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Triggers : how we can stop reacting and start healing
\"We lash out in anger. We cry and retreat. We find ourselves paralyzed. Our bodies respond powerfully to triggers, often before our minds catch up to make sense of a situation. This book helps us learn to manage our immediate reactions in these difficult moments. It also goes much deeper to help us understand why we are affected by certain things and the powerful lessons we can learn from these instinctive responses to move towards healing. Bestselling author and psychologist David Richo explains the brain science behind our immediate reactions and discusses fear, anger, sadness, and relationship triggers in depth. When we are triggered, he writes that \"we are being bullied by our own unfinished business.\" By looking deeply at the roots of what provokes us, Richo invites readers to cultivate our inner resources and develop practices to find more peace\"-- Provided by publisher.
Book
Automorphism Orbits and Element Orders in Finite Groups: Almost-Solubility and the Monster
For a finite group
eBook
Congruence Lattices of Ideals in Categories and (Partial) Semigroups
This monograph presents a unified framework for determining the congruences on a number of monoids and categories of transformations,
diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative process of stacking certain
normal subgroup lattices on top of each other to successively build congruence lattices of a chain of ideals. This is applied to several
specific categories of: transformations; order/orientation preserving/reversing transformations; partitions; planar/annular partitions;
Brauer, Temperley–Lieb and Jones partitions; linear and projective linear transformations; and partial braids. Special considerations
are needed for certain small ideals, and technically more intricate theoretical underpinnings for the linear and partial braid
categories.
eBook
The Bounded and Precise Word Problems for Presentations of Groups
We introduce and study the bounded word problem and the precise word problem for groups given by means of generators and defining
relations. For example, for every finitely presented group, the bounded word problem is in
eBook
Decorated Dyck Paths, Polyominoes, and the Delta Conjecture
We discuss the combinatorics of decorated Dyck paths and decorated parallelogram polyominoes, extending to the decorated case the
main results of both Haglund (“A proof of the
eBook
Cell complexes, poset topology and the representation theory of algebras arising in algebraic combinatorics and discrete geometry
In recent years it has been noted that a number of combinatorial structures such as real and complex hyperplane arrangements,
interval greedoids, matroids and oriented matroids have the structure of a finite monoid called a left regular band. Random walks on the
monoid model a number of interesting Markov chains such as the Tsetlin library and riffle shuffle. The representation theory of left
regular bands then comes into play and has had a major influence on both the combinatorics and the probability theory associated to such
structures. In a recent paper, the authors established a close connection between algebraic and combinatorial invariants of a left
regular band by showing that certain homological invariants of the algebra of a left regular band coincide with the cohomology of order
complexes of posets naturally associated to the left regular band.
The purpose of the present monograph is to further develop and
deepen the connection between left regular bands and poset topology. This allows us to compute finite projective resolutions of all
simple modules of unital left regular band algebras over fields and much more. In the process, we are led to define the class of CW left
regular bands as the class of left regular bands whose associated posets are the face posets of regular CW complexes. Most of the
examples that have arisen in the literature belong to this class. A new and important class of examples is a left regular band structure
on the face poset of a CAT(0) cube complex. Also, the recently introduced notion of a COM (complex of oriented matroids or conditional
oriented matroid) fits nicely into our setting and includes CAT(0) cube complexes and certain more general CAT(0) zonotopal complexes. A
fairly complete picture of the representation theory for CW left regular bands is obtained.
eBook
Computational aspects of discrete subgroups of Lie groups : Virtual Conference Computational Aspects of Discrete Subgroups of Lie Groups, June 14-18, 2021, Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island
This volume contains the proceedings of the virtual workshop on Computational Aspects of Discrete Subgroups of Lie Groups, held from June 14 to June 18, 2021, and hosted by the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island.The major theme deals with a novel domain of computational algebra: the design, implementation, and application of algorithms based on matrix representation of groups and their geometric properties. It is centered on computing with discrete subgroups of Lie groups, which impacts many different areas of mathematics such as algebra, geometry, topology, and number theory. The workshop aimed to synergize independent strands in the area of computing with discrete subgroups of Lie groups, to facilitate solution of theoretical problems by means of recent advances in computational algebra.
eBook
The Irreducible Subgroups of Exceptional Algebraic Groups
This paper is a contribution to the study of the subgroup structure of exceptional algebraic groups over algebraically closed fields
of arbitrary characteristic. Following Serre, a closed subgroup of a semisimple algebraic group
A result of Liebeck and Testerman shows that each irreducible connected subgroup
eBook
Sums of Reciprocals of Fractional Parts and Multiplicative Diophantine Approximation
There are two main interrelated goals of this paper. Firstly we investigate the sums
eBook
C-polynomials and LC-functions: towards a generalization of the Hurwitz zeta function
Let
f
(
t
)
=
∑
n
=
0
+
∞
C
f
,
n
n
!
t
n
be an analytic function at 0, and let
C
f
,
n
(
x
)
=
∑
k
=
0
n
n
k
C
f
,
k
x
n
-
k
be the sequence of Appell polynomials, referred to as
C-polynomials associated to
f
, constructed from the sequence of coefficients
C
f
,
n
. We also define
P
f
,
n
(
x
)
as the sequence of C-polynomials associated to the function
p
f
(
t
)
=
f
(
t
)
(
e
t
-
1
)
/
t
, called
P-polynomials associated to
f
. This work investigates three main topics. Firstly, we examine the properties of C-polynomials and P-polynomials and the underlying features that connect them. Secondly, drawing inspiration from the definition of P-polynomials and subject to an additional condition on
f
, we introduce and study the bivariate complex function
P
f
(
s
,
z
)
=
∑
k
=
0
+
∞
z
k
P
f
,
k
s
z
-
k
, which generalizes the
s
z
function and is denoted by
s
(
z
,
f
)
. Thirdly, the paper’s main contribution is the generalization of the Hurwitz zeta function and its fundamental properties, most notably Hurwitz’s formula, by constructing a novel class of functions defined by
L
(
z
,
f
)
=
∑
n
=
n
f
+
∞
n
(
-
z
,
f
)
, which are intrinsically linked to C-polynomials and referred to as
LC-functions associated to
f
(the constant
n
f
is a positive integer dependent on the choice of
f
).
Journal Article