Differentiable Research Articles

Understanding salinity evolution in the Moroccan Ghiss-Nekor aquifer using differential mapping technique

Assessing spatiotemporal groundwater hydrochemistry evolution is crucial for sustainable aquifer management. The Ghiss-Nekor aquifer, located in a semi-arid coastal region, requires a comprehensive grasp of hydrochemical shifts for proactive degradation mitigation. Accordingly, the differential mapping technique (DMT) has been employed to assess the salinity evolution in the study area. In 2015 and 2022, 48 and 52 groundwater samples were respectively analyzed. As a result, an overall increase in salinity was observed within the Ghiss-Nekor aquifer, particularly near the shoreline, where in some areas the TDS variations (ΔTDS) exceeded +7000 mg/L. ΔCl- reached up to +129 meq/L near the coast. Similarly, ΔNa+, ΔSO42-, ΔMg2+, ΔCa2+, ΔK+, and ΔHCO3-, showed values up to +94 meq/L, +22 meq/L, +17 meq/L, +10 meq/L, +1 meq/L, and +5 meq/L, respectively, along the coast. In contrast, a decline in the levels of these ions was noted across most of the plain, especially in the southern portion. Positive major ions levels near the sea indicate ongoing freshwater degradation due to seawater intrusion. DMT approach showed its effectiveness in assessing the spatiotemporal changes occurring within aquifers. These findings advocate for broader DMT application in safeguarding aquifers impacted by salinization, promoting sustainable development.

RESEARCH ON THE SEQUENTIAL QUADRATIC PROGRAMMING DIFFERENTIAL EVOLUTION, JAYA, AND JAYA'S EVOLUTIONARY ALGORITHM

This study focuses on researching and comparing optimization algorithms such as Sequential Quadratic Programming, Differential Evolution, Jaya, and Jaya's evolutionary algorithm. Sequential Quadratic Programming is an optimization method based on mathematical programming, where constraints and objective functions are represented by convex and differentiable functions. Differential Evolution is a combinatorial evolutionary algorithm that utilizes genetic operators such as crossover and mutation to generate new generations of individuals. Jaya is an optimization algorithm based on continuous improvement of the population, where individuals are updated based on the current best solution. This study focuses on the specific application of the Jaya evolutionary algorithm (iJaya) compared to other algorithms and compares the performance of these algorithms in solving optimization problems through real-world examples of fiber orientation optimization in stiffened composite plates. Experiments on popular optimization problems and measure factors such as runtime, accuracy, and the ability to search for optimal solutions were conducted. The research results will provide an overview of the performance and advantages of each algorithm, thereby providing recommendations for selecting the appropriate algorithm for corresponding problems in the construction field.

On signs of certain Toeplitz-Hessenberg determinants whose elements involve Bernoulli numbers

In the paper, by virtue of Wronski's formula and Kaluza's theorem related to a power series and its reciprocal, by means of Cahill and Narayan's recursive relation, and with the aid of the logarithmic convexity of the sequence of the Bernoulli numbers, the author presents the signs of certain Toeplitz-Hessenberg determinants whose elements involve the Bernoulli numbers and combinatorial numbers. Moreover, with the help of a derivative formula for the ratio of two differentiable functions, the author provides an alternative proof of Wronski's formula.

Home, Shelter, Trap Experiences of Pandemic Con finement in Bogotá, Colombia

Drawing on data from two distinct ethnographic research projects, in this article I examine the equation of home, house, and security, as implied in the stay-at-home COVID-19 pandemic mandate. My investigation involving domestic workers in Bogotá revealed that the house is not necessarily a safe space and can sometimes even become a trap. Women's everyday lives are constrained by local labour dynamics, gender paradigms, socio-economic diff erentiation, and urban segregation, while their ontological security hinges on the proximity of close social relations. Meanwhile, research in social housing compounds demonstrates that the built environment can contribute positively to low-income residents' wellbeing. These socio-spatial contexts apparently fostered latent communal bonds that were activated during the pandemic crisis. Supported by feminist critique, which underscores the inseparable connection between the domestic and labour sphere, anthropological research that examines the diverse meanings of house and home urban research, elucidating the role of the built environment in our experience of ontological security, I argue that the home is not an independent cell, containing people within brick-and-mortar con fines. Instead, it emerges as a fluid, interlinked, and expansive realm, de fined by processes beyond the physical edi fice. To build more humane cities that off er ontological security and contribute to the wellbeing of all residents, a paradigm shift is imperative: one that situates this expanded concept of 'home' at the centre of conceiving living environments that not only accommodate, but also nurture interpersonal bonds.

