Two-dimensional Integration Research Articles

Comparison of Two Wavelet Methods for Accurate Solution of Two-Dimensional Nonlinear Volterra Integral Equation

Comparison of Two Wavelet Methods for Accurate Solution of Two-Dimensional Nonlinear Volterra Integral Equation

Surface Plasmonic Sensors: Sensing Mechanism and Recent Applications.

Surface plasmonic sensors have been widely used in biology, chemistry, and environment monitoring. These sensors exhibit extraordinary sensitivity based on surface plasmon resonance (SPR) or localized surface plasmon resonance (LSPR) effects, and they have found commercial applications. In this review, we present recent progress in the field of surface plasmonic sensors, mainly in the configurations of planar metastructures and optical-fiber waveguides. In the metastructure platform, the optical sensors based on LSPR, hyperbolic dispersion, Fano resonance, and two-dimensional (2D) materials integration are introduced. The optical-fiber sensors integrated with LSPR/SPR structures and 2D materials are summarized. We also introduce the recent advances in quantum plasmonic sensing beyond the classical shot noise limit. The challenges and opportunities in this field are discussed.

Fragmentation functions for a quark into a spin-singlet quarkonium: Different flavor case

In the paper, we calculate the fragmentation functions for a quark to fragment into a spin-singlet quarkonium, where the flavor of the initial quark is different from that of the constituent quark in the quarkonium. The ultraviolet divergences in the phase space integral are removed through the operator renormalization under the modified minimal subtraction scheme. The fragmentation function $D_{q \to \eta_Q}(z,\mu_F)$ is expressed as a two-dimensional integral. Numerical results for the fragmentation functions of a light quark or a bottom quark to fragment into the $\eta_c$ are presented. As an application of those fragmentation functions, we study the processes $Z \to \eta_c+q\bar{q}g(q=u,d,s)$ and $Z \to \eta_c+b\bar{b}g$ under the fragmentation and the direct nonrelativistic QCD approaches.

Solving Fractional Two-Dimensional Nonlinear Partial Volterra Integral Equation by Using Bernoulli Wavelet

Solving Fractional Two-Dimensional Nonlinear Partial Volterra Integral Equation by Using Bernoulli Wavelet

Ventromedial Prefrontal Cortex Activity and Sympathetic Allostasis During Value-Based Ambivalence.

Anxiety is characterized by low confidence in daily decisions, coupled with high levels of phenomenological stress. Ventromedial prefrontal cortex (vmPFC) plays an integral role in maladaptive anxious behaviors via decreased sensitivity to threatening vs. non-threatening stimuli (fear generalization). vmPFC is also a key node in approach-avoidance decision making requiring two-dimensional integration of rewards and costs. More recently, vmPFC has been implicated as a key cortical input to the sympathetic branch of the autonomic nervous system. However, little is known about the role of this brain region in mediating rapid stress responses elicited by changes in confidence during decision making. We used an approach-avoidance task to examine the relationship between sympathetically mediated cardiac stress responses, vmPFC activity and choice behavior over long and short time-scales. To do this, we collected concurrent fMRI, EKG and impedance cardiography recordings of sympathetic drive while participants made approach-avoidance decisions about monetary rewards paired with painful electric shock stimuli. We observe first that increased sympathetic drive (shorter pre-ejection period) in states lasting minutes are associated with choices involving reduced decision ambivalence. Thus, on this slow time scale, sympathetic drive serves as a proxy for “mobilization” whereby participants are more likely to show consistent value-action mapping. In parallel, imaging analyses reveal that on shorter time scales (estimated with a trial-to-trial GLM), increased vmPFC activity, particularly during low-ambivalence decisions, is associated with decreased sympathetic state. Our findings support a role of sympathetic drive in resolving decision ambivalence across long time horizons and suggest a potential role of vmPFC in modulating this response on a moment-to-moment basis.

