Complementary Expressions Research Articles

A New Odd Fréchet Lehmann Type II–G Family of Distributions: A Power Function Distribution With Theory and Applications

Modeling complex random phenomena frequently observed in reliability engineering and medical science once thought to be an enigma. Scientists and practitioners agree that an appropriate but simple model is the best choice for this investigation. We contribute a new family referred to as an odd Fréchet Lehmann type-II (OFrLII) G family of distributions to address these issues. This new family has involved a shape parameter that modulated the tails of new models. Furthermore, we develop a list of eight new sub-models for a new family and a power function distribution (OFrLII–PF) nominated for detailed discussion. We derive several complementary mathematical properties and explicit expressions for the moments, quantile function, and order statistics. We plot possible shapes of the density and the hazard rate functions over the particular choices of the model parameters. We follow a technique known as maximum likelihood estimation to estimate unknown model parameters and a simulation study established to assess the asymptotic behavior of these MLEs. The applicability of the OFrLII–G family, is evaluated via OFrLII –PF distribution. For this, we fit two engineering and one COVID–19 pandemic dataset. Supportive results of OFrLII–PF distribution declare it as a better fit model against the well-established competitor’s ones. A modified odd Fréchet Lehmann Type II–G Family of Distributions: A Power Function Distribution with Theory and Applications

Construction of micromorphic continua by homogenization based on variational principles

The present contribution aims to revisit higher-order homogenization schemes towards micromorphic media based on variational principles and an extension of Hill macrohomogeneity condition. Starting from the microscopic Cauchy balance equations, the local balance equations of the micromorphic continuum are formulated, highlighting the micromorphic stress measures. Relying on both energy and complementary energy expressions combined with the extended Hill macrohomogeneity condition, the complete homogeneous microscopic displacement field representative of the effective micromorphic continuum is obtained as a quartic expansion of the macroscopic micromorphic kinematic variables. This procedure leads to a higher-grade micromorphic theory, with the relative stress and hyperstress tensors including respectively second-order and third order polynomials of the relative position within the unit cell. The microscopic displacement is completed by a fluctuating part evaluated from a variational principle and characterized by three unit cell boundary value problems. Numerical applications are done for inclusion based composite materials. The obtained results highlight that the higher-order moduli converge very quickly with unit cell size, due to the consideration of correction factors based on the higher-order moments of area.

Beyond Nation and Empire

Beyond Nation and Empire Leo T. S. Ching (bio) Every discursive formation has its own institutional itinerary and condition of possibilities, and Asian studies and Asian American studies are no exceptions. Asian studies emerged out of American Cold War policy that divided the world into delimited regions. The underlying logic was that a region formed a complex whole that was unique and bounded, and could be distinguished from other regions by its sociocultural particularities. Asian American studies was institutionalized in response to the civil rights movement in the late 1960s United States as a politics of recognition and to create a broad coalition with African American studies and ethnic studies programs. Despite their common origins in the American Empire, abroad and at home, Asian studies and Asian American studies, until recently, have remained largely insulated from each other. This disengagement, for example, has obscured the parallelism between modernization theory as applied to Japan and later other East Asian countries and the model minority myth that aimed to divide Asian Americans from other underrepresented populations, specifically Black and brown peoples. Reading modernization theory and the model minority myth contrapuntally allows us to apprehend American imperial design as a dialectical process of expansion and domestication under the ideology of postwar liberalism. As a process of decolonizing American studies, one needs to be more attentive to this liberal imperial dialectic by opening itself to the seemingly non-American histories, aspirations, and polemics. This forum provides a much-needed conversation to deepen our understanding of this transpacific entanglement with a focus on Taiwan and Taiwan/America. This collection of essays intervenes not only in the critique of American empire but also the complicity of Taiwan's desire for a "normative" nation-state status. Unlike the conventional understanding of nation and empire as antithetical—the nation is homogeneous, egalitarian, and particular, whereas empire is diverse, hierarchical, and universal—Taiwan's aspiration for national independence and the disavowal of its settler colonialism tell another story. Instead of oppositions, nation and empire are seen as alternative or complementary expressions of the same phenomenon of power. Unlike earlier [End Page 383] scholarship that has lamented the marginalization of Taiwan, hence the desire for recognition and inclusion that often finds itself having to choose between Chinese and American empires, younger scholars included here resolutely refute this discourse of victimhood and false choices. Taiwan's long history within global coloniality, or what Arif Dirlik has referred to as "the land colonialisms made,"1 its ambiguous nation-state status, and fledging digital democracy offer possible alternatives to imagine a different relationship to nation and empire. Wendy Cheng's account of the arrest and prosecution of Chen Yu-hsi highlights the entanglement of Taiwanese/American history and the hypocrisy of American liberalism in adjudicating freedom and unfreedom that in turn silences voices of those prosecuted under Cold War anticommunism. Cheng's critique of American freedom reminds us of the long history of liberalism's intimate relationship to imperialism and colonialism. One only needs to recall that the founding of American freedom is on the backs of the unfreedom of others: the dispossessions of the indigenous population and the enslavement of people from Africa. The "rescue" of Chen Yu-hsi from the silencing of Taiwan/American history reveals the complicity of American hegemony and the institutionalization of area studies. While the East-West Center at the University of Hawai'i was ostensibly established as an instrument of Cold War policy, the transpacific network of scholars and allies mobilized in support of Chen opens up the possibility of resistance to state-sanctioned violence. Cheng demonstrates that the freedom to speak and the freedom to remain silent concomitantly enables and incapacitates, includes and excludes, certain inconvenient narratives. Cheng implores us to resist this "silencing of the past" and to expose the complicity between state power and institutional formation. If Chen Yu-hsi's case represents the "silenced" history of Taiwan/America, Yukari Yoshihara's George H. Kerr and his transpacific traversing constitutes the dominant history of American studies' institutionalization in Asia. At the same time, Yoshihara alerts us to the "forgotten" imbrication of Asian studies and American studies in Asia. As a proficient Asianist trained...

