Related papers: Logarithmic and absolute-value like properties of …
We prove a functorial correspondence between a category of logarithmic $\mathfrak{sl}_2$-connections on a curve $X$ with fixed generic residues and a category of abelian logarithmic connections on an appropriate spectral double cover $\pi :…
The geometric and algebraic theory of valuations on cones is applied to understand identities involving summing certain rational functions over the set of linear extensions of a poset.
We use fast-growing finite and infinite sequences of natural numbers and more complicated constructs to define models of hypercomputation and interpret non-arithmetic predicates, with the strongest extensions reaching full second order…
We explore a well-known integral representation of the logarithmic function, and demonstrate its usefulness in obtaining compact, easily-computable exact formulas for quantities that involve expectations and higher moments of the logarithm…
This article establishes several remarkably simple identities relating certain metric invariants of level curves of real and complex functions. In particular, we relate lengths of level curves to their curvature and to the gradient field of…
In this technical report, certain interesting classification of arithmetical functions is proposed. The notion of additively decomposable and multiplicatively decomposable arithmetical functions is proposed. The concepts of arithmetical…
We study the properties of the logarithm of the derivative operator and show that its action on a constant is not zero, but yields the sum of the logarithmic function and the Euler-Mascheroni constant. We discuss more general aspects…
We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is…
In this paper, some monotonicity and concavity results of several functions involving the psi and polygamma functions are proved, and then some known inequalities are extended and generalized.
Abstrct: In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.
In the paper, the authors concisely survey and review some functions involving the gamma function and its various ratios, simply state their logarithmically complete monotonicity and related results, and find necessary and sufficient…
In this paper we give some conditions for a class of functions related to Bessel functions to be positive definite or strictly positive definite . We present some properties and relationships involving logarithmically completely monotonic…
Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring theme in regularization approaches is the selection of regularization parameters, and their effect on the solution and on the optimal…
Some basic properties of the ring of integers $\mathbb{Z}$ are extended to entire rings. In particular, arithmetic in entire principal rings is very similar than arithmetic in the ring of integers $\mathbb{Z}$. These arithmetic properties…
We compare some algebras appeared in the recent attempts to prove resolution of singularities in positive characteristic. We also construct an algebra which encodes the same information and it is equivalent, up to integral closure, to the…
We show that Hermite's approximations to values of the exponential function at given algebraic numbers are nearly optimal when considered from an adelic perspective. We achieve this by taking into account the ratio of these values whenever…
We present a complete logic for reasoning with functional dependencies (FDs) with semantics defined over classes of commutative integral partially ordered monoids and complete residuated lattices. The dependencies allow us to express…
We use well-known limit theorems in probability theory to derive a Wallis-type product formula for the gamma function. Our result immediately provides a probabilistic proof of Wallis's product formula for $\pi$, as well as the duplication…
In this tutorial I will present how a combination of linear and dependent type can be useful to describe different properties about higher order programs. Linear types have been proved particularly useful to express properties of functions;…
In the paper, we extend Binet's first formula for the logarithm of the gamma function and investigate some properties, including inequalities, star-shaped and sub-additive properties and the complete monotonicity, of the extended remainder…