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Jun Yu

Publications and source records attributed to Jun Yu.

317 records · Page 18Linked to original sources
arXiv2013

New symmetry reductions related with the residual symmetry of Boussinesq equation

The Backlund transformation related symmetry is nonlocal, which is hardly to apply in constructing solutions for nonlinear equations. In this paper, we first localize nonlocal residual symmetry to Lie point symmetry by introducing multiple new variables and obtain new Baaklund transformation. Then, by solving out the general form of localized the residual symmetry, we reduce the enlarged system by classical symmetry approach and obtain the corresponding reduction solutions as well as related reduction equations. The localization procedure provides a new way to investigate interaction solutions between different waves.

nlin.SI↗
arXiv2013

Residual Symmetry Reductions and Interaction Solutions of (2+1)-Dimensional Burgers Equation

The (2+1)-dimensional Burgers equation has been investigated first from prospective of symmetry by localizing the nonlocal residual symmetries and then studied by a simple generalized tanh expansion method. New symmetry reduction solutions has been obtained by using the standard Lie point symmetry group approach. A new Bäklund transformation for Burgers equation has been given with the generalized tanh expansion method . From this BT, interactive solutions among different nonlinear excitations which is hard to obtain by other methods has also been obtained easily.

nlin.SI↗
arXiv2013

Methods for scoring the collective effect of SNPs: Minor alleles of common SNPs quantitatively affect traits/diseases and are under both positive and negative selection

Most common SNPs are popularly assumed to be neutral. We here developed novel methods to examine in animal models and humans whether extreme amount of minor alleles (MAs) carried by an individual may represent extreme trait values and common diseases. We analyzed panels of genetic reference populations and identified the MAs in each panel and the MA content (MAC) that each strain carried. We also analyzed 21 published GWAS datasets of human diseases and identified the MAC of each case or control. MAC was nearly linearly linked to quantitative variations in numerous traits in model organisms, including life span, tumor susceptibility, learning and memory, sensitivity to alcohol and anti-psychotic drugs, and two correlated traits poor reproductive fitness and strong immunity. Similarly, in Europeans or European Americans, enrichment of MAs of fast but not slow evolutionary rate was linked to autoimmune and numerous other diseases, including type 2 diabetes, Parkinson's disease, psychiatric disorders, alcohol and cocaine addictions, cancer, and less life span. Therefore, both high and low MAC correlated with extreme values in many traits, indicating stabilizing selection on most MAs. The methods here are broadly applicable and may help solve the missing heritability problem in complex traits and diseases.

q-bio.GN↗
arXiv2013

On the dimension datum problem and the linear dependence problem

The dimension datum of a closed subgroup of a compact Lie group is the sequence of invariant dimensions of irreducible representations by restriction. In this article we classify closed connected subgroups with equal dimension data or linearly dependent dimension data. This classification should have applications to the isospectral geometry and automorphic form theory. We also study the equality/linear dependence of not necessarily connected subgroups of unitary group acting irreducibly on the natural representation.

math.GR↗
arXiv2013

A rigidity result for dimension data

The dimension datum of a closed subgroup of a compact Lie group is a sequence by assigning the invariant dimension of each irreducible representation restricting to the subgroup. We prove that any sequence of dimension data contains a converging sequence with limit the dimension datum of a subgroup interrelated to subgroups giving this sequence. This rigidity has an immediate corollary that the space of dimension data of closed subgroups in a given compact Lie group is sequentially compact.

math.GR↗
arXiv2012

A note on closed subgroups of compact Lie groups

We reduce the classification of finite subgroups in compact Lie groups to that of quasi-simple ones, prove the number of conjugacy classes is finite and each cojugacy class is Zariski closed in mapping space, and classify "strongly controlling fusions" symmetric pairs.

math.GR↗
arXiv2012

Elementary abelian 2 subgroups of compact Lie groups

We classify elementary abelian 2 subgroups of compact simple Lie groups of adjoint type. This finishes the classification of elementary abelian $p$ subgroups of compact (or linear algebraic) simple groups of adjoint type.

math.GR↗
arXiv2011

Klein Four subgroups of Lie Algebra Automorphisms

By calculating the symmetric subgroups $\Aut(\fru_0)^θ$ and their involution classes, we classify the Klein four subgroups $Γ$ of $\Aut(\fru_0)$ for each compact simple Lie algebra $\fru_0$ up to conjugation. This leads to a new approach of classification of semisimple symmetric pairs and $\bbZ_2\times \bbZ_2$-symmetric spaces. We also determine the fixed point subgroup $\Aut(\fru_0)^Γ$.

math.GR↗
arXiv2007

Existence of Universal Entangler

A gate is called entangler if it transforms some (pure) product states to entangled states. A universal entangler is a gate which transforms all product states to entangled states. In practice, a universal entangler is a very powerful device for generating entanglements, and thus provides important physical resources for accomplishing many tasks in quantum computing and quantum information. This Letter demonstrates that a universal entangler always exists except for a degenerated case. Nevertheless, the problem how to find a universal entangler remains open.

quant-ph↗
arXiv1998

Magnetoresistance, Micromagnetism and Domain Wall Effects in Epitaxial Fe and Co Structures with Stripe Domains

We review our recent magnetotransport and micromagnetic studies of lithographically defined epitaxial thin film structures of bcc Fe and hcp Co with stripe domains. Micromagnetic structure and resistivity anisotropy are shown to be the predominant sources of low field magnetoresistance (MR) in these microstructures, with domain wall (DW) effects smaller but observable (DW-MR $\lesssim 1 %$). In Fe, at low temperature, in a regime in which fields have a significant effect on electron trajectories, a novel negative DW contribution to the resistivity is observed. In hcp Co microstructures, temperature dependent transport measurements for current perpendicular and parallel to walls show that any additional resistivity due to DW scattering is very small.

cond-mat.mes-hall↗