Arithmetically Cohen--Macaulay bundles on homogeneous varieties of Picard rank one

In this paper, we study arithmetically Cohen--Macaulay (ACM) bundles on homogeneous varieties $G/P$. Indeed we characterize the homogeneous ACM bundles on $G/P$ of Picard rank one in terms of highest weights. This is a generalization of the result on $G/P$ of classical types presented by Costa and Mir\'{o}-Roig for type $A$, and Du, Fang, and Ren for types $B,C$ and $D$. As a consequence we prove that only finitely many irreducible homogeneous ACM bundles, up to twisting line bundles, exist over all such $G/P$. Moreover, we derive the list of the highest weights of the irreducible homogeneous ACM bundles on particular homogeneous varieties of exceptional types such as the Cayley Plane and the Freudenthal variety.Comment: 13 page

Gravitino Problem in Inflation Driven by Inflaton-Polonyi K\"ahler Coupling

We discuss the cosmological gravitino problem in inflation models in which the inflaton potential is constructed from K\"ahler potential rather than superpotential: a representative model is $\overline{\text{D}3}$-induced geometric inflation. A critical ingredient in this type of models is the coupling of the inflaton and Polonyi (supersymmetry-breaking) field in the K\"ahler potential, which is needed to build the inflaton potential. We point out the same coupling let the inflaton dominantly decay into a pair of inflatino and gravitino causing the gravitino problem. We propose some possible solutions to this problem.Comment: 14 pages; accepted by PLB, title and abstract changed to clarify the topic, conclusion not changed, references adde

Borrowable Fractional Ownership Types for Verification

Automated verification of functional correctness of imperative programs with references (a.k.a. pointers) is challenging because of reference aliasing. Ownership types have recently been applied to address this issue, but the existing approaches were limited in that they are effective only for a class of programs whose reference usage follows a certain style. To relax the limitation, we combine the approaches of ConSORT (based on fractional ownership) and RustHorn (based on borrowable ownership), two recent approaches to automated program verification based on ownership types, and propose the notion of borrowable fractional ownership types. We formalize a new type system based on the borrowable fractional ownership types and show how we can use it to automatically reduce the program verification problem for imperative programs with references to that for functional programs without references. We also show the soundness of our type system and the translation, and conduct experiments to confirm the effectiveness of our approach.Comment: An extended version of the paper to appear in Proceedings of VMCAI 202

Matrix Configurations for Spherical 4-branes and Non-commutative Structures on S^4

We present a Matrix theory action and Matrix configurations for spherical 4-branes. The dimension of the representations is given by N=2(2j+1) (j=1/2,1,3/2,...). The algebra which defines these configurations is not invariant under SO(5) rotations but under SO(3) \otimes SO(2). We also construct a non-commutative product for field theories on S^4 in terms of that on S^2. An explicit formula of the non-commutative product which corresponds to the N=4 dim representation of the non-commutative S^4 algebra is worked out. Because we use S^2 \otimes S^2 parametrization of S^4, our S^4 is doubled and the non-commutative product and functions on S^4 are indeterminate on a great circle (S^1) on S^4. We will however, show that despite this mild singularity it is possible to write down a finite action integral of the non-commutative field thoery on S^4. NS-NS B field background on S^4 which is associated with our Matrix S^4 configurations is also constructed.Comment: 22 pages; Discussion on commutative limit and some explanation adde

Lachmanテスト時に発生する膝関節音 : 健常膝と前十字靭帯損傷膝での比較検討

BACKGROUND: The Lachman test is clinically considered to be a reliable physical examination for anterior cruciate ligament (ACL) deficiency. However, the test involves subjective judgement of differences in tibial translation and endpoint quality. An auscultation system has been developed to allow assessment of the Lachman test. The knee joint sound during the Lachman test was analyzed using fast Fourier transformation. The purpose of the present study was to quantitatively evaluate knee joint sounds in healthy and ACL-deficient human knees. METHODS: Sixty healthy volunteers and 24 patients with ACL injury were examined. The Lachman test with joint auscultation was evaluated using a microphone. Knee joint sound during the Lachman test (Lachman sound) was analyzed by fast Fourier transformation. As quantitative indices of the Lachman sound, the peak sound (Lachman peak sound) as the maximum relative amplitude (acoustic pressure) and its frequency were used. RESULTS: In healthy volunteers, the mean Lachman peak sound of intact knees was 100.6 Hz in frequency and -45 dB in acoustic pressure. Moreover, a sex difference was found in the frequency of the Lachman peak sound. In patients with ACL injury, the frequency of the Lachman peak sound of the ACL-deficient knees was widely dispersed. In the ACL-deficient knees, the mean Lachman peak sound was 306.8 Hz in frequency and -63.1 dB in acoustic pressure. If the reference range was set at the frequency of the healthy volunteer Lachman peak sound, the sensitivity, specificity, positive predictive value, and negative predictive value were 83.3%, 95.6%, 95.2%, and 85.2%, respectively. CONCLUSION: Knee joint auscultation during the Lachman test was capable of judging ACL deficiency on the basis of objective data. In particular, the frequency of the Lachman peak sound was able to assess ACL condition.博士（医学）・甲第673号・平成29年6月28日Copyright © 2016 The Japanese Orthopaedic Association. Published by Elsevier B.V. All rights reserved