Polynomial Dependence Research Articles

Abundance: Asymmetric graph removal lemmas and integer solutions to linear equations

AbstractWe prove that a large family of pairs of graphs satisfy a polynomial dependence in asymmetric graph removal lemmas. In particular, we give an unexpected answer to a question of Gishboliner, Shapira and Wigderson by showing that for every , there are ‐abundant graphs of chromatic number . Using similar methods, we also extend work of Ruzsa by proving that a set which avoids solutions with distinct integers to an equation of genus at least two has size . The best previous bound was and the exponent of is best possible in such a result. Finally, we investigate the relationship between polynomial dependencies in asymmetric removal lemmas and the problem of avoiding integer solutions to equations. The results suggest a potentially deep correspondence. Many open questions remain.

Higher-order Newton methods with polynomial work per iteration

We present generalizations of Newton's method that incorporate derivatives of an arbitrary order d but maintain a polynomial dependence on dimension in their cost per iteration. At each step, our dth-order method uses semidefinite programming to construct and minimize a sum of squares-convex approximation to the dth-order Taylor expansion of the function we wish to minimize. We prove that our dth-order method has local convergence of order d. This results in lower oracle complexity compared to the classical Newton method. We show on numerical examples that basins of attraction around local minima can get larger as d increases. Under additional assumptions, we present a modified algorithm, again with polynomial cost per iteration, which is globally convergent and has local convergence of order d.

Resilience and Stress at Professional Work: Analysis of the Research Landscape and Public Interest

Stress has a negative impact on the efficiency and productivity of employees and, accordingly, brings additional costs or losses to companies. A company’s proactive role in ensuring its employees’ resilience to stress in the workplace is crucial in creating an effective working environment and reducing staff turnover. The article analyses the scientific environment (using Descriptive bibliometric analysis and Science Mapping) and public interest (using Google Trends) in resilience and stress at professional work and in management in this area. The bibliometric analysis was conducted using VOSviewer based on publications from the Scopus database (Elsevier) without restrictions on the year of publication, country, author, language and category; the trend analysis was conducted for the period 2004‒2024 for all categories and countries, all Internet traffic was restricted to “Web searches”. The study showed a steady increase in Internet searches for the concept of “resilience training”, with peaks in 2004 and 2005 (coinciding with known terrorist attacks); interest in the query “resilience at professional work” is highest in the United States and the United Kingdom, and 12 leading countries were identified for the query “stress at professional work”. The dynamics of scientific papers in this area are described in the article by a 3rd-degree polynomial dependence equation with a determination coefficient of R² = 0.9676; a significant surge in publication activity occurred in 2014, with the number of papers increasing by 472% and an annual growth rate of 20% in 2014‒2024. The dominant subject areas of these publications are medicine (34.50%), social sciences (15.08%) and psychology (14.47%); countries are the USA, the UK, Australia, Canada, and China. The article identifies scientists who are leaders of scientific thought in this area, the most developed research networks, authoritative publications and journals (based on citation analysis), the most powerful international and national institutions that have funded research in this area (among the world leaders are the US National Institutes of Health and the US Department of Defence). The article structures the scientific work in this area: 1) based on the content and contextual feature, nine thematic clusters are identified, the most significant of which is the one that studies stress at work and professional burnout from a medical point of view; 2) based on the content and chronological feature, the most significant number of works were those on the human factor and gender issues of stress and resilience published in 2017‒2018.

