Complete Solution Research Articles

Uncertainties associated with integral-based solutions to geodetic boundary-value problems

Physical geodesy applies potential theory to study the Earth’s gravitational field in space outside and up to a few km inside the Earth’s mass. Among various tools offered by this theory, boundary-value problems are particularly popular for the transformation or continuation of gravitational field parameters across space. Traditional problems, formulated and solved as early as in the nineteenth century, have been gradually supplemented with new problems, as new observational methods and data are available. In most cases, the emphasis is on formulating a functional relationship involving two functions in 3-D space; the values of one function are searched but unobservable; the values of the other function are observable but with errors. Such mathematical models (observation equations) are referred to as deterministic. Since observed data burdened with observational errors are used for their solutions, the relevant stochastic models must be formulated to provide uncertainties of the estimated parameters against which their quality can be evaluated. This article discusses the boundary-value problems of potential theory formulated for gravitational data currently or in the foreseeable future used by physical geodesy. Their solutions in the form of integral formulas and integral equations are reviewed, practical estimators applicable to numerical solutions of the deterministic models are formulated, and their related stochastic models are introduced. Deterministic and stochastic models represent a complete solution to problems in physical geodesy providing estimates of unknown parameters and their error variances (mean squared errors). On the other hand, analyses of error covariances can reveal problems related to the observed data and/or the design of the mathematical models. Numerical experiments demonstrate the applicability of stochastic models in practice.

Counting QBF solutions at level two

We lift the problem of enumerative solution counting to quantified Boolean formulas (QBFs) at the second quantifier block. In contrast to the well-explored model counting problem for SAT (#SAT), where models are simply assignments to the Boolean variables of a formula, we are now dealing with tree (counter-)models reflecting the dependencies between the variables of the first and the second quantifier block. It turns out that enumerative counting on the second level does not give the complete solution count and more fine-grained view is necessary. We present a level-2 solution counting approach that works for true and false formulas. We implemented the presented approach in a counting tool exploiting state-of-the-art QBF solving technology. We present several kinds of benchmarks for testing our implementation and show that even with this very basic approach of solution enumeration the solution counts of challenging benchmarks can be found.

Compact Pollution Control and Sound Indicator Device

Abstract: The increasing urbanisation of cities globally has intensified worries about car pollution, leading to substantial environmental damage and public health risks. Current Pollution Under Control (PUC) systems, which primarily focus on reducing exhaust emissions, often encounter usability problems and neglect the issue of noise pollution. This study presents a new and innovative approach called the Compact Pollution Control and Sound Indicator Device (CPCSID), which aims to overcome these limitations. The project includes state-of-the-art sensors capable of discriminating and measuring several exhaust gases generated by cars, including nitrogen oxides (NOx), carbon monoxide (CO), and carbon dioxide (CO2). Additionally, it contains an integrated microphone to assess engine-generated noise levels. The LCD panel presents real-time data of pollution and noise, providing consumers with practical insights into the environmental effects of their car. In addition, our invention is integrated with a GSM module, which allows it to send SMS notifications to car owners. These warnings aim to promote environmentally aware behaviour and enable quick responses to reduce pollution. The small size and easy-to-use design make it suited for both individual car owners and fleet managers, providing a complete solution for reducing automobile pollution in urban areas.

Detection and analysis technologies for single biological nanoparticles

In recent years, nanoscale detection has played an increasingly important role in the research on viruses, exosomes, small bacteria, and organelles. The small size and complex biological natures of these particles, with the smallest known virus particle measuring only 17 nm in diameter and exosomes ranging from 30 nm to 150 nm in size, pose challenges to the classical large-scale (typically micron-scale) characterization methods, which has become a major obstacle in the research. The emergence of nanoscale detection and analysis technologies has filled the gap of optical microscopy, a conventional technique in this field. These technologies enable the sensitive and robust detection of objects that exceed the lower limit of optical detection, revealing the molecular composition and biological roles simultaneously. Currently, several commercialized instruments based on nanotechnology have emerged, providing complete single-particle detection solutions and achieving unique functionality based on their respective technological advantages. However, it is inevitable that these technologies have limitations in terms of application and detection capabilities, as they continue to evolve. This paper offers a thorough overview of the principles, advantages, limitations, and future development trends of several mainstream commercial instruments, aiming to serve researchers in selecting and utilizing these technologies.

Certain functional identities on division rings of characteristic two

Let D be a noncommutative division ring. In a recent paper, Lee and Lin proved that if charD≠2, the only solution of additive maps f,g on D satisfying the identity f(x)=xng(x−1) on D∖{0} with n≠2 a positive integer is the trivial case, that is, f=0 and g=0. Applying Hua's identity and the theory of functional and generalized polynomial identities, we give a complete solution of the same identity for any nonnegative integer n if charD=2.

