Analytical Condition Research Articles

Dissipation of AGN Jets in a Clumpy Interstellar Medium

Accreting supermassive black holes frequently power jets that interact with the interstellar medium (ISM)/circumgalactic medium, regulating star formation in the galaxy. Highly supersonic jets launched by active galactic nuclei (AGN) power a cocoon that confines them and shocks the ambient medium. We build on the models of narrow conical jets interacting with a smooth ambient medium, including the effect of dense clouds, which are an essential ingredient of a multiphase ISM. The key physical ingredient of this model is that the clouds along the supersonic jet beam strongly decelerate the jet head but the subsonic cocoon easily moves around the clouds without much resistance. We propose scalings for important physical quantities—cocoon pressure, head and cocoon speed, and jet radius. For the first time, we obtain the analytic condition on the ambient medium’s clumpiness for the jet to dissipate within the cocoon and verify it with numerical simulations of conical jets interacting with a uniform ISM with embedded spherical clouds. A jet is defined to be dissipated when the cocoon speed exceeds the speed of the jet head. We compare our models with more sophisticated numerical simulations and direct observations of jet–ISM interaction (e.g., quasar J1316+1753), and we discuss implications for the Fermi/eROSITA bubbles. Our work also motivates effective subgrid models for AGN jet feedback in a clumpy ISM unresolved by the present generation of cosmological galaxy formation simulations.

Electrothermal filamentation of igniting plasmas.

Dense, hot plasmas are susceptible to the electrothermal instability: a collisional process which permits temperature perturbations in electron currents to grow. It is shown here that linearizing a system comprised of two opposing currents and a mobile ion background as three distinct fluids yields unstable modes with rapid growth rates (∼10^{13}s^{-1}) for wavenumbers below a threshold k_{th}. An analytical threshold condition is derived, this being surpassed for typical hot-spot and shell parameters. Particle-in-cell simulations successfully benchmark the predicted growth rates and threshold behavior. Electrothermal filamentation within the shell will impact the burn wave propagation into the cold fuel and resulting burn dynamics.

Canonical torsor bundles of prescribed rational functions on complex curves

The prescribed rational functions constitute a subset of rational functions satisfying certain symmetry and analyticity conditions. Over a smooth complex curve [Formula: see text], we construct explicitly a bundle [Formula: see text] with values in the prescribed rational functions. An intrinsic coordinate-independent formulation (the main result of the paper, Proposition 1) for such bundles is given. The construction presented in this paper is useful for studies of the canonical cosimplicial cohomology of infinite-dimensional Lie algebras on smooth manifolds, as well as for the purposes of conformal field theory and the theory of foliations.

Dynamics and bifurcations in genetic circuits with fibration symmetries.

Circuit building blocks of gene regulatory networks (GRN) have been identified through the fibration symmetries of the underlying biological graph. Here, we analyse analytically six of these circuits that occur as functional and synchronous building blocks in these networks. Of these, the lock-on, toggle switch, Smolen oscillator, feed-forward fibre and Fibonacci fibre circuits occur in living organisms, notably Escherichia coli; the sixth, the repressilator, is a synthetic GRN. We consider synchronous steady states determined by a fibration symmetry (or balanced colouring) and determine analytic conditions for local bifurcation from such states, which can in principle be either steady-state or Hopf bifurcations. We identify conditions that characterize the first bifurcation, the only one that can be stable near the bifurcation point. We model the state of each gene in terms of two variables: mRNA and protein concentration. We consider all possible 'admissible' models-those compatible with the network structure-and then specialize these general results to simple models based on Hill functions and linear degradation. The results systematically classify using graph symmetries the complexity and dynamics of these circuits, which are relevant to understand the functionality of natural and synthetic cells.

A Novel Apparatus for the Fully Automated Extraction and Online Liquid Chromatographic Analysis of Solid Environmental Samples: Application to the Pressurized Hot Water Extraction of Pharmaceuticals in Soil.

A new self-assembled apparatus for the extraction of solid samples was designed and implemented to perform a recirculated pressurized hot water extraction (R-PHWE) directly coupled to liquid chromatography-tandem mass spectrometry. To investigate the potential of this new extraction apparatus, 34 target pharmaceutical compounds were analyzed in loam, silt-loam, and silty-clay-loam soils. The target analytes were characterized by heterogeneous physicochemical properties (e.g., -1.60 ≤ log D ≤ 5.91 at pH = 7.2, i.e., at the mean pH values of the three soils). Design of experiments (DoE) was used to identify the best extraction conditions for the target analytes by studying temperature, pressure, and number of extraction cycles. The results of DoE optimization pointed out the significant influence of the number of cycles on recovery. The application of DoE set point to the three reference soils provided recoveries ≥60% for 21-25 out the 34 target analytes, depending on soil. Good recovery precision (<25%) and moderate suppressive matrix effect (≤40%) were found for most target analytes, regardless of the soil considered. The optimized R-PHWE procedure evidenced statistically higher recoveries for 16 out of 34 target analytes when compared to conventional off-line dynamic PHWE.

