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High-frequency sea level observations from long-term tide gauges are indispensable for a wide array of scientific inquires, including storm surges, ocean tides, and tsunamis. The University of Hawaii Sea Level Center (UHSLC) stands as a pivotal sea level database, offering meticulously curated, hourly sea level records across the global ocean through rigorous and time-consuming quality control measures. These records are widely recognized as reliable and suitable for scientific analysis. However, this consensus is challenged by our research, which examines 595 tide gauges from the UHSLC distributed worldwide. Utilizing a newly developed detection algorithm, we identify significant timing errors in 35 tide gauges from the UHSLC, with these errors potentially altering tidal amplitude estimates of main constituents by more than 10 mm. Notably, at specific tide gauges, such as Tanjong Pagar and Manila, abnormal tidal amplitude changes caused by timing errors can be larger than 50 mm. Most tide gauges with severe timing errors lie on the coasts of developing countries, suggesting inadequate management. Conversely, sea level observations from developed countries generally exhibit high quality, albeit with some potential timing errors identified. Beyond timing issues, datum shifts and other exceptions are also uncovered in the UHSLC database. Consequently, when analyzing ‘science-ready’ sea level observations, caution is warranted. Anomalous variations in sea levels and tidal parameters may not reflect physical phenomena but rather artifacts stemming from multifarious observation errors. [ABSTRACT FROM AUTHOR]

Structural advancements in underwater vehicle design necessitate lightweight materials, driving interest in Fiber Metal Laminates (FMLs), known for their high specific strength, stiffness, and corrosion resistance. This study investigates the vibration response of FMLs through combined experimental and numerical analyses, specifically evaluating the novel effects of layerwise acoustic impedance matching on vibration damping within the 0-500 Hz frequency range, which aligns with ocean current frequencies. Various FML stackup sequences were characterized through ASTM E756-05 compliant experiments and ANSYS Harmonic Response simulations. Notably, the introduction of paperboard-epoxy ply results in a rightward shift in natural frequencies, while the exclusion of the metallic face ply leads to a leftward shift across different stackups. Moderate agreement between experimental and numerical results for material modulus highlights the robustness of our findings. Overall, this study provides valuable insights for leveraging FMLs in submersible hulls, underscoring their potential for enhanced vibration-damping characteristics in marine environments. [ABSTRACT FROM AUTHOR]

Let S be a semigroup, z 0 be a fixed element in the center of S, and τ : S → S be an involution (an involutive anti-automorphism). Furthermore we let F be a division ring of characteristic different from 2 and H be the skew field of quaternions. Our main objective is to solve each of the functional equations K (x y z 0) + K (x τ (y) z 0) = 2 K (x) K (y) , x , y ∈ S , V (x τ (y) z 0) - V (x y z 0) = 2 V (x) V (y) , x , y ∈ S , in which K : S → F and V : S → H are the unknown functions. [ABSTRACT FROM AUTHOR]

We study the algebra of differential operators on non-compact simply connected harmonic manifolds and provide sufficient conditions for them to have a radial fundamental solution and be surjective on the space of smooth function. Furthermore, we show that the algebra of differential operators that commute with taking averages over geodesic spheres is generated by the Laplacian. As an application of this, we show that the heat-semi group is dense in the radial L 1 space of a non-compact simply connected harmonic manifold. In the process, we provide a characterisation of the eigenfunctions of the Laplacian and therefore of the eigenfunctions of all differential operators commuting with taking spherical averages. [ABSTRACT FROM AUTHOR]

The Casamance estuary in Senegal is experiencing hypersalinisation and siltation, which are negatively impacting the mangrove ecosystem and maritime navigation, with implications for biodiversity and the regional economy. This study investigates the influence of tidal distortion on extreme water levels by analysing tidal data from the upstream Ziguinchor station and the estuary mouth using the Tide Peaks Toolbox and UTide. The results reveal significant tidal asymmetry between ebb and flood tides, with greater distortion observed upstream compared to the estuary mouth. At Ziguinchor, spring tides exhibit pronounced asymmetry in the duration of ebb and flood, leading to heightened extreme water levels, while neap tides remain nearly symmetrical. In contrast, Carabane experiences higher water levels with less pronounced asymmetry across different tidal cycles. Harmonic analysis shows a reduction of over 45% in the amplitudes of major tidal constituents (M2, S2, K1) and a notable increase in higher harmonics (M4, M6), which intensifies asymmetry, particularly upstream. The reduction of M2 plays a key role in increasing tidal asymmetry, especially upstream, while M4 and M6 further amplify this effect. This tidal distortion contributes to water stagnation at Ziguinchor during spring tides, raising extreme water levels at low tide. The study reveals a complex tidal dynamic in the Casamance estuary, with greater asymmetry and distortion upstream compared to the mouth, and underscores the contrasting evolution of extreme water levels. These findings highlight the need for further research on tidal deformation in inverse microtidal estuaries, particularly in tropical regions with pronounced climatic variations. [ABSTRACT FROM AUTHOR]

We study a summability method called almost convergence for bounded measurable functions defined on a locally compact abelian group. We define almost convergence using topologically invariant means and exhibit two different kinds of necessary and sufficient conditions, one is analytic and the other is functional analytic, for a given function to be almost convergent. As an application, we show complex Tauberian theorems for almost convergence on the integers and the real numbers. These results are closely related to some of the classical Tauberian theorems like the Ingham–Karamata and Katznelson–Tzafriri theorems. [ABSTRACT FROM AUTHOR]

