Torsion Elements Research Articles

Patterns in synchrotron near-free-rotor FIR spectra of CH3OH and CD3OH – The tau of methanol

Analysis of high-resolution synchrotron far-infrared spectra of CH3OH and CD3OH has been extended up to high vt = 3 to 5 torsional levels in the near-free rotor region. In this region, the free-rotor angular momentum quantum number m becomes the natural label for the torsional levels, and sub-bands with Δm = 0 have torsional overlap matrix elements close to unity giving rise to surprisingly strong features in the spectrum. A simple graphical picture of free rotor parabolas gives a convenient spectral predictor for the locations of the strong sub-bands, and shows that they display systematic patterns when classified by Dennison’s torsional index τ instead of the customary A and E symmetries. The initial lines of observed near-free-rotor sub-bands with the same τ connections fall in tight τ-groups encompassing a wide range in K with a constant separation between groups of different Δτ, confirming a pattern predicted from the earliest literature on internal rotation in methanol. Together with previously known data, results for newly assigned sub-bands illustrate the τ-grouping and extend the information database of ground-state methanol term values.

Effect of rotational restraints on the stability of curved composite panels under shear loading

The present work focuses on the effect of rotational restraints on the shear buckling of symmetrically laminated curved composite panels. The Sanders–Koiter shell theory and a first-order shear deformation scheme were used for the mathematical representation of the deformation kinematics of cylindrical shells. The eigenvalue buckling equations were obtained using the principle of minimum total potential energy and by employing the Ritz method. The solution for the deformed shape was approximated as a series of trigonometric functions compatible with the essential boundary conditions of the problem. The effect of the rotational and torsional springs was incorporated by adding their corresponding potential energy to the total potential energy of the panel-loading system. Using the developed formulation, the effect of the influential parameters such as aspect ratio, panel curvature and restraint stiffness on the buckling strength of a specific class of laminates was studied extensively. To present the results in a more insightful manner, non-dimensional parameters were used in parametric studies. To normalize the effect of torsional elements, a new non-dimensional parameter was introduced.

On the mechanical characteristics of graphene nanosheets: a fully nonlinear modified Morse model

In this paper, the mechanical properties of graphene nanosheets are evaluated based on the nonlinear modified Morse model. The interatomic interactions including stretching and bending of the covalent bonds between carbon atoms, are replaced by nonlinear extensional and torsional spring-like elements. The finite element method is implemented to analyze the model under different loading conditions and linear characteristics of the graphene structure including the Young’s modulus, surface modulus, shear modulus and Poisson’s ratio are evaluated for various geometries and chirality where these properties are shown to be size and aspect ratio dependent. It is also found that when the dimensions of the sheets are greater than a certain threshold, the structure behaves quasi-isotropically and the directional elastic moduli become close to each other by a relative difference no more than 1%. Using the nonlinear stress–strain curve, the yielding point and ultimate stress and strains of the graphene sheet are also evaluated. The results of this study are compared with available experimental data and previous numerical simulations, where good agreement is achieved.

Effect of Torsional Element towards High-Speed Rotating Shaft’s Critical Speed at Different Boundary Conditions

Efficiency improvement that can be provided by the high-speed rotating equipment becomes a concern for designers nowadays. Since the high-speed rotating machinery was capable of rotating at very near to critical speed, the accurate estimation of critical speed needs to be considered. This paper investigated the effect of torsional element towards critical speed of high-speed rotating shaft system for pinned-pinned (P-P), clamped-free (C-F) and clamped-free (C-F) boundaries condition. The Nelson’s finite element model that considers the torsional effect was developed for formulating the finite element (FE) model. This FE model was used to derive Mathieu-Hill’s equation and then solved by applying the Bolotin’s theory. From the solution, the Campbell’s diagram of the high-speed shaft was plotted. It was found that torsional motion has significant effect on the critical speed for different boundary conditions. The difference between critical speed of 4DOF and 5DOF models can be as high as 6.91 %.

