arXiv subjects

Feng Wei

Publications and source records attributed to Feng Wei.

At least 55 records · Page 3Linked to original sources

arXiv2018

Broken mirror symmetry tuned topological transport in PbTe/SnTe heterostructures

The tunability of topological surface states and controllable opening of the Dirac gap are of great importance to the application of topological materials. In topological crystalline insulators (TCIs), crystal symmetry and topology of electronic bands intertwine to create topological surface states and thus the Dirac gap can be modulated by symmetry breaking structural changes of lattice. By transport measurement on heterostructures composed of p-type topological crystalline insulator SnTe and n-type conventional semiconductor PbTe, here we show a giant linear magnetoresistance (up to 2150% under 14 T at 2 K) induced by the Dirac Fermions at the PbTe/SnTe interface. In contrast, PbTe/SnTe samples grown at elevated temperature exhibit a cubic-to-rhombohedral structural phase transition of SnTe lattice below 100 K and weak antilocalization effect. Such distinctive magneto-resistance behavior is attributed to the broken mirror symmetry and gapping of topological surface states. Our work provides a promising application for future magneto-electronics and spintronics based on TCI heterostructures.

cond-mat.mtrl-sci↗

arXiv2018

Investigate Invertibility of Sparse Symmetric Matrix

In this paper, we investigate the invertibility of sparse symmetric matrices. We show that for an $n\times n$ sparse symmetric random matrix $A$ with $A_{ij} = δ_{ij} ξ_{ij}$ is invertible with high probability. Here, $δ_{ij}$s, $i\ge j$ are i.i.d. Bernoulli random variables with $\mathbb{P} \left(ξ_{ij}=1 \right) =p \ge n^{-c}$, $ξ_{ij}, i\ge j$ are i.i.d. random variables with mean 0, variance 1 and finite forth moment $M_4$, and $c$ is constant depending on $M_4$. More precisely, $$ s_{\rm min} (A) > \varepsilon \sqrt{\frac{p}{n}}. $$ with high probability.

math.PR↗

arXiv2018

Normal elements of completed group algebras over ${\rm SL}_3(\mathbb{Z}_p) $

Let $p$ be a prime integer and $\mathbb{Z}_p$ be the ring of $p$-adic integers. By a purely computational approach we prove that each nonzero normal element of a completed group algebra over the special linear group ${\rm SL}_3(\mathbb{Z}_p)$ is a unit. This give a positive answer to an open question in \cite{WeiBian2} and make up for an earlier mistake in \cite{WeiBian1} simultaneously.

math.NT↗

arXiv2017

Lie-Type Derivations of Nest Algebras on Banach Spaces

Let $\mathcal{X}$ be a Banach space over the complex field $\mathbb{C}$ and $\mathcal{B(X)}$ be the algebra of all bounded linear operators on $\mathcal{X}$. Let $\mathcal{N}$ be a non-trivial nest on $\mathcal{X}$, ${\rm Alg}\mathcal{N}$ be the nest algebra associated with $\mathcal{N}$, and $L\colon {\rm Alg}\mathcal{N}\longrightarrow \mathcal{B(X)}$ be a linear mapping. Suppose that $p_n(x_1,x_2,\cdots,x_n)$ is an $(n-1)$-th commutator defined by $n$ indeterminates $x_1, x_2, \cdots, x_n$. It is shown that $L$ satisfies the rule $$ L(p_n(A_1, A_2, \cdots, A_n))=\sum_{k=1}^{n}p_n(A_1, \cdots, A_{k-1}, L(A_k), A_{k+1}, \cdots, A_n) $$ for all $A_1, A_2, \cdots, A_n\in {\rm Alg}\mathcal{N}$ if and only if there exist a linear derivation $D\colon {\rm Alg}\mathcal{N}\longrightarrow \mathcal{B(X)}$ and a linear mapping $H\colon {\rm Alg}\mathcal{N}\longrightarrow \mathbb{C}I$ vanishing on each $(n-1)$-th commutator $p_n(A_1,A_2,\cdots, A_n)$ for all $A_1, A_2, \cdots, A_n\in {\rm Alg}\mathcal{N}$ such that $L(A)=D(A)+H(A)$ for all $A\in {\rm Alg}\mathcal{N}$.