On prime end distortion estimates of mappings with the Poletsky condition in domains with the Poincar´e inequality

This article is devoted to the study of mappings with bounded andfinite distortion defined in some domain of the Euclidean space. Weconsider mappings that satisfy some upper estimates for thedistortion of the modulus of families of paths, where the order ofthe modulus equals to $p,$ $n-1&lt;p\leqslant n.$ The main problemstudied in the manuscript is the investigation of the boundarybehavior of such mappings, more precisely, the distortion of thedistance under mappings near boundary points. The publication isprimarily devoted to definition domains with ``bad boundaries'', inwhich the mappings not even have a continuous extension to theboundary in the Euclidean sense. However, we introduce the conceptof a quasiconformal regular domain in which the specified continuousextension is valid and the corresponding distance distortionestimates are satisfied; however, both must be understood in thesense of the so-called prime ends. More precisely, such estimateshold in the case when the mapping acts from a quasiconformal regulardomain to an Ahlfors regular domain with the Poincar\'e inequality.The consideration of domains that are Ahlfors regular and satisfythe Poincar\'e inequality is due to the fact that, lower estimates forthe modulus of families of paths through the diameter of thecorresponding sets hold in these domains. (There are the so-calledLoewner-type estimates). We consider homeomorphisms and mappingswith branching separately. The main analytical condition under whichthe results of the paper were obtained is the finiteness of theintegral averages of some majorant involved in the defining modulusinequality under infinitesimal balls. This condition includes thesituation of quasiconformal and quasiregular mappings, because forthem the specified majorant is itself bounded in a definitiondomain. Also, the results of the article are valid for more generalclasses for which Poletsky-type upper moduli inequalities aresatisfied, for example, for mappings with finite length distortion.

Development and Validation of Ultra-Performance Liquid Chromatography (UPLC) Method for Simultaneous Quantification of Hydrochlorothiazide, Amlodipine Besylate, and Valsartan in Marketed Fixed-Dose Combination Tablet

Fixed-dose combination therapy is considered a practical approach in the treatment of various diseases, as it can simultaneously target different mechanisms of action that achieve the required therapeutic efficacy through a synergistic effect. A combination of hydrochlorothiazide (HTZ), amlodipine (AMD), and valsartan (VLS) has been created for the treatment of hypertension. Therefore, the aim of this study was to develop an optimized UPLC method for the simultaneous quantification of this combination. A DoE at a level of 32 was used to investigate the effects of column temperature (20, 30, and 40 °C) and formic acid concentration (0.05, 0.15, and 0.25%) on the retention time of each active pharmaceutical ingredient (API), the peak area, and the peak symmetry, as well as the resolution between HTZ-AMD and AMD-VLS peaks. The optimized analytical method was validated and used to extract the three APIs from the marketed product. The optimized analytical condition with a column temperature of 27.86 °C and a formic acid concentration of 0.172% showed good separation of the three APIs in 1.62 ± 0.006, 3.59 ± 0.002, and 3.94 ± 0.002 min for HTZ, AMD, and VST, respectively. The developed method was linear with the LOQ for a HTC, AMD, and VST of 0.028, 0.038, and 0.101 ppm, respectively. Moreover, the developed assay was sustainable and robust, with an RSD % of less than 2%. The application of this method in the extraction of HTZ, AMD, and VST from the Exforge® marketed product showed good separation with a measurable drug content of 23.5 ± 0.7, 9.68 ± 0.1, and 165.2 ± 5.2 mg compared to the label claims of 25/10/160 for HTZ, AMD, and VST, respectively.

