DermResearch (United States)

Hotel Inbox Brazil: Business Model Strategy in Roadside Hospitality

Summary The hospitality industry has undergone significant digital transformation, driven by changing guest expectations, mobile technology adoption, and increasing competition among accommodation providers. In Brazil, where messaging applications such as WhatsApp are deeply embe...

A Complete Proof That No Odd Perfect Numbers Exist, Version v2.0 (Chinese‑English Dual‑Document)

This archive contains two separate PDF manuscripts (Chinese and English versions v2.0). This paper presents a complete argument that no odd perfect numbers exist. Based on Euler’s classical structural characterization for odd perfect numbers, we combine multiplicative properties...

Discernibility Profiles and Mechanism Repertoires of Legal Reply Systems in Shogi

For a fixed legal shogi position and a legal candidate move, consider the complete finite set of legal replies. We observe each reply through three shogi-specific components: actor action edges lost after the reply ($\Lost$), actor action edges newly gained ($\Gain$), and the com...

Discernibility Profiles and Mechanism Repertoires of Legal Reply Systems in Shogi

For a fixed legal shogi position and a legal candidate move, consider the complete finite set of legal replies. We observe each reply through three shogi-specific components: actor action edges lost after the reply ($\Lost$), actor action edges newly gained ($\Gain$), and the com...

Canonical Chain–Node Encoding and Finite-Width Return Renormalization for the Accelerated Collatz Map

We select a canonical orientation of an alternating signed-binary representation of positive odd integers and refine it into a chain--node encoding, called the canonical CPE. The signed representation itself is classical in spirit and closely matches the alternating binary system...

Canonical Chain–Node Encoding and Finite-Width Return Renormalization for the Accelerated Collatz Map

We select a canonical orientation of an alternating signed-binary representation of positive odd integers and refine it into a chain--node encoding, called the canonical CPE. The signed representation itself is classical in spirit and closely matches the alternating binary system...

A Sharp Multiplier-Dimension Threshold for Orthogonal-Dual Product Spaces

Let $A$ be a finite-dimensional commutative symmetric Frobenius algebra over a field $k$, let $\dim_k A=2n$, and let $U\subset A$ be an $n$-dimensional subspace with orthogonal complement $V=U^\perp$. For a multiplier subspace $L\subset A$, write $LU$ for the span of all products...

A Local Toeplitz--Hankel Criterion Equivalent to the Riemann Hypothesis

Let $\xi(s)=\frac12 s(s-1)\pi^{-s/2}\Gamma(s/2)\zeta(s)$ be the completed Riemann xi-function, and let $F(x)=\frac{\xi'}{\xi}\!\left(\frac{1}{1-x}\right)=\sum_{n\ge 0} f_nx^n$ initially denote its germ at the origin. We introduce the real symmetric Toeplitz--Hankel matrix $c_{ij}...

Sharp Defect Envelopes for Orthogonal-Dual Product Spaces

Let $A$ be a finite-dimensional commutative symmetric Frobenius algebra over a field $k$, with $\dim_k A=2n$. Let $U\subset A$ have dimension $n$, put $V=U^\perp$, and let $L\subset A$ contain $1$ with $\dim_k L=m+1$. Classical linear additive combinatorics minimizes a single pro...

A Local Toeplitz--Hankel Criterion Equivalent to the Riemann Hypothesis

Let $\xi(s)=\frac12 s(s-1)\pi^{-s/2}\Gamma(s/2)\zeta(s)$ be the completed Riemann xi-function, and let $F(x)=\frac{\xi'}{\xi}\!\left(\frac{1}{1-x}\right)=\sum_{n\ge 0} f_nx^n$ initially denote its germ at the origin. We introduce the real symmetric Toeplitz--Hankel matrix $c_{ij}...

Sharp Defect Envelopes for Orthogonal-Dual Product Spaces

Let $A$ be a finite-dimensional commutative symmetric Frobenius algebra over a field $k$, with $\dim_k A=2n$. Let $U\subset A$ have dimension $n$, put $V=U^\perp$, and let $L\subset A$ contain $1$ with $\dim_k L=m+1$. Classical linear additive combinatorics minimizes a single pro...

A Sharp Multiplier-Dimension Threshold for Orthogonal-Dual Product Spaces

Let $A$ be a finite-dimensional commutative symmetric Frobenius algebra over a field $k$, let $\dim_k A=2n$, and let $U\subset A$ be an $n$-dimensional subspace with orthogonal complement $V=U^\perp$. For a multiplier subspace $L\subset A$, write $LU$ for the span of all products...