Trivial Terms Research Articles

Gravitational vacua in the Newman-Penrose formalism

In this paper, we derive the generic solution of the Newman-Penrose equations in the Newman-Unti gauge with vanishing curvature tensor. The obtained solutions are the vacua of the gravitational theory which are connected to the derivations in metric formalism from exponentiating the infinitesimal BMS generators in the Bondi-Metzner-Sachs (BMS) gauge in Compère and Long [ and ] by a radial transformation. The coordinate transformations in the Newman-Unti gauge connecting each vacuum are also obtained. We confirm that the supertranslation charge of the gravitational vacua with respect to global considerations vanishes exactly not only in the Einstein theory but also when including the Holst, Pontryagin, and Gauss-Bonnet terms, which verifies that the gravitational vacua are not affected by those trivial or boundary terms. Published by the American Physical Society 2024

Null boundary gravitational charges from local Lorentz symmetries

In this paper, we revisit the null boundary gravitational charge in the Newman-Penrose formalism with special emphasis on the charges from local Lorentz transformations. We find that there is one more charge derived from the local Lorentz transformation and the new charge is purely from the Holst term. This reveals a remarkable fact that trivial terms which do not change classical equations of motion can not only affect the boundary degrees of freedom through their contributions to the boundary charges but also have their own rights to create new boundary degrees of freedom.

Small perturbations in the type of boundary conditions for an elliptic operator

In this article, we study the impact of a change in the type of boundary conditions of an elliptic boundary value problem. In the context of the conductivity equation we consider a reference problem with mixed homogeneous Dirichlet and Neumann boundary conditions. Two different perturbed versions of this “background” situation are investigated, when (i) The homogeneous Neumann boundary condition is replaced by a homogeneous Dirichlet boundary condition on a “small” subset ωε of the Neumann boundary; and when (ii) The homogeneous Dirichlet boundary condition is replaced by a homogeneous Neumann boundary condition on a “small” subset ωε of the Dirichlet boundary. The relevant quantity that measures the “smallness” of the subset ωε differs in the two cases: while it is the harmonic capacity of ωε in the former case, we introduce a notion of “Neumann capacity” to handle the latter. In the first part of this work we derive representation formulas that catch the structure of the first non trivial term in the asymptotic expansion of the voltage potential, for a general ωε, under the sole assumption that it is “small” in the appropriate sense. In the second part, we explicitly calculate the first non trivial term in the asymptotic expansion of the voltage potential, in the particular geometric situation where the subset ωε is a vanishing surfacic ball.

Contrast and verb phrase ellipsis: The case of tautologous conditionals

This paper argues that verb phrase ellipsis requires contrast. The central observation is that ellipsis is ungrammatical in tautologous conditionals; e.g., *If John wins, then he does. Ellipsis is correctly ruled out by a focus-based theory of ellipsis (Rooth 1992a,b), but one that crucially imports focus’s requirement for contrast: an elliptical constituent must have an antecedent that is not merely an alternative to it, but a ‘proper’ alternative. An explanation in terms of contrast failure proves superior to alternative explanations in terms of triviality and matching form. Showing as much catalogues what counts for contrast in ellipsis, encompassing negation, questions, and intensionality. Subjecting ellipsis to a contrast requirement is in direct conflict with the traditional analysis of MaxElide effects (Takahashi and Fox 2005), favouring alternative explanations (e.g., Jacobson 2019a,b), perhaps in terms of contrast itself (Griffiths 2019). Overall, this paper establishes that contrast has explanatory power in ellipsis licensing.

Importance of non-flow background on the chiral magnetic wave search

An observable sensitive to the chiral magnetic wave (CMW) is the charge asymmetry dependence of the π− and π+ anisotropic flow difference, Δνn(Ach). We show that, due to non-flow correlations, the flow measurements by the Q-cumulant method using all charged particles as reference introduce a trivial linear term to Δνn(Ach). The trivial slope contribution to the triangle flow difference Δν3(Ach) can be negative if the non-flow is dominated by back-to-back pairs. This can explain the observed negative Δν3(Ach) slope in the preliminary STAR data. We further find that the non-flow correlations give rise to additional backgrounds to the slope of Δν2(Ach) from the competition among different pion sources and from the larger multiplicity dilution to π+ (π−) at positive (negative) Ach.

