Canadian Mathematical Bulletin最新文献

Let ${mathcal {R}} subset mathbb {P}^1_{mathbb {C}}$ be a finite subset of markings. Let G be an almost simple simply-connected algebraic group over $mathbb {C}$. Let $K_G$ denote the compact real form of G. Suppose for each lasso l around the marked point, a conjugacy class $C_l$ in $K_G$ is prescribed. The aim of this paper is to give verifiable criteria for the existence of an irreducible homomorphism of $pi _{1}(mathbb P^1_{mathbb {C}} ,{backslash}, {mathcal {R}})$ into $K_G$ such that the image of l lies in $C_l$.

A digraph group is a group defined by non-empty presentation with the property that each relator is of the form $R(x, y)$, where x and y are distinct generators and $R(cdot , cdot )$ is determined by some fixed cyclically reduced word $R(a, b)$ that involves both a and b. Associated with each such presentation is a digraph whose vertices correspond to the generators and whose arcs correspond to the relators. In this article, we consider digraph groups for strong digraphs that are digon-free and triangle-free. We classify when the digraph group is finite and show that in these cases it is cyclic, giving its order. We apply this result to the Cayley digraph of the generalized quaternion group, to circulant digraphs, and to Cartesian and direct products of strong digraphs.

The paper deals with boundedness of solutions and uniform asymptotic stability of the zero solution. In our current undertaking, we aim to solve two open problems that were proposed by the author in his book Qualitative theory of Volterra difference equations (2018, Springer, Cham). Our approach centers on finding the appropriate Lyapunov functional that satisfies specific conditions, incorporating the concept of wedges.

We resolve some questions posed by Handelman in 1996 concerning log convex $L^1$ functions. In particular, we give a negative answer to a question he posed concerning the integrability of $h^2(x)/h(2x)$ when h is $L^1$ and log convex and $h(n)^{1/n}rightarrow 1$.

In this paper, we study the $(s, C(s))$-Harnack inequality in a domain $Gsubset mathbb {R}^n$ for $sin (0,1)$ and $C(s)geq 1$ and present a series of inequalities related to $(s, C(s))$-Harnack functions and the Harnack metric. We also investigate the behavior of the Harnack metric under K-quasiconformal and K-quasiregular mappings, where $Kgeq 1$. Finally, we provide a type of harmonic Schwarz lemma and improve the Schwarz–Pick estimate for a real-valued harmonic function.

Let f and g be analytic functions on the open unit disk ${mathbb D}$ such that $|f|=|g|$ on a set A. We give an alternative proof of the result of Perez that there exists c in the unit circle ${mathbb T}$ such that $f=cg$ when A is the union of two lines in ${mathbb D}$ intersecting at an angle that is an irrational multiple of $pi $, and from this, deduce a sequential generalization of the result. Similarly, the same conclusion is valid when f and g are in the Nevanlinna class and A is the union of the unit circle and an interior circle, tangential or not. We also provide sequential versions of this result and analyze the case $A=r{mathbb T}$. Finally, we examine the most general situation when there is equality on two distinct circles in the disk, proving a result or counterexample for each possible configuration.

In this paper, we give Pieri rules for skew dual immaculate functions and their recently discovered row-strict counterparts. We establish our rules using a right-action analogue of the skew Littlewood–Richardson rule for Hopf algebras of Lam–Lauve–Sottile. We also obtain Pieri rules for row-strict (dual) immaculate functions.

We determine the adjoint Reidemeister torsion of a $3$-manifold obtained by some Dehn surgery along K, where K is either the figure-eight knot or the $5_2$-knot. As in a vanishing conjecture (Benini et al. (2020, Journal of High Energy Physics 2020, 57), Gang et al. (2020, Journal of High Energy Physics 2020, 164), and Gang et al. (2021, Advances in Theoretical and Mathematical Physics 25, 1819–1845)), we consider a similar conjecture and show that the conjecture holds for the 3-manifold.