This paper presents the effect of dead time on active power transfer of the dual active bridge (DAB) and a novel mitigation technique for the same. The whole power range is categorized into five zones based on the switching instant link current direction and the modified active power expressions with effect of dead time are derived for each zone. The novel compensation method for dead time improves the performance of any general optimized techniques for DAB with extended phase shift. Firstly, the link current values at different switching instants are estimated using the mathematical expressions obtained using a linear piece-wise method. Secondly, the values are used for compensation logic formulation in the whole power range. The compensation process is applied to two different configurations, open loop (circulating mode) and close loop (voltage control mode). The mid-power zone is compensated using a constant phase shift modification and the low power zone is compensated using a PI controller based phase shift modification. Finally, the effectiveness of the proposed compensation technique is verified through MATLAB Simulink model and 1.2 kW experimental prototype. [ABSTRACT FROM AUTHOR]

The Manin–Peyre conjecture is established for smooth spherical Fano threefolds of semisimple rank one and type N. Together with the previously solved case T and the toric cases, this covers all types of smooth spherical Fano threefolds. The case N features a number of structural novelties; most notably, one may lose regularity of the ambient toric variety, the height conditions may contain fractional exponents, and it may be necessary to exclude a thin subset with exceptionally many rational points from the count, as otherwise Manin's conjecture in its original form would turn out to be incorrect. [ABSTRACT FROM AUTHOR]

By improving upon previous estimates on a problem posed by L. Moser, we prove a conjecture of Erdős that the density of any measurable planar set avoiding unit distances is less than 1/4. Our argument implies the upper bound of 0.2470. [ABSTRACT FROM AUTHOR]

The tide plays a pivotal role in the ocean, affecting the global ocean circulation and supplying the bulk of the energy for the global meridional overturning circulation. To further investigate internal tides and their impacts on circulation, it is imperative to incorporate tidal forcing into the eddy-resolving global ocean circulation model. In this study, we successfully incorporated explicit tides (eight major constituents) into a global eddy-resolving general ocean circulation model and evaluated its tidal simulation ability. We obtained harmonic constants by analyzing sea surface height through tidal harmonic analysis and compared them with the analysis data Topex Poseidon Cross-Overs v9 (TPXO9), the open ocean tide dataset from 102 open-ocean tide observations, and tide gauge stations from World Ocean Circulation Experiment. The results demonstrated that the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics/Institute of Atmospheric Physics (LASG/IAP) Climate System Ocean Model 3.0 (LICOM3.0) effectively simulated tides, with errors predominantly occurring in nearshore regions. The tidal amplitude simulated in LICOM3.0 was greater than that of TPXO9, and these high-amplitude areas exhibited greater errors. The amplitude error of the M2 constituent was larger, while the phase error of the K1 constituent was more significant. Furthermore, we further compared our results with those from other models. [ABSTRACT FROM AUTHOR]

Cutting force monitoring may be established as a functional control system for machining processes, helping determine the optimal time for tool change since a relationship between tool wear and milling forces exists. However, these forces result from various effect, including chip removal, friction, and vibrations. Predicting the end of functional tool life becomes challenging due to these complex interactions. In this study, it is proposed a decomposed action methodology based on force analysis using the fast Fourier transform and harmonic analysis. In pursuit of a comprehensive understanding of cutting forces during milling process, it is proposed a methodology to capture the signal given by a rotary dynamometer in selective cutting tests directed to discriminate and isolate external friction and other effects. The methodology has been tuned for slot milling of Ti48Al2Cr2Nb titanium aluminide using a single uncoated tungsten carbide insert, under different combinations of depth of cut and feed per tooth, for a fixed cutting speed value. The friction force in the tool flank zone has been demonstrated as the main action due to the small chip section removed, which leads to explain the rapid tool wear in titanium aluminides machining. Friction coefficients ranging from 0.412 to 0.579 have been found in real cutting conditions. This methodology will allow the evaluation of different tool geometries to reduce tool-workpiece friction and wear phenomena, enhancing the tool life. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the global well-posedness for the 3D Boussinesq equations. Firstly, we prove the global existence and uniqueness of the solution in critical space for small initial data. Then, aimed at the large initial data giving rise to global solution, we obtain a certain class of large solutions with initial data slowly varying in one direction. The proof relies on the special structure of the equation and some new refined estimates for the velocity and temperature. [ABSTRACT FROM AUTHOR]

This paper uses an improved switching table-based direct torque control space vector selection technique with a nine-level hysteresis band to reduce torque ripple in a PMBLDC drive. The commutation torque ripple is mitigated by different rates of correction of torque depending upon the error quantum. Multi-rates of correction are applied using three sets of lookup tables corresponding to low, medium and high torque errors. In general, the existing state of the art incorporates an observer-based controller that optimizes complex objective functions. This increases computational cost and complexity. The proposed method is based on modified switching tables. This decreases the computational cost and improves the dynamic response. Frequency-domain analysis of torque response establishes the minimization of high-frequency components. The experimental validation is obtained on 1 kw BLDC motor using DSPACE 1104 real-time controller. [ABSTRACT FROM AUTHOR]