math.FA↗

arXiv2016

Upper bound for the Dvoretzky dimension in Milman-Schechtman theorem

For a symmetric convex body $K\subset\mathbb{R}^n$, the Dvoretzky dimension $k(K)$ is the largest dimension for which a random central section of $K$ is almost spherical. A Dvoretzky-type theorem proved by V.~D.~Milman in 1971 provides a lower bound for $k(K)$ in terms of the average $M(K)$ and the maximum $b(K)$ of the norm generated by $K$ over the Euclidean unit sphere. Later, V.~D.~Milman and G. Schechtman obtained a matching upper bound for $k(K)$ in the case when $\frac{M(K)}{b(K)}>c(\frac{\log(n)}{n})^{\frac{1}{2}}$. In this paper, we will give an elementary proof of the upper bound in Milman-Schechtman theorem which does not require any restriction on $M(K)$ and $b(K)$.

math.FA↗

arXiv2016

The Iwasawa Algebra $Ω_G$ and Its Dual Artin Coalgebra

For any compact $p$-adic Lie group $G$, the Iwasawa algebra $Ω_G$ over finite field $\mathbb{F}_p$ is a complete noetherian semilocal algebra. It is shown that $Ω_G$ is the dual algebra of an artinian coalgebra $C$. We induce a duality between the derived category $\mathcal{D}^b_{fg}(_{Ω_G}\mathcal{M})$ of bounded complexes of left $Ω_G$-modules with finitely generated cohomology modules and the derived category $\mathcal{D}^b_{qf}(^C\mathcal{M})$ of bounded complexes of left $C$-comodules with quasi-finite cohomology comodules.

math.RA↗

arXiv2016

Characterizations of Lie Higher Derivations on J-Subspace Lattice Algebras

Let $\mathcal{L}$ be a $\mathcal{J}$-subspace lattice on a Banach space $X$ over the real or complex field $\mathbb{F}$ and $ \mathrm{Alg}\mathcal{L}$ be the associated $\mathcal{J}$-subspace lattice algebras. In this paper, we characterize the structure of a family $\{L_n\}_{n=0}^{\infty}: \mathrm{Alg}\mathcal{L}\rightarrow \mathrm{Alg}\mathcal{L}$ of linear mappings satisfying the condition $$L_n([A, B])=\sum_{i+j=n}[L_i(A), L_j(B)]$$ for any $A, B\in\mathrm{Alg}\mathcal{L}$ with $AB = 0$. Moreover, the family $\{L_n\}_{n=0}^{\infty}: \mathrm{Alg}\mathcal{L}\rightarrow \mathrm{Alg}\mathcal{L}$ of linear mappings satisfying $L_n([A, B]_ξ)=\sum_{i+j=n}[L_i(A), L_j(B)]_ξ$ for any $A, B\in\mathrm{Alg}\mathcal{L}$ with $AB = 0$ and $1\neq ξ\in \mathbb{F}$ is also considered in the current work.

math.RA↗

arXiv2016

Upper bound for intermediate singular values of random matrices

In this paper, we prove that an $n\times n$ matrix $A$ with independent centered subgaussian entries satisfies \[ s_{n+1-l}(A) \le C_1t \frac{l}{\sqrt{n}} \] with probability at least $1-\exp(-C_2tl)$. This yields $s_{n-l}(A) \sim \frac{cl}{\sqrt{n}}$ in combination with a known lower bound. These results can be generalized to the rectangular matrix case.

