Residual Field Research Articles

Ext modules related to syzygies of the residue field

Let R be a commutative noetherian ring. In this paper, we find out close relationships between the module M being embedded in a module of projective dimension at most n and the (n+1)-torsionfreeness of the nth syzygy of M. As an application, when R is local with residue field k, we compute the dimensions as k-vector spaces of Ext modules related to syzygies of k.

On integral class field theory for varieties over p-adic fields

Let K be a finite extension of the p-adic numbers Qp with ring of integers OK and residue field κ. Let X a regular scheme, proper, flat, and geometrically irreducible over OK of dimension d, and XK its generic fiber. We show, under some assumptions on X, that there is a reciprocity isomorphism of locally compact groups Har2d−1(XK,Z(d))≃π1ab(XK)W from the cohomology theory defined in [10] to an integral model π1ab(XK)W of the abelianized fundamental group π1ab(XK). After removing the contribution from the base field, the map becomes an isomorphism of finitely generated abelian groups. The key ingredient is the duality result in [10].

Linear and nonlinear beam dynamics of vertical fixed-field accelerators

Vertical fixed-field accelerators (vFFAs) feature a magnetic field that increases exponentially in the vertical direction, resulting in vertically stacked nonplanar orbits. Their magnetic field is highly nonlinear, and their solenoid and quadrupolar components induce strongly coupled optics. The detailed study of their beam dynamics must account for the transverse motion linear and nonlinear coupling. Specifically, the study of linear beam dynamics requires adequate coupling parametrizations, and the study of nonlinear beam dynamics, including the characterization of the dynamic aperture (DA), must be performed in the full 4D phase space. The ray-tracing code is ideally suited to study the vFFA transverse dynamics, as it can perform step-by-step particle tracking in vFFA complex geometry and magnetic fields. This paper provides an in-depth study of the vFFA prototype ring designed under the ISIS-II proton driver prototype project to accelerate proton beams from 3 to 12 MeV. The magnets of this vFFA ring exhibit slow magnetic field falloffs, resulting in a significant influence of the neighboring cells on the optical lattice parameters. The determination of stable orbits and tunes requires superimposing 3D magnetic field maps in to account for the neighboring cell residual fields. The study of nonlinear beam dynamics revealed the appearance of fourth-order stability islands. A complete characterization of the DA in the 4D phase space was conducted to give a measure of the stability domain and characterize the performance and limitations of this lattice. This study paves the way for further validation studies with experimental data and field maps. Published by the American Physical Society 2024

Neuromyelitis Optica Spectrum Disorder (NMOSD) or Chronic-Relapsing Inflammatory Optic Neuropathy (CRION)?: A Challenge in Diagnosis and Treatment

Abstract
 Introduction : Neuromyelitis optica spectrum disorder (NMOSD) is a chronic inflammatory, immune-mediated central nervous system disease targeting the AQP4-water channel membrane protein of the optic nerve and the spinal cord. This case report aims to present a case of seroconverting NMOSD which was initially diagnosed as chronic relapsing inflammatory optic neuropathy (CRION).
 Case Illustration : 15-year-old female with recurrent, steroid-dependent optic neuritis of the LE. During the first attack, brain MRI showed optic nerve inflammation with normal brain findings. Initial test for AQP4-IgG, MOG-Ab and ANA profile were negative. The diagnosis of CRION was made. Treatment with corticosteroid and immunosuppressant agent was maintained for one year. After treatment cessation, however, LE optic neuritis recurred with bilateral lower limb weakness. Spinal MRI showed signs of longitudinal extensive transverse myelitis. Re-testing for AQP4-IgG showed positive result. Diagnosis of NMOSD was made, and the patient was treated with high-dose intravenous corticosteroid followed by oral dose, and immunosuppressant. Final visual acuity of the LE was 1.0, with minimal residual visual field defect and good motor function.
 Discussion : During the initial attack, the patient did not meet the 2015 NMOSD international consensus diagnostic criteria. The AQP4-IgG was negative and no other corresponding signs and symptoms. The criteria was met one year after: optic neuritis, LETM and positive seroconversion of AQP4-IgG.
 Conclusion : Diagnosing NMOSD is at times challenging especially during initial attack. Retesting of the AQP4- IgG is at times necessary in seronegative patients, especially in children showing ADEM-like event with optic neuritis and LETM to achieve diagnosis and proper treatment strategy.

