Linear Relation Research Articles

A Zn/Cd/Ni Metal-Organic Framework-Based Solid and Flexible Fluoroprobes for Highly Selective Detection of 4-Nitroaniline in Real Water Samples.

The combination of diazabicyclic compound i.e. 1,4-diazabicyclo[2.2.2]octane (DABCO) and dicarboxylate linker 1,4-dicarboxylic acid are employed to self-assemble with three divalent metal ions such as Zn2+, Cd2+, Ni2+ led to the formation of highly stable pillar layered luminescent metal-organic frameworks. The emissive response of as-synthesized MOFs was studied in organic solvents with different functionalities resulting in the development of fluoroprobes having excellent recognition ability for 4-nitroaniline with detection limit upto micromolar. All the MOFs display a good linear relation between the fluorescence intensity and concentration of 4-NA in the range of 10-90µmol L-1. The values of Ksv for Zn-MOF, Cd-MOF, and Ni-MOF are found to be 1.75 × 104mol-1L, 1.25 × 104mol-1L, and 28.0 × 104mol-1L, respectively. The calculated detection limit values are 19.7µmol L-1, 27.6µmol L-1, and 1.19µmol L-1 respectively. Moreover, the study was further extended to fabricate the solid membrane-based fluoroprobe using a linear chitosan polysaccharide and act as an efficient solid fluoroprobe for the detection of 4-NA. This proposed synthesis of polymeric membrane facilitates the MOF@chitosan fluorophore to transfer its fluorescence-emissive nature to a solid state.

Identification of Novel Regulators of Leaf Senescence Using a Deep Learning Model.

Deep learning has emerged as a powerful tool for investigating intricate biological processes in plants by harnessing the potential of large-scale data. Gene regulation is a complex process that transcription factors (TFs), cooperating with their target genes, participate in through various aspects of biological processes. Despite its significance, the study of gene regulation has primarily focused on a limited number of notable instances, leaving numerous aspects and interactions yet to be explored comprehensively. Here, we developed DEGRN (Deep learning on Expression for Gene Regulatory Network), an innovative deep learning model designed to decipher gene interactions by leveraging high-dimensional expression data obtained from bulk RNA-Seq and scRNA-Seq data in the model plant Arabidopsis. DEGRN exhibited a compared level of predictive power when applied to various datasets. Through the utilization of DEGRN, we successfully identified an extensive set of 3,053,363 high-quality interactions, encompassing 1430 TFs and 13,739 non-TF genes. Notably, DEGRN's predictive capabilities allowed us to uncover novel regulators involved in a range of complex biological processes, including development, metabolism, and stress responses. Using leaf senescence as an example, we revealed a complex network underpinning this process composed of diverse TF families, including bHLH, ERF, and MYB. We also identified a novel TF, named MAF5, whose expression showed a strong linear regression relation during the progression of senescence. The mutant maf5 showed early leaf decay compared to the wild type, indicating a potential role in the regulation of leaf senescence. This hypothesis was further supported by the expression patterns observed across four stages of leaf development, as well as transcriptomics analysis. Overall, the comprehensive coverage provided by DEGRN expands our understanding of gene regulatory networks and paves the way for further investigations into their functional implications.

Uniqueness of the Eigenvalue Inverse Problem for a Class of X-type Matrices with Linear Relations

Constraining a matrix by adding additional conditions to determine the matrix if given eigenpairs is called the eigenvalue inverse problem for matrices. The eigenvalue inverse problem of a matrix can be based on a given combination of different eigenvectors and real numbers to inverse a matrix method, and the method of inversion varies for different types of matrices. In this paper, we investigate the eigenvalue inverse problem for a class of X-type matrices characterized by linear relations, Invert the matrix based on its characteristics, determine eigenvalues and eigenvectors, and finally, prove that the solution of the problem exists and is unique, derive a series of expressions and recursive formulas, and we also check the algorithm’s accuracy correctness by giving different instances.

