Academic literature on the topic 'Tenseur de Nye'

An extension to a previously published, novel stereological method is reported which infers experimentally inaccessible components of the Nye GND tensor. Limitations imposed by electron-opacity of metals prevent direct measurement of four components of the Nye tensor, but it is possible to use additional experimentally-obtainable information in connection with underlying field equilibrium equations to estimate these additional components. This approach uses derivatives to the infinitesimal elastic distortion tensor to reduce error imposed by pattern center inaccuracy.

From the lattice orientation of a sample, elements of the Nye-tensor can be determined. With the help of Nye’s tensor, dislocation density can be calculated for the certain sample. Since the measures were carried out with scanning electronmicroscope (SEM), just superficial orientations can be measured. Hence the Nye-tensor is an incomplete matrix, with five elements. Because of the absence of the other four elements just a quasi-dislocation density can be obtained. The algorithm of the calculation was programmed on the language C#.

Significant advances are reported in the application of HR-EBSD to the imaging of the dislocation structure of polycrystalline materials. The central assumption of the method is the compatibility of the total displacement field, which relates the (Nye) dislocation tensor to the (partially measurable) curl of the elastic displacement field. Two key challenges must be addressed, including: a) the fundamental limitation imposed by the electron-opacity of typical materials, which limits the measurement of gradients in the displacement field in the direction normal to the sample surface; and b) the inability of HR-EBSD to recover the spherical (elastic) distortions of the lattice. This second challenge can be overcome if a traction free boundary condition is applied. It is illustrated that consideration of the familiar stress equilibrium relations gives additional information, which may enable estimates of the missing components of the Nye tensor. An example of application of HR-EBSD to a Mg-Ce sample is presented.

AbstractDuring recrystallization, the growth of fresh grains initiated within a deformed microstructure causes dramatic changes in the dislocation structure and density of a heavily deformed matrix. In this paper, the microstructure of a cold rolled and partially recrystallized Al-Mg alloy (AA5052) was studied via electron backscattered diffraction (EBSD) analysis. The structure and density of the geometrically necessary dislocations (GNDs) were predicted using a combination of continuum mechanics and dislocation theory. Accordingly, the Nye dislocation tensor, which determines the GND structure, was estimated by calculation of the lattice curvature. To do so, five components of the Nye dislocation tensor were directly calculated from the local orientation of surface points of the specimen, which was determined by two-dimensional EBSD. The remaining components of GNDs were determined by minimizing a normalized Hamiltonian equation based on dislocation energy. The results show the elimination of low angle boundaries, lattice curvature, and GNDs in recrystallized regions and the formation of low angle boundaries with orientation discontinuities in deformed grains, which may be due to static recovery.

В настоящей работе процедура построения двумерных фигур Ная модифицируется для асимметричных матриц и применяется для представления определяющих псевдотензоров демитропных микрополярных упругих континуумов. Указанные матричные представления используются для упрощения тензорной записи уравнений анизотропных тел. Метод матричного представления Ная позволяет изобразить тензоры и псевдотензоры четвертого и второго рангов в виде своеобразных двумерных фигур. Получена матричная форма асимметричных определяющих уравнений демитропного микрополярного упругого тела. Основное изложение статьи проводится в декартовой прямоугольной системе координат в терминах инвариантного элемента объема. In this work, the process of constructing two-dimensional figures is modified for asymmetric matrices and is used to represent the defining pseudotensors of demitropic micropolar elastic continua. The specified matrix representations are used to simplify the tensor representation of the material of anisotropic bodies. This method allows us to represent tensors and pseudotensors of the fourth and second ranks in the form of peculiar two-dimensional figures. A matrix form is obtained that defines the basis of a demitropic micropolar elastic body. The main presentation of the article is carried out in a Cartesian rectangular coordinate system.