Torsion elements of order 𝑝2 in the Nottingham group

Abstract Let κ be a characteristic p finite field of q elements and 𝔑 κ {\mathfrak{N}_{\kappa}} the Nottingham group over κ. Lubin associated to every conjugacy class of torsion element of 𝔑 κ {\mathfrak{N}_{\kappa}} a type. We establish an upper bound B ⁢ ( q ; l , m ) {B(q;l,m)} on the number of conjugacy classes of order p 2 {p^{2}} torsion elements u of 𝔑 κ {\mathfrak{N}_{\kappa}} of type 〈 l , m 〉 {\langle l,m\rangle} . In the case where l < p {l<p} , the bound B ⁢ ( q ; l , m ) {B(q;l,m)} is the exact number of conjugacy classes. Moreover, we give a criterion on when u and u n {u^{n}} are conjugate.

Simple closed curves, finite covers of surfaces, and power subgroups of Out(Fn)

We construct examples of finite covers of punctured surfaces where the first rational homology is not spanned by lifts of simple closed curves. More generally, for any set $\mathcal{O} \subset F_n$ which is contained in the union of finitely many $Aut(F_n)$-orbits, we construct finite-index normal subgroups of $F_n$ whose first rational homology is not spanned by powers of elements of $\mathcal{O}$. These examples answer questions of Farb-Hensel, Kent, Looijenga, and Marche. We also show that the quotient of $Out(F_n)$ by the subgroup generated by kth powers of transvections often contains infinite order elements, strengthening a result of Bridson-Vogtmann saying that it is often infinite. Finally, for any set $\mathcal{O} \subset F_n$ which is contained in the union of finitely many $Aut(F_n)$-orbits, we construct integral linear representations of free groups that have infinite image and map all elements of $\mathcal{O}$ to torsion elements.

Generalized torsion and decomposition of 3–manifolds

A nontrivial element in a group is a generalized torsion element if some nonempty finite product of its conjugates is the identity. We prove that any generalized torsion element in a free product of torsion-free groups is conjugate to a generalized torsion element in some factor group. This implies that the fundamental group of a compact orientable 3 3 –manifold M M has a generalized torsion element if and only if the fundamental group of some prime factor of M M has a generalized torsion element. On the other hand, we demonstrate that there are infinitely many toroidal 3 3 –manifolds whose fundamental group has a generalized torsion element, while the fundamental group of each decomposing piece has no such elements. Additionally, in the course of the proof of the first result, we give an upper bound for the stable commutator length of generalized torsion elements.

The set of strong torsion elements of a module over a noncommutative ring

Let [Formula: see text] be an arbitrary ring and [Formula: see text] be a nonzero right [Formula: see text]-module. In this paper, we introduce the set [Formula: see text], for some nonzero ideal [Formula: see text] of [Formula: see text] of strong torsion elements of [Formula: see text] and the properties of this set are investigated. In particular, we are interested when [Formula: see text] is a submodule of [Formula: see text] and when it is a union of prime submodules of [Formula: see text].

Kunneth formula for graded rings associated to 𝐾-theories of Rost motives

In this paper, we study the graded ring g r ∗ ( X ) gr^*(X) defined by K K -theory of a twist flag variety X X . In particular, the Kunneth map g r ∗ ( R ′ ) ⊗ g r ∗ ( R ′ ) → g r ∗ ( R ) gr^*(R’)\otimes gr^*(R’)\to gr^*(R) is studied explicitly for an original Rost motive R ′ R’ and a generalized Rost motive R R . Using this, we give examples T o r ( X ) 2 ≠ 0 Tor(X)^2\not =0 for the ideal T o r ( X ) Tor(X) of torsion elements in the Chow ring C H ∗ ( X ) CH^*(X) .

