scholarly journals p-adic distribution of CM points and Hecke orbits, I : Convergence towards the Gauss point

2020 ◽  
Vol 14 (5) ◽  
pp. 1239-1290
Author(s):  
Sebastián Herrero ◽  
Ricardo Menares ◽  
Juan Rivera-Letelier
Keyword(s):  
Gauss Point ◽  
Cm Points

Reconstruction of complex shaped crack from ECT signals based on a fast forward solver using an advanced multi-media element

2020 ◽  
Vol 64 (1-4) ◽  
pp. 621-629
Author(s):  
Yingsong Zhao ◽  
Cherdpong Jomdecha ◽  
Shejuan Xie ◽  
Zhenmao Chen ◽  
Pan Qi ◽  
...  
Keyword(s):  
Coefficient Matrix ◽  
Crack Edge ◽  
Numerical Accuracy ◽  
Gauss Point ◽  
Current Testing ◽  
Efficient Simulation ◽  
Shaped Crack ◽  
Multi Media ◽  
Profile Reconstruction ◽  
Crack Profile

In this paper, the conventional database type fast forward solver for efficient simulation of eddy current testing (ECT) signals is upgraded by using an advanced multi-media finite element (MME) at the crack edge for treating inversion of complex shaped crack. Because the analysis domain is limited at the crack region, the fast forward solver can significantly improve the numerical accuracy and efficiency once the coefficient matrices of the MME can be properly calculated. Instead of the Gauss point classification, a new scheme to calculate the coefficient matrix of the MME is proposed and implemented to upgrade the ECT fast forward solver. To verify its efficiency and the feasibility for reconstruction of complex shaped crack, several cracks were reconstructed through inverse analysis using the new MME scheme. The numerical results proved that the upgraded fast forward solver can give better accuracy for simulating ECT signals, and consequently gives better crack profile reconstruction.

scholarly journals Non-linear deflection and stress analysis of laminated composite sandwich plate with elliptical cutout under different transverse loadings in hygro-thermal environment

2020 ◽  
Vol 7 (1) ◽  
pp. 80-100
Author(s):  
Rahul Kumar ◽  
Achchhe Lal ◽  
B. M. Sutaria
Keyword(s):  
Stress Concentration ◽  
Sandwich Plate ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Gauss Point ◽  
Composite Sandwich ◽  
Aspect Ratios ◽  
Present Solution ◽  
Non Linear

AbstractIn this paper, non-linear transverse deflection, stress and stress concentration factors (SCF) of isotropic and laminated composite sandwich plate (LCSP) with and without elliptical cutouts subjected to various trans-verse loadings in hygrothermal environment are studied. The basic formulation is based on secant function-based shear deformation theory (SFSDT) with von-Karman nonlinearity. The governing equation of non-linear deflection is derived using C0 finite element method (FEM) through minimum potential energy approach. Normalized trans-verse maximum deflections (NTMD) along with stress concentration factor is determined by using Newton’s Raphson method through Gauss point stress extrapolation. Influence of fiber orientations, load parameters, fiber volume fractions, plate span to thickness ratios, aspect ratios, thickness of core and face, position of core, boundary conditions, environmental conditions and types of transverse loading in MATLAB R2015a environment are examined. The numerical results using present solution methodology are verified with the results available in the literatures.

scholarly journals The Chowla–Selberg formula for abelian CM fields and Faltings heights

2015 ◽  
Vol 152 (3) ◽  
pp. 445-476 ◽  
Author(s):  
Adrian Barquero-Sanchez ◽  
Riad Masri
Keyword(s):  
Gamma Function ◽  
Abelian Varieties ◽  
Modular Function ◽  
Rational Numbers ◽  
Explicit Formulas ◽  
Arithmetic Properties ◽  
Hilbert Modular ◽  
Cm Points ◽  
Analogous Function

In this paper we establish a Chowla–Selberg formula for abelian CM fields. This is an identity which relates values of a Hilbert modular function at CM points to values of Euler’s gamma function ${\rm\Gamma}$ and an analogous function ${\rm\Gamma}_{2}$ at rational numbers. We combine this identity with work of Colmez to relate the CM values of the Hilbert modular function to Faltings heights of CM abelian varieties. We also give explicit formulas for products of exponentials of Faltings heights, allowing us to study some of their arithmetic properties using the Lang–Rohrlich conjecture.

scholarly journals On two arithmetic theta lifts

2018 ◽  
Vol 154 (10) ◽  
pp. 2090-2149 ◽  
Author(s):  
Stephan Ehlen ◽  
Siddarth Sankaran
Keyword(s):  
Modular Forms ◽  
Theta Functions ◽  
Chow Group ◽  
Shimura Varieties ◽  
Green Functions ◽  
Theta Lift ◽  
Moderate Growth ◽  
Generating Series ◽  
Cm Points ◽  
The Difference

Our aim is to clarify the relationship between Kudla’s and Bruinier’s Green functions attached to special cycles on Shimura varieties of orthogonal and unitary type, which play a key role in the arithmetic geometry of these cycles in the context of Kudla’s program. In particular, we show that the generating series obtained by taking the differences of the two families of Green functions is a non-holomorphic modular form and has trivial (cuspidal) holomorphic projection. Along the way, we construct a section of the Maaß lowering operator for moderate growth forms valued in the Weil representation using a regularized theta lift, which may be of independent interest, as it in particular has applications to mock modular forms. We also consider arithmetic-geometric applications to integral models of $U(n,1)$ Shimura varieties. Each family of Green functions gives rise to a formal arithmetic theta function, valued in an arithmetic Chow group, that is conjectured to be modular; our main result is the modularity of the difference of the two arithmetic theta functions. Finally, we relate the arithmetic heights of the special cycles to special derivatives of Eisenstein series, as predicted by Kudla’s conjecture, and describe a refinement of a theorem of Bruinier, Howard and Yang on arithmetic intersections against CM points.

