A small spheroid settling in a quiescent fluid experiences an inertial torque that aligns it so settles with its broad side first. Here we show active particle such too, as at rest. For spherical squirmer, the is $\boldsymbol {T}^\prime = -{\frac {9}{8}} m_f (\boldsymbol {v}_s^{(0)} \wedge \boldsymbol {v}_g^{(0)})$ where {v}_s^{(0)}$ swimming velocity, {v}_g^{(0)}$ velocity Stokes approximation...

This paper gives a criterion for the non-vanishing of Dirac cohomology $\mathcal{L}_S(Z)$, where $\mathcal{L}_S(\cdot)$ is cohomological induction functor, while inducing module $Z$ irreducible, unitarizable, and in good range. As an application, we give formula counting number strings series. Using this formula, classify all irreducible unitary representations $E_{6(2)}$ with non-zero cohomolo...

We consider a gauge field theory which admits p-dimensional topological defects, expanding the equations of motion in powers of the defect thickness. In this way we derive an effective action and effective equation of motion for the defect in terms of the coordinates of the p-dimensional worldsurface defined by the history of the core of the defect. (_'.,'-\ ,t-b-!-] .7_-7.__ "_;:'CTIV_: Ac<:'l...

in this paper, an iterative method is proposed for solving matrix equation $sum_{j=1}^s a_jx_jb_j = e$. this method is based on the global least squares (gl-lsqr) method for solving the linear system of equations with the multiple right hand sides. for applying the gl-lsqr algorithm to solve the above matrix equation, a new linear operator, its adjoint and a new inner product are dened. it is ...

in this paper we discuss on the fixed points of asymptotic contractions and boyd-wong type contractions in uniform spaces equipped with an e-distance. a new version ofkirk's fixed point theorem is given for asymptotic contractions and boyd-wong type contractions is investigated in uniform spaces.

A bstract search for the $$ {B}_{\mathrm{s}}^0 B s 0 → D *± ∓ decay is performed using proton-proton collision data at centre-of-mass energies of 7, 8 and 13 TeV collected by LHCb experiment, corresponding to an integrated luminosity 9 fb − 1 . Th...

An angular analysis of the rare decay $B^0_s\rightarrow\phi\mu^+\mu^-$ is presented, using proton-proton collision data collected by LHCb experiment at centre-of-mass energies $7$, $8$ and $13~\rm{TeV}$, corresponding to an integrated luminosity $8.4~\rm{fb}^{-1}$. The observables describing distributions are determined in regions $q^2$, square dimuon invariant mass. results consistent with Sta...

A bstract The infinite chain of transitions one pair mesons (channel I) into another II) can produce bound states and resonances in both channels even if no interactions inside exist. These which occur also meson-baryon are called channel-coupling (CC) resonances. new mechanism CC is proposed where due to a rearrangement confining strings each channel — the recoupling mechanism. amplitude this ...

in this paper, we establish and prove the existence of best proximity points for multivalued cyclic $f$- contraction mappings in complete metric spaces. our results improve and extend various results in literature.