Hadamard Type Asymptotics for Eigenvalues of the Neumann Problem for Elliptic Operators

This paper considers how the eigenvalues of the Neumann problem for an elliptic operator depend on the domain. The proximity of two domains is measured in terms of the norm of the difference between the two resolvents corresponding to the reference domain and the perturbed domain, and the size of eigenfunctions outside the intersection of the two domains. This construction enables the possibility of comparing both nonsmooth domains and domains with different topology. An abstract framework is presented, where the main result is an asymptotic formula where the remainder is expressed in terms of the proximity quantity described above when this is relatively small. We consider two applications: the Laplacian in both $C^{1,\alpha}$ and Lipschitz domains. For the $C^{1,\alpha}$ case, an asymptotic result for the eigenvalues is given together with estimates for the remainder, and we also provide an example which demonstrates the sharpness of our obtained result. For the Lipschitz case, the proximity of eigenvalues is estimated

Domain-general Stroop Performance and Hemispheric Asymmetries: A Resting-state EEG Study

The ability to suppress irrelevant information while executing a task or interference resistance is a function of pFC that is critical for successful goal-directed human behavior. In the study of interference resistance and, more generally, executive functions, two key questions are still open: Does pFC contribute to cognitive control abilities through lateralized but domain-general mechanisms or through hemispheric specialization of domain-specific processes? And what are the underlying causes of interindividual differences in executive control performance? To shed light on these issues, here we employed an interindividual difference approach to investigate whether participants' hemispheric asymmetry in resting-state electrophysiological brain dynamics may reflect their variability in domain-general interference resistance. We recorded participants' resting-state electroencephalographic activity and performed spectral power analyses on the estimated cortical source activity. To measure participants' lateralized brain dynamics at rest, we computed the right-left hemispheric asymmetry score for the \u3b2/\u3b1 power ratio. To measure their domain-general interference resistance ability, verbal and spatial Stroop tasks were used. Robust correlations followed by intersection analyses showed that participants with stronger resting-state-related left-lateralized activity in different pFC regions, namely the mid-posterior superior frontal gyrus, middle and posterior middle frontal gyrus, and inferior frontal junction, were more able to inhibit irrelevant information in both domains. The present results confirm and extend previous findings showing that neurophysiological difference factors may explain interindividual differences in executive functioning. They also provide support for the hypothesis of a left pFC hemispheric specialization for domain-independent phasic cognitive control processes mediating Stroop performance

Time-Explicit Simulation of Wave Interaction in Optical Waveguide Crossings at Large Angles

The time-explicit finite-difference time-domain method is used to simulate wave interaction in optical waveguide crossings at large angles. The wave propagation at the intersecting structure is simulated by time stepping the discretized form of the Maxwell’s time dependent curl equations. The power distribution characteristics of the intersections are obtained by extracting the guided-mode amplitudes from these simulated total field data. A physical picture of power flow in the intersection is also obtained from the total field solution; this provides insights into the switching behavior and the origin of the radiations

Driver Behavior Analysis of Older Adults at Road Intersections Using Naturalistic Driving Data

In this study, I have understood driving behavior difference between drivers with Mild Cognitive Impairment (MCI) and drivers without Mild Cognitive Impairment (Non-MCI) and understood the relationship between cognitive abilities of different individuals and their driving behavior. I have developed different methodologies to extract different measures representing driving behavior at road intersections. Multiple driving individuals residing in MCI and Non-MCI were recruited and their driving data and physiological data were recorded. Driving behavior was represented in two domains (Physiological domain and Vehicular domain). First goal of this study was to find out driving behavior difference between MCI and Non-MCI group of drivers using both physiological domain measures as well as vehicular domain measures using statistical analysis. Second goal of this study was to find relationship between cognitive abilities and driving performance measures. To find out this difference braking patterns of drivers were analyzed just before the intersection to understand the effect of declined cognitive abilities on the effectiveness of driving. Based on the results of the experiments machine learning model was trained to classify drivers in two different classes based on their vehicular and physiological domain driving performance measures. From the experiments performed, I found out that there is some significant difference between MCI and Non-MCI group of drivers in both Physiological domain measures as well as Vehicle domain measures.Master of Science in EngineeringElectrical Engineering, College of Engineering & Computer ScienceUniversity of Michigan-Dearbornhttps://deepblue.lib.umich.edu/bitstream/2027.42/152437/1/Manan Patel Final Thesis.pdfDescription of Manan Patel Final Thesis.pdf : Thesi

Controversial article on geonomastics

This article aims to discuss, firstly, the substantiation of a new discipline within the applied onomastics with a short excursion into the historical domain, its relationship to other sub-disciplines, then its difference from toponymics, and finally to give an example of contemporary works at the intersection of geography, linguistics, onomastics, cartography, map semantics and others

Integer-valued polynomials over matrices and divided differences

Let $D$ be an integrally closed domain with quotient field $K$ and $n$ a positive integer. We give a characterization of the polynomials in $K[X]$ which are integer-valued over the set of matrices $M_n(D)$ in terms of their divided differences. A necessary and sufficient condition on $f\in K[X]$ to be integer-valued over $M_n(D)$ is that, for each $k$ less than $n$, the $k$-th divided difference of $f$ is integral-valued on every subset of the roots of any monic polynomial over $D$ of degree $n$. If in addition the intersection of the maximal ideals of finite index is $(0)$ then it is sufficient to check the above conditions on subsets of the roots of monic irreducible polynomials of degree $n$, that is, conjugate integral elements of degree $n$ over $D$.Comment: minor changes, notation made uniform throughout the paper. Fixed a wrong assumption we used in (4), (5) and Thm 4.1: "$D$ has zero Jacobson radical" has to be replaced with "the intersection of the maximal ideals of finite index is $(0)$". Keywords: Integer-valued polynomial, Divided differences, Matrix, Integral element, Polynomial closure, Pullback. In Monatshefte f\"ur Mathematik, 201

Identity complexity and integration in lesbian, gay, bisexual and heterosexual adolescents and emerging adults: Implications for clinical practice

The present study aimed at assessing whether differences exist in identity complexity and integration between 31 lesbian, gay, and bisexual (LGB) and 33 heterosexual youths (mean age 21.47, SD = 3.27), both Italian and US. Participants completed a newly created questionnaire, the Identity Labels and Life Contexts Questionnaire (ILLCQ), which assesses the interplay between identity dimensions and life contexts. The ILLCQ assesses identity integration on three levels: (a) integration among the different domains of identity in their intersection with the various life contexts (assessed through salience and centrality); (b) integration between an individual’s self-definition and the definition of self made by others (perceived self-recognition); and (c) the integration between how the person perceives her/himself to be and the way she/he shows her/himself to others. Results suggest that identity salience varies significantly across life contexts for both LGB and heterosexual youths. The only significant difference between the LGB and heterosexual groups was higher salience and centrality of the sexual orientation domain for LGB youths. Sexuality represents a core identity domain for LGB participants, and perhaps less so for heterosexual participants. LGB youths reported lower general identity recognition from other people. Implications for clinical practice are discussed