math.PR↗

arXiv2014

Centralizing traces and Lie triple isomorphisms on generalized matrix algebras

Let $\mathcal{G}$ be a generalized matrix algebra over a commutative ring $\mathcal{R}$ and $\mathcal{Z(G)}$ be the center of $\mathcal{G}$. Suppose that ${\mathfrak q}\colon \mathcal{G}\times \mathcal{G}\longrightarrow \mathcal{G}$ is an $\mathcal{R}$-bilinear mapping and ${\mathfrak T}_{\mathfrak q}\colon \mathcal{G}\longrightarrow \mathcal{G}$ is the trace of $\mathfrak{q}$. We describe the form of ${\mathfrak T}_{\mathfrak q}$ satisfying the condition $[{\mathfrak T}_{\mathfrak q}(G), G]\in \mathcal{Z(G)}$ for all $G\in \mathcal{G}$. The question of when ${\mathfrak T}_{\mathfrak q}$ has the proper form is considered. Using the aforementioned trace function, we establish sufficient conditions for each Lie triple isomorphism of $\mathcal{G}$ to be almost standard. As applications we characterize Lie triple isomorphisms of full matrix algebras, of triangular algebras and of certain unital algebras with nontrivial idempotents. Some topics for future research closely related to our current work are proposed at the end of this article.

math.RA↗

arXiv2013

Jordan Derivations of some extension algebras

In this paper, we mainly study Jordan derivations of dual extension algebras and those of generalized one-point extension algebras. It is shown that every Jordan derivation of dual extension algebras is a derivation. As applications, we obtain that every Jordan generalized derivation and every generalized Jordan derivation on dual extension algebras are both generalized derivations. For generalized one-point extension algebras, it is proved that under certain conditions, each Jordan derivation of them is the sum of a derivation and an anti-derivation.

math.RA↗

arXiv2013

Lie Derivations of Dual Extension Algebras

Let $K$ be a field and $Γ$ a finite quiver without oriented cycles. Let $Λ$ be the path algebra $K(Γ, ρ)$ and let $\mathscr{D}(Λ)$ be the dual extension of $Λ$. In this paper, we prove that each Lie derivation of $\mathscr{D}(Λ)$ is of the standard form.

math.RA↗

arXiv2013

Centralizing Traces and Lie Triple Isomorphisms on Triangular Algebras

Let $\mathcal{T}$ be a triangular algebra over a commutative ring $\mathcal{R}$ and $\mathcal{Z(T)}$ be the center of $\mathcal{T}$. Suppose that ${\mathfrak q}\colon \mathcal{T}\times \mathcal{T}\longrightarrow \mathcal{T}$ is an $\mathcal{R}$-bilinear mapping and that ${\mathfrak T}_{\mathfrak q}\colon: \mathcal{T}\longrightarrow \mathcal{T}$ is a trace of $\mathfrak{q}$. We describe the form of ${\mathfrak T}_{\mathfrak q}$ satisfying the condition $[{\mathfrak T}_{\mathfrak q}(T), T]\in \mathcal{Z(T)}$ for all $T\in \mathcal{T}$. The question of when ${\mathfrak T}_{\mathfrak q}$ has the proper form will be addressed. Using the aforementioned trace function, we establish sufficient conditions for each Lie triple isomorphism on $\mathcal{T}$ to be almost standard. As applications we characterize Lie triple isomorphisms of triangular matrix algebras and nest algebras. Some further research topics related to current work are proposed at the end of this article.

math.RA↗

arXiv2012

Commuting Traces and Lie Isomorphisms on Generalized Matrix Algebras

Let $\mathcal{G}$ be a generalized matrix algebra over a commutative ring $\mathcal{R}$, ${\mathfrak q}\colon \mathcal{G}\times\mathcal{G}\longrightarrow \mathcal{G}$ be an $\mathcal{R}$-bilinear mapping and ${\mathfrak T}_{\mathfrak q}\colon:\mathcal{G}\longrightarrow \mathcal{G}$ be a trace of $\mathfrak{q}$. We describe the form of ${\mathfrak T}_{\mathfrak q}$ satisfying the condition ${\mathfrak T}_{\mathfrak q}(G)G=G{\mathfrak T}_{\mathfrak q}(G)$ for all $G\in \mathcal{G}$. The question of when ${\mathfrak T}_{\mathfrak q}$ has the proper form is considered. Using the aforementioned trace function, we establish sufficient conditions for each Lie isomorphism of $\mathcal{G}$ to be almost standard. As applications we characterize Lie isomorphisms of full matrix algebras, of triangular algebras and of certain unital algebras with nontrivial idempotents. Some further research topics related to current work are proposed at the end of this article.

