Search Results (3,462)

Based on a new general solution, we derive three skew-symmetric variants of the method of fundamental solutions (MFS) for solving the three-dimensional Stokes equations: the symmetric/skew-symmetric MFS (SSMFS), the separated MFS (SeMFS) as an extension of the conventional MFS that incorporates an additional skew-symmetric part, and the symmetric/skew-symmetric separated MFS (SSeMFS) as an extension of the SSMFS by further adding a skew-symmetric component. In these methods, a skew-symmetric tensor interlaced with the Oseen tensor is employed to regularize the Stokeslet. Numerical examinations show that the SeMFS and SSeMFS outperform the conventional MFS, achieving faster convergence and an improvement in accuracy of approximately one order of magnitude. We construct six families of kth-order homogeneous harmonic polynomials that possess rich properties. These polynomials are arranged into two harmonic vectors, which are then inserted into the Liu–Hsu–Tsai formula to yield the LHT method (LHTM), into the Liu–Tsai formula to yield the LT method (LTM), and into the Slabodyanskii formula to yield the Slabodyanskii method (SM). The resulting methods solve the Stokes equations via a simple collocation technique that enforces the prescribed boundary conditions. In addition, we derive a particular solution of the Stokes equations by means of an integration method (IM). Six numerical examples, including a benchmark three-dimensional lid-driven cavity problem, are tested to assess the efficiency and accuracy of these newly developed harmonic-polynomial-type methods. They are superior to the MFS-type methods, delivering improvements in accuracy of several orders of magnitude together with much faster convergence rates. Full article

Digital rock technology is essential for characterizing the petrophysical properties of tight reservoirs. However, conventional construction methods often yield models with insufficient pore connectivity due to low porosity and complex nanopore structures. To address this limitation, we propose a novel connectivity algorithm for isolated pore systems. First, a digital rock model is constructed using a random particle packing algorithm that integrates high-resolution SEM parameters, including kaolinite particle morphologies and randomly distributed microfractures. Subsequently, the connectivity algorithm sequentially links isolated pore clusters to the largest continuous pore system, forming an interconnected channel. Pore network extraction reveals that the algorithm produces significantly denser and more continuous structures, with pore–throat size distributions aligning well with experimental observations. Single-phase flow simulations demonstrate that the enhanced model yields porosity and permeability values consistent with laboratory measurements, whereas unenhanced models deviate substantially. To further advance microscale flow characterization, we derive explicit fitting formulas for the dimensionless conductivity of canonical pore cross-sections (equilateral triangle, square, and circle) considering water film boundary layer (WFBL) effects. These formulations are based on a comprehensive parametric study using the ab initio finite element method, followed by regression analysis to yield closed-form expressions. Two-phase flow simulations reveal that the WFBL increases residual saturations, reduces relative permeabilities, and decreases waterflooding displacement efficiency, with effects being more pronounced during secondary imbibition. This integrated approach provides a robust framework for constructing representative digital rock models of tight reservoirs and offers essential theoretical support for accurately modeling nanoscale flow behaviors in complex subsurface systems. Full article

We investigate the Euler polynomials of the second kind (EPs2) and develop a collection of structural identities for this modified Euler family. The analysis begins with an explicit expansion and a compact inverse relation, followed by connections with the classical Euler basis. We then obtain formulas governing differentiated moments and products, together with linearization relations. Higher-order derivatives are expanded in symmetric and non-symmetric bases, including Bernoulli, Laguerre, Jacobi, and generalized Fibonacci and Lucas polynomials. Converse expansions are established as well. We then evaluate several definite integrals to illustrate how the derived identities can be applied. Full article