Detangling the quantum tapestry of intrachannel interference in below-threshold nonsequential double ionization with few-cycle laser pulses

We perform a systematic analysis of single-channel quantum interference in laser-induced nonsequential double ionization with few-cycle pulses, using the strong-field approximation. We focus on a below-threshold intensity for which the recollision-excitation with subsequent ionization (RESI) mechanism is prevalent. We derive and classify several analytic interference conditions for single-channel RESI in arbitrary driving fields and address specific issues for few-cycle pulses. Since the cycles in a short pulse are no longer equivalent, there are several events whose dominance varies. We quantify this dominance for single excitation channels by proposing a dominance parameter. Moreover, there will be many types of superimposed interference fringes that must be taken into consideration. We find an intricate tapestry of patterns arising from phase differences related to symmetrization, temporal shifts and a combination of exchange and event interference. Published by the American Physical Society 2024

Fabric phase sorptive extraction increases the accuracy of liquid chromatography-fluorescence detection of zearalenone in food samples

ABSTRACT The accuracy of mycotoxins detection in the food samples has always been controversial and more sensitive methods help better regulatory activities and, therefore, the quality of final products. Zearalenone is a toxic substance from mycotoxins mainly produced by Fusarium fungi that has proven endocrine effects and is potentially carcinogenic. This research aimed to apply the fabric phase sorptive extraction (FPSE) technique to the liquid chromatography- fluorescence detection method to increase the sensitivity and accuracy of zearalenone extraction and determination in food samples. Applying graphene nanoparticles in the sol-gel process modifies the method depending on the amount of nanoparticles, volume and type of the back-extraction solvent, sample pH, ionic strength, and back-extraction time, which are all considered and investigated. At analytical conditions, the limit of quantification (LOQ) 16.57 and detection (LOD) of 4.97 ng/mL were observed. The method’s accuracy was determined by three spiking levels of 100, 150, and 200 ng/mL in the real samples. The mean recovery percentage in wheat were 61.69, 70.56, and 97.95%, and in the rice, 58.13, 66.00, and 102.59, respectively. The average percentages of the relative standard deviation of the instrument for intra-and inter-laboratory repeatability were less than 1.7%. This work provided a superior analytical condition to the conventional detection procedures in food safety laboratories.

Bohr–Sommerfeld quantization condition for self-adjoint Dirac operators

We study the eigenvalue problem for a self-adjoint 1D Dirac operator. It is known that, near an energy level where the square of the potential makes a simple well, the eigenvalues are approximated by a Bohr–Sommerfeld type quantization rule. A remarkable difference from the Schrödinger case appears in the Maslov correction term. This fact was recently found by Hirota [Real eigenvalues of a non-self-adjoint perturbation of the self-adjoint Zakharov–Shabat operator, J. Math. Phys. 58 (2017) 102–108] under the analyticity condition of the potential using a complex WKB method. In this paper, we approach this problem with a microlocal technique focusing on the asymptotic behavior of the eigenfunction along the characteristic set to generalize the result to [Formula: see text] potentials.

The Fourier spectrum and sumset type problems

AbstractWe introduce and study the Fourier spectrum which is a continuously parametrised family of dimensions living between the Fourier dimension and the Hausdorff dimension for both sets and measures. We establish some fundamental theory and motivate the concept via several applications, especially to sumset type problems. For example, we study dimensions of convolutions and sumsets, and solve the distance set problem for sets satisfying certain Fourier analytic conditions.

A mathematical model to study low-dose metronomic scheduling for chemotherapy

Metronomic chemotherapy refers to the frequent administration of chemotherapeutic agents at a lower dose and presents an attractive alternative to conventional chemotherapy with encouraging response rates. However, the schedule of the therapy, including the dosage of the drug, is usually based on empiricism. The confounding effects of tumor-endothelial-immune interactions during metronomic administration of drugs have not yet been explored in detail, resulting in an incomplete assessment of drug dose and frequency evaluations. The present study aimed to gain a mechanistic understanding of different actions of metronomic chemotherapy using a mathematical model. We have established an analytical condition for determining the dosage and frequency of the drug depending on its clearance rate for complete tumor elimination. The model also brings forward the immune-mediated clearance of the tumor during the metronomic administration of the chemotherapeutic agent. The results from the global sensitivity analysis showed an increase in the sensitivity of drug and immune-mediated killing factors toward the tumor population during metronomic scheduling. Our results emphasize metronomic scheduling over the maximum tolerated dose (MTD) and define a model-based approach for approximating the optimal schedule of drug administration to eliminate tumors while minimizing harm to the immune cells and the patient’s body.

Energy-Efficient Distributed Formation Control of Sampled-Data Multiagent Systems With Packet Losses.

