Using the method of breaking of circular symmetry and of subsequent symmetry restoration via projection techiques, we present calculations for the ground-state energies and excitation spectra of N -electron parabolic quantum dots in strong magnetic fields in the medium-size range 10 ≤ N ≤ 30. The physical picture suggested by our calculations is that of finite rotating electron molecules (REMs)...

Front Cover: New bat siloxanes fly to the moon: Tricyclic laddersiloxanes with larger side rings are prepared for first time from Janus rings. The obtained novel, 12-8-12-membered ring laddersiloxane has a rigid silsesquioxane body flexible oligosiloxane “wings”. Like real bat, they can move wings freely apply into host molecules or highfunctional materials. This work is found in article number...

We present a formal scheme based cycle model for the motivic cohomology of fat points defined by truncated polynomial rings $$k[t]/(t^m)$$ with $$m \ge 2$$ , in one variable over field k. compute their Milnor range class groups when has sufficiently many elements. With some aids from rigid analytic geometry and Gersten conjecture K-theory resolved M. Kerz, we prove that resulting are isomorphic...

‎Let $I$ be an ideal in a regular local ring $(R,n)$‎, ‎we will find‎ ‎bounds on the first and the last Betti numbers of‎ ‎$(A,m)=(R/I,n/I)$‎. ‎if $A$ is an Artinian ring of the embedding‎ ‎codimension $h$‎, ‎$I$ has the initial degree $t$ and $mu(m^t)=1$‎, ‎we call $A$ a {it $t-$extended stretched local ring}‎. ‎This class of‎ ‎local rings is a natural generalization of the class of stretched ...

we show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. as aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. this generalizes and simplifies a result of  dung and   smith. as another consequen...

OBJECTIVES Mitral annulus reconstruction is now a common surgical procedure for the treatment of mitral regurgitation. However, there are still controversies in the selection of materials for annuloplasty in the clinical controlled studies available. The purpose of the present systematic review of the literature is to address whether a flexible ring is superior to a rigid ring in terms of impro...

Rigid rod oligo(phenylene-ethynylene-butadiynylene)s (oPEBs), "half-rings" of two rigid rods connected via a molecular clamp unit, and shape-persistent macrocycles (cyclic "half-ring dimers") are synthesized and their self-assembled monolayers (SAMs) are investigated by scanning tunneling microscopy (STM) at the interface of 1,2,4-trichlorobenzene (TCB)/highly oriented pyrolytic graphite (HOPG)...

Let Λ be a preprojective algebra of Dynkin type, and let G be the corresponding semisim-ple simply connected complex algebraic group. We study rigid modules in subcategories Sub Q for Q an injective Λ-module, and we introduce a mutation operation between complete rigid modules in Sub Q. This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to G.

Let Λ be a preprojective algebra of Dynkin type, and let G be the corresponding complex semisimple simply connected algebraic group. We study rigid modules in subcategories Sub Q for Q an injective Λ-module, and we introduce a mutation operation between complete rigid modules in Sub Q. This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to G.