Does Church-Kleene ordinal ω1CK\omega_1^{CK} exist?

A question is proposed if a nonrecursive ordinal, the so-called Church-Kleene ordinal $\omega_1^{CK}$ really exists.Comment: 4 pages, LaTe

Is mathematics consistent?

A question is proposed whether or not set theory is consistent.Comment: 8 pages, LaTe

Fundamental solution global in time for a class of Schr\"odinger equations with time-dependent potentials

Fundamental solution for a Schr\"odinger equation with a time-dependent potential of long-range type is constructed. The solution is given as a Fourier integral operator with a symbol uniformly bounded global in time, when measured in natural semi-norms of a symbol class.Comment: To appear in Communications in Mathematical Analysis, Volume 1 No. 2 (2006

A possible solution for the non-existence of time

A possible solution for the problem of non-existence of universal time is given by utilizing Goedel's incompleteness theorem.Comment: LaTeX, 7 pages, English corrected and a miscellaneous change in section

An implication of G\"odel's incompleteness theorem

A proof of G\"odel's incompleteness theorem is given. With this new proof a transfinite extension of G\"odel's theorem is considered. It is shown that if one assumes the set theory ZFC on the meta level as well as on the object level, a contradiction arises. The cause is shown to be the implicit identification of the meta level and the object level hidden behind the G\"odel numbering. An implication of these considerations is stated.Comment: LaTeX, 50 page

Quantum Mechanical Clock and Classical Relativistic Clock

A cyclic nature of quantum mechanical clock is discussed as ``quantization of time." Quantum mechanical clock is seen to be equivalent to the relativistic classical clock.Comment: LaTeX, 8 page

Scattering Spaces and a Decomposition of Continuous Spectral Subspace

We introduce the notion of scattering space $S_b^r$ for $N$-body quantum mechanical systems, where $b$ is a cluster decomposition with $2\le |b|\le N$ and $r$ is a real number $0\le r\le 1$. Utilizing these spaces, we give a decomposition of continuous spectral subspace by $S_b^1$ for $N$-body quantum systems with long-range pair potentials V_\alpha^L(x_\alpha)=O(|x_\al|^{-\ep}). This is extended to a decomposition by $S_b^r$ with $0\le r\le 1$ for some long-range case. We also prove a characterization of ranges of wave operators by $S_b^0$.Comment: 36 pages, AmSTe

Three dimensional time and energy operators and an uncertainty relation

Three dimensional time and energy operators are introduced and an uncertainty relation between them is proved.Comment: 4 page

Skin lesion classification with ensemble of squeeze-and-excitation networks and semi-supervised learning

In this report, we introduce the outline of our system in Task 3: Disease Classification of ISIC 2018: Skin Lesion Analysis Towards Melanoma Detection. We fine-tuned multiple pre-trained neural network models based on Squeeze-and-Excitation Networks (SENet) which achieved state-of-the-art results in the field of image recognition. In addition, we used the mean teachers as a semi-supervised learning framework and introduced some specially designed data augmentation strategies for skin lesion analysis. We confirmed our data augmentation strategy improved classification performance and demonstrated 87.2% in balanced accuracy on the official ISIC2018 validation dataset.Comment: 6 pages, 4 figures, ISIC201

Quantum mechanical time contradicts the uncertainty principle

The a priori time in conventional quantum mechanics is shown to contradict the uncertainty principle. A possible solution is given.Comment: 3 page