Narrow Results

In this paper, we explore the power of quantum computers with restricted transition amplitudes. In 1997 Adleman, DeMarrais, and Huang showed that quantum Turing machines (QTMs) with the amplitudes from are computationally equivalent to ones with the polynomial-time computable amplitudes as machines implementing bounded-error polynomial-time algorithms. We show that QTMs with the amplitudes from is polynomial-time equivalent to deterministic Turing machines as machines implementing exact algorithms, i.e., algorithms that output correct answers with certainty. By extending this result, it is shown that exact quantum computers with rational biased coins are equivalent to classical computers. Moreover, we discuss the computational power of exact quantum computers with multiple types of coins. We also show that, from the viewpoint of zero-error polynomial-time algorithms, is not more powerful than as the set of amplitudes taken by QTMs; however, it is sufficient to solve the factoring problem.

The objective of this study is to investigate the impact of different surface roughness levels on a staggered arrangement of tubes in a cross-flow configuration, with water as the fluid being used. The focus lies in comparing the data obtained from the rough surface configuration with that of a smooth cylinder reference point. To assist this comparison, a comprehensive two-dimensional computational fluid dynamics (CFD) model is created, which accurately represents the distinctive characteristics of each surface shape. This study also included modifying the Remax within a range of 10 000–16 000 and analyzing the outcomes of using four different tube types, each with different supernatant thicknesses labeled as $\mathrm{\text{A}}=0$, $\mathrm{\text{A}}=0.1$, $\mathrm{\text{A}}=0.2$ and $\mathrm{\text{A}}=0.4$ accordingly. Surprisingly, the tube with a 0.4 wave surface had significantly higher average Nusselt numbers (Nu) compared to the other tubes, indicating superior performance. The ideal tube design was found based on three main metrics: The performance evaluation criterion (PEC), the global performance criterion (GPC) and the average Nu. The performance metrics encompassed the PEC, GPC and the Colburn factor $(j)$. The average Nu of the wavy_0.4 tube was higher than that of the SM by 31.66–32.54%, higher than that of the wavy_0.2 tube by 19.76–20.74%, and higher than that of the wavy_0.1 tube by 9.38–16.58%. According to the statistics, a heat exchanger that cools and has a wave with an amplitude of 0 is the most efficient choice for offshore energy systems. The smooth bundle tube (SBT) demonstrated the most significant increase in GPC, with values of 9.3–12.7% and 20.3–28.3% higher than those of wavy tubes with amplitudes of 0.1 and 0.2, respectively. In addition, correlations for the Nu are given, with results verified using empirical data from Balabani et al.

The lowest order contribution of the amplitude of the Dirac–Coulomb scattering in de Sitter spacetime is calculated assuming that the initial and final states of the Dirac field are described by exact solutions of the free Dirac equation on de Sitter spacetime with a given momentum and helicity. One studies the difficulties that arises when one passes from the amplitude to cross section.

The lowest order contribution of the amplitude of Dirac–Coulomb scattering in de Sitter space–time is calculated assuming that the initial and final states of the Dirac field are described by exact solutions of the free Dirac equation on de Sitter space–time with a given energy and helicity. We find that the total energy is conserved in the scattering process.

Multiple solutions exist in many experimental situations where several interfering amplitudes are summed to fit experimentally measured distributions, such as cross sections, mass spectra, and/or angular distributions. We show a few examples where multiple solutions are found, but only one solution is reported in publications. Since there is no standard rule for choosing one among the solutions as the physics one, we propose a simple rule that agrees with what has been adopted in previous literature: the solution corresponding to the minimal magnitudes of the amplitudes must be the physical solution. We suggest testing this rule in future analyses.

A large number of simultaneous frequency and amplitude data from an electronic chaotic circuit (Chua's circuit) have been obtained. These acquisitions are validated by plotting the bifurcation diagrams of the experimental data versus the bifurcation parameter. We introduce a topological parallel between the Colpitts oscillator and Chua's circuit, and look for similar behavior of the frequency fluctuations using the Allan deviation.