This article investigates an energy-efficient formation control problem for multiagent systems with sampled data and random packet losses. A Bernoulli stochastic variable is used to describe packet losses, which is defined relative to the transmission energy consumed by antennas. A distributed sampled-data formation control law is designed and some analytic sufficient conditions on the formation control are derived. It is revealed that the sampling period, control parameters, network topology, as well as the transmission energy used by sensors impose inherent limitations in achieving the formation. Also, a method for searching the minimum allowable transmission energy is presented. Finally, numerical simulations are shown for illustration and verification.

Nonlinear spreading behavior across multi-platform social media universe.

Understanding how harmful content (mis/disinformation, hate, etc.) manages to spread among online communities within and across social media platforms represents an urgent societal challenge. We develop a non-linear dynamical model for such viral spreading, which accounts for the fact that online communities dynamically interconnect across multiple social media platforms. Our mean-field theory (Effective Medium Theory) compares well to detailed numerical simulations and provides a specific analytic condition for the onset of outbreaks (i.e., system-wide spreading). Even if the infection rate is significantly lower than the recovery rate, it predicts system-wide spreading if online communities create links between them at high rates and the loss of such links (e.g., due to moderator pressure) is low. Policymakers should, therefore, account for these multi-community dynamics when shaping policies against system-wide spreading.

Distributed Nash Equilibrium Seeking and Disturbance Rejection for High-Order Integrators Over Jointly Strongly Connected Switching Networks.

In this article, we study the problem of Nash equilibrium (NE) seeking of N -player games with high-order integrator agents over jointly strongly connected networks. The same problem was studied recently over static, undirected, and connected networks. Since a jointly strongly connected network can be directed and disconnected at every time instant, our result strictly includes the existing results as special cases. Moreover, in addition to some analytic conditions on the payoff functions, the existing results also rely on the satisfaction of an inequality involving some Lipschitz constant and the smallest nonzero eigenvalue of the Laplacian of the network graph. By adopting a different approach, our result does not rely on the satisfaction of this inequality. Furthermore, our result can also be extended to the case where the additive disturbances are imposed on the input of each agent. Our design is illustrated by two numerical examples.

Prefrontal engagement predicts the effect of museum visit on psychological well-being: an fNIRS exploration.

Recent research suggests that museum visits can benefit psychological well-being by reducing symptoms of stress and anxiety. However, these reported relaxing effects remain inconsistent between studies. Shedding light on the underlying cerebral mechanisms of museum visits might support a better understanding of how it affects psychological well-being. This study aimed to investigate the prefrontal engagement evoked by artwork analysis during a museum visit and to determine if these prefrontal substrates are associated with the museum's effect on psychological well-being in older adults. Nineteen adults aged between 65 and 79, toured a Baroque-style exhibit at the Montreal Museum of Fine Arts for approximately 20 minutes while equipped with a near-infrared spectroscopy system measuring the prefrontal cortex's hemodynamic activity. For each painting, participants received the instruction to either (1): analyze the painting and produce a personal interpretation of its signification (analytic condition) or (2) visualize the painting without any specific thoughts (visualization condition). Questionnaires measuring stress, anxiety, and well-being were administered before and after the visit. Sixteen older women (71.5 ± 4 years) were included in the analyses. Results showed that, at the group level, the analytic condition was associated with an increased activation pattern in the left ventrolateral prefrontal region, typically related to attentional processes (not observed in the visualization condition). The activation associated with the analytic condition predicted pre-/post-visit reductions in self-reported anxiety and stress in the sample of older women. These observations suggest that the level of engagement of attentional processes during artwork analysis may play a major role in the effect of a museum's visit on self-reported symptoms of anxiety.

Analytic States in Quantum Field Theory on Curved Spacetimes

We discuss high energy properties of states for (possibly interacting) quantum fields in curved spacetimes. In particular, if the spacetime is real analytic, we show that an analogue of the timelike tube theorem and the Reeh–Schlieder property hold with respect to states satisfying a weak form of microlocal analyticity condition. The former means the von Neumann algebra of observables of a spacelike tube equals the von Neumann algebra of observables of a significantly bigger region that is obtained by deforming the boundary of the tube in a timelike manner. This generalizes theorems by Araki (Helv Phys Acta 36:132–139, 1963) and Borchers (Nuovo Cim (10) 19:787–793, 1961) to curved spacetimes.

