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A general theory of extremals

Lucien W. Neustadt
1969 Journal of computer and system sciences (Print)  
A general concept of extremality is introduced. This concept is shown to be central for a large class of constrained optimization problems.  ...  A general set of necessary conditions, which must be satisfied by all solutions of the previously indicated optimization problems.  ...  INTRODUCTION The principal aim of this paper is to present a unified, general theory of necessary conditions for optimization problems.  ... 
doi:10.1016/s0022-0000(69)80007-3 fatcat:mb32ym27ujewbcc3owgvcucrqq

Implications of extreme flatness in a general f ( R ) theory

Michał Artymowski, Zygmunt Lalak, Marek Lewicki
2016 Physics Letters B  
Our results show that a Starobinsky-like model is the only possible realisation of f(R) theory with an extremely flat area in the Einstein frame potential.  ...  We consider both finite and infinite number of terms in the series while requiring that the Einstein frame potential of the theory has a flat area around any of its stationary points.  ...  ZL thanks DESY Theory Group for hospitality.  ... 
doi:10.1016/j.physletb.2016.07.027 fatcat:mtpvvl3wqvhyzhfavtqyfuktjy

Optimization of high harmonic generation by optimal control theory – climbing a mountain in extreme conditions [article]

Ido Schaefer, Ronnie Kosloff
2019 arXiv   pre-print
A theoretical optimization method of high-harmonic-generation (HHG) is developed in the framework of optimal-control-theory (OCT).  ...  The target of optimization is the emission radiation of a particular frequency.  ...  THEORY Our basic OCT formulation of the general HG problem is reviewed in Sec. II A. A more detailed description can be found in [43, 44] .  ... 
arXiv:1906.08137v3 fatcat:whfp6ejopvbwde5oa6dfzh5i4i

Towards a General Theory of Extremes for Observables of Chaotic Dynamical Systems

Valerio Lucarini, Davide Faranda, Jeroen Wouters, Tobias Kuna
2014 Journal of statistical physics  
In this paper we provide a connection between the geometrical properties of a chaotic dynamical system and the distribution of extreme values.  ...  This result agrees with what was derived recently using the generalized extreme value approach.  ...  Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s)  ... 
doi:10.1007/s10955-013-0914-6 pmid:24532855 pmcid:PMC3919652 fatcat:x75enllg7rfuda3ya2x3xxhj2u

A generalized Einstein-Maxwell theory: Seeley-DeWitt coefficients and logarithmic corrections to the entropy of extremal and non-extremal black holes [article]

Sudip Karan, Binata Panda
2021 arXiv   pre-print
Following the manual, we calculate the first three Seeley-DeWitt coefficients and logarithmic corrections to the entropy of extremal and non-extremal black holes in a generalized Einstein-Maxwell theory  ...  Seeley-DeWitt coefficients for the quadratic fluctuations of a concern gravity theory appeared to be the key ingredients.  ...  Strategies for extremal and non-extremal of Kerr-Newman black holes Kerr-Newman black holes are the most general stationary solutions to the equations of motion of Einstein-Maxwell theory [46] .  ... 
arXiv:2104.06381v2 fatcat:5fqow3micnhgvnimavichrm6oa

A Method for Estimation of Extreme Values of Wind Pressure on Buildings Based on the Generalized Extreme-Value Theory

Yong Quan, Fei Wang, Ming Gu
2014 Mathematical Problems in Engineering  
The relationship between the parameters of the extreme value distribution of wind pressure and its observation length is then deduced based on the generalized extreme value theory and the independence  ...  By analysis of statistical characteristics and probability density distribution of extreme values of wind pressures on the surfaces of a typical low-rise building model and a typical high-rise building  ...  of their extreme values will obey the generalized extreme value distribution.  ... 
doi:10.1155/2014/926253 fatcat:incraqyx5veylbq55havfkftky

A general strong law of large numbers and applications to associated sequences and to extreme value theory [article]

Harouna Sangare, Gane Samb Lo
2015 arXiv   pre-print
The purpose of this paper is to establish a general strong law of large numbers (SLLN) for arbitrary sequences of random variables (rv's) based on the squared indice method and to provide applications  ...  An interesting issue that is related to extreme value theory (EVT) is handled here.  ...  This new general SLLN is used to solve a remarkable issue of extreme value theory by using a pure probabilistic method. Here is how this paper is organized.  ... 
arXiv:1506.08304v1 fatcat:2da2mnasb5hyxifv6vytgqriym

A General Extreme Value Theory Model for the Adaptation of DNA Sequences Under Strong Selection and Weak Mutation

