Linear Form Research Articles

A novel bounded ℤ-valued autoregressive model with its application on crime data

This paper tackles the challenge of autoregressive modelling for bounded Z -valued count time series, a topic that has been largely overlooked in the existing literature. To bridge this gap, we introduce the trinomial difference bounded Z -valued autoregressive (TDBZAR) model utilizing the trinomial difference thinning operator, and we explore its stochastic properties in detail. Two notable advantages of the TDBZAR model are that the incorporated trinomial difference thinning operator ensures the conditional expectation takes a linear form and allows its 1-step transition probability to be expressed as the convolution of two independent trinomial difference distributions. This significantly simplifies the computation of both the conditional least squares (CLS) and conditional maximum likelihood (CML) estimates, making them more practical and straightforward. Second, we examine the two-step CLS and CML estimates, establishing their asymptotic properties. Third, we compare the performance of these estimators through simulation studies. Finally, we apply the proposed model to a real dataset to investigate which type of crime (rape or sex offense) was more prevalent in police reports from January 1990 to December 1998.

Research on intelligent optimal allocation control strategy for stability and braking of heavy tyre blowout vehicle

The traditional control strategy mainly compensates and corrects the driving state of heavy vehicles with a tyre blowout, and rarely considers the need for emergency braking. It is also difficult to effectively coordinate the problems of lateral yaw, slip and tailspin, and longitudinal braking performance degradation. For this, an intelligent optimization allocation control strategy combining stability control and braking control is innovatively designed in this article. The joint simulation model for heavy tyre blowout vehicles is built based on the Dugoff tyre blowout model and the TruckSim vehicle model. A linear quadratic form regulator stable control based on the particle swarm optimization algorithm optimization is used to dynamic equilibrium of the additional yaw moment generated by the vehicle tyre blowout. A logic threshold braking control based on adaptive adjustment is adopted to achieve an ideal braking effect for the vehicle. In order to simultaneously consider the stability and braking performance of vehicles with blowout tyre, a braking force distribution strategy and a fuzzy optimization allocation algorithm are proposed to achieve coordination of lateral and longitudinal control strategies. The results indicate that intelligent optimized allocation control can effectively correct the deviation trajectory of a heavy tyre blowout vehicle, enabling it to achieve rapid braking while maintaining stability.

Data‐driven estimation for multithreshold accelerated failure time model

AbstractThis article develops a novel estimation framework for the multithreshold accelerated failure time model, which has distinct linear forms within different subdomains. One major challenge is to determine the number of threshold effects. We first show the selection consistency of a modified Bayesian information criterion under mild conditions. It is useful sometimes but heavily depends on the penalization magnitude, which usually varies from the model configuration and data distribution. To address this issue, we leverage a cross‐validation criterion alongside an order‐preserved sample‐splitting scheme to yield a consistent estimation. The new criterion is completely data driven without additional parameters and thus robust to model setting and data distributions. The asymptotic properties for the parameter estimates are also carefully established. Additionally, we propose an efficient score‐type test to examine the existence of threshold effects. The new statistic is free of estimating any potential threshold effects and is thus suitable for multithreshold scenarios. Numerical experiments validate the reliable finite‐sample performance of our methodologies, which corroborates the theoretical results.

Generalized uncertainty principle from the regularized self-energy

We use the Schrödinger–Newton equation to calculate the regularized self-energy of a particle using a regular self-gravitational and electrostatic potential derived in string T-duality. The particle mass M is no longer concentrated into a point but is diluted and described by a quantum-corrected smeared energy density resulting in corrections to the energy of the particle, which is interpreted as a regularized self-energy. We extend our results and find corrections to the relativistic particles using the Klein–Gordon, Proca and Dirac equations. An important finding is that we extract a form of the generalized uncertainty principle (GUP) from the corrected energy. This form of the GUP is shown to depend on the nature of particles; namely, for bosons (spin 0 and spin 1) we obtain a quadratic form of the GUP, while for fermions (spin 1/2) we obtain a linear form. The correlation we find between spin and GUP may offer insights for investigating quantum gravity.