Взаимосвязь окружной скорости и потерь энергии в проточной части центростремительной турбины с частичным облопачиванием рабочего колеса

Low-consumption turbomachines are devices that play an important role in the drive of various units in the field of shipbuilding, aircraft engineering and other branches of heavy engineering. They have some advantages over a high-average power turbine. The largest number of low-consumption turbomachines are made partial, i.e. with partial intake. The principle of a turbine with partial flapping of the impeller is considered as one of the types of partial turbomachines. The influence of the main velocity characteristic of the turbine stage on the loss of kinetic energy in the stage is investigated. The simulation of gas dynamic processes occurring in the turbine stage was carried out using the ANSYS Workbench software package. With the help of this complex, a three-dimensional geometric model of the turbine stage with varying degrees of impeller damping was created. By applying the finite element method, a computational grid, a computational model are generated, and boundary conditions of a numerical experiment are set. The result of the numerical experiment is graphs of the dependence of kinetic energy loss on the circumferential velocity (speed characteristics of the turbine stage). This dependence can be represented not only graphically, but also with the help of mathematical apparatus. An example of such an apparatus is the polynomial dependence. The considered mathematical design can be used in order to optimize mathematical models of gas flow in the flow part of a low-flow turbine. Cubic two-parameter polynomials of kinetic energy losses in the flow part of the nozzle and impeller are obtained, and an assessment of its applicability in the current mathematical model is given.

Application of kinetic models to study the sorption rate in the ‘ammonium ions–calcined sorbent’ system

This study examines sorption kinetics for the extraction of ammonium ions from an aqueous solution under static conditions using 5 g of sorbent. The sorbent was obtained by calcining ash and slag waste accumulated in the ash dump following hydraulic ash removal. The initial concentrations of ammonium ions in the model solutions were 5, 20, 50 and 100 mg/dm3. The volume of the model solution was 50 cm3. For each initial concentration, the kinetic curves of the ammonium ion sorption at the sorption duration of 10, 30, 60, 90, 120, 150 and 180 min were obtained. The kinetic curves were processed using the Lagergren (pseudo-first order), Ho and McKay (pseudo-second order), Morris-Weber (diffusion) and Elovich kinetic equations. It was demonstrated that all kinetic equations adequately describe the experimental data. The linear correlation of the equations was given. The Boyd equation was used to determine the limiting stage in the Morris–Weber model. It was established that the external diffusion mechanism is limiting for the sorption of ammonium ions by a calcined sorbent. The Lagergren model, with a coefficient of determination R2 of 0.9801–0.9949, best described the experimental data on sorption kinetics. Sorption rate curves as a function of the adsorption value and sorption time were given. The latter are described by exponential and polynomial dependence according to the Lagergren model, polynomial dependence according to the Ho and McKay model and exponential dependence according to the Morris–Weber and Elovich models. The sorption rate was the highest at the initial stage of sorption for all dependencies, which is consistent with previous studies on the sorption of pollutants from aqueous solutions using various sorbents.

Linear Monte Carlo quadrature with optimal confidence intervals

We study the numerical integration of functions from isotropic Sobolev spaces Wps([0,1]d) using finitely many function evaluations within randomized algorithms, aiming for the smallest possible probabilistic error guarantee ε>0 at confidence level 1−δ∈(0,1). For spaces consisting of continuous functions, non-linear Monte Carlo methods with optimal confidence properties have already been known, in few cases even linear methods that succeed in that respect. In this paper we promote a method called stratified control variates (SCV) and by it show that already linear methods achieve optimal probabilistic error rates in the high smoothness regime without the need to adjust algorithmic parameters to the uncertainty δ. We also analyse a version of SCV in the low smoothness regime where Wps([0,1]d) may contain functions with singularities. Here, we observe a polynomial dependence of the error on δ−1 in contrast to the logarithmic dependence in the high smoothness regime.