Cette thèse propose un cadre multiéchelle pour modéliser de manière continue les structures de cœur des défauts cristallins, tels que les dislocations et les joints de grains, ainsi que leurs interactions élastiques et les énergies de cœur associées, en combinant des approches atomistiques et de mécanique des milieux continus. L'idée centrale de cette étude est de transformer les structures atomiques de coeurs des défauts en champs continus de densités de dislocations, tout en préservant les détails atomistiques essentiels. L'approche développée repose sur un modèle micromécanique récent basé sur la mécanique des champs de dislocations qui utilise le tenseur de densité de dislocation de Nye, dérivé des données atomistiques, pour modéliser les champs mécaniques à courte et longue portée associés à ces défauts. La méthode a été appliquée avec succès à des dislocations vis compactes dans le tungstène, issues de simulations extit{ab initio}, ainsi que sur des joints de grains dans le cuivre, simulés par statique moléculaire. Cette approche s'est révélée capable de reproduire remarquablement les vecteurs de Burgers et les champs mécaniques des défaut, démontrant l'absence de perte significative d'information au niveau des cœurs des défauts. Il a été possible de reproduire des joints de grains de tout angle de désorientation en utilisant une densité équivalente de dislocations, tout en capturant les champs élastiques continus. Par ailleurs, cette étude a permis d'intégrer les champs élastiques et les densités de dislocations dans des fonctionnelles énergétiques basées sur le tenseur de Nye, typiquement utilisées au sein de modèles de plasticité à gradient, afin d'évaluer leur contribution respective à l'énergie totale des joints de grains. Nous avons ainsi analysé et discuté les formes de fonctionnelles pertinentes pour ces modèles énergétiques, en explorant l'origine physique du paramètre de longueur interne inhérent à ces fonctionnelles, et sa dépendance aux types de joints de grains, aux structures atomistiques, et à l'échelle de résolution spatiale. Cette formulation nous a permis d'établir des corrélations entre les structures atomiques des joints de grains et les énergies de cœur, apportant des perspectives nouvelles pour la compréhension et la modélisation des défauts cristallins dans les matériaux polycristallins
This thesis proposes a multiscale framework aimed at providing a continuous representation of the core structures of crystalline defects, such as dislocations and grain boundaries, as well as their elastic interactions and associated core energies, by combining atomistic and continuum mechanics approaches. The central idea of this study is to transform the atomic core structures of defects into continuous fields of dislocation densities, while preserving the essential atomistic details. The approach developed relies on a recent micromechanical model based on field dislocation mechanics, , which uses the Nye dislocation density tensor, derived from atomistic data, to reproduce the short and long-range mechanical fields associated with these defects. The method has been successfully applied to compact screw dislocations in tungsten, derived from extit{ab initio} simulations, as well as to grain boundaries in copper, simulated by molecular statics. This approach is capable of remarkably reproducing Burgers vectors and defect mechanical fields, demonstrating the lack of any significant loss of information at defect cores. It was possible to reproduce grain boundaries of any misorientation angle using an equivalent density of dislocations, while capturing the continuous elastic fields. Furthermore, this study enables to integrate elastic fields and dislocation densities into Nye tensor-based energy functionals, typically used within strain gradient plasticity models, in order to assess their respective contribution to the total energy of grain boundaries. We analyzed and discussed the relevant forms of energy functionals, explored the physical origin of the internal length parameter inherent to these functionals, and its dependence on grain boundary types, atomistic structures, and spatial resolution scale. This formulation enables to establish correlations between grain boundary atomistic structures and core energies, providing new insights into the understanding and modeling of crystal defects in polycrystalline materials

Une condition préalable pour toute étude d’une protéine par RMN est l’attribution des résonances du spectre 15N-1H HSQC à leurs atomes correspondants du squelette peptidique. Un nouveau type de stratégie d’attribution exploite l’information donnée par une structure 3D déjà disponible de la même protéine ou d’une protéine homologue. Jusqu’à présent, les algorithmes, développés autour de cette stratégie, ont deux inconvénients majeurs : ils ne peuvent pas garantir l’exactitude de l’attribution et ils ne sont pas applicables à des protéines de grande taille. Dans un premier temps, il est montré que l’utilisation des couplages dipolaires résiduels (RDC) pour l’attribution basée sur la structure peut poser des problèmes, notamment liée à l’estimation du tenseur d’alignement. Une nouvelle méthode d’attribution basée sur la structure, nommée NOEnet, est présentée ici. NOEnet n’est pas basée sur les RDCs mais sur les effets Overhauser nucléaire (NOEs). RDCs, déplacements chimiques (CS) et presque tout type de donnée peuvent être inclus dans NOEnet grâce à une approche générale de filtre. NOEnet exploite le réseau de contraintes NOE HN-HN non ambiguës en réalisant une recherche exhaustive de tous les appariements possibles entre le réseau des NOEs et le réseau de la structure 3D. Son algorithme efficace de recherche complète garantit l’exactitude du résultat d’attribution. NOEnet a été testé avec succès sur plusieurs protéines jusqu’à 28 kDa, en utilisant uniquement des données NOE ou une combinaison de données NOE, RDC et CS
A prerequisite for any protein study by NMR is the assignment of the resonances from the 15N-1H HSQC spectrum to their corresponding atoms of the protein backbone. A new type of assignment strategy exploits the information given by an already available 3D structure of the same or a homologous protein. Up to now, the algorithms that have been developed around this strategy have two important drawbacks: they cannot guarantee the accuracy of the assignment and they are not applicable to large proteins. First is shown that the use of residual dipolar couplings (RDC) for the structure based assignment can be problematic, especially the estimation of the alignment tensor is difficult. A novel structure based assignment approach, called NOEnet, is presented here. NOEnet is not based on RDCs but on Nuclear Overhauser Effects (NOEs). RDCs, chemical shifts (CS) and almost any kind of data can be included in NOEnet through a general filter approach. NOEnet exploits the network property of unambiguous HN-HN NOE constraints to realize an exhaustive search of all matching possibilities of the NOE network on the structural one. Its efficient complete search algorithm ensures the correctness of the assignment results. NOEnet has been successfully tested on several proteins up to 28 kDa, using only NOE data or a combination of NOE, RDC and CS data