Bentonite as substrate conditioner under different water regimes – A Eucalyptus dunnii seedling assay

The substrate has a lot of functions in the process to develop a high-quality seedling, including the responsibility to hold water and to make the water available for the plants. A compound that can be used to hold water is bentonite. So, the research aimed to evaluate the effects of different proportions of bentonite as a substrate component under two water conditions in the production of Eucalyptus dunniii seedlings. The research was carried out in the forest seedlings nursery in Curitiba/PR - Brazil. For the treatments, bentonite substrate conditioner was used in different proportions, 0 %, 5 %, 10 %, 15 % and 20 %, in a commercial substrate (with sphagnum peat) here named as S0, S5, S10, S15 and S20 respectively, in two water regimes for the blocks. The seedlings produced with these bentonite proportions was analyzed by the height, stem diameter, dry matter (shoot, root and total), and two parameters: height/stem diameter ratio (H/SD) and Dickson Quality Index (DQI). The substrate analysis shown a contrary behavior of expected. The bentonite in the substrate for seedlings of E. dunnii did not increase water holding capacity in a linear form and the high proportion of bentonite did not improve seedling in the lower water regime, although the 5 % of bentonite gave a good results of seedlings growth, so the purpose of bentonite in the substrate to improve water holder capacity and minimize the irrigation would not be fully attended.

Removal, mechanistic and kinetic studies of Cr(VI), Cd(II), and Pb(II) cations using Fe3O4 functionalized Schiff base chelating ligands.

The Schiff base chelating ligands; (E)-2-(3,3-dimethoxy-2-oxa-7,10-diaza-3-silaundec-10-en-11-yl)phenol (L1), (E)-N-(2-((pyridine-2ylmethylene)amino)ethyl)-3-(trimethoxysilyl)propan-1-amine (L2) and (E)-N-(2-((thiophen-2-ylmethylene)amino)ethyl)-3-(trimethoxysilyl)propan-1-amine (L3) were immobilized on Fe3O4 magnetic nanoparticles (MNPs) and utilized in the extraction of Cr(VI), Cd(II) and Pb(II) metal cations from aqueous solutions. The compounds synthesized, denoted as L1@ Fe3O4, L2@Fe3O4, and L3@Fe3O4, were characterized using FT-IR spectroscopy, TEM-SEM, VSM, and BET/BHJ techniques for analysis of functional groups, surface morphology, magnetic properties, and degree of porosity of the adsorbents, respectively. BET/BHJ technique confirmed the mesoporous nature of the compounds as their pore diameters ranged between 15 and 17nm. The initial optimization conditions of pH, adsorbent dosage, initial metal concentration, and contact time on adsorption were studied using L1@ Fe3O4. The optimum efficiencies recorded were 68% and 46% for Cr(VI) and Cd(II), respectively, obtained at pH 3, and a metal concentration of 20ppm while an efficiency of 99% was recorded for Pb(II) cations at pH 7 and a metal concentration of 100ppm. Compounds L2@Fe3O4 and L3@ Fe3O4 were also used in the extraction of metal cations from aqueous solution and gave efficiencies of 22%, 56%, and 78% for L2@ Fe3O4 and 19%, 90%, and 59% using L3@ Fe3O4 for Cr(VI), Cd(II), and Pb(II), respectively. The maximum adsorption capacities of L1@ Fe3O4 for Cr(VI), Cd(II), and Pb(II) cations were obtained from the Langmuir isotherm as 32.84, 41.77, and 450.45mg/g, respectively. The experimental data was analyzed using pseudo-first-order, pseudo-second-order, intraparticle diffusion, and Elovich kinetic models. Both linear and non-linear forms of kinetic isotherms; Langmuir, Freundlich, Redlich-Peterson, and Temkin were utilized to investigate the nature of adsorption on L1@Fe3O4. The mechanistic studies deduced that the Langmuir isotherm and pseudo-second-order kinetic model better described the adsorption process both yielding high correlation coefficient values (R2 > 0.98).