Psycholinguistic Content of Complements in English and Ukrainian

The purpose of the article is: to show functions of compliments in the English and Ukrainian languages; to describe the differences between praise, flattery and compliments; to analyze a system of actual methods of modeling the associative content of the meanings of complementary expressions in the semantic field of the philological consciousness of the respondents of different ethnic groups (Englishmen and Ukrainians).
 The methods of the research are: theoretical ones – categorical and structurally-functional analysis of the texts, the methods of systematization, modeling, generalization; empirical methods – the analysis of novels, a free associative experiment.
 The results of the research. It was distinguished that among the respondents of the Ukrainian ethnic group we diagnosed the largest number of positive correlations between: the way of the explication of compliments in a form of a sentence and: syntactic constructions (phrases); semantically related compliments formed by the way of identity; creative compliments; semantically related compliments formed by the way of logical adjectivation and: semantically related compliments formed by the way of identity; semantically related compliments formed by the way of belonging, etc. The respondents of the English ethnic group had the highest number of positive correlations between: the way of the explication of compliments in a form of phrases and: semantically similar compliments; creative compliments; emotional and evaluative compliments and: semantically related compliments formed by the way of identity; semantically related compliments formed by the way of logical adjectivation, etc.
 Conclusions. We’ll formulate the psycholinguistic features of the explication of compliments in Ukrainian and English languages. Such features are: respondents of both Ukrainian and English ethnic groups are characterized by dominated subjective (ideosyncrasic) way of forming complementary expressions. English respondents are also dominated by emotional and evaluative way, while Ukrainians – by creative way in modeling the compliments. English people are more emotional in choosing phrases, word combinations and speech patterns that are complementary expressions, their speech is characterized by expressiveness and imagery. In turn, Ukrainians are more able to form creative expressions in their content, they form associative schemes, which, on the one hand, seem illogical, but, on the other hand, contain a creative context that enriches speech in a great degree, etc.

An Aridity Index‐Based Formulation of Streamflow Components

AbstractDirect runoff and baseflow are the two primary components of total streamflow, and their accurate estimation is indispensable for a variety of hydrologic applications. While direct runoff is the quick response stemming from surface and shallow subsurface flow paths and is often associated with floods, baseflow represents the groundwater contribution from stored sources (e.g., groundwater) to streams and is crucial for environmental flow regulations, and water supply, among others. L'vovich (1979) proposed a two‐step water balance partitioning, where precipitation is divided into direct runoff and catchment wetting, followed by the disaggregation of the latter into baseflow and evapotranspiration. Here, we investigate the role of the aridity index (ratio between mean‐annual potential evapotranspiration and precipitation) in controlling the long‐term (mean‐annual) fluxes of direct runoff and baseflow. We present an analytical solution beginning with similar assumptions as proposed by Budyko (1974), leading to two complementary expressions for the two fluxes. The aridity index explained 77% and 89% of variability in direct runoff and baseflow from 378 catchments within the continental United States, while our formulations were able to reproduce the patterns of water balance partitioning proposed by L'vovich (1979) at the mean‐annual timescale. Our approach can be used to further understand how climate and landscape controls the terrestrial water balance at mean‐annual timescales, while also representing a step toward the prediction of baseflow and direct runoff at ungauged basins.

