Reduction of the singularities of codimension one singular foliations in dimension three
By Felipe Cano Contents 0. Introduction 1. Blowing-up singular foliations 1.1. Adapted singular foliations 1.2. Permissible centers 1.3. Vertical invariants 1.4. First properties of presimple singularities 2. Global strategy 2.1. Reduction to presimple singularities. Statement 2.2. Good points. Bad points. Equi-reduction 2.3. Finiteness of bad points 2.4. The inﬂuency locus 2.5. The local control theorem 2.6. Destroying cycles 2.7. Global criteria of blowing-up 3. Local control 3.1.
We establish an exact relation between self-avoiding branched polymers in D + 2 continuum dimensions and the hard-core continuum gas at negative activity in D dimensions. We review conjectures and results on critical exponents for D + 2 = 2, 3, 4 and show that they are corollaries of our result. We explain the connection (ﬁrst proposed by Parisi and Sourlas) between branched polymers in D + 2 dimensions and the Yang-Lee edge singularity in D dimensions.
Nowadays, huge amount of multimedia data are being constantly generated in
various forms from various places around the world. With ever increasing complexity
and variability of multimedia data, traditional rule-based approaches
where humans have to discover the domain knowledge and encode it into a
set of programming rules are too costly and incompetent for analyzing the
contents, and gaining the intelligence of this glut of multimedia data.
The challenges in data complexity and variability have led to revolutions
in machine learning techniques.
One of the major problems of K-means is that one must use dense vectors for its centroids, and therefore it is infeasible to store such huge vectors in memory when the feature space is high-dimensional. We address this issue by using feature hashing (Weinberger et al., 2009), a dimension-reduction technique, which can reduce the size of dense vectors while retaining sparsity of sparse vectors.
Some years ago a consortium of enterprises and a university from different European countries and industrial sectors was established
to work together in the development of lighter lead–acid batteries for electrical and conventional vehicles with new innovative materials
and process techniques, with the final goal of increasing the energy density by means of a battery weight reduction. Its main idea was to
substitute the heavy lead alloy grids mechanical support of the active masses and collectors of the current produced during the charge
and discharge reactions.
Main Receive Aperture and Analog Beamforming Data to be Processed The Processing Needs and Major Issues Temporal DOF Reduction Adaptive Filtering with Needed and Sample-Supportable DOF and Embedded CFAR Processing 70.6 Scan-To-Scan Track-Before-Detect Processing 70.7 Real-Time Nonhomogeneity Detection and Sample Conditioning and Selection 70.8 Space or Space-Range Adaptive Pre-Suppression of Jammers 70.9 A STAP Example with a Revisit to Analog Beamforming 70.
IFA (“Institutions for Floods in Asia”) project focuses on institutional dimension of river floods risk reduction in the Asian countries that along with structural approaches constitutes the core in human responses to floods. IFA aggregates and compares results of country-based research in order to further explore the problem How to strengthen capacities and performance of institutions to reduce flood risks. Rich evidence for testing IFA approaches is provided from recent case-studies of big river floods in Bangladesh, Burma/Myanmar, Japan, Russia,......
Distance, range number, bilaterial tolerance Width, range number Constant Helix diameter Dimensional operator Young's modulus Error using n applications of Simpson's rule The /th exponent Function The /th derivative of function / Fundamental dimension of force, fractional reduction of interval of uncertainty Function Function, ordinate spacing Index Second area moment, value of integral Approximate value of integral using i applications of Simpson's rule Spring rate
It is more than a century since Karl Pearson invented the concept of Principal
Component Analysis (PCA). Nowadays, it is a very useful tool in data analysis in
many fields. PCA is the technique of dimensionality reduction, which transforms
data in the high-dimensional space to space of lower dimensions. The advantages of
this subspace are numerous. First of all, the reduced dimension has the effect of
retaining the most of the useful information while reducing noise and other
undesirable artifacts. Secondly, the time and memory that used in data processing
This discussion first reviews early theoretical clarifications of how population
health change is linked to reduction in mortality at older ages. We briefly
discuss evidence of trends prior to recent decades, subsequent understanding of
trends from empirical models of health, and developments in understanding the
dimensions of health and the process of health change for an aging population.
Recent trends in each dimension of health are then reviewed, ending with a discussion
of trends in healthy life, which is a combination of mortality and morbidity
MINIMIZING ENGINEERING EFFORT
Charles R. Mischke, Ph.D., P.E. Professor Emeritus of Mechanical Engineering Iowa State University Ames, Iowa
11.1 INTRODUCTION/11.2 11.2 REDUCING THE NUMBER OF EXPERIMENTS /11.3 11.3 SIMILITUDE/11.7 11.4 OPTIMALITY/11.9 11.5 QUADRATURE/11.13 11.6 CHECKING/11.15 REFERENCES/11.
The general picture is that older people of today are healthier than older people
of two decades ago. There have been improvements in most dimensions of health.
People live longer and have fewer disabilities, have less functioning loss, and
report themselves to be in better health. Over time there has been some reduction
in risk from smoking and a lowering of cholesterol and average triglyceride levels.
However, weight increase has been notable during this period.
Let G be a connected reductive group. The late Ramanathan gave a notion of (semi)stable principal G-bundle on a Riemann surface and constructed a projective moduli space of such objects. We generalize Ramanathan’s notion and construction to higher dimension, allowing also objects which we call semistable principal G-sheaves, in order to obtain a projective moduli space: a principal G-sheaf on a projective variety X is a triple (P, E, ψ), where E is a torsion free sheaf on X, P is a principal G-bundle on the open set U where E is locally free and ψ is an isomorphism...
Historically rich in novel, subtle, often controversial ideas, Molecular Bi-
ology has lately become heir to a huge legacy of standardized data in the
form of polynucleotide and polypeptide sequences. Fred Sanger received
two, well deserved Nobel Prizes for his seminal role in developing the basic
technology needed for this reduction of core biological information to one
This document is the result of efforts by the DAC Working Party on Development Co-
operation and Environment to clarify the key linkages between poverty and environmental
degradation, with special attention paid to their gender dimension - and the policy implications at the
local, sectoral and national levels. The objective is not to provide a comprehensive coverage of all
pertinent issues, but to provide an analytical road-map which could be used as reference for more
detailed sector and country-specific examinations.
Work is underway to review and update the Bank’s policy state-
ments on investment and adjustment lending; these reviews will
provide the framework for considering appropriate integration of the
gender dimension into these policy statements.
Because analytical work and JSAs are central to this strategy, the
Bank’s Poverty Reduction and Economic Management Network will
play an important role in implementation.
One of the important tools of geometric mechanics is reduction theory (either
Lagrangian or Hamiltonian),which provides a well-developed method for dealing
with dynamic constraints. In this theory the dynamic constraints and the sym-
metry group are used to lower the dimension of the system by constructing an
associated reduced system. We develop the Lagrangian version of this theory for
nonholonomic systems in this paper. We have focussed on Lagrangian systems
because this is a convenient context for applications to control theory. ...