Doutoramento em Bioquímica
The work presented in this Thesis investigates the dynamics and molecular interactions of p22HBP and the p22HBP-tetrapyrrole complex. Specifically, the key residues involved when a tetrapyrrole binds to p22HBP were sought. Previous molecular modelling studies identified three possible charged residues R56, K64 and K177 as possibly being important in tetrapyrrole binding via electrostatic interactions with the propionate groups of the tetrapyrrole. A number of variants of murine p22HBP were therefore prepared and fluorescence quenching and NMR used to verify the integrity of the variants and their interaction with tetrapyrrole. The same molecular modelling studies identified a mobile loop Y171-R180 in p22HBP that decreased in mobility on tetrapyrrole binding, therefore to confirm this mobility change dynamics studies based on NMR relaxation experiments were carried out. Finally in order to obtain a non heme-binding form of human p22HBP a chimeric p22HBP was designed and constructed. This construct, and the resulting protein, will be important for future siRNA knockdown studies where rescue or recovery of function experiments are required to prove the knockdown results. Chapter one discusses the current state of the art in terms of the biological, structural and functional aspects of p22HBP. The main objectives of the Thesis are also introduced here. Chapter two presents a detailed description of the different expression vectors (pNJ2 and pet28-a) and procedures used for overexpression and purification of murine p22HBP and its variants and human p22HBP. All expression and purification systems used gave good yields and allowed isotopic labeling to be carried out. The fluorescence quenching results for tetrapyrrole binding to murine p22HBP and variants are presented in chapter three along with the dissociation constants that were found to be in the nanomolar range for wild type murine and human p22HBP. The same studies were performed for murine p22HBP variants, with hydrophobic and polar changes being introduced at R56, K64 and K177. The dissociation constants were found to double in some cases but no significant changes in the strength of hemin-protein interactions were observed. The tetrapyrrole interaction with p22HBP was also followed by NMR spectroscopy, where chemical shift mapping was used to identify binding pocket location. All the variants and wild type human p22HBP were found to bind at the same location. Chapter 4 contains the data from 2D and 3D experiments carried out on 15N/13C labelled human p22HBP that was used to obtain backbone assignments. Comparison with wild type murine p22HBP assignments, PPIX titrations and theoretical calculations based on chemical shifts (Talos+) allowed 82% of the backbone resonances to be assigned. The results from the relaxation experiments used to probe the dynamics of the mobile loop in p22HBP on binding to tetrapyrrole are presented in chapter 5. The overall protein was found to tumble isotropically in the free and bound forms however the results to probe mobility changes in the 171-180 loop on tetrapyrrole binding proved inconclusive as only residue could be assigned and this did not seem to become significantly less mobile. The final chapter describes the design and construction of a chimeric p22HBP. For these purpose, the alfa1-helix sequence of human p22HBP in the phHBP1 plasmid was replaced by its homologous sequence in hSOUL, a non heme-binding protein with identical 3D structure. The results however indicated that either the incorrect sequence was introduced into the plasmid or the purification procedure was inadequate.