The N2pc component as a neural index of early attention allocation among adults with chronic musculoskeletal pain.

Recent evidence from event-related potentials (ERPs) has identified N2 posterior contralateral (pc) amplitudes as a neural marker of early attention allocation. The N2pc has been used to evaluate attention biases (ABs) in samples with anxiety-based problems, but its utility has yet to be considered among persons with chronic pain, another group theorized to display ABs that perpetuate their difficulties. To address this gap, we assessed N2pc responses of adults with chronic pain (N=70) and pain-free controls (N=70) during a dot-probe task comprising painful-neutral and happy-neutral facial expression image pairs. Analyses indicated that (1) larger N2pc amplitudes were elicited by both painful and happy expressions compared to complementary neutral expressions in each sample, (2) the chronic pain sample displayed larger N2pc amplitudes during exposure to both painful and happy expressions than controls did and (3) no group differences were evident for N2pc latencies. Overall N2pc results reflected general biases in early allocation of attention towards affectively valenced expressions rather than pain-specific ABs among chronic pain cohorts. SIGNIFICANCE: Although numerous researchers have examined pain-related attention biases, these data are based exclusively upon behavioural measures of attention such as reaction times and eye movements. Drawing from relevant event-related potentials research, this study is the first to evaluate and identify differences in orienting of attention between adults with chronic pain and pain-free controls based on N2 posterior contralateral (pc) amplitudes which provide a neural index of early attention allocation.

A moment within the psychoanalytic psychotherapy of an adult female patient – The meanings of nonverbal and bodily expressions

ABSTRACT This case study adresses the multiple meanings of a moment of strong non-verbal and bodily expression within a course of psychoanalytic psychotherapy. One therapy session was video-recorded in the private practice of the therapist-researcher. In selecting important moments for qualitative analysis, two criteria were used: 1) the moment included intense nonverbal or bodily expression 2) the moment was experienced by the therapist as intensely affecting, both in meanings and in bodily experiences. The automatic silence detection (ASD) algorithm was used to detect and locate changes in sound energy in the session audio. The moment selected for this study involved unexpected laughter. To capture the multiple layers of the psychotherapeutic interactions, the moment was analyzed using a micro-analytic approach, applying the Sandwich model of Harrison, which takes into consideration both the verbal and nonverbal interaction. Animated complementary bodily expressions were observed, mostly in congruence with the words. It appeared that the moment marked a rift in communication and at the same time the possibility to open up new insights into intergenerational traumas. The paper discusses the benefits of the research in the work of the therapist.

Analysis of Human-Machine Interaction Through Facial Expression and Hand-Gesture Recognition

This paper focuses on a review of recent work on facial expression and hand gesture recognitions. Facial expressions and hand gestures are used to express emotions without oral communication. The human brain has the ability to identify the emotions of persons using expressions or hand gestures within a fraction of a second. Research has been conducted on human–machine interactions (HMIs), and the expectation is that systems based on such HMI algorithms should respond similarly. Furthermore, when a person intends to express emotions orally, he or she automatically uses complementary facial expressions and hand gestures. Extant systems are designed to express these emotions through HMIs without oral communication. Other systems have added various combinations of hand gestures and facial expressions as videos or images. The meaning or emotions conveyed by particular hand gestures and expressions are predefined in these cases. Accordingly, the systems were trained and tested. Further, certain extant systems have separately defined the meanings of such hand gestures and facial expressions

Music, Text, Stuttering: An Intermedial Approach to Dramatick Opera in The Fairy Queen

