a novel FCFS discipline which enables a closed-form analysis. For the multi-server multi-stage Jackson-type supply chain network, to enable analysis, we convert the system into an equivalent single server single stage system with state-dependent rates. For each case, we present detailed numerical examples for both measurement and the optimization of supply chain responsiveness.     

Cooperative game analysis of retail space-exchange problems

We analyze retail space-exchange problems where two or more retailers exchange their excess retail spaces to improve the utilization of their space resource. We first investigate the two-retailer space exchange problem. In order to entice both retailers with different bargaining powers to exchange their spaces, we use the generalized Nash bargaining scheme to allocate the total profit surplus between the two retailers. Next, we consider the space-exchange problem involving three or more retailers, and construct a cooperative game in characteristic function form. We show that the game is essential and superadditive, and also prove that the core is non-empty. Moreover, in order to find a unique allocation scheme that ensures the stability of the grand coalition, we propose a new approach to compute a weighted Shapley value that satisfies the core conditions and also reflects retailers’ bargaining powers. Our analysis indicates that the space exchange by more retailers can result in a higher system-wide profit surplus and thus a higher allocation to each retailer under a fair scheme.     

A comparative analysis of linear,nonlinear and improved nonlinear thermodynamic models of voltage-dependent ion channel kinetics

The linear, nonlinear and improved nonlinear thermodynamic models of the voltage-dependent ion channels were proposed to deduce the exact functional form of the rate constants. In this context, we present a comparative analysis of the linear, nonlinear and improved nonlinear thermodynamic models of voltage-dependent channel kinetics based on the sodium activation experimental data of Cav3.1 channel. We also provide some insight on the assumptions used to derive the thermodynamic models of the channels and show that the improved nonlinear thermodynamic model provides a simple and physically plausible approach to describe the behavior of the voltage-dependent ion channels.     

One Pot Synthesis of Graphene through Microwave Assisted Liquid Exfoliation of Graphite in Different Solvents

This study presents an easy and quick method for the synthesis of graphene from graphite in a set of solvents, including n-Hexadecane (n-Hexa), dimethylsulfoxide (DMSO), sodium hydroxide (NaOH), 1-octanol (OCTA), perchloric acid (PA), N,N-Dimethylformamide (DMF), ethylene glycol (EG), and ethylene diamine (ED), via microwave (MW) energy. The properties of final products were determined by X-ray diffraction spectroscopy (XRD), Fourier transform infrared spectroscopy (FTIR), ultraviolet-visible (UV-Vis) spectroscopy, and the four-point probe technique. The XRD spectra of most of the MW-assisted graphene products showed peaks at 2θ = 26.5° and 54°. Layer numbers extend from 2 and 25, and the leading comes about were gotten by having two-layered products, named as graphene synthesized in dimethylsulfoxide (G-DMSO), graphene synthesized in ethylene glycol (G-EG), and graphene synthesized in 1-octanol (G-OCTA). G-DMF has the highest electrical conductivity with 22 S/m. The electrical conductivity is higher when the dipole moment of the used solvent is between 2 and 4 Debye (D). The FTIR spectra of most of the MW-assisted graphene products are in line with commercial graphene (CG). The UV-Vis spectra of all MW-assisted graphene products showed a peak at 223 nm referring to characteristic sp2 C=C bonds and 273 nm relating to the n → π * transition of C-O bonds.     

Novel C2-symmetric macrocycles bearing diamide-diester groups: synthesis and enantiomeric recognition for primary alkyl ammonium salts

We synthesized a series of novel macrocycles with diamide-diester groups (S,S)-1, (S,S)-2, (S,S)-3, and (R,R)-1, derived from dimethyloxalate and amino alcohols by high dilution technique, and evaluated enantiomeric recognition properties of these macrocycles toward primary alkyl ammonium salts by 1H NMR titration. Taking into account the host employed, important differences were observed in the Ka values of (R)-Am and (S)-Am for (S,S)-1 and (R,R)-1 hosts, KS/KR = 5.55 and KR/KS = 3.65, Delta Delta Go = 0.43 and -0.32 kJ mol-1, respectively. There seems a general tendency for the host to include the guests with the same absolute configuration.     

Co(II) and Cu(II) Schiff base complexes of bis(<Emphasis Type="Italic">N</Emphasis>-(4-diethylamino-2-methylphenyl)-3,5-di-<Emphasis Type="Italic">tert</Emphasis>-butylsalicylaldimine): Electrochemical and X-ray structural study

Copper(II) and cobalt(II) complexes of salicylaldimine obtained by the condensation of N,N-diethyl-2-methyl-1,4-phenylenediamine with 3,5-di-tert-butyl-2-hydroxybenzaldehyde have been synthesized and characterized by elemental analyses, magnetic susceptibility measurements, cyclic voltammetry, and FT-IR and UV–Vis spectroscopy. The molecular structure of the title copper(II) complex was determined by the single crystal X-ray diffraction technique. The Cu(II) center is coordinated by four atoms of the donor set in a compressed tetrahedral trans-[N₂O₂] environment, which can be essentially ascribed to the presence of bulky fragments of the ligand. The computed bond valences of the copper verify +2 oxidation state and indicate that the copper bonds, in particular Cu–N bonds, are elongated due to steric effects from bulky substituents in the ligands, N-(4-diethylamino-2-methylphenyl). Intermolecular C–H···π interactions leading to centrosymmetric synthons serve to stabilize periodic organization of the molecules.     

Spatial distribution and risk assessment of radioactivity and heavy metal levels of sediment,surface water and fish samples from Lake Van,Turkey

In this study, radioactivity levels of 228 lake water samples, 63 upper and depth sediment samples and 12 fish samples from Lake Van were investigated from 2005 to 2008 and the distribution patterns of the radionuclides were presented. Analysis included gross alpha–beta and total radium isotopes activities and uranium concentrations of the water, and gross alpha and gross beta activities and relevant ²³⁸U, ²³²Th and ⁴⁰K activity of the sediment and fish samples of the lake. Mean gross alpha, gross beta and radium isotopes activities of lake water were found 0.74 ± 0.46, 0.02 ± 0.01 and 0.06 ± 0.04 Bq/L, respectively. Mean gross alpha and beta activities in upper and depth sediments were found to be 41 ± 6 and 1,514 ± 74 Bq/kg; 77 ± 5 and 394 ± 24 Bq/kg at a 95 % confidence level, respectively. Mean activities of ²³⁸U, ²³²Th and ⁴⁰K activity concentrations in upper and depth sediments were determined to be 225 ± 22, 70 ± 7 and 486 ± 39 Bq/kg; 174 ± 4, 63 ± 3 and 263 ± 25 Bq/kg, respectively. The mean gross alpha and beta, ²³⁸U, ²³²Th and ⁴⁰K aktivities in fish samples were established as 47 ± 18, 470 ± 12, 0.57 ± 0.220, 0.022 ± 0.006, 319 ± 11 Bq/kg, respectively. The transfer factor from lake water to fish tissues, annual intake by humans consuming fish, and annual committed effective doses were estimated and evaluated.