Elementary Proofs Of Two Theorems Involving Arguments Of Eigenvalues Of A Product Of Two Unitary Matrices

We give elementary proofs of two theorems concerning bounds on the maximum argument of the eigenvalues of a product of two unitary matrices --- one by Childs \emph{et al.} [J. Mod. Phys., \textbf{47}, 155 (2000)] and the other one by Chau [arXiv:1006.3614]. Our proofs have the advantages that the necessary and sufficient conditions for equalities are apparent and that they can be readily generalized to the case of infinite-dimensional unitary operators.Comment: 8 pages in Revtex 4.1 preprint format, to appear in Journal of Inequalities and Application

Simultaneous multiwavelength study of the reaction of phenolphthalein with sodium hydroxide

A photodiode array (PDA) spectrophotometer was used to study the fading reaction of phenolpthalein in dilute sodium hydroxide solution. The principal component analysis (PCA) method was employed to identify the number of light absorbing species in the kinetics system. The target factor analysis (TFA) procedure, coupled with the Broyden-Fletcher-Goldfard-Shanno (BFGS) optimization method, was applied to the observed data to deduce the rate constants and the concentration-time profile of the reaction. The internal referencing method was shown to be essential in improving the quality of data obtained by a single beam PDA spectrophotomer

On the Second-Order Statistics of Correlated Cascaded Rayleigh Fading Channels

The second-order statistics of two correlated cascaded (double) Rayleigh fading channels are analyzed, where different relevant second-order cross-correlation functions of in-phase and quadrature components of the cascaded Rayleigh channels are derived. The level crossing rate (LCR) and average fade duration (AFD) of the cascaded channels are evaluated, and a single-integral form of the LCR is derived. Numerical results of the LCR and AFD are presented, and the effect of the correlation is illustrated

Relation Between Quantum Speed Limits And Metrics On U(n)

Recently, Chau [Quant. Inform. & Comp. 11, 721 (2011)] found a family of metrics and pseudo-metrics on $n$-dimensional unitary operators that can be interpreted as the minimum resources (given by certain tight quantum speed limit bounds) needed to transform one unitary operator to another. This result is closely related to the weighted $\ell^1$-norm on ${\mathbb R}^n$. Here we generalize this finding by showing that every weighted $\ell^p$-norm on ${\mathbb R}^n$ with 1\le p \le \limitingp induces a metric and a pseudo-metric on $n$-dimensional unitary operators with quantum information-theoretic meanings related to certain tight quantum speed limit bounds. Besides, we investigate how far the correspondence between the existence of metrics and pseudo-metrics of this type and the quantum speed limits can go.Comment: minor amendments, 6 pages, to appear in J.Phys.

How Does Competition Help Future Learning in Serious Games? An Exploratory Study in Learning Search Engine Optimization

Serious games, many of which are multi-player games, have been commonly used in information technology education and training. Competition can be intuitively associated with games; however, it is not always considered as a necessary attribute of serious games. Particularly, the learning impact results of competition are mixed. Challenge and control are two game attributes that are highly relevant to competition. With the use of a multi-player serious game, SEO War, this study aims to explore the relationships among competition, perceived control, perceived challenge, and self-efficacy in a game-based learning environment. Particularly, it investigates whether competition leads to self-efficacy. It also examines whether perceived challenge and perceived control mediate the relationship between competition and self-efficacy in serious games. This study contributes to the expanding literature on selecting important attributes for serious games, and it advances our understanding of the mechanism of how competition leads to self-efficacy. Moreover, it will help game designers decide on important game attributes through which games can be enhanced

Flavor SU(3) symmetry and QCD factorization in B→PPB \to PP and PVPV decays

Using flavor SU(3) symmetry, we perform a model-independent analysis of charmless $\bar B_{u,d} (\bar B_s) \to PP, ~PV$ decays. All the relevant topological diagrams, including the presumably subleading diagrams, such as the QCD- and EW-penguin exchange diagrams and flavor-singlet weak annihilation ones, are introduced. Indeed, the QCD-penguin exchange diagram turns out to be important in understanding the data for penguin-dominated decay modes. In this work we make efforts to bridge the (model-independent but less quantitative) topological diagram or flavor SU(3) approach and the (quantitative but somewhat model-dependent) QCD factorization (QCDF) approach in these decays, by explicitly showing how to translate each flavor SU(3) amplitude into the corresponding terms in the QCDF framework. After estimating each flavor SU(3) amplitude numerically using QCDF, we discuss various physical consequences, including SU(3) breaking effects and some useful SU(3) relations among decay amplitudes of $\bar B_s \to PV$ and $\bar B_d \to PV$.Comment: 47 pages, 3 figures, 28 table