Music, Text, Stuttering: An Intermedial Approach to Dramatick Opera in The Fairy Queen Sharon J. Harris Critics, from the Restoration to the near past, have not always accorded much respect to Restoration adaptations of Shakespeare plays, nor to the partially overlapping genre of Restoration dramatick opera. From Samuel Pepys—for whom a 1662 adaptation of A Midsummer Night’s Dream was “the most insipid ridiculous play that I saw in my life”—to George C. D. Odell—who wrote in 1920 that George Granville’s adaptation of Merchant of Venice was “a gross vulgarisation” —and beyond, many critics have treated these adaptations as, at best, having “a certain charm and interest” but have dismissed or decried them as “imitative and derivative.”1 In recent decades we have come to better understand the social, legal, political, and cultural contexts of Restoration playmaking, including how the eventual elevation of Shakespeare as The Bard has conditioned our assessments of his Restoration adapters.2 Appreciation for the artistry of these adaptations as plays remains scarce, however. In this special issue, Amanda Eubanks Winkler shows how scholars have failed to engage Restoration dramatic art in general and makes a persuasive case for an intermedial approach to dramatick opera in particular. As she notes, the biases of bardolatry and theoretical traditions that privilege text, along with “anxieties about intermediality and the supposed subordination of the poet have been transmuted into a critical revulsion toward the writers and adapters who produced dramatick operas’ texts.”3 An intermedial approach to Restoration drama helps us see, feel, and analyze that drama better. In this essay I examine how three media—music, text, and stuttering—interact and draw on each other in the scene of the Drunken Poets in the dramatick opera, The Fairy Queen, an adaptation of Shakespeare’s A Midsummer Night’s Dream. (Following the stage directions and final lyrics in the scene, I refer to this scene as the plural Drunken Poets [End Page 65] rather than the singular Drunken Poet.) The various media and their interactions in this scene interrogate the function and identity of the poet figure and of Restoration poetics, revealing the dynamic and complementary expressions of interacting media. My analysis proceeds in four parts. First, a review of the origins of The Fairy Queen and its Drunken Poets scene establishes the intermedial nature of the dramatick opera, and a survey of discipline-specific critical responses illustrates the need for a more interdisciplinary approach. Music, text, and stuttering are then discussed in turn as media forms. Throughout this essay I consider mediation not as the act of disbursing messages or specific content but, as Richard Grusin describes, “as the process, action, or event that generates or provides the conditions for the emergence of subjects and objects.”4 As Grusin goes on to say, and as this essay illustrates, mediation—a relational, generative, and ontological process—scales large and small and is closely tied to creation, whether that be the broader creation of a Restoration aesthetic or the creativity of producing a specific Restoration dramatick opera such as The Fairy Queen.5 I approach three types of mediation—music, text, and stuttering—as different and intertwined processes and actions within the dramatick opera. My sections on each medium take the form, respectively, of a musical analysis, a recovery of historical intertextuality, and an interpretation guided by disability and media studies. My mixture of methodological approaches thus mirrors the assortment and fragmentation that characterized the aesthetics of Restoration performance, especially dramatick opera, toward the end of revealing the pleasures of this aesthetic that have escaped many commentators. I show that, although The Fairy Queen may seem a failure as a textual work and may be merely passable as a musical work, it is a success as an intermedia work. In so doing, I hope to encourage future intermedial analysis of Restoration dramatick opera. Historical Origins and Critical Responses Explaining how the The Fairy Queen was conceived and received sets up the discussion of the different media that will follow. This dramatick opera premiered at the Dorset Garden Theater in May 1692 as an altered and heavily cut version of A Midsummer Night’s Dream interspersed...

Friends with a Mandate: Friendship and Family in Bonhoeffer’s Ecclesiology

Several social and cultural developments have led to a rethinking of the place and meaning of friendship within the life of the Church, not least its relation to family (and marriage). Dietrich Bonhoeffer’s theology has great potential for informing such renewed reflection. At face value, he appears to count both Church and family among the divine ‘mandates’, leaving friendship to a realm of ‘freedom’ outside the mandates. Yet closer reading of his writings—not least his correspondence with Bethge—reveals, first, a more singular role of the Church vis-à-vis the mandates (including family); and secondly, congeniality between friendship and the ‘vicarious representative’ practices that lie at the heart of Bonhoeffer’s ecclesiology. Together, these findings allow us to recognise family and friendship as complementary expressions of discipleship, each supporting the other precisely by setting a limit to the specific type of ‘vicarious representative’ responsibility entrusted to each.