Two-dimensional integration approach to teaching cardiovascular physiology: effectiveness and students\u2019 perspectives

BackgroundPre-clerkship medical curriculums consist of a series of organ system-based courses and lectures but often lack an integration between organ systems. Such integration could be beneficial for clerkship years and students’ future career. Hence, we aimed to share our process of organising an integrative teaching approach in a large class of pre-clerkship medical students and to reflect the students’ perspective toward the teaching process in this observational study. In addition, we tested effectiveness of this integrative approach compared with the traditional teaching (lecture).MethodsWe organised a two-dimensional (2D)-integrative teaching for 309 students in selected topics of cardiovascular physiology of the medical curriculum of the Faculty of Medicine, Chulalongkorn University, Thailand. The first dimension of integration is the incorporation of physiology of other organ systems into the cardiovascular physiology class. The second is the integration of multiple teaching methods and strategies, including small group discussion, student presentation, wrap-up, quiz, and question-and-answer sessions. Unless opting out, students evaluated this integrative teaching by filling in a questionnaire. The summative scores were also used to determine their comprehensive understandings of the content.ResultsThe course evaluation showed that most students (81.9–91.2%) had positive attitudes toward all organised sessions, i.e. this teaching method helps promote their basic and applied physiology knowledge, critical thinking, information searching, presentation, and teamwork skills. In general, students at all performance levels attained higher scores in the summative exam for the 2D-integrative-class–relevant questions (74.4±16.1%) than for the lecture-pertinent questions (65.2±13.6%).ConclusionsIn a large class size of pre-clerkship students, 2D-integrative teaching strategies with careful planning and preparation can be successfully implemented, based on positive attitudes and relatively high summative scores of students in this study. Hence, this comprehensive teaching could be incorporated in current medical curriculums, particularly for the complex learning topics.

Deadlock Avoidance Algorithms for Recursion-Tree Modeled Requests in Parallel Executions

We present an extension of the bankers algorithm to resolve deadlock for programs whose resource-request graph can be modeled as a recursion tree for parallel execution. Our algorithm implements the bankers logic, with the key difference being that some properties of the tree are fully exploited to improve the resource utilization and safety check in deadlock avoidance. For an n-node tree modeled program making requests to m types of resources, our recursion-tree based algorithm can obtain a time complexity of O(mn loglogn) on average in safety check while reducing the conservativeness in resource utilization. We reap these benefits by proposing a concept of the resource critical tree and leverage it to localize the maximum claim associated with each node in the tree. To tackle the case when the tree model is not statically known, we relax the definition of a local maximum claim by sacrificing some resource utilization. With this trade-off, the algorithm can resolve the deadlock and achieve more efficient safety checks within time of O(m loglogn). Our empirical studies on a two-dimensional integration problem on sparse grids show that the proposed algorithms can reduce resource utilization conservativeness and improve avoidance performance by minimizing the number of safety checks.

Polyolefin Analyses with a 10 mm Multinuclear NMR Cryoprobe.

Polyolefins are important and broadly used materials. Their molecular microstructures have direct impact on macroscopic properties and dictate end-use applications. 13C NMR is a powerful analytical technique used to characterize polyolefin microstructures, such as long-chain branching (LCB), but it suffers from low sensitivity. Although the 13C sensitivity of polyolefin samples can be increased by about 5.5 times with a cryoprobe, when compared with a conventional broadband observe (BBO) probe, further sensitivity enhancement is in high demand for studying increasingly complex polyolefin microstructures. Toward this goal, distortionless enhancement by polarization transfer (DEPT) and refocused insensitive nuclei enhanced by polarization transfer (RINEPT) are explored. The use of hard, regular, and new short adiabatic 180° 13C pulses in DEPT and RINEPT is investigated. It is found that RINEPTs perform better than DEPTs and a sensitivity enhancement of 3.1 can be achieved with RINEPTs. The results of RINEPTs are further analyzed with statistics software JMP and recommendations for optimal usage of RINEPTs are suggested. An example of analyzing saturated chain ends in an ethylene-octene copolymer sample with a hard 180° 13C RINEPT pulse is demonstrated. It is shown that the experimental time can be further reduced in half because of faster proton relaxation, where the total experimental time is about 580 times shorter when compared to using a conventional method and a 10 mm BBO probe. A naturally abundant nitrogen-containing polyolefin is analyzed using 1H-15N HMBC and, to our knowledge, is the first 1H-15N HMBC presented in the field of polyolefin characterization. The relative amount of similar nitrogen-containing structures is quantified by two-dimensional integration of 1H-15N HMBC. Two pragmatic technical challenges related to using high-sensitivity NMR cryoprobes are also addressed: (1) A new 1H decoupling sequence Bi_Waltz_65_256pl is proposed to address decoupling artifacts in 13C{1H} NMR spectra which contain a strong 13C signal with a high signal-to-noise ratio (S/N). (2) A simple pulse sequence that affords zero-slope spectral baselines and quantitative results is presented to address acoustic ringing that is often associated with high-sensitivity cryoprobe use.

