Quantum Mechanics of Guiding Center Motion in Strong Magnetic Field (Coherent State Path Integral Approach)

A new approach is proposed for the quantum mechanics of guiding center motion in strong magnetic field. This is achieved by use of the coherent state path integral for the coupled systems of the cyclotron and the guiding center motion. We are specifically concerned with the effective action for the guiding center degree, which can be used to get the Bohr- Sommerfeld quantization scheme. The quantization rule is similar to the one for the vortex motion as a dynamics of point particles.

Analytic Renormings of C(K) Spaces

The aim of our present note is to show the strength of the existence of an equivalent analytic renorming of a Banach space, even compared to C∞-Fréchet smooth renormings. It was Haydon who first showed in [8] that C(K) spaces for K countable admit an equivalent C∞-Fréchet smooth norm. Later, in [7] and [9] he introduced a large clams of tree-like (uncountable) compacts K for which C(K) admits an equivalent C∞-Fréchet smooth norm. Recently, it was shown in [3] that C(K) spaces for K countable admit an equivalent analytic norm. Our Theorem 1 shows that in the class of C(K) spaces this result is the best possible.

A quiz-based game for addressing growing population issues:linking learning mechanics to the GROWTH serious game

This paper discusses the integration of quiz mechanism into digital game-based learning platform addressing environmental and social issues caused by population growth. 50 participants' learning outcomes were compared before and after the session. Semi-structured interview was used to gather participants' viewpoints regarding of issues presented in the game. Phenomenography was used as a methodology for data collection and analysis. Preliminary outcomes have shown that the current game implementation and quiz mechanism can be used to: (1) promote learning and awareness on environmental and social issues and (2) sustain players' attention and engagements.

ROC Curves within the Framework of Neural Network Assembly Memory Model: Some Analytic Results

On the basis of convolutional (Hamming) version of recent Neural Network Assembly Memory Model (NNAMM) for intact two-layer autoassociative Hopfield network optimal receiver operating characteristics (ROCs) have been derived analytically. A method of taking into account explicitly a priori probabilities of alternative hypotheses on the structure of information initiating memory trace retrieval and modified ROCs (mROCs, a posteriori probabilities of correct recall vs. false alarm probability) are introduced. The comparison of empirical and calculated ROCs (or mROCs) demonstrates that they coincide quantitatively and in this way intensities of cues used in appropriate experiments may be estimated. It has been found that basic ROC properties which are one of experimental findings underpinning dual-process models of recognition memory can be explained within our one-factor NNAMM.

Inclusion Properties for Certain Classes of Analytic Functions Involving a Family of Fractional Integral Operators

2000 Math. Subject Classification: 30C45

Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics

Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.

Coefficient Estimates for Analytic Functions Concerned with Hankel Determinant

MSC 2010: 30C45

Note on Radius Problems for Certain Class of Analytic Functions

MSC 2010: 30C45

Where do bright ideas occur in our brain? Meta-analytic evidence from neuroimaging studies of domain-specific creativity

Many studies have assessed the neural underpinnings of creativity, failing to find a clear anatomical localization. We aimed to provide evidence for a multi-componential neural system for creativity. We applied a general activation likelihood estimation (ALE) meta-analysis to 45 fMRI studies. Three individual ALE analyses were performed to assess creativity in different cognitive domains (Musical, Verbal, and Visuo-spatial). The general ALE revealed that creativity relies on clusters of activations in the bilateral occipital, parietal, frontal, and temporal lobes. The individual ALE revealed different maximal activation in different domains. Musical creativity yields activations in the bilateral medial frontal gyrus, in the left cingulate gyrus, middle frontal gyrus, and inferior parietal lobule and in the right postcentral and fusiform gyri. Verbal creativity yields activations mainly located in the left hemisphere, in the prefrontal cortex, middle and superior temporal gyri, inferior parietal lobule, postcentral and supramarginal gyri, middle occipital gyrus, and insula. The right inferior frontal gyrus and the lingual gyrus were also activated. Visuo-spatial creativity activates the right middle and inferior frontal gyri, the bilateral thalamus and the left precentral gyrus. This evidence suggests that creativity relies on multi-componential neural networks and that different creativity domains depend on different brain regions.

Fekete-Szegoe problem for certain subclasses of analytic functions with respect to symmetric points

MSC 2010: 30C45

Efficient algorithm for routing optimization via statistical mechanics

Many practical routing algorithms are heuristic, adhoc and centralized, rendering generic and optimal path configurations difficult to obtain. Here we study a scenario whereby selected nodes in a given network communicate with fixed routers and employ statistical physics methods to obtain optimal routing solutions subject to a generic cost. A distributive message-passing algorithm capable of optimizing the path configuration in real instances is devised, based on the analytical derivation, and is greatly simplified by expanding the cost function around the optimized flow. Good algorithmic convergence is observed in most of the parameter regimes. By applying the algorithm, we study and compare the pros and cons of balanced traffic configurations to that of consolidated traffic, which provides important implications to practical communication and transportation networks. Interesting macroscopic phenomena are observed from the optimized states as an interplay between the communication density and the cost functions used. © 2013 IEEE.

Supersymmetry and Ghosts in Quantum Mechanics

2000 Mathematics Subject Classification: 81Q60, 35Q40.

On Sandwich Theorem of Analytic Functions Involving Integral Operator

2000 Mathematics Subject Classification: 30C45

To move or not to move, that is the question! Body schema and non-action oriented body representations:an fMRI meta-analytic study

Many studies have attempted to identify the different cognitive components of body representation (BR). Due to methodological issues, the data reported in these studies are often confusing. Here we summarize the fMRI data from previous studies and explore the possibility of a neural segregation between BR supporting actions (body-schema, BS) or not (non-oriented-to-action-body-representation, NA). We performed a general activation likelihood estimation meta-analysis of 59 fMRI experiments and two individual meta-analyses to identify the neural substrates of different BR. Body processing involves a wide network of areas in occipital, parietal, frontal and temporal lobes. NA selectively activates the somatosensory primary cortex and the supramarginal gyrus. BS involves the primary motor area and the right extrastriate body area. Our data suggest that motor information and recognition of body parts are fundamental to build BS. Instead, sensory information and processing of the egocentric perspective are more important for NA. In conclusion, our results strongly support the idea that different and segregated neural substrates are involved in body representations orient or not to actions.