Search Results (1,124)

Background: Current low milk supply (LMS) definitions use subjective maternal perceptions or arbitrary thresholds for 24 h milk production (MP), potentially misclassifying cases. This study aimed to re-evaluate the definition of LMS using data-driven approaches and investigate associated maternal risk factors. Methods: Lactating mothers 4–26 weeks postpartum (n = 460) provided demographic, obstetric, and infant data and measured 24 h MP and infant milk intake using the test-weighing method. Infant growth was calculated as their weight-for-age z-score. Latent profile analysis, receiver operating characteristic curve analysis, and multinomial logistic regression were used for classification, diagnostic evaluation, and risk factor assessment for LMS. Results: Four milk supply classes emerged: Class 1 with adequate MP, infant intake and infant growth (n = 254); Class 2 with high MP exceeding infant demand and adequate growth (n = 30); Class 3 with slow infant growth despite moderate MP (n = 120); and Class 4 with extremely low MP and high formula intake (n = 56). Classes 1 and 2 were grouped as the normal milk supply group (61.7%), while Classes 3 and 4 formed the LMS group (38.3%). New thresholds were identified for 24 h MP (708 mL/24 h, area under the curve (AUC) = 0.92) and infant breast milk intake (694 mL/24 h, AUC = 0.94) with high diagnostic accuracy. Moreover, practical alternative thresholds for infant average daily weight gain (26 g, AUC = 0.89), formula intake (122 mL/24 h, AUC = 0.89) and formula-to-growth ratio (4 mL/g, AUC = 0.94) were established for the identification of LMS. Minimal breast growth during pregnancy (Odds ratio (OR) = 4.6, 95% confidence interval (CI): 2.3–9.6), advanced maternal age (OR = 2.1, 95% CI: 1.0–4.5), and gestational diabetes mellitus (OR = 2.1, 95% CI: 1.1–4.0) were significant risk factors related to the LMS subgroups. Co-existence of maternal advanced age and overweight showed greatly amplified risk of LMS (OR = 3.7, 95% CI: 1.3–10.5), and a more pronounced risk was observed for the combination of minimal breast growth and advanced maternal age (OR = 9.2, 95% CI: 3.0–28.3). Conclusions: This data-driven classification of LMS and identified risk factors may enhance the precision of LMS diagnosis and guide targeted interventions for lactating mothers. Full article

Backgrounds: Non-alcoholic fatty liver disease (NAFLD) is a multifaceted metabolic disorder that has become a prominent public health problem worldwide. As a traditional Chinese medicine formula, the ErChen decoction (ECD) possesses significant effects on metabolic syndrome. Methods: To determine whether ECD can relieve lipid accumulation and insulin resistance (IR) in liver cells, NAFLD and IR cell models were established by treating HepG2 cells with free fatty acids and an overdose of insulin, respectively. Bioinformatics and experimental evidence demonstrated that ECD could ameliorate NAFLD by modulating multiple pathways. The optimal combination of the key compounds in ECD was identified by the orthogonal experiment. Results: For lipid homeostasis, ECD suppressed de novo lipogenesis and reduced the cholesterol level by activating the AMPK signaling pathway. Concurrently, ECD enhanced hepatic β-oxidation by inducing PPARα-mediated upregulation of ACOX-1 and CPT-1α. ECD also resolved hepatic insulin resistance by activating the IRS1-Akt-FoxO1 pathway. The combined treatment with 100 μM liquiritin (LQ), 200 μM glycyrrhizic acid (GA) and 200 μM hesperidin (HEN) exhibited the best effect in reducing TG content in NAFLD model cells. Conclusions: ECD exhibited superior activities in activating the AMPK signaling pathway compared to the optimal compound combination. The comparison between the ECD and its key compounds demonstrated the superior synergistic effects of the herbs in ECD. Full article