Chow Filtration on Representation Rings of Algebraic Groups

Abstract We introduce and study a filtration on the representation ring $R(G)$ of an affine algebraic group $G$ over a field. This filtration, which we call Chow filtration, is an analogue of the coniveau filtration on the Grothendieck ring of a smooth variety. We compare it with the other known filtrations on $R(G)$ and show that all three define on $R(G)$ the same topology. For any $n\geq 1$, we compute the Chow filtration on $R(G)$ for the special orthogonal group $G:=O^+(2n+1)$. In particular, we show that the graded group associated with the filtration is torsion-free. On the other hand, the Chow ring of the classifying space of $G$ over any field of characteristic $\ne 2$ is known to contain non-zero torsion elements. As a consequence, any sufficiently good approximation of the classifying space yields an example of a smooth quasi-projective variety $X$ such that its Chow ring is generated by Chern classes and at the same time contains non-zero elements vanishing under the canonical homomorphism onto the graded ring associated with the coniveau filtration on the Grothendieck ring of $X$.

An Efficient Finite Element For Restrained Torsion Of Thin-Walled Beams Including The Effect Of Warping And Shear Deformation

An efficient torsion element is developed to describe the restrained torsion of thin-walled beams based on the first-order torsion theory. The element has two nodes, each with two degree of freedoms, namely, total rotation and warping function of cross section. The element stiffness matrix is directly obtained on the basis of first-order torsion theory without the assumption of interpolation function and the derivation of classical finite element method, which is more convenient and applicable than the initial parameter method. This element can consider not only the warping deformation but also the shear deformation of cross section due to restrained torsion. Finally, numerical examples are presented to demonstrate the validity and reliability of current torsion element, and the comparison between the results obtained from current method and those from other approaches is also illustrated.

Acylindrically hyperbolic groups with exotic properties

We prove that every countable family of countable acylindrically hyperbolic groups has a common finitely generated acylindrically hyperbolic quotient. As an application, we obtain an acylindrically hyperbolic group Q with strong fixed point properties: Q has property FLp for all p∈[1,+∞), and every action of Q on a finite dimensional contractible topological space has a fixed point. In addition, Q has other properties which are rather unusual for groups exhibiting “hyperbolic-like” behavior. E.g., Q is not uniformly non-amenable and has finite generating sets with arbitrary large balls consisting of torsion elements.

토션엘리먼트가 있는 단축압출기의 균질화 구간에서 고분자 용융액의 혼합 성능 향상에 대한 수치모사

토션엘리먼트가 있는 단축압출기의 균질화 구간에서 고분자 용융액의 혼합 성능 향상에 대한 수치모사

Commensurability for certain right-angled Coxeter groups and geometric amalgams of free groups

We give explicit necessary and sufficient conditions for the abstract commensurability of certain families of 1-ended, hyperbolic groups, namely right-angled Coxeter groups defined by generalized \Theta -graphs and cycles of generalized \Theta -graphs, and geometric amalgams of free groups whose JSJ graphs are trees of diameter \leq 4 . We also show that if a geometric amalgamof free groups has JSJ graph a tree, then it is commensurable to a right-angled Coxeter group, and give an example of a geometric amalgam of free groups which is not quasi-isometric (hence not commensurable) to any group which is finitely generated by torsion elements. Our proofs involve a new geometric realization of the right-angled Coxeter groups we consider, such that covers corresponding to torsion-free, finite-index subgroups are surface amalgams.

Infinitely generated virtually free pro‐p groups and p‐adic representations

We prove the pro-$p$ version of the Karras, Pietrowski, Solitar, Cohen and Scott result stating that a virtually free group acts on a tree with finite vertex stabilizers. If a virtually free pro-$p$ group $G$ has finite centralizes of all non-trivial torsion elements more stronger statement is proved: $G$ embeds into a free pro-$p$ product of a free pro-$p$ group and finite $p$-group. The integral $p$-adic representation theory is used in the proof; it replaces the Stallings theory of ends in the pro-$p$ case.

