Existence and uniqueness of limit cycles in a class of second order ODE's with inseparable mixed terms

We prove a uniqueness result for limit cycles of the second order ODE $\ddot x + \dot x \phi(x,\dot x) + g(x) = 0$. Under mild additional conditions, we show that such a limit cycle attracts every non-constant solution. As a special case, we prove limit cycle's uniqueness for an ODE studied in \cite{ETA} as a model of pedestrians' walk. This paper is an extension to equations with a non-linear $g(x)$ of the results presented in \cite{S}

On Compound Poisson Processes Arising in Change-Point Type Statistical Models as Limiting Likelihood Ratios

Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In a previous paper of one of the authors it was established that one of these likelihood ratios, which is an exponential functional of a two-sided Poisson process driven by some parameter, can be approximated (for sufficiently small values of the parameter) by another one, which is an exponential functional of a two-sided Brownian motion. In this paper we consider yet another likelihood ratio, which is the exponent of a two-sided compound Poisson process driven by some parameter. We establish, that similarly to the Poisson type one, the compound Poisson type likelihood ratio can be approximated by the Brownian type one for sufficiently small values of the parameter. We equally discuss the asymptotics for large values of the parameter and illustrate the results by numerical simulations

The bifurcation phenomena in the resistive state of the narrow superconducting channels

We have investigated the properties of the resistive state of the narrow superconducting channel of the length L/\xi=10.88 on the basis of the time-dependent Ginzburg-Landau model. We have demonstrated that the bifurcation points of the time-dependent Ginzburg-Landau equations cause a number of singularities of the current-voltage characteristic of the channel. We have analytically estimated the averaged voltage and the period of the oscillating solution for the relatively small currents. We have also found the range of currents where the system possesses the chaotic behavior

Ewens measures on compact groups and hypergeometric kernels

On unitary compact groups the decomposition of a generic element into product of reflections induces a decomposition of the characteristic polynomial into a product of factors. When the group is equipped with the Haar probability measure, these factors become independent random variables with explicit distributions. Beyond the known results on the orthogonal and unitary groups (O(n) and U(n)), we treat the symplectic case. In U(n), this induces a family of probability changes analogous to the biassing in the Ewens sampling formula known for the symmetric group. Then we study the spectral properties of these measures, connected to the pure Fisher-Hartvig symbol on the unit circle. The associated orthogonal polynomials give rise, as $n$ tends to infinity to a limit kernel at the singularity.Comment: New version of the previous paper "Hua-Pickrell measures on general compact groups". The article has been completely re-written (the presentation has changed and some proofs have been simplified). New references added

Effects of NCMS Coverage on Access to Care and Financial Protection in China

The introduction of the New Cooperative Medical Scheme in rural China is one of the largest health care reforms in the developing world since the millennium. The literature to date has mainly used the uneven rollout of NCMS across counties as a way of identifying its effects on access to care and financial protection. This study exploits the cross-county variation in NCMS generosity in 2006 and 2008 in Ningxia and Shandong province and adopts an instrumenting approach to estimate the effect of a continuous measure of coverage level. Our results confirm earlier findings of NCMS being effective in increasing access to care, but not increasing financial protection. In addition, we find that NCMS enrollees are sensitive to the incentives set in the NCMS design when choosing their provider, but also that providers seem to respond by increasing prices and/or providing more expensive care

Electric Field Control of Spin Transport

Spintronics is an approach to electronics in which the spin of the electrons is exploited to control the electric resistance R of devices. One basic building block is the spin-valve, which is formed if two ferromagnetic electrodes are separated by a thin tunneling barrier. In such devices, R depends on the orientation of the magnetisation of the electrodes. It is usually larger in the antiparallel than in the parallel configuration. The relative difference of R, the so-called magneto-resistance (MR), is then positive. Common devices, such as the giant magneto-resistance sensor used in reading heads of hard disks, are based on this phenomenon. The MR may become anomalous (negative), if the transmission probability of electrons through the device is spin or energy dependent. This offers a route to the realisation of gate-tunable MR devices, because transmission probabilities can readily be tuned in many devices with an electrical gate signal. Such devices have, however, been elusive so far. We report here on a pronounced gate-field controlled MR in devices made from carbon nanotubes with ferromagnetic contacts. Both the amplitude and the sign of the MR are tunable with the gate voltage in a predictable manner. We emphasise that this spin-field effect is not restricted to carbon nanotubes but constitutes a generic effect which can in principle be exploited in all resonant tunneling devices.Comment: 22 pages, 5 figure

