Cyclic Extension Research Articles

A parametrization of nonassociative cyclic algebras of prime degree

We determine and explicitly parametrize the isomorphism classes of nonassociative quaternion algebras over a field of characteristic different from two, as well as the isomorphism classes of nonassociative cyclic algebras of odd prime degree m when the base field contains a primitive mth root of unity. In the course of doing so, we prove that any two such algebras can be isomorphic only if the cyclic field extension and the chosen generator of the Galois group are the same. As an application, we give a parametrization of nonassociative cyclic algebras of prime degree over a local nonarchimedean field F, which is entirely explicit under mild hypotheses on the residual characteristic. In particular, this gives a rich understanding of the important class of nonassociative quaternion algebras up to isomorphism over nonarchimedean local fields.

Non-zero central values of Dirichlet twists of elliptic L-functions

We consider heuristic predictions for small non-zero algebraic central values of twists of the L-function of an elliptic curve E/Q by Dirichlet characters. We provide computational evidence for these predictions and consequences of them for instances of an analogue of the Brauer-Siegel theorem associated to E/Q extended to chosen families of cyclic extensions of fixed degree.

Signal amplification by cyclic extension enables high-sensitivity single-cell mass cytometry.

Mass cytometry uses metal-isotope-tagged antibodies to label targets of interest, which enables simultaneous measurements of ~50 proteins or protein modifications in millions of single cells, but its sensitivity is limited. Here, we present a signal amplification technology, termed Amplification by Cyclic Extension (ACE), implementing thermal-cycling-based DNA in situ concatenation in combination with 3-cyanovinylcarbazole phosphoramidite-based DNA crosslinking to enable signal amplification simultaneously on >30 protein epitopes. We demonstrate the utility of ACE in low-abundance protein quantification with suspension mass cytometry to characterize molecular reprogramming during the epithelial-to-mesenchymal transition as well as the mesenchymal-to-epithelial transition. We show the capability of ACE to quantify the dynamics of signaling network responses in human T lymphocytes. We further present the application of ACE in imaging mass cytometry-based multiparametric tissue imaging to identify tissue compartments and profile spatial aspects related to pathological states in polycystic kidney tissues.

Unboundedness of Tate–Shafarevich groups in fixed cyclic extensions

Unboundedness of Tate–Shafarevich groups in fixed cyclic extensions

Transverse patella fracture fixation: A cadaveric biomechanical comparison of cannulated screws and anterior tension band versus low-profile, multiplanar mesh plating

IntroductionMultiplanar mesh plating of patella fractures has become more popular in recent years. It was the goal of this study to compare the biomechanical stability of cannulated screw with anterior tension band to multiplanar mesh plating for fixation of transverse patella fractures in cadaver specimens. Materials and MethodsEight matched pairs of fresh frozen cadaveric knees were obtained and soft tissues dissected leaving the extensor mechanism, joint capsule, and retinaculum intact. Transverse fractures were created at the mid-portion of the patella. For each pair, one specimen was repaired using cannulated screws with anterior tension band, and the second was repaired using multiplanar mesh plating. Each specimen underwent cyclic extension loading with loads increasing by 1.1 kg after every 50 cycles. Interfragmentary displacement was measured at the end of each interval at both 5° and 45° of knee flexion angle, with fixation failure defined by >2 mm displacement. ResultsThe specimens fixed with multiplanar mesh plating survived more cycles and higher loads than the specimens fixed with cannulated screws with anterior tension band (p = 0.011 comparing survival plots). After 150 cycles of extension loading, 3 of 8 of the specimens fixed with screws/tension band had failed, whereas none of the mesh plated specimens had failed. After 400 cycles, 7 of 8 of the screws/tension band had failed, whereas half of the mesh plated specimens had failed. ConclusionsWhile a more technically challenging and expensive technique, mesh plating for patella fractures appears to offer greater durability than traditional cannulated screw with tension banding.

Ranks of elliptic curves in cyclic sextic extensions of [formula omitted]

For an elliptic curve E/Q we show that there are infinitely many cyclic sextic extensions K/Q such that the Mordell–Weil group E(K) has rank greater than the subgroup of E(K) generated by all the E(F) for the proper subfields F⊂K. For certain curves E/Q we show that the number of such fields K of conductor less than X is ≫X.

On the capitulation problem of some pure metacyclic fields of degree 20 II

Let $n$ be a $5^{th}$ power-free natural number and $k_0\,=\,\mathbb{Q}(\zeta_5)$ be the cyclotomic field generated by a primitive $5^{th}$ root of unity $\zeta_5$. Then $k\,=\,\mathbb{Q}(\sqrt[5]{n},\zeta_5)$ is a pure metacyclic field of absolute degree $20$. In the case that $k$ possesses a $5$-class group $C_{k,5}$ of type $(5,5)$ and all the classes are ambiguous under the action of $Gal(k/k_0)$, the capitulation of $5$-ideal classes of $k$ in its unramified cyclic quintic extensions is determined.

