arXiv preprints from January 1, 2026 through September 23, 2026 — 03:24:25 EST
A principal screens an agent whose technology has a minimum efficient scale, so the Spence-Mirrlees condition fails along a monotone dividing curve: the locus at which every type values marginal output equally. For the class in which this curve and the relaxed solution are both strictly monotone, the optimal contract obeys a...
We study $G$-equivariant Hörmander pseudodifferential operators on a noncompact symmetric space $G/K$. We define a notion of a complete symbol function, called the Harish-Chandra symbol function, on the spherical tempered dual of $G$, for operators that satisfy a rapid off-diagonal decay condition on their Schwartz kernels, and we...
We present a systematic development of the arithmetic of the class of linear orders under the ordered sum $(LO, +)$ and prove a number of new results. Our approach is based on a Euclidean algorithm for pairs of linear orders that almost additively commute. Among our results: (i.) We generalize and give unified proofs of the main...
The Kahn--Lovász theorem gives a sharp upper bound on the number of perfect matchings in a graph in terms of its degree sequence, extending the classical Brégman--Minc inequality for bipartite graphs. In this paper, we establish an asymptotically sharp extension of the Kahn--Lovász theorem to $F$-factors for every Hamiltonian graph...
We consider a reference wave, a radiation solution, and the sum of these solutions (total solution) for the Helmholtz equation in an exterior region. We give two-point formulas for approximate phase recovering of the radiation solution from the intensity of the total solution for the case of spherical reference wave. We show that...
Transformational electric vertical take-off and landing (eVTOL) vehicles have gained significant attention over the past decade due to their efficient wing-borne cruise capabilities and reduced reliance on ground-based infrastructure. However, control system design for these vehicles remains challenging, as they must operate across...
Variable active power injections arising from device behavior or compromised dispatch complicate voltage regulation in electric power networks with distributed energy resources (DERs). An operator can limit the resulting voltage deviations by remotely selecting DER reactive power parameters before observing the active power...
Sparse pursuit after dictionary learning can yield a precise atom support even when its physical interpretation is not justified by the calibration data, especially for highly coherent dictionaries where alternative calibration-compatible dictionaries may assign different physical meanings to the same selected support. We develop...
The growth rate of Av(1324) is the last unknown Stanley-Wilf limit of a length-four pattern. The best rigorous lower bound has been 10.271012 since Bevan, Brignall, Elvey Price and Pantone obtained it in 2020; we raise it to 10.617. Their scheme relaxes an interleaving rule in one direction only. Relaxing it in both is valid, and the...
The Viterbo isomorphism relates the symplectic cohomology of a cotangent bundle to the homology of the free loop space of its base. We lift this to a relation of modules over (1) the complex bordism spectrum MU and (2) the sphere spectrum $\mathbb{S}$. In particular, by a result of Porcelli and the present author [BP26], it is not the...
We propose computationally efficient tests for equality of mean vectors of two or more high-dimensional populations. Central to our approach is an equivalence between equality of means and a zero population logistic regression parameter. We establish this equivalence for independently distributed observations without imposing common...
In Markov chain Monte Carlo sampling, light-tailed target distributions present something of a poisoned chalice: their light tails offer good confinement, and tend to imply good mixing properties for natural continuous-time dynamics, but the steepness of their tail decay means that they often fall outside of the scope of modern...
In this study, we present an analytical approach based on the extended Nikiforov-Uvarov method to solve the generalized Klein-Gordon oscillator in the presence of a uniform magnetic field within the Som-Raychaudhuri space-time. Exact eigenstate solutions are obtained for two distinct potential models, namely the linear potential and...
In this paper, we show that the codimension of the singular set of a stable stationary harmonic map to a round $k$-sphere is at least $k+1$ when $k$ is between 3 and 6, and is at least 7 when $k$ is at least 7. The result is sharp in the sense that there exist energy minimizing 0-homogeneous maps in the aforementioned critical...
We construct an explicit finite chain of non-aspherical group presentation complexes $K(\mathcal X)\subset K(\mathcal Y)\subset K(\mathcal Z)$ in which $K(\mathcal Y)$ is Cockcroft, both inclusion-induced maps on $π_2$ are zero, and the pair $(K(\mathcal Y),K(\mathcal X))$ has the identity property. This answers a question of...
Let $G$ be a stratified Lie group and $\mathcal L$ its sub-Laplacian. We prove that the full horizontal Riesz transform $\nabla_{H} \mathcal L^{-1/2}$ is of weak type $(1,1)$ on real-valued functions, with constant at most $2$. In particular, the constant is independent of the horizontal dimension, the homogeneous dimension, the step,...
We study the role of Banach space geometry in deterministic and stochastic maximal regularity. We first construct an example showing that the UMD assumption in Weis' characterisation of maximal $L^p$-regularity in terms of $R$-sectoriality cannot be omitted. Combining this construction with an equivalence between stochastic maximal...
We solve John Milnor's problem: among all convex regions of a given area on the sphere, the round disk requires the greatest distortion in cartographic projections onto the plane.
A unit-area translation surface is called \emph{maximal} if it maximizes the length of the shortest saddle connection among all surfaces in the same stratum. We investigate whether a non-maximal translation surface can be continuously deformed into a maximal one while the systole increases strictly monotonically. Although such a...
A scalar field alone does not determine a quantum theory: states, effects, processes, symmetries, composition, and discard are equally structural. Realification illustrates this point: an orthogonal complex structure J^2 = -I selects the physical real operators and the balanced composite. Quaternionic quantum mechanics has an...
In these lecture notes, we discuss various `hydrodynamic LLN' and `CLT' scaling limits, among others, in types of stochastic interacting particle systems, connecting `microscopic' behaviors to continuum laws. Via `short stories', the aim is to present some of the `basics' for students and those entering the field, as a complement to...
A notable feature of confined active matter systems is the tendency for motile particles to accumulate near solid boundaries. In various linear models with no-flux boundary conditions, this accumulation is realized through the development of sharp boundary layers at small particle diffusivity $κ$. In this paper, we present the first...
Let $\mathrm{Sym(n,k)}$ denote the set of permutations on $\{1,2,\ldots,n\}$ with exactly $k$ cycles. A family $\mathcal{F}\subset\mathrm{Sym}(n,k)$ is said to be intersecting if $σ^{-1}τ$ has a fixed point for all $σ,τ\in\mathcal{F}$. In this paper, we investigate the size and structure of maximum-sized intersecting families of...
Strong light-matter interactions in optical microcavities give rise to hybrid light-matter states known as polaritons. While actively used in modern technologies, theoretical descriptions of such systems are often restricted to the single-excitation case, limiting their ability to capture many-excitation physics and hindering further...
JWST has enabled the discovery of dozens of extremely metal-poor galaxies (EMPGs) with metallicities below $5\%\,Z_{\odot}$, representing a significant leap toward detecting the first galaxies without metals. However, accurate metallicity measurements require careful determination of physical conditions in the ionized gas. In this...