BALANCE BETWEEN LEADING AND FOLLOWING AND INTERNATIONAL PEDAGOGICAL INNOVATIONS

The primary goal of this paper is to portray how the balance between leading and following can often guide us to new pedagogical innovations and leadership. First of all, we will examine how students’ feedback plays an essential role in devising new teaching styles that enhance the amiable learning atmosphere and directs us to new innovations and leadership. Second of all, we will focus on how feedback from colleagues can open new opportunities for new seminars, for new research projects, for writing new papers and textbooks and welcome us to new international and interdisciplinary teaching and learning atmosphere and new innovations. In addition, our aim is to address and understand the concerns and questions from students’ and colleagues’ feedback can be used to minimize the risk of failure and to steer us in designing new innovations and leadership. Furthermore, our intent is to portray that balance between leading and following is an essential technique in development of new ideas and innovations. Moreover, we will share examples of successful pedagogical innovations that were suggested by students and colleagues. Throughout this paper we will remit the following vital question: do creativity and innovations come directly from us

VALUE ORIENTATIONS, EMOTIONAL INTELLIGENCE AND INTERNATIONAL PEDAGOGICAL INNOVATIONS

The primary goal of this paper is to portray how the value orientations and priorities can direct us to new pedagogical cores and innovations and leadership. First of all, we will examine how the students’ value orientations and priorities become a pertinent factor in conceiving new teaching practices that enhance the amiable learning atmosphere and guides us to new ideas and leadership. Second of all, we will focus on how value orientations and priorities expand our current knowledge and comprehension of the students’ learning styles and demands and gravitate teachers and students to the concept of emotional intelligence; this then leads students and teachers to new international and interdisciplinary environment(s) and to new teaching and learning practices. In addition, our aim is to address the students’ value orientations and priorities and apply them to steer us to design new learning environment(s) and to the transformational and primal leaderships. Furthermore, our intent is to render how value orientations guide to the emotional intelligence, which then directs to new practices, ideas and innovations. Moreover, we will share specific examples of successful pedagogical innovations that lead to the emotional intelligence and were guided by the students’ value orientations and priorities. Throughout this paper we will remit the following vital question: how do we link the value orientations together with the emotional intelligence and the transformational and primal leaderships

Chaotic single neuron model with periodic coefficients with period two

Our goal is to investigate the piecewise linear difference equation xn+1 = βnxn – g(xn). This piecewise linear difference equation is a prototype of one neuron model with the internal decay rate β and the signal function g. The authors investigated this model with periodic internal decay rate βn as a period-two sequence. Our aim is to show that for certain values of coefficients βn, there exists an attracting interval for which the model is chaotic. On the other hand, if the initial value is chosen outside the mentioned attracting interval, then the solution of the difference equation either increases to positive infinity or decreases to negative infinity

UNIVERSITY LEVEL TEACHING STYLES WITH HIGH SCHOOL STUDENTS AND INTERNATIONAL TEACHING AND LEARNING

The main aim of this paper is to render how university level courses are taught in high school. In fact, we will focus on what styles are used to teach university level courses and illustrate the international contrasts that happen quite frequently. In addition, we will analyse the details of teaching styles that were implemented in the American and the Latvian educational systems. Furthermore, we will discuss what specific teaching styles and innovations work successfully, and what teaching styles and innovations had difficulties and need improvements. In particular, implementing the hands-on teaching and learning styles and repetitive type teaching and learning styles. Moreover, we will also discuss the risk involved with introducing and transforming university level courses and teaching styles with high school students and how to manage these risks

ONLINE EDUCATION: LEARNING OUTCOME, SUCCESS & CHALLENGES

This paper’s intents are to render the learning outcome, success and challenges that emerge in an online teaching and learning environment in comparison to the traditional face to face classroom environment. First of all, we will examine how the students acclimate to the new online digital learning atmosphere after the traditional face to face learning environment; what challenges and barriers the students encounter in a synchronous and in an asynchronous online learning environments? Second of all, we will focus on how professors adapt to the new digital online teaching styles and examine the new essential teaching innovations that arise in order to achieve and go beyond the expected learning outcomes; how to remit to the students’ challenges and retain the positive and engaging learning environment? In addition, our aims are to examine new pedagogical innovations that naturally emerge while responding to the students’ travails and to smoothly navigate them to achieve the expected learning outcomes.Furthermore, our paper’s intents are to portray how an online learning environment can attain more effective learning outcomes in comparison to the traditional face to face classroom environment; how to think beyond our horizons and to enhance the learning outcomes in a digital learning atmosphere while addressing the students’ challenges? Moreover, we will emphasize how the immediate graded feedback and students’ feedback serve as pertinent tools in achieving the learning outcome and inspires students to learn in an online atmosphere.

Two-point correlation properties of stochastic "cloud processes''

We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically that there may be non-trivial correlations in the displacement fields describing the positions of the different daughters of the same "mother" particle, and then treat separately the cases in which there are, or are not, correlations also between the displacements of daughters belonging to different mothers. For both cases exact formulae are derived relating the structure factor (power spectrum) of the daughter distribution to that of the mother. These results can be considered as a generalization of the analogous equations obtained in ref. [1] (cond-mat/0409594) for the case of stochastic displacement fields applied to particle distributions. An application of the present results is that they give explicit algorithms for generating, starting from regular lattice arrays, stochastic particle distributions with an arbitrarily high degree of large-scale uniformity.Comment: 14 pages, 3 figure

A radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns

Diffraction images with continuous rotation symmetry arise from amorphous systems, but also from regular crystals when investigated by powder diffraction. On the theoretical side, pinwheel patterns and their higher dimensional generalisations display such symmetries as well, in spite of being perfectly ordered. We present first steps and results towards a general frame to investigate such systems, with emphasis on statistical properties that are helpful to understand and compare the diffraction images. An alternative substitution rule for the pinwheel tiling, with two different prototiles, permits the derivation of several combinatorial and spectral properties of this still somewhat enigmatic example. These results are compared with properties of the square lattice and its powder diffraction.Comment: 16 pages, 8 figure

Fractal spectral triples on Kellendonk's C∗C^*-algebra of a substitution tiling

We introduce a new class of noncommutative spectral triples on Kellendonk's $C^*$-algebra associated with a nonperiodic substitution tiling. These spectral triples are constructed from fractal trees on tilings, which define a geodesic distance between any two tiles in the tiling. Since fractals typically have infinite Euclidean length, the geodesic distance is defined using Perron-Frobenius theory, and is self-similar with scaling factor given by the Perron-Frobenius eigenvalue. We show that each spectral triple is $\theta$-summable, and respects the hierarchy of the substitution system. To elucidate our results, we construct a fractal tree on the Penrose tiling, and explicitly show how it gives rise to a collection of spectral triples.Comment: Updated to agree with published versio