On a q-analogue of the p-adic generalized twisted L-functions and p-adic q-integrals

The purpose of this paper is to define generalized twisted q-Bernoulli numbers by using p-adic q-integrals. Furthermore, we construct a q-analogue of the p-adic generalized twisted L-functions which interpolate generalized twisted q-Bernoulli numbers. This is the generalization of Kim's h-extension of p-adic q-L-function which was constructed in [5] and is a partial answer for the open question which was remained in [3]Comment: 12 page

Equilibria in a large production economy with an infinite dimensional commodity space and price dependent preferences

We prove the existence of a competitive equilibrium in a production economy with infinitely many commodities and a measure space of agents whose preferences are price dependent. We employ a saturated measure space for the set of agents and apply recent results for an infinite dimensional separable Banach space such as Lyapunov's convexity theorem and an exact Fatou's lemma to obtain the result.Comment: JEL Classification Numbers: C62, D51. Keywords: Separable Banach space, Saturated measure space, Price dependent preferences, Lyapunov's convexity theorem, Fatou's lemm

Profitable Double-Spending Attacks

Our aim in this paper is to investigate the profitability of double-spending (DS) attacks that manipulate a priori mined transaction in a blockchain. Up to date, it was understood that the requirement for successful DS attacks is to occupy a higher proportion of computing power than a target network's proportion; i.e., to occupy more than 51% proportion of computing power. On the contrary, we show that DS attacks using less than 50% proportion of computing power can also be vulnerable. Namely, DS attacks using any proportion of computing power can occur as long as the chance to making a good profit is there; i.e., revenue of an attack is greater than the cost of launching it. We have novel probability theory based derivations for calculating time finite attack probability. This can be used to size up the resource needed to calculate the revenue and the cost. The results enable us to derive sufficient and necessary conditions on the value of a target transaction which make DS attacks for any proportion of computing power profitable. They can also be used to assess the risk of one's transaction by checking whether or not the transaction value satisfies the conditions for profitable DS attacks. Two examples are provided in which we evaluate the attack resources and the conditions for profitable DS attacks given 35% proportion of computing power against Syscoin and BitcoinCash networks, and quantitatively shown how vulnerable they are.Comment: 13 pages, 1 figure. Submitted to IEEE Transactions on Information Forensics and Security. Table 1 Has been correcte

Current Status of Indirect CP Violation in Neutral Kaon System

In the standard model (SM), the CP violation is introduced through a single phase in the CKM matrix. The neutral kaon system is one of the most precise channels to test how the SM theory describes the experiment data such as $\epsilon_K$ accurately. The indirect CP violation is parametrized into $\epsilon_{K}$, which can be calculated directly using lattice QCD. In this calculation, the largest uncertainty comes from two sources: one is $\hat{B}_K$ and the other is $V_{cb}$. We use the lattice results of $\hat{B}_K$ and exclusive $V_{cb}$ to calculate the theoretical estimate of $\epsilon_K$, which turns out to be $3.1\sigma$ away from its experimental value. Here, the error is evaluated using the standard error propagation method.Comment: 7 pages, 2 figures, Lattice 2012 conference proceedin

q-analogue of Euler-Barnes' numbers and polynomials

We construct the q-analogue of Euler-Barnes' numbers and polynomials, and investigate their some properties.Comment: 9 page

On Evaluating Perceptual Quality of Online User-Generated Videos

This paper deals with the issue of the perceptual quality evaluation of user-generated videos shared online, which is an important step toward designing video-sharing services that maximize users' satisfaction in terms of quality. We first analyze viewers' quality perception patterns by applying graph analysis techniques to subjective rating data. We then examine the performance of existing state-of-the-art objective metrics for the quality estimation of user-generated videos. In addition, we investigate the feasibility of metadata accompanied with videos in online video-sharing services for quality estimation. Finally, various issues in the quality assessment of online user-generated videos are discussed, including difficulties and opportunities.Comment: Published in IEEE Transactions on Multimedi

Two-Way Quantum Number Distribution Based on Entanglement and Bell-State Measurements

A scheme is proposed by which two parties, Alice and Bob, can securely exchange real numbers. The scheme requires Alice and Bob to share entanglement and both to perform Bell-state measurements. With a qubit system two real numbers can each be sent by Alice and Bob, resulting in four real numbers shared by them. The number of real numbers that can be shared increases if higher-dimensional systems are utilized. The number of significant figures of each shared real number depends upon the number of Bell-state measurements that Alice and Bob perform. The security of the scheme against individual eavesdropping attacks is analyzed and the effects of channel losses and errors discussed.Comment: 6 pages, 3 figure

The Distance to M101 Hosting Type Ia SN 2011fe Based on the Tip of the Red Giant Branch

