Major Arcs Research Articles

Estimates for Smooth Weyl Sums on Major Arcs

Abstract We present estimates for smooth Weyl sums of use on sets of major arcs in applications of the Hardy–Littlewood method. In particular, we derive mean value estimates on major arcs for smooth Weyl sums of degree $k$ delivering essentially optimal bounds for moments of order $u$ whenever $u>2\lfloor k/2\rfloor +4$.

Efficiency of the decision support system for determining the severity of scoliotic spinal deformity by the analysis of radiographs

BACKGROUND: In 2020, a decision support system was developed at expense of grant from Innovation Promotion Fund and integrated into medical base of prosthetic and orthopedic center “Sсoliologic.ru.” It is the first computer program for determining severity of scoliotic spinal deformity in analysis of radiographs. AIM: To evaluate performance of a computer program for determining Cobb angle by comparing obtained automated data with manual measurement data by various specialists. MATERIALS AND METHODS: From medical base of prosthetic and orthopedic center “Sсoliologic.ru,” 411 digital radiographs of spine of children and adolescents were selected, which were drawn by a radiologist (BP-etalon), an orthopedic traumatologist with 5 years of experience and experience in vertebrology (OO), and an orthopedic traumatologist with less than 1 year of experience and no experience in vertebrology (OB) and computer program (KP). The number and proportion of exact matches and mean absolute percentage error (MAPE) of results of measuring the Cobb angle of reference data were compared with indicators obtained by OO, OB, and KP in, for various types of scoliosis according to the classification of Rigо, as well as in determining the main arc. Bland–Altman graphs were used. The mean absolute deviation (MAD) and MAPE for the main arc with magnitude ranging from 20° to 50° were calculated. RESULTS: The exact matches of KP with standard were 21%. Hence, every fifth measurement of the Cobb angle on X-ray, calculated automatically, was identical to standard. The highest proportion of matches with standard was noted in OO (33%), and the lowest in OB (16%). The highest accuracy of KP was found at types E1 and E2, and the arc of 3 was 30% and 24%, respectively. The proportion of KP matches with standard increased to 61%, with an error of 3°, and to 75%, with an error of 5°; with an error of 7°, the proportion of matches reached 84%. Moreover, the proportion of coincidences of a non-experienced researcher increased from 34% to 58%. When determining magnitude of the main arc of scoliosis, OO increased his/her accuracy by almost 2,6 times, KP by 2,1 times, and OB by 1,5 times. The MAD of KP for all major arcs was 3.8°. Good reliability of the obtained KP indicators compared to the reference (ICC = 0.9) was noted. CONCLUSIONS: The use of a computer program may be recommended for automated determination of Cobb angle, because current algorithm of computer program has been found to be accurate compared to reference measurement. Its accuracy was significantly higher than that of novice orthopedic traumatologists with no experience in vertebrology.

Love, actually

Abstract Individuals create both personal and culturally shared meaning through narratives; however, sparse research has explored the specific ways in which individuals might use such cultural narratives in creating meaning from developmentally important experiences. In this study, we examine how emerging adults narrate positive romantic relationships, both because emerging adulthood is critical for the development of intimacy and because romantic relationship narratives are pervasive in cultural media. Thematic analysis of 31 narratives from mostly European-descent students attending a private liberal arts university in the Southeast US (mean age 19; 16 self-identified females) revealed three major narrative arcs, Love Grows, Firecrackers and Fairytale, which varied in coherence, coda, and mutuality of the relationship, but did not differ by gender. Further examination and discussion of these narratives suggest how emerging adults are making sense of their first romantic relationships in ways that inform efforts to educate and intervene to promote healthy and positive relationships.

Purpose for Elijah and Elisha in the Books of Kings

The study of 1 and 2 Kings often assumes that the division between the two books was an arbitrary one that was made about halfway between the beginning and end of the text of Kings. The investigation of this question reveals not only a rationale behind the division between the two ‘books’; it also raises the larger question of the contrasting roles played by the kings who begin and end the text, and by the prophets whose central role in the books provides hope and life. By tracing major narrative arcs across the beginning and end of 1 and 2 Kings as well as across the appearances and departures of Elijah and Elisha, the themes of physical death and spiritual life set a dramatic tone in the pages of these accounts and provide hope in the midst of judgement.