On Logarithmic Holder Condition and Local Extrema of Power Takagi Functions

This paper studies one class of real functions, which we call Takagi power functions. Such functions have one positive real parameter; they are continuous, but nowhere differentiable, and are given on a real line using functional series. These series are similar to the series defining the continuous, nowhere differentiable Takagi function described in 1903. For each parameter value, we derive a functional equation for functions related to Takagi power functions. Then, using this equation, we obtain an accurate two-sides estimate for the functions under study. Next, we prove that for parameter values not exceeding 1, Takagi power functions satisfy the Holder logarithmic condition, and find the smallest value of the constant in this condition. As a result, we get the usual Hölder condition, which follows from the logarithmic Hölder condition. Moreover, for parameter values ranging from 0 to 1, we investigate the behavior of Takagi power functions in the neighborhood of their global maximum points. Then we show that the functions under study reach a strict local minimum on the real axis at binary-rational points, and only at them. Finally, we describe the set of points at which our functions reach a strict local maximum. The benefit of our research lies in the development of methods applicable to continuous functions that cannot be differentiated anywhere. This can significantly expand the set of functions being studied.

On the stability of a nonlinear nonautonomous scalar equation with variable delay

The stability problem of a scalar functional differential equation is a classical one. It has been most fully studied for linear equations. Modern research on modeling biological, infectious and other processes leads to the need to determine the qualitative properties of the solutions for more general equations. In this paper we study the stability and the global limit behavior of solutions to a nonlinear one-dimensional (scalar) equation with variable delay with unbounded and bounded right-hand sides. In particular, our research is reduced to a problem on the stability of a non-stationary solution of a nonlinear scalar Lotka-Volterra-type equation, on the stabilization and control of a non-stationary process described by such an equation. The problem posed is considered depending on the delay behavior: is it a bounded differentiable function or a continuous and bounded one. The study is based on the application of the Lyapunov-Krasovsky functionals method as well as the corresponding theorems on the stability of non-autonomous functional differential equations of retarded type with finite delay. Sufficient conditions are derived for uniform asymptotic stability of the zero solution, including global stability, for every continuous initial function. Using the theorem proven by one of the co-authors on the limiting behavior of solutions to a non-autonomous functional differential equation based on the Lyapunov functional with a semidefinite derivative, the properties of the solutions’ attraction to the set of equilibrium states of the equation under study are obtained. In addition, illustrative examples are provided.

FAUC-S: Deep AUC maximization by focusing on hard samples

Deep AUC maximization (DAM) is a popular method to deal with complex imbalanced classification problems. It learns a deep neural network by minimizing a surrogate AUC loss. The mostly used surrogates are the pairwise square loss and its variants. However, they are usually used in regression problems and are sensitive to noise samples. The easy samples suffer larger losses than those without correct classification, which is unreasonable in optimization problems. In this paper, we propose a focus AUC loss based on samples (FAUC-S) by constructing a differentiable weight function that identifies hard and easy samples, which makes easy samples have small losses, and hard samples have large losses. It is more reasonable than the traditional AUC loss while having the same advantages on large-scale datasets. In experiments, we use an end-to-end compositional DAM to investigate the effect of different weight functions on the AUC loss and compare it with other methods. Experimental results on several benchmark datasets demonstrate that FAUC-S achieves superior performance in terms of AUC compared to existing state-of-the-art methods.

Delta Calculus on Time Scale Formulas That Are Similar to Hilbert-Type Inequalities

In this article, we establish some new generalized inequalities of the Hilbert-type on time scales’ delta calculus, which can be considered similar to formulas for inequalities of Hilbert type. The major innovation point is to establish some dynamic inequalities of the Hilbert-type on time scales’ delta calculus for delta differentiable functions of one variable and two variables. In this paper, we use the condition aj(sj)=0 and aj(sj,zj)=aj(wj,nj)=0, ∀j=1,2,…,n. These inequalities will be proved by applying Hölder’s inequality, the chain rule on time scales, and the mean inequality. As special cases of our results (when T=N and T=R), we obtain the discrete and continuous inequalities. Also, we can obtain other inequalities in different time scales, like T=qZ−, q>1.