Melatonin exchange in infertile women with repeated implantation failures

Background. Repeated implantation failure occurs in approximately 10–15% of women undergoing in vitro fertilization and embryo transfer (IVF-ET) cycles. One of the important factors is the changed morpho-functional state of the endometrium and chronodestruction in the woman’s body. Objective of the study: to determine the characteristics of melatonin (MT) metabolism in infertile women with repeated implantation failures in IVF-ET cycles. Material and methods. 103 women of reproductive age with infertility and repeated implantation failures who were treated in IVF-ET cycles were observed. Depending on the onset of pregnancy in the current IVF-ET cycle, women were divided into 2 groups: group A – 35 women with the onset of pregnancy, group B – 68 patients without the onset of pregnancy. The control group (group C) included 32 healthy fertile women. The MT level in blood serum and 6-sulfatoxymelatonin (aMT6s) in urine was determined. Results. The initial levels of MT in patients of group A (11.38 ± 0.38 pg/ml) and in group B (9.55 ± 0.27 pg/ml) were lower than in group C (13.67 ± 0.65 pg/ml) in 1.20 (p < 0.01) and 1.43 (p < 0.01) times, respectively. At the same time, the level of MT in women of group A was 1.19 times higher than in the group B (p < 0.03). Excretion of aMT6s in urine in group A (5.09 ± 0.19 ng/ml Cr) and in group B (3.03 ± 0.09 ng/ml Cr) were lower than in group C (6.12 ± 0.21 ng/ml Cr) respectively in 1.20 (p < 0.01) and 2.02 (p < 0.01) times. The aMT6s concentration in urine in patients of group A was 1.68 times higher than in group B (p < 0.01). A direct relationship was established between the levels of serum MT and urinary aMT6s, which was most adequately approximated by a polynomial dependence: y = 0.0139x2 – 0.1127x + 3.2978, R² = 0.2994, r = 0.51, p < 0.01. Conclusions. Women with repeated implantation failures are characterized by a decrease in the level of MT in blood serum and its main metabolite aMT6s in urine, which may be one of the key factors of implantation failure.

Discrete Event Systems Theory for Fast Stochastic Simulation via Tree Expansion

Discrete Event Systems Theory for Fast Stochastic Simulation via Tree Expansion

Invariant scaling laws for plane Couette flow with wall-transpiration

The effect of the wall-transpiration Reynolds number ReV0 on the large-scale rolls of the plane Couette flow with wall-transpiration is investigated using resolvent analysis. We observe streamwise-elongated large-scale rolls, moving closer to the suction wall and becoming narrower in the wall-normal and spanwise direction as well as shortened in the streamwise direction for growing ReV0 due to the decreasing characteristic length of the sheared region. Invariant scaling laws describing the growth of the amplification gain over various parameters and determining the optimal parameters yielding most amplification are found enhancing our understanding of the influence on the coherent structures, which can be used to predict their exact size. In a potential second step, this allows to manipulate and efficiently modify these flow characteristics increasing the functionality for various engineering applications as for mass, momentum and heat transfer, which is dominated by turbulent superstructures. For large enough wall-transpiration, the most amplified structures are oblique at optimal streamwise wavenumbers αmax≠0 growing linearly with ReV0. The optimal spanwise wavenumber βmax yielding most amplified structures shows a polynomial dependence of second order on ReV0. For a constant ratio of the wall-transpiration and streamwise Reynolds numbers γ=ReV0Re, the most amplified structures occur at optimal streamwise Reynolds numbers represented by Remax·γa=C. The amplification gain changes its trend from growing with Re2 to decreasing with Re−1.368 after Remax is reached. The resulting streamwise structures are identical for each set of Remax and γ within this invariant scaling law.

Technogenic Reservoirs Resources of Mine Methane When Implementing the Circular Waste Management Concept

From a commercial viewpoint, mine methane is the most promising object in the field of reducing emissions of climate-active gases due to circular waste management. Therefore, the task of this research is to estimate the technogenic reservoirs resources of mine methane when implementing the circular waste management concept. The novelty of the authors’ approach lies in reconstructing the response space for the dynamics of methane release from the front and cross projections: CH4 = ƒ(S; t) and CH4 = ƒ(S; L), respectively. The research established a polynomial dependence of nonlinear changes in methane concentrations in the mixture extracted by type 4 wells when a massif is undermined as a result of mining in a full-retreat panel. And the distance from the face to the start of mining the panel is reduced by 220 m. For this reason, the emission of mine methane, in case of degasification network disruption in 15 days, can amount to more than 660 thousand m3 only for wells of type no. 4.

