### Spatial impact trends on debris flow fans in southwestern British Columbia : [supplementary material]

Sophia Zubrycky
The attached files are supplements to the author’s master’s thesis at http://hdl.handle.net/2429/74688

### The Number of Automorphisms of Random Trees

Stephan Wagner
By means of an asymptotic analysis of generating functions, we determine the limiting distribution of the order of the automorphism group of a random labeled tree. To be precise, we show that the logarithm of the number of automorphisms, suitably renormalized, converges weakly to a standard normal distribution. This result is also further extended to other random tree models.

Vincent Vatter

James Allen Fill

### Periods of iterations of mappings over finite fields with restricted preimage sizes

Daniel Panario
Let $[n] = \{1, \dots, n\}$ and let $\Omega_n$ be the set of all mappings from $[n]$ to itself. Let $f$ be a random uniform element of $\Omega_n$ and let $\mathbf{T}(f)$ and $\mathbf{B}(f)$ denote, respectively, the least common multiple and the product of the length of the cycles of $f$. Harris proved in 1973 that $\log \mathbf{T}$ converges in distribution to a standard normal distribution and, in 2011, E. Schmutz obtained an asymptotic estimate on...

### Recognizing graphs with linear random structure

Jeannette Janssen
In many real life applications, network formation can be modelled using a spatial random graph model: vertices are embedded in a metric space S, and pairs of vertices are more likely to be connected if they are closer together in the space. A general geometric graph model that captures this concept is G(n, w), where w : S × S → [0, 1] is a symmetric “link probability” function with the property that, for fixed...

### BP MUR CAN P L486

The pre-formatted plate for awards is printed in black ink and multiple fonts, and filled in with a single hand. Above the text sits a cross entwined in daffodils with the motto of the religious order on scrolls above and below the cross, all encircled with a border. The text and insignia are enclosed in a thick, detailed decorative border. Bookplate Type : Textual, Pictorial ; Bookplate Function : Prize

### BP MUR CAN P F565a

Black on yellow paper; A beaded border surrounds the name of the owner and the town; Bookplate Type: Textual; Bookplate Function: Ownership.

### BP MUR CAN I O987c

Printed in black ink on cream paper, an intricate border evocative of a tabernacle and constructed of geometric repeating patterns topped with a cross surrounds the text. Above the text is a symbol featuring a cannon and two flags. Textual ; Ownership

### Canonical structures in traffic spaces: with a view toward random matrices

Benson Au
For a tracial $*$-probability space $(\mathcal{A}, \varphi)$, Cébron, Dahlqvist, and Male constructed an enveloping traffic space $(\mathcal{G}(\mathcal{A}), \tau)$ that extends the trace $\varphi$ [CDM16]. This construction comes equipped with some canonical independence structure: in a joint work in progress with Male, we show that $(\mathcal{G}(\mathcal{A}), \tau)$ can be realized as the free product of three natural subalgebras (in the sense of Voiculescu), and that there exists a canonical homomorphic conditional expectation $P$ onto a subalgebra...

### Recent progress in bi-free harmonic analysis

Jiun-Chau Wang
We will discuss new results and open questions in bi-free harmonic analysis, in which the left and right variables are assumed to commute with each other. The topics include limit theorems and the bi-free Levy-Khintchine formulas for multiplicative and additive bi-free convolutions. These are joint with Hao-Wei Huang and Takahiro Hasebe.

### Asymptotic *-moments of random Vandermonde matrices

Ken Dykema
We show that a sequence of random Vandermonde matrices based on i.i.d entries on the unit circle has asymptotic *-distribution, which is that of a B-valued R-diagonal elements, where B is the algebra $C[0,1]$. (Joint work with March Boedihardjo.)

### Investigation of Convergence Characteristics of the Parareal method for Hyperbolic PDEs using the Reduced Basis Methods

Mikio Iizuka
In this study, we introduce the reduced basis methods (RBMs) to improve a convergence rate of the Parareal method for hyperbolic PDEs. We extract a small subspace consisting of main modes that compose the accurate solution from the data calculated by the fine solver during iterations. Once we got a set of reduced basis, the computational cost of time marching becomes low because of the small subspace, and therefore we can use a fine time...