Higher Lie characters and cyclic descent extension on conjugacy classes

Higher Lie characters and cyclic descent extension on conjugacy classes

Lithospheric reworking and thinning by cyclical continental extension: a synthesis of Cretaceous extensional domes in the South China Block

Lithospheric reworking and thinning by cyclical continental extension: a synthesis of Cretaceous extensional domes in the South China Block

The interconnection between local and global m-th powers and Grunwald-Wang theorem

The relation between local and global solution of an equation can be discussed with the method of class field theory and algebraic number theory. In this piece of writing, the author will introduce the behavior of both local and global m-th power in some specific number field. Of course, the result in this paper can be extended into the function field, but it will not be involved in this paper. This paper will prove that if k(_(2^t ))/k is cyclic then the Local m-th powers everywhere is equivalent to the global m-th power. In the Non-cyclic case this decomposition becomes P(m,S)=k^mk^m. This paper will also prove some useful propositions in topological group theory, which will be used in the proof of Grunwald-Wang theorem. Grunwald-Wang theorem states that we can find a cyclic extension with given local behaviors. To describe the extension, this paper combines character theory with a topological group, one can depict the cyclic extension. This theorem can be used in the further exploration of central simple algebra.

Norm tori of étale algebras and unramified Brauer groups

Let k be a field, and let L be an étale k-algebra of finite rank. If a∈k×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a \\in {k^ \ imes }$$\\end{document}, let Xa be the affine variety defined by NL/k(x)=a\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${N_{L/k}}(x) = a$$\\end{document}. Assuming that L has at least one factor that is a cyclic field extension of k, we give a combinatorial description of the unramified Brauer group of Xa.

Protecting car engines and controlling their temperature by using shape memory alloy as an automatic mechanical cooling sensor

Shape memory alloys (SMA) are smart materials with a dual function as a sensor as well as an actuator that can generate cyclic contraction and extension when exposed to an increasing and decreasing temperature. In this work, the potential of SMA in the form of spring as an actuator that activates a warning system for detecting high temperatures in vehicle engine is investigated. The working principle of SMA spring is it activates thermomechanically to generate linear reciprocating motion as a result of the contraction (heated) and extension (cooled). This unique feature is employed in the design of a new type of smart automatic switch that regulates and controls the temperature of the vehicle engine instead of using conventional sensors such as thermocouple. The smart automatic switch has two poles positive and negative, where the positive pole represents the SMA spring, which is completely immersed in the water of the engine. While the negative pole is the operating shaft that collects all the parts of the smart switch and is installed on the engine body. A lab scale experiment was conducted to analyse the displacements and results shown that contraction of 20 mm can be produced from the SMA spring due to pulling force when the temperature of the engine increases from 50 ℃ to 80 ℃ and the recovery of the SMA spring to the original position can be obtained by the pushing force 0.5 N from a bias spring when the temperature decreased. From this experiment, a design of the smart switch is that can be utilized the shape memory function is presented. The simplified design proposed demonstrates the shape memory alloy as having good potential in automotive applications such as this as it low cost, space saving, silent operation, and simple in design aspect.

One-Dimensional Consolidation Properties of Soft Clay under Multi-Stage Loading

The consolidation characteristics of soft clay under multi-stage loading and single-stage loading exhibit significant differences. In order to investigate the consolidation behavior of soft clay under multi-stage loading, one-dimensional oedometer tests were conducted on marine sedimentary soft clay from northern China. The results indicate that the overall time-deformation pattern of multi-stage loading is a cyclic nonlinear extension of that of single-stage loading. The final deformation between multi-stage loading and single-stage loading is approximately equal; however, the consolidation rate of single-stage loading is four times that of multi-stage loading. Furthermore, the coefficient of consolidation (Cv) decreases with increasing stress. Subsequently, the traditional Terzaghi one-dimensional consolidation equation was modified and a consolidation equation suitable for multi-stage loading is proposed in this study. The analysis of engineering applications demonstrates that the traditional theory provides more accurate predictions of consolidation rate and settlement when the load is small. However, when the load is large, the settlement predicted using the Terzaghi one-dimensional consolidation equation may have an error of 0–25% compared to that using the modified equation. The modified Terzaghi one-dimensional consolidation equation provides a more accurate representation of the actual consolidation of soft soil.