Complications in the interpretation of the charge-asymmetry-dependent π flow for the chiral magnetic wave

The charge asymmetry ($A_{\rm ch}$) dependence of the $\pi^{-}$ and $\pi^{+}$ elliptic flow difference, $\Delta v_{2}(A_{\rm ch})$, has been regarded as a sensitive observable for the possible chiral magnetic wave (CMW) in relativistic heavy ion collisions. In this work, we first demonstrate that, due to non-flow backgrounds, the flow measurements by the Q-cumulant method using all charged particles as reference introduce a trivial linear term to $\Delta v_{2}(A_{\rm ch})$. The trivial slope can be negative in the triangle flow difference $\Delta v_{3}(A_{\rm ch})$ if the non-flow is dominated by back-to-back pairs. After eliminating the trivial term, we find that the non-flow between like-sign pairs gives rise to an additional positive slope to $\Delta v_{2}(A_{\rm ch})$ because of the larger dilution effect to $\pi^{+}$ ($\pi^{-}$) at positive (negative) $A_{\rm ch}$. We further find that the competition between different $\pi$ sources can introduce another non-trivial linear-$A_{\rm ch}$ term due to their different multiplicity fluctuations and anisotropic flows. We then study the effect of neutral cluster (resonance) decays as a mechanism for local charge conservation on the slope parameter of $\Delta v_{2}(A_{\rm ch})$. We find that the slope parameter is sensitive to the kinematics of those neutral clusters. Light resonances give positive slopes while heavy resonances give negative slopes. Local charge conservation from continuum cluster mass distribution can give a positive slope parameter comparable to experimental data. Our studies indicate that many non-CMW physics mechanisms can give rise to a $A_{\rm ch}$-dependent $\Delta v_{2}(A_{\rm ch})$ and the interpretation of $\Delta v_{2}(A_{\rm ch})$ in terms of the CMW is delicate.

Thermoelectric property of a one dimensional channel in the presence of a transverse magnetic field

We studied the thermal conduction through a quantum point contact (QPC), defined in a GaAs-AlxGa1−x As heterostructure, in the presence of a transverse magnetic field. A shift in the position of a thermo-voltage peak is observed with increasing field. The position of the thermo-voltage peak follows the Cutler-Mott relation in the small field regime (B < 0.5 T); it starts diverging from the Cutler-Mott relation in the moderate field regime, where a cubic magnetic field term dominates over the trivial quadratic term; eventually, the shift saturates in the large field regime (B > 3.0 T). Our results suggest that additional calibration is necessary when using QPC as thermometry, especially when the transverse magnetic field is applied.

On the exchange of sensible and latent heat between the atmosphere and melting snow

The snow energy balance is difficult to measure during the snowmelt period, yet critical for predictions of water yield in regions characterized by snow cover. Robust simplifications of the snowmelt energy balance can aid our understanding of water resources in a changing climate. Research to date has demonstrated that the net turbulent flux (FT) between a melting snowpack and the atmosphere is negligible if the sum of atmospheric vapor pressure (ea) and temperature (Ta) equals a constant, but it is unclear how frequently this situation holds across different sites. Here, we quantified the contribution of FT to the snowpack energy balance during 59 snowmelt periods across 11 sites in the FLUXNET2015 database with a detailed analysis of snowmelt in subarctic tundra near Abisko, Sweden. At the Abisko site we investigated the frequency of occurrences during which sensible heat flux (H) and latent heat flux (λE) are of (approximately) equal but opposite sign, and if the sum of these terms, FT, is therefore negligible during the snowmelt period. H approximately equaled -λE for less than 50% of the melt period and FT was infrequently a trivial term in the snowmelt energy balance at Abisko. The reason is that the relationship between observed ea and Ta is roughly orthogonal to the “line of equality” at which H equals -λE as warmer Ta during the melt period usually resulted in greater ea. This relationship holds both within melt periods at individual sites and across different sites in the FLUXNET2015 database, where FT comprised less than 20% of the energy available to melt snow, Qm, in 44% of the snowmelt periods studied here. FT/Qm was significantly related to the mean ea during the melt period, but not mean Ta, and FT tended to be near 0 W m−2 when ea averaged ca. 0.5 kPa. FT may become an increasingly important term in the snowmelt energy balance across many global regions as warmer temperatures are projected to cause snow to melt more slowly and earlier in the year under conditions of lower net radiation (Rn). Eddy covariance research networks such as Ameriflux must improve their ability to observe cold-season processes to enhance our understanding of water resources and surface-atmosphere exchange in a changing climate.

Lifshitz anomalies, Ward identities and split dimensional regularization

We analyze the structure of the stress-energy tensor correlation functions in Lifshitz field theories and construct the corresponding anomalous Ward identities. We develop a framework for calculating the anomaly coefficients that employs a split dimensional regularization and the pole residues. We demonstrate the procedure by calculating the free scalar Lifshitz scale anomalies in 2 + 1 spacetime dimensions. We find that the analysis of the regularization dependent trivial terms requires a curved spacetime description without a foliation structure. We discuss potential ambiguities in Lifshitz scale anomaly definitions.

