Search Results (214)

In this paper, we generalize an inequality for a convex function in one dimension ${\mathbb{R}}^1$ on three intervals to a function with nondecreasing increments in k dimensions ${\mathbb{R}}^k$ on $(2n+1)$ intervals. We prove all the situations when $n=1,2$ and prove a very special case for a general n as well as the discrete version. The proofs are based on a general conclusion for convex functions, and analogues of this conclusion are established. We apply the discrete case of the inequality to Csiszár $\varphi$-divergence $I_{\varphi }(p,q)$ in information theory, and the continuous case $I_{\varphi }(p_1,q_1)\le I_{\varphi }(p_2,q_2)$ on a measurable set is also established. The same inequality for an $ϵ$-approximately convex function on a discrete set is also established and can be used to prove a similar Landau–Kolmogorov-type inequality. Full article

This study introduces a novel subclass of q-starlike functions that is defined by the application of the q-difference operator and q-analogue of hyperbolic secant function. By making certain variations to the parameter “q”, the geometric interpretation of the domain hyperbolic secant function has also been discussed. The primary objective is to investigate and establish key results on the differential subordination of various orders within this newly defined class. Furthermore, convolution properties are explored and coefficient bounds are derived for these functions. A deeper analysis of these coefficients bounds unveils intriguing geometric insights and significant mathematical problems. Full article

This study aimed to develop a shelf-stable, plant-based whole hard-boiled egg analogue, available in both regular and low-allergenic versions. Six plant proteins—soy, mung bean, pea, rice, potato, and wheat—were formulated into egg white and yolk components, with mung bean and wheat proteins showing the most promising sensory and visual qualities. Two preservation methods, thermal pasteurization (75–85 °C, 15–20 min) and gamma irradiation (2–5 kGy), were applied to extend shelf life while maintaining product quality. Thermal treatment at 75 °C for 15 min and gamma irradiation at 3.5 kGy were identified as optimal conditions, balancing sensory acceptability and microbial safety. Sensory evaluation by 100 untrained panelists revealed favorable scores for appearance, texture, and overall liking, without significant differences among selected formulations (p > 0.05). Accelerated shelf life testing and Q10 modeling predicted a shelf life of 188 days for thermally pasteurized eggs and 253 days (8.42 months) for gamma-irradiated eggs at 30 °C. These results demonstrate the feasibility of developing a consumer-acceptable, plant-based hard-boiled egg analogue with extended ambient shelf life. Full article

Traumatic brain injury (TBI) leads to persistent pro-inflammatory microglial activation implicated in neurodegeneration. Idebenone, a coenzyme Q10 analogue that interacts with both mitochondria and the tyrosine kinase adaptor SHC1, inhibits aspects of microglial activation in vitro. We used the NanoString Neuropathology Panel to test the hypothesis that idebenone post-treatment mitigates TBI-pathology-associated acute gene expression changes by moderating the pro-inflammatory microglial response to injury. Controlled cortical impact to adult male mice increased the microglial activation signature in the peri-lesional cortex at 24 h post-TBI. Unexpectedly, several microglial signature genes upregulated by TBI were further increased by post-injury idebenone administration. However, idebenone significantly attenuated TBI-mediated perturbations to gene expression associated with behavior, particularly in the gene ontology–biological process (GO:BP) pathways “ephrin receptor signaling” and “dopamine metabolic process”. Gene co-expression analysis correlated levels of microglial complement component 1q (C1q) and the neurotrophin receptor gene Ntrk1 to large (>3-fold) TBI-induced decreases in dopamine receptor genes Drd1 and Drd2 that were mitigated by idebenone treatment. Bioinformatics analysis identified SUZ12 as a candidate transcriptional regulator of idebenone-modified gene expression changes. Overall, the results suggest that idebenone may enhance TBI-induced microglial number within the first 24 h of TBI and identify ephrin-A and dopamine signaling as novel idebenone targets. Full article

