Showing 50 of 25456 papers

New Derivations of the Mean Square Error of a Single Measurement

V. S. Nuvaryev
1951 SovietRxiv: ru-195101.08045

This paper revisits derivations of the root mean square error of a single measurement in least squares adjustment, comparing indirect and conditional observation formulations. It derives the usual formulas by first expressing corrections as functions of true errors and by using the relation between …

Relationship Between Indirect and Conditional Observations

V. S. Nuvaryev
1951 SovietRxiv: ru-195101.08044

This paper examines the mathematical relationship between indirect observations, expressed through error equations involving unknown functions of measured quantities, and conditional observations, expressed through exact relations among observations or their corrections. It argues that the usual tex…

Theorems on the Most Probable Value of an Adjusted Quantity

V. S. Nuvar’ev
1951 SovietRxiv: ru-195101.08043

This paper develops an alternative derivation of least squares adjustment by proceeding from exact relations among true quantities to approximate values obtained from observations. It formulates two theorems: for direct observations subject to exact conditions, and for functions of observations dete…

Mixed Method for Solving the Direct Plane Resection

B. F. Krutoy
1951 SovietRxiv: ru-195101.08041

This paper presents a mixed graphical and computational method for solving the direct plane resection problem in geodesy, where the coordinates of an unknown point are determined from observed rays drawn from two fixed points. The method begins with an accurate scaled working drawing, then uses succ…

Two-Group Adjustment of a Geodetic Pentagon

B. F. Krutoi
1951 SovietRxiv: ru-195101.08040

This paper presents a computational scheme for least squares adjustment of a geodetic pentagon using a two-group method intended to reduce the burden of forming and solving nine simultaneous normal equations. The condition equations are divided into six figure equations, chosen with simple coefficie…

Analytical Solution of a Single Resection (for a Mechanical Calculator)

B. F. Krutoi
1951 SovietRxiv: ru-195101.08039

The paper presents an analytical solution to the single resection, or Pothenot, problem intended for computation on a mechanical calculator. It derives coordinate formulas for an unknown point from two measured angles to three known control points by translating the coordinate origin, expressing the…

Can a Crystal Be Both Isotropic and Anisotropic?

A. V. Shubnikov
1951 SovietRxiv: ru-195101.01907

In this note, we wish to show that, despite a certain plausibility of the aforementioned and similar doubts, the coexistence in one and the same crystal of such seemingly contradictory and mutually exclusive properties as discontinuity and continuity, isotropy and anisotropy, etc., is logically nece…

Current Problems in the Application of Ultrasound

S. Ya. Sokolov
1950 SovietRxiv: ru-195001.98377

The generation of hypersonic waves opens up new, far-reaching possibilities for studying the nature of thermal vibrations and the mechanism of light scattering by a medium. In addition, they will evidently find a number of important technical applications. This article examines the principal issues …

Meteor Ionization and Ionospheric Anomalies\*

A. Lovell
1950 SovietRxiv: ru-195001.93640

This review is divided into two main parts: the first part is devoted to the history of the study of anomalies in the ionospheric layer and to a discussion of current views on the nature of the sporadic layer; the second part considers contemporary studies of short-duration reflections from meteor t…

PHYSICAL THEORY OF THE DOMAIN STRUCTURE OF FERROMAGNETS\*)

Ch. Kittel
1950 SovietRxiv: ru-195001.89927

This article presents a comprehensive review of the physical foundations of domain theory and the most important experiments confirming it. At the beginning of this article, a brief overview of the physical foundations of domain theory is given. In the subsequent sections, the theory is developed in…

Quantum Theories of Adsorption

V. L. Bonch-Bruevich
1950 SovietRxiv: ru-195001.88012

Some problems in the theory of adsorption, as one type of interaction of gas molecules with the surface of a solid, undoubtedly require quantum-mechanical consideration. At present, there are already quite a number of works devoted to quantum-mechanical problems in the theory of adsorption, and it s…