保持拟可逆性或拟零因子的可加映射

设X和Y是维数大于1的复Banach空间,A和B分别是B(X)和B(Y)中包含有限秩算子的范数闭子代数.A,B∈A,定义A。B=A+B-AB,称。为A,B的拟积.刻画了从A到B的双边保持算子的(左,右)拟可逆性或(左,右,半)拟零因子的可加满射的结构.     

Teachers attending to student reasoning: Do beliefs matter?

We present the results of a quasi-experimental study of pre-service elementary teachers' learning to recognize students' mathematical reasoning from classroom videos. Researchers examined the nature of participants’ beliefs regarding mathematics education. We found that pre-service elementary teachers whose beliefs were consistent with NCTM Process Standards (NCTM, 2000), or that transitioned in the direction of consistency with the Standards, regarding the teaching and learning of mathematics, were more successful in recognizing students' reasoning than those whose beliefs were generally inconsistent. Predictive Analytics and Generalized Linear Regression modeling were used to quantify the magnitude of experimental pre-service teachers’ reasoning growth and combined pre/post study assessment reasoning success in contrast to that of the comparison groups. The resulting model explained nearly 90% of the variability in success on the reasoning assessment, showing that beliefs do indeed matter for recognition of reasoning.     

Response of saturated porous media subjected to local thermal loading on the surface of semi-infinite space

Heat source function method is adopted in the present paper to derive elementary solutions of coupled thermo-hydro-mechanical consolidation for saturated porous media under conjunct actions of instantaneous point heat source, instantaneous point fluid source and constant volume force. By using the so-called fictitious heat source method and images method, the solutions of a semi-infinite saturated porous medium subjected to a local heat source with time-varied intensity on its free surface are developed from elementary solutions. The numerical integral methods for calculating the unsteady temperature, pore pressure and displacement fields are given. The thermomechanical response are analyzed for the case of a circular planar heat source. Besides, the thermal consolidation characteristics of a saturated porous medium subjected to a harmonic thermal loading are also given, and the fluctuation processes of the field variables located below the center of heat source are analyzed. The project supported by the National Natural Science Foundation of China (50578008) The English text was polished byYunming Chen.     

Automorphisms of Hilbert schemes of points on a generic projective K3 surface

We study automorphisms of the Hilbert scheme of n points on a generic projective K3 surface S, for any . We show that is either trivial or generated by a non‐symplectic involution and we determine numerical and divisorial conditions which allow us to distinguish between the two cases. As an application of these results we prove that, for any , there exist infinitely many admissible degrees for the polarization of the K3 surface S such that admits a non‐natural involution. This provides a generalization of the results of [7] for .     

Quasipatterns versus superlattices resulting from the superposition of two hexagonal patterns

We present a short review of the experimental observations and mechanisms related to the generation of quasipatterns and superlattices by the Faraday instability with two-frequency forcing. We show how two-frequency forcing makes possible triad interactions that generate hexagonal patterns, twelvefold quasipatterns or superlattices that consist of two hexagonal patterns rotated by an angle α relative to each other. We then consider which patterns could be observed when α does not belong to the set of prescribed values that give rise to periodic superlattices. Using the Swift–Hohenberg equation as a model, we find that quasipattern solutions exist for nearly all values of α. However, these quasipatterns have not been observed in experiments with the Faraday instability for $\alpha \ne \mathrm{\pi }/6$. We discuss possible reasons and mention a simpler framework that could give some hint about this problem.     

An analysis of the form and content of quadrilateral definitions composed by novice pre-service teachers

Mathematical definitions are an important mathematical construct which has been noted as a challenging topic for both teachers and students. This study provides an analysis of the form and content of a set of 308 definitions of quadrilateral types provided by 44 novice pre-service elementary teachers (NPSTs) who had not yet studied geometry or definitions on the college level. Analysis of definition structure including necessary, sufficient, and minimal conditions, as well as hierarchical and partitional structure, provides insight into what NPSTs may think about the form of mathematical definitions in general. Analysis of the properties used in definitions of each shape type and the frequency of those properties reveals the shape types with which NPSTs are most and least familiar. These results are presented alongside possible applications and implications for instruction.