This paper presents a novel symmetric q-analogue differential operator designed for meromorphic multivalent functions analytic in the punctured open unit disk. Employing this operator, a new family of meromorphic multivalent functions is proposed and examined in this work. A detailed investigation of this newly defined class of meromorphic multivalent functions is presented, highlighting key geometric characteristics, including sufficiency criteria, coefficient inequalities, distortion and growth behavior, as well as the radii of starlikeness and convexity. Full article

In the present paper, using the q-difference operator, we introduce two classes of q-starlike functions and q-convex functions subordinate to secant hyperbolic functions. As functions in these classes have unique characteristic of missing coefficients on the second term in their analytic expansions, we define a new functional to unify the Hankel determinants with entries of the original coefficients, inverse coefficients, logarithmic coefficients, and inverse logarithmic coefficients for these functions. We obtain the sharp bounds on the new functional for functions in the two classes, and as a consequence, the best results on Hankel determinant for the starlike and convex functions subordinate to secant hyperbolic functions are given. The outcomes include some existing findings as corollaries and may help to deepen the understanding the properties of q-analogue analytic functions. Full article

Background: In recent decades, the adoption of minimally invasive (non-endoscopic) cervical techniques has grown significantly. Advancements in surgical instrumentation have broadened the spectrum of available percutaneous interventions, thus providing viable alternative treatment options for patients with prolonged, conservative treatment-resistant ailments due to contained cervical disc herniation. The aim of this study was to perform a systematic review and meta-analysis in order to evaluate the effectiveness and safety of minimally invasive percutaneous (non-endoscopic) cervical techniques. Methods: A comprehensive literature search was conducted using the PubMed, Cochrane Library, and SCOPUS databases up to July 2024, in accordance with the PRISMA guidelines. Outcomes measured included Visual Analogue Scale (VAS) scores, the Neck Disability Index (NDI), and MacNab scores, assessing pain relief and functional recovery. The risk of bias was evaluated using the Cochrane risk of bias tool (RoB 2) and the risk of bias in nonrandomized studies of interventions (ROBINS-I) tool, with statistical analyses conducted in R software (version 4.3.1). Results: Out of 847 records, 21 studies (covering 1580 patients) were included in the final analysis. Five different percutaneous minimally invasive cervical procedures were incorporated into this review: nucleoplasty (n = 973), discectomy (n = 311), a combination of nucleoplasty and discectomy (n = 98), annuloplasty (n = 33), and pulsed radiofrequency (n = 17). The mean patient age was 49.5, with a gender distribution of 47.7% male and 52.3% female. A meta-analysis of six studies on cervical nucleoplasty (400 patients) demonstrated a significant reduction in pain scores, with a standardized mean difference (SMD) of −4.68 (95% CI: −8.77; −0.59, p = 0.032). However, a high heterogeneity (I² = 98.8%, Q = 407.31, p < 0.001) was observed, indicating significant variability across studies. The reoperation rate among patients was 3.4%, with discitis and device-related complications being the most frequently reported adverse events. Conclusions: Minimally invasive percutaneous cervical interventions provide effective pain relief and functional improvement for patients with cervical disc herniation, as evidenced by reductions in VAS scores and positive MacNab outcomes. The choice of the most appropriate technique should be based on individual clinical scenarios, surgeon expertise, and patient preferences, as no single method demonstrates clear superiority according to clinical outcomes or complication rates. Full article

Curcumin is recognized for its diverse biological activities, including the ability to induce apoptosis and ferroptosis. Therefore, it represents a promising candidate for the development of new compounds with neuroprotective and anticancer properties. In order to synthesize mimics with improved pharmacokinetic properties (better solubility and stability than curcumin) here, we present the design and synthesis of novel curcumin analogues named Ethylphosphonate-based curcumin mimics (EPs), which preserve the pharmacophoric features of curcumin. New EP mimics were synthesized by tyrosol- and melatonin-based building blocks using an orthogonal protection approach of the different precursors’ OH functions with good yields and in a few steps. Comparative screenings of the cytotoxic and cytoprotective properties (curcumin was used as a reference compound) were carried out on all new mimics in different cell lines (HeLa, A375, WM266, MDA-MB-231, LX2, and HDF). Assays with inhibitors of ferroptosis (Ferrostatin-1, Fer-1) and apoptosis (Quinoline-Val-Asp-difluorophenoxymethyl ketone, Q-VD), in combination with curcumin, suggested the specific cell death pathway (apoptotic or ferroptotic) of EPs, depending on the aromatic moieties contained in them. Interestingly, EP4 exhibited substantial cytotoxic effects against various human cancer cell lines (HeLa, A375, WM266) while sparing normal cells (HDFs). EP4 displayed a five-times-higher toxicity in triple-negative MDA-MB-231 and LX2 stellate cells than curcumin. The cytotoxicity exerted by EP4 involves only an apoptotic mechanism, contrary to curcumin, which exerts both apoptotic and ferroptotic effects. Additionally, EP4 was also found to be a very potent inhibitor of the ubiquitin-activating enzyme E1, reinforcing the anticancer potential of this compound. Furthermore, EP2 possesses high antioxidant properties, efficiently protects against cell death by ferroptosis, and inhibits the amyloid aggregation involved in AD. Full article

