Optimal residuals and the Dahlquist test problem

Numerical Algorithms - We show how to compute the optimal relative backward error for the numerical solution of the Dahlquist test problem by one-step methods. This is an example of a general...     

SVL fluorescence and duschinskii effect in the S1 state of pyridine

SVL fluorescence spectra from principal bands in the S₁ state of pyridine h₅ and -d₅ were measured. A large displacement of the normal coordinate origin of v_6a and the Duschinskii rotation of v_10a and v_16a were established.     

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 \(\text {genus}(X_0(N)) = 1\).     

PBL as a pedagogical approach for integrated STEM: Evidence from prospective teachers

Problem-based learning (PBL) and science, technology, engineering, and mathematics (STEM) are two acronyms widely visible in education literature today. However, few studies have explored these in connection with one another, specifically with regard to teacher preparation. This study investigated how 47 prospective elementary teachers developed PBL units and how they integrated STEM and other disciplines into those units. It also addressed the affordances and constraints of integrated STEM as perceived by the prospective elementary teachers. Data sources in this multimethod study included PBL units and interviews. Findings revealed that all of the units integrated at least two of the STEM disciplines, as well as literacy, in a variety of ways. The prospective teachers articulated perceived benefits of integrated STEM, such as: making connections across content areas, preparing students for the real world, teaching students that failure is not a bad thing, and providing future opportunities. They also addressed perceived barriers of integrated STEM, such as: having limited experience with the content, diminishing the effect of individual content areas, and needing better curriculum alignment. Overall, this study provides evidence that PBL can be a pedagogical approach to integrate STEM. Implications for teachers, teacher educators, and curriculum specialists are discussed.     

Optimization Over the Efficient Set of Multi-objective Convex Optimal Control Problems

We consider multi-objective convex optimal control problems. First we state a relationship between the (weakly or properly) efficient set of the multi-objective problem and the solution of the problem scalarized via a convex combination of objectives through a vector of parameters (or weights). Then we establish that (i) the solution of the scalarized (parametric) problem for any given parameter vector is unique and (weakly or properly) efficient and (ii) for each solution in the (weakly or properly) efficient set, there exists at least one corresponding parameter vector for the scalarized problem yielding the same solution. Therefore the set of all parametric solutions (obtained by solving the scalarized problem) is equal to the efficient set. Next we consider an additional objective over the efficient set. Based on the main result, the new objective can instead be considered over the (parametric) solution set of the scalarized problem. For the purpose of constructing numerical methods, we point to existing solution differentiability results for parametric optimal control problems. We propose numerical methods and give an example application to illustrate our approach.     

Room temperature magnetocaloric effect in Pr1.75Sr1.25Mn2O7 double-layered perovskite manganite system

Abstract

In this work, we have studied on double-layered perovskite (Ruddlesden–Popper) manganite structure in Pr_1.75Sr_1.25Mn₂O₇ synthesised by sol–gel method. The crystal structure of the double-layered perovskite is found as tetragonal from the X-ray diffraction analysis with I4/mmm space group. A high Curie temperature, T_C = 305 K is observed from the temperature dependence of magnetisation measurement. The isothermal magnetisation curves showed that magnetic phase transition is second order due to the positive slope of the Arrott plots. Maximum magnetic entropy change (ΔS_M) and adiabatic temperature change (ΔT_ad) values are calculated as 3.99 J kg^?1 K^?1 and 2.1 K under external magnetic field of 70 kOe, respectively. Since our double-layered perovskite manganite sample has desired T_C value and relatively high ΔS_M, it can be a potential candidate as a magnetocaloric material for room temperature magnetic cooling systems.