Reciprocal Transformation Research Articles

Research through Collaborative Relationships: A Middle Ground for Reciprocal Transformations and Translations?

Research through Collaborative RelationshipsA Middle Ground for Reciprocal Transformations and Translations? Claudia Briones (bio) Joanne Rappaport's article has two main virtues. On the one hand, she provides a thoughtful summary of very diverse experiences of collaborative research. On the other, she expands the field of vision of our discussions by means of key displacements of focus: from collaborative research to research through collaborative relationships; and from products to processes. She does so by means of a very ethnographic contextualization and historization of the initiatives of La Rosca de Investigación y Acción Social (Circle of Social Research and Action), a group deeply related to Orlando Fals Borda's appealing methodology of "action research." One common problem in our attempts to discuss collaborative endeavors results from the fact that we always produce situated knowledge within situated contexts and histories. Thus, instead of general statements on the topic, what we all can share are situated experiences. Against such a backdrop, I cannot but make explicit that the reading I can make of Rappaport's contributions mostly comes from my experience with members of the Mapuche-Tewelche people of northwestern Patagonia, in Argentina. I am aware that other experiences might bring about different ruminations. In any event, during more of thirty years of interactions and exchanges, my interlocutors have expected and demanded from me (and I from them) very different things. Hence several of the resulting activities can be thought of as collaborations, but not as what we all try to grasp through the idea of collaborative research and methodologies, [End Page 32] if by these we plainly mean practices aiming at a co-theorization and co-analysis that emanate from an explicit agreement to do so. Therefore, of the many interesting points raised by Joanne, I concentrate on two. First, the idea of collaboration as a chain of multifaceted conversations and then the notion that what seems to be "already there" is "in a continuous state of flux, an ongoing process of creation." Colleagues performing conversational analysis point out that what counts in any conversation is who rules the exchange—how and following whose agenda. In terms of a collaborative methodology and from a pragmatic viewpoint, the key point is that there can be different forms of proposing and performing conversations. Some interactions can indeed take on dialogical dynamics. However, others are monologues even if giving the appearance of an exchange. Closed questions that imply expected responses or allow mostly for yes/no answers end up in one party controlling and passing the floor and even in unilateral decisions about when the game is over. Moreover, if we approach conversations as processes, within a single talk there can be more than one form of exchange. In any event, we can invest "conversations" with a significance that surpass the idea of mere exchange. According to the Online Etymology Dictionary, conversation is not a mere dialogue, because it comes from and means "living together, having dealings with others," and also reflects a "manner of conducting oneself in the world." Coming from the Latin conversationem—a noun of action from the past participle stem of conversari, "to live with, keep company with," literally "to turn about with," from the Latin com, "with" + vertare, frequentative of vertere—it also means "to turn, turn back, be turned, convert, transform, translate, be changed" (see http://www.etymonline.com/index.php?term = conversation). We can thus assume that conversations can also involve reciprocal transformations and translations. But what is it that should be transformed or translated through collaborations as chains of conversations? What or who is it that we attempt to transform and translate? The collaborative turn can be seen as the result of the severe and necessary criticisms that anthropology has developed of science and scientific research in general, and of our discipline in particular. I believe that what moves most of us to engage in collaborations of different sorts is mainly our aim of neutralizing asymmetries and of undoing the unilateral privileges that researchers have as members of a dominant educated class or group, gender, or region. Now then, insofar as we keep on defining [End Page 33] ourselves as researchers (and in that...

Reciprocal Transformations of Two Camassa–Holm Type Equations**Supported by the Global Change Research Program of China under Grant No. 2015CB953904, National Natural Science Foundation of China under Grant Nos.11275072, 11375090 and 11435005, Research Fund for the Doctoral Program of Higher Education of China (No. 20120076110024), The Network Information Physics Calculation of basic research innovation research group of China under Grant No.

The relation between the Camassa–Holm equation and the Olver–Rosenau–Qiao equation is obtained, and we connect a new Camassa–Holm type equation proposed by Qiao etc. with the first negative flow of the KdV hierarchy by a reciprocal transformation.

The Korteweg capillarity system. Integrable reduction via gauge and reciprocal links

This classical Korteweg capillarity system is here encapsulated in a quintic derivative nonlinear Schrodinger equation for a model Karman-Tsien type capillarity law. An integrable subsystem is isolated and invariants of motion are use to construct novel exact solutions. The latter involve parameters introduced via a gauge and reciprocal transformation.