Identifying the Structure and Propagation of Dawnside Pc5 ULF Waves Using Space‐Ground Conjunctions

AbstractPc5 ultralow frequency waves are important for transferring energy between the magnetosphere and ionosphere. While many observations have been performed on Pc5 waves properties, it has been difficult to determine the source region, signal propagation path, and the two‐dimensional structure of Pc5 waves beyond coverage by a small number of satellites. Pc5 waves often show a dawn‐dusk asymmetry, but the cause of the asymmetry is under debate. To address these issues, we used conjunction events between the THEMIS satellites and all‐sky imagers and analyzed two Pc5 wave events that were stronger on the dawnside. For both events, the Pc5 waves propagated from dawnside magnetopause toward the nightside magnetosphere. The Pc5 waves were also associated with dawnside magnetopause surface waves, which were probably induced by the Kelvin‐Helmholtz instability. The ionospheric equivalent currents identified multiple vortices on the dawnside associated with quasi‐periodic auroral arcs and much weaker perturbations on the duskside. Global auroral imaging also presented a similar dawn‐dusk asymmetry with multiple arcs on the dawnside, while only one or two major arcs existed on the duskside. Pc5 waves in the magnetosphere had an anti‐phase relation between the total magnetic field and thermal pressure, with a slower propagation velocity compared with magnetohydrodynamic waves. The Poynting flux was anti‐sunward with an oscillating field‐aligned component. These properties suggest that Pc5 waves were slow or drift mirror mode waves coupled with standing Alfven waves. The ground‐based and multi‐satellite observations provide crucial information for determining the Pc5 waves properties, possible source region, and signal propagation path.

Experimental study on continuous spectrum bubble generator with a new overlapping bubbles image processing technique

• The CSBG, which can produce bubbles with continuous sizes is developed. • Experimental results show that CSBG can generate bubbles of continuous sizes. • Overlapping bubbles processing technique (OBPT) based on CPD & FSAC is proposed. • Accuracy of OBPT exceeds 95% with a sub-second response time per hundred bubbles. The parameter of bubble size is of great significance to the bubbly flow. In this paper, the Continuous Spectrum Bubble Generator (CSBG), consisting of a sparger and impeller, was developed to realize the continuous control of bubble sizes. By introducing a new variable, rotation rate of the impeller, bubble size and gas superficial velocity are successfully decoupled. Experimental results show that bubble sizes continuously drops from 3 to 1 mm, without changing gas superficial velocity. Also, the spectrum of bubble size can be expanded by increasing or decreasing mass flow rates. To detect the overlapping bubbles, a new overlapping bubbles processing technique based on fast segmented arcs clustering was proposed. It’s efficient to cluster the segmented arcs through detecting the Major and Pair arcs and connecting the Multi-segment arcs through concave points connection methods. Test results show that the accuracies of mean diameter exceed 95% with sub-second response time per hundred bubbles.

THE IONESCU–WAINGER MULTIPLIER THEOREM AND THE ADELES

The Ionescu–Wainger multiplier theorem establishes good L p bounds for Fourier multiplier operators localized to major arcs; it has become an indispensible tool in discrete harmonic analysis. We give a simplified proof of this theorem with more explicit constants (removing logarithmic losses that were present in previous versions of the theorem), and give a more general variant involving adelic Fourier multipliers. We also establish a closely related adelic sampling theorem that shows that ℓ p ( Z d ) norms of functions with Fourier transform supported on major arcs are comparable to the L p ( A Z d ) norm of their adelic counterparts.

Estimates of short exponential sums with primes in major arcs

Estimates of short exponential sums with primes in major arcs

Dense packings of hard circular arcs.

This work investigates dense packings of congruent hard infinitesimally thin circular arcs in the two-dimensional Euclidean space. It focuses on those denotable as major whose subtended angle θ∈(π,2π]. Differently than those denotable as minor whose subtended angle θ∈[0,π], it is impossible for two hard infinitesimally thin circular arcs with θ∈(π,2π] to arbitrarily closely approach once they are arranged in a configuration, e.g., on top of one another, replicable ad infinitum without introducing any overlap. This makes these hard concave particles, in spite of being infinitesimally thin, most densely pack with a finite number density. This raises the question as to what are these densest packings and what is the number density that they achieve. Supported by Monte Carlo numerical simulations, this work shows that one can analytically construct compact closed circular groups of hard major circular arcs in which a specific, θ-dependent, number of them (counter) clockwise intertwine. These compact closed circular groups then arrange on a triangular lattice. These analytically constructed densest-known packings are compared to corresponding results of Monte Carlo numerical simulations to assess whether they can spontaneously turn up.

Major arcs and moments of arithmetical sequences

We give estimates for the first two moments of arithmetical sequences in progressions. Instead of using the standard approximation, we work with a generalization of Vaughan's major arcs approximation which is similar to that appearing in earlier work of Browning and Heath-Brown on norm forms. We apply our results to the sequence $\tau_k(n)$, and obtain unconditional results in a wide range of moduli.

