On equating the difference between optimal and marginal values of general convex programs

1981 ◽  
Vol 33 (1) ◽  
pp. 57-68 ◽  
Author(s):  
K. O. Kortanek ◽  
A. L. Soyster
Filomat ◽  
2018 ◽  
Vol 32 (19) ◽  
pp. 6809-6818 ◽  
Author(s):  
Xiao-Bing Li ◽  
Qi-Lin Wang

In this paper, the notion of the radius of robust feasibility is considered for a convex program with general convex and compact uncertainty set. An exact calculating formula for the radius of robust feasibility is given for this uncertain convex program. Moreover, we give a necessary and suficient condition for robust feasibility for uncertain convex programs to be positive. We also give some examples to illustrate our results.


2006 ◽  
Vol 16 (04) ◽  
pp. 333-343
Author(s):  
MOSHE DROR ◽  
YUSIN LEE ◽  
JAMES B. ORLIN ◽  
VALENTIN POLISHCHUK

This paper introduces a new notion related to the traveling salesperson problem (TSP) — the notion of the TSP ratio. The TSP ratio of a TSP instance I is the sum of the marginal values of the nodes of I divided by the length of the optimal TSP tour on I, where the marginal value of a node i ∈ I is the difference between the length of the optimal tour on I and the length of the optimal tour on I\i. We consider the problem of establishing exact upper and lower bounds on the TSP ratio. To our knowledge, this problem has not been studied previously. We present a number of cases for which the ratio is never greater than 1. We establish a tight upper bound of 2 on the TSP ratio of any metric TSP. For the TSP on six nodes, we determine the maximum ratio of 1.5 in general, 1.2 for the case of metric TSP, and 10/9 for the geometric TSP in the L1 metric. We also compute the TSP ratio experimentally for a large number of random TSP instances on small number of points.


1962 ◽  
Vol 14 ◽  
pp. 149-155 ◽  
Author(s):  
E. L. Ruskol

The difference between average densities of the Moon and Earth was interpreted in the preceding report by Professor H. Urey as indicating a difference in their chemical composition. Therefore, Urey assumes the Moon's formation to have taken place far away from the Earth, under conditions differing substantially from the conditions of Earth's formation. In such a case, the Earth should have captured the Moon. As is admitted by Professor Urey himself, such a capture is a very improbable event. In addition, an assumption that the “lunar” dimensions were representative of protoplanetary bodies in the entire solar system encounters great difficulties.


1997 ◽  
Vol 161 ◽  
pp. 491-504 ◽  
Author(s):  
Frances Westall

AbstractThe oldest cell-like structures on Earth are preserved in silicified lagoonal, shallow sea or hydrothermal sediments, such as some Archean formations in Western Australia and South Africa. Previous studies concentrated on the search for organic fossils in Archean rocks. Observations of silicified bacteria (as silica minerals) are scarce for both the Precambrian and the Phanerozoic, but reports of mineral bacteria finds, in general, are increasing. The problems associated with the identification of authentic fossil bacteria and, if possible, closer identification of bacteria type can, in part, be overcome by experimental fossilisation studies. These have shown that not all bacteria fossilise in the same way and, indeed, some seem to be very resistent to fossilisation. This paper deals with a transmission electron microscope investigation of the silicification of four species of bacteria commonly found in the environment. The Gram positiveBacillus laterosporusand its spore produced a robust, durable crust upon silicification, whereas the Gram negativePseudomonas fluorescens, Ps. vesicularis, andPs. acidovoranspresented delicately preserved walls. The greater amount of peptidoglycan, containing abundant metal cation binding sites, in the cell wall of the Gram positive bacterium, probably accounts for the difference in the mode of fossilisation. The Gram positive bacteria are, therefore, probably most likely to be preserved in the terrestrial and extraterrestrial rock record.


1994 ◽  
Vol 144 ◽  
pp. 421-426
Author(s):  
N. F. Tyagun

AbstractThe interrelationship of half-widths and intensities for the red, green and yellow lines is considered. This is a direct relationship for the green and yellow line and an inverse one for the red line. The difference in the relationships of half-widths and intensities for different lines appears to be due to substantially dissimilar structuring and to a set of line-of-sight motions in ”hot“ and ”cold“ corona regions.When diagnosing the coronal plasma, one cannot neglect the filling factor - each line has such a factor of its own.


Author(s):  
Jules S. Jaffe ◽  
Robert M. Glaeser

Although difference Fourier techniques are standard in X-ray crystallography it has only been very recently that electron crystallographers have been able to take advantage of this method. We have combined a high resolution data set for frozen glucose embedded Purple Membrane (PM) with a data set collected from PM prepared in the frozen hydrated state in order to visualize any differences in structure due to the different methods of preparation. The increased contrast between protein-ice versus protein-glucose may prove to be an advantage of the frozen hydrated technique for visualizing those parts of bacteriorhodopsin that are embedded in glucose. In addition, surface groups of the protein may be disordered in glucose and ordered in the frozen state. The sensitivity of the difference Fourier technique to small changes in structure provides an ideal method for testing this hypothesis.


Author(s):  
P. Maupin-Szamier ◽  
T. D. Pollard

We have studied the destruction of rabbit muscle actin filaments by osmium tetroxide (OSO4) to develop methods which will preserve the structure of actin filaments during preparation for transmission electron microscopy.Negatively stained F-actin, which appears as smooth, gently curved filaments in control samples (Fig. 1a), acquire an angular, distorted profile and break into progressively shorter pieces after exposure to OSO4 (Fig. 1b,c). We followed the time course of the reaction with viscometry since it is a simple, quantitative method to assess filament integrity. The difference in rates of decay in viscosity of polymerized actin solutions after the addition of four concentrations of OSO4 is illustrated in Fig. 2. Viscometry indicated that the rate of actin filament destruction is also dependent upon temperature, buffer type, buffer concentration, and pH, and requires the continued presence of OSO4. The conditions most favorable to filament preservation are fixation in a low concentration of OSO4 for a short time at 0°C in 100mM sodium phosphate buffer, pH 6.0.


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