To send content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about sending content to .
To send content items to your Kindle, first ensure firstname.lastname@example.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about sending to your Kindle.
Note you can select to send to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
We consider the Klein–Gordon equation on asymptotically anti-de-Sitter spacetimes subject to Neumann or Robin (or Dirichlet) boundary conditions and prove propagation of singularities along generalized broken bicharacteristics. The result is formulated in terms of conormal regularity relative to a twisted Sobolev space. We use this to show the uniqueness, modulo regularizing terms, of parametrices with prescribed
-wavefront set. Furthermore, in the context of quantum fields, we show a similar result for two-point functions satisfying a holographic Hadamard condition on the
Using the Baire Category Theorem, we prove the Principle of Uniform Boundedness, which allows us to deduce uniform bounds on collections of bounded linear operators from pointwise properties. We use the powerful corollary known as the “Condensation of Singularities” to show that there are continuous periodic functions whose Fourier series do not converge pointwise everywhere.
We develop some foundational results in a higher-dimensional foliated Mori theory, and show how these results can be used to prove a structure theorem for the Kleiman–Mori cone of curves in terms of the numerical properties of
for rank 2 foliations on threefolds. We also make progress toward realizing a minimal model program (MMP) for rank 2 foliations on threefolds.
This paper presents the computation of the safe working zone (SWZ) of a parallel manipulator having three degrees of freedom. The SWZ is defined as a continuous subset of the workspace, wherein the manipulator does not suffer any singularity, and is also free from the issues of link interference and physical limits on its joints. The proposed theory is illustrated via application to two parallel manipulators: a planar 3-R̲RR manipulator and a spatial manipulator, namely, MaPaMan-I. It is also shown how the analyses can be applied to any parallel manipulator having three degrees of freedom, planar or spatial.
Wave propagation in a non-uniform medium is formulated and the basic governing partial differential equations are derived. Two geometries are considered: the Cartesian system and the cylindrical polar system. The fundamental ordinary differential equations governing wave propagation are obtained. Singularities in the system are introduced. The idea of phase mixing is introduced. Again, the special cases of the incompressible medium and a $\beta = 0$ plasma are formulated
In this paper, we prove that the set of all
-pure thresholds on a fixed germ of a strongly
-regular pair satisfies the ascending chain condition. As a corollary, we verify the ascending chain condition for the set of all
-pure thresholds on smooth varieties or, more generally, on varieties with tame quotient singularities, which is an affirmative answer to a conjecture given by Blickle, Mustaţǎ and Smith.
This paper presents a unified formulation for the kinematics, singularity and workspace analyses of parallel delta robots with prismatic actuation. Unlike the existing studies, the derivations presented in this paper are made by assuming variable angles and variable link lengths. Thus, the presented scheme can be used for all of the possible linear delta robot configurations including the ones with asymmetric kinematic chains. Referring to a geometry-based derivation, the paper first formulates the position and the velocity kinematics of linear delta robots with non-iterative exact solutions. Then, all of the singular configurations are identified assuming a parametric content for the Jacobian matrix derived in the velocity kinematics section. Furthermore, a benchmark study is carried out to determine the linear delta robot configuration with the maximum cubic workspace among symmetric and semi-symmetric kinematic chains. In order to show the validity of the proposed approach, two sets of experiments are made, respectively, on the horizontal and the Keops type of linear delta robots. The experiment results for the confirmation of the presented kinematic analysis and the simulation results for the determination of the maximum cubic workspace illustrate the efficacy and the flexible applicability of the proposed framework.
We generalise Simpson’s nonabelian Hodge correspondence to the context of projective varieties with Kawamata log terminal (klt) singularities. The proof relies on a descent theorem for numerically flat vector bundles along birational morphisms. In its simplest form, this theorem asserts that given any klt variety
and any resolution of singularities, any vector bundle on the resolution that appears to come from
numerically, does indeed come from
. Furthermore, and of independent interest, a new restriction theorem for semistable Higgs sheaves defined on the smooth locus of a normal, projective variety is established.
We study frames in ℝ3 and mapping from a surface M in ℝ3 to the space of frames. We consider in detail mapping frames determined by a unit tangent principal or asymptotic direction field U and the normal field N. We obtain their generic local singularities as well as the generic singularities of the direction field itself. We show, for instance, that the cross-cap singularities of the principal frame map occur precisely at the intersection points of the parabolic and subparabilic curves of different colours. We study the images of the asymptotic and principal foliations on the unit sphere by their associated unit direction fields. We show that these curves are solutions of certain first order differential equations and point out a duality in the unit sphere between some of their configurations.
