Long-range interactions play a key role in several phenomena of quantum physics and chemistry. To study these phenomena, analog simulators provide an appealing alternative to classical numerical methods. Gate-defined dots have been established as platform for simulation, but those experiments the effect long-range between electrons did not crucial role. Here we present first detailed experiment...

to enhance the closed loop performance in presence of disturbance, uncertainties and delay a double loop mixture of mpc and robust controller is proposed. this double loop controller ensures smooth tracking for a 3-axis gyro-stabilized platform which has delay intrinsically. this control idea is suggested to eliminate high frequency disturbances and minimize steady state error with minimum powe...

Abstract Houghton’s groups $$H_2, H_3, \ldots $$ H 2 , 3 … are certain infinite permutation acting on a countably set; they have been studied, among other things, for their finiteness properties. ...

Let $$(T^k,h_k)=(S_{r_1}^1\times S_{r_2}^1 \times \cdots S_{r_k}^1, dt_1^2+dt_2^2+\cdots +dt_k^2)$$ be flat tori, $$r_k\ge \ge r_2\ge r_1>0$$ and $$({\mathbb {R}}^n,g_E)$$ the Euclidean space with metric. We compute isoperimetric profile of $$(T^2\times {\mathbb {R}}^n, h_2+g_E)$$ , $$2\le n\le 5$$ for small big values volume. These computations give explicit lower bounds $$T^2\times {R}}^...

We work in the smooth category. Let $N$ be a closed connected orientable 4-manifold with torsion free $H_1$, where $H_q:=H_q(N;Z)$. Our main result is complete readily calculable classification of embeddings $N\to R^7$, up to equivalence relation generated by isotopy and embedded sum $S^4\to R^7$. Such was already known only for $H_1=0$ Boechat, Haefliger Hudson from 1970. involves Boechat-Haef...

We obtain a complete description of local anisotropic scaling limits for class fractional random fields $X$ on ${\mathbb{R}}^2$ written as stochastic integral with respect to infinitely divisible measure. The procedure involves increments over points the distance between which in horizontal and vertical directions shrinks $O(\lambda)$ $O(\lambda^\gamma)$ respectively $\lambda \downarrow 0$, som...