Realistic phenomena can be described more appropriately using generalized canonical ensemble, with proper parameter sets involved. We have generalized the Einstein's theory for specific heat of solid in Tsallis statistics, where the temperature fluct...
This is the first paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In this paper, we lay the foundations for this study by introducing the notion of...
The multiple detections of gravitational waves by LIGO (the Laser Interferometer Gravitational-Wave Observatory), operated by Caltech and MIT, have been acclaimed as confirming Einstein's prediction, a century ago, that gravitational waves propagatin...
We provide a complete set of game-theoretic conditions equivalent to the existence of a transformation from one quantum channel into another one, by means of classically correlated pre/post processing maps only. Such conditions naturally induce tests...
This monograph considers a few topics in the theory of primitive roots g(p) modulo a prime p>=2. A few estimates of the least primitive roots g(p) and the least prime primitive roots g^*(p) modulo p, a large prime, are determined. One of the estimate...
We study various aspects of the structure and representation theory of singular Artin monoids. This includes a number of generalizations of the desingularization map and explicit presentations for certain finite quotient monoids of diagrammatic natur...
We study the Demazure-Lusztig operators induced by the left multiplication on partial flag manifolds $G/P$. We prove that they generate the Chern-Schwartz-MacPherson classes of Schubert cells (in equivariant cohomology), respectively their motivic Ch...
The distributive laws of ring theory are fundamental equalities in algebra. However, recently in the study of the Yang-Baxter equation, many algebraic structures with alternative "distributive" laws were defined. In an effort to study these "left dis...
We introduce an extension of the propositional calculus to include abstracts of predicates and quantifiers, employing a single rule along with a novel comprehension schema and a principle of extensionality, which are substituted for the Bernays postu...
AlphaFold, a groundbreaking protein prediction model, has revolutionized protein structure prediction, populating the AlphaFold Protein Database (AFDB) with millions of predicted structures. However, AlphaFold's accuracy in predicting proteins with i...
Strategic classification, i.e. classification under possible strategic manipulations of features, has received a lot of attention from both the machine learning and the game theory community. Most works focus on analysing properties of the optimal de...
I HATE PHYSICS!!!! LIKE BRO WHY TF DO YOU EVEN EXIST? I would like to ask: Can I skip derivations? I have done the theory and formulas ????...
Haken n-manifolds have been defined and studied by B. Foozwell and H. Rubinstein in analogy with the classical Haken manifolds of dimension 3, based upon the the theory of boundary patterns developed by K. Johannson. The Euler characteristic of a Hak...
We extend the earlier model of condensate growth of Davis et al [Davis MJ, Gardiner CW and Ballagh RJ 2000, Phys. Rev. A 62, 063608] to include the effect of gravity in a magnetic trap. We carry out calculations to model the experiment reported by...
A non-technical introduction to the theory of magnets with strong geometric frustration is given, concentrating on magnets on corner-sharing (kagome, pyrochlore, SCGO and GGG) lattices. Their rich behaviour is traced back to a large ground-state de...
We propose a holographic model for local quench in 1+1 dimensional Conformal Field Theory (CFT). The local quench is produced by joining two identical CFT's on semi-infinite lines. When these theories have a zero boundary entropy, we use the AdS/Boun...
Modern Yo-Yo play has developed into a sophisticated international subculture, featuring elite competition and intricate tricks. Despite this, no systematic knot-theoretic treatment has yet been applied to the numerous string configurations realised...
In this article, the maximal length of a chain of paramagnetic particles with magnetic anisotropy in a rotating magnetic field is studied. The theory of paramagnetic particle chains usually assumes that the particles are magnetically isotropic and do...
The existence of Anderson localization, characterized by vanishing diffusion due to strong randomness, has been demonstrated in numerous ways. A systematic approach based on the Anderson quantum model of the Fermi gas in random lattices that can desc...
Is it confirmed who it is, or is it still a mystery? According to my theory (the most obvious one), it's Kadisha, but from the present day lol. What do you think?...