Constructing non-AMNM weighted convolution algebras for every semilattice of infinite breadth

The AMNM property for commutative Banach algebras is a form of Ulam stability for multiplicative linear functionals. We show that on any semilattice of infinite breadth, one may construct a weight for which the resulting weighted convolution algebra fails to have the AMNM property. Our work is the culmination of a trilogy started in [4] and continued in [5]. In particular, we obtain a refinement of the main result of [5], by establishing a dichotomy for union-closed set systems that has a Ramsey-theoretic flavour.

Development of mathematical models of heat conductivity for modern electronic devices with elements containing foreign inclusions

This paper considers the heat conduction process for an isotropic medium containing a foreign half-through inclusion and heated by a locally concentrated heat flow. Linear and non-linear mathematical models for determining the temperature field have been built to establish the temperature regimes for the effective operation of electronic devices. The coefficient of thermal conductivity of a non-uniform structure is represented as a whole, using asymmetric unit functions, which automatically provides the conditions of ideal thermal contact on the surfaces of materials. This results in solving one heat conduction equation with discontinuous and singular coefficients. A linearizing function was introduced to linearize the nonlinear boundary value problem. Analytical-numerical solutions of linear and nonlinear boundary-value problems have been obtained in a closed form. A linear temperature dependence of the coefficient of thermal conductivity of structural materials was chosen for a heat-sensitive medium. As a result, an analytical-numerical solution was derived, which determines the temperature distribution in this medium. On this basis, a numerical experiment was performed, the results of which are graphically displayed and confirm the adequacy of the constructed mathematical models to a real physical process. The materials of the plate and inclusion are silicon and silver. The results for these materials based on the linear and non-linear model differ by 7 %. Their slight difference is explained by the fact that the values of the temperature coefficient of thermal conductivity are small. The models built make it possible to analyze the given environments in terms of their thermal resistance. As a result, it becomes possible to improve it, and protect structures from overheating, which could lead to the failure of individual nodes and their elements and the entire electronic device

Study of anisotropic quark stars with interacting quark matter in f(R,T) gravity

We explore the structural properties of quark stars (QSs) in a modified gravity theory known as f(R,T) gravity, which introduces a coupling between matter and spacetime geometry, through a basic linear functional form f(R,T)=R+2βT. Our study focuses on QSs made of interacting quark matter (IQM) as an equation of state. We first derive the modified Tolman-Oppenheimer-Volkoff (TOV) equations for anisotropic matter in a spherically symmetric context and solve them numerically to obtain the structural properties of QSs. Stability is analyzed through static stability analysis, critical adiabatic indices, and sound speed profiles. Using astrophysical constraints from the “black widow” pulsar PSR J0952-0607 and the GW190814 event, we calibrate our model parameters. Our results indicate that with higher λ¯, both the maximum mass and radius of QSs increase, achieving a maximum mass of over 2M⊙, peaking at 3.15M⊙ for a radius of 14.90km at λ¯=0.9. The maximum compactness also rises to M/R=0.313 while adhering to the Buchdahl limit. Additionally, varying β in the range [−0.2,0.2] with fixed parameters shows that lower β values enhance the maximum mass of QSs, reaching 2.65M⊙ at β=−0.2, with the compactness remaining around M/R≈0.3. Furthermore, changes in μ from [−1.0,1.0] significantly affect maximum mass; at μ=1.0, the mass peaks at 3.15M⊙ and decrease to 2.68M⊙ at μ=0. The compactness increases with μ, indicating that anisotropic pressure influences the M−R relations. In summary, our findings reveal that the parameters λ¯, β, and μ play crucial roles in shaping the physical properties of QSs in the f(R,T) gravity framework, consistent with astrophysical observations from pulsars and gravitational wave events.

Revisiting Pyrimidine-Embedded Molecular Frameworks to Probe the Unexplored Chemical Space for Protein-Protein Interactions.

