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Yu Fu

Publications and source records attributed to Yu Fu.

133 records · Page 8Linked to original sources
arXiv2015

Magnetic phase transitions in Ta/CoFeB/MgO multilayers

We study thin films and magnetic tunnel junction nanopillars based on Ta/Co$_{20}$Fe$_{60}$B$_{20}$/MgO multilayers by electrical transport and magnetometry measurements. These measurements suggest that an ultrathin magnetic oxide layer forms at the Co$_{20}$Fe$_{60}$B$_{20}$/MgO interface. At approximately 160 K, the oxide undergoes a phase transition from an insulating antiferromagnet at low temperatures to a conductive weak ferromagnet at high temperatures. This interfacial magnetic oxide is expected to have significant impact on the magnetic properties of CoFeB-based multilayers used in spin torque memories.

cond-mat.mtrl-sci↗
arXiv2014

On biharmonic hypersurfaces with constant scalar curvatures in $\mathbb E^5(c)$

We prove that proper biharmonic hypersurfaces with constant scalar curvature in Euclidean sphere $\mathbb S^5$ must have constant mean curvature. Moreover, we also show that there exist no proper biharmonic hypersurfaces with constant scalar curvature in Euclidean space $\mathbb E^5$ or hyperbolic space $\mathbb H^5$, which give affirmative partial answers to Chen's conjecture and Generalized Chen's conjecture.

math.DG↗
arXiv2014

$δ$(3)-ideal null 2-type hypersurfaces in Euclidean spaces

In the theory of finite type submanifolds, null 2-type submanifolds are the most simple ones, besides 1-type submanifolds (cf. e.g., [3, 12]). In particular, the classification problems of null 2-type hypersurfaces are quite interesting and of fundamentally important. In this paper, we prove that every $δ$(3)-ideal null 2-type hypersurface in a Euclidean space has constant mean curvature and constant scalar curvature.

math.DG↗
arXiv2014

Biharmonic hypersurfaces with three distinct principal curvatures in spheres

We obtain a complete classification of proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces with arbitrary dimension. Precisely, together with known results of Balmuş-Montaldo-Oniciuc, we prove that compact orientable proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces $\mathbb S^{n+1}$ are either the hypersphere $\mathbb S^n(1/\sqrt2)$ or the Clifford hypersurface $\mathbb S^{n_1}(1/\sqrt2)\times\mathbb S^{n_2}(1/\sqrt2)$ with $n_1+n_2=n$ and $n_1\neq n_2$. Moreover, we also show that there does not exist proper biharmonic hypersurface with at most three distinct principal curvatures in hyperbolic spaces $\mathbb H^{n+1}$.

math.DG↗
arXiv2014

Biharmonic hypersurfaces with three distinct principal curvatures in Euclidean space

The well known Chen's conjecture on biharmonic submanifolds states that a biharmonic submanifold in a Euclidean space is a minimal one ([10-13, 16, 18-21, 8]). For the case of hypersurfaces, we know that Chen's conjecture is true for biharmonic surfaces in $\mathbb E^3$ ([10], [24]), biharmonic hypersurfaces in $\mathbb E^4$ ([23]), and biharmonic hypersurfaces in $\mathbb E^m$ with at most two distinct principal curvatures ([21]). The most recent work of Chen-Munteanu [18] shows that Chen's conjecture is true for $δ(2)$-ideal hypersurfaces in $\mathbb E^m$, where a $δ(2)$-ideal hypersurface is a hypersurface whose principal curvatures take three special values: $λ_1, λ_2$ and $λ_1+λ_2$. In this paper, we prove that Chen's conjecture is true for hypersurfaces with three distinct principal curvatures in $\mathbb E^m$ with arbitrary dimension, thus, extend all the above-mentioned results. As an application we also show that Chen's conjecture is true for $O(p)\times O(q)$-invariant hypersurfaces in Euclidean space $\mathbb E^{p+q}$.

math.DG↗
arXiv2014

A New Kind of High-Order Multi-step Schemes for Forward Backward Stochastic Differential Equations

In this work, we concern with the high order numerical methods for coupled forward-backward stochastic differential equations (FBSDEs). Based on the FBSDEs theory, we derive two reference ordinary differential equations (ODEs) from the backward SDE, which contain the conditional expectations and their derivatives. Then, our high order multi-step schemes are obtained by carefully approximating the derivatives and the conditional expectations in the reference ODEs. Motivated by the local property of the generator of diffusion processes, the Euler method is used to solve the forward SDE, however, it is noticed that the numerical solution of the backward SDE is still of high order accuracy. Such results are obviously promising: on one hand, the use of Euler method (for the forward SDE) can dramatically simplifies the entire computational scheme, and on the other hand, one might be only interested in the solution of the backward SDE in many real applications such as option pricing. Several numerical experiments are carried out to demonstrate the effectiveness of the numerical method.

math.NA↗