scholarly journals Lelong numbers, complex singularity exponents, and Siu's semicontinuity theorem

2017 ◽  
Vol 355 (4) ◽  
pp. 415-419
Author(s):  
Qi'an Guan ◽  
Xiangyu Zhou
Keyword(s):  
Complex Singularity ◽  
Lelong Numbers ◽  
Singularity Exponents

Stress Singularities near Interface Crack Tip for Mode II of Orthotropic Bi-Material

2014 ◽  
Vol 1004-1005 ◽  
pp. 473-478
Author(s):  
Mu Yang Li ◽  
Jun Lin Li ◽  
Xiu Feng Xie
Keyword(s):  
Composite Material ◽  
Interface Crack ◽  
Crack Tip ◽  
Mode Ii ◽  
Stress Singularities ◽  
Intensity Factors ◽  
Complex Singularity ◽  
Singularity Exponents ◽  
Analytic Expressions ◽  
Stress Functions

Using the method of composite material complex and constructing new stress functions with complex singularity exponents, the problem of singularities near interface crack tip for mode II of orthotropic bi-material is studied. Boundary value problems of generalized bi-harmonic equations can be solved with the help of boundary conditions, then four kinds of stress singularities are deduced, respectively, such as the constant singularity at λ=-1/2, the non-constant singularity at λ=-1/2+ε , the constant oscillation singularity at λ=-1/2+iε, and non-constant oscillation singularity at λ=-1/2+c+iε. For each case, the analytic expressions for stress intensity factors near the central-penetrated interface crack tip for mode II of orthotropic bi-material are obtained.

Restriction formula and subadditivity property related to multiplier ideal sheaves

2020 ◽  
Vol 2020 (769) ◽  
pp. 1-33
Author(s):  
Qi’an Guan ◽  
Xiangyu Zhou
Keyword(s):  
Necessary Conditions ◽  
Extremal Case ◽  
Complex Singularity ◽  
Plurisubharmonic Functions ◽  
Singularity Exponents ◽  
Ideal Sheaves ◽  
Multiplier Ideal

AbstractWe give a restriction formula on jumping numbers which is a reformulation of Demailly–Ein–Lazarsfeld’s important restriction formula for multiplier ideal sheaves and a generalization of Demailly–Kollár’s important restriction formula on complex singularity exponents, and then we establish necessary conditions for the extremal case in the reformulated formula; we pose the subadditivity property on the complex singularity exponents of plurisubharmonic functions which is a generalization of Demailly–Kollár’s fundamental subadditivity property, and then we establish necessary conditions for the extremal case in the generalization. We also obtain two sharp relations on jumping numbers, introduce a new invariant of plurisubharmonic singularities and get its decreasing property for consecutive differences.

scholarly journals Relative non-pluripolar product of currents

2021 ◽  
Author(s):  
Duc-Viet Vu
Keyword(s):  
Kähler Manifold ◽  
Monotonicity Property ◽  
Necessary Condition ◽  
Positive Current ◽  
Lelong Numbers ◽  
Kahler Manifold ◽  
Closed Positive Current ◽  
Positive Currents ◽  
Compact Kähler Manifold

AbstractLet X be a compact Kähler manifold. Let $$T_1, \ldots , T_m$$ T 1 , … , T m be closed positive currents of bi-degree (1, 1) on X and T an arbitrary closed positive current on X. We introduce the non-pluripolar product relative to T of $$T_1, \ldots , T_m$$ T 1 , … , T m . We recover the well-known non-pluripolar product of $$T_1, \ldots , T_m$$ T 1 , … , T m when T is the current of integration along X. Our main results are a monotonicity property of relative non-pluripolar products, a necessary condition for currents to be of relative full mass intersection in terms of Lelong numbers, and the convexity of weighted classes of currents of relative full mass intersection. The former two results are new even when T is the current of integration along X.

scholarly journals Variation of singular Kähler–Einstein metrics: Positive Kodaira dimension