Galactooligosaccharides (GOS) typically consist of 2-8 D-galactose units linked together, terminating in a D-glucose unit. GOS are commonly used in dairy products, infant formulas, and functional foods. GOS offer beneficial properties for food processing, such as low caloric value, mild clean taste, and excellent solubility in water. Additionally, GOS function as non-digestible prebiotics, supporting microbiota balance and offering benefits such as promoting infant health, immune modulation, laxative effects, and potential metabolic advantages. β-galactosidase plays a key role in GOS production, catalyzing both hydrolysis and transglycosylation reactions. In this study, a putative GH2 family β-galactosidase from Kosakonia oryzendophytica (Koor β-gal) was identified. The enzyme exhibited optimal activity at pH 7.0 and 45–50 °C with the addition of 1 mM Mg²⁺, showing a specific activity of approximately 288.6 U/mg towards o-nitrophenyl-β-D-galactopyranoside (ONPG). After optimizing the reaction conditions, Koor β-gal successfully produced 124.7 g/L of GOS from 300 g/L D-lactose, achieving a GOS yield of 41.6%. LC-MS analysis revealed that the primary products consisted of GOS with degrees of polymerization (DP) ranging from 2 to 4. Additionally, Koor β-gal was heterologously expressed in Bacillus subtilis following comprehensive optimization of the promoter and 5′-UTR, resulting in an enzyme activity in culture filtrate of 106.2 U/mL after 60 h. Full article

Objective: Obesity increases the risk of endometrial cancer (EC). In this study, we aimed to investigate the prognostic effect of sarcopenia, sarcopenic obesity and sarcopenic visceral obesity, calculated with the help of cross-sectional imaging methods of muscle and visceral adipose tissue from body composition parameters, in EC. Methods: Patients diagnosed with EC were identified between January 2014 and June 2024. The combination of radiological markers and patient outcomes can predict prognosis. The skeletal muscle index (SMI) and visceral fat index (VFI) were calculated from computed tomography (CT) and/or abdominal magnetic resonance (MR) scans taken at the time of diagnosis at the Lumbal 3 (L3) vertebra level. The findings of these analyses demonstrate the strongest correlation with the ratio of muscle and visceral fat tissue throughout the body. The loss of muscle and fat is an unfavourable indicator in patients with EC. The present study analysed the prognostic values of sarcopenia, sarcopenic obesity, sarcopenic visceral obesity, and the visceral fat index in EC. The total skeletal muscle area was calculated in square centimetres. Body surface area (m²) was calculated using the Mosteller formula: ((height (cm) × weight (kg))/3600)^1/2. To normalize body composition components, the skeletal muscle index was calculated as cm²/m². Results: The study comprised a total of 236 EC patients. The prevalence of sarcopenia, sarcopenic obesity, and sarcopenic visceral obesity were found to be 48.31%, 33.47%, and 22.88%, respectively. The presence of sarcopenia, high VFI levels, sarcopenic obesity, and sarcopenic visceral obesity did not demonstrate statistical significance in the survival analysis. However, stage increase (p = 0.001), primary tumour localization in the lower uterine segment (p = 0.001), serous carcinoma (p = 0.001), increased grade in endometrioid carcinoma (p = 0.023), and lymphovascular invasion (p = 0.001) were significantly associated with increased mortality risk. The presence of sarcopenia was found to be significant in patients with obesity (p = 0.008) and those aged ≥ 65 years (p = 0.001). Conclusions: In EC survival, established prognostic factors such as serous histopathology, LVI positivity, and the extent of surgical staging are prioritised. The presence of these well-established markers means the potential effect of BMI-based observations, such as the ‘obesity paradox’, and even body composition measurements, such as sarcopenic obesity, are now statistically insignificant. Our findings suggest that aggressive tumour biology (serous type, LVI) and surgery, rather than metabolic variables such as sarcopenia, sarcopenic obesity and sarcopenic visceral obesity, are the direct reason for the survival difference. This is due to the tumour’s aggressive nature and clinical characteristics (e.g., age at diagnosis, operability, stage, primary tumour localization in the lower uterine segment, serous carcinoma, grade, and LVI positivity) rather than metabolic variables. Full article

In this paper, we introduce and investigate the concept of K-g-fusion frames in the Cartesian product of two Hilbert $C^{*}$-modules over the same unital $C^{*}$-algebra. Our main result establishes that the Cartesian product of two K-g-fusion frames remains a K-g-fusion frame for the direct-sum module. We give explicit formulae for the associated synthesis, analysis, and frame operators and prove natural relations (direct-sum decomposition of the frame operator). Furthermore, we prove a perturbation theorem showing that small perturbations of the component families, measured in the operator or norm sense, still yield a K-g-fusion frame for the product module, with explicit new frame bounds obtained. Full article