ConspectusProtein-protein interactions (PPIs) are essential in numerous biological processes and diseases, making them attractive yet challenging drug targets. While many advances have been made in traditional drug discovery, targeting PPIs has been difficult due to a lack of specialized chemical libraries designed to modulate these interactions. Current libraries mainly focus on conventional target proteins like enzymes or receptors as substrate analogs rather than small-molecule modulators targeting PPIs. These traditional drug targets behave differently from PPIs. Conventional druggable targets have relatively small surfaces and binding pockets that have allowed them to be targeted with current libraries, but PPIs behave differently than these traditional drug targets. As a result, there is an urgent need for an innovative approach to expand the druggable space.To address this, we developed a privileged substructure-based diversity-oriented synthesis (pDOS) strategy, aimed at creating maximal skeletal diversity to explore broader biochemical space. Pyrimidine serves as the privileged substructure in our approach, which employs several strategies: (i) silver-catalyzed or iodine-mediated tandem cyclizations to generate pyrimidine-embedded polyheterocycles; (ii) diverse pairing strategies to produce pyrimidodiazepine-containing polyheterocyclic skeletons with enhanced scaffold saturation; (iii) skeletal transformation to develop pyrimidine-fused medium-sized azacycles via chemoselective cleavages or migrations of N-N or C-N bond; (iv) design of small-molecule peptidomimetics that systematically mimic three pivotal protein secondary structures using pyrimidodiazepine-based scaffolds; and (v) identification of pyrimidodiazepine-based small-molecules that allosterically inhibits the interaction between human ACE2 and the receptor-binding domain (RBD) of the SARS-CoV-2 spike protein to block viral entry into host cells.Through these approaches, we generated 39 distinct pyrimidine-embedded frameworks, demonstrating significant molecular diversity validated by chemoinformatic analyses such as Tanimoto similarity and principal moment of inertia (PMI) analysis. This molecular diversity extends pyrimidine structures beyond traditional linear or bicyclic forms, creating polyheterocycles with enhanced 3D structural diversity. These novel frameworks overcome the limitation of simpler privileged scaffolds, offering promising tools for modulating PPIs.Our pDOS approach highlights how privileged structure-embedded polyheterocycles, particularly those based on pyrimidine, can effectively target previously undruggable PPIs. This strategy provides a new direction for drug discovery, allowing for the development of small molecules that operate beyond traditional drug-like rules. In addition to expanding the chemical space for PPI modulation, our pDOS strategy enables the creation of scaffolds that are particularly suited for targeting complex and dynamic protein interfaces. This innovation could significantly impact therapeutic development, offering solutions for previously intractable drug targets. By expanding the scope of pyrimidine-based scaffolds, we have opened up new possibilities for targeting PPIs and advancing chemical biology.This perspective demonstrates the potential outlines of our pDOS strategy in creating structurally diverse frameworks, offering a platform for the discovery of PPI modulators and facilitating the exploration of untapped biochemical spaces in drug development, potentially transforming the way we approach these complex biological interactions.

APPLICATION OF SUPPORT VECTOR MACHINE AND ORDINARY KRIGING (SVM-OK) TO SPATIAL INTERPOLATION OF POROSITY ATTRIBUTE OF AGBABU BITUMEN DEPOSIT

The lack of geostatistical modelling of volumetric characteristics of Nigeria's long-discovered heavy oil and bitumen deposits in Agbabu was accountable for the discrepancies in the hydrocarbon-in-place calculations. The absence of spatial variability evaluation in such efforts is responsible for the inconsistency and divergence that define the impacts of the existing attempts to estimate the porosity attribute. Due to its optimum features and simplicity of estimate, Kriging is reported as the most generally used approach to evaluate the connection between variables (inputs and output). However, Kriging reveals that the relationship between variables requires a linear form, which is frequently not the case. Thus, the necessity for a procedure with no fixed shape is built based on information acquired directly from the data. Consequently, support vector regression, a form of the support vector machine, is employed as a choice in contrast to kriging. This research is a comparative application of support vector machine and kriging (SVM-OK) to the spatial interpolation of the porosity property of the Agbabu bitumen field. The porosity values from existing data are trained, cross-validated, and verified with the help of the support vector machine, and they are interpolated by ordinary kriging. The geographical patterns of the predictions have been checked visually using graphs based on these three diagnostics: variance of the error terms and correlation of the error terms. The findings of this study illustrate the performance of the combination of the Support vector machine and conventional kriging in the spatial interpolation of volumetric characteristics in the Agbabu bitumen deposit. The approach exhibited great predictive performance. SVM-kriging will be employed in reservoir characterisation with the least mean absolute error (MAE) and mean squared error (MSE).