Biclustering is a two-dimensional data analysis paradigm that aims to identify subsets of rows and columns in a data matrix whose intersection forms a submatrix satisfying predefined properties. In the case of binary data, a bicluster is typically defined as a submatrix containing exclusively ones or exclusively zeros. Numerous approaches to binary biclustering have been proposed over the last several decades. Among them, a distinctive line of research relies on Boolean reasoning, transforming the biclustering task into the problem of finding prime implicants of a data-dependent Boolean function. From a theoretical perspective, it has been shown that every prime implicant of the data-dependent Boolean function corresponds to an inclusion–maximal bicluster in the original dataset, and vice versa. Here, inclusion maximality means that no additional row or column can be added without violating the bicluster property. For discrete datasets, the corresponding Boolean function can be represented in Conjunctive Normal Form (CNF), where clauses contain up to three variables, reducing the general biclustering problem to an instance of the 3-SAT problem. Furthermore, the computational complexity of discrete-data biclustering can be reduced to the analysis of binary matrices. In this case, the associated Boolean functions consist of clauses containing at most two literals, yielding monotone 2-CNF formulas. This paper focuses on improving the efficiency of computations required to derive a disjunctive normal form (DNF) representation composed exclusively of prime implicants. Since the extraction of prime implicants constitutes the computational core of the Boolean biclustering framework, accelerating this process directly enhances the scalability and practical applicability of biclustering methods based on Boolean reasoning. Full article

This paper studies local and global existence, uniqueness, and Lipschitz continuous dependence of mild solutions for a semilinear Hadamard fractional integro-differential equation in a Banach space ${\displaystyle X}$, with nonlocal initial conditions, a state-dependent Volterra kernel embedded in the nonlinearity, and impulsive effects at finitely many fixed times, where ${\displaystyle -A}$ generates a compact ${\displaystyle C_0}$-semigroup on ${\displaystyle X}$. The mild-solution formula is derived from first principles via ${\displaystyle \tau =lnt}$ and the Riemann–Liouville variation of parameters formula. Local existence follows from Schauder’s fixed-point theorem, global existence from a Hadamard–Gronwall inequality with an explicit blow-up alternative, uniqueness from a logarithmic power-weight contraction with an explicit condition on the Lipschitz constants, and continuous dependence with an explicit stability constant ${\displaystyle C_{\mathrm{dep}}}$; two concrete examples verify all hypotheses. Beyond this compact-semigroup theory, we prove two further results: an existence theorem under a Kuratowski measure-of-noncompactness condition via a Hadamard-adapted Mönch fixed-point argument, removing the compactness assumption on ${\displaystyle {\left\{T\left(t\right)\right\}}_{t\ge 1}}$ altogether, and an Ulam Hyers Rassias stability theorem whose constant reuses the same contraction weight ${\displaystyle {\lambda }^{*}}$ from the uniqueness theorem. Both extend recent noncompact-semigroup and Ulam-stability results in the literature to the present nonlocal, impulsive, state-dependent-kernel setting. Full article

This article presents a two-way convolution of the Mittag-Leffler function with Sheffer polynomials via the umbral algebraic method, thereby introducing the Mittag-Leffler–Sheffer polynomials (MLSPs) and the Sheffer–Mittag-Leffler function (SMLF). We establish their generating functions, series definitions, quasi-monomial properties, and differential equations. Using Wronskian and Pascal functional matrices, we derive recursive formulas and differential recursive identities for these hybrid polynomials. Various special cases including Mittag-Leffler–Appell, Mittag-Leffler–Hermite, and Mittag-Leffler–Miller–Lee polynomials are examined. Additionally, a graphical investigation of the zero distributions of selected members of these polynomial families is presented using computational tools. Full article

Automatically extracted chemical records can appear complete even when names, depictions, formulas, masses, and spectra disagree. Because databases consume records rather than evidence, such errors propagate silently. TRACE-Chem (Typed Relational Attestation with Counterfactual Editing for Chemistry) is an inference-time framework for verifying and repairing them. It organizes source-linked observations, candidate fields, and verifier outcomes in a Symmetric–Asymmetric Evidence Graph (SAEG) separating symmetric identity checks from directional scientific derivations. Counterfactual Localization and Dependency-Constrained Re-decoding (CLDR) masks candidate fault nodes to identify the view whose removal most restores coherence, then revises only dependency-affected fields. Executable checks and spectral compatibility feed a calibrated accept, repair, or abstain decision. On 124 open-access synthesis papers containing 1852 compound and 638 reaction records, TRACE-Chem achieved 84.3% canonical-record hard-match F1, 9.7 percentage points above the same extractor without verification. Against a single-pass multimodal baseline, invalid structures fell from 10.8% to 0.8%, unsupported fields from 14.3% to 2.4%, and expected calibration error from 0.281 to 0.052. Removing derivation direction lowered fault-localization accuracy from 91.2% to 82.8%; removing dependency discounting raised the unsafe-edit rate from 2.4% to 4.1%. Explicitly modeling relational symmetry and asymmetry therefore improves verifiability, calibration, and repair safety in multimodal chemical extraction. Full article