We study compactness for the complex Green operator ${\mathsf{G}}_q$ associated with the Kohn Laplacian ${\square }_b$ on boundaries of pseudoconvex domains in Stein manifolds. Let $\Omega ⋐X$ be a bounded pseudoconvex domain in a Stein manifold X of complex dimension n with $C^1$ boundary. For $1\le q\le n-2$, we first prove a compactness theorem under weak potential-theoretic hypotheses: if $b\Omega$ satisfies weak $\left({\mathcal{P}}_q\right)$ and weak $\left({\mathcal{P}}_{n-1-q}\right)$, then ${\mathsf{G}}_q$ and ${\mathsf{G}}_{n-1-q}$ are compact on ${\mathsf{L}}_{p,q}^2\left(b\Omega \right)$. This extends known $C^{\infty }$ results in ${\mathbb{C}}^n$ to the minimal regularity $C^1$ and to the Stein setting. On locally convexifiable $C^1$ boundaries, we obtain a full characterization: compactness of ${\mathsf{G}}_q$ is equivalent to simultaneous compactness of ${\mathsf{G}}_q$ and ${\mathsf{G}}_{n-1-q}$, to compactness of the $\overline{\partial }$-Neumann operators ${\mathsf{N}}_q$ and ${\mathsf{N}}_{n-1-q}$ in the interior, to weak $\left({\mathcal{P}}_q\right)$ and $\left({\mathcal{P}}_{n-1-q}\right)$, and to the absence of (germs of) complex varieties of dimensions q and $n-1-q$ on $b\Omega$. A key ingredient is an annulus compactness transfer on ${\Omega }_{+}={\Omega }_2\setminus \overline{{\Omega }_1}$, which yields compactness of ${\mathsf{N}}_q^{{\Omega }_{+}}$ from weak $\left(\mathcal{P}\right)$ near each boundary component and allows us to build compact ${\overline{\partial }}_b$-solution operators via jump formulas. Consequences include the following: compact canonical solution operators for ${\overline{\partial }}_b$, compact resolvent for ${\square }_b$ on the orthogonal complement of its harmonic space (hence discrete spectrum and finite-dimensional harmonic forms), equivalence between compactness and standard compactness estimates, closed range and ${\mathsf{L}}^2$ Hodge decompositions, trace-class heat flow, stability under $C^1$ boundary perturbations, vanishing essential norms, Sobolev mapping (and gains under subellipticity), and compactness of Bergman-type commutators when $q=1$. Full article

This paper analyzes a finite-capacity $GI/M/2/N$ queue with two heterogeneous servers operating under a multiple working-vacation policy, Bernoulli feedback, and customer impatience. Using the supplementary-variable technique in tandem with a tailored recursive scheme, we derive the stationary distributions of the system size as observed at pre-arrival instants and at arbitrary epochs. From these, we obtain explicit expressions for key performance metrics, including blocking probability, average reneging rate, mean queue length, mean sojourn time, throughput, and server utilizations. We then embed these metrics in an economic cost function and determine service-rate settings that minimize the total expected cost via the Bat Algorithm. Numerical experiments implemented in R validate the analysis and quantify the managerial impact of the vacation, feedback, and impatience parameters through sensitivity studies. The framework accommodates general renewal arrivals ($GI$), thereby extending classical ($M/M/2/N$) results to more realistic input processes while preserving computational tractability. Beyond methodological interest, the results yield actionable design guidance: (i) they separate Palm and time-stationary viewpoints cleanly under non-Poisson input, (ii) they retain heterogeneity throughout all formulas, and (iii) they provide a cost–optimization pipeline that can be deployed with routine numerical effort. Methodologically, we (i) characterize the generator of the augmented piecewise–deterministic Markov process and prove the existence/uniqueness of the stationary law on the finite state space, (ii) derive an explicit Palm–time conversion formula valid for non-Poisson input, (iii) show that the boundary-value recursion for the Laplace–Stieltjes transforms runs in linear time $\mathcal{O}\left(N\right)$ and is numerically stable, and (iv) provide influence-function (IPA) sensitivities of performance metrics with respect to $({\mu }_1,{\mu }_2,\nu ,\alpha ,\varphi ,\beta )$. Full article