On input and Langlands parameters for epipelagic representations

A paper of Reeder–Yu [J. Amer. Math. Soc. 27 (2014), pp. 437–477] gives a construction of epipelagic supercuspidal representations of p p -adic groups. The input for this construction is a pair ( λ , χ ) (\lambda , \chi ) where λ \lambda is a stable vector in a certain representation coming from a Moy–Prasad filtration, and χ \chi is a character of the additive group of the residue field. We say two such pairs are equivalent if the resulting supercuspidal representations are isomorphic. In this paper we describe the equivalence classes of such pairs. As an application, we give a classification of the simple supercuspidal representations for split adjoint groups. Finally, under an assumption about unramified base change, we describe properties of the Langlands parameters associated to these simple supercuspidals, showing that they have trivial L-functions and minimal Swan conductors, and showing that each of these simple supercuspidals lies in a singleton L-packet.

Relationship between residual visual field and full-field stimulus testing in patients with late-stage retinal degenerative diseases

This study aimed to investigate how the extent and central/peripheral location of the residual visual field (VF) in patients with late-stage inherited retinal diseases (IRDs) are related to retinal sensitivity detected using full-field stimulus testing (FST). We reviewed the results of Goldmann perimetry and FST from the medical records of patients with IRDs whose VF represents central (within 10°) and/or peripheral islands, or undetectable. In total, 19 patients (19 eyes) were analyzed in this study. The median value of residual VF area was 1.38%. The median values of rod and cone sensitivities were − 14.9 dB and 7.4 dB, respectively. Patients with only the peripheral island (− 33.9 dB) had better median rod sensitivity than other groups (only central, − 18.9 dB; both, − 3.6 dB). VF area significantly correlated with rod sensitivity (r = − 0.943, p = 0.005) in patients with only peripheral island, but not with cone sensitivity. Peripheral VF islands were significant contributors to FST results, especially rod sensitivity. With reduced or loss of central vision, the extent of residual peripheral VF significantly affected rod sensitivity, suggesting that FST can be useful in quantitatively estimating the overall remaining vision in patients with late-stage IRD.

Magnetic Field Enhanced Oxygen Reduction Reaction via Oxygen Diffusion Speedup.

The mass-transfer of oxygen in liquid phases (including in the bulk electrolyte and near the electrode surface) is a critical step to deliver oxygen to catalyst sites (especially immersed catalyst sites) and use the full capacity of oxygen reduction reaction (ORR). Despite the extensive efforts of optimizing the complex three-phase reaction interfaces to enhance the gaseous oxygen transfer, strong limitations remain due to oxygen's poor solubility and slow diffusion in electrolytes. Herein, a magnetic method for boosting the directional hydrodynamic pumping of oxygen toward immersed catalyst sites is demonstrated which allows the ORR to reach otherwise inaccessible catalytic regions where high currents normally would have depleted oxygen. For Pt foil electrodes without forced oxygen saturation in KOH electrolytes, the mass-transfer-limited current densities can be improved by 60% under an external magnetic field of 435mT due to the synergistic effect between bulk- and surface-magnetohydrodynamic (MHD) flows induced by Lorentz forces. The residual magnetic fields are further used at the surface of magnetic materials (such as CoPt alloys and Pt/FeCo heterostructures) to enhance the surface-MHD effect, which helps to retain part of the ORR enhancement permanently without applying external magnetic fields.

Achieving ultra-low and -uniform residual magnetic fields in a very large magnetically shielded room for fundamental physics experiments

High-precision searches for an electric dipole moment of the neutron (nEDM) require stable and uniform magnetic field environments. We present the recent achievements of degaussing and equilibrating the magnetically shielded room (MSR) for the n2EDM experiment at the Paul Scherrer Institute. We present the final degaussing configuration that will be used for n2EDM after numerous studies. The optimized procedure results in a residual magnetic field that has been reduced by a factor of two. The ultra-low field is achieved with the full magnetic-field-coil system, and a large vacuum vessel installed, both in the MSR. In the inner volume of ∼1.4m3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim 1.4~\\hbox {m}^3$$\\end{document}, the field is now more uniform and below 300 pT. In addition, the procedure is faster and dissipates less heat into the magnetic environment, which in turn, reduces its thermal relaxation time from 12h\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$12~\ ext {h}$$\\end{document} down to 1.5h\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1.5~\ ext {h}$$\\end{document}.

