Related papers: An Integral Identity Relating Diamond and Square D…
In this paper, we introduce a new notion, called the integral dimension, for noetherian rings. It can be regarded as the weak Briancon-Skoda numbers of rings. The point is that every noetherian local ring has finite integral dimension.
We introduce a self-inverse function via an integral equivalent to a two-term combination of dilogarithms. We refer to this function as a fundamental form, since there is a family of extensions of this function that satisfy similar…
In this paper, a general integral identity for convex functions is derived. Then, we establish new some inequalities of the Simpson and the Hermite-Hadamard's type for functions whose absolute values of derivatives are convex. Some…
A commutative ring $R$ is stable if every non-zero ideal $I$ of $R$ is projective over its ring of endomorphisms. Motivated by a paper of Bass in the 1960s, stable rings have received wide attention in the literature ever since then. Much…
Deep learning models dealing with image understanding in real-world settings must be able to adapt to a wide variety of tasks across different domains. Domain adaptation and class incremental learning deal with domain and task variability…
While investigating the properties of a galaxy model used in Stellar Dynamics, a curious integral identity was discovered. For a special value of a parameter, the identity reduces to a definite integral with a very simple symbolic value;…
Let $L_H$ denote the set of all normalized locally one-to-one and sense-preserving harmonic functions in the unit disc $\Delta$. It is well-known that every complex-valued harmonic function in the unit disc $\Delta$ can be uniquely…
We study a new biholomorphic invariant of holomorphic maps between domains in different dimensions based on generic initial ideals. We start with the standard generic monomial ideals to find invariants for rational maps of spheres and…
In courses on integration theory, Chasles property is usually considered as elementary and so "natural" that this is sometimes left to the reader. When the functions take their values in finite dimensional spaces, the property is always…
The basic properties of the Daniell integral are presented. We do not use the standard approach of introducing auxiliary spaces of the "over-functions" and "under-functions." Instead, we use a simple and direct approach based on…
Inverse semigroups are a class of semigroups whose structure induces a compatible partial order. This partial order is examined so as to establish mirror properties between an inverse semigroup and the semilattice of its idempotent…
Eigenfunctions of integrable planar billiards are studied - in particular, the number of nodal domains, $\nu$, of the eigenfunctions are considered. The billiards for which the time-independent Schr\"odinger equation (Helmholtz equation) is…
It is well-known that an integrally closed domain $D$ can be express as the intersection of its valuation overrings but, if $D$ is not a Pr\"{u}fer domain, the most of valuation overrings of $D$ cannot be seen as localizations of $D$. The…
In this paper, we tackle unresolved inquiries by Ferreira et al. \cite{bruno} in their recent publication, ``Functional Identity on Division Algebras". We delve into the intricate behavior of additive functions on matrix algebras over…
We propose a new symmetric cryptographic scheme based on functional invariants defined over discrete oscillatory functions with hidden parameters. The scheme encodes a secret integer through a four-point algebraic identity preserved under…
This paper explores the properties of multipliers associated with discrete analogues of fractional integrals, revealing intriguing connections with Dirichlet characters, Euler's identity, and Dedekind zeta functions of quadratic imaginary…
We prove that the domain of the local Dirichlet form is strictly contained in the domain of any stable-like non-local Dirichlet form on general metric measure spaces.
Although a significant progress has been witnessed in supervised person re-identification (re-id), it remains challenging to generalize re-id models to new domains due to the huge domain gaps. Recently, there has been a growing interest in…
Let X be a complex analytic manifold and D \subset X a free divisor. Integrable logarithmic connections along D can be seen as locally free {\cal O}_X-modules endowed with a (left) module structure over the ring of logarithmic differential…
Recent advances in domain adaptation, especially those applied to heterogeneous facial recognition, typically rely upon restrictive Euclidean loss functions (e.g., $L_2$ norm) which perform best when images from two different domains (e.g.,…