Related papers: Finite mean dimesnion and marker property

The principle of detailed balance (DB) states that every kinetic transition in a system with many micro-states, $\mu$, is balanced, on average, with the opposite transition, $\mu_i\leftrightharpoons\mu_j$. Since its introduction by…

For each 1 < p < infinity, there exists a positive constant c_p, depending only on p, such that the following holds. Let (d_k), (e_k) be real-valued martingale difference sequences. If for for all bounded nonnegative predictable sequences…

A 1952 result of Davenport and Erd\H{o}s states that if $p$ is an integer-valued polynomial, then the real number $0.p(1)p(2)p(3)\dots$ is Borel normal in base ten. A later result of Nakai and Shiokawa extends this result to polynomials…

In this short note, we extend to the continuous case a mean projection theorem for discrete determinantal point processes associated with a finite range projection, thus strengthening a known result in random linear algebra due to Ermakov…

We show that for any finite $p$-group $P$ of rank at least 2 and any algebraically closed field $k$ of characteristic $p$ the graded center $Z^*(\modbar(kP))$ of the stable module category of finite-dimensional $kP$-modules has infinite…

This paper pursues positive characteristic analogues of the results of Furusho, Komori, Matsumoto and Tsumura on $p$-adic multiple $L$-functions. We consider $\infty$-adic and $v$-adic multiple zeta functions concerned by Angl\`{e}s, Ngo…

In this paper, we introduce a large class of (so-called) conditional indicators, on a complete probability space with respect to a sub $\sigma$-algebra. A conditional indicator is a positive mapping, which is not necessary linear, but may…

This work is dedicated to the promotion of the results Hadamard, Landau E., Walvis A., Estarmann T and Paul R. Chernoff for pseudo zeta functions. The properties of zeta functions are studied, these properties can lead to new regularities…

Let H[a_0,n] be the class of functions f(z)=a_0+a_nz^n+...which are analytic in the open unit disk U}. For f(z) in H[a_0,n], S. S. Miller and P. T. Mocanu (J. Math. Anal. Appl. 65(1978), 289-305) have shown Miller and Mocanu lemma which is…

We consider a planar Hamiltonian system of the type $Jz' = \nabla_z H(t,z)$, where $H: \mathbb{R} \times \mathbb{R}^2 \to \mathbb{R}$ is a function periodic in the time variable, such that $\nabla_z H(t,0) \equiv 0$ and $\nabla_z H(t,z)$ is…

A new indicator, a real valued $s$-index, is suggested to characterize a quality and impact of the scientific research output. It is expected to be at least as useful as the notorious $h$-index, at the same time avoiding some its obvious…

We present the most general at this moment results on the discrete mixed joint value-distribution and the universality property for the class of Matsumoto zeta-functions and periodic Hurwitz zeta-functions under certain linear independence…

We use topological ideas to show that, assuming the conjecture of Erd\"(o)s on subsets of positive integers having no $p$ terms in arithmetic progression (A. P.), there must exist a subset $M_p$ of positive integers with no $p$ terms in A.…

We review the construction and theoretical implications of the USp(2k) matrix model in zero dimension introduced in ref. \cite{IT1,IT2}. It is argued that the model provides a constructive approach to Type I superstrings and is at the same…

In this first article of a multi-part series, we inspect a surprising relationship between the set of fixed points of a polynomial map $\varphi_{d, c}$ defined by $\varphi_{d, c}(z) = z^d + c$ for all $c, z \in \mathbb{Z}$ and the…

We revisit the classical dissipativity theorem of linear-quadratic theory in a generalized framework where the quadratic storage is negative definite in a p-dimensional subspace and positive definite in a complementary subspace. The…

We study the theoretical properties of the generalized dynamic principal components introduced in Pe\~na and Yohai (2016). In particular, we prove that when the data follows a dynamic factor model, the reconstruction provided by the…

In a polynomial ring over a perfect field, the symbolic powers of a prime ideal can be described via differential operators: a classical result by Zariski and Nagata says that the $n$-th symbolic power of a given prime ideal consists of the…

The behaviour of the generalised Riesz function defined by \[S_{m,p}(x)=\sum_{k=0}^\infty \frac{(-)^{k-1}x^k}{k! \zeta(mk+p)}\qquad (m\geq 1,\ p\geq 1)\] is considered for large positive values of $x$. A numerical scheme is given to compute…

This part of a multi-paper project studies the lattice properties of the arithmetic mean ideals of B(H) introduced by Dykema, Figiel, Weiss, and Wodzicki. We prove: the lattices of all principal ideals, of arithmetic mean or arithmetic mean…