Identifying epileptogenic abnormality by decomposing intracranial EEG and MEG power spectra

BackgroundAccurate identification of abnormal electroencephalographic (EEG) activity is pivotal for diagnosing and treating epilepsy. Recent studies indicate that decomposing brain activity into periodic (oscillatory) and aperiodic (trend across all frequencies) components can illuminate the drivers of spectral activity changes. New methodsWe analysed intracranial EEG (iEEG) data from 234 subjects, creating a normative map. This map was compared to a cohort of 63 patients with refractory focal epilepsy under consideration for neurosurgery. The normative map was computed using three approaches: (i) relative complete band power, (ii) relative band power with the aperiodic component removed, and (iii) the aperiodic exponent. Abnormalities were calculated for each approach in the patient cohort. We evaluated the spatial profiles, assessed their ability to localize abnormalities, and replicated the findings using magnetoencephalography (MEG). ResultsNormative maps of relative complete band power and relative periodic band power exhibited similar spatial profiles, while the aperiodic normative map revealed higher exponent values in the temporal lobe. Abnormalities estimated through complete band power effectively distinguished between good and bad outcome patients. Combining periodic and aperiodic abnormalities enhanced performance, like the complete band power approach. Comparison with existing methods and conclusionsSparing cerebral tissue with abnormalities in both periodic and aperiodic activity may result in poor surgical outcomes. Both periodic and aperiodic components do not carry sufficient information in isolation. The relative complete band power solution proved to be the most reliable method for this purpose. Future studies could investigate how cerebral location or pathology influences periodic or aperiodic abnormalities.

Complete Solutions for the Approximate Synthesis of Spherical Four-Bar Function Generators

Abstract Kinematic synthesis to meet an approximate motion specification naturally forms a constrained optimization problem. Instead of using local methods, we conduct global design searches by direct computation of all critical points. The idea is not new, but performed at scale is only possible through modern polynomial homotopy continuation solvers. Such a complete computation finds all minima, including the global, which allows for a full exploration of the design space, whereas local solvers can only find the minimum nearest to an initial guess. We form equality-constrained objective functions that pertain to the synthesis of spherical four-bar linkages for approximate function generation. We consider the general case where all mechanism dimensions may vary and a more specific case that enables the placement of ground pivots. The former optimization problem is shown to permit 268 sets of critical points, and the latter permits 61 sets. Critical points are classified as saddles or minima through a post-process eigenanalysis of the projected Hessian. The discretization points are contained within the coefficients of the stationarity polynomials, so the algebraic structure of the synthesis equations remains invariant to the number of points. The results of our computational work were used to design a mechanism that coordinates the folding wings. We also use this method to parameterize mechanism dimensions for a family of hyperbolic curves.

Vortex shedding from bluff bodies: a conformal mapping approach

A model to calculate flow around bluff bodies of various geometries is presented. A conformal map between the plane of the bluff body and the plane of a unit circular cylinder is established by using a combination of Karman–Trefftz transformations and Fornberg’s method. Flow in the circle plane is calculated using the authors’ Hybrid Potential Flow (HPF) model and mapped back to the shape plane. By joining this calculated near-body flow with von Karman’s model for a vortex wake, forces due to vortex shedding and shedding frequencies are calculated. In this manner, a complete solution for the flow around bluff bodies of various geometries is established. Results for two shapes are presented, along with recommendations for further work.

Q3D: a complete solution for quality control and inspection in additive manufacturing processes

PurposeThis paper aims to present an integrated system designed for quality control and inspection in additive manufacturing (AM) technologies.Design/methodology/approachThe study undertakes a comprehensive examination of the process in three distinct stages. First, the quality of the feedstock material is inspected during the preprocessing step. Subsequently, the main research topic of the study is directed toward the 3D printing process itself with real-time monitoring procedures using computer vision methods. Finally, an evaluation of the 3D printed parts is conducted, using measuring methods and mechanical experiments.FindingsThe main results of this technical paper are the development and presentation of an integrated solution for quality control and inspection in AM processes.Originality/valueThe proposed solution entails the development of a promising tool for the optimization of the quality in 3D prints based on machine learning algorithms.

Quantum graph wave external triggering: Energy transfer and damping.

