arXiv subjects

Saeed Rasouli

Publications and source records attributed to Saeed Rasouli.

10 recordsLinked to original sources

arXiv2026

Reduction of intrinsic losses in nanomechanical silicon nitride resonators through thermal treatment in ultrahigh vacuum

Since the discovery of dissipation dilution, silicon nitride (SiN) nanomechanical resonators have set the benchmark for ultracoherent mechanical systems, with geometry and strain engineering driving remarkable gains in the $f \cdot Q$ product. Surface loss, however, has remained the dominant and largely unaddressed dissipation channel. Here, we demonstrate a geometry-independent approach that directly targets surface loss: thermal treatment in ultrahigh vacuum. Treatment at 1000$^{\circ}$C enhances the intrinsic quality factor of dissipation-diluted SiN membrane resonators by up to a factor of 20, reduces the surface loss eightfold, and simultaneously increases the tensile stress. Photothermal infrared spectroscopy and $\textit{in situ}$ X-ray photoelectron spectroscopy trace the enhancement to thermally activated silanol condensation - the conversion of surface hydroxyl terminations into siloxane bridges - and the reversibility of both quality factor and stress under controlled humidity confirms the surface-chemical origin. These results establish surface chemistry as a tunable parameter for next-generation ultracoherent nanomechanical resonators.

physics.app-ph↗

arXiv2025

Expected Confidence Dependency: A Novel Rough Set-Based Approach to Feature Selection

This paper proposes Expected Confidence Dependency (ECD), a novel, soft computing-oriented, accuracy driven dependency measure for feature selection within the rough set theory framework. Unlike traditional rough set dependency measures that rely on binary characterizations of conditional blocks, ECD assigns confidence-based contributions to individual equivalence blocks and aggregates them through a normalized expectation operator. We formally establish several desirable properties of ECD, including normalization, compatibility with classical dependency, monotonicity, and invariance under structural and label-preserving transformations.

cs.IT↗

arXiv2025

Sheaf of Residuated Lattices

This paper explores the interface between algebra, topology, and logic by developing the theory of sheaves and etale spaces for residuated lattices, algebraic structures central to substructural and fuzzy logics. We construct stalkwise-residuated etale spaces and demonstrate that they form a subcategory of the category of etale spaces of sets. A categorical and topological characterization of the sheaf condition is presented, with particular emphasis on filters, congruences, and the topologies induced on prime spectra.

math.LO↗

arXiv2024

Etale spaces of residuated lattices

This paper explores the concept of étalé spaces associated with residuated lattices. Notions of bundles and étalés of residuated lattices over a given topological space are introduced and investigated. For a topological space $\mathscr{B}$, we establish that the category of étalés of residuated lattices over $\mathscr{B}$ with morphisms of étalés of residuated lattices is coreflective in the category of bundles of residuated lattices over $\mathscr{B}$ along with morphisms of bundles of residuated lattices. We provide a method for transferring an étalé of residuated lattices over a topological space to another, utilizing a continuous map. Finally, we define a contravariant functor, called the section functor, from the category of étalés of residuated lattices with inverse morphisms to the category of residuated lattices.

math.RA↗

arXiv2022

The pure spectrum of a residuated lattice

This paper studies a fascinating type of filter in residuated lattices, the so-called pure filters. A combination of algebraic and topological methods on the pure filters of a residuated lattice is applied to obtain some new structural results. The notion of purely-prime filters of a residuated lattice has been investigated, and a Cohen-type theorem has been obtained. It is shown that the pure spectrum of a residuated lattice is a compact sober space, and a Grothendieck-type theorem has been demonstrated. It is proved that the pure spectrum of a Gelfand residuated lattice is a Hausdorff space, and deduced that the pure spectrum of a Gelfand residuated lattice is homeomorphic to its usual maximal spectrum. Finally, the pure spectrum of an mp-residuated lattice is investigated and verified that a given residuated lattice is mp iff its minimal prime spectrum is equipped with the induced dual hull-kernel topology, and its pure spectrum is the same.

cs.IT↗

arXiv2022

Mp-residuated lattices

This paper is devoted to the study of a fascinating class of residuated lattices, the so-called mp-residuated lattice, in which any prime filter contains a unique minimal prime filter. A combination of algebraic and topological methods is applied to obtain new and structural results on mp-residuated lattices. It is demonstrated that mp-residuated lattices are strongly tied up with the dual hull-kernel topology. Especially, it is shown that a residuated lattice is mp if and only if its minimal prime spectrum, equipped with the dual hull-kernel topology, is Hausdorff if and only if its prime spectrum, equipped with the dual hull-kernel topology, is normal. The class of mp-residuated lattices is characterized by means of pure filters. It is shown that a residuated lattice is mp if and only if its pure filters are precisely its minimal prime filters, if and only if its pure spectrum is homeomorphic to its minimal prime spectrum, equipped with the dual hull-kernel topology.

math.RA↗

arXiv2022

Gelfand residuated lattices

In this paper, a combination of algebraic and topological methods is applied to obtain new and structural results on Gelfand residuated lattices. It is demonstrated that Gelfand's residuated lattices strongly tied up with the hull-kernel topology. Especially, it is shown that a residuated lattice is Gelfand if and only if its prime spectrum, equipped with the hull-kernel topology, is normal. The class of soft residuated lattices is introduced, and it is shown that a residuated lattice is soft if and only if it is Gelfand and semisimple. Gelfand residuated lattices are characterized using the pure part of filters. The relation between pure filters and radicals in a Gelfand residuated lattice is described. It is shown that a residuated lattice is Gelfand if and only if its pure spectrum is homeomorphic to its usual maximal spectrum. The pure filters of a Gelfand residuated lattice are characterized. Finally, it is proved that a residuated lattice is Gelfand if and only if the hull-kernel and the $\mathscr{D}$-topology coincide on the set of maximal filters.

math.LO↗

arXiv2019

Quasicomplemented residuated lattices

In this paper, the class of quasicomplemented residuated lattices is introduced and investigated, as a subclass of residuated lattices in which any prime filter not containing any dense element is a minimal prime filter. The notion of disjunctive residuated lattices is introduced and it is observed that a residuated lattice is Boolean if and only if it is disjunctive and quasicomplemented. Finally, some characterizations for quasicomplemented residuated lattices are given by means of the new notion of $α$-filters.

math.RA↗

arXiv2018

The hull-kernel topology on residuated lattices

The notion of hull-kernel topology on a collection of prime filters in a residuated lattice is introduced and investigated. It is observed that any collection of prime filters is a $T_0$ topological space under the hull-kernel and the dual hull-kernel topologies. It is proved that any collection of prime filters is a $T_1$ space if and only if it is an antichain, and it is a Hausdorff space if and only if it satisfies a certain condition. Some characterizations in which maximal filters forms a Hausdorff space are given. At the end, it is focused on the space of minimal prim filters, and it is shown that this space is a totally disconnected Hausdorff space. This paper is closed by a discussion abut the various forms of compactness and connectedness of this space.

math.GN↗

arXiv2018

$n$-normal residuated lattices

The notion of $n$-normal residuated lattice, as a class of residuated lattices in which every prime filter contains at most $n$ minimal prime filters, is introduced and studied. Before that, the notion of $ω$-filter is introduced and it is observed that the set of $ω$-filters in a residuated lattice forms a distributive lattice on its own, which includes the set of coannulets as a sublattice. The class of $n$-normal residuated lattices is characterized in terms of their prime filters, minimal prime filters, coannulets and $ω$-filters.

math.RA↗