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Books > Science & Mathematics > Mathematics
Hoermander operators are a class of linear second order partial
differential operators with nonnegative characteristic form and
smooth coefficients, which are usually degenerate
elliptic-parabolic, but nevertheless hypoelliptic, that is highly
regularizing. The study of these operators began with the 1967
fundamental paper by Lars Hoermander and is intimately connected to
the geometry of vector fields.Motivations for the study of
Hoermander operators come for instance from
Kolmogorov-Fokker-Planck equations arising from modeling physical
systems governed by stochastic equations and the geometric theory
of several complex variables. The aim of this book is to give a
systematic exposition of a relevant part of the theory of
Hoermander operators and vector fields, together with the necessary
background and prerequisites.The book is intended for self-study,
or as a reference book, and can be useful to both younger and
senior researchers, already working in this area or aiming to
approach it.
500 Ways to Achieve Your Highest Score
We want you to succeed on the Math sections of the ACT. That's
why we've selected these 500 questions to help you study more
effectively, use your preparation time wisely, and get your best
score. These questions are similar to the ones you'll find on the
ACT, so you will know what to expect on test day. Each question
includes a concise, easy-to-follow explanation in the answer key
for your full understanding of the concepts. Whether you have been
studying all year or are doing a last-minute review, "McGraw-Hill's
500 ACT Math Questions to Know by Test Day" will help you achieve
the high score you desire.
Sharpen your subject knowledge, and build your test-taking
confidence with: 500 ACT Math questions Full explanations for each
question in the answer key A format parallel to that of the ACT
exam
Perfect and amicable numbers, as well as a majority of classes of
special numbers, have a long and rich history connected with the
names of many famous mathematicians. This book gives a complete
presentation of the theory of two classes of special numbers
(perfect numbers and amicable numbers) and gives much of their
properties, facts and theorems with full proofs of them, as well as
their numerous analogue and generalizations.
This study guide for Varsity Maths Preparation has been compiled by
Emeritus Professor John Webb in response to the dire challenges
experienced by first year university students, in Mathematics as
well as in courses in Science, Engineering and Business Science,
all heavily dependent on mathematical thinking. By working through
the problem sets in this self-study book, learners should develop
and test their skills, on their own, in areas such as algebraic
expertise, trigonometry skills, word problems, geometric insight,
numerical facility, logical reasoning and flexible thinking. This
cannot be taught and is best achieved without assistance and
timeously, i.e. prior to students entering university. The
problem-solving techniques which learners could acquire from
dedicated, independent use of this outstanding booklet will
contribute significantly to their success in the National Benchmark
tests (NBTs). Varsity Maths Prep is a gem for learners who are
serious about an academic future.
Calculi of temporal logic are widely used in modern computer
science. The temporal organization of information flows in the
different architectures of laptops, the Internet, or supercomputers
would not be possible without appropriate temporal calculi. In the
age of digitalization and High-Tech applications, people are often
not aware that temporal logic is deeply rooted in the philosophy of
modalities. A deep understanding of these roots opens avenues to
the modern calculi of temporal logic which have emerged by
extension of modal logic with temporal operators. Computationally,
temporal operators can be introduced in different formalisms with
increasing complexity such as Basic Modal Logic (BML), Linear-Time
Temporal Logic (LTL), Computation Tree Logic (CTL), and Full
Computation Tree Logic (CTL*). Proof-theoretically, these
formalisms of temporal logic can be interpreted by the sequent
calculus of Gentzen, the tableau-based calculus, automata-based
calculus, game-based calculus, and dialogue-based calculus with
different advantages for different purposes, especially in computer
science.The book culminates in an outlook on trendsetting
applications of temporal logics in future technologies such as
artificial intelligence and quantum technology. However, it will
not be sufficient, as in traditional temporal logic, to start from
the everyday understanding of time. Since the 20th century, physics
has fundamentally changed the modern understanding of time, which
now also determines technology. In temporal logic, we are only just
beginning to grasp these differences in proof theory which needs
interdisciplinary cooperation of proof theory, computer science,
physics, technology, and philosophy.
The study of the geometry of structures that arise in a variety of
specific natural systems, such as chemical, physical, biological,
and geological, revealed the existence of a wide range of types of
polytopes of the highest dimension that were unknown in classical
geometry. At the same time, new properties of polytopes were
discovered as well as the geometric patterns to which they obey.
There is a need to classify these types of polytopes of the highest
dimension by listing their properties and formulating the laws to
which they obey. The Classes of Higher Dimensional Polytopes in
Chemical, Physical, and Biological Systems explains the meaning of
higher dimensions and systematically generalizes the results of
geometric research in various fields of knowledge. This book is
useful both for the fundamental development of geometry and for the
development of branches of science related to human activities. It
builds upon previous books published by the author on this topic.
Covering areas such as heredity, geometry, and dimensions, this
reference work is ideal for researchers, scholars, academicians,
practitioners, industry professionals, instructors, and students.
New Optimization Algorithms and Applications: Atom-Based,
Ecosystem-Based and Economics-Based presents the development of
three new optimization algorithms - an Atom Search Optimization
(ASO) algorithm, an Artificial Ecosystem-Based Optimization
algorithm (AEO), a Supply Demand Based Optimization (SDO), and
their applications within engineering. These algorithms are based
on benchmark functions and typical engineering cases. The book
describes the algorithms in detail and demonstrates how to use them
in engineering. The title verifies the performance of the
algorithms presented, simulation results are given, and MATLAB (R)
codes are provided for the methods described. Over seven chapters,
the book introduces ASO, AEO and SDO, and presents benchmark
functions, engineering problems, and coding. This volume offers
technicians and researchers engaged in computer and intelligent
algorithm work and engineering with one source of information on
novel optimization algorithms.
Advances in Computers, Volume 123 presents innovations in computer
hardware, software, theory, design and applications, with this
updated volume including new chapters on Downlink Resource
Allocations of Satellite-Airborne-Terrestrial Networks Integration,
Evaluating Software Testing Techniques: A Systematic Mapping Study,
The Screening Phase in Systematic Reviews: Can we speed up the
process?, A Survey on Cloud-Based Video Streaming Services, and
User Behavior-Ensemble Learning based Improving QoE Fairness in
HTTP Adaptive Streaming over SDN approach.
Symmetry is all around us. Of fundamental significance to the
way we interpret the world, this unique, pervasive phenomenon
indicates a dynamic relationship between objects. Combining a rich
historical narrative with his own personal journey as a
mathematician, Marcus du Sautoy takes a unique look into the
mathematical mind as he explores deep conjectures about symmetry
and brings us face-to-face with the oddball mathematicians, both
past and present, who have battled to understand symmetry's elusive
qualities.
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