Reflection in Studying Electronic Tables at School

The present study is dedicated on forming skills for producing reflections from both students and teachers in studying the topic ‘Electronic Tables’ at school. This study provides a detailed explanation of the applications of the ALACT model where the process of reflection is realized via a cyclic model. An overlook is given on specific examples from the IT education which realize reflection.

About Learning Discrete Mathematics at Bulgarian School

The present work is dedicated to the learning discrete mathematics at Bulgarian school. A review of syllabuses and standards has been made. A project of learning discrete mathematics elements from first to twelve class is proposed.

Dual-parameters sensing based on multimode microfiber with Fresnel reflection

A compact and low cost fiber sensor based on microfiber with Fresnel reflection is proposed and demonstrated for simultaneous measurement of refractive index (RI) and temperature with high sensitivities. © OSA 2015.

Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory

2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20.

A Geometrical Construction for the Polynomial Invariants of some Reflection Groups

2000 Mathematics Subject Classification: Primary 20F55, 13F20; Secondary 14L30.

Notes on the Solution of Dynamic Optimization Problems with Explicit Controls in Discrete-Time Economic Models

Йордан Йорданов, Андрей Василев - В работата се изследват методи за решаването на задачи на оптималното управление в дискретно време с безкраен хоризонт и явни управления. Дадена е обосновка на една процедура за решаване на такива задачи, базирана на множители на Лагранж, коята често се употребява в икономическата литература. Извеждени са необходимите условия за оптималност на базата на уравнения на Белман и са приведени достатъчни условия за оптималност при допускания, които често се използват в икономиката.

Discrete Generalization of Gronwall-Bellman Inequality with Maxima and Application

Снежана Христова, Кремена Стефанова, Лиляна Ванкова - В работата са решени няколко нови видове линейни дискретни неравенства, които съдържат максимума на неизвестната функция в отминал интервал от време. Някои от тези неравенства са приложени за изучаване непрекъснатата зависимост от смущения при дискретни уравнения с максимуми.

An edge-based matching kernel through discrete-time quantum walks

In this paper, we propose a new edge-based matching kernel for graphs by using discrete-time quantum walks. To this end, we commence by transforming a graph into a directed line graph. The reasons of using the line graph structure are twofold. First, for a graph, its directed line graph is a dual representation and each vertex of the line graph represents a corresponding edge in the original graph. Second, we show that the discrete-time quantum walk can be seen as a walk on the line graph and the state space of the walk is the vertex set of the line graph, i.e., the state space of the walk is the edges of the original graph. As a result, the directed line graph provides an elegant way of developing new edge-based matching kernel based on discrete-time quantum walks. For a pair of graphs, we compute the h-layer depth-based representation for each vertex of their directed line graphs by computing entropic signatures (computed from discrete-time quantum walks on the line graphs) on the family of K-layer expansion subgraphs rooted at the vertex, i.e., we compute the depth-based representations for edges of the original graphs through their directed line graphs. Based on the new representations, we define an edge-based matching method for the pair of graphs by aligning the h-layer depth-based representations computed through the directed line graphs. The new edge-based matching kernel is thus computed by counting the number of matched vertices identified by the matching method on the directed line graphs. Experiments on standard graph datasets demonstrate the effectiveness of our new kernel.

A quantum Jensen-Shannon graph kernel using discrete-time quantum walks

In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel.

Discrete Time Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80

A Computational Approach for the Statistical Estimation of Discrete Time Branching Processes with Immigration

2010 Mathematics Subject Classification: 60J80.

Joining the dots:using structured e-portfolio assignments to enhance reflection

Although there has been an increased interest in the use of electronic portfolios in higher education over the last five years, relatively little is known about the potential of such tools to support the development of higher order abilities for students, such as reflection, in a structured way that is suitable for assessment. This paper reports the findings from a small-scale research which sets out to compare the outcomes of reflective assignments in two cohorts of participants in a Postgraduate Certificate in Professional Practice in Higher Education in the UK. Participants in the programme were asked to submit reflective accounts using an e-portfolio system as part of their formal assessment. One cohort completed the assessment using some generic guidelines of how to reflect and construct an e-portfolio page without a given template or structure, whereas another cohort was given a specific template with clear assessment criteria to gauge the assembly of their reflections. The authors, who are also tutors in the programme, analysed the submitted reflections following open coding procedures. The analysis found a tendency for the reflection in the first cohort to be merely descriptive without progressing to speculating objectively about answers to relevant analytical questions about the process involved in the ability under scrutiny. In contrast the assignments of cohort two were found to be more insightful in terms of assimilating random bits of materials, thoughts and self-questions into complete reflective accounts. These findings bring some evidence to support and indeed promote a more structured approach to reflective practice, which can be further enhanced through a carefully created e-portfolio template and associated assessment criteria.

Thermalized polarization dynamics of a discrete optical-waveguide system with four-wave mixing

Statistical mechanics of two coupled vector fields is studied in the tight-binding model that describes propagation of polarized light in discrete waveguides in the presence of the four-wave mixing. The energy and power conservation laws enable the formulation of the equilibrium properties of the polarization state in terms of the Gibbs measure with positive temperature. The transition line T=∞ is established beyond which the discrete vector solitons are created. Also in the limit of the large nonlinearity an analytical expression for the distribution of Stokes parameters is obtained, which is found to be dependent only on the statistical properties of the initial polarization state and not on the strength of nonlinearity. The evolution of the system to the final equilibrium state is shown to pass through the intermediate stage when the energy exchange between the waveguides is still negligible. The distribution of the Stokes parameters in this regime has a complex multimodal structure strongly dependent on the nonlinear coupling coefficients and the initial conditions.