I've been working on an alternative attention mechanism that treats language as a physical field system instead of using standard O(n²) self-attention. **How it works:** - Tokens are mapped onto a ...
I've been working on an alternative attention mechanism that treats language as a physical field system instead of using standard O(n²) self-attention. **How it works:** - Tokens are mapped onto a ...
I've been working on an alternative attention mechanism that treats language as a physical field system instead of using standard O(n²) self-attention. **How it works:** - Tokens are mapped onto a ...
We give a pedagogical introduction to certain aspects of supersymmetric field theories in anti-de Sitter space. Among them are the presence of masslike terms in massless wave equations, irreducible unitary representations and the phenomenon of mult...
In this article we give solution of the general quintic equation by means of the Rogers-Ramanujan continued fraction. More precisely we express a root of the quintic as a known algebraic function of the Rogers-Ramanujan continued fraction....
In an earlier paper Cooper, Shepard, and Sodano introduced a generalized KdV equation that can exhibit the kinds of compacton solitary waves that were first seen in equations studied by Rosenau and Hyman. This paper considers the PT-symmetric exten...
This article introduces a new geophysical theory, in the form of a single simple partial integro-differential equation, to explain how frictional abrasion alone of a stone on a planar beach can lead to the oval shapes observed empirically. The underl...
The influence of the medium dependent finite width of QGP bags on their equation of state is analyzed within an exactly solvable model. It is argued that the large width of the QGP bags not only explains the observed deficit in the number of hadron...
We have performed first-principles molecular-dynamics simulations based on density-functional theory to study the thermophysical properties of ethane under extreme conditions. We present new results for the equation of state of fluid ethane in the wa...
Very recently Harada has proposed a gravitational theory which is of third order in the derivatives of the metric tensor with the property that any solution of Einstein's field equations (EFEs) possibly with a cosmological constant is necessarily a s...
We review the vacuum solutions of Einstein's equations in higher dimensions known as Myers-Perry metrics. In many respects, these solutions describing spinning black holes admit the same remarkable properties as the standard Kerr black hole in four d...
We derive the algebraic generating function for inversion sequences avoiding the patterns $201$ and $210$ by describing a set of succession rules, converting them to a system of generating function equations with one catalytic variable, and then solv...
Enlarged Krylov subspace methods and their s-step versions were introduced [7] in the aim of reducing communication when solving systems of linear equations Ax = b. These enlarged CG methods consist of enlarging the Krylov subspace by a maximum of t...
Long waves in shallow water propagating over a background shear flow towards a sloping beach are being investigated. The classical shallow-water equations are extended to incorporate both a background shear flow and a linear beach profile, resulting...
We investigate the spectral properties of the time-dependent linear transport equation with bounce-back boundary conditions. A fine analysis of the spectrum of the streaming operator is given and the explicit expression of the strongly continuous s...
We present a formalization of the spine change of measure approach for branching diffusions that improves on the scheme laid out for branching Brownian motion in Kyprianou (2004) ["Travelling wave solutions to the KPP equation, Ann. Inst. H. Poinca...
Recently, Lad, Patel, and Pratap (LP&P) [Phys. Rev. E 105, 064107 (2022)] revisited a microscopic theory of molecular motion in liquids, proposed by Glass and Rice [Phys. Rev. 176, 239 (1968)]. Coming from this theory, LP&P derived a new equation of...
The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved nonconvex relaxations...
In the framework of the European research project MeteoMet, the LNE-CNAM and the LNE-CETIAT are developing novel copper cells for the determination of the water vapour pressure equation and the measurement of the triple point of water temperature at...
One of the most important topics in quantum scientific computing is solving differential equations. In this paper, generalized quantum functional expansion (QFE) framework is proposed. In the QFE framework, a functional expansion of solution is encod...