Reciprocal NUT spacetimes

In this paper, we study the Ehlers' transformation (sometimes called gravitational duality rotation) for reciprocal static metrics. First, we introduce the concept of reciprocal metric. We prove a theorem which shows how we can construct a certain new static solution of Einstein field equations using a seed metric. Later, we investigate the family of stationary spacetimes of such reciprocal metrics. The key here is a theorem from Ehlers', which relates any static vacuum solution to a unique stationary metric. The stationary metric has a magnetic charge. The spacetime represents Newman-Unti-Tamburino (NUT) solutions. Since any stationary spacetime can be decomposed into a 1 + 3 time-space decomposition, Einstein field equations for any stationary spacetime can be written in the form of Maxwell's equations for gravitoelectromagnetic fields. Further, we show that this set of equations is invariant under reciprocal transformations. An additional point is that the NUT charge changes the sign. As an instructive example, by starting from the reciprocal Schwarzschild as a spherically symmetric solution and reciprocal Morgan–Morgan disk model as seed metrics we find their corresponding stationary spacetimes. Starting from any static seed metric, performing the reciprocal transformation and by applying an additional Ehlers' transformation we obtain a family of NUT spaces with negative NUT factor (reciprocal NUT factors).

Three-dimensional rock slope stability analysis considering the surface load distribution

Previous studies on slope stability mainly focused on conditions under gravity load in which the slope tends to slide down along the potential slip surface. However, the existence of a horizontal load on the slope surface can restrain the slope-slipping trend and improve the stability of the slope, similar to the effect of a retaining wall. The slope failure mode can be altered by a sufficiently large horizontal surface load. In this case, the slope stability problem will be converted to a rock foundation stability problem. However, the reciprocal transformation of slope stability and rock foundation stability has been rarely studied. This study considers the Ice and Snow World project in Changsha, China, as the engineering background. This project is located at an abandoned mine pit, the structural load of which mainly acts on the top of the pit. To study the three-dimensional (3D) slope stability under the slope surface load, a 3D slope model is established using the numerical commercial code. The mechanical parameters of the rock mass, as well as the value and the distribution areas of the surface load, are changed to identify the corresponding safety factor of rock mass, deformation and failure mode.

Moving boundary problems for the Harry Dym equation and its reciprocal associates

Moving boundary problems of generalised Stefan type are considered for the Harry Dym equation via a Painleve II symmetry reduction. Exact solutions of such nonlinear boundary value problems are obtained in terms of Yablonski–Vorob’ev polynomials corresponding to an infinite sequence of values of the Painleve II parameter. The action of two kinds of reciprocal transformation on the moving boundary problems is described.

New complex function space related to both entangled state representation and spin coherent state

A new complex function space whose basis is the single-variable Hermite polynomial H2jξ*+τξ2τ is constructed, which is related to both entangled state representation and spin coherent state in Schwinger bosonic realization. New binomial theorem involving two-variable Hermite polynomial is derived, which helps to constitute the new complex function space. We also present a new integration transformation of the basis H2jξ*+τξ2τ with its reciprocal transformation which is useful to deriving some operator identities.

A harmonic means pooling strategy for structural similarity index measurement in image quality assessment

Structural similarity index measurement (SSIM) is one of the most well known method in full reference image quality assessment metrics (FR-IQA). In this paper, a novel pooling strategy based on harmonic mean is proposed to enhance the performance of SSIM. Instead of arithmetic mean, the proposed pooling by harmonic mean tends to emphasize the contributions from the local severely distorted regions or pixels in the definition of assessment function using reciprocal transformation. The proposed object function has higher correlation with human perception, which is mostly affected with the regions having severely distorted points or regions. In addition, salience information is introduced to the object function for a better consideration of subject visual attention. The proposed pooling strategy is applied to classical SSIM and its variants, GSSIM and FSIM. The experimental results have demonstrated that the FR-IQA metrics with proposed pooling strategy have better performances compared to the standard versions, especially on the images with small but seriously distorted regions.

Integrable semi-discretization of a multi-component short pulse equation

In the present paper, we mainly study the integrable semi-discretization of a multi-component short pulse equation. First, we briefly review the bilinear equations for a multi-component short pulse equation proposed by Matsuno [J. Math. Phys. 52, 123702 (2011)] and reaffirm its N-soliton solution in terms of pfaffians. Then by using a Bäcklund transformation of the bilinear equations and defining a discrete hodograph (reciprocal) transformation, an integrable semi-discrete multi-component short pulse equation is constructed. Meanwhile, its N-soliton solution in terms of pfaffians is also proved.