Circ-CAMTA1 regulated by Ca2+ influx inhibited pyruvate carboxylase activity and modulate T cell function in patients with systemic lupus erythematosus

ObjectivesTo investigate the roles of Ca2+ influx-regulated circular RNAs (circRNAs) in T cells from patients with systemic lupus erythematosus (SLE).MethodsThe expression profile of circRNAs in Jurkat cells, co-cultured with and without ionomycin, was analyzed by next-generation sequencing and validated using real-time polymerase chain reaction. The identified Ca2+ influx-regulated circRNAs were further examined in T cells from 42 patients with SLE and 23 healthy controls. The biological function of specific circRNA was investigated using transfection and RNA pull-down assay.ResultsAfter validation, we confirmed that the expression levels of circ-ERCC4, circ-NFATC2, circ-MYH10, circ-CAMTA1, circ-ASH1L, circ-SOCS7, and circ-ASAP1 were consistently increased in Jurkat cells following Ca2+ influx. The expression levels of circ-CAMTA1, circ-ASH1L, and circ-ASAP1 were significantly lower in T cells from patients with SLE, with even lower levels observed in those with higher disease activity. Interferon (IFN)-α was found to suppress the expression of circ-CAMTA1. Circ-CAMTA1 bound to pyruvate carboxylase and inhibited its biological activity. Overexpression of circ-CAMTA1, but not its linear form, significantly decreased extracellular glucose levels. Furthermore, increased expression of circ-CAMTA1, but not its linear form, decreased miR-181c-5p expression, resulting increased IL-2 secretion.ConclusionThree Ca2+ influx-regulated circ-RNAs—circ-CAMTA1, circ-ASH1L, and circ-ASAP1 —were significantly reduced in T cells from patients with SLE and associated with disease activity. IFN-α suppressed the expression of circ-CAMTA1, which interacted with pyruvate carboxylase, inhibited its activity, affected glucose metabolism, and increased IL-2 secretion. These findings suggest that circ-CAMTA1 regulated by Ca²⁺ influx modulated T cell function in patients with SLE.

Representation and inequalities involving continuous linear functionals and fractional derivatives

We investigate how continuous linear functionals can be represented in terms of generic operators and certain kernels (Peano kernels), and we study lower bounds for the operators as a consequence, in the space of square-integrable functions. We apply and develop the theory for the Riemann–Liouville fractional derivative (an inverse of the Riemann–Liouville integral), where inequalities are derived with the Gaussian hypergeometric function. This work is inspired by the recent contributions by Fernandez and Buranay (J Comput Appl Math 441:115705, 2024) and Jornet (Arch Math, 2024).

On the Diophantine equations of the form λ1Un1+λ2Un2+⋯+λkUnk=wp1z1p2z2⋯pszs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda _1U_{n_1} + \\lambda _2U_{n_2} +\\cdots + \\lambda _kU_{n_k} = wp_1^{z_1}p_2^{z_2} \\cdots p_s^{z_s}$$\\end{document}