Unveiling very young O stars

Context. O-type stars are known to significantly contribute to both the dynamics and evolution of galaxies. Massive and luminous, they probably control and regulate the galaxies star formation rates. The stellar feedback generated by such cosmic beasts can strongly affect the local star formation rate, with effects in the current (and future) generations of low and intermediate mass stars, and possibly also in the disruption process of the galaxies’ giant gas reservoirs. Aims. For this work I performed a redetermination of the spectral types and effective temperatures of the Galactic O-type stars MSP182, MSP183, MSP199, VPHAS-01338, and VPHAS-01273. Methods. From a careful examination of the spectral features present in the blue optical spectral region, it was possible to identify several nitrogen lines usually only seen in the blue optical spectra of O2–O3 stars. From the nitrogen ionic equivalent width ratios measured in the spectra of MSP182, MSP183, MSP199, VPHAS-01338, and VPHAS-01273, and in those of standard stars of the O2–O4 spectral types, earlier spectral types and hotter effective temperature values were derived. Results. Two O2V((f*))z, together with three new O3 V stars are now firmly identified in the Westerlund 2 region. Besides RFS1 in NGC 3603, the O2 V stars found in Westerlund 2 are the only other exemplars known to date in the Milky Way. From the nitrogen equivalent width line ratios measured in the spectra of standard stars of the O2–O4 spectral types, linear relations between the N IVλ4058/N IIIλ4640 ratio and the effective temperature in the 47 000–51 000 K range were derived. Based on my spectroscopic analysis of the science targets and the use of a HRD, a mean heliocentric distance of 5 kpc to Westerlund 2 was computed, a result that is in line with the mean heliocentric distance of 5.3 ± 1.5 kpc obtained from the associated Gaia DR3 parallaxes and distances. Conclusions. The Westerlund 2 massive stars studied in this work probably share a common evolutionary process that might be representative of the evolutionary ages of a large fraction of the cluster’s O-type stellar population, which seems to be much younger than 1 Myr.

Textural indices of aerial images reveal urban landscapes temporal dynamics and their effects on plants and birds

Landscape temporal dynamics are a crucial concern in ecology to understand current biodiversity. But historical environmental data are often not easily available. This study assesses for the first time the potential of historical orthophotographs to describe past landscape conditions and determine the temporal lag between landscape changes and biotic communities responses.This method utilizes Gray level Co-occurrence Matrix (GLCM) texture indices computed from black and white orthophotographs to construct continuous metrics of landscape composition. Metrics were first developed using present-day data, i.e. 2015, and calibrated with categorical land cover maps of the Strasbourg Eurometropolis, France. Subsequently, these metrics were applied to historical orthophotographs from 1966, 1976, 1986, and 2000. Plant and bird data from research and citizen science programs were used to estimate the time delay in which these communities respond to evolutions in built areas and high vegetation.Obtained texture-based models reveal that built areas exhibit high contrast and homogeneity, depicted through a linear relation, and that high vegetation display low pixel brightness and high brightness diversity, better described via a nonlinear model. We successfully applied those findings to historical orthophotographs, and revealed dependencies on landscape composition up to 50 years ago for plants and up to 30 years ago for birds, with the time lag and the influence of built and high vegetation areas depending on the selected biodiversity indices.These results demonstrate the utility of archive black and white orthophotographs' texture indices for describing urban landscapes over the past five decades, making them valuable tools for ecological research. These indices are more accessible than categorical data like land cover maps for past years. They have the potential to greatly benefit future studies investigating time lags in landscape ecology, simplifying access to historical landscape features and contributing to sustainable urban planning efforts.

Fluid simulations of resistive drift-wave turbulence with diamagnetic flow in ZPED experiments

We derive a diamagnetic resistive fluid model (DRF) and develop an associated two-dimensional fluid simulation code (DRF-2D) to explore the dynamics of resistive drift modes within the plasmas of the Zheda Plasma Experiment Device (ZPED). The validation of the linear dispersion relation for the DRF-2D code revealed a harmonious agreement between analytical theory and linear numerical simulations. Leveraging plasma parameters obtained from the ZPED experiments, we conducted a comprehensive series of nonlinear simulations using the DRF-2D code. Our simulations successfully replicate the nonlinear trends in turbulent fluctuations and transport observed in the ZPED experiments, particularly demonstrating a remarkably accurate alignment of the turning point in the magnetic field. Notably, the DRF model sheds light on the observed frequency sign reversal from the electron diamagnetic direction to the ion diamagnetic direction in the ZPED experiments. This is demonstrated through well-matched turning points in the confining magnetic field between the nonlinear simulations and ZPED experiments. The fidelity of our model in capturing these phenomena underscores its efficacy in providing valuable insights and predictive capabilities for the intricate dynamics observed in the ZPED plasmas.