Matrices of simple spectrum in irreducible representations of cyclic extensions of simple algebraic groups

Matrices of simple spectrum in irreducible representations of cyclic extensions of simple algebraic groups

Equidistribution of elements of norm 1 in cyclic extensions

Equidistribution of elements of norm 1 in cyclic extensions

Cyclic Descents, Matchings and Schur-Positivity

A new descent set statistic on involutions, defined geometrically via their interpretation as matchings, is introduced in this paper, and shown to be equidistributed with the standard one. This concept is then applied to construct explicit cyclic descent extensions on involutions, standard Young tableaux and Motzkin paths. Schur-positivity of the associated quasisymmetric functions follows.

RANK JUMPS AND GROWTH OF SHAFAREVICH–TATE GROUPS FOR ELLIPTIC CURVES IN -EXTENSIONS

AbstractLet p be a prime. In this paper, we use techniques from Iwasawa theory to study questions about rank jump of elliptic curves in cyclic extensions of degree p. We also study growth of the p-primary Selmer group and the Shafarevich–Tate group in cyclic degree-p extensions and improve upon previously known results in this direction.

Nonassociative Algebras, Rings and Modules over Them

The review is devoted to nonassociative algebras, rings and modules over them. The main actual and recent trends in this area are described. Works are reviewed on radicals in nonassociative rings, nonassociative algebras related with skew polynomials, commutative nonassociative algebras and their modules, nonassociative cyclic algebras, rings obtained as nonassociative cyclic extensions, nonassociative Ore extensions of hom-associative algebras and modules over them, and von Neumann finiteness for nonassociative algebras. Furthermore, there are outlined nonassociative algebras and rings and modules over them related to harmonic analysis on nonlocally compact groups, nonassociative algebras with conjugation, representations and closures of nonassociative algebras, and nonassociative algebras and modules over them with metagroup relations. Moreover, classes of Akivis, Sabinin, Malcev, Bol, generalized Cayley–Dickson, and Zinbiel-type algebras are provided. Sources also are reviewed on near to associative nonassociative algebras and modules over them. Then, there are the considered applications of nonassociative algebras and modules over them in cryptography and coding, and applications of modules over nonassociative algebras in geometry and physics. Their interactions are discussed with more classical nonassociative algebras, such as of the Lie, Jordan, Hurwitz and alternative types.

The Back Muscle Surface Electromyography-Based Fatigue Index: A Digital Biomarker of Human Neuromuscular Aging?

As part of our quest for digital biomarkers of neuromuscular aging, and encouraged by recent findings in healthy volunteers, this study investigated if the instantaneous median frequency (IMDF) derived from back muscle surface electromyographic (SEMG) data monitored during cyclic back extensions could reliably differentiate between younger and older individuals with cLBP. A total of 243 persons with cLBP participated in three experimental sessions: at baseline, one to two days after the first session, and then again approximately six weeks later. During each session, the study participants performed a series of three isometric maximal voluntary contractions (MVC) of back extensors using a dynamometer. These were followed by an isometric back extension at 80% MVC, and-after a break-25 slow cyclic back extensions at 50% MVC. SEMG data were recorded bilaterally at L5 (multifidus), L2 (longissimus dorsi), and L1 (iliocostalis lumborum). Linear mixed-effects models found the IMDF-SEMG time-course changes more rapidly in younger than in older individuals, and more prominently in male participants. The absolute and relative reliabilities of the SEMG time-frequency representations were well compared between older and younger participants. The results indicated an overall good relative reliability, but variable absolute reliability levels. IMDF-SEMG estimates derived from cyclic back extensions proved to be successful in reliably detecting differences in back muscle function in younger vs. older persons with cLBP. These findings encourage further research, with a focus on assessing whether an IMDF-SEMG-based index could be utilized as a tool to achieve the preclinical detection of back muscle aging, and possibly predict the development of back muscle sarcopenia.

Arithmetic statistics and diophantine stability for elliptic curves

We study the growth and stability of the Mordell–Weil group and Tate–Shafarevich group of an elliptic curve defined over the rationals, in various cyclic Galois extensions of prime power order. Mazur and Rubin introduced the notion of diophantine stability for the Mordell–Weil group an elliptic curve $$E_{/{{\mathbb {Q}}}}$$ at a given prime p. Inspired by their definition of stability for the Mordell–Weil group, we introduce an analogous notion of stability for the Tate–Shafarevich group, called -stability. From the perspective of Iwasawa theory, it benefits us to introduce a stronger notion of diophantine stability for the Mordell–Weil group. It is shown that any non-CM elliptic curve of rank 0 defined over the rationals is strongly diophantine stable and -stable at $$100\%$$ of primes p. Next, we show that standard conjectures on rank distribution give lower bounds for the proportion of rational elliptic curves E that are strongly diophantine stable at a fixed prime $$p\ge 11$$ . Related questions are studied for rank jumps and growth of ranks Tate–Shafarevich groups on average in prime power cyclic extensions.