APPROXIMATION OF DIFFERENTIATION OPERATORS BY BOUNDED LINEAR OPERATORS IN LEBESGUE SPACES ON THE AXIS AND RELATED PROBLEMS IN THE SPACES OF \((p,q)\)-MULTIPLIERS AND THEIR PREDUAL SPACES

We consider a variant \(E_{n,k}(N;r,r;p,p)\) of the four-parameter Stechkin problem \(E_{n,k}(N;r,s;p,q)\) on the best approximation of differentiation operators of order \(k\) on the class of \(n\) times differentiable functions \((0<k<n)\) in Lebesgue spaces on the real axis. We discuss the state of research in this problem and related problems in the spaces of multipliers of Lebesgue spaces and their predual spaces. We give two-sided estimates for \(E_{n,k}(N;r,r;p,p)\). The paper is based on the author's talk at the S.B. Stechkin's International Workshop-Conference on Function Theory (Kyshtym, Chelyabinsk region, August 1–10, 2023).

Grey matter structural alterations in anxiety disorders: a voxel-based meta-analysis.

Anxiety disorders (ADs) are a group of prevalent and destructive mental illnesses, but the current understanding of their underlying neuropathology is still unclear. Employing voxel-based morphometry (VBM), previous studies have demonstrated several common brain regions showing grey matter volume (GMV) abnormalities. However, contradictory results have been reported among these studies. Considering that different subtypes of ADs exhibit common core symptoms despite different diagnostic criteria, and previous meta-analyses have found common core GMV-altered brain regions in ADs, the present research aimed to combine the results of individual studies to identify common GMV abnormalities in ADs. Therefore, we first performed a systematic search in PubMed, Embase, and Web of Science on studies investigating GMV differences between patients with ADs and healthy controls (HCs). Then, the anisotropic effect-size signed differential mapping (AES-SDM) was applied in this meta-analysis.A total of 24 studies (including 25 data sets) were included in the current study, and 906 patients with ADs and 1003 HCs were included. Compared with the HCs, the patients with ADs showed increased GMV in the left superior parietal gyrus, right angular gyrus, left precentral gyrus, and right lingual gyrus, and decreased GMV in the bilateral insula, bilateral thalamus, left caudate, and right putamen. In conclusion,the current study has identified some abnormal GMV brain regions that are related to the pathological mechanisms of anxiety disorders. These findings could contribute to a better understanding of the underlying neuropathology of ADs.

МОВНА ПОЛІТИКА УКРАЇНИ: АНАЛІЗ СУЧАСНОГО СТАНУ В РЕЦЕПЦІЇ ПОГЛЯДІВ ІВАНА ОГІЄНКА

The article outlines the state of language policy development in Ukraine through the prism of Ivan Ohiienko’s views (on the example of the works «Faith and Culture», «Saving Ukraine», «Culture and Science», «The Science of Native Language Responsibilities: Native Language Catechism for Teachers, Pen Workers, clergy, law-yers, students and the general public» «Saving Ukraine», «Our Literary Language»). In particular, it was emphasized that the legal status of the Ukrainian language as a state language, its high development, codifi cation and stylistic diff erentiation, com-petitiveness in the European language space. The concept of language policy is out-lined, which, being a component of the general system of national policy, refl ects its specifi c principles and supports the dominant ideology. The interpretation of language policy is presented as a conscious and purposeful infl uence, which aims to promote the eff ective functioning of the language in various areas of its application; a set of ideological principles and practical measures to solve language problems in society and the state; a set of political and administrative measures aimed at giving language development the desired direction; part of the national policy of a certain state, as it concerns the change or preservation of the existing functional distribution of lan-guages in a multilingual society. It is emphasized that the works of Ivan Ohiienko, substantiating the problematic issues of the language, are of great importance for the education of a nationally conscious generation, encourage creative thought, under-standing of the science of Ukrainian studies. Examples are given from the works of Ivan Ohiienko, in which he highlighted the problem of the struggle for the purity of the native language, as well as condemned linguistic Russifi cation in post-Soviet Ukraine, for example, his distinct anti-Moscow position in the message-appeal to the Committee for the Protection of Ukrainian Culture and the People, as well as the need to educate a highly cultured, patriotic determined personality. The vision of Ivan Ohiienko regarding the essence of the native language is indicated. The Metropolitan predicted a situation when the native language would serve the Ukrainian people in various spheres of public life

