On the Static Dielectric Permittivity for Coulomb System in the Long Wavelength Limit

On the basis of the exact relations the general formula for the static dielectric permittivity for Coulomb system is found in the region of small wave vectors. The obtained formula describes the dielectric function of the Coulomb system in both limits: in the "metallic" state and in the "dielectric" one. On this basis the determinations of the "apparent" dielectric and the "apparent" radius of screening are introduced. In the random phase approximation (RPA) the exact relations for the function dielectric function of the electron gas in the long-wavelength region of the wave vectors are found for an arbitrary degeneration of the particles.Comment: 5 pages, no figure

Equation of state SAHA-S meets stellar evolution code CESAM2k

We present an example of an interpolation code of the SAHA-S equation of state that has been adapted for use in the stellar evolution code CESAM2k. The aim is to provide the necessary data and numerical procedures for its implementation in a stellar code. A technical problem is the discrepancy between the sets of thermodynamic quantities provided by the SAHA-S equation of state and those necessary in the CESAM2k computations. Moreover, the independent variables in a practical equation of state (like SAHA-S) are temperature and density, whereas for modelling calculations the variables temperature and pressure are preferable. Specifically for the CESAM2k code, some additional quantities and their derivatives must be provided. To provide the bridge between the equation of state and stellar modelling, we prepare auxiliary tables of the quantities that are demanded in CESAM2k. Then we use cubic spline interpolation to provide both smoothness and a good approximation of the necessary derivatives. Using the B-form of spline representation provides us with an efficient algorithm for three-dimensional interpolation. The table of B-spline coefficients provided can be directly used during stellar model calculations together with the module of cubic spline interpolation. This implementation of the SAHA-S equation of state in the CESAM2k stellar structure and evolution code has been tested on a solar model evolved to the present. A comparison with other equations of state is briefly discussed. The choice of a regular net of mesh points for specific primary quantities in the SAHA-S equation of state, together with accurate and consistently smooth tabulated values, provides an effective algorithm of interpolation in modelling calculations. The proposed module of interpolation procedures can be easily adopted in other evolution codes.Comment: 8 pages, 5 figure

Exact aymptotic expansions for the thermodynamics of hydrogen gas in the Saha regime

We consider the hydrogen quantum plasma in the Saha regime, where it almost reduces to a partially ionized atomic gas. We briefly review the construction of systematic expansions of thermodynamical functions beyond Saha theory, which describes an ideal mixture of ionized protons, ionized electrons and hydrogen atoms in their ground-state. Thanks to the existence of rigorous results, we first identify the simultaneous low-temperature and low-density limit in which Saha theory becomes asymptotically exact. Then, we argue that the screened cluster representation is well suited for calculating corrections, since that formalism accounts for all screening and recombination phenomena at work in a more tractable way than other many-body methods. We sketch the corresponding diagrammatical analysis, which leads to an exact asymptotic expansion for the equation of state. That scaled low-temperature expansion improves the analytical knowledge of the phase diagram. It also provides reliable numerical values over a rather wide range of temperatures and densities, as confirmed by comparisons to quantum Monte Carlo data.Comment: 10 page

Problem of Reinterpretation of the Achievements of the 16th Century French Historiography in the Work of Philippe Labbe (1607-1667) “A New Library of Manuscript Books»

Using the key historians of the so-called “French school” as an example, it is shown that the tendency of historical writing, laid down in the 16th century, underwent a critical reappraisal in the subsequent period. The authors of the article show that F. Labbe (1607-1667) in his work “The New Library of Manuscript Books” ( Nova Bibliotheca Manuscriptorum Librorum ) conceptually rethought the list of those historians who, in his opinion, deserve the attention of his contemporaries. It is alleged that works which subject matter was closely related to the interests of national monarchies appeared to be out of view. It is noted that F. Lubbe, as a representative of the Jesuit Order and, therefore, the spokesman for the interests of the Catholic Church, insisted on the need for cooperation between the papacy and the French kingdom. It is emphasized that, from the point of view of Labbe, the historical works of the 16th century deserved attention, which emphasized primarily the common historical fate of Western European states under the auspices of the church and the papacy as continuers of the Roman Empire’s tradition threatened by o the spread of the Reformation. The authors conclude that the reevaluation of the works of French historians of the 16th century by researchers of the next generation was far from always determined by a purely confessional point of view or proximity to royal power