The feedback controllers are designed to modify the amplitude of limit cycles in van der Pol oscillator and generalized van der Pol oscillator. Bifurcation control equations of weakly nonlinear systems are obtained by using the method of multiple scales. Gain-amplitude curves of controlled systems are drawn. Based on numerical study, the brief results of controlling amplitude of limit cycle are given for strongly nonlinear system.

P53 plays a vital role in DNA repair, and several mathematical models of the p53-Mdm2 feedback loop were used to explain the biological mechanism. In this paper, a p53-Mdm2 model described by a delay reaction–diffusion equation is studied both analytically and numerically. This research aims to provide an understanding of the impact of delay and sustained pressure on the p53-Mdm2 dynamics and tries to explain some biological mechanism. It is found that the type of pattern formation is affected by Hopf bifurcation. Also, the amplitude equation in delay diffusive system is derived and it is shown that sustained stress plays an essential role in the function of p53. Finally, simulation is used to verify the theoretical results.

Many service systems provide customers with information about the system so that customers can make an informed decision about whether to join or not. Many of these systems provide information in the form of an update. Thus, the information about the system is updated periodically in increments of size $\mathrm{\Delta }$. It is known that these updates can cause oscillations in the resulting dynamics. However, it is an open problem to explicitly characterize the size of these oscillations when they occur. In this paper, we solve this open problem and show how to exactly calculate the amplitude of these oscillations via a fixed point equation. We also calculate closed form approximations via Taylor expansions of the fixed point equation and show that these approximations are very accurate, especially when $\mathrm{\Delta }$ is large. Our analysis provides new insight for systems that use updates as a way of disseminating information to customers.

Background: The influence of water immersion on neuromuscular function is of importance to a number of disciplines; however, the reliability of surface electromyography (SEMG) following water immersion is not known. This study examined the reliability of SEMG amplitude during maximal voluntary isometric contractions (MVICs) of the vastus lateralis following water immersion. Methods: Using a Biodex isokinetic dynamometer and in a randomized order, 12 healthy male subjects performed four MVICs at 60° knee flexion on both the dominant and nondominant kicking legs, and the SEMG was recorded. Each subject's dominant and nondominant kicking leg was then randomly assigned to have SEMG electrodes removed or covered during 15 min of water immersion (20°C–25°C). Following water immersion, subjects performed a further four MVICs. Results: Intraclass correlation coefficient (ICC) and the relative standard error of measurement (%SEM) of SEMG amplitude showed moderate to high trial-to-trial reliability when electrodes were covered (0.93% and 2.79%) and removed (0.95% and 2.10%, respectively). Conclusions: The results of the this study indicate that SEMG amplitude of the vastus lateralis may be accurately determined during maximal voluntary contractions following water immersion if electrodes are either removed or covered with water-resistive tape during the immersion.

Mathematical simulations of embryological fluid dynamics are fundamental to improving clinical understanding of the intricate mechanisms underlying sperm locomotion. The strongly rheological nature of reproductive fluids has been established for a number of decades. Complimentary to clinical studies, mathematical models of reproductive hydrodynamics provide a deeper understanding of the intricate mechanisms involved in spermatozoa locomotion which can be of immense benefit in clarifying fertilization processes. Although numerous non-Newtonian studies of spermatozoa swimming dynamics in non-Newtonian media have been communicated, very few have addressed the micro-structural characteristics of embryological media. This family of micro-continuum models include Eringen’s micro-stretch theory, Eringen’s microfluid and micropolar constructs and V. K. Stokes’ couple stress fluid model, all developed in the 1960s. In the present paper we implement the last of these models to examine the problem of micro-organism (spermatozoa) swimming at low Reynolds number in a homogenous embryological fluid medium with couple stress effects. The micro-organism is modeled as with Taylor’s classical approach, as an infinite flexible sheet on whose surface waves of lateral displacement are propagated. The swimming speed of the sheet and rate of work done by it are determined as function of the parameters of orbit and the couple stress fluid parameter ($\alpha$). The perturbation solutions are validated with a Nakamura finite difference algorithm. The perturbation solutions reveal that the normal beat pattern is effective for both couple stress and Newtonian fluids only when the amplitude of stretching wave is small. The swimming speed is observed to decrease with couple stress fluid parameter tending to its Newtonian limit as alpha tends to infinity. However the rate of work done by the sheet decreases with $\alpha$ and approaches asymptotically to its Newtonian value. The present solutions also provide a good benchmark for more advanced numerical simulations of micro-organism swimming in couple-stress rheological biofluids.