Including Neutrino-driven Convection in the Force Explosion Condition to Predict Explodability of Multidimensional Core-collapse Supernovae (FEC+)

Most massive stars end their lives with core collapse. However, it is not clear which explode as a core-collapse supernova (CCSN), leaving behind a neutron star, and which collapse to a black hole, aborting the explosion. One path to predict explodability without expensive multidimensional simulations is to develop analytic explosion conditions. These analytic conditions also provide a deeper understanding of the explosion mechanism and they provide some insight into why some simulations explode and some do not. The analytic force explosion condition (FEC) reproduces the explosion conditions of spherically symmetric CCSN simulations. In this follow-up manuscript, we include the dominant multidimensional effect that aids explosion—neutrino-driven convection—in the FEC. This generalized critical condition (FEC+) is suitable for multidimensional simulations and has potential to accurately predict explosion conditions of two- and three-dimensional CCSN simulations. We show that adding neutrino-driven convection reduces the critical condition by ∼30%, which is consistent with previous multidimensional simulations.

Fe Kα XANES, Fe Kβ HERFD XANES and EPMA flank method determinations of the oxidation state of Fe in garnet

The ferric to total iron ratios (Fe3+/∑Fe) of garnets can be paired with thermodynamic mineral activity models to quantify the oxygen fugacity of garnet-bearing rocks. However, techniques with a high analytical and spatial resolution are necessary to distinguish differences in garnet Fe3+/∑Fe ratios at the percent level and to accurately measure garnets that are zoned or contain inclusions. We acquired conventional Fe Kα and high-resolution energy fluorescence detection (HERFD) Fe Kβ X-ray absorption near edge structure (XANES) spectra and electron microprobe flank method analyses on a suite of 27 peridotitic and eclogitic garnets with Fe3+/∑Fe ratios previously determined by Mössbauer spectroscopy to evaluate the precision of each technique. We examined variations in the energy and intensity of three XANES spectral features as a function of Fe3+/∑Fe ratios: 1) the intensity ratio of two-post edge features (I-ratio; Fe Kα only); 2) the energy of the Fe edge at 90% normalized intensity (E0.9; Fe Kα only) and 3) the pre-edge centroid energy (Fe Kα and HERFD Fe Kβ). In accordance with previous work, we find the energies of garnet pre-edge centroids are relatively insensitive to Fe3+/∑Fe ratios. The I-ratios of peridotitic and eclogitic garnets are offset from each other at low Fe3+/∑Fe ratios (≤0.13); I-ratio garnet XANES calibrations are composition-specific. The E0.9 feature is independent of garnet major element composition in spectra that have been corrected for the effects of self-absorption. We produce two Fe Kα garnet XANES calibrations based on variations in the E0.9 feature; one calibration with all garnet reference materials included (Fe3+/∑Fe up to 1.0; “all garnet calibration”) and another calibration specific to garnets with low Fe3+/∑Fe ratios (“low ferric calibration”). Fe3+/∑Fe ratios calculated from the mean of up to 25 flank method measurements on eight garnet reference materials fall within 4% absolute of a one-to-one correlation with Fe3+/∑Fe ratios measured by Mössbauer. The standard error of the mean Fe3+/∑Fe ratio calculated from flank method approaches the Mössbauer-determined Fe3+/∑Fe ratio within estimated error (3%) after three analyses. Flank method precision is enhanced at higher beam current; however, the precision of the flank method does not approach the precision of XANES under any microprobe analytical condition tested here. Garnet reference materials detailed here are available by request to the Smithsonian Institution.

Reading tea leaves or tracking true constructs? An assessment of personality-based latent profiles in eating disorders.

Eating disorder (ED) subtyping studies have often extracted an undercontrolled, an overcontrolled and a resilient profile based on trait impulsivity and perfectionism. However, the extent to which methodological choices impact the coherence and distinctness of resulting subtypes remains unclear. In this paper, we aimed to assess the robustness of these findings by extracting personality-based subtypes on a sample of ED patients (N = 221) under different analytic conditions. We ran four latent profile analyses (LPA), varying the extent to which we constrained variances and covariances during model parametrization. We then performed a comparative analysis also including state ED symptom measures as indicators. Finally, we used cross-method validation via k-means clustering to further assess the robustness of our profiles. Our results demonstrated a four-profile model based on variances in impulsivity and perfectionism to fit the data well. Across model solutions, the profiles with the most and least state and trait disturbances were replicated most stably, while more nuanced variations in trait variables resulted in less consistent profiles. Inclusion of ED symptoms as indicator variables increased subtype differentiation and similarity across profiles. Validation cluster analyses aligned most with more restrictive LPA models. These results suggest that ED subtypes track true constructs, since subtypes emerged method-independently. We found analytic methods to constrain the theoretical and practical conclusions that can be drawn. This underscores the importance of objective-driven analytic design and highlights its relevance in applying research findings in clinical practice.