Multiple solutions to a magnetic nonlinear Choquard equation

We consider the stationary nonlinear magnetic Choquard equation [(-\mathrm{i}\nabla+A(x))^{2}u+V(x)u=(\frac{1}{|x|^{\alpha}}\ast |u|^{p}) |u|^{p-2}u,\quad x\in\mathbb{R}^{N}%] where $A\$is a real valued vector potential, $V$ is a real valued scalar potential$,$ $N\geq3$, $\alpha\in(0,N)$ and $2-(\alpha/N) <p<(2N-\alpha)/(N-2)$. \ We assume that both $A$ and $V$ are compatible with the action of some group $G$ of linear isometries of $\mathbb{R}^{N}$. We establish the existence of multiple complex valued solutions to this equation which satisfy the symmetry condition $$u(gx)=\tau(g)u(x)\text{\ \ \ for all}g\in G,\text{}x\in\mathbb{R}^{N},$$ where $\tau:G\rightarrow\mathbb{S}^{1}$ is a given group homomorphism into the unit complex numbers.Comment: To appear on ZAM

Dvoretzky type theorems for multivariate polynomials and sections of convex bodies

In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on $\mathbb R^n$, and improve bounds on the number $n(d,k)$ in the analogous conjecture for odd degrees $d$ (this case is known as the Birch theorem) and complex polynomials. We also consider a stronger conjecture on the homogeneous polynomial fields in the canonical bundle over real and complex Grassmannians. This conjecture is much stronger and false in general, but it is proved in the cases of $d=2$ (for $k$'s of certain type), odd $d$, and the complex Grassmannian (for odd and even $d$ and any $k$). Corollaries for the John ellipsoid of projections or sections of a convex body are deduced from the case $d=2$ of the polynomial field conjecture

Centerscope

Centerscope, formerly Scope, was published by the Boston University Medical Center "to communicate the concern of the Medical Center for the development and maintenance of improved health care in contemporary society.

Determination of Inflationary Observables by Cosmic Microwave Background Anisotropy Experiments

Inflation produces nearly Harrison-Zel'dovich scalar and tensor perturbation spectra which lead to anisotropy in the cosmic microwave background (CMB). The amplitudes and shapes of these spectra can be parametrized by $Q_S^2$, $r\equiv Q_T^2/Q_S^2$, $n_S$ and $n_T$ where $Q_S^2$ and $Q_T^2$ are the scalar and tensor contributions to the square of the CMB quadrupole and $n_S$ and $n_T$ are the power-lawspectral indices. Even if we restrict ourselves to information from angles greater than one third of a degree, three of these observables can be measured with some precision. The combination $130^{1-n_S}Q_S^2$ can be known to better than $\pm 0.3\%$. The scalar index $n_S$ can be determined to better than $\pm 0.02$. The ratio $r$ can be known to about $\pm 0.1$ for $n_S \simeq 1$ and slightly better for smaller $n_S$. The precision with which $n_T$ can be measured depends weakly on $n_S$ and strongly on $r$. For $n_S \simeq 1$ $n_T$ can be determined with a precision of about $\pm 0.056(1.5+r)/r$. A full-sky experiment with a $20'$beam using technology available today, similar to those being planned by several groups, can achieve the above precision. Good angular resolution is more important than high signal-to-noise ratio; for a given detector sensitivity and observing time a smaller beam provides significantly more information than a larger beam. The uncertainties in $n_S$ and $r$ are roughly proportional to the beam size. We briefly discuss the effects of uncertainty in the Hubble constant, baryon density, cosmological constant and ionization history.Comment: 28 pages of uuencoded postscript with 8 included figures. A postscript version is also available by anonymous ftp at ftp://astro.uchicago.edu/pub/astro/knox/fullsim.p

Hysteresis and hierarchies: dynamics of disorder-driven first-order phase transformations

We use the zero-temperature random-field Ising model to study hysteretic behavior at first-order phase transitions. Sweeping the external field through zero, the model exhibits hysteresis, the return-point memory effect, and avalanche fluctuations. There is a critical value of disorder at which a jump in the magnetization (corresponding to an infinite avalanche) first occurs. We study the universal behavior at this critical point using mean-field theory, and also present preliminary results of numerical simulations in three dimensions.Comment: 12 pages plus 2 appended figures, plain TeX, CU-MSC-747

From an experimental paper to a playful screen : How the essence of materiality modulates the process of creation

The article seeks to develop a better understanding of the contribution of materiality in a discourse between a creator (content producer) and an interface, dealing with analogue and digital artefacts. Focus is in the materiality of the two different art-creation learning processes, acrylic painting and digital painting. The objective of this paper is to consider especially the affect and meaning of these two different content creation modalities and intra-action within that. Through reflective autoethnographic consideration, the purpose is to consider the essences of materials manifesting and modulating the processes of content creation as a posthumanist phenomenon. It will be shown that the creation processes with paper are more experimental whereas the processes with digital screen are more playful. There is a growing need to deeper understand the cultural change of material cultures and the people's intra-action with the materials also enabling arts creation. This paper will widen our limited understanding and deepen our theoretical perspectives of the essence of materials which then avails confronting analogue and digital when developing teaching and learning in the posthuman era especially in early education. Practitioner Notes What is already known about this topic There is a growing interest in the new materialism and posthuman thinking amongst educational technology research and development. Reading analogue versus digital is well-documented. What this paper adds New materialist thinking offers a useful perspective in education for looking at the essence of analogue and digital materiality modulating content creation. Characterising the nuances in analogue and digital production can help in evaluating their educational potential. Implications for practice and/or policy As practitioners we should critically question the political vision of education digitalisation especially concerning early childhood education. There is a need to move beyond debates about analogue versus digital to look at more specific examples of their advantages (and disadvantages) in developing posthumanist education and intra-active pedagogy especially for young children.Peer reviewe

Hysteresis, Avalanches, and Disorder Induced Critical Scaling: A Renormalization Group Approach

We study the zero temperature random field Ising model as a model for noise and avalanches in hysteretic systems. Tuning the amount of disorder in the system, we find an ordinary critical point with avalanches on all length scales. Using a mapping to the pure Ising model, we Borel sum the $6-\epsilon$ expansion to $O(\epsilon^5)$ for the correlation length exponent. We sketch a new method for directly calculating avalanche exponents, which we perform to $O(\epsilon)$. Numerical exponents in 3, 4, and 5 dimensions are in good agreement with the analytical predictions.Comment: 134 pages in REVTEX, plus 21 figures. The first two figures can be obtained from the references quoted in their respective figure captions, the remaining 19 figures are supplied separately in uuencoded forma