Some Weighted Inequalities for Higher-Order Partial Derivatives in Two Dimensions and Its Applications

We establish some Ostrowski type inequalities involving higher-order partial derivatives for two-dimensional integrals on Lebesgue spaces (L_{∞}, L_{p} and L₁). Some applications in Numerical Analysis in connection with cubature formula are given. Finally, with the help of obtained inequality, we establish applications for the kth moment of random variables.

Reducing a Class of Two-Dimensional Integrals to One-Dimension with an Application to Gaussian Transforms

Quantum theory is awash in multidimensional integrals that contain exponentials in the integration variables, their inverses, and inverse polynomials of those variables. The present paper introduces a means to reduce pairs of such integrals to one dimension when the integrand contains powers multiplied by an arbitrary function of xy/(x+y) multiplying various combinations of exponentials. In some cases these exponentials arise directly from transition-amplitudes involving products of plane waves, hydrogenic wave functions, and Yukawa and/or Coulomb potentials. In other cases these exponentials arise from Gaussian transforms of such functions.

Determination of Riboflavin by Nanocomposite Modified Carbon Paste Electrode in Biological Fluids Using Fast Fourier Transform Square Wave Voltammetry

Herein, fast Fourier transformation square-wave voltammetry (FFT-SWV) as a novel electrochemical determination technique was used to investigate the electrochemical behavior and determination of Riboflavin at the surface of a nanocomposite modified carbon paste electrode. The carbon paste electrode was modified by nanocomposite containing Samarium oxide (Sm2O3)/reduced graphene oxide (RGO) (2:1) to improve detection sensitivity of Riboflavin under optimal experimental conditions. Furthermore, the signal-to-noise ratio was significantly increased by application of discrete fast Fourier transformation analysis, background subtraction and two-dimensional integration of the electrode response over the selected potential range and the time window. Obtained cyclic voltammograms demonstrated a diffusion-controlled reversible electron transfer reaction for Riboflavin in phosphate buffer solution (pH=7.2). The peak potential values were pH-dependent, involving the same numbers of protons and electrons. To obtain the maximum sensitivity, some effective parameters such as scan rate (10 mV/s), accumulation time (0.2 s) and potential (+400 mV), frequency (1420 Hz) and amplitude (20 mV) were optimized. As a result, determination of Riboflavin using FFT-SWV showed a linear range of response from 10 to 400 nM (R2=0.9993), with limit of detection of 0.86 nM. An acceptable recovery percent was also obtained for Riboflavin in human plasma samples as criteria of measurement applicability of the proposed modified electrode.

Fast hybrid numerical-asymptotic boundary element methods for high frequency screen and aperture problems based on least-squares collocation