Ultraprecision aerostatic spindles are the key functional component of ultraprecision machining tools and precision measuring instruments. The uniformity and consistency of air film thickness are influenced by the shape errors of the ultraprecision aerostatic spindle. However, given that mass-produced rotors have different local error characteristics, existing shape error models fail to express the variation of the air film thickness accurately when the rotor rotates in the flow field. Thus, the influence of the distribution characteristics of rotor shape errors on the aerostatic bearing flow field and rotor performance cannot be accurately evaluated. In this study, a multistrategy fusion and improved sparrow search algorithm (ISSA) was proposed to optimize the backpropagation (BP) neural network, and a regression model of rotor shape error was established on the basis of the ISSA-BP algorithm. Numerous rotor surface profiles were collected by a cylindricity instrument, and the Gaussian-RK filter was applied to remove the noise and burrs from the rotor profiles. The distribution regularity of local error characteristics was statistically analyzed, and the ISSA-BP neural network was used to fit the rotor surface profiles. The shape error regression model of the rotor was established by regression analysis. Error and harmonic analyses were performed on the model and experimental measurement data. Experimental results showed that the relative error of the rotor shape error regression model in harmonic analysis was less than 1 %, and the maximum relative error of the rotor profile was lower than 0.1 %. Thus, the accuracy of the constructed rotor shape error regression model is verified. [ABSTRACT FROM AUTHOR]

Fine particulate matter (PM 2.5 ) poses a significant public health risk due to its association with respiratory and cardiovascular diseases. Given the limited availability of PM 2.5 monitoring stations, there is a pressing need for reliable real-time forecasting models. This study introduces TSPPM25, a novel Transformer-based model designed for spatiotemporal prediction of PM 2.5 levels. TSPPM25 leverages multiple data embedding techniques and various attention layers to effectively capture the intricate spatiotemporal relationships in multivariate data. The model's performance is evaluated using a California Aerosol Optical Depth PM 2.5 dataset and compared with several baseline models, including LSTM, Bi-LSTM, Linear Regression, and basic heuristics models. The results demonstrate that TSPPM25 exhibits superior spatiotemporal learning capabilities, robustness, and stability, outperforming other models across MSE, MAE, and SMAPE metrics. Furthermore, the study explores the underlying patterns in PM 2.5 data through harmonic analysis, revealing that TSPPM25 performs exceptionally well even in complex scenarios characterized by mixed wave patterns. Conclusively, TSPPM25 emerges as a valuable tool for predicting PM 2.5 levels demonstrating its efficacy in the California region, and thereby contributing significantly to the field of air quality forecasting. [ABSTRACT FROM AUTHOR]

In order to study temporal variations in the mixing ratios of greenhouse carbon-containing gases and factors influencing them, local measurements of CO2, CH4 (January 2013–January 2020), and CO (January 2013–January 2019) mixing ratios in atmospheric air at the monitoring station of St. Petersburg State University are analyzed taking into account trends and seasonal fluctuations. Linear trends for CO2, CH4, and CO, which are 2.42 ppm/year (0.60%), 8.6 ppb/year (0.49%), and −3.8 ppb/year (−2.2%), respectively, are in a good agreement with independent estimates of both global/background changes and changes in urban areas. The analysis of the CO/CO2 emission ratio confirmed that motor vehicles are the dominant anthropogenic source affecting the composition of atmospheric air near the monitoring station of St. Petersburg State University. The results can be used for validation of atmospheric models and independent estimation of greenhouse gas fluxes. [ABSTRACT FROM AUTHOR]

In the present study, the precipitation regime (PR) was investigated as a feature of the structure of Iran's climate and its relationship with spatial-topographic variables and its spatial pattern. Spatial patterns of the indices of the PR used in the present study exhibited significant agreement in illustrating the diverse PRs of Iran. The diversity of spatial factors provided the spatial diversity of precipitation characteristics, including PR. Harmonic analysis (HA) results confirmed the country's diverse PRs, which were attributed to different mechanisms affecting Iran's precipitation patterns throughout the year. Using multiple methods in the present study, four PRs were identified. According to the methods used, the increase in precipitation in each location was associated with a reduction in the month-to-month difference in precipitation and an enhancement in the uniform distribution of precipitation. All indices indicated that the northern regions of Iran, including the Iranian coast of the Caspian Sea (ICCS), exhibited a uniform PR. The northwestern (NWI) and southeastern (SEI) regions displayed a relatively uniform regime, while the remaining parts of the country experienced a seasonal regime characterized by a longer dry season. Furthermore, there was a notable correlation between the PR and latitude, particularly from approximately 35 degrees northward. Moreover, there was a notable correlation between the PR and latitude, particularly from approximately 35 degrees northward. As for the southern regions of the country, beyond the latitude of 35 degrees, the spatial distribution of PRs was influenced not only by latitude but also by other variables such as longitude, altitude, and the shape and length of the Persian Gulf coast adjacent to the eastern deserts. [ABSTRACT FROM AUTHOR]

We establish optimal (p, q) ranges for the weighted convolution operator associated with a complex polynomial curve. Establishing this estimate comes down to establishing a lower bound for the Jacobian of a mapping associated with the complex curve in question. [ABSTRACT FROM AUTHOR]