In this paper, we consider the Diophantine equation λ1Un1+⋯+λkUnk=wp1z1…pszs,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda _1U_{n_1}+\\cdots +\\lambda _kU_{n_k}=wp_1^{z_1} \\ldots p_s^{z_s},$$\\end{document} where {Un}n≥0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\{U_n\\}_{n\\ge 0}$$\\end{document} is a fixed non-degenerate linear recurrence sequence of order greater than or equal to 2; w is a fixed non-zero integer; p1,⋯,ps\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_1,\\dots ,p_s$$\\end{document} are fixed, distinct prime numbers; λ1,⋯,λk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda _1,\\dots ,\\lambda _k$$\\end{document} are strictly positive integers; and n1,⋯,nk,z1,⋯,zs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_1,\\dots ,n_k,z_1,\\dots ,z_s$$\\end{document} are non-negative integer unknowns. We prove the existence of an effectively computable upper-bound on the solutions (n1,⋯,nk,z1,⋯,zs)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n_1,\\dots ,n_k,z_1,\\dots ,z_s)$$\\end{document}. In our proof, we use lower bounds for linear forms in logarithms, extending the work of Pink and Ziegler (Monatshefte Math 185(1):103–131, 2018), Mazumdar and Rout (Monatshefte Math 189(4):695–714, 2019), Meher and Rout (Lith Math J 57(4):506–520, 2017), and Ziegler (Acta Arith 190:139–169, 2019).

Epithelial splicing regulatory protein 1 promotes peritoneal dissemination of ovarian cancer by inducing the formation of circular RNAs modulating epithelial plasticity

Peritoneal metastases prevalently occur in ovarian cancer, deteriorating patient prognosis. During the metastatic cascade, tumor plasticity enables cells to adapt to environmental changes, thereby facilitating dissemination. We previously found that epithelial splicing regulatory protein 1 (ESRP1) is linked to peritoneal metastasis and epithelial-mesenchymal plasticity in ovarian cancer. This study delves into the underlying mechanism. We found that ESRP1 preserves epithelial plasticity in ovarian cancer cells in vitro and in vivo. Functionally, ESRP1 enhances ovarian cancer cell growth and peritoneal dissemination. High-throughput sequencing revealed several ESRP1-related epithelial RNAs, encompassing both linear and circular forms. Specifically, ESRP1 triggers the cyclization of circPAFAH1B2 and circUBAP2 through binding to the GGU sequences in adjacent introns. The two ESRP1-induced circular RNAs stabilize DKK3 and AHR mRNAs, which are critical for epithelial plasticity, through interaction with IGF2BP2. Collectively, ESRP1 triggers the formation of circPAFAH1B2 and circUBAP2, which in turn stabilizes DKK3 and AHR through IGF2BP2 binding, thereby modulating the epithelial plasticity and aiding the peritoneal spread of ovarian cancer cells. The findings unveiled a biological network, orchestrated by ESRP1, that governs the epithelial-mesenchymal plasticity of ovarian cancer cells, emphasizing the therapeutic potential of ESRP1 and its induced circular RNAs for ovarian cancer treatment.

Cnicus Benedictus roots as a low-cost adsorbent for methylene blue dye removal from aqueous solution: kinetic and equilibrium studies

In this research, Cnicus Benedictus roots powder (CBRP) was utilized as a low-cost adsorbent for removing methylene blue (MB) as a cationic dye from aqueous solution. Characterization of CBRP by Boehm titration method, Fourier transform infrared (FT-IR) and environmental scanning electron microscope (ESEM) indicates the presence of different types of functional groups and a very rough surface filled with cavities, suitable for MB adsorption. The effect of various parameters such as CBRP dose (0.2–2 g/1L), contact time (0–180 min), initial pH (1–10), coexisting anions/cations and the initial MB concentration (100–500 mg L−1) on MB adsorption were examined, the results showed that MB uptake depends on the pH of solution, the electrostatic attraction forces, the formation of H-bonds and π–π interactions are the possible CBRP–MB interaction mechanisms. Adsorption kinetic of MB on CBRP was best represented by linear and non-linear form of the pseudo-second order model. The experimental equilibrium data were best described by linear and non-linear forms of Langmuir and Redlich–Peterson isotherm models (R 2> 0.98) with a maximum MB adsorption capacity of 85.47 mg g−1 at 25 °C, the adsorption efficiency R (%) was greater than 90 (%). MB adsorption-desorption experiments showed the reusability of CBRP for five consecutive cycles. According to the obtained results, CBRP can be used as a natural adsorbent material for cationic dyes removal from aqueous solution.

