Related papers: The $\infty$-Oreo$^{^\circledR}$
Structurally and chemically complex materials such as amorphous metallosilicates underpin major catalytic and separation technologies, yet their intrinsic complexity challenges reliable atomistic modeling under realistic conditions.…
We study the fair allocation of a cake, which serves as a metaphor for a divisible resource, under the requirement that each agent should receive a contiguous piece of the cake. While it is known that no finite envy-free algorithm exists in…
The problem of fair division known as "cake cutting" has been the focus of multiple papers spanning several decades. The most prominent problem in this line of work has been to bound the query complexity of computing an envy-free outcome in…
We study the problem of fairly allocating a divisible resource, also known as cake cutting, with an additional requirement that the shares that different agents receive should be sufficiently separated from one another. This captures, for…
Experience goods such as sporting and artistic events, songs, videos, news stories, podcasts, and television series, are often packaged and consumed in bundles. Many such bundles are ordered in the sense that the individual items are…
Cake filtration is a widely used solid-liquid separation process. However, the high flow resistance of the nanoporous filter cake lowers the efficiency of the process significantly. The structure and thus the permeability of the filter…
It has been shown that univalent circle packings filling in the complex plane $\bold C$ are unique up to similarities of $\bold C$. Here we prove that bounded degree branched circle packings properly covering $\bold C$ are uniquely…
Fruits and vegetables are usually composed of exocarp and sarcocarp and they take a variety of shapes when they are ripe. Buckled and wrinkled fruits and vegetables are often observed. This work aims at establishing the geometrical…
Many differentiated products have key attributes that are unstructured and thus high-dimensional (e.g., design, text). Instead of treating unstructured attributes as unobservables in economic models, quantifying them can be important to…
A rising number of HCI scholars have begun to use materiality as a starting point for exploring the design's potential and restrictions. Despite the theoretical flourishing, the practical design process and instruction for beginner…
As a model of composite material, the fiber bundle model has been chosen -where a bundle of fibers is subjected to external load and fibers have distributed thresholds. For different loading conditions, such a system shows few precursors…
Using a sample of face-on star-forming galaxies selected from the Sloan Digital Sky Survey, we statistically derive the typical optical depth $\tau_{\rm{cl}}$ of individual HII regions based on the ``Chocolate Chip Cookie" model of Lu2022.…
$R$ is a unital ring with involution. We investigate the characterizations and representations of weighted core inverse of an element in $R$ by idempotents and units. For example, let $a\in R$ and $e\in R$ be an invertible Hermitian…
In the present paper, the pasta phase is studied at finite temperatures within a Thomas-Fermi (TF) approach. Relativistic mean field models, both with constant and density-dependent couplings, are used to describe this frustrated system. We…
In this paper we consider a scenario, consisting of a de Sitter phase followed by a phase described by a scale factor $a(t)\sim t^{q}$, where $1/3<q<1$, which can be viewed as an inflationary toy model. It is argued that this scenario…
Let A#_{\alpha, \omega}H be a partial crossed product. In this paper, we first generalize the theorem about the existence of an enveloping action to twisted partial actions. Second, we construct a Morita context between the partial crossed…
An exactly solvable Quantum Field Theory (QFT) model of Lee-type is constructed to study how neutrino flavor eigenstates are created through interactions and how the localization properties of neutrinos follows from the parent particle that…
We formulate a simplified model of a limit order book, in which the arrival process is independent of the current state. We prove a phase transition result: there exist prices $\kappa_b$ and $\kappa_a$ such that, for any $\epsilon > 0$,…
The Hopf sign conjecture states that a compact Riemannian 2d-manifold M of positive curvature has Euler characteristic X(M)>0 and that in the case of negative curvature X(M) (-1)^d >0. The Hopf product conjecture asks whether a positive…
We give a self contained introduction to A$_\infty$-algebras, A$_\infty$-bimodules and maps between them. The case of A$_\infty$-bimodule-map between $A$ and its dual space $A^{*}$, which we call $\infty$-inner-product, will be investigated…