### A new invariant for difference fields

Zoé Chatzidakis
If $(K,f)$ is a difference field, and a is a finite tuple in some difference field extending $K$, and such that $f(a)$ in $K(a)^{alg}$, then we define $dd(a/K) = lim [K(f^k(a),a):K(a)]^{1/k}$, the distant degree of $a$ over $K$. This is an invariant of the difference field extension $K(a)^{alg}/K$. We show that there is some $b$ in the difference field generated by $a$ over $K$, which is equi-algebraic with $a$ over $K$, and such that $dd(a/K)=[K(f(b),b):K(b)]$,...

Rolf Krause

### BP MUR CAN P G439

Black ink on cream paper. Design has some heraldic features. At the top of the bookplate is a banner featuring black, serif, capitalized font. The banner sits atop a stylized castle with multiple towers and a circular wall. Behind the castle to the left and right extend wing-like features. In front of the castle is a shield argent with sable dots charged with a sable lion passant. Shield has a sable chief charged with three...

### BP MUR CAN P G357

Printed in black ink on cream paper. In the centre of the bookplate, a family shield depicts an ‘X’ contained within a diamond, which is surrounded on all sides by eight trefoils with stems. At the top of the shield, a stylized iron helmet with a visor is framed on both sides by elaborate scrolling leaves. Above this, a demi-leopard is shown rampant (in profile, rearing, with its front paws in the air). Below the...

### A Whitham-Boussinesq long-wave model for variable topography

Rosa Vargas-Magana
We study the propagation of water waves in a channel of variable depth using the long-wave asymptotic regime. We use the Hamiltonian formulation of the problem in which the non-local Dirichlet-Neumann (DN) operator appears explicitly in the Hamiltonian and due to the complexity of the expressions of the asymptotic expansion associated with this operator in the presence of a non-trivial bottom topography. We perform an ad-hoc modification of these terms using a pseudo differential operator...

### Nonlinear waves in ice sheets

Guyenne Philippe
This talk concerns the mathematical modeling and numerical simulation of waves in ice sheets as occurring, e.g., in polar regions. A three-dimensional Hamiltonian formulation for ice sheets deforming on top of an ideal fluid of arbitrary depth is presented and nonlinear wave solutions are examined. In certain asymptotic regimes, analytical solutions are derived and compared with fully nonlinear solutions obtained numerically by a pseudospectral method.

### Wave breaking and modulational instability in full-dispersion shallow water models

Vera Mikyoung Hur
In the 1960s, Benjamin and Feir, and Whitham, discovered that a Stokes wave would be unstable to long wavelength perturbations, provided that (the carrier wave number) $\times$ (the undisturbed water depth) $> 1.363....$ In the 1990s, Bridges and Mielke studied the corresponding spectral instability in a rigorous manner. But it leaves some important issues open, such as the spectrum away from the origin. The governing equations of the water wave problem are complicated. One may...

Benjamin Recht

### The Emergence of Higher Order Dispersion from Periodic Waves

Daniel Ratliff
Following the method of Bridges (2013, PRSA), it is demonstrated how one may derive PDEs with fifth order dispersion from periodic waves (and, in general, relative equilibrium). Many of the coefficients of the emerging nonlinear approximations are directly related to the system's conservation laws, and those of the dispersive terms are tied to a Jordan chain analysis. Examples illustrating how the theory applies will also be discussed.

### Relationships between pressure, bathymetry, and wave-height

Katie Oliveras
A new method is proposed to relate the pressure at the bottom of a fluid, the shape of the bathymetry, and the surface elevation of a wave for steady flow or traveling waves. Given a measurement of any one of these physical quantities (pressure, bathymetry, or surface elevation), a numerical representation of the other two quantities is obtained via a nonlocal nonlinear equation obtained from the Euler formulation of the water-wave problem without approximation. From...

### Contact! unload : a narrative study and filmic exploration of veterans performing stories of war and transition : [supplementary materials]

Blair William McLean
The attached files are supplements to the author's doctoral dissertation at http://hdl.handle.net/2429/61004

### Pacific herring (Clupea pallasii) trophodynamics and fisheries in the Northeast Pacific Ocean : [supplementary material]

Szymon Surma
The attached files are supplements to the author’s doctoral dissertation at https://circle.library.ubc.ca/handle/2429/68682

• 2021
15
• 2020
8
• 2019
5
• 2018
3
• 2017
179

• Other
210