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At its most basic level, set theory describes the relationship between objects and whether they are elements (or members) of a given set. Sets are also objects, and thus can also be related to each …
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Jul 23, 2025 · Set theory is a branch of mathematics that deals with collections of objects, called sets. A set is simply a collection of distinct elements, such as numbers, letters, or even everyday objects, …
arxiv.org/abs/hep-th/0008217v1
String theory is accused by some of its critics to be a purely abstract mathematical discipline, having lost the contact to the simple yet deeply rooted questions which physics provided until the beginning of this century. We argue that, in contrar...
arxiv.org/abs/1403.3772v4
Around 2000, J.-Y. Girard developed a logical theory, called Ludics. This theory was a step in his program of Geometry of Interaction, the aim of which being to account for the dynamics of logical proofs. In Ludics, objects called designs keep only w...
arxiv.org/abs/1606.05221v2
The effective field theory of heterotic vacua that realise $\mathbb{R}^{3,1}$ preserving $\mathcal{N} =1$ supersymmetry are studied. The vacua in question admit large radius limits taking the form $\mathbb{R}^{3,1}\times {X}$ , with ${X}$ a smooth th...
arxiv.org/abs/2509.00666v2
We investigate the unsteady lift response of compliant membrane wings in hovering kinematics by combining analytical inviscid theory with experimental results. An unsteady aerodynamic model is derived for a compliant thin aerofoil immersed in incompr...
arxiv.org/abs/2405.19156v1
Many machine learning models appear to deploy effortlessly under distribution shift, and perform well on a target distribution that is considerably different from the training distribution. Yet, learning theory of distribution shift bounds performanc...
arxiv.org/abs/0704.2503v4
In this note we explain that homotopy coherent simplicial nerve has to used intead of the standard definition in the author's papers on formal deformation theory. A convenient version of the notion of fibered category is presented which is useful onc...
arxiv.org/abs/2301.03685v2
In this note, we study the delooping of spaces and maps in homotopy type theory. We show that in some cases, spaces have a unique delooping, and give a simple description of the delooping in these cases. We explain why some maps, such as group homomo...
arxiv.org/abs/2405.03823v3
Hebbian learning theory is rooted in Pavlov's Classical Conditioning. While mathematical models of the former have been proposed and studied in the past decades, especially in spin glass theory, only recently it has been numerically shown that it is...
arxiv.org/abs/1301.1491v3
We introduce an equivariant algebraic kk-theory for G-algebras and G-graded algebras. We study some adjointness theorems related with crossed product, trivial action, induction and restriction. In particular we obtain an algebraic version of the Gree...
arxiv.org/abs/1408.1639v2
Let $\mathcal{G}$ be an algebraic quantum group. We introduce an equivariant algebraic $kk$-theory for $\mathcal{G}$-module algebras. We study an adjointness theorem related with smash product and trivial action. We also discuss a duality property....
arxiv.org/abs/1003.3392v1
In this paper we set up the theory of acid zeta function and ajoint acid zeta function, based on the theory, we point out a reason to doubt the truth of the Riemann hypothesis and also as a consequence, we give out some new RH equivalences....
arxiv.org/abs/physics/0611211v1
The Broensted and Lowry acid base theory is based on the capacity of proton donation or acceptance (in the presence or absence of a solvent) whereas the Lewis acid base theory is based on the propensity of electron pair acceptance or donation. We e...
arxiv.org/abs/1002.4208v1
We introduce a theoretical formalism to describe disorder-induced extrinsic scattering in slow-light photonic crystal waveguides. This work details and extends the optical scattering theory used in a recent \emph{Physical Review Letter} [M. Patters...
arxiv.org/abs/hep-th/9607183v2
String-bit models are both an efficient way of organizing string perturbation theory, and a possible non-perturbative composite description of string theory. This is a summary of ideas and results of string-bit and superstring-bit models, as presen...
arxiv.org/abs/2009.05715v1
In this article we find the solution of the Burger equation with viscosity applying the boundary layer theory. In addition, we will observe that the solution of Burger equation with viscosity converge to the solution of Burger stationary equation in...
arxiv.org/abs/hep-ph/9507258v2
We explore some of the constraints imposed by positivity of the QCD measure (Weingarten's inequalities) on the parameters defining chiral perturbation theory. We find, in particular, that $2 m_q (μ)\leq B_0(μ) Z(μ)$. The use of further propertie...
arxiv.org/abs/2208.07941v2
In 2006, Jeff Smith proposed a theory of ideals for rings in a triangulated symmetric monoidal category such as ring spectra or DGAs. We show that his definition is equivalent to a `central' $R$-$R$-bimodule map $ I \to R$....
arxiv.org/abs/hep-th/9304032v1
We examine the dynamics of a free massless scalar field on a figure eight network. Upon requiring the scalar field to have a well defined value at the junction of the network, it is seen that the conserved currents of the theory satisfy Kirchhoff's...