Visualization evaluation of damage degree on remanufacturing cores based on residual magnetic scanning measurement

A novel residual magnetic scanning measurement (RMSM) method with easy operation, low cost and good universality based on metal magnetic memory (MMM) is proposed to evaluate the damage degree of remanufacturing cores. The two-dimensional (2-D) grayscale maps of residual magnetic field (RMF) and residual stress can be visualized, respectively, by constructing the relationship among magnetic field, stress and pixel gray value. The contour of high residual stress zone which enters the plastic stage can be extracted from the 2-D grayscale map based on the gray thresholds representing the yield strength. The defect size can also be inverted with the evaluation error below 10 % and the resolution reaching 0.2 mm. To prove the feasibility of RMSM applying into the damage evaluation on remanufacturing cores, the RMF distribution and the high residual stress zone of a damaged gear are also visualized. The 2-D grayscale maps of RMF and residual stress can clearly show the profile of gear and the plastic deformation damage zone. The RMSM method can facilitate the accurate damage evaluation on remanufacturing cores and provide the support for the subsequent repairing process design.

Maximum spherical mean value filtering for whole-brain QSM.

To develop a tissue field-filtering algorithm, called maximum spherical mean value (mSMV), for reducing shadow artifacts in QSM of the brain without requiring brain-tissue erosion. Residual background field is a major source of shadow artifacts in QSM. The mSMV algorithm filters large field-magnitude values near the border, where the maximum value of the harmonic background field is located. The effectiveness of mSMV for artifact removal was evaluated by comparing existing QSM algorithms in numerical brain simulation as well as using in vivo human data acquired from 11 healthy volunteers and 93 patients. Numerical simulation showed that mSMV reduces shadow artifacts and improves QSM accuracy. Better shadow reduction, as demonstrated by lower QSM variation in the gray matter and higher QSM image quality score, was also observed in healthy subjects and in patients with hemorrhages, stroke, and multiple sclerosis. The mSMV algorithm allows QSM maps that are substantially equivalent to those obtained using SMV-filtered dipole inversion without eroding the volume of interest.

Objective Lagrangian Vortex Cores and their Visual Representations.

The numerical extraction of vortex cores from time-dependent fluid flow attracted much attention over the past decades. A commonly agreed upon vortex definition remained elusive since a proper vortex core needs to satisfy two hard constraints: it must be objective and Lagrangian. Recent methods on objectivization met the first but not the second constraint, since there was no formal guarantee that the resulting vortex coreline is indeed a pathline of the fluid flow. In this paper, we propose the first vortex core definition that is both objective and Lagrangian. Our approach restricts observer motions to follow along pathlines, which reduces the degrees of freedoms: we only need to optimize for an observer rotation that makes the observed flow as steady as possible. This optimization succeeds along Lagrangian vortex corelines and will result in a non-zero time-partial everywhere else. By performing this optimization at each point of a spatial grid, we obtain a residual scalar field, which we call vortex deviation error. The local minima on the grid serve as seed points for a gradient descent optimization that delivers sub-voxel accurate corelines. The visualization of both 2D and 3D vortex cores is based on the separation of the movement of the vortex core and the swirling flow behavior around it. While the vortex core is represented by a pathline, the swirling motion around it is visualized by streamlines in the correct frame. We demonstrate the utility of the approach on several 2D and 3D time-dependent vector fields'.

Improving the Uniformity of the Residual Magnetic Field in the MSR Using Independent Coils Compensation Method

Improving the Uniformity of the Residual Magnetic Field in the MSR Using Independent Coils Compensation Method

Temperature control of atomic gas chamber using a nonmagnetic heating chip fabricated on quartz substrate

Nonmagnetic electrical heating and temperature sensing chip fabricated on quartz substrate is developed, and a high-precision digital temperature control system is designed based on this chip. The heating resistance and temperature sensing resistance are prepared by depositing two layers of Ti/Pt alloy electrodes on quartz substrate through magnetic field cancellation design. The temperature coefficient of fabricated Ti/Pt temperature sensing resistance is +0.197%/℃. The simulation results show that the residual magnetic field generated by the heating current in the atomic gas chamber closely adjacent to the chip is less than 0.1 nT. Temperature control in the range of 100~150 ℃ is realized, and the temperature stability is about 0.02 ℃. Due to the high light transmittance of quartz glass, this heating chip has significant advantages for optical integration and miniaturization of atomic magnetometers.