This paper deals with investigating the properties of pseudo-state matrices in multi-order dynamic systems which generate steady-state oscillations combined of some sinusoidal components with different frequencies (multi-frequency steady state oscillations). In this investigation, a Routh array based criterion is found which should be satisfied by the pseudo-state matrix of a multi-order multi-frequency oscillatory system. In design of multi-frequency oscillators, this criterion can be rewritten as a system of monomial equations whose variables are the tunable elements of the pseudo-state matrix of the oscillator. Furthermore, a class of transformations on the pseudo-state matrix of a multi-order multi-frequency oscillator is obtained which can guarantee the preservation of the multi-frequency feature in the dynamic structure constructed based on the transformed pseudo-state matrix. [ABSTRACT FROM AUTHOR]

In this paper, firstly, optimal sizing and placement of photovoltaic-based distributed generation units (PVDGUs) and passive harmonic filters (PFs) are proposed to improve both the PVDGU hosting capacity and bus voltage profile of the distorted radial distribution systems. The objective of the proposed approach (PA) is defined as minimizing the rms deviation and total harmonic distortion of the bus voltages while maximizing the hosting capacity. Its constraints are considered as bus voltage total and individual harmonic distortion limits placed in IEEE standard 519, permissible bus voltage rms intervals, and the numbers and total powers of the PVDGUs and PFs. Secondly, it is aimed to investigate the performance of the PA on the improvement of the hosting capacity and voltage profile. Thus, for the modified IEEE 33 bus test system containing nonlinear loads, it is comparatively evaluated with a traditional PF planning approach (TA) based on minimization of the total voltage harmonic distortion. Finally, the effects of the harmonic analysis algorithm and PVDGU harmonic model preferences on the solutions of both approaches are also analysed. One of the major conclusions obtained from the analysis is that PA achieves significantly higher PVDGU hosting capacity while providing total voltage harmonic distortion mitigation performance very close to TA. In addition, PA achieves almost the same hosting capacity for all considered harmonic models and harmonic analysis algorithms. However, this is not the case for TA. [ABSTRACT FROM AUTHOR]

Purpose: Intracranial stenosis is a critical cardiovascular disorder which may lead to recurrent ischemic stroke. The flow in a stenosed artery tends to have a chaotic pattern, resulting in fluctuating pressures on the artery wall. These acoustic pressures are known as the sources of arterial noise and vibration. The generated vibro-acoustic signals on the stenosed artery propagate through the surrounding body tissues and reach the epidermal surface. In this study, the stenosis-induced vibration on the epidermal surface is aimed to be utilized for the diagnosis of occlusion in the intracranial artery. Methods: An intracranial stenosis is modeled considering a simplified head geometry consisted of brain, skull, and skin. The simplified head model has an idealized spherical form. Three different stenosis severities are employed to elucidate the effects of mild, moderate, and severe intracranial stenosis. ADINA finite element analysis software package is used to perform harmonic and modal analyses to determine the biodynamic responses on the epidermal surface of a human head. Results: According to the results obtained, vibration amplitudes on the epidermal surface tend to increase with increasing stenosis severity. The stenosis-induced effects on the vibration responses are particularly prominent in the frequency range of 400–1000 Hz. Abnormal increase in vibration amplitudes between 400 and 1000 Hz can be an indicator of further occlusion in the intracranial artery. Conclusions: The stenosis-induced vibro-acoustic effects provide important clues about arterial health. Excessive vibration amplitudes indicate a potential arterial occlusion and can be used as an early diagnostic tool for intracranial stenosis detection. [ABSTRACT FROM AUTHOR]

A novel hybrid control strategy for reducing torque ripple in permanent magnet brushless direct current motors has been developed by combining the deterministic nature of direct torque control and the adaptive nature of fuzzy logic control. Direct torque control using space vector pulse width modulation has been developed. This technique ensures the near-sinusoidal nature of the stator and rotor current. The impact of commutation ripple corresponding to the sinusoidal current is reduced compared to square wave current in conventional direct torque control. Further, the fuzzy logic controller provides adaptive modulation in space vector to mitigate the torque ripple. The response of the proposed method has been analyzed in the time domain as well as in the frequency domain. Experimental results establish a significant reduction in torque ripple and minimization of high-frequency components. A comparative study with conventional direct torque control methods has also been presented. [ABSTRACT FROM AUTHOR]

The harmonic response of a tuned wire/cylindrical monopole antenna has been determined in terms of its input impedance, VSWR, gain, and radiation patterns. The analysis on monopole antenna has been performed using two simulation tools; Numerical Electromagnetic Code (NEC) and CST microwave studios. The designed monopole antenna is mounted on an infinite ground plane using NEC creating an ideal scenario for simulation, whereas, more realistically, the monopole antenna is mounted on a finite ground plane using CST considering the practical requirements. A perfect conductor is used to design the monopole antenna as well as the ground plane. Simulated results using both the software are validated experimentally. The analysis establishes that the Electromagnetic Interference is efficiently radiated by monopole antenna at odd harmonics as the input impedance matching is good at these frequencies and also the gain is high. A mitigation technique without any additional circuitry has been proposed to suppress radiated off-band harmonics. The central idea behind the proposed mitigation technique is to create an input impedance mismatch at the interfering harmonic frequencies, which is achieved by increasing the diameter of the designed monopole antenna causing reduction in input impedance at higher harmonics. The increased diameter in terms of wavelength is still small at fundamental mode. Thus, the performance of the antenna at fundamental frequency remains largely unaffected, whereas, reflection co-efficient becomes very high at harmonics. [ABSTRACT FROM AUTHOR]

