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We present optimal bounds for expectations of kth records and differences of kth records based on sequences of independent identically distributed random variables with a bounded support. Bounds are expressed in terms of support length units.

Find a connection of two points in the plane with minimal cost, the cost per length unit depending on the location, and the curvature of the curve being limited. For simple cases, as a necessary condition, the known optical law of refraction is supplemented by a “circular law of refraction”. For the general case, a practicable numerical procedure is developed on the foundation of graph theory. This procedure is able to additionally take into consideration the given directions of the curve in the end points. Several examples demonstrate fundamental solution structures for classical basic problems and also solutions for routing problems in planning traffic ways.

The Moscow State University of Geodesy and Cartography (MIIGAIK) investigations in the field of interferometric methods for metrological confirmation of geodetic distance measurement are reviewed. The theoretical and experimental results of the refinement of interferometric methods and means are reported. Main attention is given to the problem of the transfer of the length unit from the length standards to the linear base-line used for the calibration of distance-measuring instruments, and also to the problem of correction for atmospheric influences. A number of new long-length interferometry methods are demonstrated, and some prospective ideas and proposals, such as creating highest accuracy base-line and picosecond interferometry, are discussed.

This paper deals with the major factors affecting the resolving power of imaging devices employing pyroelectric radiation detector arrays. These include thermal and electrical crosstalk between discrete elements of the array. The role and effect of the number of sensitive elements per unit of length and dimension of spacing between them on array resolution magnitude have been analysed.

In NC-lathe operation, the spindle speed is programmed for the spindle revolutions per minute or the unit length per minute for the constant circumferential cutting speed. Additionally, the tool feed can be coded in terms of the unit length per minute or per revolution. This paper describes the derivation of formulas which enable calculation of tool movement time when the real tool feederate with velocity unit varies during linear and/or circular interpolation with the most widely used cutting conditions, that is, cutting speed in terms of the length unit per minute and feed in terms of length unit per spindle revolution.