Related papers: Integer-valued valuations

In this short paper, I introduce an elementary method for exactly evaluating the definite integrals $\, \int_0^{\pi}{\ln{(\sin{\theta})}\,d\theta}$, $\int_0^{\pi/2}{\ln{(\sin{\theta})}\,d\theta}$,…

We present a new approach to termination analysis of logic programs. The essence of the approach is that we make use of general term-orderings (instead of level mappings), like it is done in transformational approaches to logic program…

We prove that variances of non-negative random variables have the following monotonicity property: For all $0 < r < s \le 1$, and all $0 \le X \in L^2$, we have $\operatorname{Var}(X^r)^{1/r} \le \operatorname{Var}(X^s)^{1/s}$. We also…

We show that arithmetic definability of henselian valuations is preserved by the tilting correspondence. Moreover, we show that if a perfectoid valuation is arithmetically definable, then no parameters are needed. We also investigate…

We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…

We revisit a classical theme of (general or translation invariant) valuations on convex polyhedra. Our setting generalizes the classical one, in a ``dual'' direction to previously considered generalizations: while previous research was…

In this paper, we study the value distribution of zeros of certain nonlinear difference polynomials of entire functions of finite order.

In this paper, we investigate the monotone property of the continued fractions $G(m,\lambda)$ as a function of $m$ and $\lambda$. In particular, we obtain new inequality for the relative continued fractions.

We derive sufficient conditions for the convex and monotonic g-stochastic ordering of diffusion processes under nonlinear g-expectations and g-evaluations. Our approach relies on comparison results for forward-backward stochastic…

We consider two operations on the Mittag-Leffler function which cancel the exponential term in the expansion at infinity, and generate a completely monotonic function. The first one is the action of a certain differential-difference…

We characterize all logarithmic, holomorphic vector-valued modular forms which can be analytically continued to a region strictly larger than the upper half-plane.

The construction of numerical value scales (or priority values) is a recurrent topic in decision-aiding research. However, in real contexts, uncertainty and limited cognitive precision often lead decision-makers to provide interval…

We give explicit evaluations of the linear and non-linear Euler sums of hyperharmonic numbers $h_{n}^{\left( r\right) }$ with reciprocal binomial coefficients. These evaluations enable us to extend closed form formula of Euler sums of…

We review computations of joint invariants on a linear symplectic space, discuss variations for an extension of group and space and relate this to other equivalence problems and approaches, most importantly to differential invariants.

We study observables on monotone $\sigma$-complete effect algebras. We find conditions when a spectral resolution implies existence of the corresponding observable. The set of sharp elements of a monotone $\sigma$-complete homogeneous…

We consider tilings of Euclidean spaces by polygons or polyhedra, in particular, tilings made by a substitution process, such as the Penrose tilings of the plane. We define an isomorphism invariant related to a subgroup of rotations and…

This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…

We investigate operator-valued monotone independence, a noncommutative version of independence for conditional expectation. First we introduce operator-valued monotone cumulants to clarify the whole theory and show the moment-cumulant…

Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward…

We give a complete and elementary proofs of "Jordan's sums" and study Euler's types sums. In particular we give a formula for the sum of series with same weight, which is similar to this one of classical 2-Euler's sums.