Knockoffs-SPR: Clean Sample Selection in Learning With Noisy Labels.

A noisy training set usually leads to the degradation of the generalization and robustness of neural networks. In this article, we propose a novel theoretically guaranteed clean sample selection framework for learning with noisy labels. Specifically, we first present a Scalable Penalized Regression (SPR) method, to model the linear relation between network features and one-hot labels. In SPR, the clean data are identified by the zero mean-shift parameters solved in the regression model. We theoretically show that SPR can recover clean data under some conditions. Under general scenarios, the conditions may be no longer satisfied; and some noisy data are falsely selected as clean data. To solve this problem, we propose a data-adaptive method for Scalable Penalized Regression with Knockoff filters (Knockoffs-SPR), which is provable to control the False-Selection-Rate (FSR) in the selected clean data. To improve the efficiency, we further present a split algorithm that divides the whole training set into small pieces that can be solved in parallel to make the framework scalable to large datasets. While Knockoffs-SPR can be regarded as a sample selection module for a standard supervised training pipeline, we further combine it with a semi-supervised algorithm to exploit the support of noisy data as unlabeled data. Experimental results on several benchmark datasets and real-world noisy datasets show the effectiveness of our framework and validate the theoretical results of Knockoffs-SPR.

A Nonlinear Relation between Body Mass Index and Long-Term Poststroke Functional Outcome-The Importance of Insulin Resistance, Inflammation, and Insulin-like Growth Factor-Binding Protein-1.

Both high serum insulin-like growth factor-binding protein-1 (s-IGFBP-1) and insulin resistance (IR) are associated with poor functional outcome poststroke, whereas overweight body mass index (BMI; 25-30) is related to fewer deaths and favorable functional outcome in a phenomenon labeled "the obesity paradox". Furthermore, IGFBP-1 is inversely related to BMI, in contrast to the linear relation between IR and BMI. Here, we investigated s-IGFBP-1 and IR concerning BMI and 7-year poststroke functional outcome. We included 451 stroke patients from the Sahlgrenska Study on Ischemic Stroke (SAHLSIS) with baseline measurements of s-IGFBP1, homeostasis model assessment of IR (HOMA-IR), BMI (categories: normal-weight (8.5-25), overweight (25-30), and obesity (>30)), and high-sensitivity C-reactive protein (hs-CRP) as a measure of general inflammation. Associations with poor functional outcome (modified Rankin scale [mRS] score: 3-6) after 7 years were evaluated using multivariable binary logistic regression, with overweight as reference due to the nonlinear relationship. Both normal-weight (odds-ratio [OR] 2.32, 95% confidence interval [CI] 1.30-4.14) and obese (OR 2.25, 95% CI 1.08-4.71) patients had an increased risk of poor functional outcome, driven by deaths only in the normal-weight. In normal-weight, s-IGFBP-1 modestly attenuated (8.3%) this association. In the obese, the association was instead attenuated by HOMA-IR (22.4%) and hs-CRP (10.4%). Thus, a nonlinear relation between BMI and poor 7-year functional outcome was differently attenuated in the normal-weight and the obese.

Elasticity of the Cervix in Relation to Uterus Position.

Strain elastography allows the evaluation of tissue elasticity. Background/Objectives: Tissue elasticity depends on the content and distribution of collagen fibers and is shaped by the applied tensile forces that may differ in uteri with a different angle of flexion of the corpus on the cervix. The objective was to investigate whether the angle of uterine flexion is related to cervical tissue elasticity. Methods: The anterior angle between the longitudinal axis of the uterus corpus and that of the cervix was measured in 275 non-pregnant young women by transvaginal ultrasonography and considered both as an absolute value or categorized as ≤150°, between >150° and ≤210°, and >210°. Strain elastography was used to assess tissue elasticity by placing the probe in the anterior vaginal fornix. Tissue elasticity was evaluated in the middle of the anterior cervical compartment (ACC), in the middle of the posterior cervical compartment (PCC), in the middle portion of the cervical canal (MCC), and at the internal cervical os (ICO). In a sagittal plane MCC was evaluated across the cervical canal, and ACC and PCC at a distance equal between the cervical canal and the outer anterior or posterior part of the cervix. MCC, ACC and PCC were evaluated at equal distance between the ICO and the external cervical os. Elasticity was expressed as a color score ranging from 0.1 (low elasticity) to 3 (high elasticity). Results: The angle of uterine flexion show a negative linear relation with the elasticity of the ACC (p = 0.001) and MCC (p = 0.002) and a positive relation with the elasticity of the PCC (p = 0.054). In comparison to uteri with an angle of flexion of <150°, those with an angle of flexion of >210° had lower elasticity of the ACC (p = 0.001) and MCC (p = 0.001) and higher elasticity of the PCC (p = 0.004). The ACC/PCC and PCC/MCC elasticity ratios were also significantly different (p = 0.001). Conclusions: The angle of uterine flexion is associated with changes in cervix elasticity. Retroflexion is associated with stiffer ACC and MCC and a more elastic PCC. Differences in tissue elasticity suggest structural changes of the cervix that may have implication in variate obstetric and gynecological conditions.