BERTRAND CURVES AND RAZZABONI SURFACES IN MINKOWSKI 3-SPACE

In this paper, we generalize some results about Bertrand curves and Razzaboni surfaces in Euclidean 3-space to the case that the ambient space is Minkowski 3-space. Our discussion is divided into three different cases, i.e., the parent Bertrand curve being timelike, spacelike with timelike principal normal, and spacelike with spacelike principal nor- mal. For each case, first we show that Razzaboni surfaces and their mates are related by a reciprocal transformation; then we give Backlund trans- formations for Bertrand curves and for Razzaboni surfaces; finally we prove that the reciprocal and Backlund transformations on Razzaboni surfaces commute.

On a class of reciprocal Stefan moving boundary problems

This paper concerns the action of reciprocal transformations on a class of moving boundary problems of Stefan type. Thus, an established integral representation is combined with a reciprocal transformation to obtain parametric exact solution to classes of moving boundary problems which arise, in particular, in the context of the percolation of liquids through a porous medium such as soil. Importantly, the procedure is shown to extend to a wide class of moving boundary value problems which incorporate heterogeneity in the porous medium.

Reference values for pulse wave Doppler and tissue Doppler imaging in pediatric echocardiography.

In pediatric echocardiography, pulse wave Doppler, and tissue Doppler imaging velocities are widely used to assess cardiac function. Current reference values and Z scores, allowing adjustment for growth are limited by inconsistent methodologies and small sample size. Using a standardized approach for parametric modeling and Z score quality assessment, we propose new pediatric reference values and Z score equations for most left ventricular pulse wave Doppler and tissue Doppler imaging measurements. Two hundred thirty-three healthy pediatric subjects 1 to 18 years of age were prospectively recruited. Thirteen pulse wave Doppler and 14 tissue Doppler imaging measurements were recorded. Normalization for growth was done via a complete and standardized approach for parametric nonlinear regression modeling. Several analyses were performed to ensure adequate Z score distribution and to detect potential residual associations with growth or residual heteroscedasticity. Most measurements adopted a nonlinear relationship with growth and displayed significant heteroscedasticity. Compared with age, height, and weight, normalization for body surface area was most efficient in removing the effect of growth. Generally, polynomial and allometric models yielded adequate goodness-of-fit. Residual values for several measurements had significant departure from the normal distribution, which could be corrected using logarithmic or reciprocal transformation. Overall, weighted parametric nonlinear models allowed us to compute Z score equations with adequate normal distribution and without residual association with growth. We present Z scores for normalized pulse wave Doppler and tissue Doppler imaging in pediatric echocardiography. Further studies are needed to define the threshold beyond which health becomes a disease by integrating other important factors such as ventricular morphology, loading conditions, and heart rate.

Some properties for a new integrable soliton equation

In this paper, we introduce an integrable soliton equation and present its Lax pair and bi-Hamiltonian structure. We demonstrate that this integrable equation possesses special kink waves. The relationship between the integrable soliton equation and Gardner's equation is established by a reciprocal transformation. Our study extends previous research through a comparison between the soliton equation and its generalized version.

Links between(γn,σk)-KP Hierarchy,(γn,σk)-mKP Hierarchy, and (2+1)-(γn,σk)-Harry Dym Hierarchy

The new (2+1)-(γn,σk)-Harry Dym hierarchy and(γn,σk)-mKP hierarchy with two new time seriesγnandσk, which consist ofγn-flow,σk-flow, and mixedγnandσkevolution equations of eigenfunctions, are proposed. Gauge transformations and reciprocal transformations between(γn,σk)-KP hierarchy,(γn,σk)-mKP hierarchy, and (2+1)-(γn,σk)-Harry Dym hierarchy are studied. Their soliton solutions are presented.

El diálogo local-global en la transformación de nuestros territorios contemporáneos

The changes that are happening, in the last few decades, around the logic of the market, the new modes of production and the flows of capital, have their reciprocal transformation of our territories. On the one hand, globalization tends to cancel the spatial correlation of these processes, homogenizing the geographical landscape, but on the other hand, the local -in relation to their values and characteristics- is positioned as a key strategic component in this context. Thus, the local-global dialectical pair, although it is seen as conflicting dichotomy, also is a key joint to confront and understand the issues present in our contemporary territories, in order to improve the living conditions of the whole population.