Plant-based enteral formulas represent a hypoallergenic alternative to dairy-derived products, but incorporation of underutilized pseudocereals into enteral formulas remains insufficiently characterized. This study developed a laboratory-scale prototype of a fortified beverage for enteral administration (FBEA) from the soluble fraction of Amaranthus hypochondriacus, with added pea protein isolate, safflower oil, and carbohydrate components. Sequential enzymatic treatment with α-amylase and Alcalase hydrolyzed amaranth grain flour into soluble fraction, increasing free amino acid content relative to the unhydrolyzed flour, including arginine from 0.52 to 241.39 mg kg⁻¹, lysine from 3.91 to 129.10 mg kg⁻¹, and glutamic acid from 103.62 to 368.54 mg kg⁻¹. Fortification yielded a protein content of 25.46% DW, a lipid content of 24.95% DW, and an energy density of 1014 kcal L⁻¹, consistent with isocaloric formulas, with seven essential amino acids meeting FAO/WHO/UNU reference adequacy values. In vitro digestion showed that the soluble fraction and FBEA exceeded amaranth flour in bioaccessibility of antioxidant activity and phenolic content, with FBEA achieving the highest intestinal phenolic release. The formula met ESPEN physicochemical recommendations, with osmolality at 292 mOsm kg⁻¹ and viscosity at 51 mPa·s, and simulated tube flowability comparable to two commercial formulas. These findings indicate that enzymatically hydrolyzed amaranth shows potential as a plant-based enteral formulation prototype, though clinical suitability requires further safety, shelf-life, and tolerance data. Full article

We study an Eulerian pantograph equation with proportional delay by means of a logarithmic change of variables, which transforms the problem into a constant-shift equation on the half-line. The main object is the maximal left-transport realization on $L^p(0,\infty )$, with derivative domain $W^{1,p}(0,\infty )$ and no boundary condition at the endpoint. For the characteristic function $m\left(\mu \right)=v\mu +B+C\exp \left(L\mu \right)$, we prove that both the spectrum and the approximate point spectrum equal the closure of the image of the open left half-plane under m. Points obtained from the open half-plane are genuine eigenvalues, while the image of the boundary line supplies approximate eigenvalues. The resolvent outside this closed image is constructed directly as a one-sided convolution operator. The auxiliary semigroup generated by the half-line operator has the sharp norm identity $\parallel T\left(\tau \right)\parallel =\exp \left(\right(\mathrm{Re}B+\left|C\right|\left)\tau \right)$ and is exponentially stable exactly when $\mathrm{Re}B+\left|C\right|<0$; this concerns an additional evolution parameter, not stability in the original pantograph variable. We transfer the spectral theorem back to $L^p((0,1),\mathrm{d}t/t)$: interior modes decay at $t=0$, while boundary approximate modes are Mellin waves concentrating at the singular endpoint. As a secondary representation result, logarithmic pullback of the Hermite basis gives a Mellin–Hermite basis on $L^2({\mathbb{R}}_{+},\mathrm{d}t/t)$ with explicit Galerkin matrices for the Euler operator and dilations. The corresponding translation truncations converge strongly, and the shifted Gaussian admits an exact truncation-error formula. Full article

Non-additive measures and integrals have become important mathematical tools in modern research. They offer powerful frameworks for modelling interaction, uncertainty, and handling incomplete data where traditional additive techniques fail. This paper focuses on the Choquet integral and the corresponding non-additive measure derivatives, which can be considered mutually inverse problems. A comprehensive review of existing direct and indirect approaches is provided for analysis of the derivatives, aiming to refine and generalise current results while highlighting their inconsistencies and limitations. In the discrete case, Choquet integration reduces to a finite sum, and the necessary and sufficient conditions for the existence of measure derivatives form a linear system. In the continuous case, three existing frameworks are evaluated: studying the invariance under rearrangement of integrating functions for the integral; using generalised integral equations for Choquet computations to derive formulas for the result of integration as well as for measure derivatives; and the resulting measure approach, which uses the inverse nature of integration and measure derivatives and pairs integrating and resulting measures to derive explicit derivative formulas. Ultimately, this work maps out current perspectives on non-additive measure derivatives with respect to the Choquet integral, and outlines possible directions for their future theoretical and applied advancements. Full article