Boolean Combination of Circular Arcs using Orthogonal Spheres

An orthogonal sphere representation of arcs on spatial circles can be used to compactly perform Boolean combinations of such arcs. We formulate this using conformal geometric algebra, of which the oriented nature allows both minor and major arcs to be treated. Easily computable quantities discriminate the cases of relative positions. An application in the first stages of a problem in Discretizable Molecular Distance Geometry is included. We give a suggestion on how to extend this characterization by orthogonal spheres to the manifolds of arcs in the subsequent stages, using probabilistic eigenspheres of the distributions.

Behaviour of minor arcuate shapes hosted in curved fold-and-thrust belts: an example from the Northern Apennines (Italy)

AbstractArcuate fold-and-thrust belts have been extensively studied in the literature. Less attention, however, has been paid to the characteristics of local-scale arcuate structures, meaning 5–10 km long fold or thrust traces that display map-view curvature. Nevertheless, detailed investigation of small arcuate structures hosted in major arcs can contribute to understanding the pervasiveness of deformation mechanisms. We performed a combined geological and palaeomagnetic study on 21 sites from ac. 60 km2area in the Northern Apennines in order to analyse minor arcs at a kilometric scale. As evidenced by the geological and structural analysis performed on the 21 sites, the fold axial trend changes from N–S to NW–SE in the study area. The comparison with palaeomagnetic results shows the lack of correlation between vertical axis rotations and fold axial trends. As a consequence, the minor arcuate shapes of thrusts and related folds are interpreted as mostly primary features inherited from the geometry of the palaeomargin, represented by pre-orogenic faults, according to a context of inversion tectonics.

Enlarged major arcs in the Waring–Goldbach problem

In this short note, we treat the enlarged major arcs of circle method in the Waring–Goldbach problem.

Weyl sums, mean value estimates, and Waring's problem with friable numbers

In this paper we study Weyl sums over friable integers (more precisely $y$-friable integers up to $x$ when $y = (\log x)^C$ for a large constant $C$). In particular, we obtain an asymptotic formula for such Weyl sums in major arcs, nontrivial upper bounds for them in minor arcs, and moreover a mean value estimate for friable Weyl sums with exponent essentially the same as in the classical case. As an application, we study Waring's problem with friable numbers, with the number of summands essentially the same as in the classical case.

Characterisation of Mitochondrial DNA Deletions by Long-PCR in Central Nervous System Regions of Young, Middle- and Old-aged Rats

The causes of ageing remain poorly understood, although a role for mitochondria is widely accepted. These unique organelles that are responsible for a cell's energy, rely on their own small genome and translational machinery to produce proteins that, together with nuclear genome encoded proteins, form the electron transport chain complexes necessary for ATP production. Various forms of mitochondrial genome mutation and rearrangements are thought to be involved in the ageing process, particularly in post-mitotic cells, such as those of the nervous system. In the present study, we have characterised mitochondrial DNA (mtDNA) deletion mutations in five central nervous system (CNS) regions of the young, middle-aged, and old Fischer 344 (F344) rats. DNA was extracted from the cerebral cortex, striatum, midbrain, cerebellum and spinal cord, and long-PCR was used to detect mtDNA with deletions in the minor and major arcs. This approach has the advantage that all deletions can be detected without a priori knowledge of breakpoints. In the minor arc, we found evidence for deletions in the striatum of five out of six old animals and in the spinal cords from two of six old animals. In contrast, mtDNA deletions in the major arc appeared markedly more abundant, both in terms of affected CNS regions and number of deleted mtDNA molecules. Furthermore, major arc deletions were apparent earlier with a number of CNS regions showing deletions in the middle-aged group. The cerebral cortex, striatum and spinal cord were the most affected regions, while the midbrain and cerebellum were relatively spared. These findings are remarkably consistent with previous human brain data and further underscore the value of the rat model for investigation of ageing-related changes in the mitochondrial genome.

A Bombieri-type theorem for exponential sums

Let fk(n) be the characteristic function of n with Ω(n) = k, and $$T_k \left( {x,\alpha } \right) = \sum\limits_{n \leqslant x} {f_k \left( n \right)e\left( {n\alpha } \right)} .$$ The main purpose of this paper is to establish a Bombieri-type mean-value theorem for Tk(x, α), via using the modified Huxley-Hooley contour and the large-sieve type zero-density estimate for Dirichlet L-functions. The result plays an important role in handling the enlarge major arcs when we try to solve the Waring-Goldbach type problem by the circle method.

Every odd number greater than $1$ is the sum of at most five primes

We prove that every odd number $N$ greater than 1 can be expressed as the sum of at most five primes, improving the result of Ramar\'e that every even natural number can be expressed as the sum of at most six primes. We follow the circle method of Hardy-Littlewood and Vinogradov, together with Vaughan's identity; our additional techniques, which may be of interest for other Goldbach-type problems, include the use of smoothed exponential sums and optimisation of the Vaughan identity parameters to save or reduce some logarithmic losses, the use of multiple scales following some ideas of Bourgain, and the use of Montgomery's uncertainty principle and the large sieve to improve the $L^2$ estimates on major arcs. Our argument relies on some previous numerical work, namely the verification of Richstein of the even Goldbach conjecture up to $4 \times 10^{14}$, and the verification of van de Lune and (independently) of Wedeniwski of the Riemann hypothesis up to height $3.29 \times 10^9$.