O trabalho apresentado nesta Tese focou-se na dinâmica e nas interações moleculares da p22HBP e do complexo p22HBP-tetrapirrol, nomeadamente nos resíduos chave envolvidos nesta interação. Estudos prévios de modelação molecular identificaram três possíveis resíduos chave R56, K64 e K177 como sendo importantes na interação com os tetrapirróis, através de interações eletrostáticas com os grupos propionato do tetrapirrol. Foram desenhados e construídos variantes da p22HBP murina e foram desenvolvidos estudos de extinção de fluorescência e RMN para avaliar a integridade dos variantes e a sua interação com os tetrapirróis. Os mesmos estudos de modelação molecular identificaram ainda uma zona flexível (Y171-R180) na p22HBP que diminui a mobilidade com a interação do tetrapirrol. Para confirmar esta alteração de mobilidade, foram realizados estudos de dinâmica, baseados em RMN. Por fim, com o intuito de obter uma versão não funcional da p22HBP humana, foi planeada e construída uma versão quimérica da p22HBP humana. No futuro, esta nova versão da p22HBP quimérica, será importante para os estudos de knockdown envolvendo siRNA. O capítulo um introduz uma revisão dos aspetos biológicos da p22HBP nomeadamente os estudos estruturais e as possíveis funções que foram identificadas. Os principais objetivos da tese são também apresentados neste capítulo. No capítulo dois é apresentada uma descrição detalhada dos diferentes vectores de sobreexpressão (pNJ2 e pet28-a) e dos métodos de sobreexpressão e purificação da p22HBP murina e respectivos variantes, bem como da p22HBP humana. Todos os sistemas de sobreexpressão e purificação utilizados obtiveram bons rendimentos e permitiram a marcação isotópica das proteínas. No capítulo 3 são apresentados os resultados de extinção de fluorescência para a interação da p22HBP murina e humana com hemina através das constantes de dissociação determinadas na ordem dos nanomolar. Os mesmos estudos foram realizados para os variantes da p22HBP murina, com alterações hidrofóbicas e de polaridade nos resíduos R56, K64 e K177. Em alguns casos, as constantes de dissociação determinadas são mais elevadas, embora não se tenham verificado alterações significativas na força da interação proteína-hemo. As interações tetrapirrólicas com a p22HBP foram também estudadas por espectroscopia de RMN, onde foram mapeadas as diferenças nos desvios químicos para identificar a localização da zona de interação. A localização da zona de interação dos variantes da p22HBP e a p2HBP humana mantém-se igual à p22HBP murina. No capítulo 4 encontram-se os resultados das experiências 2D e 3D realizadas na p22HBP humana, isotopicamente marcada com 15N/13C, para identificar as ressonâncias da cadeia principal. 82% dos sistemas de spin da cadeia principal foram identificados através da comparação com a p22HBP murina, das titulações com PPIX e de cálculos teóricos baseados nos desvios químicos (Talos+). No capítulo 5 são apresentados os resultados das experiências de relaxação, usados para comprovarem a dinâmica do loop na p22HBP aquando da interação com o tetrapirrol. A proteína no seu todo move-se de uma forma isotrópica na forma livre e ligada. No entanto os resultados para comprovar as alterações de mobilidade no loop 171-180 na presença de hemo, foram inconclusivos uma vez que só a um resíduo foi atribuído um sistema de spin, e não foi indicativo da perda significativa de mobilidade. O último capítulo descreve o planeamento e a construção da p22HBP quimérica. Para tal, a sequência que codifica a hélix alfa 1 da p22HBP humana, no plasmídeo phHBP1, foi substituída pela sequência homóloga da SOUL humana, uma proteína com uma estrutura 3D semelhante mas não liga ao hemo. Os resultados no entanto demonstraram que ou a sequência não foi introduzida corretamente no plasmídeo ou o sistema de purificação não foi adequado.