Contactless in-vivo temperature sensing in spinal cord based on magnetically bistable microwire

We have employed a magnetically bistable glass coated microwire as a passive contactless sensing element for in-vivo temperature monitoring in the rat’s spinal cord. The single piece (1 cm long) of Fe76Cr2Mo6B15Cu1 microwire was epidurally implanted into the adult female Wistar rats. The magnetization switching was measured in-vivo within the temperature range of 34.5–41.0 °C. Results show a monotonous temperature decrease of the switching time whose fitting to a second order polynomial dependence allows one to conclude a sensitivity down to 0.01ºC within the measured interval. Biocompatibility study shows that cells have a high affinity to the glass-coated microwire, and their viability is not influenced by the experimental condition under which the microwire’s response is measured. Finally, a histology study reveals that no histopathological changes or tissue reactions were observed even after 9 months of implantation.

Delayed dynamic-feedback controller design for multi-frequency vibration suppression

We present a methodology for designing a dynamic controller with delayed output feedback for achieving non-collocated vibration suppression with a focus on the multi-frequency case. To synthesize the delay-based controller, we first remodel the system of equations as a delay-differential algebraic equation (DDAE) in such a way that existing tools for design of a static output feedback controller can be easily adapted. The problem of achieving non-collocated vibration suppression with sufficient damping is formulated as a constrained optimization problem of minimizing the spectral abscissa in the presence of zero-location constraints, with the constraints exhibiting polynomial dependence on its parameters. We transform the problem into an unconstrained one using elimination, following which we solve the resulting non-convex, non-smooth optimization problem.

EXPERIMENTAL STUDIES OF NOISE POLLUTION OF MECHANICAL PROCESSING PLANTS

Purpose. Determination of noise pollution at the workplace of workers of metal-cutting machines of turning, milling and drilling groups. Methodology. An experimental study of the noise load at the workplace of workers working on lathes, milling and drilling group machines. The research was carried out using a testo 816-1 digital noise level meter, Sound Forge Pro software and a mathematical package for the formation of noise dependences on the type and mode of operation of the machines. Results. An experimental study of the noise load at the workplace of workers working on metal-cutting machines, namely universal lathe-screw-cutting machines (type 1K62 and CA6136), vertical milling machines (type 6P11A and F2-250), vertical milling machine with CNC (type XS5036C) and radial drilling machine (type 2L53U). In addition, it was established that the type of machine affects the level of noise pollution at the workplace of metal-cutting machine workers. For example, the machines used for drilling are characterized by high noise values in all octave frequency ranges and all operating modes, increasing the noise level by 15 dB (16.5%) on average. Milling machines, compared to lathes, show higher noise values at medium and high octave frequencies by 7 dB (8.4%). Based on the results of the study, an adequate polynomial dependence of the fifth order was determined, which describes the noise levels relative to the frequency and corresponds to the results of the natural experiment. The resulting dependencies have practical applications in the development of component materials for simultaneous shielding of both magnetic fields of an electromagnetic field of industrial frequency and electromagnetic fields of different frequencies. Scientific novelty. The solution of this problem can be used in the future to assess the risk of occupational diseases among workers working at mechanical processing stations. Practical significance. The determined dependence will allow further consideration of the issue related to the protection of employees of mechanical processing stations from noise pollution arising during the operation of metal-cutting machines of various groups. Key words: railway, metalworking machine, noise pollution, noise.

Worst-Case Iteration Bounds for Log Barrier Methods on Problems with Nonconvex Constraints

Interior point methods (IPMs) that handle nonconvex constraints such as IPOPT, KNITRO and LOQO have had enormous practical success. We consider IPMs in the setting where the objective and constraints are thrice differentiable, and have Lipschitz first and second derivatives on the feasible region. We provide an IPM that, starting from a strictly feasible point, finds a μ-approximate Fritz John point by solving [Formula: see text] trust-region subproblems. For IPMs that handle nonlinear constraints, this result represents the first iteration bound with a polynomial dependence on [Formula: see text]. We also show how to use our method to find scaled-KKT points starting from an infeasible solution and improve on existing complexity bounds. Funding: This work was supported by Air Force Office of Scientific Research [9550-23-1-0242]. A significant portion of this work was done at Stanford where O. Hinder was supported by the PACCAR, Inc., Stanford Graduate Fellowship and the Dantzig-Lieberman fellowship.