Analysis of Two-Body Decays of Charmed Baryons Using the Quark-Diagram Scheme

We give a general formulation of the quark-diagram scheme for the nonleptonic weak decays of baryons. We apply it to all the decays of the antitriplet and sextet charmed baryons and express their decay amplitudes in terms of the quark-diagram amplitudes. We have also given parametrizations for the effects of final-state interactions. For SU(3) violation effects, we only parametrize those in the horizontal $W$-loop quark diagrams whose contributions are solely due to SU(3)-violation effects. In the absence of all these effects, there are many relations among various decay modes. Some of the relations are valid even in the presence of final-state interactions when each decay amplitude in the relation contains only a single phase shift. All these relations provide useful frameworks to compare with future experiments and to find out the effects of final-state interactions and SU(3) symmetry violations.Comment: 28 pages, 20 Tables in landscape form, 4 figures. Main changes are: (i) some errors in the Tables and in the relations between the quark-diagram amplitudes of this paper and those of Ref.[10] are corrected, (ii) improvements are made in the presentation so that comparisons with previous works and what have been done to include SU(3) breaking and final-state interactions are more clearly stated; to appear in the Physical Review

Implications of Recent Bˉ0→D(∗)0X0\bar{B}^0\to D^{(*)0}X^0 Measurements

The recent measurements of the color-suppressed modes $\bar B^0\to D^{(*)0}\pi^0$ imply non-vanishing relative final-state interaction (FSI) phases among various $\bar B\to D\pi$ decay amplitudes. Depending on whether or not FSIs are implemented in the topological quark-diagram amplitudes, two solutions for the parameters $a_1$ and $a_2$ are extracted from data using various form-factor models. It is found that $a_2$ is not universal: $|a_2(D\pi)|= 0.40-0.55$ and $|a_2(D^*\pi)|= 0.25-0.35$ with a relative phase of order $(50-55)^\circ$ between $a_1$ and $a_2$. If FSIs are not included in quark-diagram amplitudes from the outset, $a_2^{eff}/a_1^{eff}$ and $a_2^{eff}$ will become smaller. The large value of $|a_2(D\pi)|$ compared to $|a_2^{eff}(D\pi)|$ or naive expectation implies the importance of long-distance FSI contributions to color-suppressed internal $W$-emission via final-state rescatterings of the color-allowed tree amplitude.Comment: 17 pages. The Introduction is substantially revised and the order of the presentation in Sec. 2 is rearranged. To appear in Phys. Re

入院患者のサルモネラ保菌率およびその分離のための増菌培地の比較

The efficiencies of Rappaport medium, strontium chloride, strontium selenite and selenite F broths for enrichment in the isolation of salmonellas from human stools were compared. The study showed that Rappaport medium when used in conjunction with strontium selenite broth gave the most satisfactory result, because they covered the isolation of a wider range of salmonellas. With these media, the carriage rate of Salmonella serotypes of 3,325 hospital patients who were admitted without complaints of diarrhoea or gastroenteritis or enteric fever, were tested. The result revealed that 5.6% of them carried Salmonella serotypes ranging from those that may produce food-poisoning to those which are causal agents of enteric fever. Moreover, patients who were infected with the liver-fluke, Clonorchis sinensis, had a higher carriage rate than those who were infected with other intestinal parasites or non-infected.サルモネラ分離に際してRappaport培地,strontium chlorideブイヨン,strontium seleniteブイヨンおよびselenite Fブイヨンの4種の増菌培地を用い,その成績を比較した.その結果,Rappaport培地にstrontium seleniteブイヨンを併用すると,サルモネラの各種類の分離に最も満足すべき成績がえられた.これらの培地を用いて,下痢を全く伴わない患者,胃腸炎あるいはチフス性疾患の患者3,325名についてサルモネラ保菌率を検査した.その結果,22の血清型に属する189株のサルモネラを分離した.検出率は5.6%である.その血清型は,食中毒の原因と推定されたものから,チフス性疾患の原因菌に至るさまぎまの型が含まれていたが,最も多く分離されたのはS. derbyとS. anatumであった.また,Clonorchis sinensisに感染していた患者は,他の腸寄生虫感染者あるいは非感染者より高率にサルモネラを保有していた