Background/Objectives: Bronchopulmonary dysplasia (BPD) is a common chronic complication of prematurity, associated with significant morbidity. Nutrition is a key modifiable factor influencing lung growth, repair, and overall development. This review summarizes current evidence on nutritional strategies for BPD prevention and management. Methods: Narrative review was conducted with literature search in major databases using relevant keywords. Results: Early nutritional deficits are strongly associated with BPD. Higher early protein (3.5–4 g/kg/day) and energy intake (>60 kcal/kg/day in the first week, with progressive increases) reduce ventilator dependence. Lipids are essential to achieve caloric goals. Fluid restriction may reduce BPD risk but often results in undernutrition. Nutrient density, rather than fluid volume, is critical. Enteral nutrition, particularly mother’s own milk, consistently reduces BPD risk, whereas formula feeding is linked to higher BPD incidence. In established BPD, nutritional requirements are substantially increased. Feeding is frequently complicated by fluid restriction, gastroesophageal reflux, and poor oral coordination. Management strategies include higher energy intake (130–150 kcal/kg/day), adequate protein provision (3.5–4 g/kg/day), and careful use of lipid-based energy sources. Fortified human milk or enriched preterm formulas are essential, with individualized fortification improving growth. Micronutrient support is critical, and long-term follow-up is required, as post-discharge growth remains vulnerable and predicts later outcomes. Conclusions: Nutritional strategies to mitigate BPD should focus on early optimization of protein and energy intake, prioritization of nutrient density and promotion of human milk feeding. Targeted micronutrient support, individualized fortification and multidisciplinary care are essential to improve pulmonary and neurodevelopmental outcomes. Full article

Although the composition of hearth gas in a blast furnace is still composed of CO, H₂, and N₂, after injecting shale gas, which replaces some pulverized coal, the proportion of CO, H₂, and N₂ in the hearth gas will change with the introduction of H₂. Further, the reduction process of vanadium-titanium magnetite sinter (VTMS) will be significantly impacted. Hence, the energy–mass balance and replacement ratio model was used to calculate the composition of hearth gas under different injection conditions using production data from a VTM blast furnace in the Panxi area of China. In order to investigate how shale gas injection affects the reduction process, the weight loss rates of VTMS under various reduction atmospheres were obtained through a series of thermogravimetric experiments. Additionally, X-ray diffraction (XRD) analysis was performed on select reduced samples to determine the alterations in sinter phases before and after the reaction. The impact of shale gas injection on the reduction process of VTMS was analyzed by phase transformation and kinetic analysis. The results of the research show that the reduction process of VTMS is improved with the increase in shale gas injection. Using the ln-ln analytical method, the linear relationship between ln(−ln(1 − α)) and lnt under different cases was found. The reaction mechanism of VTMS under shale gas injection circumstances is characterized by random nucleation, which is subsequently followed by growth. The integration formula associated with its dynamic function is G(α) = [−ln(1 − α)]^3/4. Full article

When drilling inclined and horizontal sections, a significant part of the drill string is in a compressed state which leads to a loss of stability and longitudinal bending. Modeling of the stress–strain state (SSS) of the drill string (DS), including prediction of its stability loss, is carried out using modern software packages; the basis of the software’s mathematical apparatus and algorithms is represented by deterministic statically defined formulae and equations. At the same time, a number of factors such as the friction of the drill string against the borehole wall, the presence of tool joints, drill string dynamic operating conditions, and the uncertainty of the position of the borehole in space cast doubt on the accuracy of the calculations and the reliability of the predictive models. This paper attempts to refine the actual behavior of the drill string in critical and post-critical conditions. To study the influence of dynamic conditions in the well on changes in the SSS of the DS due to its buckling, the following initial data were used: a drill pipe with an outer diameter of 88.9 mm and tool joints causing pipe deflection under gravitational acceleration of 9.81 m/s² placed in a horizontal wellbore with a diameter of 152.4 mm; axial vibrations with an amplitude of variable force of 15–80 kN and a frequency of 1–35 Hz; lateral vibrations with an amplitude of variable impact of 0.5–1.5 g and a frequency of 1–35 Hz; and an increasing axial load of up to 500 kN. A series of experiments are conducted with or without friction of the drill string against the wellbore walls. The results of computational experiments indicate a stabilizing effect of friction forces. It should be noted that the distance between tool joints and their diametrical ratio to the borehole, taking into account gravitational acceleration, has a stabilizing effect due to the formation of additional contact force and bending stresses. It was established that drill string vibrations may either provide a stabilizing effect or lead to a loss of stability, depending on the combination of their frequency and vibration type, as well as the amplitude of variable loading. In the experiments without friction, the range of critical loads under vibration varied from 85 to >500 kN, compared to 268 kN as obtained in the reference experiment without vibrations. In the presence of friction, the range was 150 to >500 kN, while in the reference experiment without vibrations, no buckling was observed. Based on the results of this study, it is proposed to monitor the deformation rate of the string during loading as a criterion for identifying buckling in the DS stress–strain state monitoring system. Full article