We present a new determination of the distance to M101, host of the type Ia SN 2011fe, based on the tip of the red giant branch method (TRGB). Our determination is based on {\it Hubble Space Telescope} archival $F555W$ and $F814W$ images of nine fields within the galaxy. Color-magnitude diagrams of arm-free regions in all fields show a prominent red giant branch (RGB). We measure the $I$-band magnitudes of the TRGB, obtaining a mean value of $I_{\rm TRGB}=25.28\pm0.01$ (where the error is a standard error), using an edge-detection method. We derive a weighted mean value of distance modulus $(m-M)_0=29.30\pm0.01 ({\rm random})\pm0.12 ({\rm systematic})$, corresponding to a linear distance of $7.24\pm0.03\pm0.40$ Mpc. While previous estimates for M101 show a large range (TRGB distances of $(m-M)_0=29.05$ to 29.42 and Cepheid distances of $(m-M)_0=29.04$ to 29.71), our measurements of the TRGB distances for nine fields show a small dispersion of only 0.02. We combine our distance estimate and photometry in the literature to derive absolute peak magnitudes in optical and near-infrared bands of SN 2011fe. Absolute maximum magnitudes of SN 2011fe are $\sim0.2$ mag brighter in the optical band and much more in the NIR than the current calibrations of SNe Ia in the literature. From the optical maximum magnitudes of SN 2011fe we obtain a value of the Hubble constant, $H_0=65.0\pm0.5({\rm random})\pm5.7({\rm systematic})$ \kmsMpc, slightly smaller than other recent determinations of $H_0$.Comment: 16 pages, 4 figures, 1 table, Accepted for publication in ApJ Letter

The Tip of the Red Giant Branch Distances to Type Ia Supernova Host Galaxies. III. NGC 4038/39 and NGC 5584

We present the tip of the red giant branch (TRGB) distances to Type Ia supernova (SNe Ia) host galaxies NGC 4038/39 and NGC 5584. Based on the deep images constructed using archival Hubble Space Telescope data, we detect red giant branch stars in each galaxy. VI photometry of the resolved stars and corresponding I-band luminosity functions show the TRGB to be at I_{TRGB} = 27.67 \pm 0.05 for NGC 4038/39 and I_{TRGB} = 27.77 \pm 0.04 for NGC 5584. From these estimates, we determine the distance modulus to NGC 4038/39 to be (m-M)_0 = 31.67 \pm 0.05 (random) \pm 0.12 (systematic) (corresponding to a linear distance of 21.58 \pm 0.50 \pm 1.19 Mpc) and the distance modulus to NGC 5584 to be (m-M)_0 = 31.76 \pm 0.04 (random) \pm 0.12 (systematic) (corresponding to a linear distance of 22.49 \pm 0.41 \pm 1.24 Mpc). We derive a mean absolute maximum magnitude of SNe Ia of M_V = -19.29 \pm 0.08 from the distance estimates of five SNe Ia (including two SNe in this study and three SNe Ia from our previous studies), and we derive a value of M_V = -19.19 \pm 0.10 using three low-reddened SNe Ia among the five SNe Ia. With these estimates, we derive a value of the Hubble constant, H_0 = 69.8 \pm 2.6 (random) \pm 3.9 (systematic) km/s/Mpc and 72.2 \pm 3.3 (random) \pm 4.0 (systematic) km/s/Mpc, respectively. The value from the five SNe is similar to those from the cosmic microwave background analysis, and not much different within errors, from those of recent Cepheid calibrations of SNe Ia. The value from the three SNe is between the values from the two methods.Comment: 12 pages, 9 figures, 6 tables, accepted for publication in Ap

Resolving the Discrepancy of Distance to M60, a Giant Elliptical Galaxy in Virgo

There is a well-known discrepancy in the distance estimation for M60, a giant elliptical galaxy in Virgo: the planetary nebula luminosity function (PNLF) distance moduli for this galaxy are, on average, $~0.4$ mag smaller than the values based on the surface brightness fluctuation (SBF) in the literature. We present photometry of the resolved stars in an outer field of M60 based on deep F775W and F850LP images in the Hubble Space Telescope obtained as part of the Pure Parallel Program in the archive. Detected stars are mostly old red giants in the halo of M60. With this photometry we determine a distance to M60 using the tip of the red giant branch (TRGB). A TRGB is detected at $F850LP_{\rm TRGB}=26.70\pm0.06$ mag, in the luminosity function of the red giants. This value corresponds to $F814W_{0,\rm TRGB}=27.13\pm0.06$ mag and $QT_{\rm TRGB}=27.04\pm0.07$ mag, where $QT$ is a color-corrected F814W magnitude. From this we derive a distance modulus, $(m-M)_0=31.05\pm0.07{\rm(ran)}\pm0.06{\rm (sys)}$ ($d=16.23\pm0.50{\rm (ran)}\pm0.42{\rm (sys)}$ Mpc). This value is $0.3$ mag larger than the PNLF distances and $0.1$ mag smaller than the SBF distances in the previous studies, indicating that the PNLF distances to M60 in the literature have larger uncertainties than the suggested values.Comment: 8 pages, 7 figures, 3 tables, ApJ in pres