Layout and cross-sectional size optimization of truss structures with mixed design variables based on gradient method

The object of the study was truss-type rod structures, which were investigated for the purpose of finding the optimal design solution in a mixed (continuous and discrete) space of variables. The parameters of the geometric scheme of the truss, as well as the dimensions of the cross-sections of its elements, were considered as design variables. The stated optimization problem is represented as a nonlinear programming task, in which the objective function and nonlinear constraints of the mathematical model are continuously differentiable functions of the design variables. The system of constraints includes strength and stability inequalities, formulated for the design cross-sections of the rod elements of the structure, which is subject to the effect of the design load combinations of the ultimate limit states. As a part of the system of constraints, the displacement constraints formulated for the specified structural nodes, which is subject to the action of design load combinations of the serviceability limit states, are considered. To solve the stated optimization problem, a method of the objective function gradient on the surface of active constraints was used, with the simultaneous elimination of residuals in the violated restrictions. For design variables, the variation of which must be performed according to a given set of possible discrete values, a discretization procedure for the optimal solution obtained in the continuous space of design variables is proposed. A comparison of the proposed optimization methodology with alternative metaheuristic methods and algorithms reported in the literature was performed. On the considered problem of parametric optimization of a 47-span tower structure, a design solution with a weight of 835,403 kg was obtained, which is 1.53...4.6 % better than the optimal solutions obtained by other authors

Current decoupling control of permanent magnet synchronous motor based on improved nonlinear extended state observer

Precise current decoupling is required to achieve good control performance in the vector control of permanent magnet synchronous motor (PMSM), but traditional decoupling methods are unable to solve the problem of poor current decoupling effectiveness when the system inductance parameters are mismatched. Therefore, a decoupling control method of PMSM based on improved nonlinear extended state observer (INESO) is proposed in this paper. Firstly, a smooth, differentiable nonlinear function is used to replace the traditional fal function, which overcomes the problem of discontinuous gain changes. Secondly, a time-varying gain is designed to address the problem of reduced observer performance due to differential peak values in traditional NESO. Finally, the stability of INESO and the current loop closed-loop system is proven, followed by simulation and experimental verification. The simulation and experimental results show the proposed method effectively observes and compensates for system uncertainties, including parameter perturbations, external disturbances, and unmodeled dynamics. This method achieves complete decoupling of d and q-axes currents, while suppressing interference and enhancing the control performance of PMSM. The proposed INESO decoupling method reduces the d-axis current fluctuation about 96% and 90% when the load changes abruptly under motor inductance parameter mismatch, and can reduce q-axis current fluctuation about 88% and 78% when the d-axis current steps, respectively, compared with the conventional Current Feedback Decoupling Control (CFDC) and CDDC decoupling methods.

Cauchy Problem for the Nonlinear Liouville Equation in the Class of Periodic Infinite-Gap Functions

The inverse spectral problem method is used to integrate the nonlinear Liouville equation in the class of periodic infinite-gap functions. The evolution of the spectral data of the periodic Dirac operator whose coefficient is a solution of the nonlinear Liouville equation is introduced. The solvability of the Cauchy problem for an infinite system of Dubrovin differential equations in the class of three times continuously differentiable periodic infinite-gap functions is proved. It is shown that the sum of a uniformly convergent function series constructed by solving the Dubrovin system of equations and using the first trace formula satisfies the Liouville equation.

On Nonlinear Boundary Value Problems for Differential Inclusions

We consider autonomous differential inclusions with nonlinear boundary conditions. Sufficient conditions for the existence of solutions in the class of absolutely continuous functions are obtained for these inclusions. It is shown that the corresponding existence theorem applies to the Cauchy problem and the antiperiodic boundary value problem. The result is used to derive a new mean value inequality for continuously differentiable functions.

