Applications of the Heine and Bauer-Muir transformations to Rogers-Ramanujan type continued fractions

In this paper we show that various continued fractions for the quotient of general Ramanujan functions G(aq, b, λq)/G(a, b, λ) may be derived from each other via Bauer-Muir transformations. The separate convergence of numerators and denominators play a key part in showing that the continued fractions and their Bauer-Muir transformations converge to the same limit. We also show that these continued fractions may be derived from either Heine’s continued fraction for a ratio of 2φ1 functions, or other similar continued fraction expansions of ratios of 2φ1 functions. Further, by employing essentially the same methods, a new continued fraction for G(aq, b, λq)/G(a, b, λ) is derived. Finally we derive a number of new versions of some beautiful continued fraction expansions of Ramanujan for certain combinations of infinite products, with the following being an example: (−a, b; q)∞ − (a, −b; q)∞ (−a, b; q)∞ + (a, −b; q)∞ = (a − b) 1 − ab − (1 − a2)(1 − b2)q 1 − abq2 − (a − bq2)(b − aq2)q 1 − abq4 − (1 − a2q2)(1 − b2q2)q3 1 − abq6 − (a − bq4)(b − aq4)q3 1 − abq8 − ···

EFFECTS OF CONTACT SURFACE PROPERTIES ON MULTI-FINGER FORCE PRODUCTION TASKS IN HUMANS

The purpose of the current study was to investigate the effect of contact surface properties, which presumably determine the level of stimulation on the cutaneous receptors, on multifinger force production and synergic actions of finger forces. The framework of the uncontrolled manifold (UCM) hypothesis was used to quantify indices of multi-finger synergies stabilizing total force in normal and tangent directions as well as the direction of resultant force (i.e., force angle) during steady-state force production. There was significant effect of contact surface on the magnitude of maximal voluntary contraction force. Also, there was a significant effect of the contact surface on the indices of force-direction (i.e., force angle) stabilizing synergies meaning that the stimulation on the cutaneous receptors could be an effective way to enhance the abili to organize the direction of finger forces

Complete amplitude and phase control of light using broadband holographic metasurface

Reconstruction of light profiles with amplitude and phase information, called holography, is an attractive optical technique to display three-dimensional images. Due to essential requirements for an ideal hologram, subwavelength control of both amplitude and phase is crucial. Nevertheless, traditional holographic devices have suffered from their limited capabilities of incomplete modulation in both amplitude and phase of visible light. Here, we propose a novel metasurface that is capable of completely controlling both amplitude and phase profiles of visible light independently with subwavelength spatial resolution. The simultaneous, continuous, and broadband control of amplitude and phase is achieved by using X-shaped meta-atoms based on expanded concept of the Pancharatnam-Berry phase. The first experimental demonstrations of complete complex-amplitude holograms with subwavelength definition are achieved and show excellent performances with remarkable signal-to-noise ratio compared to traditional phase-only holograms. Extraordinary control capability with versatile advantages of our metasurface paves a way to an ideal holography, which is expected to be a significant advance in the field of optical holography and metasurfaces

Naïve Bayesian Classifier for Selecting Good/Bad Projects during the Early Stage of International Construction Bidding Decisions

Since the 1970s, revenues generated by Korean contractors in international construction have increased rapidly, exceeding USD 70 billion per year in recent years. However, Korean contractors face significant risks from market uncertainty and sensitivity to economic volatility and technical difficulties. As the volatility of these risks threatens project profitability, approximately 15% of bad projects were found to account for 74% of losses from the same international construction sector. Anticipating bad projects via preemptive risk management can better prevent losses so that contractors can enhance the efficiency of bidding decisions during the early stages of a project cycle. In line with these objectives, this paper examines the effect of such factors on the degree of project profitability. The Naïve Bayesian classifier is applied to identify a good project screening tool, which increases practical applicability using binomial variables with limited information that is obtainable in the early stages. The proposed model produced superior classification results that adequately reflect contractor views of risk. It is anticipated that when users apply the proposed model based on their own knowledge and expertise, overall firm profit rates will increase as a result of early abandonment of bad projects as well as the prioritization of good projects before final bidding decisions are made

Comparative Analysis of Lunge Techniques: Forward, Reverse, Walking Lunge

The study aims to find the basis for the efficiency of lunge and risk of injury by comparing mechanical variables in various lunges (forward lunge, reverse lunge, and walking lunge). Four participants who were familiar with the three lunge movements were recruited to achieve the purpose of the study. The resultant hip joint moment, resultant knee joint moment, and resultant knee joint force were analyzed during the three lunge movements. Eight muscle of lower extremity were also analyzed using EMG. In conclusion, reverse lunge movement was found to be favorable in achieving the primary goal of lunge exercise, which is the development of gluteus maximus and quadriceps femoris, as it resulted in higher agonist muscle activities with relatively low momentary maximum knee shearing force compared to the other lunge techniques

Correlation between Short-Form 36 Scores and Neck Disability Index in Patients Undergoing Anterior Cervical Discectomy and Fusion

Study Design Case control study. Purpose To determine how the Neck Disability Index (NDI), a cervical spine-specific outcome, reflects health-related quality-of-life, and if NDI is correlated to the 36-item Short-Form Health Survey (SF-36) scores. Overview of Literature NDI is a useful tool for assessing health-related quality of life in patients with neck pain. Methods We used the Pearson product-moment correlation coefficient to assess the validity of all items under NDI and SF-36, and the Pearson’s correlation coefficient to assess the correlation between NDI and total SF-36 scores. The primary outcome measures were spine-specific health status- and general health status-measures after spine surgery, and these were evaluated every year for 2 years, using both NDI and SF-36 scores. Results NDI had a strong linear correlation with SF-36 and its two scales, the Physical Component Score (PCS) and the Mental Component Score (MCS), attesting to the validity of these two instruments. Among the eight subscales of SF-36, there was a strong linear correlation between NDI and PCS-physical functioning, PCS-bodily pain, and MCS-role emotional. Further, a moderate linear correlation was observed between NDI and subscales of PCS-role physical, PCS-general health, and MCS-social functioning, and between NDI and MCS-vitality and MCS-mental health. Conclusions Our findings suggest that the NDI adequately reflects the patient’s physical and mental quality of life, implying that the use of NDI to assess functional outcomes can also be ultimately used to evaluate the patient’s quality of life

Polarization Dependence Suppression of Optical Fiber Grating Sensor in a π-Shifted Sagnac Loop Interferometer

In the sensing applications of optical fiber grating, it is necessary to reduce the transmission-type polarization dependence to isolate the sensing parameter. It is experimentally shown that the polarization-dependent spectrum of acousto-optic long-period fiber grating sensors can be suppressed in the transmission port of a π-shifted Sagnac loop interferometer. General expressions for the transmittance and reflectance are derived for transmission-type, reflection-type, and partially reflecting/transmitting-type polarization-dependent optical devices. The compensation of polarization dependence through the counter propagation in the Sagnac loop interferometer is quantitatively measured for a commercial in-line polarizer and an acousto-optic long-period fiber grating sensor