Multiple Beads on a String: Dark-matter-deficient Galaxy Formation in a Mini-Bullet Satellite–Satellite Galaxy Collision

Dark-matter-deficient galaxies (DMDGs) discovered in the survey of ultra-diffuse galaxies (UDGs), in apparent conflict with standard cold dark matter, may be produced by high-velocity galaxy–galaxy collisions, the so-called Mini-Bullet scenario. Recent observations of an aligned trail of 7–11 UDGs near NGC 1052, including DMDGs DF2 and DF4, suggesting a common formation event, ∼8.9 ± 1.5 Gyr ago, provide a test.Hydro/N-body simulations, supplemented by galaxy orbit integrations, demonstrate that satellite–satellite collisions outside the host-galaxy virial radius can reproduce the observed UDGs in the NGC 1052 group. A trail of ∼10 DMDGs is shown to form, including 2 massive ones that replicate the observed motions of DF2 and DF4. The linear relation, v = A x + v 0, conjectured previously to relate positions ( x ) and velocities ( v ) of the aligned DMDGs as a signature of the collision event, is approximately obeyed, but individual DMDGs can deviate significantly from it. The progenitors whose collision spawned the trail of DMDGs survive the collision without themselves becoming DMDGs. We predict that one progenitor is located at the end of the trail, which can be tested by observing the difference between its stars, formed pre-collision, from those of the DMDGs, formed post-collision. By contrast, stellar ages and metallicities of the DMDGs are nearly identical. We further offer a hint that the tidal field of host NGC 1052 may contribute to making DMDGs diffuse. ΛCDM simulation in a 100 cMpc box finds our required initial conditions ∼10 times at z < 3. These results indicate current observations are consistent with the Mini-Bullet scenario.

Boussinesq-type equations of hydroelastic waves in shallow water

Accurate computation of hydroelastic waves in shallow water is critical because many hydroelastic wave applications are nearshores, such as sea-ice and floating infrastructures. In this paper, Boussinesq assumptions for shallow water are employed to derive nonlinear Boussinesq-type equations of hydroelastic waves, in which non-uniform distribution of structural stiffness and varying water depth are considered rigorously. Application of Boussinesq assumptions enables complicated three-dimensional problems to be reduced and formulated on the two-dimensional horizontal plane, therefore the proposed Boussinesq-type models are straightforward and versatile for a wide range of hydroelastic wave applications. Two configurations, a floating plate and a submerged plate, are studied. The first-order linear governing equations are solved analytically with periodic conditions assuming constant depth and uniform stiffness, and the linear dispersion relations are subsequently derived for both configurations. For flexural-gravity waves of a floating plate, unique behaviours of flexural-gravity waves different from shallow-water waves are discussed, and a generalized solitary wave solution is investigated. A nonlinear numerical solver is developed, and nonlinear flexural-gravity waves are found to have smaller wavelength and celerity than their linear counterparts. For hydroelastic waves of a submerged plate, dual-mode analytical solutions are discovered for the first time. Numerical computation has demonstrated that a plate with decreasing submerged depth is able to transfer wave energy from the deeper water to the surface layer.

Tuning Electrocatalytic Activities of Dealloyed Nanoporous Catalysts by Macroscopic Strain Engineering.