Paul Joyce, Darin R. Rokyta, Craig J. Beisel, H. Allen Orr
2008 Genetics  
To explore the consequences of relaxing the Gumbel assumption, we generalize previous adaptation theory to allow all three domains.  ...  However, extreme value theory shows that two other domains of attraction are also possible: the Fréchet and Weibull domains.  ...  We thank Holly A. Wichman for many useful discussions and support on this project. This work was supported by grants from the National Institutes of Health (NIH) to P.J. (R01GM076040) and H.A.O.  ... 
doi:10.1534/genetics.108.088716 pmid:18791255 pmcid:PMC2581963 fatcat:v2y3ln6effeonkjomm6zatikvm

Existence of extremal solutions of a three-point boundary value problem for a general second order p-Laplacian integro-differential equation

Bashir Ahmad, Ahmed Alsaedi
2010 Electronic Journal of Qualitative Theory of Differential Equations  
In this paper, we prove the existence of extremal positive, concave and pseudo-symmetric solutions for a general three-point second order p−Laplacian integro-differential boundary value problem by using  ...  Existence of extremal solutions Theorem 3.1 Assume that (A 1 ) − (A 4 ) hold.  ...  In this paper, we allow the nonlinear function f to depend on x ′ along with x and consider a more general three-point second order p−Laplacian integro-differential boundary value problem of the form x  ... 
doi:10.14232/ejqtde.2010.1.3 fatcat:lruw5axx7nec3g33k62huov6ke

Non-Einsteinian black holes in generic 3D gravity theories

Metin Gürses, Tahsin Çağrı Şişman, Bayram Tekin
2019 Physical Review D  
Among these, the deformed non-extremal BTZ black hole loses its event horizon while the deformed extremal one remains intact as a black hole in any generic gravity theory.  ...  Here, we find, in all generic higher derivative gravity theories, new universal non-Einsteinian solutions obtained as Kerr-Schild type deformations of the BTZ black hole.  ...  Without a further specification of the field equations of the theory, one cannot proceed further with this most general deformation in a theory independent way.  ... 
doi:10.1103/physrevd.100.064053 fatcat:vhmdbja2fjf2dgcllcbmsgy4j4

On some interconnections between combinatorial optimization and extremal graph theory

Dragos Cvetkovic, Pierre Hansen, Vera Kovacevic-Vujcic
2004 Yugoslav Journal of Operations Research  
The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most cases on a finite set.  ...  While in combinatorial optimization the point is in developing efficient algorithms and heuristics for solving specified types of problems, the extremal graph theory deals with finding bounds for various  ...  Other general tools of combinatorial optimization can be applied to the extremal graph theory at least in principle.  ... 
doi:10.2298/yjor0402147c fatcat:ayreclwmgje6ph7tu6upzvrbtq

Low-Energy Scattering of Black Holes and p-branes in String Theory [article]

R.R. Khuri, R.C. Myers
1995 arXiv   pre-print
We discuss the low-energy dynamics of generalized extremal higher membrane black hole solutions of string theory and higher membrane theories following Manton's prescription for multi-soliton solutions  ...  A flat metric is found for those solutions which possess κ-symmetry on the worldvolume.  ...  Acknowledgements: This research was supported by NSERC of Canada and Fonds FCAR du Québec. R.K. was supported by a World Laboratory Fellowship.  ... 
arXiv:hep-th/9512137v1 fatcat:mqhab7wwv5go5osv2ncvwjdqda

The rotating dyonic black holes of Kaluza-Klein theory

Dean Rasheed
1995 Nuclear Physics B  
The thermodynamic quantities of the black holes are calculated and a Smarr-type formula is obtained leading to a generalized first law of black hole thermodynamics.  ...  The most general electrically and magnetically charged rotating black hole solutions of 5 dimensional theory are given in an explicit form.  ...  Consider rst the non-rotating extreme solutions of some general theory with conserved charges Q 1 ; Q 2 ; : : : Q n each h a ving units of mass.  ... 
doi:10.1016/0550-3213(95)00396-a fatcat:djud4hkc5jawlfjroicovwjg7y

Page 3302 of Mathematical Reviews Vol. , Issue 84h [page]

1984 Mathematical Reviews  
Using the theory of point processes, the authors discuss the limiting properties of general extremal order Statistics.  ...  Galambos [The asymptotic theory of extreme order statistics, Wiley, New York, 1978; MR 80b:60040] gives a comprehensive survey of the theory of extremes in sequences of both independent and dependent random  ... 

Duality-invariant non-extreme black holes in toroidally compactified string theory

Mirjam Cvetič, Ingo Gaida
1997 Nuclear Physics B  
General non-extreme solutions of toroidally compactified string in D=4 are awaiting further investigation.  ...  We present duality invariant structure of the thermodynamic quantities of non-extreme black hole solutions of torodially compactified Type II (M-theory) and heterotic string in five and four dimensions  ...  APPENDIX In this appendix we summarize some basic facts concerning low-energy effective actions and duality symmetries of heterotic and Type II string theory.  ... 
doi:10.1016/s0550-3213(97)00379-9 fatcat:tlil6cv5ffdqtfn25hd2dobyvi
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