Objective: Our objectives were as follows: (1) to compare cognitive, motor, language, and social performance, parenting skills, and mother–child interactions among preterm children exposed to different feeding practices (exclusive breastfeeding, mixed feeding, and formula feeding) during the first two years of life; and (2) to examine the associations between the feeding type, risks and protective factors, and neurodevelopmental outcomes (cognitive, motor, language, and social domains) in these population in the first two years of life. Method: A total of 116 preterm children (<32 weeks gestational age—GA) and their mothers were recruited from a public hospital in southern Brazil and followed at a neonatal clinic. Children were organized into three groups based on feeding at NICU discharge (exclusive breastfeeding, formula, or mixed feeding). Assessments were conducted at 4, 8, 12, 18, and 24 months of corrected age using the BSITD-III and additional validated instruments measuring environment stimulation, daily activities, maternal knowledge, breastfeeding experience, and mother–child interactions. Results: Clinical and sociodemographic factors were similar across feeding groups. Group comparisons showed that exclusive breastfeeding was associated with higher motor scores at 12 (p = 0.015) and 24 (p = 0.026) months, higher cognitive scores at 12 (p = 0.049) and 18 (p = 0.013) months, and higher language scores at 12 (p < 0.001) and 18 (p = 0.014) months compared to formula feeding. In the social domain, the exclusive breastfeeding group consistently outperformed the formula group across most time points, although a temporary dip was observed at 18 months. Mixed feeding showed intermediate patterns. Children in the exclusive breastfeeding group also demonstrated higher maternal parenting skills and stronger mother–child interactions across time. Longitudinal analyses revealed that the quality of mother–child interactions predicted better motor, cognitive, language, and social outcomes, while clinical vulnerabilities (e.g., prolonged NICU stay, BPD, leukomalacia) negatively influenced trajectories. Conclusions: Exclusive breastfeeding and responsive mother–child interactions emerged as consistent protective factors across developmental domains, buffering the adverse effects of clinical risks. Breastfeeding not only enhances maternal engagement but also contributes to more favorable motor, cognitive, language, and social outcomes in preterm children. Supporting breastfeeding and promoting sensitive caregiving practices are essential strategies for optimizing developmental trajectories and improving the quality of life in this vulnerable population. Full article

Background/Objectives: Juzentaihoto (JTT), a traditional Kampo formula composed of ten medicinal herbs, is widely prescribed in Japan for immune enhancement and general health maintenance. This exploratory, open-label pilot study aimed to evaluate the feasibility and immunomodulatory effects of JTT in cancer patients and to explore its potential mechanisms of action. Methods: Ten cancer patients received oral JTT (7.5 g/day) for 14 days, while healthy volunteers served as a reference group. Peripheral natural killer (NK) cell phenotypes and CD95 expression were analyzed by flow cytometry, and serum Fas ligand (FasL) concentrations were measured by ELISA. Complementary in vitro assays using PBS-extracted, autoclaved JTT were conducted to assess Fas/FasL-mediated apoptosis in Jurkat and primary T cells by flow cytometry and Western blotting for cleaved caspase-8 and -3. Additional experiments with staurosporine (intrinsic apoptosis) and TRAIL in OSC-19 carcinoma cells were performed to determine pathway specificity. Results: In patients, most NK-cell markers showed no statistically significant within-subject changes, although a trend-level increase in NKp46 and a significant reduction in NK-cell CD95 expression (paired p = 0.014) were observed. Between-group differences primarily reflected baseline disparities between cancer patients and healthy controls. In vitro, JTT (50–100 µg/mL) partially attenuated FasL-induced apoptosis and reduced cleaved caspase-3 without affecting cleaved caspase-8, suggesting selective downstream modulation of the extrinsic pathway. Conclusions: Within the limitations of a small, non-randomized cohort without placebo, these findings are hypothesis-generating and indicate that JTT selectively modulates Fas-mediated lymphocyte apoptosis without promoting tumor immune evasion. Further randomized trials and mechanistic studies incorporating co-culture or 3D tumor–immune models are warranted to confirm these observations and identify active constituents. Full article