The intent of quantum calculus, briefly q-calculus, is to find q-analogues of mathematical entities so that the original object is achieved when a certain limit is taken. In the case of q-analogue of the ordinary derivative, the limit is $q\to 1^{-}$. Also, the study of integral as well as differential operators has remained a significant field of inquiry from the early developments of function theory. In the present article, a subclass $S_{sc}\left(\mu ,q\right)$ of functions being analytic in $\mathcal{D}=\left\{z\in \mathbb{C}:\left|z\right|<1\right\}$ is introduced. The definition of $S_{sc}\left(\mu ,q\right)$ involves the concepts of subordination, that of q-derivative and q-Ruscheweyh operators. Since coefficient estimates and coefficient functionals provide insights into different geometric properties of analytic functions, for this newly defined subclass, we investigate coefficient estimates up to $a_4$, in which both bounds for $|a_2|$ and $|a_3|$ are sharp, while that of $|a_4|$ is sharp in one case. We also discuss the sharp Fekete–Szegö functional for the said class. In addition, Toeplitz determinant bounds up to $T_3\left(2\right)$ (sharp in some cases) and sufficient condition are obtained. Several consequences derived from our above-mentioned findings are also part of the discussion. Full article

In this work, we describe the $\mathfrak{q}$-analogue of a multiplier–Ruscheweyh operator of a specific family of linear operators ${\mathfrak{I}}_{\mathfrak{q},\rho }^s(\nu ,\tau )$, and we obtain findings related to geometric function theory (GFT) by utilizing approaches established through subordination and knowledge of $\mathfrak{q}$-calculus operators. By using this operator, we develop generalized classes of quasi-convex and close-to-convex functions in this paper. Additionally, the classes ${\mathfrak{K}}_{\mathfrak{q},\rho }^s(\nu ,\tau )\left(\phi \right)$, ${\mathfrak{Q}}_{\mathfrak{q},\rho }^s(\nu ,\tau )\left(\phi \right)$ are introduced. The invariance of these recently formed classes under the $\mathfrak{q}$-Bernardi integral operator is investigated, along with a number of intriguing inclusion relationships between them. Additionally, several unique situations and the beneficial outcomes of these studies are taken into account. Full article

This paper extends the idea of subordination from the theory of fuzzy sets to the geometry theory of analytic functions with a single complex variable. The purpose of this work is to define fuzzy subordination and illustrate its main characteristics. New fuzzy differential subordinations will be introduced with the help of this effort. We define a linear operator ${\mathfrak{I}}_{\mathfrak{q},\rho }^s(\nu ,\varsigma )$ using the concept of the $\mathfrak{q}$-calculus operators. New fuzzy differential subordinations are created by employing the previously described operator, functions from the new class, and well-known lemmas. Specific corollaries derived from the operator proved the many examples created for the fuzzy differential subordinations, as well as the theorems, and demonstrate how the new theoretical conclusions apply to the fuzzy differential superordinations provided in this research. Full article