Allowed and forbidden transitions in artificial hydrogen and helium atoms

The strength of radiative transitions in atoms is governed by selection rules. Spectroscopic studies of allowed transitions in hydrogen and helium provided crucial evidence for the Bohr's model of an atom. Forbidden transitions, which are actually allowed by higher-order processes or other mechanisms, indicate how well the quantum numbers describe the system. We apply these tests to the quantum states in semiconductor quantum dots (QDs), which are regarded as artificial atoms. Electrons in a QD occupy quantized states in the same manner as electrons in real atoms. However, unlike real atoms, the confinement potential of the QD is anisotropic, and the electrons can easily couple with phonons of the material. Understanding the selection rules for such QDs is an important issue for the manipulation of quantum states. Here we investigate allowed and forbidden transitions for phonon emission in one- and two-electron QDs (artificial hydrogen and helium atoms) by electrical pump-and-probe experiments, and find that the total spin is an excellent quantum number in artificial atoms. This is attractive for potential applications to spin based information storage.Comment: slightly longer version of Nature 419, 278 (2002

Community Gardens: Giving Hope to Southeast Asian Refugees

Since 1975, over 1.3 million Southeast Asian refugees have resettled in the United States from the Southeast Asian nations of Cambodia, Laos, and Vietnam (Office of Refugee Resettlement, 2014). Many Southeast Asian refugees fled their home countries after the Vietnam War to avoid political persecution. As a result of forced migration, Southeast Asian refugees experience high levels of psychological distress attributed to premigration trauma and postmigration. Stressors may include adjusting to a new culture, finding housing, establishing employment, financial hardship, learning a new language and the feeling of identity loss of their homeland. In considering these stressors, this study sought to understand how a lack of access to affordable healthy food may be impacting Southeast Asian refugees’ social, mental, and physical health. Using basic qualitative research, nine structured participant interviews were conducted. Findings suggest one way to alleviate some stress for refugees was to increase access to culturally congruent food. Additionally, increasing economic opportunities and transportation services were identified as critical to improving access to healthy food options. The theoretical framework that guided this study was resilience theory. This framework brought to light the hardship and stress experienced by refugees. I then used it to outline ways that community gardens may build individual resilience to overcome personal hardships through social support structures. The findings highlight the importance of resettling refugees in communities close to families to build individual resilience and the need for refugee resettlement practitioners to continue to offer resettlement support beyond initial arrival to the United States and until economic self-sufficiency is achieved. Additionally, four central themes emerged from individual stories of each participant’s perceptions of how food access impacts their social, mental, and physical health. The four themes were: (1) postmigration traumas create hardships among Hmong refugees, (2) poverty and physical and mental health disabilities impact food access, (3) food cultivation is deeply rooted in the Hmong culture, and (4) gardens build social communities and give hope. The study also uncovered two unexpected findings. The first was the strong cultural belief in natural healing using herbal medicine known as “tshuaj ntsuab Hmoob” or Hmong green medicine, and, secondly, the prevalent cultivation of Hmong herbal medicine plants in the gardens. For practitioners developing housing for resettled refugees, creating green space for refugees to cultivate their traditional green medicine is vital to Hmong refugees’ identity and culture. One way to provide such access would be to incorporate green space into resettlement housing arrangements so refugees may cultivate fruits and vegetables native to their home countries. Creating green spaces for refugees may help to preserve their rich culture and empower refugee communities to practice their cultural beliefs and traditions. Lastly, I conclude the study with a proposal for development of a nonprofit community garden called Garden of Hope. My vision for the Garden of Hope is to address findings of this study through program services, which may increase access to culturally congruent food and promote individual resilience through entrepreneurship. The goal is to teach refugees how to grow and market their organic fruits and vegetables to local restaurants and or sell them at local community farmers markets. Addressing postmigration stressors for Southeast Asian refugees through the Garden of Hope may improve individual economic mobility and uplift improvised communities through entrepreneurship

Limit theorems for von Mises statistics of a measure preserving transformation

For a measure preserving transformation $T$ of a probability space $(X,\mathcal F,\mu)$ we investigate almost sure and distributional convergence of random variables of the form $$x \to \frac{1}{C_n} \sum_{i_1<n,...,i_d<n} f(T^{i_1}x,...,T^{i_d}x),\, n=1,2,...,$$ where $f$ (called the \emph{kernel}) is a function from $X^d$ to $\R$ and $C_1, C_2,...$ are appropriate normalizing constants. We observe that the above random variables are well defined and belong to $L_r(\mu)$ provided that the kernel is chosen from the projective tensor product $$L_p(X_1,\mathcal F_1, \mu_1) \otimes_{\pi}...\otimes_{\pi} L_p(X_d,\mathcal F_d, \mu_d)\subset L_p(\mu^d)$$ with $p=d\,r,\, r\ \in [1, \infty).$ We establish a form of the individual ergodic theorem for such sequences. Next, we give a martingale approximation argument to derive a central limit theorem in the non-degenerate case (in the sense of the classical Hoeffding's decomposition). Furthermore, for $d=2$ and a wide class of canonical kernels $f$ we also show that the convergence holds in distribution towards a quadratic form $\sum_{m=1}^{\infty} \lambda_m\eta^2_m$ in independent standard Gaussian variables $\eta_1, \eta_2,...$. Our results on the distributional convergence use a $T$--\,invariant filtration as a prerequisite and are derived from uni- and multivariate martingale approximations