scholarly journals Hodge theory on Cheeger spaces

2016 ◽  
Vol 0 (0) ◽  
Author(s):  
Pierre Albin ◽  
Eric Leichtnam ◽  
Rafe Mazzeo ◽  
Paolo Piazza
Keyword(s):  
Boundary Conditions ◽  
Hodge Theory ◽  
Intersection Theory ◽  
Ideal Boundary ◽  
Compact Resolvent ◽  
De Rham

AbstractWe extend the study of the de Rham operator with ideal boundary conditions from the case of isolated conic singularities, as analyzed by Cheeger, to the case of arbitrary stratified pseudomanifolds. We introduce a class of ideal boundary conditions and the notion of mezzoperversity, which intermediates between the standard lower and upper middle perversities in intersection theory, as interpreted in this de Rham setting, and show that the de Rham operator with these boundary conditions is Fredholm and has compact resolvent. We also prove an isomorphism between the resulting Hodge and

scholarly journals The geometry of Hida families II: -adic -modules and -adic Hodge theory

2018 ◽  
Vol 154 (4) ◽  
pp. 719-760
Author(s):  
Bryden Cais
Keyword(s):  
Galois Representations ◽  
Hodge Theory ◽  
Geometric Proof ◽  
De Rham Cohomology ◽  
Etale Cohomology ◽  
The Family ◽  
Étale Cohomology ◽  
De Rham ◽  
Hida Families ◽  
And Control

We construct the $\unicode[STIX]{x1D6EC}$-adic crystalline and Dieudonné analogues of Hida’s ordinary $\unicode[STIX]{x1D6EC}$-adic étale cohomology, and employ integral $p$-adic Hodge theory to prove $\unicode[STIX]{x1D6EC}$-adic comparison isomorphisms between these cohomologies and the $\unicode[STIX]{x1D6EC}$-adic de Rham cohomology studied in Cais [The geometry of Hida families I:$\unicode[STIX]{x1D6EC}$-adic de Rham cohomology, Math. Ann. (2017), doi:10.1007/s00208-017-1608-1] as well as Hida’s $\unicode[STIX]{x1D6EC}$-adic étale cohomology. As applications of our work, we provide a ‘cohomological’ construction of the family of $(\unicode[STIX]{x1D711},\unicode[STIX]{x1D6E4})$-modules attached to Hida’s ordinary $\unicode[STIX]{x1D6EC}$-adic étale cohomology by Dee [$\unicode[STIX]{x1D6F7}$–$\unicode[STIX]{x1D6E4}$modules for families of Galois representations, J. Algebra 235 (2001), 636–664], and we give a new and purely geometric proof of Hida’s finiteness and control theorems. We also prove suitable $\unicode[STIX]{x1D6EC}$-adic duality theorems for each of the cohomologies we construct.

scholarly journals Indefinite eigenvalue problem with eigenparameter in the two boundary conditions

1998 ◽  
Vol 21 (4) ◽  
pp. 775-784
Author(s):  
S. F. M. Ibrahim
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Eigenfunction Expansion ◽  
Selfadjoint Operator ◽  
Order Differential Equation ◽  
Expansion Theorem ◽  
Compact Resolvent ◽  
Second Order Differential Equation ◽  
Eigenvalue Parameter

The object of this paper is to establish an expansion theorem for a regular indefinite eigenvalue problem of second order differential equation with an eigenvalue parameter,λin the two boundary conditions. We associated with this problem aJ-selfadjoint operator with compact resolvent defined in a suitable Krein space and then we develop an associated eigenfunction expansion theorem.

scholarly journals On admissible tensor products in p-adic Hodge theory

2013 ◽  
Vol 149 (3) ◽  
pp. 417-429 ◽  
Author(s):  
Giovanni Di Matteo
Keyword(s):  
Tensor Product ◽  
Tensor Products ◽  
Hodge Theory ◽  
Schur Functor ◽  
De Rham

AbstractWe prove that if W and W′ are non-zero B-pairs whose tensor product is crystalline (or semi-stable or de Rham or Hodge–Tate), then there exists a character μ such that W(μ−1) and W′(μ) are crystalline (or semi-stable or de Rham or Hodge–Tate). We also prove that if W is a B-pair and if F is a Schur functor (for example Sym n or Λn) such that F(W) is crystalline (or semi-stable or de Rham or Hodge–Tate) and if the rank of W is sufficiently large, then there is a character μ such that W(μ−1) is crystalline (or semi-stable or de Rham or Hodge–Tate). In particular, these results apply to p-adic representations.

scholarly journals Hodge theory in the Sobolev topology for the de Rham complex

1998 ◽  
Vol 131 (622) ◽  
pp. 0-0 ◽  
Author(s):  
Luigi Fontana ◽  
Steven G. Krantz ◽  
Marco M. Peloso
Keyword(s):  
Hodge Theory ◽  
De Rham Complex ◽  
Rham Complex ◽  
De Rham

The Dynamics of MEMS Arches of Non-Ideal Boundary Conditions

2011 ◽  
Author(s):  
Sami A. Alkharabsheh ◽  
Mohammad I. Younis
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Electrostatic Force ◽  
Dynamical Behavior ◽  
Experimental Investigations ◽  
Harmonic Load ◽  
Ideal Boundary ◽  
Shooting Technique ◽  
Softening Behavior ◽  
The Stability

We present an investigation into the dynamics of MEMS arches when actuated electrically including the effect of their flexible (non-ideal) supports. First, the eigenvalue problem of a nonlinear Euler-Bernoulli shallow arch with torsional and transversal springs at the boundaries is solved analytically. Several results are shown to demonstrate the possibility of tuning the theoretically obtained natural frequencies of an arch to match the experimentally measured. Then, simulation results are shown for the forced vibration response of an arch when excited by a DC electrostatic force superimposed to an AC harmonic load. Shooting technique is utilized to find periodic motions. The stability of the captured periodic motion is examined using the Floquet theory. The results show several jumps in the response during snap-through motion and pull-in. Theoretical and experimental investigations are conducted on a microfabricated curved beam actuated electrically. Results show softening behavior and superharmonic resonances. It is demonstrated that non-ideal boundary conditions can have significant effect on the qualitative dynamical behavior of the MEMS arch, including its natural frequencies, snap-through behavior, and dynamic pull-in.

Energy Method for the Calculation of High-Pier's Effective Length Factor at the Finished Stage

2013 ◽  
Vol 361-363 ◽  
pp. 1115-1118
Author(s):  
Peng Liu ◽  
Jie Rui ◽  
Bo Lei ◽  
Fei Zheng
Keyword(s):  
Boundary Conditions ◽  
Energy Method ◽  
Good Accuracy ◽  
Shape Function ◽  
Great Influence ◽  
Effective Length ◽  
Ideal Boundary ◽  
Effective Length Factor ◽  
High Pier ◽  
The One

This paper establishes the shape function of high-pier with non-ideal boundary conditions in the top and uses the energy method to calculate its critical load. Then its effective length factor is achieved by using Euler's formula. Further, the FEM and energy method are respect used to calculate the effective length factor of the engineering example and comparative analysis is carried on. Results show that: The non-ideal boundary conditions have great influence on the effective length factor and should be considered in the calculation. The result from the formula of energy method is nearly the same as the one from the FEM which demonstrates this method is of good accuracy to calculate the effective length factor of high-pier. In addition, it is also of great convenience in the design of high-piers.

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