Let and be distinct primes, and consider the expression defined by the formal series , where is a -adic integer variable, is the integer in congruent to mod , and where, for any integer , is the number of s in the binary expansion of . When , reduces to a geometric series with as its common ratio. This series converges in the topology of , and its sum is a rational number which is also a -adic integer. For , as , and so converges in the -adic topology to a -adic integer. In this way, we can define a " -adic function" by the sum of in for and as the sum of in for all other . Thus, while is well-defined as a -adic integer for all , the topology of convergence used to sum the series representation of to compute its value at any given depends on the value of . This represents an entirely new type of point-wise convergence, one where the topology in which the limit of a sequence of functions is evaluated depends on the point at which the sequence is evaluated. In a manner comparable to the adèle ring of a number field, functions defined by -series require considering different metric completions of an underlying field in order to be properly understood. This paper catalogues a variety of examples of this new, unstudied convergence phenomenon, and presents the concept of a "frame", a rigorous formalism for defining and studying -series and their peculiar modes of convergence. [ABSTRACT FROM AUTHOR]

The authors carry out detailed calculations of group character sums attached to the multiplicative representation of positive rationals by pairs of sequences a n + b , A n + B , n = 1 , 2 ⋯ , with the integer coefficients a, b, A, B satisfying a > 0 , A > 0 , a B - A b ≠ 0 . Non-intuitive examples are given. [ABSTRACT FROM AUTHOR]

For the frequency spectrum leakage and fence effect generated in Fast Fourier Transform (FFT) during asynchronous sampling and integral period truncation affect the precision of harmonic detection, a new algorithm for harmonic analysis based on four-spectrum-line interpolation FFT with second-order self-convolution window with five-term Maximum-Sidelobe-Decay (MSD) was proposed and the polynomial fitting method was used to construct the four-spectrum-line interpolation correction formula. The simulation results showed that this algorithm could improve the detection accuracy of amplitude, phase and frequency by 1–2 orders of magnitude compared with other commonly used windowed interpolation algorithms. [ABSTRACT FROM AUTHOR]

The machining performance of an ultrasonic machine mainly depends on the ability of the design of ultrasonic tool. A tool is a significant component in the ultrasonic machining process that contacts the abrasive particles to remove the material from the workpiece. The present investigation has considered the design of three different tool profiles as cylindrical, conical and stepped. A defect is introduced in three different orientations namely longitudinal, perpendicular and inclined about the vibration axis in all the respective tool profiles. The effect of vibration frequency during the machining on the defective and non-defective tools is analysed using numerical simulation technique. The study also presents the modal analysis to obtain the mode shapes and natural frequencies of the tool profiles with and without the defect. The induced stress is computed by performing the harmonic analysis for the defective and non-defective tools. Out of the three profiles analysed in this investigation, the conical tool profile without defect results in a maximum stress of 133 MPa and the same in presence of the internal defect in the inclined orientation is 537 MPa, which is 35% higher than the ultimate tensile strength of the tool material. The comparison of the tool profiles demonstrates that the stepped tool results in maximum Eigen frequency of 134.24 kHz with maximum stress of 453 MPa with the defect in the inclined axis at 30 kHz excitation frequency. [ABSTRACT FROM AUTHOR]

The spectral theory on the S-spectrum was introduced to give an appropriate mathematical setting to quaternionic quantum mechanics, but it was soon realized that there were different applications of this theory, for example, to fractional heat diffusion and to the spectral theory for the Dirac operator on manifolds. In this seminal paper we introduce the harmonic functional calculus based on the S-spectrum and on an integral representation of axially harmonic functions. This calculus can be seen as a bridge between harmonic analysis and the spectral theory. The resolvent operator of the harmonic functional calculus is the commutative version of the pseudo S-resolvent operator. This new calculus also appears, in a natural way, in the product rule for the F-functional calculus. [ABSTRACT FROM AUTHOR]

The paper discusses the stages of structural identification of a dynamic scheme based on the results of test calibration moment perturbations of the spacecraft during flight tests. [ABSTRACT FROM AUTHOR]

The objectivity of the phenomenon of wave-like changes in the number of cells of microbial populations and communities in nature or in a pure culture of microorganisms and the significance of understanding this phenomenon for ecology and biotechnology are experimentally and theoretically substantiated. A brief history of the problem is discussed. Three basic general laws of population ecology are given. A mathematical model is proposed, which, based on the parameters included in the equations, makes it possible to describe the wave-like dynamics of the growth of a population of a pure bacterial culture. This model is a mathematical expression of the third law of population ecology, reflecting the dynamics of the existence of a pure culture of microorganisms: dX/dt = (µ(S) −D(S)) × X. dS/dt = −X × µ (S)/Y + Kr × X × D(S). The experimental and theoretical material presented in the work will be of interest to microbiologists, biotechnologists—theorists and practitioners in the field of cultivation of microorganisms—and specialists in the field of population ecology. [ABSTRACT FROM AUTHOR]