From Narrative to Analysis: “The Great French Monarchy” by Claude de Seyssel as Reflection of Trends in Development of Historical Worldview between Late Middle Ages and Early Modern Age

The work of Claude de Seyssel “The Great French Monarchy” is considered in the context of new data on the development of historical writing in the late Middle Ages and early modern times. It is noted that this treatise is not similar to the traditional historical works of the era of humanism, since in it the ancient idealism in the field of assessing social structures was replaced by explicit realism in the understanding that the basis of social relations was the nobility. Attention is paid to the method and approach that distinguishes this treatise, considering the views on the development of science, formulated by M. Foucault. It is indicated that de Seyssel considered the Renaissance an era of imitation and comparison, and only the time of the scientific revolution of the 17th — 18th centuries as a period of interest in the analysis of the structure of society and power. It is shown that, at the same time, in the work of de Seyssel, written around 1519, we see precisely the method of structural analysis, and not a comparative narrative. The authors conclude that, like the Venetian historian Domenico Morosini, who did not idealize the Venetian Republic, de Seissel did not idealize the French monarchy and viewed it as the power of the noble class in all its aspects

Claude de Seyssel and Society Concept of George Gemistus Plethon

The article deals with the ideas of Claude de Seyssel (1450—1520). Attention is paid to the fact that these ideas were based on an analysis, based on the model proposed by Plato, of the oligarchic form of government as a real form of existence of the republic in contemporary Venice and a study of the applicability of this model to France. The relevance of the work is due to the appearance of a number of works in which one can see that the views of Claude de Seyssel were similar not only to the views of the Italian humanists, but also to the utopian ideas of the reorganization of Byzantium by George Gemistus Plethon (1355/1360—1452/1454). The authors of the article argue that the ideas of Claude de Seyssel should be considered in a broader context than was previously accepted in historical science. It is shown in the article that it was Claude de Seyssel who drew attention to the importance of the military class and its rights as the most important principle for the formation of European monarchies in the context of problems common to Italian and Byzantine humanists. It is proved that he became a kind of transmission link between Italian and Byzantine humanism, on the one hand, and French humanism, on the other, and significantly influenced the development of socio-political and historical concepts of French thinkers of the 16th-17th centuries

Periodization of Antiquity’s History in Studies of I. M. Grevs and N. I. Kareev in Late XIX — Early XX Centuries

The periodization of history and the definition of the framework of Antiquity and the Middle Ages were questions open for scientific discussion at the turn of the 19th-20th centuries, when the Russian school of ancient and medieval studies was actively developing in Russia and especially in St. Petersburg. The concept of I. M. Grevs was that the Roman Empire marked the beginning of Late Antiquity with its special economic structure in the form of large land ownership, but this period ended with the onset of the era of barbarian kingdoms. I. M. Grevs separated the Roman Empire from the period of classical Antiquity and at the same time showed its difference from the way of the early Middle Ages. In his courses on general history, read after I. M. Grevs, N. I. Kareev described the ancient universal monarchies, which sought to extend their power to the limits of the ecumene and unite the various traditions of organizing power. It should be concluded that N. I. Kareev supplemented the periodization proposed by I. M. Grevs, finding in the Ancient world the same turning point in the form of the Hellenistic monarchy, similar to that found in Late Antiquity by I. M. Grevs

Humanistic Ideas about History and Foundations of the New Chronology by Joseph Justus Scaliger (1540-1609)

The question of the development of humanistic historiography in the Renaissance and early Modern era is considered. Special attention is paid to the contribution of Joseph Justus Scaliger (1540-1609) to the creation of a new chronology. The novelty of the research is that Scaliger’s achievements in the field of chronology are considered as an important component of the process of formation of a new historical narrative and the development of scientific principles of historical research. It is emphasized that earlier works written by Italian humanist historians used outdated calendar systems, which developed in the late Antique era and were characterized by a lack of understanding of the true significance of the change of historical epochs. The authors show that Scaliger’s achievements in the field of chronology allowed historians of the early Modern era, especially the French historians, to make significant progress in the understanding of the relevant for the history of Europe period of transition from Late Antiquity to the early Middle Ages. The article concludes that due to the achievements of Scaliger the time scale of the Roman Empire and barbarian kingdoms was able to line up in a meaningful sequence. The history of the Frankish Kingdom as the initial period of the Middle Ages was able to take its place of honor in the writings of historians