Reconfigurable Visible Light-Driven Liquid Crystalline Network Showing Off-Equilibrium Motions Enabled by Mesogen-Grafted Donor-Acceptor Stenhouse Adducts.

Liquid crystalline network (LCN)-based soft actuators have opened up great opportunities to fabricate emerging and intriguing smart materials, serving as potential building blocks for intelligent soft robotics. Endowing LCN actuators with complex responsive behaviors to enhance their intelligence is both challenging and highly demanded. Herein, Donor-Acceptor Stenhouse Adducts (DASAs) molecules with rod-like mesogen and the polymerizable group are judiciously designed and synthesized, which is strong-colored at linear form and de-coloration at cyclic form after visible light. In the colored state, the DASA presents a striking photothermal effect that is capable of driving the motions of LCN film. Upon visible light irradiation, the DASA becomes colorless, making the diminishing photothermal effect. The light-gated switching of the photothermal effect renders the LCN films to be reconfigurable and perform off-equilibrium motions. The varying glass transition temperature of LCN matrix endowing tunable isomerization rates of DASAs and the equilibrium balance of photo- and thermal-isomerization at different temperatures in LCN-P-DASA film mainly guiding the off-equilibrium or stable motions, providing high adjustability of the novel visible light-driven LCN actuators. The multiply modulated LCN-P-DASA film holds great potential in constructing complex visible light-driven soft actuators based on the synergetic effect and interactions of photochemical and photothermal effects.

Powers as Fibonacci sums

We examine the equation for positive integers y, a ≥ 2 and k ≥ 3. This equation can be expressed as a problem in terms of the Zeckendorf representations of integers. Using bounds on linear forms in logarithms and Baker-Davenport reduction methods, we are able to completely solve the equation for y ≤ 25000 when k = 3, for y ≤ 1000 when k = 4, for y ≤ 40 when k = 5, and for y ≤ 3 when k = 6.

Quark Stars in $f(R,T)$ Gravity: Mass-to-Radius Profiles and Observational Data

Abstract In this paper, we explore the $f(R,T)$ gravity theory, which introduces a coupling between matter and curvature, through the simplest linear functional form $f(R,T)= R + 2\beta T$. We derive the modified Einstein field equations and conservation equations for this theory. We then apply this framework to study the structural properties of quark stars (QSs) composed of interacting quark matter, considering perturbative QCD corrections and color superconductivity. By solving the modified Tolman-Oppenheimer-Volkoff equations, we investigate the mass-radius relation, stability criteria, and energy conditions of QSs. Our results indicate that the $f(R,T)$ gravity significantly influences the properties of QSs, leading to deviations from General Relativity. The analysis shows consistency with recent observational data, suggesting that the modified gravity framework could provide viable models for the study of compact stars.

Light-guided actin polymerization drives directed motility in protocells.

Motility is a hallmark of life's dynamic processes, enabling cells to actively chase prey, repair wounds, and shape organs. Recreating these intricate behaviors using well-defined molecules remains a major challenge at the intersection of biology, physics, and molecular engineering. Although the polymerization force of the actin cytoskeleton is characterized as a primary driver of cell motility, recapitulating this process in protocellular systems has proven elusive. The difficulty lies in the daunting task of distilling key components from motile cells and integrating them into model membranes in a physiologically relevant manner. To address this, we developed a method to optically control actin polymerization with high spatiotemporal precision within cell-mimetic lipid vesicles known as giant unilamellar vesicles (GUVs). Within these active protocells, the reorganization of actin networks triggered outward membrane extensions as well as the unidirectional movement of GUVs at speeds of up to 0.43 µm/min, comparable to typical adherent mammalian cells. Notably, our findings reveal a synergistic interplay between branched and linear actin forms in promoting membrane protrusions, highlighting the cooperative nature of these cytoskeletal elements. This approach offers a powerful platform for unraveling the intricacies of cell migration, designing synthetic cells with active morphodynamics, and advancing bioengineering applications, such as self-propelled delivery systems and autonomous tissue-like materials.