Assessment of consistency in seasonal variability of CO2 fluxes between GOSAT-IM, NASA-GEOS, and NOAA-CT databases was carried out over major biogeographic regions across the globe. A blended data product was composited through a linear least square error optimization procedure from the weighted mean of the three datasets. The blended-product is in closer agreement with GOSAT-IM followed by NOAA-CT and NASA-GEOS for most parts of the globe; however, the blended-product was found to be closer to NASA-GEOS for the Arabian Sea and India. Comparison with limited in-situ FLUXNET observations shows NASA-GEOS has a better agreement for India, and NOAA-CT is better for Europe, Africa, and the US. The mean climatology of these datasets exhibits spatially distinct and coherent patterns of positive and negative fluxes that characterize the source and sink of atmospheric CO2 across the globe. The tropical oceanic and terrestrial regions and the southern circumpolar oceans have been playing as the sources, whereas the temperate oceanic and terrestrial ecosystems and the Eurasian Boreal are the sinks. The seasonal cycles of the fluxes are intense over the northern temperate and boreal terrestrial and oceanic regions; wherein annual amplitudes dominate over the semi-annual amplitudes. The mean climatology varies in the range of −6 to 6 gC m−2 month−1 for oceans as well as continents; however, amplitudes of the seasonal cycle are one order higher for the continents (>20 gC m−2 month−1) than that of the oceans (<1 gC m−2 month−1). The tropical desert tracts, especially Sahara and Thar, and the equatorial oceans show minima in their climatological mean with the reduced seasonal cycle. All these data, however, depict a broad agreement in their seasonal cycle and mean climatology; they exhibit significant differences in their annual budgets, amplitude, and phases of annual and semi-annual harmonics. [ABSTRACT FROM AUTHOR]

Northern Hemisphere planetary waves exhibit an abrupt change in early summer and a significant impact on East Asian summer monsoon rainfall. Although great achievements have been made toward understanding the characteristics and maintenance of planetary waves during winter and summer, the transition of planetary waves during the abrupt-change period is less well understood. This study aims to assess the relative contribution of harmonic waves to the planetary wave transition and mechanism from the perspective of full nonlinear responses to the mountains of Asia (above 500 m) during May and June, with a primary focus on the largest positive geopotential height anomaly over northeastern Asia. The largest positive geopotential height anomaly over northeastern Asia is primarily contributed by wavelengths of around 7000 km, which corresponds to zonal wavenumber 3. The mid–high latitudes planetary waves mainly consist of wavelengths of around 10,000 km (zonal wavenumber 2, roughly) and 7000 km, which are in-phase (out-of-phase) with each other over the Western (Eastern) Hemisphere. Wavelengths of around 10,000 km weaken and displace eastward, while those of 7000 km magnify and hence contribute to the largest positive geopotential height anomaly over northeastern Asia. The full nonlinear response to the forcing by the mountains of Asia provides a considerable contribution to the largest geopotential height anomaly over northeastern Asia. Such a positive contribution comes mainly from the full nonlinear response to sensible heating associated with the mountains over Asia, which is partially offset by the full nonlinear response to dynamical forcing of the Asian mountains. [ABSTRACT FROM AUTHOR]

Heat transport through short and closed vegetation such as grass is modelled by a simple diffusion process. The grass is treated as a homogeneous 'sponge layer' with uniform thermal diffusivity and conductivity, placed on top of the soil. The temperature and heat-flux dynamics in both vegetation and soil are described using harmonic analysis. All thermal properties have been determined by optimization against observations from the Haarweg climatological station in The Netherlands. Our results indicate that both phase and amplitude of soil temperatures can be accurately reproduced from the vegetation surface temperature. The diffusion approach requires no specific tuning to, for example, the daily cycle, but instead responds to all frequencies present in the input data, including quick changes in cloud cover and day–night transitions. The newly determined heat flux at the atmosphere–vegetation interface is compared with the other components of the surface energy balance at this interface. The budget is well-closed, particularly in the most challenging cases with varying cloud cover and during transition periods. We conclude that the diffusion approach (either implemented analytically or numerically) is a physically consistent alternative to more ad hoc methods, like 'skin resistance' approaches for vegetation and bulk correction methods for upper soil heat storage. However, more work is needed to evaluate parameter variability and robustness under different climatological conditions. From a numerical perspective, the present representation of vegetation allows for both slow and rapid feedbacks between the atmosphere and the surface. As such, it would be interesting to couple the present surface parametrization to turbulence-resolving models, such as large-eddy simulations. [ABSTRACT FROM AUTHOR]

The problem of estimation of the force loading the channel gain of the electrohydraulic strength test bench is considered, in particular, on the basis of frequency response analysis, the gradient method, the least mean squares the method with sliding window, the recursive least squares method with forgetting factor and based on harmonic analysis. The calculation relations of the algorithms for obtaining an estimate of the force loading channel gain are given, the results of implementation of these methods on the experimental bench are presented, and a comparison of the estimates obtained by different methods is performed. As a result of the conducted research, there were given recommendations for building an adaptive control system with the force loading channel coefficient identification loop on the aircraft structures strength test stand. The results make it possible to automate the process of regulators adjustment for electric hydraulic actuators of the stand and to speed up the process of strength and fatigue strength tests of aircraft structures. [ABSTRACT FROM AUTHOR]

This paper studies certain aspects of harmonic analysis on nonabelian free groups. We focus on the concept of a positive definite function on the free group and our primary goal is to understand how such functions can be extended from balls of finite radius to the entire group. Previous work showed that such extensions always exist and we study the problem of simultaneous extension of multiple positive definite functions. More specifically, we define a concept of ‘relative energy’ which measures the proximity between a pair of positive definite functions, and show that a pair of positive definite functions on a finite ball can be extended to the entire group without increasing their relative energy. The proof is analytic, involving differentiation of noncommutative Szegö parameters. [ABSTRACT FROM AUTHOR]

