We consider a closed Riemannian manifold $M$ of negative curvature and dimension at least 3 with marked length spectrum sufficiently close (multiplicatively) to that of a locally symmetric space $N$. Using the methods of Hamenstädt, we show the volu...
We consider a closed negatively curved surface $(M, g)$ with marked length spectrum sufficiently close (multiplicatively) to that of a hyperbolic metric $g_0$ on $M$. We show there is a smooth diffeomorphism $F:M \to M$ with derivative bounds close t...
We have implemented upgrades to the University of Wyoming's Red Buttes Observatory (RBO) to allow remote and autonomous operations using the 0.6 m telescope. Detailed descriptions of hardware and software components provide sufficient information to...
The nature and origin of supermassive black holes (SMBHs) remain an open matter of debate within the scientific community. While various theoretical scenarios have been proposed, each with specific observational signatures, the lack of sufficiently s...
This paper examines a class of singular stochastic control problems with convex objective functions. In Section 2, we use tools from convex analysis to derive necessary and sufficient first order conditions for this class of optimisation problems. Th...
Researchers worried about catastrophic risks from advanced AI have argued that we should expect sufficiently capable AI agents to pursue power over humanity because power is a convergent instrumental goal, something that is useful for a wide range of...
The perfect NOT transformation, probabilistic perfect NOT transformation and conjugate transformation are studied. Perfect NOT transformation criteria on a quantum state set $S$ of a qubit are obtained. Two necessary and sufficient conditions for rea...
sufficient and more efficient, as no copying occurs. Objects in general store composite data. While in simple cases copying can be done by allocating a new
For which monomial supports do most polynomials generate a prime ideal? We give necessary and sufficient conditions for the radical of the ideal to be prime over an algebraically closed field. In characteristic zero, the same conditions give primenes...
When gas giant protoplanets grow sufficiently massive, circumplanetary disks would form. While solid bodies captured by the circumplanetary disks likely contribute to the growth of the planets and regular satellites around them, some of captured bodi...
We present a new sufficient condition on stability number and toughness of the graph to have an f-factor....
In terms of Turaev's shadows, we provide a sufficient condition for a compact, smooth, acyclic 4-manifold with boundary the 3-sphere to be diffeomorphic to the standard 4-ball. As a consequence, we prove that if a compact, smooth, acyclic 4-manifold...
We give a necessary and sufficient condition for the mapping class group of the pair of the 3-sphere and a graph embedded in it to be isomorphic to the topological symmetry group of the embedded graph....
This note adds three annexes to my previous paper math/9904044 Annex 1. A sufficient condition for self-adjointness Annex 2. Invariant closed operators on locally compact abelian groups Annex 3. The trace of Connes for quaternions This last it...
Not everybody can be equipped with professional photography skills and sufficient shooting time, and there can be some tilts in the captured images occasionally. In this paper, we propose a new and practical task, named Rotation Correction, to automa...
In this paper, we investigate a novel family of polar codes based on multi-kernel constructions, proving that this construction actually polarizes. To this end, we derive a new and more general proof of polarization, which gives sufficient conditions...
A chain of metallic particles, of sufficiently small diameter and spacing, allows linearly polarized plasmonic waves to propagate along the chain. In this paper, we describes how these waves are altered when the liquid crystal host is a nematic or a...
A new criterion necessary and sufficient for the separability of pure bipartite systems for arbitrary finite dimensions is demonstrated; and the corresponding finer quantitative measures or characterizations of entanglement (beyond mere separability...
Nonlinear effects were observed in a forced vibrating string. The motion of the string becomes elliptic as the amplitude of the vibration increases. The fundamental resonance frequency depends on the amplitude of the vibration. At sufficient high a...
The research field of end-user programming has largely been concerned with helping non-experts learn to code sufficiently well in order to achieve their tasks. Generative AI stands to obviate this entirely by allowing users to generate code from natu...