Abstract:
We derive some simple sufficient conditions on the amplitude , the phase and the instantaneous frequency such that the so-called chirp function is fractal oscillatory near a point , where and is a periodic function on . It means that oscillates near , and its graph is a fractal curve in such that its box-counting dimension equals a prescribed real number and the -dimensional upper and lower Minkowski contents of are strictly positive and finite. It numerically determines the order of concentration of oscillations of near . Next, we give some applications of the main results to the fractal oscillations of solutions of linear differential equations which are generated by the chirp functions taken as the fundamental system of all solutions. 1. Introduction The brilliant heuristic approach of Tricot [1] to the fractal curves such as the graph of functions and gave the main motivation for studying the fractal properties near of graph of oscillatory solutions of various types of differential equations: linear Euler-type equation (see [2]), general second-order linear equation (see [3]) where satisfies the Hartman-Wintner asymptotic condition near , half-linear equation (see [4]), linear self-adjoint equation (see [5]), and -Laplace differential equations in an annular domain (see [6]). A function is said to be a chirp function if it possesses the form , where and denote, respectively, the amplitude and phase of , and is a periodic function on . In all previously mentioned papers [2–5], authors are dealing with the fractal oscillations of second-order differential equations and are deriving some sufficient conditions on the coefficients of considered equations such that all their solutions together with the first derivative admit asymptotic behaviour near . It is formally written in the form of a chirp function, that is, and near . According to it, one can say that the asymptotic formula for solutions of considered equations satisfies the chirp-like behaviour near (on the asymptotic formula for solutions near , see [7, 8]). Then, in the dependence of a prescribed real number , authors give some asymptotic conditions on , , and such that all solutions are fractal oscillatory near with the fractal dimension . In this paper, independently of the asymptotic theory of differential equations, we firstly study the fractal oscillations of a chirp function; see Theorems 8 and 11. Second, taking two linearly independent chirp functions and , we generate some new classes of fractal oscillatory linear differential equations which are not considered in [2–5] and have the

Abstract:
A compact data taking electronics was developed for high-speed multi-layer muon radiography in order to minimize the operation failure rate. By requesting a linear trajectory within the number of redundant position sensitive detectors (PSDs), the background (BG) events produced by vertical electromagnetic (EM) showers are effectively reduced. In order to confirm the feasibility of this method, the system comprising 4 PSD layers were tested by imaging the internal structure of a parasitic cone and the adjacent craterlets formed in the 1910 eruption at the base of Usu volcano, Hokkaido with a conventional (MURG08) readout system (Kusagaya et al., 2012; Tanaka et al., 2012). The new mountain has been believed to be a cryptodome since its formation. According As knowledge on lava domes is are accumulated at various volcanoes, the definition of "cryptodome" is now doubted in its validity. The results of the preliminary 290-h muon radiographic survey revealed that the "cryptodome" is not underlain by any lava mass and that a main craterlet is accompanied by magma intrusions at shallow depths. The former verifies that the new mountain is not a cryptodome but a volcanogenetic mound, and the latter interprets the phreatic explosions forming the craterlets as intrusions of magma into the aquifer. However, a higher data taking failure rate was observed with a software-based MURG08 system when the size of the active area of the detection system was enlarged to improve the detection ability of the system. The newly developed MURG12 is a complete hardware-based electronics system that can simultaneously process signals from 192 scintillation counters of data size of 600 kbps ch 1 without operation failure. We anticipate that the observation speed would be further improved by employing MURG12. At the base of Usu volcano, in 20th century, four eruptions occurred. Some of them demonstrated three characteristic magma intrusions. First, a magma branch remained at a depth leaving an upheaval of the ground, second, it rose and reached aquifers causing phreatic explosions but not extruded, and third, it reacted with aquifers causing phreatic explosions and further extruded over the ground forming a lava dome. In order to clarify the eruption mechanism of Usu, it is necessary for us to image many parasitic cones. Based on the result of the test measurement, we anticipate that MURG12 would be a strong tool for high-speed muon radiography.

Abstract:
Single and double universal seesaw mechanisms and the hypothesis of universal strength for Yukawa couplings are applied to formulate a unified theory of fermion mass spectrum in a model based on an extended Pati-Salam symmetry. Five kinds of Higgs fields are postulated to mediate scalar interactions among electroweak doublets of light fermions and electroweak singlets of heavy exotic fermions with relative Yukawa coupling constants of exponential form. At the first-order seesaw approximation, quasi-democratic mass matrices with equal diagonal elements are derived for all charged fermion sectors and a diagonal mass matrix is obtained for the neutrino sector under an additional ansatz. Assuming the vacuum neutrino oscillation, the problems of solar and atmospheric neutrino anomalies are investigated.

