A5112259288- Advanced Combinatorial Mathematics
- Advanced Mathematical Identities
- Algebraic structures and combinatorial models
- Commutative Algebra and Its Applications
- Mathematics and Applications
- graph theory and CDMA systems
- Algebraic Geometry and Number Theory
- Polynomial and algebraic computation
- Geometric and Algebraic Topology
- Extracellular vesicles in disease
- Nanoplatforms for cancer theranostics
- Advanced Algebra and Logic
- Advanced Differential Equations and Dynamical Systems
- Mathematical Dynamics and Fractals
- Advanced Topics in Algebra
- Finite Group Theory Research
- Point processes and geometric inequalities
- Advanced Topology and Set Theory
- Advanced Sensor and Energy Harvesting Materials
- Analytic Number Theory Research
- Advanced biosensing and bioanalysis techniques
- Meromorphic and Entire Functions
- Smart Materials for Construction
- Product Development and Customization
- Adenosine and Purinergic Signaling
The University of Texas MD Anderson Cancer Center
2024
Southern University of Science and Technology
2024
Kaifeng University
2024
Xi'an Railway Survey and Design Institute
2024
Beijing Institute of Technology
2024
Massachusetts Institute of Technology
2011-2019
Affiliated Hospital of Zunyi Medical College
2017
Guangzhou Medical University
2017
Shandong University
2015
Pennsylvania State University
2013
Order polytope and chain are two polytopes that arise naturally from a finite partially ordered set. These have been deeply studied viewpoints of both combinatorics commutative algebra. Even though these possess remarkable combinatorial algebraic resemblance, they seem to be rarely unimodularly equivalent. In the present paper, we prove following simple elegant result: order for poset equivallent if only avoid 5-element "X" shape subposet. We also explore few equivalent statements main result.
Let $P$ be a polytope with rational vertices. A classical theorem of Ehrhart states that the number lattice points in dilations $P(n) = nP$ is quasi-polynomial $n$. We generalize this by allowing vertices P(n) to arbitrary functions In case we prove for $n$ sufficiently large. Our work was motivated conjecture on solutions parametrized linear Diophantine equations whose coefficients are polynomials $n$, and explain how these two problems related.
Given compact metric spaces X and Z with Hausdorff dimension n, if there is a distance-nonincreasing onto map f : → X, then the nvolumes satisfy vol(X) ≤ vol(Z).The relatively maximum volume conjecture says that are both Alexandrov = vol(Z), isometric to gluing space produced from along its boundary ∂ length-preserving.We partially verify this give further classification for n-spaces in terms of fixed radius directions.We also an elementary proof pointed version Bishop-Gromov relative...
The semiconductor thin film engineering technique plays a key role in the development of advanced electronics. Printing uniform nanofilms on freeform surfaces with high efficiency and low cost is significant for actual industrialization Herein, high-throughput colloidal printing (HTCP) strategy reported fabricating large-area surfaces. High-throughput rely balance atomization evaporation, as well introduced thermal Marangoni flows dispersion, that suppresses outward capillary flows....
Abstract Background Small extracellular vesicle (sEV) analysis can potentially improve cancer detection and diagnostics. However, this potential has been constrained by insufficient sensitivity, dynamic range, the need for complex labeling. Methods In study, we demonstrate combination of PANORAMA fluorescence imaging single sEV analysis. The co-acquisition images enables label-free visualization, enumeration, size determination, cargo microRNAs ( miRs ). Results An increased count is...
Given two families X and Y of integral polytopes with nice combinatorial algebraic properties, a natural way to generate new class is take the intersection P = P1 ∩ P2, where ∈ X, P2 Y. Two basic questions then arise: 1) when 2) whether inherits "old type" from P1, or has "new type", that is, unimodularly equivalent polytope in ∪ not. In this paper, we focus on order chain polytopes. Following above framework, create which are named order-chain When studying their volumes, discover relation...
It will be shown that the toric ring of chain polytope a finite partially ordered set is an algebra with straightening laws on distributive lattice. Thus in particular every possesses regular unimodular triangulation arising from flag complex.
Zonotopal algebra studies pairs of dual algebraic structures that are associated with a linear matroid X and connected to corresponding geometries. Both the geometry encode in their statistics combinatorial properties matroid. We provide this paper general, unified, framework for chapter zonotopal is known as external. The approach critically based on employing simultaneously two constructs invokes underlying matroidal geometric an essential way.
Semiconductor nanofilm fabrication with advanced technology is of great importance for next-generation electronics/optoelectronics. Fabrication high-quality and perfectly oriented semiconductor thin films integration into high-performance electronic devices low cost high efficiency are huge challenges. Here we exquisitely utilized the Marangoni effect to guide tin disulfide (SnS2) nanocoins an ordered assembly in milliseconds, resulting uniaxial-oriented monolayer film. Further exploration...
Recently, the second author studied an Eulerian statistic (called cover) in context of convex polytopes, and proved equal joint distribution (cover,des) with (des,exc). In this paper, we present several direct bijective proofs that cover is Eulerian, examine its generalizations their Mahonian partners. We also a quasi-symmetric function proof (suggested by Michelle Wachs) above distribution.