Cities have adopted evolving urban digitization strategies, and most of those increasingly focus on data, especially in the field of public transportation. Transportation data have intuitively spatial and temporal characteristics, for they are often described with when and where the trips occur. Since a trip is often described with many attributes, the transportation data can be presented with a tensor, a container which can house data in $N$-dimensions. Unlike a traditional data frame, which only has column variables, tensor is intuitively more straightforward to explore spatio-temporal data-sets, which makes those attributes more easily interpreted. However, it requires unique techniques to extract useful and relatively correct information in attributes highly correlated with each other. This work presents a mixed model consisting of tensor decomposition combined with seasonal vector autoregression in time to find latent patterns within historical taxi data classified by types of taxis, pick-up and drop-off times of services in NYC, so that it can help predict the place and time where taxis are demanded. We validated the proposed approach using the experiment evaluation with real NYC tax data. The proposed method shows the best prediction among alternative models without geographical inference, and captures the daily patterns of taxi demands for business and entertainment needs.

Niemasz that is the phrase nie masz in the existential function as a problem of Old Polish text transcription Summary The present author while working on the final edition of Jan Kochanowski’s Dzieła wszystkie became interested in the problem of Old Polish transcription of the phrase nie masz and in its placement in word indexes. On the basis of Polish lexicons, dictionaries of Old Polish and Old Polish texts the author contrary to some editors’ practice who write niemasz or nie ma-ż concludes that the spelling nie masz is justified. Following the semantics of the quoted forms she shows that they are synonymous and follows a history of their occurrence in Polish. She also claims that despite the fact that in both forms the present tense expresses timelessness and they are generalized in the 2nd and 3rd person singular, formally they are predicates and they should be treated as other verbs in indexes.

Abstract As remarked in 533, the evidence from the earliest lnlr. texts suggests that the optative was not a mood correlative with the indicative and derived from inflected stems, but was itself an eventive stem per se, formed directly from the root like all stem-forming elements; and only in the evolution of the IE daughter languages did it become freely derivable from STEMS, including (though in some groups only) the stative (perfect) stems. Note that the use of ‘secondary endings’ in the optative (and the absence, in G and lnlr., of the augment, 441) implies no affinity with anterior tenses (the imperf. and aor.): the optative, being a conditional or irreales form, was neither real present (as marked by primary endings) nor real past (as marked by the augment). Its closest formal/functional yokefellow, in the sense of being marked with generic person endings, would have been the so-called injunctive (416). This is, once again, a grammatical rather than a pragmatic limitation: overtly preterital conditionals, like NE would have (written), are not only semantically coherent, they are widespread, and L for example did develop tense-marked optatives, as did Gmc.

This chapter explores the promise of social unity through networks by looking at the religious nationalism that emerged in the United States around the Atlantic telegraph. As Americans tensely watched the struggle to transmit the world’s first transatlantic telegram, a diverse community—from Protestant missionaries to civic leaders—spoke of the newly united world that electric speech would create in explicitly Christian terms. Public statements that claimed the telegraph as destined and blessed by God were not merely religious ways of speaking about the telegraph; the affective weight born by this Christian vocabulary and imagery forged the affiliation of the telegraph with dreams of global unity in particularly durable ways. This chapter examines alternative imaginaries of obsolete telegraphs (e.g., grapevine telegraph, spiritual telegraph, optical telegraph) that have lost cultural meaning to demonstrate that affect, not the technology itself, produced and sustained network imaginaries of national and global connection. The fragile cable of 1858 and the united “whole world” it was said to create point to the materiality and contingency inherent in the discursive and affective labor of forming public culture.

Abstract The Active Eventive Participles In -nt-. In PIE this participle was formed from the STEM, by means of the suffix *-ont-/*-11t-. That is, in contrast to such verbals as the infin. and verbals in * -to-- and * -no--, which were originally built directly to the root, there might be a distinct pple. in -nt- to every pres./imperf. or aor. stem, including denominatives. The often-repeated statement that the pple. was built to a TENSE stem is however not exactly correct. A contrast between a pres. and an imperfpple. was never possible-not because the distinction is irrelevant but because the two tenses were built to the same stem. The original meaning of the affix was essentially that of the NE participle in -iny;. functionally, the noun modified by the pple. corresponds to the noun that would stand in subject relation to a finite verb. If formed to a transitive verb, a participle would construe with a noun object exactly as a finite verb would (Lincoln Freeing the Slaves was a favorite theme for litho­ graphs, or Beware of Greeks bearing gifts). 555. PARTICIPLES AS NOMINA AGENTIS. Semantically, present participles and agent nouns have much in common: a ‘dancing [one]’ and a ‘dancer’ are functionally very similar. In a variety of IE languages, verbals in ..-ont­ routinely have some agentive role, as in Ved. safctint-‘pursuer, enemy’ (root sac- ‘follow’), next to stifcant- ‘assisting’; sravtint-‘stream’ (lit. ‘fl.ow-er’, root sru- ‘fl.ow’),

This chapter discusses how Muslim and non-Muslim American residents in Hamtramck became embroiled in contestation over a proposed municipal ordinance involving the rights of LGBTQ residents to equal access in housing, employment, and public accommodation. The issue brought about an identity rupture between progressives and conservatives in the city, sundering interfaith relationships that had been formed earlier, while new alliances were being built. The chapter analyzes how a sense of moral urgency onboth sides contributed to a temporal sensibility shift that I call “ordinance time.” This schema entailed a loosening of civility standards in rhetorical comportment, encouraging the public expression of Islamophobia and homophobia. In attending to both the pace and tenor of social relations during this tense period, the chapter considers the essentialism attached to religious and secular moralities, while addressing how the municipal debate influenced boundary formation processes.