Simplification of high order polynomial calibration model for fringe projection profilometry

In fringe projection profilometry systems, high order polynomial calibration models can be employed to improve the accuracy. However, it is not stable to fit a high order polynomial model with least-squares algorithms. In this paper, a novel method is presented to analyze the significance of each polynomial term and simplify the high order polynomial calibration model. Term significance is evaluated by comparing the loading vector elements of the first few principal components which are obtained with the principal component analysis, and trivial terms are identified and neglected from the high order polynomial calibration model. As a result, the high order model is simplified with significant improvement of computation stability and little loss of reconstruction accuracy. An interesting finding is that some terms of 0 and 1st order, as well as some high order terms related to the image direction that is vertical to the phase change direction, are trivial terms for this specific problem. Experimental results are shown to validate of the proposed method.

Quantum phase transitions of topological insulators without gap closing

We consider two-dimensional Chern insulators and time-reversal invariant topological insulators and discuss the effect of perturbations breaking either particle-number conservation or time-reversal symmetry. The appearance of trivial mass terms is expected to cause quantum phase transitions into trivial phases when such a perturbation overweighs the topological term. These phase transitions are usually associated with a bulk-gap closing. In contrast, the chiral Chern insulator is unaffected by particle-number breaking perturbations. Moreover, the topological insulator undergoes phase transitions into topologically trivial phases without bulk-gap closing in the presence of any of such perturbations. In certain cases, these phase transitions can be circumvented and the protection restored by another U(1) symmetry, e.g. due to spin conservation. These findings are discussed in the context of interacting topological insulators.

Algebraic description of chiral anomalies and superspace geometry

The supersymmetry of the non abelian chiral anomaly is exhibited, up to trivial terms, using descent equations and triangle formulas in the framework of N=1 superspace geometry in four dimensions.

ТАНЕЦ В ЛОКАЛЬНОЙ ТРАДИЦИИ ЧЕРКЕСОВ АНАТОЛИИ: ИДЕНТИФИКАЦИЯ ЖАНРА И СОЦИАЛЬНЫЕ ФУНКЦИИ

The article is dedicated to the history of one of the most popular with the young Circassian diaspora dancing genres — the shcheshchen. The author of the article tries to study the ways of correlation between the local exhibitions of the dancing genre and its trivial terms, local folk tunes, social taboos and the precepts of a definite diaspora society using the shcheshchen as an example. The purpose of the study is the synchronous description of the genre features of the endemically formed choreographic phenomenon called “adyghe shcheshchen” (the Circassian shcheshchen), tracking of the universal analogues (the terminological, musical, choreographic ones), detection of its social and semantic functions in the definite local culture. The subject of the study is the discursive practices about public merrymaking traditions, and also the context relations between the archival explorative texts and the historical sources which give the narrative description of the choreographic phenomena of the “metropolis” — the Caucasus — analogous with the shcheshchen. The object of the study is a verbal (oral) and non-verbal text (collected in the folklore field of Turkey and in the Internet) which actualize the information about the dance called shcheshchen. The field methods: the participant observation and informal conversation, the method of memory boosting established by the author of the article, the online poll. The methods of analytical processing of the materials: structural/functional, pragmatic analyses, discourse analyses. The shcheshchen acts as a cultural complex which equalizes people according to the rules of a public merrymaking and maintains the civilizational identity of Anatolia Circassians at the same time. The author of the article explains the reasons of some inconsistency of the deliberations about the ‘little prestige” of the shcheshchen and its popularity simultaneously. These conclusions would be useful for theoretical researches of the history of folklore genres, the culture of Circassian diaspora, and also for applied purposes: the ethnographical information collected by the author of the article and the complex theoretical observations data about the forms of the folk dances included in the article are published for the first time and would be interesting for specialists engaged in searching of the traditional ethno-choreographical styles and stage performances.

A numerical scale for non-locally connected planar continua

We introduce a numerical scale to quantify to which extent a planar continuum is not locally connected. For a locally connected continuum, the numerical scale is zero; for a continuum like the topologist's sine curve, the scale is one; for an indecomposable continuum, it is infinite. We use a purely topological framework of fibers and further characterize the local connectedness of a planar continuum in terms of triviality of its fibers.

Multiphase double‐porosity homogenization for perimeter functionals

In this paper, we study a homogenization problem for perimeter energies in highly contrasted media; the analysis of the previous paper is carried out by removing the hypothesis that the perforated medium Rn ∖ E is composed of disjoint compact components. Assuming E to be the union of a finite number N of connected components E1, … ,EN, the Γ‐limit F is a multiphase energy with a ‘decoupled’ surface part, obtained by homogenization from the surface tensions in each E j, a trivial bulk term obtained as a weak limit, and a further interacting term between the phases, involving an asymptotic formula for a family minimum problems on invading an asymptotic formula for a family of minimum problems on invading domains with prescribed boundary conditions. Copyright © 2012 John Wiley & Sons, Ltd.