We present a hybrid numerical-asymptotic (HNA) boundary element method (BEM) for high frequency scattering by two-dimensional screens and apertures, whose computational cost to achieve any prescribed accuracy remains bounded with increasing frequency. Our method is a collocation implementation of the high order hp HNA approximation space of Hewett et al. (IMA J Numer Anal 35:1698–1728, 2015), where a Galerkin implementation was studied. An advantage of the current collocation scheme is that the one-dimensional highly oscillatory singular integrals appearing in the BEM matrix entries are significantly easier to evaluate than the two-dimensional integrals appearing in the Galerkin case, which leads to much faster computation times. Here we compute the required integrals at frequency-independent cost using the numerical method of steepest descent, which involves complex contour deformation. The change from Galerkin to collocation is nontrivial because naive collocation implementations based on square linear systems suffer from severe numerical instabilities associated with the numerical redundancy of the HNA basis, which produces highly ill-conditioned BEM matrices. In this paper we show how these instabilities can be removed by oversampling, and solving the resulting overdetermined collocation system in a weighted least-squares sense using a truncated singular value decomposition. On the basis of our numerical experiments, the amount of oversampling required to stabilise the method is modest (around 25% typically suffices), and independent of frequency. As an application of our method we present numerical results for high frequency scattering by prefractal approximations to the middle-third Cantor set.

A new approach for ergonomic risk assessment integrating KEMIRA, best–worst and MCDM methods

In this study, a new three-phase ergonomic risk assessment approach was proposed for manual lifting tasks to determine which worker has the highest ergonomic risk level considering two criteria sets as lifting-related criteria and human-related criteria. In the first phase, Modified Kemeny Median Indicator Ranks Accordance (KEMIRA-M) and a novel two-dimensional best–worst method (BWM) integration were proposed for weighting ergonomic risk criteria in two sets. In this way, weighting procedure of KEMIRA-M was advanced by the proposed two-dimensional BWM in a consistent manner and subjectivity in determining the best and the worst criteria in traditional BMW was prevented by using KEMIRA-M. Thus, the weaknesses of both methods have been developed. In the second phase, the rankings of workers were determined via utilizing multi-objective optimization on the basis of simple ratio analysis, multi-objective optimization by ratio analysis (MOORA) ratio, MOORA reference point and complex proportional assessment to see how worker rankings differ despite using the same advanced weighting approach based on KEMIRA-M and two-dimensional BWM integration. Finally, to aggregate these different ranking results, technique of precise order preference was applied. In this way, different viewpoints of each ranking approach can be reflected on a single worker’s priority. The applicability of the proposed ergonomic risk assessment approach was demonstrated with a real application in tube manufacturing.

Analysis of soft and hard nanoparticle alternating multilayers for the development of theory for long-period stacking order structure prepared by Langmuir-Blodgett method

Two types of hard and soft nanoparticles with a size of 5 nm were alternately layered to adjust the multi-particle structure with high regularity, and structural analysis was performed. Specifically, we alternately transferred two kinds of single-particle layers composed of surfactant-modified organo-magnetite and a hydrophobic polymer to a solid substrate using the Langmuir-Blodget (LB) method. The morphology of two-dimensional particle integration in each single particle layer was confirmed by atomic force microscopy observations. The obtained LB multilayers exhibited almost the same periodicity, crystallite size, and lattice distortion, based on X-ray diffraction (XRD) analysis. The alternating multilayers composed of hard and soft particle monolayers were not inferior to single component multilayers in terms of periodicity and regularity. The utilization of this preparation method facilitates effective control of the period of hard and soft layers. It is asserted that the high degree of regularity was attained due to the affinity and miscibility between the organic polymer particle layer and the modified organic chains on the inorganic nanoparticle surface. The most notable result is that in the XRD data, the spacing between inorganic nanoparticles was not enhanced, and the period of the hard-soft particle correlation was confirmed. Therefore, it seems that both layers have the same high degree of regularity.

A Fast Bistatic ISAR Imaging Approach for Rapidly Spinning Targets via Exploiting SAR Technique

