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[00884] Time-Frequency Analysis of Functional Datasets

  • Session Date & Time : 3C (Aug.23, 13:20-15:00)
  • Type : Contributed Talk
  • Abstract : We introduce an operator valued Short-Time Fourier Transform for certain classes of operators with operator window, and show that the transform acts in an analogous way to the STFT for functions. This object reflects the time-frequency behaviour for datasets of functional data in both a intra- and inter-functional manner, showing the function-wise time-frequency distribution and cross correlation of time-frequency concentration between datapoints, hence combining desirable aspects of existing basis selection methods for functional data science.
  • Classification : 46-XX, 62R10
  • Author(s) :
    • Monika Dörfler (University of Vienna)
    • Franz Luef (Norwegian University of Science and Technology (NTNU))
    • Henry McNulty (Norwegian University of Science and Technology (NTNU))
    • Eirik Skrettingland (NA)

[02369] Unique continuation results for generalized ray transforms

  • Session Date & Time : 3C (Aug.23, 13:20-15:00)
  • Type : Contributed Talk
  • Abstract : We discuss unique continuation results for certain generalized ray transforms. We prove that if the generalized ray transform of a function vanishes along all lines passing through an open set in Euclidean space, and the function vanishes in that same open set, then the function vanishes identically. We give an example to show that the second assumption cannot be removed. We also consider generalized transforms on higher order objects such as vector fields, symmetric 2-tensor fields etc., and under the same hypotheses, show that a certain component vanishes. Since such ray transforms have a non-trivial kernel, this is the optimal result that one can expect.
  • Classification : 46F12, 35J40, 45Q05
  • Author(s) :
    • Divyansh Agrawal (TIFR Centre for Applicable Mathematics (CAM))
    • Venkateswaran P. Krishnan (TIFR Centre for Applicable Mathematics (CAM))
    • Suman Kumar Sahoo (University of Jyvaskyla)

[00724] Applicability to information engineering using the Sato’s hyperfunction

  • Session Date & Time : 3C (Aug.23, 13:20-15:00)
  • Type : Contributed Talk
  • Abstract : Wavelet transform and discrete image processing are one of the important subjects in the field of information engineering. However, although the use of the generalised function in Fourier transform is possible, it is difficult to apply to wavelet transform by using the generalised function. On the other hand, the delta function is mainly used in discrete image analysis. In this study, we have considered their applicability using the Sato’s hyperfunction.
  • Classification : 46F15, 32A45, 65T60, 65D18, 46T30
  • Author(s) :
    • HIROSHI MURAYAMA (Graduate School of Science and Engineering, SOKA University)
    • Yoshio ISHII (Faculty of Science and Engineering, SOKA University)

[00726] Considerations of similarity with Sato's hyperfunction and Birkhoff-Rott equation

  • Session Date & Time : 3C (Aug.23, 13:20-15:00)
  • Type : Contributed Talk
  • Abstract : Many fluid phenomena such as vortices have singularities, and these phenomena can be mathematically described by distribution functions. However, the vortex layer has not been described by distribution functions yet. In this study, we have compared the Sato’s hyperfunction with the Birkhoff-Rott equation, which describes the time evolution of the vortex layer, and discussed whether the Sato’s hyperfunction is useful for describing the vortex layer. Moreover, we have considered the similarity between these two equations.
  • Classification : 46F15, 32A45, 76B47, 76F10, 76F40
  • Author(s) :
    • Yuya Taki (Graduate School of Science and Engineering, SOKA University)
    • Yoshio Ishii (Faculty of Science and Engineering, SOKA University)

[02534] Solving a Tree Genetic Diversity Via Homogeneous Self Dual Embedding

  • Session Date & Time : 3C (Aug.23, 13:20-15:00)
  • Type : Industrial Contributed Talk
  • Abstract : This research discusses another way to solve Second-Order Cone Programming of a tree genetic diversity. We propose a method based on a splitting augmented Lagrangian method (SALM) and an implementation of a homogenous self-dual (HSD) concept to a sub-problem that belongs to convex programming. Furthermore, we utilize operator splitting to review the existence of HSD. An optimal solution for tree genetic diversity can be obtained by using the modified SALM.
  • Classification : 46N10, 47N10, 90C26, 35Q49, 97M40
  • Author(s) :
    • Alvian Alif Hidayatullah (Sepuluh Nopember Institute of Technology)
    • Sena Safarina (Sepuluh Nopember Institute of Technology)
    • Subchan Subchan (Sepuluh Nopember Institute of Technology)