Background: Acute alcohol intoxication causes liver injury and delays recovery via oxidative stress, ferroptosis, inflammation, and gut dysbiosis. This study investigated whether pretreatment with an Alcohol Relief Formula (ARF), composed of soybean peptides, botanical extracts, and probiotics, protects against alcohol-induced liver damage in a preventive model and explored the underlying mechanisms. Methods: Mice with acute alcohol intoxication were pretreated with ARF. Liver damage, hepatic alcohol-metabolizing enzymes, antioxidant capacity, inflammatory cytokines, and lipid peroxidation were measured. Ferroptosis markers and AMP-activated protein kinase (AMPK) signaling were assessed. Gut microbiota composition and cecal short-chain fatty acids (SCFAs) were analyzed. Correlations between SCFAs, ferroptosis suppression, and AMPK activation were evaluated. Results: ARF pretreatment alleviated acute liver damage and accelerated sobriety. It enhanced alcohol dehydrogenase (ADH) and aldehyde dehydrogenase (ALDH) activities, inhibited CYP2E1 expression, and improved alcohol metabolism. ARF pretreatment restored antioxidant capacity, decreased pro-inflammatory cytokines and lipid peroxidation, and ameliorated hepatic histopathological changes. Notably, ARF pretreatment was associated with suppressed ethanol-induced ferroptosis markers, including increased glutathione peroxidase 4 (GPX4), solute carrier family 7 member 11 (SLC7A11), and ferroptosis suppressor protein 1 (FSP1) expression, elevated AMPK phosphorylation, and reduced hepatic total iron content. In parallel, ARF pretreatment was associated with modulation of the alcohol-disrupted gut microbiota, increased short-chain fatty acid (SCFA)-producing bacteria, and maintained cecal acetate, propionate, and butyrate levels. Correlation analysis revealed that SCFA restoration was positively associated with ferroptosis marker modulation and AMPK activation, suggesting a potential link between gut metabolites and hepatic protection. Conclusions: ARF may serve as a potential preventive nutritional strategy for acute alcohol intoxication by promoting recovery and mitigating liver damage in this acute binge pretreatment model. The observed effects may involve the modulation of gut microbiota-derived SCFAs and AMPK signaling associated with ferroptosis markers. Full article

Hepatocellular carcinoma (HCC) remains difficult to control because recurrence, impaired hepatic reserve, and treatment resistance limit durable benefit. Natural products and traditional Chinese medicine (TCM) provide resources that range from drug-lead discovery to adjunctive multicomponent therapy. This review integrates pharmacological and clinical evidence for purified compounds, semisynthetic derivatives, extracts, formulas, and delivery systems. It focuses on metabolic reprogramming and redox homeostasis, stress responses and regulated cell death, tumor cell plasticity and vascular remodeling, and the immune microenvironment and host response. Recent studies have strengthened selected mechanistic claims through chemical probes, functional perturbation, and resistance models. Clinical research has concentrated on recurrence control after surgery or minimally invasive treatment and on combinations with transarterial chemoembolization, targeted agents, and immunotherapy. Randomized trials and prospective cohorts suggest potential benefit in specific settings, although product standardization, external validation, and long-term follow-up remain limited. Major translational barriers include uncertain active constituents, inadequate batch comparability, missing tumor-exposure data, and sparse herb–drug interaction studies. Future development should match target validation, pharmacokinetics, safety assessment, and clinical endpoints to each product class and clarify whether a candidate is best positioned as a drug lead, adjunctive therapy, or supportive intervention. Full article