Abstract Verb Systems Generally Considered. The verb system of most languages is a complicated affair. This has nothing to do with elaborate paradigms, but with functional categories however they are marked. The formal categories of a language in fact cannot be depended upon to mark functional categories straightforwardly. First, functional categories are commonly combined in various ways: in PIE you could not specify a subject’s person without also specifying number, and vice-versa. Second, functional categories are often expressed by formally inconsistent means. A few examples from English will make these points clearly, since English is usually regarded as elementary in these regards compared to the luxuriance of G, L, and Skt. But the relationships between form and function in English are anything but elementary, as we shall see, and have little congruence with the terminology of the school grammars. In English the present tense is usually regarded as self-explanatory; in the words of a dictionary, s.v. present: ‘Gramm. Denoting, or pertaining to, time that now is; as the present tense. To the contrary: the ‘present tense’ of English turns out to have very little in the way of reference to ‘time that now is’. The four principal functions of the NE ‘present tense’ are: (1) it is used of future events; (2) it is used of reiterated or habitual events; (3) it is used of a state, which has no tense; (4) it is used with a special class of verbs known as performatives, such as say, declare, promise.

Abstract One of the distinctive syntactic features of Black English Vernacular (BEV) is the variable use of be. Among the more detailed studies on variation in the copula in BEV are Labov (1969, 1972), Wolfram (1969, 1974), and Baugh (1980). Perhaps the best-known work in this area is Labov’s (1969) ‘Contraction, Deletion, and Inherent Variability of the English Copula’. In this article, Labov argues that the deletion of be is largely a result of phonological processes. After the present tense full forms of be in constructions such as he is, they are have been contracted, the remaining ‘s and “re are deleted. However, deletion does not apply to ‘m as ‘there are phonological processes which operate upon final [z] and [r] in BEV, but not upon final [m]’ (Labov 1969:721). He further states that ‘wherever SE [standard English] can contract, NNE [non-standard Negro English] can delete is and are, and vice versa; wherever SE cannot contract, NNE cannot delete is and are, and vice versa’ (Labov 1969:722). This analysis lends support to the hypothesis that BEV does not have creole origins, but is in fact a ‘dialect’ of English and has an underlying copula.

Hyper-Rayleigh Scatttering (HRS) measurements have become an important method for measuring the first hyperpolarizabilities β of organic chromophores [1]. This technique is more flexible and much simpler than the alternative Electric-Field-Induced Second Harmonic Generation (EFISH) method for determining β. However, unresolved difficulties with the absolute calibration of solution EFISH measurements [2] have not been avoided, but only compounded, because the uncertain EFISH values are used to calibrate HRS, and because different combinations of tensor components are measured in the two experiments. Furthermore, HRS signals from liquid phase samples can include large intermolecular contributions [3], which have usually been ignored.

Nash Equilibrium (NE) is the canonical solution concept of game theory, which provides an elegant tool to understand the rationalities. Though mixed strategy NE exists in any game with finite players and actions, computing NE in two- or multi-player general-sum games is PPAD-Complete. Various alternative solutions, e.g., Correlated Equilibrium (CE), and learning methods, e.g., fictitious play (FP), are proposed to approximate NE. For convenience, we call these methods as ``inexact solvers'', or ``solvers'' for short. However, the alternative solutions differ from NE and the learning methods generally fail to converge to NE. Therefore, in this work, we propose REinforcement Nash Equilibrium Solver (RENES), which trains a single policy to modify the games with different sizes and applies the solvers on the modified games where the obtained solution is evaluated on the original games. Specifically, our contributions are threefold. i) We represent the games as alpha-rank response graphs and leverage graph neural network (GNN) to handle the games with different sizes as inputs; ii) We use tensor decomposition, e.g., canonical polyadic (CP), to make the dimension of modifying actions fixed for games with different sizes; iii) We train the modifying strategy for games with the widely-used proximal policy optimization (PPO) and apply the solvers to solve the modified games, where the obtained solution is evaluated on original games. Extensive experiments on large-scale normal-form games show that our method can further improve the approximation of NE of different solvers, i.e., alpha-rank, CE, FP and PRD, and can be generalized to unseen games.