Eriophyoidea (Acariformes), a superfamily of obligate phytophagous and highly host-specific mites, comprises four early-diverging lineages (Pentasetacidae, Phytoptidae s. str., Nalepellidae, and Eriophyidae s.l.) with unresolved inter-relationships. The clade Phytoptidae s. str. is restricted to angiosperms and includes a group of six genera associated with palms (Arecaceae) and classified in tribes Mackiellini and Phytoptini. Global distribution patterns of Phytoptidae s. str. are biased towards the Americas and Europe. Current knowledge of Asian palm-associated phytoptids is limited to a single record of Borassia from India and the new Calventer arengii n. g. et sp. (Sierraphytoptinae: Mackiellini) described here as a vagrant on the lower surface of fronds of Arenga westerhoutii Griff. (Arecaceae) from Vietnam. Maximum likelihood COI analyses did not support the monophyly of Mackiellini but revealed a sister-group relationship between Mackiella and Calventer and questioned the taxonomic position of Borassia. Notably, Calventer possesses one of the most reduced chaetoms in Phytoptidae, illustrating a recurring trend of setal loss across Eriophyoidea. Plesiomorphically, females of eriophyoids have 65 setae, with most being prone to homoplastic reduction; however, a stable subset (h2, 3a, emp, and ω) is consistently retained. Excluding these “stable setae,” the remaining chaetom can be expressed as a “setal formula” incorporated into generic diagnoses for the efficient, rapid delimitation of genera. Full article

Background: Necrotizing enterocolitis (NEC) remains a leading cause of morbidity and mortality in very low birthweight (VLBW) infants. Human milk feeding and standardized feeding protocols are protective, but clinical practice varies, particularly in fortifier choice. Whether human milk-derived fortifiers reduce NEC risk compared with cow milk-derived fortifiers remains unclear. Methods: We conducted a systematic state-of-evidence review and meta-analysis, searching PubMed, Web of Science, and Scopus through July 2025. Eligible studies included RCTs and observational cohorts of VLBW infants comparing an exclusive human milk diet (EHMD) including human milk-derived fortifiers to cow milk-derived diets. Two reviewers independently screened and extracted data. Both RCTs and observational studies were included to evaluate consistency of effect estimates across designs and to account for heterogeneity in control group feeding practices. Pooled odds ratios (ORs) with 95% CIs were calculated using a Sidik–Jonkman random-effects model. Sensitivity analyses by study design and exclusion of infant formula from controls were performed. Results: Twenty studies (five RCTs, 15 observational; n = 6794 infants) met inclusion criteria, most enrolling infants born ≤1250 g. Compared with cow milk-containing diets, EHMD was associated with lower odds of Bell Stage ≥ 2 NEC (OR: 0.59; 95% CI: 0.42, 0.81; p < 0.001; n = 4625) and surgical NEC (OR: 0.43; 95% CI: 0.32, 0.58; p < 0.0001; n = 4754). In direct comparisons of fortifier type with a base diet of human milk, estimates suggested lower odds of Bell Stage ≥ 2 NEC by 35% (OR: 0.65; 95% CI: 0.44, 0.97; p = 0.03, n = 2102) and surgical NEC by 49% (OR: 0.51; 95% CI: 0.26, 0.98; p = 0.04; n = 1659) with human milk-derived fortifiers. Effect estimates were generally consistent across study designs, although precision and statistical significance varied. Conclusions: EHMD with human milk-derived fortifiers was associated with lower odds of medical and surgical NEC in VLBW infants, with most evidence from infants born ≤1250 g, reflecting current clinical use in the highest-risk population. Although the number and sample sizes of RCTs remain limited, the consistency of effect estimates across both RCTs and observational studies, together with significance of pooled analyses, strengthens confidence in these findings. Pragmatic and registry-based studies using standardized fortification protocols may provide the most efficient pathway to strengthen the evidence base. Full article

We study an integral transform—here called the Master Integral Transform—in which the kernel is an arbitrary entire function of finite order. When the nonzero Taylor coefficients of the kernel have positive Beurling–Malliavin density, we prove completeness and global injectivity in a Cauchy-weighted Hilbert space, and we furnish explicit Mellin–Fourier inversion formulae with exponentially decaying integrands. Classical Fourier, Laplace, and Mellin transforms appear only as strict special cases. Beyond these, we establish structural properties (multiplier/composition law, dilation covariance, parameter regularity) and present applications not captured by fixed-kernel frameworks, including inverse-kernel identification and hybrid boundary value models, e.g., the Poisson–Airy pair produces a closed-form transformed Green’s function and a solvable variable-coefficient PDE, illustrating capabilities unavailable to fixed-kernel frameworks. Full article