The propagation of wave trains resulting from a local external trigger inside a network described by a metric graph is analyzed using quantum graph theory. The external trigger is a finite-time perturbation imposed at one vertex of the graph, leading to a consecutive wave train into the network, supposedly at rest before the applied external perturbation. A complete analytical solution for the induced wave train is found having a specific spectrum as well as mode's amplitudes. Furthermore the precise condition by which the external trigger can transfer a maximal energy to any specific natural mode of the quantum graph is derived. Finally, the wave damping associated with boundary-layer dissipation is computed within a multiple time-scale asymptotic analysis. Exponential damping rates are explicitly found related to their corresponding mode's eigenvalue. Each mode energy is then obtained, as well as their exponential damping rate. The relevance of these results to the physics of waves within networks are discussed.

Thermocapillary migration of a compound drop in an arbitrary viscous flow

The thermocapillary migration of a concentric compound drop in an arbitrary viscous flow under the consideration of negligible Reynolds number is investigated. The thermocapillary effect refers to the migration of a drop under the influence of a temperature gradient. The thermal and hydrodynamic problems are examined. The thermal field is governed by the heat conduction equation whereas the hydrodynamic fluid velocities are governed by the linearized Navier–Stokes equations. Presence of temperature gradient results in variation of the interfacial tension which is assumed to depend on temperature linearly. Variation of interfacial gradient leads to the coupling of the hydrodynamic problem with the thermal problem through the boundary condition. A complete general solution of Stokes equations is utilized to obtain closed-form expressions for the velocity vector and pressure. The hydrodynamic forces acting on the compound drop are obtained and expressed in terms of Fax́en’s law. Some important asymptotic limiting cases of hydrodynamic drag are also derived. The hydrodynamic drag for cases of uniform flow, shear flow, and heat source with the known ambient flow are derived and it is found that in the case of shear flow, the hydrodynamic drag is contributed only by the thermal component and the shear flow has no effect on it. The obtained results for drag and torque in the limiting cases are in agreement with the existing results in the literature. Furthermore, the migration velocity of the compound drop is obtained by equating the hydrodynamic drag force to zero. The results obtained for migration velocity are explained with the aid of graphs. The migration velocity is found to be a monotonic function of the Marangoni number and the radius of the innermost drop.

A general method for the estimation of moments of substitution number in molecular evolution

The random variable ‘substitution number’ N t , i.e.the number of mutations that have accumulated in a sequence under neutral evolution during a time t, is a cornerstone of the field of molecular evolution. We show here that a complete solution of the moments of this random variable can be obtained explicitly by recurrence, using a simple matrix shift method. This result leads to simple expressions for both the short and long time limits of the moments that can be computed directly from the substitution matrix used to model the neutral evolution. The method developed here is also used to compute the moments of the complementary variable, T n , the time it takes to accumulate n mutations. The method we develop here necessitates only elementary operations on the substitution matrix and does not involve spectral decomposition.

Dissolution studies during the mechanical alloying of Inconel-718 superalloy based elemental powders

Inconel-718 superalloy with a nominal composition of Ni-19.47Fe-18Cr-0.5Al-1Ti-5 Nb-3Mo-0.02Co-0.003B was synthesized by mechanical alloying of elemental powders. Mechanical alloying was carried out in a high energy Simoloyer attritor ball mill. A sufficient quantity of powder was removed at milling intervals of 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, and 22 h for characterization by XRD, SEM, and TEM. The dissolution time of different alloying elements have been discussed in view of their atomic scattering factors and Hume-Rothery principle with the help of XRD and TEM (SAED) analysis. Complete dissolution of Fe took place at 6 h of milling, Nb at 10 h, Cr at 18 h while Mo took 22 h. A complete single-phase solid solution of γ(FCC) matrix was obtained at 22 h of milling. Crystallite size was found to decrease while the lattice parameter increased with milling time. Lattice-strain and dislocation density increased initially and later decreased due to the dynamic recrystallization process taking place within the powder particles during milling. SEM analysis indicated flattening of powder particles during the initial (0 h–4 h) stages of milling followed by heavy cold-welding at the intermediate stages (6 h–12 h). In the final stages of milling (18 h–22 h), an equilibrium between cold welding and fracturing was reached.

Information bottleneck-based Hebbian learning rule naturally ties working memory and synaptic updates.