It is technically challenging to quantitatively apply strains to tune catalysis because most heterogeneous catalysts are nanoparticles, and lattice strains can only be applied indirectly via core-shell structures or crystal defects. Herein, we report quantitative relations between macroscopic strains and hydrogen evolution reaction (HER) activities of dealloyed nanoporous gold (NPG) by directly applying macroscopic strains upon bulk NPG. It was found that macroscopic compressive strains lead to a decrease, while macroscopic tensile strains improve the HER activity of NPG, which is in line with the d-band center model. The overpotential and onset potential of HER display approximately a linear relation with applied macroscopic strains, revealing an ∼2.9 meV decrease of the binding energy per 0.1% lattice strains from compressive to tensile. The methodology with the high strain sensitivity of electrocatalysis, developed in this study, paves a new way to investigate the insights of strain-dependent electrocatalysis with high precision.

Deciphering air quality index through sample entropy: A nonlinear time series analysis

Pollution and its impacts on human health have become a crisis in regions with poor air quality index (AQI), which is an indicator of concentrations of pollutants, prompting the United Nations (UN) to set sustainable development goals (SDG). The present study proposes a surrogate sample entropy-based method in tune with UN’s SDG, to assess AQI from the time series of any of the pollutants. New Delhi is one of the world's most polluted state capital, with a higher level of particulate matter (PM). The temporal data of the pollutants in New Delhi, recorded in the one-hour interval during the years 2016 and 2017, are subjected to time series analysis. The data collected from the Central Pollution Control Board of India are analyzed with special reference to PM and compared with the World Air Quality Report 2021 and University of Washington data. The dependence of PM2.5 concentration on humidity and rain is also studied. The study reveals the increase in complexity with the concentration of pollutants through the phase portrait. The sample entropy analysis of the nonlinear time series of the pollutants exhibits a linear relation with AQI suggesting the possibility of using sample entropy as a surrogate measure of AQI.

Effects of temperature and water vapour on Cr-species volatilisation, oxidation and scale adhesion of a Type 409L stainless steel for application as interconnect of low temperature solid oxide fuel cells

Though the classical transport theory does not mathematically express the Arrhenius-like relation between Cr-loss flux due to volatilisation and absolute temperature, such relation was experimentally observed for 409L stainless steel exposed at 600–750 °C. Volatilisation calculation in the present cases can be estimated giving such relation because of the nearly linear relation between mass transfer coefficient and temperature. Cr-loss fluxes in O2 with 20 and 40 % H2O are close to or coincided with the fluxes calculated from MnCr2O4 evaporation. Increasing water vapour could enhance volatilisation contributed from the raised CrO2(OH)2 pressure, reduce oxidation rate, and worsen scale adhesion.

Enhanced sonocatalytic degradation of Acid Red 27 with Fe2O3 catalyst: a kinetic study

Abstract This study is focused on elucidating the potential effectiveness of degradation as a method to eliminate dyes from aqueous systems. Specifically, it delves into the influence of ultrasound energy on the degradation kinetics of a dye. The research findings underscore the notable impact of ultrasound energy in accelerating the reaction rate constant (k p), with the degradation kinetics exhibiting a conformity to first-order kinetics. An integral aspect of the study involves the establishment of a robust relationship between time and concentration by integrating the equation governing the degradation of the dye. Additionally, the determination of the rate constant, derived from the gradients of the graphs, attests to the model’s fitting accuracy. Intriguingly, the outcomes of this analysis reveal no discernible structural changes in the dye. The accuracy of the model is further underscored by the establishment of linear relations derived from experimental data. Summarily, this kinetic study provides invaluable insights into the multifaceted impact of ultrasound energy and the Fe2O3 catalytic influence on both the degradation kinetics of the dye. The comprehensive nature of the investigation enhances our understanding of the intricate processes involved, contributing significantly to the broader field of water treatment and dye removal from aqueous environments.

Complementation and Lebesgue‐type decompositions of linear operators and relations

AbstractIn this paper, a new general approach is developed to construct and study Lebesgue‐type decompositions of linear operators or relations in the Hilbert space setting. The new approach allows to introduce an essentially wider class of Lebesgue‐type decompositions than what has been studied in the literature so far. The key point is that it allows a nontrivial interaction between the closable and the singular components of . The motivation to study such decompositions comes from the fact that they naturally occur in the corresponding Lebesgue‐type decomposition for pairs of quadratic forms. The approach built in this paper uses so‐called complementation in Hilbert spaces, a notion going back to de Branges and Rovnyak.