math.RA↗

arXiv2012

Jordan Derivations and Lie derivations on Path Algebras

Without the faithful assumption, we prove that every Jordan derivation on a class of path algebras of quivers without oriented cycles is a derivation and that every Lie derivation on such kinds of algebras is of the standard form.

math.RA↗

arXiv2012

Nonlinear Lie type Derivations of Von Neumann Algebras

Let $A$ be a von Neumann algebra with no central summands of type $I_1$. We will show that every nonlinear Lie $n$-derivation on $A$ is of the standard form, i.e. it can be expressed as a sum of an additive derivation and a central-valued mapping which annihilates each $(n-1)$-th commutator of $A$.

math.RA↗

arXiv2012

Jordan Derivations and Antiderivations of Generalized Matrix Algebras

Let $\mathcal{G}=[A & M N & B]$ be a generalized matrix algebra defined by the Morita context $(A, B,_AM_B,_BN_A, Φ_{MN}, Ψ_{NM})$. In this article we mainly study the question of whether there exist proper Jordan derivations for the generalized matrix algebra $\mathcal{G}$. It is shown that if one of the bilinear pairings $Φ_{MN}$ and $Ψ_{NM}$ is nondegenerate, then every antiderivation of $\mathcal{G}$ is zero. Furthermore, if the bilinear pairings $Φ_{MN}$ and $Ψ_{NM}$ are both zero, then every Jordan derivation of $\mathcal{G}$ is the sum of a derivation and an antiderivation. Several constructive examples and counterexamples are presented.

math.RA↗

arXiv2011

Transverse Spin Results From PHENIX

The PHENIX experiment at the Relativistic Heavy Ion Collider explores the spin structure of the proton in polarized p+p collisions at center-of-mass energies up to 500 GeV. Tremendous experimental and theoretical progress has been made toward understanding the physics involved with transversely polarized beams or targets in recent years. Not only nucleon structure and parton distribution functions but also QCD dynamics have been studied in various physics processes in high-energy polarized DIS and p+p collisions. In the 2006 and 2008 RHIC runs, the PHENIX experiment took a significant amount of transversely polarized p+p collision data at 200 GeV center-of-mass energy, with an integrated luminosity of 8 $pb^{-1}$ and beam polarizations up to 50%. Single spin asymmetries of different probes have been measured in mid- and forward-rapidities. In this report, we present the latest transverse spin results from the PHENIX experiment and discuss briefly the prospects of future transverse spin physics with the PHENIX detectors upgrades.

hep-ex↗

arXiv2011

Multicolor Graphene Nanoribbon/Semiconductor Nanowire Heterojunction Light-Emitting Diodes

We report novel graphene nanoribbon (GNR)/semiconductor nanowire (SNW) heterojunction light-emitting diodes (LEDs) for the first time. The GNR and SNW have a face-to-face contact structure, which has the merit of bigger active region. ZnO, CdS, and CdSe NWs were employed in our case. At forward biases, the GNR/SNW heterjunction LEDs could emit light with wavelengths varying from ultraviolet (380 nm) to green (513 nm) to red (705 nm), which were determined by the band-gaps of the involved SNWs. The mechanism of light emitting for the GNR/SNW heterojunction LED was discussed. Our approach can easily be extended to other semiconductor nano-materials. Moreover, our achievement opens the door to next-generation display technologies, including portable, "see-through", and conformable products.

cond-mat.mes-hall↗