Nov 28, 2023 · I'm currently working to grasp the concepts of (continuous) functional calculus, aiming to prove the spectral theorem for bounded self-adjoint operators as outlined in "Introduction to …
We present more than 50 results including some range inclusion results to characterize reverse order law for Moore-Penrose inverse of closed range Hilbert space operators. We use basic properties of Moore-Penrose inverse to prove the results. Some ex...
Fuglede-Putnam theorem is not true in general for $ EP $ operators on Hilbert spaces. We prove that under some conditions the theorem holds good. If the adjoint operation is replaced by Moore-Penrose inverse in the theorem, we get Fuglede-Putnam type...
In this paper we prove Vogan's conjecture on local Arthur packets, for Arthur parameters of $p$-adic general linear groups that are irreducible as representations of $W_F \times SL_2(\mathbb{C}) \times SL_2(\mathbb{C})$ - we refer to such parameters...
We study problems of reconfiguration of shortest paths in graphs. We prove that the shortest reconfiguration sequence can be exponential in the size of the graph and that it is NP-hard to compute the shortest reconfiguration sequence even when we kno...
We consider the dynamics of hedgehog solutions in the $(3+1)$-dimensional Skyrme model which is an energy-supercritical problem. We introduce a new strategy to prove global wellposedness for arbitrarily large initial data....
Amazon Prime Video may be able to prove otherwise. The app is brimming with brilliant films, dramas, and comedies, as well as sports and children’s TV, all available to watch on demand.
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Grab your mobile device and prove you have what it takes to best your friends and family in this addictive multiplayer game. Whether you need to relax after a long day, or are looking to train...
S.3563 — 119th Congress (2025-2026) A bill to require the Secretary of Defense assess and, as appropriate, implement open technical standards for digital content provenance, and for other purposes.
We prove existence and uniqueness of strong solutions to the two-phase Stefan problem with Gibbs-Thomson law where the free interface forms a ninety degree contact angle with the fixed boundary. We also discuss existence of global solutions and conve...
Step-by-step reasoning approaches like chain of thought (CoT) have proved to be very effective in inducing reasoning capabilities in large language models. However, the success of the CoT approach is fundamentally tied to the model size, and billion...
This paper examines the problem of obtaining a $D(4)$-quadruple by adding a smaller element to a $D(4)$-triple. We prove some relations between elements of observed hypothetical $D(4)$-quadruples under which conjecture of the uniqueness of such an ex...
Denote by Q_d the d-dimensional hypercube. Addressing a recent question we estimate the number of ways the vertex set of Q_d can be partitioned into vertex disjoint smaller cubes. Among other results, we prove that the asymptotic order of this functi...
Nature, a synthetic master, creates more than 300,000 natural products (NPs) which are the major constituents of FDA-proved drugs owing to the vast chemical space of NPs. To date, there are fewer than 30,000 validated NPs compounds involved in about...
This paper has been withdrawn by the authors because of an error in the proof. We can, however, prove a weaker spatial fall-off that is still superlinear, namely exp[-x log x]....
The Lieb-Oxford inequality provides a lower bound on the Coulomb energy of a classical system of $N$ identical charges only in terms of their one-particle density. We prove here a new estimate on the best constant in this inequality. Numerical evalua...
We prove a Lieb-Oxford-type inequality on the indirect part of the Coulomb energy of a general many-particle quantum state, with a lower constant than the original statement but involving an additional gradient correction. The result is similar to a...
We formulate a non-commutative analog of the Brascamp-Lieb inequality, and prove it in several concrete settings....
Feb 22, 2026 · How can Gentiles be saved? Why is there so many books written by scribes if the written word has already been revealed? Deuteronomy 4:2; 12:32. Proverbs 30:5,6.