We establish three identities involving Dyck paths and alternating Motzkin
paths, whose proofs are based on variants of the same bijection. We interpret
these identities in terms of closed random walks on the halfline. We explain how
these identities arise from combinatorial interpretations of certain properties of the
-Hermite and -Laguerre ensembles of random matrix theory. We conclude by
presenting two other identities obtained in the same way, for which finding combinatorial
proofs is an open problem....
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Asymptotic Analysis of Large Cooperative Relay Networks Using Random Matrix Theory
The present book contains fifteen contributions on various topics related to
Number Theory, Physics and Geometry. It presents, together with a forthcoming
second volume, most of the courses and seminars delivered at the meeting
entitled “Frontiers in Number Theory, Physics and Geometry”, which took
place at the Centre de Physique des Houches in the french Alps March 9-21,
The density matrix offers an effective technique for dealing statistically with a
system consisting of many electrons using the quantum theory for an electron.
Amixed state consisting of a statistical distribution of various quantum states
can be specified by a set of probabilities pj with which the electron is found
in a quantum state j ji.
This is a book on linear algebra and matrix theory. While it is self contained, it will work
best for those who have already had some exposure to linear algebra. It is also assumed that
the reader has had calculus. Some optional topics require more analysis than this, however.
I think that the subject of linear algebra is likely the most significant topic discussed in
undergraduate mathematics courses. Part of the reason for this is its usefulness in unifying
so many different topics. Linear algebra is essential in analysis, applied math, and even in
Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Commutativity Fuglede lý modulo lớp Hilbert Schmidt và các chức năng tạo ra cho các nhà khai thác ma trận. II...
After providing the basic background in electromagnetic theory necessary to utilize the software, the author of Ebook Antenna and EM Modeling with Matlab describes the benefits and many practical uses of the Matlab. Sergey Makarov's text utilizes the widely used Matlab(r) software, which offers a more flexible and affordable alternative to other antenna and electromagnetic modeling tools currently available.
This work gives an overview of core topics in the “investment” side of finance, stressing
the quantitative aspects of the subject. The presentation is at a moderately sophisticated
level that would be appropriate for masters or early doctoral students in
economics, engineering, finance, and mathematics. It would also be suitable for advanced
and well motivated undergraduates-provided they are adequately prepared
in math, probability, and statistics.
Alternatively, banks may be optimising their capital structure, possibly much like non-
financial firms, which would relegate capital requirements to second order importance.
Flannery (1994), Myers and Rajan (1998), Diamond and Rajan (2000) and Allen et al. (2009)
develop theories of optimal bank capital structure, in which capital requirements are not
necessarily binding. Non-binding capital requirements are also explored in the market
This work is intended to survey the basic theory that underlies the multitude of
parameter-rich models that dominate the hydrological literature today. It is concerned
with the application of the equation of continuity (which is the fundamental theorem of
hydrology) in its complete form combined with a simplified representation of the
principle of conservation of momentum. Since the equation of continuity can be
expressed in linear form by a suitable choice of state variables and is also parameterfree,
it can be readily formulated at all scales of interest.
Random matrices are widely and successfully used in physics for almost
60-70 years, beginning with the works of Wigner and Dyson. Initially proposed
to describe statistics of excited levels in complex nuclei, the Random
Matrix Theory has grown far beyond nuclear physics, and also far beyond just
level statistics. It is constantly developing into new areas of physics and mathematics,
and now constitutes a part of the general culture and curriculum of a
is symmetric. However, since the weights wj are not equal for most quadrature rules, the matrix K (equation 18.1.5) is not symmetric. The matrix eigenvalue problem is much easier for symmetric matrices, and so we should restore the symmetry if possible.
(Don’t let this notation mislead you into inverting the full matrix W(x) + λS. You only need to solve for some y the linear system (W(x) + λS) · y = R, and then substitute y into both the numerators and denominators of 18.6.12 or 18.6.13.) Equations (18.6.12)