Browsing Mathematics by Title
Now showing items 392-411 of 1478
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The evolution of knowledge within and across fields in modern physics
(2020-07-21)The exchange of knowledge across different areas and disciplines plays a key role in the process of knowledge creation, and can stimulate innovation and the emergence of new fields. We develop here a quantitative framework ... -
Evolutionary dynamics of higher-order interactions in social networks
(Nature Research, 2020)We live and cooperate in networks. However, links in networks only allow for pairwise interactions, thus making the framework suitable for dyadic games, but not for games that are played in groups of more than two players. ... -
Evolving Pinched Submanifolds of the Sphere by Mean Curvature Flow
(Springer, 2023-01-29) -
Exact solution of pulled, directed vesicles with sticky walls in two dimensions
We analyse a directed lattice vesicle model incorporating both the binding-unbinding transition and the vesicle inflation-deflation transition. From the exact solution we derive the phase diagram for this model and elucidate ... -
Existence and non-existence of global solutions for semilinear heat equations and inequalities on sub-Riemannian manifolds, and Fujita exponent on unimodular Lie groups
(Elsevier, 2021)In this paper we study the global well-posedness of the following Cauchy problem on a sub-Riemannian manifold $M$: \begin{equation*} \begin{cases} u_{t}-\mathfrak{L}_{M} u=f(u), \;x\in M, \;t>0, \\u(0,x)=u_{0}(x), \;x\in ... -
An exotic presentation of Q_28
We introduce a new family of presentations for the quaternion groups and show that for the quaternion group of order 28, one of these presentations has non-standard second homotopy group. -
Explicit refinements of Böcherer's conjecture for Siegel modular forms of squarefree level
We formulate an explicit refinement of B\"ocherer's conjecture for Siegel modular forms of degree 2 and squarefree level, relating weighted averages of Fourier coefficients with special values of L-functions. To achieve ... -
Explicit solutions for linear variable–coefficient fractional differential equations with respect to functions
(Elsevier, 2021-03-15)Explicit solutions of differential equations of complex fractional orders with respect to functions and with continuous variable coefficients are established. The representations of solutions are given in terms of some ... -
Explosive cooperation in social dilemmas on higher-order networks
(American Physical Society, 16-04-2024)Understanding how cooperative behaviors can emerge from competitive interactions is an open problem in biology and social sciences. While interactions are usually modeled as pairwise networks, the units of many real-world ... -
Explosive higher-order Kuramoto dynamics on simplicial complexes
(American Physical Society, 2020)The higher-order interactions of complex systems, such as the brain, are captured by their simplicial complex structure and have a significant effect on dynamics. However the existing dynamical models defined on simplicial ... -
Exponential Growth of Products of Non-Stationary Markov-Dependent Matrices
(Oxford University Press (OUP), 2021-10)Let (ξj)j≥1 be a non-stationary Markov chain with phase space X and let gj:X↦SL(m,R) be a sequence of functions on X with values in the unimodular group. Set gj=gj(ξj) and denote by Sn=gn…g1, the product of the matrices ...