We define Hölder classes Λ α associated with a Markovian semigroup and prove that, when the semigroup satisfies the Γ 2 ≥ 0 condition, the Riesz transforms are bounded between the Hölder classes. As a consequence, this bound holds in manifolds with nonnegative Ricci curvature. We also show, without the need for extra assumptions on the semigroup, that a version of the Morrey inequalities is equivalent to the ultracontractivity property. This result extends the semigroup approach to the Sobolev inequalities laid by Varopoulos. After that, we study certain families of operators between the homogeneous Hölder classes. One of these families is given by analytic spectral multipliers and includes the imaginary powers of the generator, the other, by smooth multipliers analogous to those in the Marcienkiewicz theorem. Lastly, we explore the connection between the Hölder norm and Campanato's formula for semigroups. [ABSTRACT FROM AUTHOR]

We improve the best known upper bound on the density of a planar measurable set A containing no two points at unit distance to 0.25442. We use a combination of Fourier analytic and linear programming methods to obtain the result. The estimate is achieved by means of obtaining new linear constraints on the autocorrelation function of A utilizing triple-order correlations in A, a concept that has not been previously studied. [ABSTRACT FROM AUTHOR]

A two-dimensional depth-averaged numerical model was developed, with the aim of describing the tidal circulation patterns in the Obhur Lagoon. The lagoon is located in the central Red Sea, on the eastern coastline, about 30 km north of Jeddah City, Saudi Arabia. The Delft3D modelling system was employed to achieve the aim of the study, using a curvilinear mesh with a high resolution of 10–30 m inside the lagoon region. The 2D numerical model was forced by the major semidiurnal (M2, S2, N2, K2) and diurnal (K1, O1, P1, Q1) tidal constituents, obtained from a regional tidal model by applying a nesting approach. The influence of different numerical and physical parameters on the model results was investigated to find the optimal settings. The performance of the tidal model was evaluated by comparing the simulated water levels with the available water level observations. The IOA parameter and Taylor diagram were considered to assess the model performance statistically. It was found that the numerical model is able to reproduce the tidal levels in the study area to a good degree. The numerical model simulates the tidal conditions in the lagoon region with correlation coefficients of 0.81 and 0.79. The RMSD was found to be ranged between 0.038 and 0.041 m. The IOA parameter confirms the model ability in reproducing the tidal elevations with value > 0.95. The tidal range is relatively small and is dominated by the principal lunar (M2) component, with an amplitude of 0.072 m. The relation F = (O1 + K1) / (M2 + S2) indicates a mixed, predominantly semidiurnal regime (F = 0.52). The simulation results suggest that the inlet of the lagoon including the southern part is tidally dominated. The model results suggest that the ebb neap tide is characterized by slightly higher velocities in comparison with the flood neap tide. This study constitutes a first step towards understanding and modelling the tidal circulation in the Obhur Lagoon. [ABSTRACT FROM AUTHOR]

The prediction for tidal level of the tidal river is affected by the upstream runoff and the tidal wave in the outer sea. The aim of this study is to overcome the harmonic constant of tidal level prediction cannot remain changed for tidal reaches. A new idea named harmonic analysis combined with the least square method, Fourier-based corrected interpolation and ridge regression analysis method was proposed. The key step of the idea is as follows: firstly, the new harmonic constant can be determined via harmonic analysis of water level station data over the corresponding period. Secondly, the Fourier-based correction method is used to interpolate the short-term tidal level data and make the data interval equal. Thirdly, the application of the ridge regression analysis method is used to deal with the multicollinearity problem which may occur in the short-term harmonic analysis. Besides, the selection rules of tidal data from data length, tide type and starting point were considered. Finally, based on an exponential function which can describe relationship between the new harmonic constant and the upstream runoff, the tidal level prediction model of Baimao station in the Yangtze River tidal reaches is constructed. The result shows that the average error of model in the water level was smaller than 0.20 m, and all the time points with a total water level error smaller than 0.25 m exceeded 69% of all points. The mean error in the tide time was smaller than 34 min, and the maximum error was smaller than 60 min. The experimental results conformed to the trend of the observed water level changes, which verified the feasibility of the established model. [ABSTRACT FROM AUTHOR]

We prove that with "high probability" a random Kostlan polynomial in n + 1 many variables and of degree d can be approximated by a polynomial of "low degree" without changing the topology of its zero set on the sphere S n . The dependence between the "low degree" of the approximation and the "high probability" is quantitative: for example, with overwhelming probability, the zero set of a Kostlan polynomial of degree d is isotopic to the zero set of a polynomial of degree O (d log d) . The proof is based on a probabilistic study of the size of C 1 -stable neighborhoods of Kostlan polynomials. As a corollary, we prove that certain topological types (e.g., curves with deep nests of ovals or hypersurfaces with rich topology) have exponentially small probability of appearing as zero sets of random Kostlan polynomials. [ABSTRACT FROM AUTHOR]

We introduce the cone of completely positive functions, a subset of the cone of positive-type functions, and use it to fully characterize maximum-density distance-avoiding sets as the optimal solutions of a convex optimization problem. As a consequence of this characterization, it is possible to reprove and improve many results concerning distance-avoiding sets on the sphere and in Euclidean space. [ABSTRACT FROM AUTHOR]