From self-tracking to smart urban infrastructures: towards an interdisciplinary research agenda on Big Data

Recent debates on surveillance have emphasised the now myriad possibilities of automated, software-based data gathering, management and analysis. One of the many terms used to describe this phenomenon is ‘Big Data’. The field of Big Data covers a large and complex range of practices and technologies from smart borders to CCTV video analysis, and from consumer profiling to self-tracking applications. The paper’s aim is to explore the surveillance dynamics inherent in contemporary Big Data trends. To this end, the paper adopts two main perspectives concerned with two complementary expressions of Big Data: (1) the individual use of various techniques of self-surveillance and tracking and (2) the simultaneous trend to optimise urban infrastructures through smart information technologies. Drawing upon exploratory research conducted by the authors, the paper shows that both expressions of Big Data present a range of common surveillance dynamics on at least four levels: agency, temporality, spatiality and normativity. On these grounds, the paper highlights a series of important issues to explore in future research.

“It Depends How You’re Saying It”: The Complexities of Everyday Racism

While racism is widely recognised as a complex social phenomenon, the basis for defining and identifying everyday racism from a lay perspective is not well understood. This exploration of factors used to frame everyday racism draws on seven cognitive interviews and four focus groups conducted in November 2010 and January 2011 with Australian adults predominantly from Anglo ethnic and cultural backgrounds. The study reveals lay theorising centring on tropes of intentionality, effect of speech, relationality and acceptability. Participants were more likely to think of racism as having negative, overtly offensive and emotional connotations. Racialised speech that was not considered to be blatantly racist was more contested, with participants engaging in complex theorising to determine whether or not such speech constituted racism. The study also highlights the potential of qualitative research to inform survey development as an unobtrusive method for in-depth participant reflection. The ambiguous nature of everyday racism demonstrated in this paper indicates a need to foster more nuanced lay understandings of racism that encompass the subtle, rational and complementary expressions that can be situated within institutions and society.

Complementary expressions for the entropy-from-work theorem

We establish an expression of the entropy-from-work theorem that is complementary to the one originally proposed by Talkner, Hanggi, and Morillo [Phys. Rev. E 77, 051131 (2008)]. In the original expression the final energy is fixed, whereas in the present expression the initial energy is fixed.

CrossRef Listing of Deleted DOIs

In this paper, the Hu-Washizu generalized variational principle is extended to nonlinear elastodynamics with five independent fields. The two kinds of framework of functional, the potential energy and complementary energy expressions containing the subsidiary conditions with Lagrange multipliers are suggested. According to the principle of stationary functional, we have the governing equations and Lagrange multipliersdetermened by the results of variation. The generalized sub-region mixed andhybrid variational principle in nonlinear elastodynamics is presented.

Resolutions of monomial ideals and cohomology over exterior algebras

This paper studies the homology of finite modules over the exterior algebra E E of a vector space V V . To such a module M M we associate an algebraic set V E ( M ) ⊆ V V_E(M)\subseteq V , consisting of those v ∈ V v\in V that have a non-minimal annihilator in M M . A cohomological description of its defining ideal leads, among other things, to complementary expressions for its dimension, linked by a ‘depth formula’. Explicit results are obtained for M = E / J M=E/J , when J J is generated by products of elements of a basis e 1 , … , e n e_1,\dots ,e_n of V V . A (infinite) minimal free resolution of E / J E/J is constructed from a (finite) minimal resolution of S / I S/I , where I I is the squarefree monomial ideal generated by ‘the same’ products of the variables in the polynomial ring S = K [ x 1 , … , x n ] S=K[x_1,\dots ,x_n] . It is proved that V E ( E / J ) V_E(E/J) is the union of the coordinate subspaces of V V , spanned by subsets of { e 1 , … , e n } \{\,e_1,\dots ,e_n\,\} determined by the Betti numbers of S / I S/I over S S .

Delay-fault testability preservation of the concurrent decomposition and factorization transformations

Recently, a new, very efficient method of multilevel logic synthesis based on factorization and decomposition of Boolean expressions has been introduced. It has been shown that the transformations used by this method preserve the single stuck-at testability of two-level circuits. This paper shows that single-cube extraction, double-cube extraction, and dual-extraction of double-cubes/spl isin/D/sub 1,1,2/ and D/sub 2,2,2/ preserve testability with respect to a general robust path-delay-fault (RPDF) test set. However, the authors show that while dual-extraction of double-cubes/spl isin/D/sub 2,2,3/ preserves RPDF testability of paths through the extracted divisors with respect to a single-input-changing test set, it does not guarantee RPDF testability preservation of unmodified paths. Furthermore, the authors provide sufficient conditions for algebraic resubstitution with complement to preserve RPDF testability that cover a larger class of complementary expressions than was known previously. The testability preservation of these transformations is demonstrated on a set of RPDF testable Berkeley PLAs. >

