This upper bound relies on the AND-weakness conjecture saying that each CC0 circuit for the n-input AND function has at least \(2^{n^{\delta }}\) gates. Thus, the AND-weakness conjecture implies that the lower bounds in Theorem 1 cannot be improved in an essential way. Finally, we ...
J. Korsch. The nonlinear Schr¨odinger equation for the delta- comb potential: quasi-classical chaos and bifurcations of periodic stationary solutions. JNMP, 16:207, 2008.D. Witthaut, K. Rapedius, and H. J. Korsch. The nonlinear Schroedinger equation for the delta-comb potential: quasi-...
Realistic models of quantum systems must include dissipative interactions with a thermal environment. For weakly-damped systems, while the Lindblad-form Markovian master equation is invaluable for this task, it applies only when the frequencies of any su
The Cauchy problem for the equation \\displaystyle \\frac{\\partial u(t,\\,x)}{\\partial t}=-i\\Delta u+f(u), \\quad f(u)=\\sum_{k=2}^\\infty f_k u^k,is investigated. The solution is sought in the class of functions u(t,\\,x) which belon... Višik, M. I,AV...
In this article we will give a characterization of solutions for the equation \\\( \\\frac{{{\\\partial ^2}}}{{\\\partial {t^2}}}u + {\\\Delta _z}u - 2x\\\cdot{abla _x}u = 0 \\\) which are Poisson-Hermite integral of L p (γ n )-functions, \\\( 1 \\\leqslan...
GLOBAL EXISTENCE AND BLOW-UP FOR A NON-NEWTON POLYTROPIC FILTRATION SYSTEM WITH NONLOCAL SOURCE This paper deals the global existence and blow-up properties of the following non-Newton polytropic filtration system with nonlocal source, \\[ u_t-\\Delta... J Zhou,MU Chunlai - 《Anziam Journal...
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A closed form solution for the one-dimensional Schrdinger equation with a finite number of δ \delta -interactions L q , I N y : = y ′′ + ( q ( x ) + ∑ k = 1 N α k δ ( x x k ) ) y = λ y , 0 < x < b , λ∈ C \mathbf{L}_{q,\mathfrak{I}_{N}}y...
Stability and Control of a Confined 1D Quantum System with Time-Dependent Delta Potentials. J. Phys. A Math. Theor. 2011, 44, 145305. [Google Scholar] [CrossRef] Posilicano, A. The Schrödinger Equation with a Moving Point Interaction in Three Dimensions. Proc. Am. Math. Soc. 2007, ...
" monitor = 'loss', patience = 100, min_delta = 1e-4,\n", " verbose = 1, mode = 'min')\n", "\n", "early_stop.set_model(model)\n", "early_stop.on_train_begin()\n", "# Training loop\n", "epochs = 7000\n", "for epoch in range(epochs):\n", " loss = train_st...