Nonlinear modeling and vibration analysis of a two-link flexible manipulator coupled with harmonically driven flexible joints

The present paper deals with the theoretical studies to determine the modal parameters and investigate the dynamic instability of a harmonically driven planar two-link manipulator with flexible joints. An appropriate dynamic model incorporating both link and joint flexibilities subjected to a harmonic motion has been developed while joint flexibility has been modeled as a combination of torsional spring-inertia elements. Modal parameters for various modes of vibration have been evaluated and graphically demonstrated. Then, method of multiple scales has been employed to further analyze the vibration attributes of steady state responses and their stability under resonance condition. The comparative mode shapes and bifurcation diagrams those describe the vibrating system have been illustrated to demonstrate the dynamics of the flexible manipulator. The effect of geometric and inertial coupling existing between the flexible arms on bifurcation states and stability of the obtained solutions has been thoroughly investigated. Analytically obtained results have been verified numerically and found to be in good agreement. The present theoretical results deliver a useful insight into the attributes of vibration characteristics along with the nonlinear dynamic behavior and operational stability of two-link flexible manipulator under joint motion.

Hyper-commutators in effect algebras

The hyper-commutators in effect algebras as a generalization of commutators in lattice effect algebras are defined, and their properties are studied. We prove that a nonzero element is in some hyper-commutator if and only if it is a torsion element in effect algebras with the maximality property. Thus, homogeneity can be characterized by hyper-commutators. Some properties of Riesz ideals related to hyper-commutators are also studied. As an application, we prove that commutators are sharp in lattice effect algebras and every block-finite lattice effect algebra is commutator-finite.

Topological K-theory of affine Hecke algebras

Let H(R,q) be an affine Hecke algebra with a positive parameter function q. We are interested in the topological K-theory of H(R,q), that is, the K-theory of its C*-completion C*_r (R,q). We will prove that $K_* (C*_r (R,q))$ does not depend on the parameter q. For this we use representation theoretic methods, in particular elliptic representations of Weyl groups and Hecke algebras. Thus, for the computation of these K-groups it suffices to work out the case q=1. These algebras are considerably simpler than for q not 1, just crossed products of commutative algebras with finite Weyl groups. We explicitly determine $K_* (C*_r (R,q))$ for all classical root data R, and for some others as well. This will be useful to analyse the K-theory of the reduced C*-algebra of any classical p-adic group. For the computations in the case q=1 we study the more general situation of a finite group \Gamma acting on a smooth manifold M. We develop a method to calculate the K-theory of the crossed product $C(M) \rtimes \Gamma$. In contrast to the equivariant Chern character of Baum and Connes, our method can also detect torsion elements in these K-groups.

An algorithm to construct candidates to counterexamples to the Zassenhaus Conjecture

Let G be a finite group, N a nilpotent normal subgroup of G and let V(ZG,N) denote the group formed by the units of the integral group ring ZG of G which map to the identity under the natural homomorphism ZG→Z(G/N). Sehgal asked whether any torsion element of V(ZG,N) is conjugate in the rational group algebra of G to an element of G. This is a special case of the Zassenhaus Conjecture.By results of Cliff and Weiss and Hertweck, Sehgal's Problem has a positive solution if N has at most one non-cyclic Sylow subgroup. We present some algorithms to study Sehgal's Problem when N has at most one non-abelian Sylow subgroup. They are based on the Cliff–Weiss inequalities introduced by the authors in a previous paper. With the help of these algorithms we obtain some positive answers to Sehgal's Problem and use them to show that for units in V(ZG,N) our method is strictly stronger than the well known HeLP Method. We then present a method to use the output of one of the algorithms to construct explicit metabelian groups which are candidates to a negative solution to Sehgal's Problem. Recently Eisele and Margolis showed that some of the examples proposed in this paper are indeed counterexamples to the Zassenhaus Conjecture. These are the first known counterexamples. Moreover, we prove that every metabelian negative solution of Sehgal's Problem satisfying some minimal conditions is given by our construction.

Torsion, torsion length and finitely presented groups

Abstract We show that a construction by Aanderaa and Cohen used in their proof of the Higman Embedding Theorem preserves torsion length. We give a new construction showing that every finitely presented group is the quotient of some C ′ ⁢ ( 1 / 6 ) {C^{\prime}(1/6)} finitely presented group by the subgroup generated by its torsion elements. We use these results to show there is a finitely presented group with infinite torsion length which is C ′ ⁢ ( 1 / 6 ) {C^{\prime}(1/6)} , and thus word-hyperbolic and virtually torsion-free.