An existence result for a nonlinear transmission problems

Let $\Omega^o$ and $\Omega^i$ be open bounded subsets of $\mathbb{R}^n$ of class $C^{1,\alpha}$ such that the closure of $\Omega^i$ is contained in $\Omega^o$. Let $f^o$ be a function in $C^{1,\alpha}(\partial\Omega^o)$ and let $F$ and $G$ be continuous functions from $\partial\Omega^i\times\mathbb{R}$ to $\mathbb{R}$. By exploiting an argument based on potential theory and on the Leray-Schauder principle we show that under suitable and completely explicit conditions on $F$ and $G$ there exists at least one pair of continuous functions $(u^o, u^i)$ such that $$\left\{ \begin{array}{ll} \Delta u^o=0&\text{in }\Omega^o\setminus\mathrm{cl}\Omega^i\,,\\ \Delta u^i=0&\text{in }\Omega^i\,,\\ u^o(x)=f^o(x)&\text{for all }x\in\partial\Omega^o\,,\\ u^o(x)=F(x,u^i(x))&\text{for all }x\in\partial\Omega^i\,,\\ \nu_{\Omega^i}\cdot\nabla u^o(x)-\nu_{\Omega^i}\cdot\nabla u^i(x)=G(x,u^i(x))&\text{for all }x\in\partial\Omega^i\,, \end{array} \right.$$ where the last equality is attained in certain weak sense. In a simple example we show that such a pair of functions $(u^o, u^i)$ is in general neither unique nor local unique. If instead the fourth condition of the problem is obtained by a small nonlinear perturbation of a homogeneous linear condition, then we can prove the existence of at least one classical solution which is in addition locally unique

Positively charged magneto-excitons in a semiconductor quantum well

A variational calculation of the lower singlet and triplet states of positively charged excitons (trions) confined to a single quantum well and in the presence of a perpendicular magnetic field is presented. We study the dependence of the energy levels and of the binding energy on the well width and on the magnetic field strength. Our results are compared with the available experimental data and show a good qualitative and quantitative agreement. A singlet-triplet crossing is found which for a 200 \AA wide GaAs is predicted to occur for B = 15 T.Comment: 5 figs. Submitted to PR

Heteropolymers in a Solvent at an Interface

Exact bounds are obtained for the quenched free energy of a polymer with random hydrophobicities in the presence of an interface separating a polar from a non polar solvent. The polymer may be ideal or have steric self-interactions. The bounds allow to prove that a ``neutral'' random polymer is localized near the interface at any temperature, whereas a ``non-neutral'' chain is shown to undergo a delocalization transition at a finite temperature. These results are valid for a quite general a priori probability distribution for both independent and correlated hydrophobic charges. As a particular case we consider random AB-copolymers and confirm recent numerical studies.Comment: 4 pages, no figure

Higgs Couplings in Composite Models

We study Higgs couplings in the composite Higgs model based on the coset SO(5)/SO(4). We show that the couplings to gluons and photons are insensitive to the elementary-composite mixings and thus not affected by light fermionic resonances. Moreover, at leading order in the mixings the Higgs couplings to tops and gluons, when normalized to the Standard Model (SM), are equal. These properties are shown to be direct consequences of the Goldstone symmetry and of the assumption of partial compositeness. In particular, they are independent of the details of the elementary-composite couplings and, under the further assumption of CP invariance, they are also insensitive to derivative interactions of the Higgs with the composite resonances. We support our conclusions with an explicit construction where the SM fermions are embedded in the 14 dimensional representation of SO(5).Comment: 13 pages, 3 figures, 2 tables; v2: small improvements in the discussion, results unchanged; typos corrected; one reference added. Matches version submitted to PR

THE IMPACT OF THE NEW ITALIAN EARLY WARNING SYSTEM PROVIDED BY THE IC-CODE ON FAMILY SMES GOVERNANCE

The Early Warning System is intended as an instrument aimed at driving the companies in the identification of the very first signs of crisis. Monitoring the occurring of the crisis is no longer a responsibility of the sole entrepreneur or of the board of directors but other legitimized subjects are identified. The IC-Code sets up new corporate governance rules for a huge number of Italian Family SMEs pretending the introduction of independent control bodies, Board of Statutory Auditors, and/or External Auditor. Some of the suggestions coming from the family business framework seems then to be enforced by law in the Italian context

The Social Appearance Anxiety Scale in Italian adolescent populations: Construct validation and group discrimination in community and clinical eating disorders samples

Anxiety in situations where one’s overall appearance (including body shape) may be negatively evaluated is hypothesized to play a central role in Eating Disorders (EDs) and in their co-occurrence with Social Anxiety Disorder (SAD). Three studies were conducted among community (N = 1995) and clinical (N = 703) ED samples of 11- to 18-year-old Italian girls and boys to (a) evaluate the psychometric qualities and measurement equivalence/invariance (ME/I) of the Social Appearance Anxiety (SAA) Scale (SAAS) and (b) determine to what extent SAA or other situational domains of social anxiety related to EDs distinguish adolescents with an ED only from those with SAD. Results upheld the one-factor structure and ME/I of the SAAS across samples, gender, age categories, and diagnostic status (i.e., ED participants with and without comorbid SAD). The SAAS demonstrated high internal consistency and 3-week test–retest reliability. The strength of the inter-relationships between SAAS and measures of body image, teasing about appearance, ED symptoms, depression, social anxiety, avoidance, and distress, as well as the ability of SAAS to discriminate community adolescents with high and low levels of ED symptoms and community participants from ED participants provided construct validity evidence. Only SAA strongly differentiated adolescents with any ED from those with comorbid SAD (23.2 %). Latent mean comparisons across all study groups were performed and discussed

Parasocial Romantic Relationships, Romantic Beliefs, and Relationship Outcomes in USA Adolescents: Rehearsing Love or Setting Oneself Up to Fail?

The study examines the associations between adolescents’ emotional and physical aspects of parasocial romantic relationships with media figures, idealized romantic beliefs, perceptions of a current dating partner, and relationship satisfaction. A two-study design included concurrent data from 153 adolescents ages 13–17 (55.6% female), and retrospective data from 274 college students ages 18–22 (79.8% female). Across both samples, emotional involvement in a PSRR was related to more idealized romantic beliefs. The intensity of emotional involvement with the media figure during adolescence was associated with lower relationship satisfaction and less favorable perceptions of a current romantic partner in college students. However, there were no significant associations between physical attraction to the media figure and relationship outcomes