Population genetic characteristics of free-living domestic cats, Felis catus L., 1758, of Russky Island (Peter the Great Bay, Primorsky Krai)

The enormous infl uence of free-living populations of the domestic cat (Felis catus L., 1758) on the wild fauna of small animals throughout the world provides the basis for a careful multilateral study of such populations with a view to their subsequent control, including their genetic structure. A description of the genetic profi le of the free-living population of domestic cats of Russky Island is given. It has been shown that the island population is genetically almost identical to the mainland population of Vladivostok. The exception is a statistically signifi cantly lower proportion of piebald cats on Russky Island (51.8 ± 4.8% versus 63.8 ± 2.0%, p < 0.02). This indicates a common origin for these populations. Due to their recent emergence (probably no more than 160 years ago) and low level of isolation, the populations experienced little genetic shift relative to each other. Similar data were obtained earlier for other pairs of settlements (urban- rural) in Primorsky Krai. A comparative analysis of the available data on the genetic diff erentiation of adjacent urban and rural populations of free-living domestic cats was carried out. The possible connection of genetic variability with the advantage in hunting activity of cats is discussed.

ADVANCED ANALYSIS TOOLS FOR THE EUROPEAN GROUND MOTION SERVICE DATA

Abstract. This paper is focused on Advanced Differential Interferometric SAR (A-DInSAR). In the first part, the paper describes the European Ground Motion Service (EGMS), a new service of the Copernicus Land Monitoring Service. The EGMS provides consistent, regular, standardized, harmonized and reliable information regarding natural and anthropogenic ground motion over Europe. It is derived from A-DInSAR analysis of Copernicus Sentinel-1 data. The EGMS includes three main products: Basic, i.e. basic deformation maps delivered for individual and consistent frames of image stacks; Calibrated, i.e. deformation map integrated into a reference Global Navigation Satellite System network; and Ortho, which includes the East-West and Up-Down deformation, obtained by combining the ascending and descending results. The second part of the paper describes examples of data analysis. The first one is a clustering of PSI results, which highlights the so-called Active Deformation Areas (ADAs). The second one is an automatic classification of the ADAs. The third analysis concerns the differential deformation maps, which are useful to highlight areas where high deformation gradients occur. Such gradients are often associated to damages in buildings and infrastructures.

Synthesis of the glycodendrimer macromolecule based on porphyrin as a targeted drug delivery system

The present study synthesized a novel dendrimer with specific functional groups and use them as pharmaceutical carriers at the nanoscale. First, a glycodendrimer was synthesized and a porphyrin substance was selected as its core. Afterward, this substance was subsequently reacted with gallic acid and bromo valerate step-by-step and it was conjugated with acrylonitrile functionalized with Tris (hydroxymethyl) aminomethane. Eventually, the composition was reacted with Tris [α-D Manos (pyrazolyl oxy) methyl] methylamine and glycodendrimer (TTP-Tr-GD) was prepared via a divergent approach to develop drug delivery system. The nanocarrier was characterized using several techniques, such as scanning electron microscopy (FE-SEM), thermal analysis (TGA), NMR, Fourier transform infrared (FT-IR), differential laser scanning (DLS), elemental mapping (EDS), and Zeta potential. Effective factors on the release of the drug delivery, including the best time to absorb, sample pH, and reaction temperature were optimized. The statistically optimized sorption efficiency (98.11%) was attained at pH = 5.5, and a contact time of 15 min. As a result of the functional groups on the surface of the TTP-Tr-GD are appropriate for simultaneous determination and high throughput analysis of drug delivery system.

A series expansion of a logarithmic expression and a decreasing property of the ratio of two logarithmic expressions containing cosine

AbstractIn this study, by virtue of a derivative formula for the ratio of two differentiable functions and with aid of a monotonicity rule, the authors expand a logarithmic expression involving the cosine function into the Maclaurin power series in terms of specific determinants and prove a decreasing property of the ratio of two logarithmic expressions containing the cosine function.

A Continuum Dimensional Algebra of Nowhere Differentiable Functions

We construct an algebra of dimension 2ℵ0 consisting only of functions which in no point possess a finite one-sided derivative. We further show that some well known nowhere differentiable functions generate algebras, which contain functions which are differentiable at some points, but where for all functions in the algebra the set of points of differentiability is quite small.