We study the properties of energy flux in wave turbulence via Majda-McLaughlin-Tabak (MMT) equation with a quadratic dispersion relation. One our purposes is to resolve inter-scale $P$ stationary state elucidate its distribution and scaling spectral level. More importantly, we perform quartet-level decomposition $P=\sum_\Omega P_\Omega$, each component $P_\Omega$ representing contribution from ...

Let X be a complex projective manifold and let $$D\subset X$$ smooth divisor. In this article, we are interested in studying limits when $$\beta \rightarrow 0$$ of Kähler–Einstein metrics $$\omega _\beta $$ with cone singularity angle $$2\pi \beta along D. our first result, assume that $$X\setminus D$$ is locally symmetric space show converges to the metric further give asymptotics ball quotien...

We study the spectral stability of nonlinear Dirac operator in dimension $$1+1$$ , restricting our attention to nonlinearities form $$f(\left\langle \psi ,\beta \right\rangle _{\mathbb {C}^2}) \beta $$ . obtain bounds on eigenvalues for linearized around standing wave solutions $$e^{-i\omega t} \phi _0$$ For case power $$f(s)= s |s|^{p-1}$$ $$p>0$$ we a range frequencies $$\omega such that has ...

We present an efficient basis for imaginary time Green's functions based on a low-rank decomposition of the spectral Lehmann representation. The are simply set well-chosen exponentials, so corresponding expansion may be thought as discrete form representation using effective density which is sum $\ensuremath{\delta}$ functions. determined only by upper bound product $\ensuremath{\beta}{\ensurem...

Using Langevin dynamics simulations, we study the hysteresis in unzipping of longer double stranded DNA chains whose ends are subjected to a time dependent periodic force with frequency $\omega$ and amplitude $G$ keeping other end fixed. We find that area loop, $A_{loop}$, scales as $1/\omega$ at higher frequencies, whereas it $(G-G_c)^{\alpha}\omega^{\beta}$ exponents $\alpha=1$ $\beta=1.25$ l...

In this paper, we study the following k-coupled nonlinear Schrödinger system with Sobolev critical exponent: $$\begin{aligned} \left\{ \begin{aligned} -\Delta u_i&+\lambda _iu_i =\mu _i u_i^{2^*-1}+\sum _{j=1,j\ne i}^{k} \beta _{ij} u_{i}^{\frac{2^*}{2}-1}u_{j}^{\frac{2^*}{2}} \quad \hbox {in}\;\Omega ,\\ u_i&>0 {in}\; \Omega {and}\quad u_i=0 {on}\;\partial , i=1,2,\dots k. \end{aligned} \right...

We consider the boundary value problem $$\displaylines{ - \Delta u + c(x) = \alpha m(x) u^+ \beta u^- +f(x,u), \quad x \in \Omega, \cr \frac{\partial u}{\partial \eta} \sigma (x) =\alpha \rho u^+- +g(x,u), \partial }$$ where \((\alpha, \beta) \mathbb{R}^2\), \(c, m L^\infty (\Omega)\), \(\sigma, (\partial\Omega)\), and nonlinearities f g are bounded continuous functions. study asymmetric (Fucik...

Omega-3 fatty acid (omega-3 FA) consumption has long been associated with a lower incidence of colon, breast and prostate cancers in many human populations. Human trials have demonstrated omega-3 FA to have profound anti-inflammatory effects in those with cancer. In vitro and small animal studies have yielded a strong body of evidence establishing omega-3 FA as having anti-inflammatory, anti-ap...