From the Farkas Lemma to the Hahn–Banach Theorem

This paper provides new versions of the Farkas lemma characterizing those inequalities of the form f(x) ≥ 0 which are consequences of a composite convex inequality (S ◦ g)(x) ≤ 0 on a closed convex subset of a given locally convex topological vector space X, where f is a proper lower semicontinuous convex function defined on X, S is an extended sublinear function, and g is a vector-valued S-convex function. In parallel, associated versions of a stable Farkas lemma, considering arbitrary linear perturbations of f, are also given. These new versions of the Farkas lemma, and their corresponding stable forms, are established under the weakest constraint qualification conditions (the so-called closedness conditions), and they are actually equivalent to each other, as well as equivalent to an extended version of the so-called Hahn–Banach–Lagrange theorem, and its stable version, correspondingly. It is shown that any of them implies analytic and algebraic versions of the Hahn–Banach theorem and the Mazur–Orlicz theorem for extended sublinear functions.This research was partially supported by MINECO of Spain, grant MTM2011-29064-C03-02, and by the NAFOSTED of Vietnam

Hausdorff dimension of critical fluctuations in abelian gauge theories

The geometric properties of the critical fluctuations in abelian gauge theories such as the Ginzburg-Landau model are analyzed in zero background field. Using a dual description, we obtain scaling relations between exponents of geometric and thermodynamic nature. In particular we connect the anomalous scaling dimension $\eta$ of the dual matter field to the Hausdorff dimension $D_H$ of the critical fluctuations, {\it which are fractal objects}. The connection between the values of $\eta$ and $D_H$, and the possibility of having a thermodynamic transition in finite background field, is discussed.Comment: Accepted for publication in PR

Vortex Interactions and Thermally Induced Crossover from Type-I to Type-II Superconductivity

We have computed the effective interaction between vortices in the Ginzburg-Landau model from large-scale Monte-Carlo simulations, taking thermal fluctuations of matter fields and gauge fields fully into account close to the critical temperature. We find a change, in the form of a crossover, from attractive to repulsive effective vortex interactions in an intermediate range of Ginzburg-Landau parameters $\kappa \in [0.76-1]/\sqrt{2}$ upon increasing the temperature in the superconducting state. This corresponds to a thermally induced crossover from \typeI to \typeII superconductivity around a temperature $T_{\rm{Cr}}(\kappa)$, which we map out in the vicinity of the metal-to-superconductor transition. In order to see this crossover, it is essential to include amplitude fluctuations of the matter field, in addition to phase-fluctuations and gauge-field fluctuations. We present a simple physical picture of the crossover, and relate it to observations in \metal{Ta} and \metal{Nb} elemental superconductors which have low-temperature values of $\kappa$ in the relevant range.Comment: 9 pages, 6 figures. Accepted for publication in Physical Review

The order of the metal to superconductor transition

We present results from large-scale Monte Carlo simulations on the full Ginzburg-Landau (GL) model, including fluctuations in the amplitude and the phase of the matter-field, as well as fluctuations of the non-compact gauge-field of the theory. {}From this we obtain a precise critical value of the GL parameter \kct separating a first order metal to superconductor transition from a second order one, \kct = (0.76\pm 0.04)/\sqrt{2}. This agrees surprisingly well with earlier analytical results based on a disorder theory of the superconductor to metal transition, where the value \kct=0.798/\sqrt{2} was obtained. To achieve this, we have done careful infinite volume and continuum limit extrapolations. In addition we offer a novel interpretation of \kct, namely that it is also the value separating \typeI and \typeII behaviour.<Comment: Minor corrections, present version accepted for publication in PR

Perceptions of Violence against Women among College Students in the United States, Japan, India, Vietnam and China

Violence against women is a global health issue that threatens the health and human rights of women. Intimate partner violence (IPV) and sexual violence are the most common forms of violence against women. While previous studies examined incidence of IPV and other forms of violence against women in the United States (US), little is known about variations in the perceptions of violence against women among college students in other countries. This study explored differences in perceptions of violence against women among college students in the US, Japan, India, Vietnam and China. A total of 1,136 college students from these countries participated in a self-administered survey in 2012-2013. The students’ perceptions about the prevalence of domestic violence is in their country varied across countries. Furthermore, more than half of the students across the countries perceived alcoholism and drug addiction to be causes of domestic violence against women. It was also found that the levels of knowledge about laws on domestic violence in their country varied among the students. These findings show the importance of understanding country level variations that may affect violence against women. The results of this study provide important insights by documenting cross country variations in students’ perceptions about violence against women that can provide helpful inputs in framing country-specific programs and policies to prevent violence against women. Keywords: Violence against women, perceptions, college students, the United States, Japan, India, Vietnam, Chin