Deep neural feedforward networks are effective models for a wide array of problems, but training and deploying such networks presents a significant energy cost. Spiking neural networks (SNNs), which are modeled after biologically realistic neurons, offer a potential solution when deployed correctly on neuromorphic computing hardware. Still, many applications train SNNs offline, and running network training directly on neuromorphic hardware is an ongoing research problem. The primary hurdle is that back-propagation, which makes training such artificial deep networks possible, is biologically implausible. Neuroscientists are uncertain about how the brain would propagate a precise error signal backward through a network of neurons. Recent progress addresses part of this question, e.g., the weight transport problem, but a complete solution remains intangible. In contrast, novel learning rules based on the information bottleneck (IB) train each layer of a network independently, circumventing the need to propagate errors across layers. Instead, propagation is implicit due the layers' feedforward connectivity. These rules take the form of a three-factor Hebbian update a global error signal modulates local synaptic updates within each layer. Unfortunately, the global signal for a given layer requires processing multiple samples concurrently, and the brain only sees a single sample at a time. We propose a new three-factor update rule where the global signal correctly captures information across samples via an auxiliary memory network. The auxiliary network can be trained a priori independently of the dataset being used with the primary network. We demonstrate comparable performance to baselines on image classification tasks. Interestingly, unlike back-propagation-like schemes where there is no link between learning and memory, our rule presents a direct connection between working memory and synaptic updates. To the best of our knowledge, this is the first rule to make this link explicit. We explore these implications in initial experiments examining the effect of memory capacity on learning performance. Moving forward, this work suggests an alternate view of learning where each layer balances memory-informed compression against task performance. This view naturally encompasses several key aspects of neural computation, including memory, efficiency, and locality.

An extended graphical solution for undrained cylindrical cavity expansion in K0‐consolidated Mohr–Coulomb soil

AbstractThis paper develops a general and complete solution for the undrained cylindrical cavity expansion problem in nonassociated Mohr‐Coulomb soil under nonhydrostatic initial stress field (i.e., arbitrary values of the earth pressure coefficient), by expanding a unique and efficient graphical solution procedure recently proposed by Chen and Wang in 2022 for the special in situ stress case with . It is interesting to find that the cavity expansion deviatoric stress path is always composed of a series of piecewise straight lines, for all different case scenarios of K0 being involved. When the cavity is sufficiently expanded, the stress path will eventually end, exclusively, in a major sextant with Lode angle θ in between and or on the specific line of . The salient advantage/feature of the present general graphical approach lies in that it can deduce the cavity expansion responses in full closed form, nevertheless being free of the limitation of the intermediacy assumption for the vertical stress and of the difficulty existing in the traditional zoning method that involves cumbersome, sequential determination of distinct Mohr–Coulomb plastic regions. Some typical results for the desired cavity expansion curves and the limit cavity pressure are presented, to investigate the impacts of soil plasticity parameters and the earth pressure coefficient on the cavity responses. The proposed graphical method/solution will be of great value for the interpretation of pressuremeter tests in cohesive‐frictional soils.

Mo-BiVO4 Photocatalytically Modified Ceramic Ultrafiltration Membranes for Enhanced Water Treatment Efficiency.

This study highlights the effectiveness of photocatalytically modified ceramic ultrafiltration (UF) membranes in alleviating two major drawbacks of membrane filtration technologies. These are the generation of a highly concentrated retentate effluent as a waste stream and the gradual degradation of the water flux through the membrane due to the accumulation of organic pollutants on its surface. The development of two types of novel tubular membranes, featuring photocatalytic Mo-BiVO4 inverse opal coatings, demonstrated a negligible impact on water permeance, ensuring consistent filtration and photocatalytic efficiency and suggesting the potential for maintaining membrane integrity and avoiding the formation of highly concentrated retentate effluents. Morphological analysis revealed well-defined coatings with ordered domains and interconnected macropores, confirming successful synthesis of Mo-BiVO4. Raman spectroscopy and optical studies further elucidated the composition and light absorption properties of the coatings, particularly within the visible region, which is vital for photocatalysis driven by vis-light. Evaluation of the tetracycline removal efficiency presented efficient adsorption onto membrane surfaces with enhanced photocatalytic activity observed under both UV and vis-light. Additionally, vis-light irradiation facilitated significant degradation, showcasing the versatility of the membranes. Total Organic Carbon (TOC) analysis corroborated complete solute elimination or photocatalytic degradation without the production of intermediates, highlighting the potential for complete pollutant removal. Overall, these findings emphasize the promising applications of Mo-BiVO4 photocatalytic membranes in sustainable water treatment and wastewater remediation processes, laying the groundwork for further optimization and scalability in practical water treatment systems.

Tri-composed fuzzy relation inequality with weighted-max-min composition and the relevant min-max optimization problem

In the existing works, the classical fuzzy relation inequality (FRI) with double-composed operators has been introduced to describe the P2P network system. In this work, considering the successful rate of the line connection within the P2P network system, we establish the so-called tri-composed FRI, with a weighted-max-min composition, for the first time. We study the solutions induced through paths and further construct the complete solution set of the tri-composed FRI using the path-induced solutions. Moreover, the whole solution set could be fully determined by all the path-induced solutions and its unique maximum solution. Furthermore, considering a specific optimal management objective in the P2P network, we further study the min-max optimization problem with the tri-composed FRI constraints. A path-based algorithm is proposed for handling the problem we studied, accompanied by an illustrative example.