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Junyan Cao ◽  
Henri Guenancia ◽  
Mihai Păun
Keyword(s):  
General Type ◽  
Einstein Metrics ◽  
Kodaira Dimension ◽  
Einstein Metric ◽  
Canonical Bundle ◽  
Fiber Space ◽  
Generic Fiber ◽  
Lelong Numbers ◽  
Kähler Einstein Metrics

Abstract Given a Kähler fiber space p : X → Y {p:X\to Y} whose generic fiber is of general type, we prove that the fiberwise singular Kähler–Einstein metric induces a semipositively curved metric on the relative canonical bundle K X / Y {K_{X/Y}} of p. We also propose a conjectural generalization of this result for relative twisted Kähler–Einstein metrics. Then we show that our conjecture holds true if the Lelong numbers of the twisting current are zero. Finally, we explain the relevance of our conjecture for the study of fiberwise Song–Tian metrics (which represent the analogue of KE metrics for fiber spaces whose generic fiber has positive but not necessarily maximal Kodaira dimension).

Multifractal analysis of uterine electromyography signals to differentiate term and preterm conditions

2019 ◽  
Vol 233 (3) ◽  
pp. 362-371
Author(s):  
N Punitha ◽  
S Ramakrishnan
Keyword(s):  
Gestational Age ◽  
Multifractal Analysis ◽  
Moving Average ◽  
Primary Source ◽  
Scaling Exponents ◽  
Average Technique ◽  
Singularity Exponents ◽  
Student’S T ◽  
Uterine Electromyography ◽  
Electromyography Signals

In this study, an attempt has been made to identify the origin of multifractality in uterine electromyography signals and to differentiate term (gestational age > 37 weeks) and preterm (gestational age ≤ 37 weeks) conditions by multifractal detrended moving average technique. The signals obtained from a publicly available database, recorded from the abdominal surface during the second trimester, are used in this study. The signals are preprocessed and converted to shuffle and surrogate series to examine the source of multifractality. Multifractal detrended moving average algorithm is applied on all the signals. The presence of multifractality is verified using scaling exponents, and multifractal spectral features are extracted from the spectrum. The variation of multifractal features in term and preterm conditions is analyzed statistically using Student’s t-test. The results of scaling exponents show that the uterine electromyography or electrohysterography signals reveal multifractal characteristics in term and preterm conditions. Further investigation indicates the existence of long-range correlation as the primary source of multifractality. Among all extracted features, strength of multifractality, exponent index, and maximum and peak singularity exponents are statistically significant ( p < 0.05) in differentiating term and preterm conditions. The coefficient of variation is found to be lower for strength of multifractality and peak singularity exponent, which reveal that these features exhibit less inter-subject variance. Hence, it appears that multifractal analysis can aid in the diagnosis of preterm or term delivery of pregnant women.

Considering the Ability for Nonsingular Transitions of Assembly Mode for Dimensional Synthesis

2009 ◽  
Author(s):  
Oscar Altuzarra ◽  
Vi´ctor Petuya ◽  
Mo´nica Uri´zar ◽  
Alfonso Herna´ndez
Keyword(s):  
Parallel Manipulator ◽  
Analytical Procedure ◽  
Parallel Manipulators ◽  
Dimensional Synthesis ◽  
Complex Singularity ◽  
Algebraic Expressions ◽  
Free Region ◽  
Dimensional Parameters ◽  
Cusp Points ◽  
Singularity Locus

An important difficulty in the design of parallel manipulators is their reduced practical workspace, due mainly to the existence of a complex singularity locus within the workspace. The workspace is divided into singularity-free regions according to assembly modes and working modes, and the dimensioning of parallel manipulators aims at the maximization of those regions. It is a common practice to restrict the manipulator’s motion to a specific singularity-free region. However, a suitable motion planning can enlarge the operational workspace by means of transitions of working mode and/or assembly mode. In this paper, the authors present an analytical procedure for obtaining the loci of cusp points of a parallel manipulator as algebraic expressions of its dimensional parameters. The purpose is to find an optimal design for non-singular transitions to be possible.

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