Minimum error discrimination of qubit states revisited

We study the problem of Minimum-Error (ME) discrimination for qubit states in detail using a geometric approach. We employ the Helstrom conditions in a constructive way and use the Bloch vector formulation. All POVM answers of the ME problem define a unique operator known as the Lagrange operator $\Gamma$, and our method starts with finding this operator. We see that in an optimal strategy there might be some non-detectable quantum states with corresponding null measurement operators. To find $\Gamma$, we introduce the notion of circumsphere for equiprobable problems. For a general problem of $N$ qubit states with arbitrary priori probabilities $\{p_i,\rho_i\}_{i=1}^N$, we introduce a structured instruction with four steps to find $\Gamma$ by using the fact that there is always a nondecomposable optimal POVM with at most four detectable states. To use this instruction, we need to know the optimal solution of two, three, and four mixed qubit states with arbitrary priori probability. Therefore, we solve the problem for these cases, including some completely new results like the ME problem of four qubit states. Moreover, we introduce some classes of POVM answers (involving the geometric of the polytope of qubit states inside the Bloch sphere), and the notion of nondecomposable POVM subsets of a given problem which provide us all we need for constructing all optimal answers

The Impact of Abacus on Mathematic Learning through Teachers’ Innovative Behavior in Elementary Schools of Iran

The purpose of this paper is to concentrate on the impact of abacus on mathematic learning through teachers’ innovative behaviour with four factors as to realize problems, create ideas, provide support for the ideas, and implement the ideas. The use of abacus is considered as the independent variable of this study and mathematic learning is defined as the dependent variable mediated by teachers’ innovative behaviour. This paper attempts to review the previous studies. This study brings about a conceptual framework for the importance of effective factors to improve mathematic learning. Key Words: Abacus, teachers’ innovative behaviour, mathematic learning

The Contribution of Abacus to Mathematic Learning through Teachers’ Motivation in Elementary Schools of Iran

The objective of this paper is to focus on the contribution of the use of abacus towards mathematic learning through teachers’ motivation. The use of abacus is defined as the independent variable of this study and mathematic learning is considered as the dependent variable mediated by motivation. This paper attempts to review the last studies. This presents a conceptual framework for the importance of effective factors to improve mathematic learning in the elementary schools. Key Words: Abacus, motivation, mathematic learning

Aleksandrov Problem, Positively Homogeneous and Affine Maps

Abstract. In this paper, Aleksandrov problem of conservative distances is solved for positively homogeneous map. Also it is shown that when an affine map can be an isometry. Mathematics Subject Classification: 51K05, 39B8

Development and psychometric evaluation of the Persian version of the Phoneme Recognition Test A central auditory processing measure

  Objectives The present study evaluating the psychometric properties of the Persian version of the Phoneme Recognition Test (P-PRT) in normal subjects and cochlear implant (CI) users. Material & Methods This study includes developing the Persian phoneme recognition test (PRT), determining its validity and reliability, and comparing the results of a control group versus CI users. The test reliability was examined through a test-retest with an approximately five-week interval. In the present survey, 363 subjects were investigated in three stages. The face validity evaluation stage was conducted on 40 subjects. The psychometric properties of the P-PRT were evaluated in 323 individuals (225 normal subjects and 98 CI users). The test-retest reliability was examined in all the 225 subjects in the control groupand 40 CI users. ResultsThe results confirmed the face validity of the P-PRT. No significant differences were observed between the two genders in terms of performance in the P-PRT. Significant differences were observed between the control and CI groups. Evaluating the test-retest reliability suggested perfect reliability (r>0.9) in both groups. Significant differences were observed in the P-PRT between the adults and the 7-year-old subjects compared to other age groups. Conclusion The P-PRT can be used as a valid and reliable test for clinically evaluating phoneme recognition abilities and monitoring the rehabilitation progres

What do Spanish men know about menopause?

Objective: The aim of the study is to evaluate the knowledge that men have about menopause and to analyze whether sociodemographic aspects influence in this knowledge. Methods: 560 consecutive surveys were collected during 2019. The surveys were completed anonymously, voluntarily and without incentives by men. A maximum score of 45 points was considered for the knowledge analysis. Results: The mean age was 49.13 ± 11.1 years. The most frequent source of information to obtain knowledge about menopause were friends (61.4%). The mean of the questionnaire score was 20.69 ± 6.1. The most frequent symptoms associated with menopause were hot flashes and vaginal dryness (93.7%; 48%) and the best-known treatment to improve vaginal health was lubricants at 69.5%. The most common treatment men know for improving menopause symptoms was menopause hormone treatment; however, 27.9% of men think there is no treatment for menopause. Differences between ages in numbers and grades were found (p=0.032). The scores by levels of study showed statistically differences (primary school, high school, professional training and university education (men with a higher level of education had significantly more knowledge) (p=0.013). Differences were showed in men who obtained information from health staff with respect to other sources (p<0.001). Conclusions: The knowledge in men in this sample is limited. Differences between ages, level of education and sources of information were found. No differences were found between public and private hospitals. The teaching of this knowledge should be carried out by trained personnel, preferably health staff.pre-print224 K

Third order nonlinear optical properties of organometal halide perovskite by means of the Z-scan technique

The nonlinear optical response of CH3NH3PbBr3 perovskites is investigated using Z-scan technique, employing 10 ns laser pulses, at 532 nm. The systems were found to exhibit strong nonlinear optical response, dominated by nonlinear refraction. The effect of organic and inorganic composition ratio on the nonlinear susceptibility is studied experimentally. In all cases, the nonlinear absorption and refraction have been determined. The corresponding third-order susceptibilities and second-order hyperpolarizability are determined to be as large as 10−6 (esu) and 10−28 (esu) under ns laser excitation respectively. Showing large third-order optical nonlinearity in CH3NH3PbBr3 thin films, suggesting their potential for photonics applications

The Effect of a Words-in-Noise Training Method on Speech Perception in Noise of Children with Unilateral Hearing Loss

Background and Aim: Despite more affordable and advanced technologies for early detection of congenital hearing loss, unilateral hearing loss is the prevalent form of hearing loss affecting school-aged children. This study aimed to examine the impact of Words-in-Noise (WIN) training on speech perception of noise in children with unilateral hearing loss. Methods: Thirteen children aged 8 to 12 years with unilateral hearing loss underwent a WIN training program in noise. The participants were tested before and after training on word identification in noise and cortical auditory evoked potentials. Results: A comparison of the mean signal-to-noise ratio 50% between pre- and post-training indicated that signal-to-noise ratio 50% score decreased after training sessions. WIN training reduced the latency in N1 and P2 waves in the Fz electrode and the N1 wave in the Pz electrode and increased the amplitude of the waves in the Fz and Pz electrodes. The observed data suggest that all participants’ performance improved on word identification in noise and some electrophysiological parameters. Cortical auditory evoked potentials components changes did not correlate with the WIN scores. Conclusion: The Persian version of the WIN training improved speech perception ability in the presence of competitive noise in children with unilateral hearing loss. Therefore, this software solution can partially solve speech comprehension problems with noise in these children