Chapter 2: Quadratic Conditions in the General Problem of the Calculus of Variations

2012 ◽  
pp. 27-126
Keyword(s):  
Calculus Of Variations ◽  
General Problem

The general double integral problem in the calculus of variations

1933 ◽  
Vol 29 (2) ◽  
pp. 207-211
Author(s):  
R. P. Gillespie
Keyword(s):  
Calculus Of Variations ◽  
General Problem ◽  
Necessary Condition ◽  
Double Integral ◽  
Integral Problem ◽  
Image Position

In a previous paper in these Proceedings the problem of the double integralwas discussed when the function F had the formwhereIt is proposed in the present paper to extend the method to the general problem, where F may have any form provided only that it satisfies the necessary condition of being homogeneous of the first degree in A, B, C.

scholarly journals On the variation of a triple integral

1843 ◽  
Vol 4 ◽  
pp. 42-42
Keyword(s):  
Calculus Of Variations ◽  
General Problem ◽  
The Given

In the calculus of variations, the discovery of which has immor­talized the name of" Lagrange, that illustrious mathematician, by differentiating the function with respect to a new variable which en­ters into it, reduced the general problem of indeterminate maxima and minima to the solution of an equation depending on the variation of the given integral, whether single or multiple, and whose differ­ential coefficient contains any number of variables, or which even de­pends on other integrals. The author investigates, in the present memoir, the case in which the given function is a triple integral; its variation being composed of two distinct parts, namely, a triple inte­gral and another part, the determination of which must be sought from the limits of the triple integral.

Influence of Magnetic Fields on Solar Hydrodynamics: Experimental Results

1977 ◽  
Vol 36 ◽  
pp. 143-180 ◽  
Author(s):  
J.O. Stenflo
Keyword(s):  
Solar Activity ◽  
Energy Balance ◽  
Magnetic Fields ◽  
Solar Atmosphere ◽  
General Problem ◽  
Solar Rotation ◽  
Active Regions ◽  
Physical Conditions ◽  
Dynamic Phenomena

It is well-known that solar activity is basically caused by the Interaction of magnetic fields with convection and solar rotation, resulting in a great variety of dynamic phenomena, like flares, surges, sunspots, prominences, etc. Many conferences have been devoted to solar activity, including the role of magnetic fields. Similar attention has not been paid to the role of magnetic fields for the overall dynamics and energy balance of the solar atmosphere, related to the general problem of chromospheric and coronal heating. To penetrate this problem we have to focus our attention more on the physical conditions in the ‘quiet’ regions than on the conspicuous phenomena in active regions.

A Better Solution to the General Problem of Creation

2017 ◽  
Vol 9 (1) ◽  
pp. 147-162
Author(s):  
Jeremy W. Skrzypek
Keyword(s):  
Recent Work ◽  
General Problem ◽  
The State ◽  
State Of Affairs ◽  
Better Than

It is often suggested that, since the state of affairs in which God creates a good universe is better than the state of affairs in which He creates nothing, a perfectly good God would have to create that good universe. Making use of recent work by Christine Korgaard on the relational nature of the good, I argue that the state of affairs in which God creates is actually not better, due to the fact that it is not better for anyone or anything in particular. Hence, even a perfectly good God would not be compelled to create a good universe.

On Asymmetric Distances

2013 ◽  
Vol 1 ◽  
pp. 200-231 ◽  
Author(s):  
Andrea C.G. Mennucci
Keyword(s):  
Total Variation ◽  
Calculus Of Variations ◽  
Distance Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Geodesic Segment ◽  
Intrinsic Metric ◽  
Typical Application ◽  
Variation Formula

Abstract In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the setting of General metric spaces of Busemann, and discuss the newly found aspects of the theory: we identify three interesting classes of paths, and compare them; we note that a geodesic segment (as defined by Busemann) is not necessarily continuous in our setting; hence we present three different notions of intrinsic metric space.

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