Complementary expressions of transcripts encoding GAD67 and GABAA receptor alpha 4, beta 1, and gamma 1 subunits in the proliferative zone of the embryonic rat central nervous system

The developmental stage at which nerve cells initially express specific neurotransmitters and their corresponding receptors remains elusive. In the present study, the distribution patterns of transcripts for the GABA-synthesizing enzyme, glutamate decarboxylase (GAD67), and specific GABAA receptor subunits were examined in the proliferative zone of the rat central nervous system using in situ hybridization. In order to define the DNA synthetic zone of the germinal matrix, tissue sections were taken from embryos whose mothers had been injected with 5-bromo-2'-deoxyuridine (BrdU) and had survived for 1 hr. BrdU immunocytochemistry was used to locate the relative position of BrdU-immunoreactive nuclei within the ventricular zone (VZ). At embryonic day (E) 15 in the alar plate of the lumbar spinal cord, and at E17 and E20 in the dorsomedial sector of the neocortex, densely packed BrdU-immunoreactive nuclei were consistently detected in lateral portions of the inner half of the germinal matrix, indicating that the inner half of the germinal matrix corresponded to the VZ, while the outer half corresponded to the transitional (TZ) or subventricular zone (SV). In situ hybridization in tissue sections adjacent to BrdU-immunoreacted ones showed that the transcripts for GABAA receptor alpha 3, beta 3, and gamma 2 subunits were found exclusively in the mantle zone, while those for alpha 4, beta 1, and gamma 1 subunits were predominantly detected in the inner half of the germinal matrix (i.e., VZ). Furthermore, in the E15 germinal matrix of the lumbar spinal cord, cells exhibiting alpha 4 subunit mRNA were much more abundant in the receding intermediate plate, which contains mostly postmitotic cells, than in the alar plate comprised of many DNA-synthesizing cells, strongly suggesting that only those cells completing final cell division expressed the subunit mRNAs. In clear contrast, GAD67 mRNA was abundant in the outer half of the germinal matrix (i.e., TZ or SV), and in the intermediate zone as well. Immunocytochemical staining of E17 neocortex with anti-GABA antibody revealed a well defined band of GABA-immunoreactive cells and processes in the SV and occasional positive cells in the VZ. It appears that cells in the proliferative zone may express GABA at the migratory stage, whereas cells in the VZ may express mRNAs for GABAA receptor alpha 4, beta 1, and gamma 1 subunits at the premigratory stage, just after completing cell division.(ABSTRACT TRUNCATED AT 400 WORDS)

Also from all so: On a set of particles in service of efficient communication

The paper examines the main semantic properties of the particle also, its complementary expressions such as either and its equivalents in other languages. Also is claimed to be an exponent of a full predicative structure with its own theme, a structure which characterizes a sentence or clause where also occurs. The theme is a sayable drawn from the relevant sentence (clause); it is assigned the property of ‘not being untrue’ of an object accessible through the sentence (clause). Furthermore, the content of also includes equivalents of some attributes restricting the sayable and expressible in form of relative clauses. The most important of these conveys the speaker's not being ready to take the sayable to be untrue of another object assumed by the speaker to be recoverable from the context or situation by the hearer no less than by him- or herself.

A complementary energy principle in magnetohydrodynamics

Variational principles for growth rates of instabilities in magnetohydrodynamics are derived. In addition to previous investigations, complementary expressions are presented. The latter are quite useful for numerical computations since they lead to upper and lower bounds for the exact growth rates.

Complementary expressions for the scaling function near a magnetic critical point

Simple asymptotic expressions for the scaling functions, h(x)=x- phi 0)gamma valid near t=0, and x(h)=- mod h- psi 0-(t) mod 1 gamma / valid in a narrow region near H=O, t 0 in a narrow region near hi=constant, where hi can be made arbitrarily close to infinity. An estimate Gamma +/ Gamma - approximately=( delta -1) for the ratio of inverse susceptibility amplitudes above and below Tc is obtained. Comparison of h(x) with very accurate recent data on Ni gives an excellent agreement which is at least as good as that obtained using an optimised set of linear parametric equations.