A setup of a two-dimensional hydrodynamic model based on Delft3D modeling system for the coastal waters of Jeddah is described. Sensitivity tests of both numerical and physical parameters defined in the model and validation of the numerical model are also described. The model was forced by major tidal constituents along the open boundary. The performance of the model was evaluated using available water level observations at four sites along Jeddah coast. The simulated tidal elevations showed a very good matching with the observed tidal elevations. The spring and neap tidal cycle are reproduced by the model with good degree. Statistical analysis showed that RMSD error ranges between 0.001 and 0.17 m, while the MAD values vary between 0.02 and 0.08 m. Comparison of simulated and observed amplitudes and phases of the main tidal components also showed a good agreement. The predicted tide-induced current flooding and ebbing features during spring and neap tides were analyzed. The model suggests that the flow in the region is weak where the strengths of the currents increase towards the shallow areas. [ABSTRACT FROM AUTHOR]

We develop an approach to finding upper bounds for the number of arithmetic operations necessary for doing harmonic analysis on permutation modules of finite groups. The approach takes advantage of the intrinsic orbital structure of permutation modules, and it uses the multiplicities of irreducible submodules within individual orbital spaces to express the resulting computational bounds. We conclude by showing that these bounds are surprisingly small when dealing with certain permutation modules arising from the action of the symmetric group on tabloids. [ABSTRACT FROM AUTHOR]

A brief biographical account of Guido Weiss' life; his accomplishments, mathematics, and diverse interests; and several anecdotes of his interactions with family, friends, colleagues, and students. [ABSTRACT FROM AUTHOR]

This study examines the response of a sea-surface at the Iraq marine water to changes in local meteorological elements [atmospheric pressure (AP), air temperature (AT), and wind field]. Harmonic analysis was conducted to extract the tidal part and nontidal part [meteorological tide or residual water level (RWL)] from the original water level data. The results showed relative changes in the meteorological tide between the seasons. The changes in the meteorological tide throughout the year correlated well with the changes in local meteorological forces. The statistical analysis results for RWL daily averages revealed that the annual range reaches 1.08 m with the maximum and minimum limits in summer and winter, respectively. The spectral analysis results indicated that the annual cycle of RWL accounts for only 21% of the total variance. Moreover, the variations in AP and AT strongly corresponded with their annual cycles. For wind stress components, the annual cycle in their spectrum was insignificant since the highest variance percentage coincided with other cycles, particularly with their high-band frequencies range. The regression analysis showed that during winter, the variations in RWL are mainly attributed to changes in AP, cross-shore wind stress (CSWS), and along-shore wind stress (ASWS), whereas during spring, the RWL variations are due to changes in CSWS, ASWS, and AP. Furthermore, in summer, the RWL variations are attributed to changes in AP, AT, and ASWS, whereas in autumn, the variations in the RWL are because of changes in AP, ASWS, and CSWS. Therefore, the results obtained could be beneficial for various activities in this important region of the Arabian Gulf. [ABSTRACT FROM AUTHOR]

The randomised Horn problem, in both its additive and multiplicative versions, has recently drawn an increasing interest. Especially, closed analytical results have been found for the rank-1 perturbation of sums of Hermitian matrices and products of unitary matrices. We will generalise these results to rank-1 perturbations for products of positive-definite Hermitian matrices and prove the other results in a new unified way. Our ideas work along harmonic analysis for matrix groups via spherical transforms that have been successfully applied in products of random matrices in the past years. In order to achieve the unified derivation of all three cases, we define the spherical transform on the unitary group and prove its invertibility. [ABSTRACT FROM AUTHOR]

We study the Littlewood–Paley–Stein functions associated with Hodge-de Rham and Schrödinger operators on Riemannian manifolds. Under conditions on the Ricci curvature, we prove their boundedness on L p for p in some interval (p 1 , 2 ] and make a link to the Riesz Transform. An important fact is that we do not make assumptions of doubling measure or estimates on the heat kernel in this case. For p > 2 , we give a criterion to obtain the boundedness of the vertical Littlewood–Paley–Stein function associated with Schrödinger operators on L p . [ABSTRACT FROM AUTHOR]

We survey the work of Elias M. Stein in the field of analysis on the Heisenberg group and other nilpotent Lie groups, together with its applications to complex analysis in several variables and partial differential equations. [ABSTRACT FROM AUTHOR]

We extend to a large class of noncompact harmonic manifolds the inversion formulas for the Radon transform on horospheres in hyperbolic spaces or Damek–Ricci spaces. Horospheres are defined here as level hypersurfaces of Busemann functions. The proof uses harmonic analysis on the manifolds considered, developed in a recent paper by Biswas, Knieper and Peyerimhoff; we also give a concise proof of their Fourier inversion theorem for harmonic manifolds. [ABSTRACT FROM AUTHOR]

An algorithm is considered for the statistical analysis of images of nanoparticles obtained by scanning probe microscopy, based on the harmonic analysis of surface profiles with a complex relief. Using harmonic analysis, the average sizes of particles are determined and the sizes of their aggregates are estimated. The algorithm enables the analysis of large samples of particles; in this work, it is tested using model natural objects with an ordered and disordered arrangement of nanoscale particles. The dependence of the analysis results on the type of particle size distribution is also considered, and the features of determining the average size for Gaussian and logarithmically normal distributions are revealed. Among the possible applications of the algorithm, we can mention analysis of the average size of particles and the value of their aggregation in microdispersed and nanodispersed structures (thin amorphous films, colloidal systems, noncrystalline substances, polymers) based on three-dimensional or pseudo-three-dimensional microscopic images. [ABSTRACT FROM AUTHOR]