Dielectrophoresis: Measurement technologies and auxiliary sensing applications.

Dielectrophoresis (DEP), which arises from the interaction between dielectric particles and an aqueous solution in a nonuniform electric field, contributes to the manipulation of nano and microparticles in many fields, including colloid physics, analytical chemistry, molecular biology, clinical medicine, and pharmaceutics. The measurement of the DEP force could provide a more complete solution for verifying current classical DEP theories. This review reports various imaging, fluidic, optical, and mechanical approaches for measuring the DEP forces at different amplitudes and frequencies. The integration of DEP technology into sensors enables fast response, high sensitivity, precise discrimination, and label-free detection of proteins, bacteria, colloidal particles, and cells. Therefore, this review provides an in-depth overview of DEP-based fabrication and measurements. Depending on the measurement requirements, DEP manipulation can be classified into assistance and integration approaches to improve sensor performance. To this end, an overview is dedicated to developing the concept of trapping-on-sensing, improving its structure and performance, and realizing fully DEP-assisted lab-on-a-chip systems.

The in vitro mechanism of Vaspinregulates the proliferation and steroidogenesis of rat lutein cells

Objective Stable luteal cell function is an important prerequisite for reproductive ability and embryonic development. However, luteal insufficiency seriously harms couples who have the desire to have a pregnancy, and the most important thing is that there is no complete solution. In addition, Vaspin has been shown to have regulatory effects on luteal cells, but the complex mechanisms involved have not been fully elucidated. Therefore, this study aimed to explore the effect of Vaspin on rat luteal cells and its mechanism. Methods Granulosa lutein cells separated from the ovary of female rats were incubated for 24h with gradient concentrations of Vaspin, and granulosa lutein cells incubated with 0.5% bovine serum albumin were used as controls. The proliferation, apoptosis, angiogenesis, progesterone (P4) and estradiol (E2) were detected by CCK-8, Anneixn-FITC/PI staining, angiogenesis experiment and ELISA. Western blot was applied to observe the expression levels of proteins related to cell proliferation, apoptosis, angiogenesis and MEK/MAPK signaling pathway. Results Compared with the Control group, Vaspin could significantly up-regulate the proliferation of granulosa lutein cells and reduce the apoptosis. Moreover, Vaspin promoted the angiogenesis of granulosa lutein cells and the production of P4 and E2 in a concentration-dependent manner. Furthermore, Vaspin up-regulated the CyclinD1, CyclinB1, Bcl2, VEGFA and FGF-2 expression in granulosa lutein cells, and down-regulated the level of Bax. Also, Vaspin increased the p-MEK1 and p-p38 levels. Conclusion Vaspin can up-regulate the proliferation and steroidogenesis of rat luteal cells and reduce apoptosis, which may be related to the influence of MEK/MAPK activity.

The La2Pd3(Si, Ge)5 complete solid solution: Crystal structure, chemical bonding, and volume chemistry

The La2Pd3Si5 intermetallic and the La2Pd3(SixGe1-x)5 solid solution were targeted for structural and computational investigations. The ternary compound and quaternary alloys with varying silicon contents (x = 0.25, 0.50, 0.70, 0.75) were prepared by arc melting and turned out to crystalize with the oI40–U2Co3Si5 (Ibam, N. 72) type structure based on powder X-ray diffraction data. The crystal structure of La2Pd3Si5 was additionally solved through X-ray diffraction on single crystal grown by recrystallization in Sn flux. Chemical bonding investigations based on QTAIM effective charges and DOS/(I)COHP analysis indicate the formation of heteropolar interactions between Si and the surrounding La/Pd metals, and between La and Pd. Covalently bonded zigzag chains of Si are also formed and considered to be the main responsible for the higher melting point of La2Pd3Si5, measured by DSC, with respect to that of La2Pd3Ge5. The formation of a complete solid solution between La2Pd3Si5 and La2Pd3Ge5 was confirmed and refined unit cell parameters and volumes change linearly with composition, displaying a Vegard trend. The calculation of atomic volumes on a quantum chemical basis (QTAIM) provides detailed insights into the volume chemistry of La2Pd3(SixGe1-x)5. Through this analysis La is found to be responsible, together with the gradual substitution of Ge with Si, for the volume contraction.