Because of the large range of cell migration (RCM) and nonstationary Doppler frequency modulation (DFM) produced by non-cooperative targets with rapid spinning motions, it is difficult to efficiently generate a well-focused bistatic inverse synthetic aperture radar (ISAR) by use of the conventional imaging algorithms. Utilizing the property of the inherent azimuth spatial invariance in strip-map synthetic aperture radar (SAR) imaging mode, in this work, an efficient bistatic ISAR imaging approach based on circular shift operation in the range-Doppler (RD) domain is proposed. First, echoes of rapidly spinning targets are transformed into the RD domain, whose exact analytical is derived on the basis of the principle of stationary phase (POSP). Second, the RCM is corrected by using an efficient circular shift operation in the RD domain. By doing so, the energies of a scatterer that span multiple range cells are concentrated into the same range cell, and the time-varying DFM can also be compensated along the rotating radius direction. Compared with existing methods, the proposed method has advantages in its computational complexity, avoiding the interpolation and multi-dimensional search operation, and in its satisfactory imaging performance under low signal to noise ratio (SNR) conditions thanks to the two-dimensional coherent integration gain utilized. Finally, several numerical simulations are conducted to show the validity of the proposed algorithm.

Dimerization and N\xe9el Order in Different Quantum Spin Chains Through a Shared Loop Representation

The ground-states of the spin-S antiferromagnetic chain H_{{text {AF}}} with a projection-based interaction and the spin-1/2 XXZ-chain H_{{text {XXZ}}} at anisotropy parameter Delta =cosh (lambda ) share a common loop representation in terms of a two-dimensional functional integral which is similar to the classical planar Q-state Potts model at sqrt{Q}= 2S+1 =2cosh (lambda ). The multifaceted relation is used here to directly relate the distinct forms of translation symmetry breaking which are manifested in the ground-states of these two models: dimerization for H_{{text {AF}}} at all S> 1/2, and Néel order for H_{{text {XXZ}}} at lambda >0. The results presented include: (i) a translation to the above quantum spin systems of the results which were recently proven by Duminil–Copin–Li–Manolescu for a broad class of two-dimensional random-cluster models, and (ii) a short proof of the symmetry breaking in a manner similar to the recent structural proof by Ray–Spinka of the discontinuity of the phase transition for Q>4. Altogether, the quantum manifestation of the change between Q=4 and Q>4 is a transition from a gapless ground-state to a pair of gapped and extensively distinct ground-states.

Erdélyi-Kober fractional integrals on Hardy space and BMO

The mapping properties of the multi. Erdelyi- Kober fractional integral operators on Hardy space and BMO. In particular, our main result gives the boundedness of the Erdelyi-Kober fractional integrals, the hypergeometric fractional integrals and the two-dimensional Weyl integrals on Hardy space and BMO.

Towards an efficient method to compute two-loop scalar amplitudes

We report on an ongoing work initiated by Prof. Shimizu, proposing a method to numerically compute two-loop scalar integrals as sums of two-dimensional integrals of generalised one-loop N-point functions analytically computed and integrated over some simple weight functions. The analytic computation of the generalised one-loop N-point functions in a systematic way motivates a novel approach sketched in this talk.

Solving Two-Dimensional Nonlinear Volterra Integral Equations Using Rationalized Haar Functions in the Complex Plane

In this work, two-dimensional rational Haar wavelet method has been used to solve the twodimensional Volterra integral equations. By using fixed point Banach theorem we achieved the order of convergence and the rate of convergence is O(n(2q)n). Numerical solutions of three examples are presented by applying a simple and efficient computational algorithm.

Content Analysis of Family Policy Instruments to Promote the Sustainable Development of Families in China from 1989–2019

Family policy involves a combination of policies enacted to address various family problems and improve the sustainable development of families. Evaluating family policy by considering policy instruments is conducive to optimizing policy allocation and promoting this sustainable development. This study constructs a two-dimensional analysis framework of policy instruments and policy themes and employs content analysis to conduct a quantitative analysis of 112 family policy texts issued by the Chinese government. The results show that the policy instruments used in China are not effective. The study also shows that environmental policy instruments are most frequently used, but the internal structure is unbalanced; supply-side policy instruments are moderately used; and the use of demand-side policy instruments is obviously limited. Policy themes focus excessively on “safeguard measures” and pay less attention to “parental welfare and protection”. Overall, China’s family policy is still in its infancy, as it focuses mainly on assistance and remains incomplete. Therefore, the parties responsible for the formulation of family policy should adjust and optimize the combinations of policy instruments that are employed are required to consider “general welfare”, and promote the two-dimensional integration of policy instruments and policy themes.