We deduce trace properties for modulation spaces (including certain Wiener-amalgam spaces) of Gelfand–Shilov distributions.We use these results to show that $\mathrm{\Psi }$dos with amplitudes in suitable modulation spaces, agree with normal type $\mathrm{\Psi }$dos whose symbols belong to (other) modulation spaces. In particular we extend earlier trace results for modulation spaces, to include quasi-Banach modulation spaces. We also apply our results to extend earlier results on Schatten-von Neumann and nuclear properties for $\mathrm{\Psi }$dos with amplitudes in modulation spaces.

Our prior studies of polymer composites subjected to stress have shown that a statistical distribution of acoustic emission damage events occur in multiscale and include several damage modes. Various multiscale modeling and simulation methods have been developed by others to obtain constitutive equations, which were used to link the variables between microscopic and macroscopic scales of continuum. Very limited experimental work exists to reveal physical evidence on the multiscale damage modes, and their relationship and consequential influence on performance of materials. This paper reports an innovative approach that experimentally evidences the response of damage events in different scales to the applied stress. It shows that a strong correlation exists between multiscale damage modes, and that ensemble-normalized entropy and physical evidence can be qualitatively and quantitatively used to integrate related damage modes at different scales.

The value of evoked potentials (EPs) in the clinical assessment of physiological function has been recognized for some time by those with specialized neurophysiological interests. Based on this concept, we have applied this novel technique for discrimination of pain intensity level and side effects using time-domain parameters extracted from the evoked pain pattern (EPP) in postoperative pain via patient-controlled analgesia (PCA). In conventional PCA systems, each delivery is similar to evoked pain stimulation, and we then count the following demands in a lockout interval. Therefore, the EPP is calculated and averaged from several lockout intervals in a period of time. From this calculation, the evoked parameters of area, latency, and amplitude of each period of time can be easily extracted. A total of 741 cases from 1519 patients at a medical center have been screened and compared with these three parameters using different visual analog scales (VAS) and side effects (SE). The results indicate that the area parameter is a good indicator for higher VAS patients and the variance of latency parameter is a better outcome for interpreting the patients with SE. However, the amplitude parameter shows no significant differences in both VAS and SE groups. Using massive information from clinical trials and a novel technique of evoked pain stimulation algorithm, we demonstrate that evoked parameters (i.e. area and latency) can serve as indicators to assess various clinical evidences, such as VAS and SE associated with postoperative pain.

Quartz crystal microbalance (QCM) has been constructed and used for chemical sensing and biochemical detecting. Frequency shift has a relation with mass changed in the gaseous condition. However, the velocity, density, and viscosity also cause frequency changed in liquid solution. We develop a new method and system to investigate the variable value of amplitude and frequency from the oscillator of quartz. In this system, piezoelectric quartz crystal (10 MHz, AT-cut) with gold electrodes was mounted under liquid solution. Crystal was exposed to the different concentrations of glucose and sodium chloride solution. The results show that the ramp-up speed of amplitude was faster as frequency in the alternative state. We figure out the largest skew through the differential curve of amplitude in different solutions. The dramatic results give a QCM more meanings to be a biochemistry detecting utility.