Partially Ordered Models

We provide a formal definition and study the basic properties of partially ordered random fields (PORF). These systems were proposed to model textures in image processing and to represent independence relations between random variables in statistics (in the latter case they are known as Bayesian networks). Our random fields are a generalization of probabilistic cellular automata (PCA) and their theory has features intermediate between that of discrete-time processes and the theory of statistical mechanical lattice fields. Its proper definition is based on the notion of partially ordered specification (POS), in close analogy to the theory of Gibbs measures. This paper contains two types of results. First, we present the basic elements of the general theory of PORFs: basic geometrical issues, definition in terms of conditional probability kernels, extremal decomposition, extremality and triviality, reconstruction starting from single-site kernels, relations between POM and Gibbs fields. Second, we prove three uniqueness criteria that correspond to the criteria known as uniform boundedness, Dobrushin uniqueness and disagreement percolation in the theory of Gibbs measures.

A Linear Relaxation Technique for the Position Analysis of Multiloop Linkages

This paper presents a new method to isolate all configurations that a multiloop linkage can adopt. The problem is tackled by means of formulation and resolution techniques that fit particularly well together. The adopted formulation yields a system of simple equations (only containing linear, bilinear, and quadratic monomials, and trivial trigonometric terms for the helical pair only) whose structure is later exploited by a branch-and-prune method based on linear relaxations. The method is general, as it can be applied to linkages with single or multiple loops with arbitrary topology, involving lower pairs of any kind, and complete, as all possible solutions get accurately bounded, irrespective of whether the linkage is rigid or mobile.

The Aldehyde Dehydrogenase Gene Superfamily Resource Center

The website http://www.aldh.org is a publicly available database for nomenclature and functional and molecular sequence information for members of the aldehyde dehydrogenase (ALDH) gene superfamily for animals, plants, fungi and bacteria. The site has organised gene-specific records. It provides synopses of ALDH gene records, marries trivial terms to correct nomenclature and links global accession identifiers with source data. Server-side alignment software characterises the integrity of each sequence relative to the latest genomic assembly and provides identifier-specific detail reports, including a graphical presentation of the transcript's exon - intron structure, its size, coding sequence, genomic strand and locus. Also included are a summary of substrates, inhibitors and enzyme kinetics. The site provides reference lists and is designed to facilitate data mining by interested investigators.

DIRICHLET TRUNCATIONS OF THE RIEMANN ZETA FUNCTION IN THE CRITICAL STRIP POSSESS ZEROS NEAR EVERY VERTICAL LINE

We study the zeros of the finite truncations of the alternating Dirichlet series expansion of the Riemann zeta function in the critical strip. We do this with an (admittedly highly) ambitious goal in mind. Namely, that this series converges to the zeta function (up to a trivial term) in the critical strip and our hope is that if we can obtain good estimates for the zeros of these approximations it may be possible to generalize some of the results to zeta itself. This paper is a first step towards this goal. Our results show that these finite approximations have zeros near every vertical line (so no vertical strip in this region is zero-free). Furthermore, we give upper bounds for the imaginary parts of the zeros (the real parts are pinned). The bounds are numerically very large. Our tools are: the inverse mapping theorem (for a perturbative argument), the prime number theorem (for counting primes), elementary geometry (for constructing zeros of a related series), and a quantitative version of Kronecker's theorem to go from one series to another.

Hypermobility

Joint hypermobility is widely prevalent in all communities yet its clinical effects are poorly understood and often overlooked by rheumatologists worldwide. They may observe the hypermobility but fail to appreciate its significance in terms of overall morbidity and, more specifically, its strong link with chronic pain, fatigue, dysautonomia and the adverse impact on quality of life. This last year's publications shed further light on this fascinating and, as yet, largely unexplored terrain within rheumatology. Perhaps the most compelling new knowledge is the finding that hypermobility, if sought, is the most common finding amongst patients presenting to a rheumatologist; more often than not, it is being overlooked. There is an urgent need for rheumatologists to accept the challenges posed by hypermobility-related disorders, which have, in the past, fallen by default to clinical geneticists untrained in rheumatology. Hypermobility, a largely unacknowledged though epidemiologically important area within rheumatology, affects almost every bodily system. Recent medical literature attests to the breadth of clinical science encompassed by the seemingly trivial term, hypermobility. Drawing readers' attentions to this fascinating, challenging, but neglected area of rheumatology will hopefully entice them to explore these conditions with greater zeal.