This paper provides a contribution to the singularity analysis of the parallel manipulators by introducing the position singularities in addition to the motion and actuation singularities. The motion singularities are associated with the linear velocity mapping between the task and joint spaces. So, they are the singularities of the relevant Jacobian matrices. On the other hand, the position singularities are associated with the nonlinear position mapping between the task and joint spaces. So, they are encountered in the position-level solutions of the forward and inverse kinematics problems. In other words, they come out irrespective of the velocity mapping and the Jacobian matrices. Considering these distinctions, a kinematic singularity is denoted here by one of the four acronyms, which are PSFK (position singularity of forward kinematics), PSIK (position singularity of inverse kinematics), MSFK (motion singularity of forward kinematics), and MSIK (motion singularity of inverse kinematics). There may also occur an actuation singularity (ACTS) concerning the kinetostatic relationships that involve forces and moments. However, it is verified that an ACTS is the same as an MSFK. Each singularity induces different consequences in the joint and task spaces. A PSFK imposes a constraint on the active joint variables and makes the end-effector position indefinite and uncontrollable. Therefore, it must be avoided. An MSFK imposes a constraint on the rates of the active joint variables and makes the end-effector motion indefinite and easily perturbable. Besides, since it is also an ACTS, it causes the actuator torques or forces to grow without bound. Therefore, it must also be avoided. On the other hand, a PSIK imposes a constraint on the end-effector position but provides freedom for the active joint variables. Similarly, an MSIK imposes a constraint on the end-effector motion but provides freedom for the rates of the active joint variables. A PSIK or MSIK need not be avoided if the constraint it imposes on the position or motion of the end-effector is acceptable or if the task can be planned to be compatible with that constraint. Besides, with such a compatible task, a PSIK or MSIK may even be advantageous, because the freedom it provides for the active joint variables can sometimes be used for a secondary purpose. This paper is also concerned with the multiplicities of forward kinematics in the assembly modes of the manipulator and the multiplicities of inverse kinematics in the posture modes of the legs. It is shown that the assembly mode changing poses of the manipulator are the same as the MSFK poses, and the posture mode changing poses of the legs are the same as the MSIK poses.
The motivic Hilbert zeta function of a variety
is the generating function for classes in the Grothendieck ring of varieties of Hilbert schemes of points on
. In this paper, the motivic Hilbert zeta function of a reduced curve is shown to be rational.
be a quasi-homogeneous polynomial with an isolated singularity in
. We compute the length of the
generated by complex powers of
in terms of the Hodge filtration on the top cohomology of the Milnor fiber. When
we obtain one more than the reduced genus of the singularity (
the exceptional fiber of a resolution of singularities). We conjecture that this holds without the quasi-homogeneous assumption. We also deduce that the quotient
is nonzero when
is a root of the
(which Saito recently showed fails to hold in the inhomogeneous case). We obtain these results by comparing these
-modules to those defined by Etingof and the second author which represent invariants under Hamiltonian flow.
This paper deals with the kinematic analysis and enumeration of singularities of the six degree-of-freedom 3-RPS-3-SPR series–parallel manipulator (S–PM). The characteristic tetrahedron of the S–PM is established, whose degeneracy is bijectively mapped to the serial singularities of the S–PM. Study parametrization is used to determine six independent parameters that characterize the S–PM and the direct kinematics problem is solved by mapping the transformation matrix between the base and the end-effector to a point in ℙ7. The inverse kinematics problem of the 3-RPS-3-SPR S–PM amounts to find the location of three points on three lines. This problem leads to a minimal octic univariate polynomial with four quadratic factors.
We prove two main results on Denjoy–Carleman classes: (1) a composite function theorem which asserts that a function
in a quasianalytic Denjoy–Carleman class
, which is formally composite with a generically submersive mapping
, at a single given point in the source (or in the target) of
can be written locally as
belongs to a shifted Denjoy–Carleman class
; (2) a statement on a similar loss of regularity for functions definable in the
-minimal structure given by expansion of the real field by restricted functions of quasianalytic class
. Both results depend on an estimate for the regularity of a
of the equation
as above. The composite function result depends also on a quasianalytic continuation theorem, which shows that the formal assumption at a given point in (1) propagates to a formal composition condition at every point in a neighbourhood.
with rational singularities, we conjecture that if
is a resolution of singularities whose reduced exceptional divisor
has simple normal crossings, then
We prove this when
has isolated singularities and when it is a toric variety. We deduce that for a divisor
with isolated rational singularities on a smooth complex
, the generation level of Saito’s Hodge filtration on the localization
is at most
We show that the anti-canonical volume of an
-Fano variety is bounded from above by certain invariants of the local singularities, namely
for ideals and the normalized volume function for real valuations. This refines a recent result by Fujita. As an application, we get sharp volume upper bounds for Kähler–Einstein Fano varieties with quotient singularities. Based on very recent results by Li and the author, we show that a Fano manifold is K-semistable if and only if a de Fernex–Ein–Mustaţă type inequality holds on its affine cone.
We define and study twisted Alexander-type invariants of complex hypersurface complements. We investigate torsion properties for the twisted Alexander modules and extend the local-to-global divisibility results of Maxim and of Dimca and Libgober to the twisted setting. In the process, we also study the splitting fields containing the roots of the corresponding twisted Alexander polynomials.
In this paper, we study the singularities of a general hyperplane section
of a three-dimensional quasi-projective variety
over an algebraically closed field of characteristic
. We prove that if
has only canonical singularities, then
has only rational double points. We also prove, under the assumption that
, that if
has only klt singularities, then so does
We prove a compactness theorem for metrics with bounded integral curvature on a fixed closed surface
. As a corollary we obtain a new convergence result for sequences of metrics with conical singularities, where an accumulation of singularities is allowed.