Synthesis of Fine-Tuning Highly Magnetic Fe@FexOy Nanoparticles through Continuous Injection and a Study of Magnetic Hyperthermia

Core@shell Fe@FexOy nanoparticles (NPs) have the potential to be promising tools for many applications, thanks to their combination of an iron core, with a high magnetic moment and an iron oxide shell which could protect the core from oxidation. However, the deterioration of NPs structure can lead to the shrinking of the core and the hollowing of the structure, diminishing the magnetic properties. The ability to retain the iron core under biomedically compatible conditions is desirable for many applications. In this paper, we have developed a synthetic method to produce core@shell α-Fe@FexOy NPs with tunable sizes and evaluated the retention of the stable magnetic α-Fe core upon exposure to air and after ligand exchange and its resulting effect on the magnetic hyperthermia. In particular, using a continuous injection of the precursor, we were able to finely tune the final size of the core@shell NPs producing four samples with average sizes of 12, 15, 18, and 20 nm. The structural properties of the particles were studied, and while the size increases, the chemical stability of the iron core is enhanced, and the magnetic properties improved accordingly. Particles larger than 20 nm were shown to be prone to aggregation, resulting in an abrupt increase of the particle size distribution. Two samples with high magnetization saturation value and low polydispersity, 15 and 18 nm, were transferred in water using a dopamine-functionalized poly(isobutylene-alt-maleic anhydride) polymer, resulting in colloidal stability over a wide range of pH and ionic strength comparable to physiological conditions. We found that the 18 nm particles retain their chemical properties over 2 months, with less oxidation of the Fe core; this results in a specific absorption rate (SAR) value of 660 W g−1 and intrinsic loss power (ILP) of 3.6 nHm2 kg−1 , while the 15 nm NPs resulted in the reduction of their properties due to oxidation of the core

Critical behavior of Ginzburg-Landau model coupled to massless Dirac fermions

We point out interesting effects of additional massless Dirac fermions with N_F colors upon the critical behavior of the Ginzburg-Landau model. For increasing N_F, the model is driven into the type II regime of superconductivity. The critical exponents are given as a function of N_F.Comment: RevTex4, 4 pages, 1 figure; author information and latest update to this paper at http://www.physik.fu-berlin.de/~kleinert/institution.html; version 2: new references and comments on chiral symmetry breaking adde

A time-domain control signal detection technique for OFDM

Transmission of system-critical control information plays a key role in efficient management of limited wireless network resources and successful reception of payload data information. This paper uses an orthogonal frequency division multiplexing (OFDM) architecture to investigate the detection performance of a time-domain approach used to detect deterministic control signalling information. It considers a type of control information chosen from a finite set of information, which is known at both transmitting and receiving wireless terminals. Unlike the maximum likelihood (ML) estimation method, which is often used, the time-domain detection technique requires no channel estimation and no pilots as it uses a form of time-domain correlation as the means of detection. Results show that when compared with the ML method, the time-domain approach improves detection performance even in the presence of synchronisation error caused by carrier frequency offset

Effect Of Leaf Surface Chemical Properties On Efficacy Of Sanitizer For Rotavirus Inactivation

The use of sanitizers is essential for produce safety. However, little is known about how sanitizer efficacy varies with respect to the chemical surface properties of produce. To answer this question, the disinfection efficacies of an oxidant-based sanitizer and a new surfactant-based sanitizer for porcine rotavirus (PRV) strain OSU were examined. PRV was attached to the leaf surfaces of two kale cultivars with high epicuticular wax contents and one cultivar of endive with a low epicuticular wax content and then treated with each sanitizer. The efficacy of the oxidant-based sanitizer correlated with leaf wax content as evidenced by the 1-log10 PRV disinfection on endive surfaces (low wax content) and 3-log10 disinfection of the cultivars with higher wax contents. In contrast, the surfactant-based sanitizer showed similar PRV disinfection efficacies (up to 3 log10) that were independent of leaf wax content. A statistical difference was observed with the disinfection efficacies of the oxidant-based sanitizer for suspended and attached PRV, while the surfactant-based sanitizer showed similar PRV disinfection efficacies. Significant reductions in the entry and replication of PRV were observed after treatment with either disinfectant. Moreover, the oxidant-based-sanitizer-treated PRV showed sialic acid-specific binding to the host cells, whereas the surfactant-based sanitizer increased the nonspecific binding of PRV to the host cells. These findings suggest that the surface properties of fresh produce may affect the efficacy of virus disinfection, implying that food sanitizers should be carefully selected for the different surface characteristics of fresh produce