Background/Objectives: Glioblastoma multiforme (GBM), an aggressive and deadly brain tumour, presents significant challenges in achieving effective treatment due to its resistance to current therapies and poor prognosis. This study aimed to synthesise and evaluate 23 novel analogues of 3,4-dihydroquinolin-2(1H)-one, designed to enhance druggability and solubility, and to investigate their potential as VEGFR2 inhibitors for GBM treatment. Methods: The synthesised compounds were analysed using in silico methods, including molecular docking and dynamics studies, to assess their interactions with key residues within the VEGFR2 binding pocket. In vitro evaluations were performed on U87-MG and U138-MG GBM cell lines using MTT assays to determine the IC50 values of the compounds. Results: Among the tested compounds, 4u (IC50 = 7.96 μM), 4t (IC50 = 10.48 μM), 4m (IC50 = 4.20 μM), and 4q (IC50 = 8.00 μM) demonstrated significant antiproliferative effects against both the U87-MG and U138-MG cell lines. These compounds exhibited markedly higher efficacy compared to temozolomide (TMZ), which showed IC50 values of 92.90 μM and 93.09 μM for U87-MG and U138-MG, respectively. Molecular docking and dynamics studies confirmed strong interactions between the compounds and VEGFR2 kinase, supporting their substantial anti-cancer activity. Conclusions: This study highlights the promising potential of 3,4-dihydroquinolin-2(1H)-one analogues, particularly 4m, 4q, 4t, and 4u, as VEGFR2-targeting therapeutic agents for GBM treatment. Further detailed research is warranted to validate and expand upon these findings. Full article

Background: Systemic sclerosis-associated pulmonary hypertension (SSc-PH) is widely recognized as the most severe subtype of connective tissue disease-associated pulmonary hypertension (CTD-PH), particularly in patients with complicating factors such as interstitial lung disease (ILD) and biventricular failure. This condition is associated with the poorest clinical outcomes among PH subtypes, presenting significant challenges in both management and prognosis. Despite the use of conventional therapies, including intravenous administration of epoprostenol, a promising prostacyclin analogue, treatment outcomes for SSc-PH remain suboptimal. While epoprostenol has demonstrated efficacy in reducing pulmonary arterial pressures, its clinical application is often constrained by the risk of ventilation–perfusion (V-Q) mismatch, particularly at higher doses. Case presentation: We report the case of a 73-year-old woman with SSc-PH complicated by ILD, who experienced progressive hemodynamic deterioration despite receiving optimized therapy with intravenous epoprostenol. Efforts to escalate the dose of epoprostenol were limited by the development of severe V-Q mismatch, precluding further dose increases. In light of these challenges, inhaled treprostinil was introduced as an adjunctive therapy. There were significant improvements in her pulmonary hypertension and hemodynamic parameters, ultimately allowing the discontinuation of intravenous dobutamine and stabilization of her hemodynamics, as well as her respiratory function, exercise capacity, and quality of life. Conclusions: This case highlights the potential clinical utility of combining inhaled treprostinil with intravenous epoprostenol for the treatment of SSc-PH in patients with concurrent ILD. By addressing the limitations associated with high-dose intravenous prostacyclin therapy, this combination approach may represent a promising therapeutic strategy for improving outcomes in this difficult-to-treat patient population. Further investigation is warranted to establish the efficacy and feasibility of this combination therapy in larger cohorts of patients with SSc-PH and associated ILD. Full article

In this paper, $\left(p,q\right)$-analogues of the generalized harmonic polynomials and the generalized hyperharmonic polynomials of order $\nu$ are defined. We found new sums of these numbers by using combinatorial operations. We also obtained the generating function and used it to reproduce new equations. The applications of matrices are made in the end. Full article

This article introduces the 2-variable q-truncated exponential–Appell (q-trunc. exp. Appell) polynomials and investigates their fundamental properties. Specific results are derived for the q-trunc. exp. Appell family along with their graphical representations which contribute to advancing the understanding of q-series and q-special functions. Potential applications of these polynomials span various disciplines, including combinatorics (such as partition theory and combinatorial identities), number theory (such as q-analogues of classical number-theoretic functions), and mathematical physics (such as in quantum groups and statistical mechanics). This study concludes with the introduction of the 2-variable q-trunc. exp. $\lambda$-polynomials, thereby broadening the scope and relevance of this research. Full article