Due 2019-12-11
1st ed. 2019, X, 94 p. 48
illus., 7 illus. in color.
Printed book
Softcover
ISBN 978-3-030-31109-4
This book is in honor of the 80th birthday of Stephen Hedetniemi. It describesadvanced
material in graph theory in the areas of domination, coloring, spanning cycles and circuits,
anddistance that grew out of research topics investigated by Stephen Hedetniemi. The purpose
of this bookis to provide background and principal results on these topics, along with same
related problems andconjectures, for researchers in these areas. The most important features
deal with material, results, andproblems that researchers may not be aware of but may find of
interest. Each chapter contains results,methods and information that will give readers the
necessary background to investigate each topic in more detail
1st ed. 2019, XXI, 729 p. 1
illus.
Printed book
Hardcover
ISBN 978-3-030-30536-9
Magnetic Schrodinger Operator 1
Research monograph for researchers and graduate students in Mathematics and Mathematical Physics
Most comprehensive work about the topic
Use of technique, developed by the author during more than 40 years
The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp
spectral asymptotics for broad classes of partial differential operators using techniques from
semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently
use the variational estimates in gsmallh domains to consider domains with singularities of
different kinds.In turn, the general theory (results and methods developed) is applied to the
Magnetic Schrodinger operator, miscellaneous problems, andmultiparticle quantum theory. In
this volume the methods developed in Volumes I and II are applied to the Schrodinger and
Dirac operators in smooth settings in dimensions 2 and 3.
1st ed. 2019, XIX, 525 p. 1illus.
Printed book
Hardcover
ISBN 978-3-030-30540-6
Functional Methods and Eigenvalue Asymptotics
Research monograph for researchers and graduate students in Mathematics and Mathematical Physics
Most comprehensive work about the topic
Use of technique, developed by the author during more than 40 years
The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp
spectral asymptotics for broad classes of partial differential operators using techniques from
semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently
use the variational estimates in gsmallh domains to consider domains with singularities of
different kinds.In turn, the general theory (results and methods developed) is applied to the
Magnetic Schrodinger operator, miscellaneous problems, andmultiparticle quantum theory. In
this volume the local spectral asymptotics of Volume I in the regular part of the domain are
combined with variational estimates in the vicinity of singularities, and global asymptotics are
derived in the general form. They are then applied to multiple cases and asymptotics with
respect to a spectral parameter. Finally, cases in which only general methods but not the
results can be applied (non-standard asymptotics) are studied
1st ed. 2019, XLIX, 889 p. 1illus.
Printed book
Hardcover
ISBN 978-3-030-30556-7
Semiclassical Microlocal Analysis and Local and Microlocal Semiclassical Asymptotics
Research monograph for researchers and graduate students in Mathematics and Mathematical Physics
Most comprehensive work about the topic
Use of technique, developed by the author during more than 40 years
The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp
spectral asymptotics for broad classes of partial differential operators using techniques from
semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently
use the variational estimates in gsmallh domains to consider domains with singularities of
different kinds.In turn, the general theory (results and methods developed) is applied to the
Magnetic Schrodinger operator, miscellaneous problems, andmultiparticle quantum theory. In
this volume the general microlocal semiclassical approach is developed, and microlocal and
local semiclassical spectral asymptotics are derived
1st ed. 2019, VIII, 102 p. 11 illus.
Printed book
Softcover
ISBN 978-981-15-0065-7
Introduces closed testing procedures for all-pairwise comparisons
Discusses multiple comparison procedures under simple ordered restrictions
of location parameters in multi-sample models
Explains the sinc method, which is optimal for computing the upper 100
percentiles of complicated distributions
This book focuses on all-pairwise multiple comparisons of means in multi-sample models,
introducing closed testing procedures based on maximum absolute values of some two-sample
t-test statistics and on F-test statistics in homoscedastic multi-sample models. It shows that
(1) the multi-step procedures are more powerful than single-step procedures and the Ryan
/Einot?Gabriel/Welsh tests, and (2) the confidence regions induced by the multi-step
procedures are equivalent to simultaneous confidence intervals. Next, it describes the multistep
test procedure in heteroscedastic multi-sample models, which is superior to the singlestep
Games?Howell procedure. In the context of simple ordered restrictions of means, the
authors also discuss closed testing procedures based on maximum values of two-sample onesided
t-test statistics and based on Bartholomew's statistics. Furthermore, the book presents
distribution-free procedures and describes simulation studies performed under the null
hypothesis and some alternative hypotheses. Although single-step multiple comparison
procedures are generally used, the closed testing procedures described are more powerful
than the single-step procedures. In order to execute the multiple comparison procedures, the
upper 100 percentiles of the complicated distributions are required. Classical integral formulas
such as Simpson's rule and the Gaussian rule have been used for the calculation of the
integral transform that appears in statistical calculations. However, these formulas are not
effective for the complicated distribution. As such, the authors introduce the sinc method, which
is optimal in terms of accuracy and computational cost.