Search results for "Complex"
showing 10 items of 5889 documents
Jacobi Fields, Conjugate Points
2001
Let us go back to the action principle as realized by Jacobi, i.e., time is eliminated, so we are dealing with the space trajectory of a particle. In particular, we want to investigate the conditions under which a path is a minimum of the action and those under which it is merely an extremum. For illustrative purposes we consider a particle in two-dimensional real space.
An Improved Method for Estimating the Time ACF of a Sum of Complex Plane Waves
2010
Time averaging is a well-known technique for evaluating the temporal autocorrelation function (ACF) from a sample function of a stochastic process. For stochastic processes that can be modelled as a sum of plane waves, it is shown that the ACF obtained by time averaging can be expressed as a sum of auto-terms (ATs) and cross-terms (CTs). The ATs result from the autocorrelation of the individual plane waves, while the CTs are due to the cross-correlation between different plane wave components. The CTs cause an estimation error of the ACF. This estimation error increases as the observation time decreases. For the practically important case that the observation time interval is limited, we pr…
THE ARITHMETIC BOHR RADIUS
2007
We study the arithmetic Bohr radius of Reinhardt domains in ℂ n which was successfully used in our study of monomial expansions for holomorphic functions in infinite dimensions. We show that this new Bohr radius is different from the radii invented by Boas and Khavinson and Aizenberg. It gives an explicit formula for the n-dimensional hypercone (which means n-dimensional variants of classical results of Bohr and Bombieri), and moreover asymptotically corrects upper and lower estimates for various types of convex and non-convex Reinhardt domains.
COMPLEX CONVEXITY AND VECTOR-VALUED LITTLEWOOD–PALEY INEQUALITIES
2003
Let 2 p 0s uch thatfHp(X) (� f(0)� p + λ (1 −| z| 2 ) p−1 � f � (z)� p dA(z)) 1/p ,f or all f ∈ H p (X). Applications to embeddings between vector-valued BMOA spaces defined via Poisson integral or Carleson measures are provided.
Twister Tries
2015
Many commonly used data-mining techniques utilized across research fields perform poorly when used for large data sets. Sequential agglomerative hierarchical non-overlapping clustering is one technique for which the algorithms’ scaling properties prohibit clustering of a large amount of items. Besides the unfavorable time complexity of O(n 2 ), these algorithms have a space complexity of O(n 2 ), which can be reduced to O(n) if the time complexity is allowed to rise to O(n 2 log2 n). In this paper, we propose the use of locality-sensitive hashing combined with a novel data structure called twister tries to provide an approximate clustering for average linkage. Our approach requires only lin…
Value Creation and Evolution of a Value Network: A Longitudinal Case Study on a Platform-as-a-Service Provider
2014
Current research on cloud computing emphasizes the important role of Platform-as-a-Service (PaaS) providers. However, little is known about how PaaS providers can offer value to the content providers and firms operating the platform. The findings demonstrate how a small PaaS provider in the cloud gaming market was able to develop a strong position in the value network by offering direct and indirect value to its partners. The findings also reveal how the firm developed its value network over fourteen years, from a complex network with several actors to a very simple value network which included only partners of prime importance. peerReviewed
Super-fit and population size reduction in compact Differential Evolution
2011
Although Differential Evolution is an efficient and versatile optimizer, it has a wide margin of improvement. During the latest years much effort of computer scientists studying Differential Evolution has been oriented towards the improvement of the algorithmic paradigm by adding and modifying components. In particular, two modifications lead to important improvements to the original algorithmic performance. The first is the super-fit mechanism, that is the injection at the beginning of the optimization process of a solution previously improved by another algorithm. The second is the progressive reduction of the population size during the evolution of the population. Recently, the algorithm…
Visualization in the integrated SimPhoNy multiscale simulation framework
2018
Abstract We describe three distinct approaches to visualization for multiscale materials modelling research. These have been developed with the framework of the SimPhoNy FP7 EU-project, and complement each other in their requirements and possibilities. All have been integrated via wrappers to one or more of the simulation approaches within the SimPhoNy project. In this manuscript we describe and contrast their features. Together they cover visualization needs from electronic to macroscopic scales and are suited to simulations made on personal computers, workstations or advanced High Performance parallel computers. Examples as well as recommendations for future calculations are presented.
Simplicity and the art of something more: A cognitive-semiotic approach to simplicity and complexity in human-technology interaction and design exper…
2018
In human–technology interaction, the balance between simplicity and complexity has been much discussed. Emphasis is placed on the value of simplicity when designing for usability. Often simplicity is interpreted as reductionism, which compromises both the affective nature of the design and usability itself. This paper takes a cognitive–semiotic approach toward understanding the dynamics between the utilitarian benefits of simplicity in design and the art of something more: considerate complexity. The cognitive–semiotic approach to human–technology design experience is a vehicle for explaining the relationship between simplicity and complexity, and this relationship’s multisensory character …
Role of Vibrational Dynamics in Electronic Relaxation of Cr(acac)3
2015
Ultrafast energy relaxation of Cr(acac)3 dissolved in tetrachloroethylene (TCE) is studied by time-resolved infrared (TRIR) spectroscopy by using electronic and vibrational excitation. After electronic excitation at 400 or 345 nm, the ground state recovers in two time scales: 15 ps (major pathway) and 800 ps (minor pathway), corresponding to fast electronic transition to the ground state and intermediate trapping on the long-lived (2)E state followed by intersystem crossing (ISC) to the ground state. The quantum yield for the fast recovery of the ground state depends on the excitation wavelength, being higher for 345 nm. Vibrational cooling (VC) occurs on the electronic excited states with …