Stability optimization of time-delay systems with zero-location constraints applied to non-collocated vibration suppression

We present an active control method for achieving non-collocated vibration absorption, implemented on a lumped mass system. The task of suppressing vibrations at a number of frequencies, at a target mass is recast into a problem of assigning zeros of the transfer function from the external excitation force to the position of the target mass. The controller design involves computing the controller parameters by utilizing the available output feedback to directly assign a set of zeros on the imaginary axis while simultaneously preserving the overall stability with a sufficient margin. The design also takes into account delays in the feedback path. The presence of delays leads to an infinite dimensional system for which, there exists in general, infinitely many characteristic roots. The requirement of achieving sufficient damping in the resulting closed-loop system together with suppressing vibrations of the desired frequency leads to a constrained optimization problem of minimizing the spectral abscissa function subject to zero-location constraints. These constraints exhibit polynomial dependence on the controller parameters. We present two approaches for controller parameterization for the single and multiple input case. Both approaches are based on constraint elimination and exploit the property that the constraints are affine in a selection of the gain parameters. Finally, the methodology is verified by simulating on a spring–mass–damper system following which, it is then validated experimentally on a laboratory setup.

Temperature-Humidity-Bias Testing and Life Prediction Modeling for Electrochemical Migration in Aerosol-Jet Printed Circuits

Abstract Aerosol-Jet Printing (AJP) technology, applied to the manufacturing of printed hybrid electronics (PHE) devices, has the capability to fabricate highly complex structures with resolution in the tens-of-microns scale, creating new possibilities for the fabrication of electronic devices and assemblies. The widespread use of AJP in fabricating PHE and package-level electronics necessitates a thorough assessment of not only the performance of AJP printed electronics but also their reliability under different kinds of life-cycle operational and environmental stresses. One important hindrance to the reliability and long-term performance of such AJP electronics is electrochemical migration (ECM). ECM is an important failure mechanism in electronics under temperature and humidity conditions because it can lead to conductive dendritic growth, which can cause dielectric breakdown, leakage current, and unexpected short circuits. In this paper, the ECM propensity in conductive traces printed with AJP process, using silver-nanoparticle (AgNP) based inks, was experimentally studied using temperature-humidity-bias (THB) testing of printed test coupons. Conductive dendritic growth with complex morphologies was observed under different levels of temperature, humidity, and electric bias in the THB experiments. Weibull statistics are used to quantify the failure data, along with the corresponding confidence bounds to capture the uncertainty of the Weibull distribution. A nonmonotonic relationship between time-to-failure and electric field strength was noticed. An empirical acceleration model for ECM is proposed, by combining the classical Peck's model with a quadratic polynomial dependence on electric field strength. This model provides good estimate of acceleration factors for use conditions where the temperature, humidity, and electrical field are within the tested range, but should be extrapolated with care beyond the tested range.

Riemann–Hilbert Problems, Polynomial Lax Pairs, Integrable Equations and Their Soliton Solutions