The influence of electron-donating compounds on the electronic state of spiroantrooxazine incorporated into thermoplastic polymers via supercritical fluid impregnation

Aromatic electron-donating compounds (EDCs), such as toluene and dibutyl phthalate, were found to affect the content of photochromic spiroantrooxazine (SAO) incorporated into thermoplastic polymer matrices (for example, polyvinylchloride and F-42 fluoropolymer) via the method of supercritical fluid impregnation (SCFI) and influence the ratio of colored B and B x forms of SAO. The presence of EDCs in impregnated polymers induces reciprocal transformations between B and B x colored forms of SAO and increases the rate of their “dark” bleaching.

Technical Research for Oil Well Variable Frequency Electromagnetic Field Paraffin Prevention

Oil well paraffin is one problem that often occurs in oil production; it will seriously affect or even suspend production. There are many kinds of paraffin prevention technologies, but limited to particular conditions or other factors, there are still shortcomings and insufficiency of all these technologies. In order to make this process environmental, efficient and energy saving, we propose the technique of variable frequency electromagnetic field paraffin. According to the principle of Maxwell's electromagnetic theory, the reciprocal transformation of electromagnetic field and magnetic field intensity are determined by diameter of coil, current intensity, as well as the turn number of coils. The optimal parameter for paraffin prevention is defined by the selection of the current intensity and frequency of the conversion electromagnetic field in the laboratory so as to achieve optimum efficiency of paraffin prevention. Judging from the practice in three wells in site, this technology can extend flushing period, increase oil production, reduce power consumption and improve efficiency of oil well production, so the application of this technology has a very broad and bright prospect.

Self-adaptive moving mesh schemes for short pulse type equations and their Lax pairs

Abstract Integrable self-adaptive moving mesh schemes for short pulse type equations (the short pulse equation, the coupled short pulse equation, and the complex short pulse equation) are investigated. Two systematic methods, one is based on bilinear equations and another is based on Lax pairs, are shown. Self-adaptive moving mesh schemes consist of two semi-discrete equations in which the time is continuous and the space is discrete. In self-adaptive moving mesh schemes, one of two equations is an evolution equation of mesh intervals which is deeply related to a discrete analogue of a reciprocal (hodograph) transformation. An evolution equations of mesh intervals is a discrete analogue of a conservation law of an original equation, and a set of mesh intervals corresponds to a conserved density which play an important role in generation of adaptive moving mesh. Lax pairs of self-adaptive moving mesh schemes for short pulse type equations are obtained by discretization of Lax pairs of short pulse type equations, thus the existence of Lax pairs guarantees the integrability of self-adaptive moving mesh schemes for short pulse type equations. It is also shown that self-adaptive moving mesh schemes for short pulse type equations provide good numerical results by using standard time-marching methods such as the improved Euler’s method.

A Reciprocal Transformation for the Constant Astigmatism Equation

We introduce a nonlocal transformation to generate exact solutions of the constant astigmatism equation $z_{yy} + (1/z)_{xx} + 2 = 0$. The transformation is related to the special case of the famous B\"acklund transformation of the sine-Gordon equation with the B\"acklund parameter $\lambda = \pm1$. It is also a nonlocal symmetry.

Asymptotic Limit of Consumption and Threshold Level of Income with Reference to Indore City

The concept of asymptotic level of consumption is defined as increase in consumption of a commodity with income but only up to a level and then after reaching a maximum level it becomes stable irrespective of income. Especially, food consumption stops increasing with an increase in income because of the limitation associated with digestive system. It is observed that empirical study on maximum food consumption as well as threshold income have not been done on Indian situation. Growing need was felt to conduct an academic study for Indore city with respect to their food consumption pattern to derive the maximum potential level of consumption termed as asymptotic limit of consumption as well as threshold level of income. Data from Indore city are collected on the basis of a sample of size of 714 household units. Then, the asymptotic limit of consumption and threshold level of income have been estimated using reciprocal transformation method. In all the cases, there exists significant positive relationship between income and food consumption. Hence, the first hypothesis, β 1 > 0, was accepted at 5% level of significance for food commodities rice, wheat, other cereals, pulses, dairy products, edible oil, eggs and other food items. This indicates that increase in income results in increase in food consumption derived from the above mentioned food categories. Consumption of these food categories seems to have reasonable prospect for expansion although at a lower rate, especially in the case of animal products. The analysis suggests that consumption is still well below saturation level(asymptotic level) and that appreciable increases are still possible.