Sequences of Operators, Monotone in the Sense of Contractive Domination

A sequence of operators Tn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_n$$\\end{document} from a Hilbert space H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathfrak {H}}}$$\\end{document} to Hilbert spaces Kn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathfrak {K}}}_n$$\\end{document} which is nondecreasing in the sense of contractive domination is shown to have a limit which is still a linear operator T from H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathfrak {H}}}$$\\end{document} to a Hilbert space K\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathfrak {K}}}$$\\end{document}. Moreover, the closability or closedness of Tn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_n$$\\end{document} is preserved in the limit. The closures converge likewise and the connection between the limits is investigated. There is no similar way of dealing directly with linear relations. However, the sequence of closures is still nondecreasing and then the convergence is governed by the monotonicity principle. There are some related results for nonincreasing sequences.

Effect of wind speed on marine aerosol optical properties over remote oceans with use of spaceborne lidar observations

Abstract. Marine aerosol affects the global energy budget and regional weather. The production of marine aerosol is primarily driven by wind at the sea–air interface. Previous studies have explored the effects of wind on marine aerosol, mostly by examining the relationships between aerosol optical depth (AOD) and surface wind speed. In this paper, utilizing the synergy of aerosol and wind observations from Aeolus, the relationships between the marine aerosol optical properties at 355 nm and the instantaneous co-located wind speeds of remote oceans are investigated at two vertical layers (within and above the marine atmospheric boundary layer (MABL)). The results show that the enhancements of the extinction and backscatter coefficients caused by wind are larger within the MABL than above it. The correlation models between extinction and backscatter with wind speed were established using power-law functions. The slope variation points occur during extinction and backscatter coefficients increasing with wind speed, indicating that the wind-driven enhancement of marine aerosol involves two phases: a rapid-growth phase with high wind dependence, followed by a slower-growth phase after the slope variation points. We also compared the AOD–wind relationship acquired from Aeolus with CALIPSO-derived results from previous research. The variation in the lidar ratio with wind speed is examined, suggesting a possible “increasing–decreasing–increasing” trend of marine aerosol particle size as wind speed increases. This study enhances the comprehension of the correlation between marine aerosol optical properties and wind speed by providing vertical information and demonstrating that their relationships are more complex than a linear or exponential relation.

Small-Scale Cosmology Independent of the Standard Model

‘Small-scale cosmology’ is a theory designed to incorporate the linear redshift versus distance relation, which is inferred from observations, into the theoretical framework independent of the global Robertson–Walker–Friedman (RWF)-type models. The motivation behind this is that the RWF cosmological models, based on the assumptions of homogeneity and a constant matter density, as well as the concept of expanding space inherent to them are not applicable on the scales of observations from which the linear Hubble law is inferred. Therefore, explaining the Hubble law as the small redshift limit of the RWF model or as an effect of expanding space is inconsistent. Thus, the Hubble linear relation between the redshift of an extragalactic object and its distance should be considered an independent law of nature valid in the range of the distances where the RWF cosmology is not valid. In general, the theory, based on that concept, can be developed in different ways. In the present paper, ‘small-scale cosmology’ is formulated as a theory operating in the (redshift–object coordinates) space, which allows developing a conceptual and computational basis of the theory along the lines of that of special relativity. In such a theory, the condition of invariance of the Hubble law with respect to a change in the observer acceleration plays a central role. In pursuing this approach, the effectiveness of group theoretical methods is exploited. Applying the Lie group method yields transformations of the variables (the redshift and space coordinates of a cosmological object) between the reference frames of the accelerated observers. In this paper, the transformations are applied to studying the effects of the solar system observer acceleration on the observed shape, distribution and rotation curves of galaxy clusters.

On the Upper Bound of Near Potential Differential Games

This letter presents an extended analysis and a novel upper bound of the subclass of Linear Quadratic Near Potential Differential Games (LQ NPDG). LQ NPDGs are a subclass of potential differential games, for which there is a distance between an LQ exact potential differential game and the LQ NPDG. LQ NPDGs exhibit a unique characteristic: The smaller the distance from an LQ exact potential differential game, the more closer their dynamic trajectories. This letter introduces a novel upper bound for this distance. Moreover, a linear relation between this distance and the resulting trajectory errors is established, opening the possibility for further application of LQ NPDGs.