Electrochemical characterization of Ni–yttria stabilized zirconia electrode for hydrogen production in solid oxide electrolysis cells

Electrochemical performance of Ni–yttria stabilized zirconia (YSZ) electrode, which is widely used as the anode for solid oxide fuel cells (SOFCs), is evaluated for H2 production in solid oxide electrolysis cells (SOECs). The impedance spectra of Ni–YSZ electrode are composed of two major depressed arcs. The high-frequency impedance (>104 Hz) can be assigned to transfer of the charged species across the Ni/YSZ interface, and the mid-frequency arc (102∼103 Hz) is possibly associated with the gas–solid interaction such as adsorption, dissociation, desorption, etc. The impedance spectra are strongly influenced by the gas composition in both fuel cell (H2 oxidation) and electrolysis (H2O reduction) reactions; polarization resistance decreases with increasing concentration of the reactant species. In fuel cell mode, both high- and mid-frequency arcs increase with decreasing H2 concentration, while the impedance spectra are dominated by the mid-frequency arc and the high-frequency arc remains negligible even at low H2O concentration in electrolysis mode. Reaction mechanisms and elementary reaction pathways for H2 oxidation and H2O reduction are suggested based on impedance spectra. The minimum impedance is observed at 50% H2O in electrolysis mode, and further increase in H2O concentration causes degradation of the electrode performance, possibly due to local oxidation of Ni.

Correction to “Discrete fractional Radon transforms and quadratic forms,” Duke Math. J. 161 (2012), 69–106

We consider discrete analogues of fractional Radon transforms involving integration over paraboloids defined by positive definite quadratic forms. We prove that such discrete operators extend to bounded operators from $\ell^p$ to $\ell^q$ for a certain family of kernels. The method involves an intricate spectral decomposition according to major and minor arcs, motivated by ideas from the circle method of Hardy and Littlewood. Techniques from harmonic analysis, in particular Fourier transform methods and oscillatory integrals, as well as the number theoretic structure of quadratic forms, exponential sums, and theta functions, play key roles in the proof.

Berlin Alexanderplatz's Serial Women

Critics of Berlin Alexanderplatz (WDR, West Germany, 1980) most often focus on the extended love plot between Franz (Günther Lamprecht) and Reinhold (Gottfried John). This focus is not surprising, given that the vexed relationship between Rainer Werner Fassbinder's leading men is the most prominent storyline in the miniseries. However, across nearly sixteen hours, Berlin Alexanderplatz also introduces us to Paula (Mechthild Grossmann), Minna (Karin Baal), Ida (Barbara Valentin), Frau Bast (Brigitte Mira), Polish Lina (Elisabeth Trissenaar), Eva (Hanna Schygulla), the widow (Angela Schmid), Fränze (Helen Vita), Cilly (Annemarie Düringer), Trude (Irm Hermann), the Whore of Babylon (uncredited), the waitress (Elke Haltaufderheide), and Mieze (Barbara Sukowa). Across successive episodes, these minor characters offer a version of seriality inside the serial form that is Berlin Alexanderplatz. Ultimately these figures make up one vast composite character, a combinatory form that echoes the superimposed photographs from the Weimar era that appear in the miniseries's credit sequence. Both the credit sequence and the serial women offer ways of representing Germany's past as a variegated, multidimensional site. Though often peripheral to the miniseries's major plot arcs, the female characters upend the interpretive authority of the voice-over. Their presence unsettles the voice-over's construction of a somewhat monolithic, omniscient, and in many ways melodramatic historical imagination of the Weimar period.Through the placement of the female minor characters, Berlin Alexanderplatz challenges the traditional terms of value often associated with the historical television miniseries. Contra contemporaneous miniseries like Heimat (WDR/SFB, West Germany, 1984), Roots (ABC, 1977), and Days of Hope (BBC, UK, 1975), Berlin Alexanderplatz does not utilize its extended running time to create an increasingly complex or multigenerational story line. Instead, the extensive breadth of the miniseries allows for an experiment with minor character forms, offering the intimacy often associated with extended serial viewing but refusing legible modes of sympathy and attachment. In Berlin Alexanderplatz, this inscrutability becomes an irritant within the miniseries's larger narrative arc, preventing the mourning of the dead women across the series and the mourning for the lost past for which they often provide a symbolic counterpart.