Physical-Layer Network Coding Based on Residual Field of Algebraic Integers in OFDM-VLC Two-Way Relay Networks

Physical-Layer Network Coding Based on Residual Field of Algebraic Integers in OFDM-VLC Two-Way Relay Networks

Variation of color of magnetic noise in Er3+ molecular magnets contacting metal surface in ferromagnetic composite

Interaction between single molecule magnets (SMMs) and metal surface is a hot topic promising controllable deposition of SMMs, programmable frequency of magnetic relaxation and addressed reading of information. In this paper, we develop strategy of the Er3+ based SMM functionalization by its penetration inside the arrays of Ferromagnetic Micro Particles (FMPs). We show that predictable residual magnetic field of the FMPs arrays is an effective tool for regulation of the frequency maximum of imaginary magnetic susceptibility. We analyzed color of magnetic noise in respect to physical origin of magnetic relaxation. An additional channel for control over spin noise is formation of chemical bonds between SMM and the FMPs surface. Oxidation of an Er complex transforms 20 ± 5 % of the initial 10-coordinated SMM complex to the 9-coordinated complex with reduced relaxation time. Memorized residual magnetization of the composite material allows one to set desirable relaxation frequency in the individual micronized cells to create a sound frequency register. The proposed compaction of SMMs of different types in ferromagnetic composites provides engineering of the chemically designed spin interface on ferromagnetic surface for spintronics and quantum computing.

Influence of inter-river water diversion on estuary pollution control: A case study of Liaodong Bay

Long-term mass transport processes in offshore seas are controlled by seasonal residual currents. The Euler residual mass transport velocity field was calculated form seasonal residual current patterns in shallow sea area, comparing with polluted water changes in typical years. The following conclusions were made: closed local large loops of the Euler residual mass transport led to polluted waters in the northeast Liaodong Bay, and the bay's optimal physical self-purification occurred in winter (Euler residual mass transport diffuses polluted water masses) and spring (overall self-purification capacity of the bay plays a role after winter). The central waters were clean while pollutants were discharged into near-shore waters, leading to perennial pollution in some near-shore waters. Pollution in Liaodong Bay could be alleviated or eliminated via diversion of water from the Daliaohe River (flowing into the northeast corner of Liaodong Bay and carrying > 65% of the total amount of pollutants discharged into the top of the bay) into the Liaohe River and Daling River. The percentage of inorganic nitrogen carried by 10% of the flux of the Daliaohe River was 5.70% of that discharged into Liaodong Bay. If 10% of the flux of the Daliaohe River was discharged into the Daling River, the annual total environmental carrying capacity of inorganic nitrogen increased 4.48%. Many bays in the world have adjacent river flows, such as Gulf of Mexico, Gulf of Guinea, and Bay of Bengal. Based on the Euler residual mass transport field, the water transfer between adjacent rivers could make better use of the Euler residual mass transport capacity to mitigate the water pollution of the estuaries.

The Koszulness of numerical semigroup rings of minimal multiplicity

Let R = k [H] be a numerical semigroup ring over a field k and grm (R) is the associated graded ring of R. In this paper, we show that grm (R) is a Cohen-Macaulay ring, provided H has minimal multiplicity. As a consequence, we conclude that the numerical semigroup ring R = k [H] of minimal multiplicity is a Koszul ring, i.e., the residue field k has a grm (R) – linear free resolution.

Strongly divisible lattices and crystalline cohomology in the imperfect residue field case

Strongly divisible lattices and crystalline cohomology in the imperfect residue field case

A degree bound for rings of arithmetic invariants

Consider a Noetherian domain R and a finite group G⊆Gln(R). We prove that if the ring of invariants R[x1,…,xn]G is a Cohen-Macaulay ring, then it is generated as an R-algebra by elements of degree at most max⁡(|G|,n(|G|−1)). As an intermediate result we also show that if R is a Noetherian local ring with infinite residue field then such a ring of invariants of a finite group G over R contains a homogeneous system of parameters consisting of elements of degree at most |G|.

Re-Distribution of Welding Residual Stress in Fatigue Crack Propagation Considering Elastic–Plastic Behavior

The welding residual stress re-distribution behavior during fatigue crack propagation in butt-welded high-strength steel plates for ship construction is investigated based on experimental test results and numerical analyses. The specimens’ initial welding residual stresses are obtained from X-ray for middle tensile (MT) specimens cut from butt-welded high-strength steel plates. Then, fatigue crack propagation experiments on MT specimens are conducted, and a strain gauge is used to measure the residual stress re-distribution field around cracks. A practical fatigue crack propagation simulation procedure is developed with a dynamic update of in-situ welding residual stress, where the residual stress intensity factor Kres of the MT specimen is deduced. The stress ratio effect on Kres during fatigue crack propagation is analyzed and a good agreement between experimental and numerical results is achieved.