Conventional diagnosis of chronic kidney disease (CKD) relies predominantly on invasive blood-based examinations, limiting the scalability of kidney health screening in resource-constrained environments. This study presents embedded engineering framework for non-invasive, breath-based CKD staging framework supported by machine learning and implemented on a low-cost embedded platform. To account for physiological sex differences in baseline creatinine production, estimated glomerular filtration rate (eGFR) values and breath ammonia concentrations were derived from two independent clinical cohorts using sex-specific MDRD equations (incorporating the standard male formula and the $0.742$ female correction factor, respectively) and creatinine–BUN conversion models, with male- and female-parameterized algorithms developed in parallel. The resulting feature space was analyzed using four unsupervised clustering approaches to stratify subjects into five clinically meaningful kidney function stages. Stage-specific ammonia thresholds were implemented within an Arduino Nano-based prototype equipped with an MQ-137 gas sensor and OLED display, enabling real-time point-of-care classification. Dataset-level classification accuracy reached 82% for the male algorithm and 92% for the female algorithm. Hospital-based validation on 29 patients (22 male, 7 female) yielded a real-world testing accuracy of 90.5% ($20/22$) for male patients and 71.4% ($5/7$) for female patients, a discrepancy largely attributable to the small female sample size. Because the current evaluation lacks healthy control subjects and is constrained by sample size, these empirical results serve primarily to demonstrate hardware-software functional integration and real-world deployment feasibility rather than definitive clinical efficacy. Despite these preliminary, sample-limited clinical datasets, results suggest this approach holds promise as an accessible, non-invasive screening complement to conventional diagnostic pathways, particularly in low-resource healthcare settings. Full article

Through-going structures are widely distributed in rock masses of underground engineering, and their dip angles act as the core factor affecting the stress field and mechanical response of surrounding rock. To reveal the mechanical mechanism of rock masses containing through-going structures with different dip angles, this study adopts a combined method of theoretical derivation, indoor model testing and numerical simulation. Firstly, a plane strain mechanical model is established to classify Tectonically-induced Stress, Residual Gravitational Stress and engineering-induced stress, and the theoretical formulas for stress components, stress residual coefficient and stress deflection angle are derived. Secondly, rock-like specimens with through-going structures of various dip angles are prepared and biaxial compression tests are carried out to monitor mechanical parameters such as surrounding rock strain and peak strength. Finally, a large-scale numerical model is built by FLAC2D (version 7.0) software to simulate the whole process of stress equilibrium and excavation unloading of rock mass under a normal stress of 20 MPa. Then the data of principal stress, stress components, stress residual coefficient and deflection angle under different dip angles are extracted. The results show that the dip angle of through-going structure exerts a prominent regulatory effect on the rock mass stress field. With the increase of the dip angle, the Tectonically-induced Stress decreases continuously while the Residual Gravitational Stress rises gradually. The variation trend of stress deflection angle is highly consistent with structural dip angle, and the influence of Residual Gravitational Stress on deflection angle is limited. Due to the differences in loading modes and model sizes between indoor tests and numerical simulations, the evolution laws of stress residual coefficient show opposite trends, but both results verify the dominant effect of structural dip angle. Combined with theoretical, experimental and numerical results, the proposed theoretical system can effectively describe the stress evolution law of rock masses with through-going structures, which provides theoretical reference and technical support for the stability analysis of surrounding rock in similar underground engineering. Full article

Salicylic acid (SA) is a central plant defense hormone, but its occurrence and metabolic context in Echinacea tissues have not been systematically characterized. This study aimed to characterize endogenous free SA, salicylate-associated features, and their organ-level distributions in selected specimens of Echinacea purpurea, E. pallida, and E. tennesseensis, and to evaluate free SA variability among individual E. purpurea flower heads. Targeted LC–MS/MS and retrospective LC–HRMS profiling were used to examine free SA, preservative panel analytes, salicylate-related pathway features, phenylpropanoid/caffeic acid derivatives, and flavonoid-related metabolites across roots, stems, leaves, and flowers of Echinacea purpurea, E. pallida, and E. tennesseensis. Free SA was detected in selected aerial and reproductive tissue extracts, whereas benzoic acid, dehydroacetic acid, and paraben esters were not detected. Confidence-qualified LC–HRMS yielded formula-level assignments and tentative candidates associated with salicylates, phenylpropanoids, caffeic-acid derivatives, and flavonoids. Free SA detection and broader salicylate-associated feature patterns were not identical, with candidate conjugated or pathway-related features also observed in roots. Analysis of 80 individual E. purpurea flower heads showed marked free SA variability (mean ± SD 4.72 ± 13.77 μg/g; range 0–121.48 μg/g). These findings support the endogenous occurrence of free SA in Echinacea within a broader, tissue-variable specialized-metabolite context. Future studies with greater biological replication, authentic standards, seasonal sampling, and mechanistic approaches should clarify salicylate biosynthesis, regulation, and biological significance in Echinacea. Full article