Monotone Hurwitz Numbers and the HCIZ Integral

I. P. Goulden; Mathieu Guay-Paquet; Jonathan Novak

Displaying similar documents to “Monotone Hurwitz Numbers and the HCIZ Integral”

Ground states of supersymmetric matrix models

Gian Michele Graf (1998-1999)

Séminaire Équations aux dérivées partielles

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We consider supersymmetric matrix Hamiltonians. The existence of a zero-energy bound state, in particular for the $d = 9$ model, is of interest in M-theory. While we do not quite prove its existence, we show that the decay at infinity such a state would have is compatible with normalizability (and hence existence) in $d = 9$ . Moreover, it would be unique. Other values of $d$ , where the situation is somewhat different, shall also be addressed. The analysis is based on a Born-Oppenheimer approximation....

Relations between the boundary values and periods for generalized analytic functions in $R^{n}$

Wolfgang Tutschke (1983)

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Analytic aspects of the circulant Hadamard conjecture

Teodor Banica, Ion Nechita, Jean-Marc Schlenker (2014)

Annales mathématiques Blaise Pascal

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We investigate the problem of counting the real or complex Hadamard matrices which are circulant, by using analytic methods. Our main observation is the fact that for $| q_{0} | = ... = | q_{N - 1} | = 1$ the quantity $Φ = \sum_{i + k = j + l} \frac{q_{i} q_{k}}{q_{j} q_{l}}$ satisfies $Φ \geq N^{2}$ , with equality if and only if $q = (q_{i})$ is the eigenvalue vector of a rescaled circulant complex Hadamard matrix. This suggests three analytic problems, namely: (1) the brute-force minimization of $Φ$ , (2) the study of the critical points of $Φ$ , and (3) the computation of the moments of $Φ$ . We explore here...

Radii of p-valence of certain analytic functions of order $α$ with negative coefficients

M. K. Aouf (1989)

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Chaotic behaviour of continuous dynamical system generated by Euler equation branching and its application in macroeconomic equilibrium model

Barbora Volná (2015)

Mathematica Bohemica

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We focus on the special type of the continuous dynamical system which is generated by Euler equation branching. Euler equation branching is a type of differential inclusion $\dot{x} \in {f (x), g (x)}$ , where $f, g : X \subset ℝ^{n} \to ℝ^{n}$ are continuous and $f (x) \neq g (x)$ at every point $x \in X$ . It seems this chaotic behaviour is typical for such dynamical system. In the second part we show an application in a new formulated overall macroeconomic equilibrium model. This new model is based on the fundamental macroeconomic aggregate equilibrium model called...

On the structure of the set of higher order spreading models

Bünyamin Sarı, Konstantinos Tyros (2014)

Studia Mathematica

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We generalize some results concerning the classical notion of a spreading model to spreading models of order ξ. Among other results, we prove that the set $S M_{ξ}^{w} (X)$ of ξ-order spreading models of a Banach space X generated by subordinated weakly null ℱ-sequences endowed with the pre-partial order of domination is a semilattice. Moreover, if $S M_{ξ}^{w} (X)$ contains an increasing sequence of length ω then it contains an increasing sequence of length ω₁. Finally, if $S M_{ξ}^{w} (X)$ is uncountable, then it contains an antichain...

Investigating generalized quaternions with dual-generalized complex numbers

Nurten Gürses, Gülsüm Yeliz Şentürk, Salim Yüce (2023)

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We aim to introduce generalized quaternions with dual-generalized complex number coefficients for all real values $α$ , $β$ and $𝔭$ . Furthermore, the algebraic structures, properties and matrix forms are expressed as generalized quaternions and dual-generalized complex numbers. Finally, based on their matrix representations, the multiplication of these quaternions is restated and numerical examples are given.

Pairs of square-free values of the type $n^{2} + 1$ , $n^{2} + 2$

Stoyan Dimitrov (2021)

Czechoslovak Mathematical Journal

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We show that there exist infinitely many consecutive square-free numbers of the form $n^{2} + 1$ , $n^{2} + 2$ . We also establish an asymptotic formula for the number of such square-free pairs when $n$ does not exceed given sufficiently large positive number.

Existentially closed II₁ factors

Ilijas Farah, Isaac Goldbring, Bradd Hart, David Sherman (2016)

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We examine the properties of existentially closed ( $^{ω}$ -embeddable) II₁ factors. In particular, we use the fact that every automorphism of an existentially closed ( $^{ω}$ -embeddable) II₁ factor is approximately inner to prove that Th() is not model-complete. We also show that Th() is complete for both finite and infinite forcing and use the latter result to prove that there exist continuum many nonisomorphic existentially closed models of Th().

Monotone substochastic operators and a new Calderón couple

Karol Leśnik (2015)

Studia Mathematica

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An important result on submajorization, which goes back to Hardy, Littlewood and Pólya, states that b ⪯ a if and only if there is a doubly stochastic matrix A such that b = Aa. We prove that under monotonicity assumptions on the vectors a and b the matrix A may be chosen monotone. This result is then applied to show that $(\tilde{L^{p}}, L^{\infty})$ is a Calderón couple for 1 ≤ p < ∞, where $\tilde{L^{p}}$ is the Köthe dual of the Cesàro space $C e s_{p^{'}}$ (or equivalently the down space $L_{↓}^{p^{'}}$ ). In particular, $(\tilde{L ¹}, L^{\infty})$ is a Calderón couple, which...

Higher order spreading models

S. A. Argyros, V. Kanellopoulos, K. Tyros (2013)

Fundamenta Mathematicae

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We introduce higher order spreading models associated to a Banach space X. Their definition is based on ℱ-sequences ${(x_{s})}_{s \in ℱ}$ with ℱ a regular thin family and on plegma families. We show that the higher order spreading models of a Banach space X form an increasing transfinite hierarchy ${(ℳ_{ξ} (X))}_{ξ < ω ₁}$ . Each $ℳ_{ξ} (X)$ contains all spreading models generated by ℱ-sequences ${(x_{s})}_{s \in ℱ}$ with order of ℱ equal to ξ. We also study the fundamental properties of this hierarchy.

On the matrix negative Pell equation

Aleksander Grytczuk, Izabela Kurzydło (2009)

Discussiones Mathematicae - General Algebra and Applications

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Let N be a set of natural numbers and Z be a set of integers. Let M₂(Z) denotes the set of all 2x2 matrices with integer entries. We give necessary and suficient conditions for solvability of the matrix negative Pell equation (P) X² - dY² = -I with d ∈ N for nonsingular X,Y belonging to M₂(Z) and his generalization (Pn) $\sum_{i = 1}^{n} X ₂_{i} - d \sum_{i = 1}^{n} Y ²_{i} = - I$ with d ∈ N for nonsingular $X_{i}, Y_{i} \in M ₂ (Z)$ , i=1,...,n.

On the completeness of $ℒ_{p}$ -spaces over a charge

Sreela Gangopadhyay (1990)

Colloquium Mathematicae

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Separately analytic functions and envelopes of holomorphy of some lower dimensional subsets of $C^{n}$

J. Siciak (1969)

Annales Polonici Mathematici

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