Semismall perturbations, semi-intrinsic ultracontractivity, and integral representations of nonnegative solutions for parabolic equations

We consider nonnegative solutions of a parabolic equation in a cylinder D \timesI, where $D$ is a noncompact domain of a Riemannian manifold and $I =(0,T)$ with $0 < T \le \infty$ or $I=(-\infty,0)$. Under the assumption [SSP] (i.e., the constant function 1 is a semismall perturbation of the associated elliptic operator on $D$), we establish an integral representation theorem of nonnegative solutions: In the case $I =(0,T)$, any nonnegative solution is represented uniquely by an integral on $(D \times \{0 \}) \cup (\partial_M D \times [0,T))$, where $\partial_M D$ is the Martin boundary of $D$ for the elliptic operator; and in the case $I=(-\infty,0)$, any nonnegative solution is represented uniquely by the sum of an integral on $\partial_M D \times (-\infty,0)$ and a constant multiple of a particular solution. We also show that [SSP] implies the condition [SIU] (i.e., the associated heat kernel is semi-intrinsically ultracontractive).Comment: 35 page

Sakurajima-Satsuma (Sz-S) and Noike-Yumugi (N-Ym) tephras: new tephrochronological marker beds for the last deglaciation, southern Kyushu, Japan

Two prominent tephras, Sakurajima-Satsuma (Sz-S) erupted from Sakurajima volcano and Noike-Yumugi (N-Ym) erupted from Kuchierabujima Island, provide new key marker beds for dating and synchronizing palaeoenvironmental and archaeological records in the last deglaciation in southern Japan. These tephras were identified on the basis of glass major-element compositions in two distal areas, a marine core (IMAGES MD98-2195) in the northern part of the East China Sea and on the central part of Tanegashima Island, and related their stratigraphic positions to the marine oxygen isotope-based chronology. In MD98-2195, Sz-S, 0.8 cm in thickness at 9.12 m depth and N-Ym, 3 cm in thickness at 9.30 m depth, are both white, vitric, ash-grade tephras. On Tanegashima Island, Sz-S, 10 cm in thickness and N-Ym, 3 cm in thickness, are stratigraphically constrained by well-characterised marker tephras Kikai-Akahoya (7,300 cal BP) and Aira-Tn (29,000 cal BP). Sz-S is rhyolitic and homogeneous on the basis of glass major-element compositions assayed by electron microprobe. Pumiceous glass shards predominant in distal Sz-S tephra indicate that it derived from pumice fall units that correspond to pumiceous and phreatomagmatic fine ash units constituting proximal Sz-S tephra. N-Ym is rhyolitic and glass major-element analyses reveal compositional diversity between units, suggesting that the lower and middle tephra units dispersed to the east, whereas the upper unit was dispersed north to north-west from the vent. Stratigraphically, Sz-S occurs at around the start of the late-glacial reversal (cooling) in oxygen isotope records of MD98-2195, corresponding to the end of GI-1 and the start of GS-1 in the ice-core events of NGRIP (GICC05), consistent with a terrestrial age of ˜12,800 cal BP. Based on the oxygen isotope stratigraphy, the tephra identified in the core as N-Ym at 9.30 m depth is close to the end of Greenland GI-1 and hence has an age of ˜13,000 cal BP, but on Kuchierabujima Island it has an age based on ¹⁴C assay of charcoal of c. 14,900 cal BP. Although this age discrepancy (14.9 vs 13.0 cal ka) needs resolution, the occurrence in core MD98-2195 of N-Ym shows that it is more widespread than hitherto demonstrated. The widespread distributions and key stratigraphic positions for the two marker tephras indicate that they are thus critical isochrons for precise correlation of palaeoenvironmental changes and prehistoric cultural events during the last deglaciation in southern Kyushu, and for relating such changes and events to the ice-core chronology via the marine oxygen isotope chronostratigraphy

Proton-induced magnetic order in carbon: SQUID measurements

In this work we have studied systematically the changes in the magnetic behavior of highly oriented pyrolytic graphite (HOPG) samples after proton irradiation in the MeV energy range. Superconducting quantum interferometer device (SQUID) results obtained from samples with thousands of localized spots of micrometer size as well on samples irradiated with a broad beam confirm previously reported results. Both, the para- and ferromagnetic contributions depend strongly on the irradiation details. The results indicate that the magnetic moment at saturation of spots of micrometer size is of the order of $10^{-10}$ emu.Comment: Invited contribution at ICACS2006 to be published in Nucl. Instr. and Meth. B. 8 pages and 6 figure

Bridging the Gap between Probabilistic and Deterministic Models: A Simulation Study on a Variational Bayes Predictive Coding Recurrent Neural Network Model

The current paper proposes a novel variational Bayes predictive coding RNN model, which can learn to generate fluctuated temporal patterns from exemplars. The model learns to maximize the lower bound of the weighted sum of the regularization and reconstruction error terms. We examined how this weighting can affect development of different types of information processing while learning fluctuated temporal patterns. Simulation results show that strong weighting of the reconstruction term causes the development of deterministic chaos for imitating the randomness observed in target sequences, while strong weighting of the regularization term causes the development of stochastic dynamics imitating probabilistic processes observed in targets. Moreover, results indicate that the most generalized learning emerges between these two extremes. The paper concludes with implications in terms of the underlying neuronal mechanisms for autism spectrum disorder and for free action.Comment: This paper is accepted the 24th International Conference On Neural Information Processing (ICONIP 2017). The previous submission to arXiv is replaced by this version because there was an error in Equation

Thermo-mechanical analysis of dental silicone polymers

Soft lining materials are used to replace the inner surface of a conventional complete denture, especially for weak elderly patients, with delicate health who cannot tolerate the hard acrylic denture base. Most of these patients have fragile supporting mucosa, excessive residual ridge resorption, particularly on the mandibular arch. The application of a soft liner to the mandibular denture allows absorbing impact forces during mastication and relieving oral mucosa. Actually, the silicone rubbers constitute the main family of commercialised soft lining materials. This study was conducted to understand the relationships between the mechanical properties and the physical structure of polysiloxanes. For this purpose, a series of polysiloxanes of various chemical compositions have been investigated. The evolution of their physical structure as a function of temperature has been followed by differential scanning calorimetry (DSC). In order to facilitate comparisons, the mechanical modulus has been analysed upon the same heating rate using dynamic mechanical analysis (DMA). Polysiloxanes actually commercialised as soft denture liners are three-dimensional networks: the flexibility of chains allows a crystalline organisation in an amorphous phase leading to the low value of the shear modulus. The dynamic mechanical analysis shows that they are used in the rubbery state. So, polysiloxanes have steady mechanical properties during physiological utilisation

Extremely Large Magnetoresistance in the Nonmagnetic Metal PdCoO2

Extremely large magnetoresistance is realized in the nonmagnetic layered metal PdCoO2. In spite of a highly conducting metallic behavior with a simple quasi-two-dimensional hexagonal Fermi surface, the interlayer resistance reaches up to 35000% for the field along the [1-10] direction. Furthermore, the temperature dependence of the resistance becomes nonmetallic for this field direction, while it remains metallic for fields along the [110] direction. Such severe and anisotropic destruction of the interlayer coherence by a magnetic field on a simple Fermi surface is ascribable to orbital motion of carriers on the Fermi surface driven by the Lorentz force, but seems to have been largely overlooked until now.Comment: Phys. Rev. Lett. 111, 056601 (2013