scholarly journals Equations with powers of singular moduli

2019 ◽  
Vol 15 (03) ◽  
pp. 445-468 ◽  
Author(s):  
Antonin Riffaut
Keyword(s):  
Rational Number ◽  
The Other ◽  
Other Hand ◽  
Singular Moduli ◽  
Cm Points ◽  
The One ◽  
Straight Lines ◽  
Positive Integers

We treat two different equations involving powers of singular moduli. On the one hand, we show that, with two possible (explicitly specified) exceptions, two distinct singular moduli [Formula: see text] such that the numbers [Formula: see text], [Formula: see text] and [Formula: see text] are linearly dependent over [Formula: see text] for some positive integers [Formula: see text], must be of degree at most [Formula: see text]. This partially generalizes a result of Allombert, Bilu and Pizarro-Madariaga, who studied CM-points belonging to straight lines in [Formula: see text] defined over [Formula: see text]. On the other hand, we show that, with obvious exceptions, the product of any two powers of singular moduli cannot be a non-zero rational number. This generalizes a result of Bilu, Luca and Pizarro-Madariaga, who studied CM-points belonging to a hyperbola [Formula: see text], where [Formula: see text].

Damage Identification in Continuum Structures From Vibration Modal Data

1997 ◽  
Vol 503 ◽  
Author(s):  
H. P. Chen ◽  
N. Bicanic
Keyword(s):  
Structural Damage ◽  
Damage Identification ◽  
Structural Parameters ◽  
Computational Technique ◽  
Gauss Point ◽  
Continuum Structures ◽  
Modal Data ◽  
Stiffness Matrices ◽  
Direct Iteration ◽  
Vibration Modal

ABSTRACTA novel procedure for damage identification of continuum structures is proposed, where both the location and the extent of structural damage in continuum structures can be correctly determined using only a limited amount of measurements of incomplete modal data. On the basis of the exact relationship between the changes of structural parameters and modal parameters, a computational technique based on direct iteration and directly using incomplete modal data is developed to determine damage in structure. Structural damage is assumed to be associated ith a proportional (scalar) reduction of the original element stiffness matrices, equivalent to a scalar reduction of the material modulus, which characterises at Gauss point level. Finally, numerical examples for plane stress problem and plate bending problem are utilised to demonstrate the effectiveness of the proposed approach.

scholarly journals Special values of the Gamma function at CM points

2014 ◽  
Vol 36 (3) ◽  
pp. 355-373 ◽  
Author(s):  
M. Ram Murty ◽  
Chester Weatherby
Keyword(s):  
Gamma Function ◽  
Special Values ◽  
Cm Points

ALGEBRAIC INDEPENDENCE OF VALUES OF MODULAR FORMS

2011 ◽  
Vol 07 (04) ◽  
pp. 1065-1074 ◽  
Author(s):  
SANOLI GUN ◽  
M. RAM MURTY ◽  
PURUSOTTAM RATH
Keyword(s):  
Recent Work ◽  
Modular Forms ◽  
Fourier Coefficients ◽  
Algebraic Independence ◽  
Singular Values ◽  
Critical Values ◽  
Cm Points

We investigate values of modular forms with algebraic Fourier coefficients at algebraic arguments. As a consequence, we conclude about the nature of zeros of such modular forms. In particular, the singular values of modular forms (that is, values at CM points) are related to the recent work of Nesterenko. As an application, we deduce the transcendence of critical values of certain Hecke L-series. We also discuss how these investigations generalize to the case of quasi-modular forms with algebraic Fourier coefficients.

Microsurgical anatomy of the distal anterior cerebral artery

1978 ◽  
Vol 49 (2) ◽  
pp. 204-228 ◽  
Author(s):  
David Perlmutter ◽  
Albert L. Rhoton
Keyword(s):  
Corpus Callosum ◽  
Cerebral Artery ◽  
Anterior Cerebral Artery ◽  
Internal Capsule ◽  
Optic Chiasm ◽  
Anterior Communicating Artery ◽  
Microsurgical Anatomy ◽  
Content Type ◽  
Cm Points ◽  
Distal Anterior Cerebral Artery

✓ The microsurgical anatomy of the distal anterior cerebral artery (ACA) has been defined in 50 cerebral hemispheres. The distal ACA, the portion beginning at the anterior communicating artery (ACoA), was divided into four segments (A2 through A5) according to Fischer. The distal ACA gave origin to central and cerebral branches. The central branches passed to the optic chiasm, suprachiasmatic area, and anterior forebrain below the corpus callosum. The cerebral branches were divided into cortical, subcortical, and callosal branches. The most frequent site of origin of the cortical branches was as follows: orbitofrontal and frontopolar arteries, A2; the anterior and middle internal frontal and callosomarginal arteries, A3; the paracentral artery, A4; and the superior and inferior parietal arteries, A5. The posterior internal frontal artery arose with approximately equal frequency from A3 and A4 and the callosomarginal artery. All the cortical branches arose more frequently from the pericallosal than the callosomarginal artery. Of the major cortical branches, the internal frontal and paracentral arteries arose most frequently from the callosomarginal artery. The distal ACA of one hemisphere sent branches to the contralateral hemisphere in 64% of brains. The anterior portions of the hemisphere between the 5-cm and 15-cm points on the circumferential line showed the most promise of revealing a recipient artery of sufficient size for an extracranial-intracranial artery anastomosis. The distal ACA was the principal artery supplying the corpus callosum. The recurrent artery, which arose from the A2 segment in 78% of hemispheres, sent branches into the subcortical area around the anterior limb of the internal capsule.

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