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We show that all possible 388 4-dim Kochen-Specker (KS) (vector) sets (of yes-no questions) with 18 through 23 vectors and 844 sets with 24 vectors all with component values from \{-1,0,1\} can be obtained by stripping vectors off a single…
In this paper we determine the exact rate of growth of the solution of a deterministic delay differential equation in which the delayed term is regularly varying at infinity and dominates, and determine criteria to characterise this…
Let $(x(t),y(t))^\top$ be a solution of a Fuchsian system of order two with three singular points. The vector space of functions of the form $P(t)x(t)+Q(t)y(t)$, where $P,Q$ are real polynomials, has a natural filtration of vector spaces,…
It is known that in systems which contain randomness explicitly in their Hamiltonians (e.g., due to impurities), the characteristic size L of the ordered domains can grow only logarithmically with time t following a quench below the…
We extend the previously developed weak noise scheme, applied to the noisy Burgers equation in 1D, to the Kardar-Parisi-Zhang equation for a growing interface in arbitrary dimensions. By means of the Cole-Hopf transformation we show that…
We study the large time behavior of classical solutions to the two-dimensional Vlasov-Poisson (VP) and relativistic Vlasov-Poisson (RVP) systems launched by radially-symmetric initial data with compact support. In particular, we prove that…
We characterize bifurcation values of polynomial functions by using the theory of perverse sheaves and their vanishing cycles. In particular, by introducing a method to compute the jumps of the Euler characteristics with compact support of…
Emergence of exceptional points in two dimensions is one of the remarkable phenomena in non-Hermitian systems. We here elucidate the impacts of symmetry on the non-Hermitian physics. Specifically, we analyze chiral symmetric correlated…
We study matching problems in which agents form one side of a bipartite graph and have preferences over objects on the other side. A central solution concept in this setting is popularity: a matching is popular if it is a (weak) Condorcet…
We show that for piecewise hereditary algebras, the periodicity of the Coxeter transformation implies the non-negativity of the Euler form. Contrary to previous assumptions, the condition of piecewise heredity cannot be omitted, even for…
The isotropic harmonic oscillator and the Kepler-Coulomb system are pivotal models in the Sciences. They are two examples of second-order (maximally) superintegrable (Hamiltonian) systems. These systems are classified in dimension two. A…
Recent results in the theory and application of Newton-Puiseux expansions, i.e. fractional power series solutions of equations, suggest further developments within a more abstract algebraic-geometric framework, involving in particular the…
We address Heath-Brown's and Serre's dimension growth conjecture (proved by Salberger), when the degree $d$ grows. Recall that Salberger's dimension growth results give bounds of the form $O_{X, \varepsilon} (B^{\dim X+\varepsilon})$ for…
The value of the dynamic critical exponent z has been studied for experimental two-dimensional superconducting and Josephson Junction array systems in zero magnetic field via the Fisher-Fisher-Huse dynamic scaling analysis. We found z~5.6,…
Let $\phi:\Bbb C^n\to X$ a holomorphic map to an $n$-dimensional connected compact complex manifold $X$. We establish links between the positivity properties of the canonical bundle of $X$ and the rate of growth of $\phi$ which extend…
We study domain growth kinetics in a random-field system in the presence of a spatially correlated disorder $h_{i}(\vec r)$ after an instantaneous quench at a finite temperature $T$ from a random initial state corresponding to $T=\infty$.…
We study the transient regime of type-II biophysical neuron models and determine the scaling behavior of relaxation times $\tau$ near but below the repetitive firing critical current, $\tau \simeq C (I_c-I)^{-\Delta}$. For both the…
In this paper, we investigate the Cauchy problem associated to a system of PDE's of Oldroyd type. The considered model describes the evolution of certain viscoelastic fluids within a corotational framework. The non-corotational setting is…
We study global regularity of nonlinear systems of partial differential equations depending on the symmetric part of the gradient with Dirichlet boundary conditions. These systems arise from variational problems in plasticity with power…
Experimental studies on the irreversible growth of field-induced chains of dipolar particles suggest an asymptotic power-law behavior of several relevant quantities. We introduce a Monte Carlo model of chain growth that explicitly…