Abstract:
We report self-consistent calculations of the microscopic electronic structure of the so-called giant vortex states. These novel multiquantum vortex states, detected by recent magnetization measurements on submicron disks, are qualitatively different from the Abrikosov vortices in the bulk. We find that, in addition to multiple branches of bound states in the core region, the local tunneling density of states exhibits Tomasch oscillations due to the single-particle interference arising from quantum confinement. These features should be directly observable by scanning tunneling spectroscopy.

Abstract:
Fragmentation of protostellar disks controls the growth of protostars and plays a key role in determining the final mass of newborn stars. In this paper, we investigate the structure and gravitational stability of the protostellar disks in the full metallicity range between zero and the solar value. Using the mass-accretion rates evaluated from the thermal evolution in the preceding collapse phase of the pre-stellar cores, we calculate disk structures and their evolution in the framework of the standard steady disks. Overall, with higher metallicity, more efficient cooling results in the lower accretion rate and lower temperature inside the disk: at zero metallicity, the accretion rate is ~ 1e-3Msun/yr and the disk temperature is ~ 1000 K, while at solar metallicity, ~ 1e-6Msun/yr and 10 K. Despite the large difference in these values, the zero- and solar-metallicity disks have similar stability properties: the Toomre parameter for the gravitational stability, which can be written using the ratio of temperatures in the disk and in the envelope as Q ~ (T_disk/T_env)^3/2, is > 1, i.e., marginally stable. At intermediate metallicities of 1e-5--1e-3Zsun, however, the disks are found to be strongly unstable with Q ~ 0.1--1 since dust cooling, which is effective only in the disks due to their high density (> 1e10 cm^-3), makes the temperature in the disks lower than that in the envelopes. This indicates that masses of the individual stars formed as a result of the protostellar disk fragmentation can be significantly smaller than their parent core in this metallicity range. The typical stellar mass in this case would be a few Msun, which is consistent with the observationally suggested mass-scale of extremely metal-poor stars.

Abstract:
In extended new general relativity, which is formulated as a reduction of $\bar{Poincar\'e} $gauge theory of gravity whose gauge group is the covering group of the Poincar\'e group, we study the problem of whether the total energy-momentum, total angular momentum and total charge are equal to the corresponding quantities of the gravitational source. We examine this for charged axi-symmetric solutions of gravitational field equations. Our main concern is the restriction on the asymptotic form of the gravitational field variables imposed by the requirement that physical quantities of the total system are equivalent to the corresponding quantities of the charged rotating source body. This requirement can be regarded as an equivalence principle in a generalized sense.

Abstract:
We prove that the twist-3 chiral-odd parton distributions obey simple GLAP evolution equations in the limit $N_c\to\infty$ and give analytic formulae for the corresponding anomalous dimensions. The results are valid to O(1/N_{c}^2) accuracy and will be useful in confronting with future experiments.

Abstract:
We prove that the twist-3 chiral-odd parton distributions obey simple Gribov-Lipatov-Altarelli-Parisi evolution equations in the limit $N_c\to\infty$ and give analytic results for the corresponding anomalous dimensions. To this end we introduce an evolution equation for the corresponding three-particle twist-3 parton correlation functions and find an exact analytic solution. For large values of n (operator dimension) we are further able to collect all corrections subleading in N_c, so our final results are valid to $O(1/N_c^2\cdot \ln(n)/n)$ accuracy.

Background: Radiofrequency
has been proven to penetrate deeper than optical light sources independent of
skin color allowing a safer treatment for the Asian skin type. Many studies have indicated the
efficacy of various types of devices, but have not included a sufficient
objective evaluation. Multisource radiofrequency
uses multiple phase controlled radiofrequency generators with real time impedance control, allowing painless, deeper dermal
heating with better adaptation to differences in individual skin impedance. In this study we used
three-dimensional imaging for the objective evaluation of facial skin
tightening by multisource
phase-controlled radiofrequency.Methods:Twenty Japanese patients were treated with a multisource phase-controlled radiofrequency device.
Three-dimensional imaging was performed with a Canfield Scientific Vectra
camera and software, and quantitative volume measurements were taken to
evaluate the change in the post-treatment volume. The patients then provided
subjective assessments.Results:Objective assessments of the treated cheek volume
evaluated by a three-dimensional color schematic representation with
quantitative volume measurements showed significant improvement three months
after the final treatment. The mean volume reduction at the last post-treatment
visit was 3.878 ± 2.86 mL. The post-treatment volume was significantly reduced
compared to the pretreatment volume in all of the volunteers (P =0.0007). Ninety-five percent of volunteers reported
satisfaction with the improvement of skin laxity, and ninety percent of
volunteers reported satisfaction with the improvement of wrinkles, such as the
nasolabial folds.Conclusions:The advantages of these multisource phase-controlled radiofrequency
treatments are its high efficacy for skin tightening associated with minimal
level of discomfort, minimal side effects, and
low cost. Taken together,