The standard approach to integrable nonlinear evolution equations (NLEE) usually uses the following steps: (1) Lax representation [L,M]=0; (2) construction of fundamental analytic solutions (FAS); (3) reducing the inverse scattering problem (ISP) to a Riemann-Hilbert problem (RHP) ξ+(x,t,λ)=ξ−(x,t,λ)G(x,tλ) on a contour Γ with sewing function G(x,t,λ); (4) soliton solutions and possible applications. Step 1 involves several assumptions: the choice of the Lie algebra g underlying L, as well as its dependence on the spectral parameter, typically linear or quadratic in λ. In the present paper, we propose another approach that substantially extends the classes of integrable NLEE. Its first advantage is that one can effectively use any polynomial dependence in both L and M. We use the following steps: (A) Start with canonically normalized RHP with predefined contour Γ; (B) Specify the x and t dependence of the sewing function defined on Γ; (C) Introduce convenient parametrization for the solutions ξ±(x,t,λ) of the RHP and formulate the Lax pair and the nonlinear evolution equations (NLEE); (D) use Zakharov–Shabat dressing method to derive their soliton solutions. This requires correctly taking into account the symmetries of the RHP. (E) Define the resolvent of the Lax operator and use it to analyze its spectral properties.

Stochastic Localization Methods for Convex Discrete Optimization via Simulation

Solving Convex Discrete Optimization via Simulation via Stochastic Localization Algorithms Many decision-making problems in operations research and management science require the optimization of large-scale complex stochastic systems. For a number of applications, the objective function exhibits convexity in the discrete decision variables or the problem can be transformed into a convex one. In “Stochastic Localization Methods for Convex Discrete Optimization via Simulation,” Zhang, Zheng, and Lavaei propose provably efficient simulation-optimization algorithms for general large-scale convex discrete optimization via simulation problems. By utilizing the convex structure and the idea of localization and cutting-plane methods, the developed stochastic localization algorithms demonstrate a polynomial dependence on the dimension and scale of the decision space. In addition, the simulation cost is upper bounded by a value that is independent of the objective function. The stochastic localization methods also exhibit a superior numerical performance compared with existing algorithms.

Error estimates with low-order polynomial dependence for the fully-discrete finite element invariant energy quadratization scheme of the Allen–Cahn equation

In this paper, for the Allen–Cahn equation, we obtain the error estimate of the temporal semi-discrete scheme, and the fully-discrete finite element numerical scheme, both of which are based on the invariant energy quadratization (IEQ) time-marching strategy. We establish the relationship between the [Formula: see text]-error bound and the [Formula: see text]-stabilities of the numerical solution. Then, by converting the numerical schemes to a form compatible with the original format of the Allen–Cahn equation, using mathematical induction, the superconvergence property of nonlinear terms, and the spectrum argument, the optimal error estimates that only depends on the low-order polynomial degree of [Formula: see text] instead of [Formula: see text] for both of the semi and fully-discrete schemes are derived. Numerical experiment also validates our theoretical convergence analysis.

Static Modulus of Deformation of Uncemented Layers of the Railway Substructure—Comparison of Values and Determination of Correlation Dependence According to the Test Procedure of the Slovak Railways and Deutsche Bahn A.G.

The paper focuses on the analysis of the values of the static modulus of deformation obtained by the application of the test procedure specified in the methodology for the diagnostics of the sub-ballast layers used for German railways (DIN 18 134) and the Railways of the Slovak Republic (Regulation TS4). The purpose of the study was to determine the correlation between the measured values of the static modulus of deformation according to the above-mentioned methodologies based on a series of experimental measurements on an experimental field built at a scale of 1:1. It also aimed to develop a numerical model characterising the behaviour of the loaded environment during the experimental measurements using the finite element method, which can subsequently be used for the design of the structural composition of the sub-ballast layers. For the purpose of the experimental measurements, a sub-ballast layer of 0/31.5 mm crushed aggregate of different design thicknesses was applied to the sub-ballast layers. A polynomial dependence with a high value of the reliability coefficient can be found between the results of the static modulus of deformation obtained using the mentioned measurement methodologies during the quality inspection of the implemented construction works. This dependence is valid for the specific boundary conditions of the experimental measurements performed (subsoil of clay with gravel admixture and the sub-ballast crushed aggregate layer of 0/31.5 mm dolomitic gravel). In the future, establishing correlation dependencies for other boundary conditions and structural material compositions can be considered.