Search Results (9)

This paper introduces a new class of Newton-type inequalities (NTIs) within the framework of extended fractional integral operators. This study begins by establishing a fundamental identity for generalized fractional Riemann–Liouville (FR-L) operators, which forms the basis for deriving various inequalities under different assumptions on the integrand. In particular, fractional counterparts of the classical $1/3$ and $3/8$ Simpson rules are obtained when the modulus of the first derivative is convex. The analysis is further extended to include functions that satisfy a Lipschitz condition or have bounded first derivatives. Moreover, an additional NTI is presented for functions of bounded variation, expressed in terms of their total variation. In all scenarios, the proposed results reduce to classical inequalities when the fractional parameters are specified accordingly, thus offering a unified perspective on numerical integration through fractional operators. Full article

Purpose: Grade II meningiomas are rarer than Grade I, and when operated on, bear a higher risk of local recurrence, with a 5-year progression free survival (PFS) ranging from 59 to 90%. Radiotherapy (RT) or radiosurgery, such as Gamma Knife radiosurgery (GKRS) can reduce the risk of relapse in patients with residual disease, even if their role, particularly after gross total resection (GTR), is still under debate. Main goal of this study was to compare the outcomes of different post-surgical management of grade II meningiomas, grouped by degree of surgical removal (Simpson Grade); next in order we wanted to define the role of GKRS for the treatment of residual disease or relapse. Methods: from November 2016 to November 2020 all patients harboring grade II meningiomas, were divided into three groups, based on post-surgical management: (1) wait and see, (2) conventional adjuvant radiotherapy and (3) stereotactic GKRS radiosurgery. Relapse rate and PFS were registered at the time of last follow up and results were classified as stable, recurrence next to or distant from the surgical cavity. In the second part of the study we collected data of all patients who underwent GKRS in our Centers from November 2017 to November 2020. Results: A total of 37 patients were recruited, including seven patients with multiple meningiomas. Out of 47 meningiomas, 33 (70.2%) were followed with a wait and see strategy, six (12.7%) were treated with adjuvant radiotherapy, and 8 patients (17.0%) with adjuvant GKRS. Follow up data were available for 43 (91.4%) meningiomas. Within the wait and see group, recurrence rates differed based on Simpson grades, lower recurrence rates being observed in three Simpson I cases (30%) compared to twelve relapses (60%) in patients with Simpson grade II/III. Finally, out of the 24 meningiomas undergoing GKRS (8 residual and 16 recurrence), 21 remained stable at follow up. Conclusions: Gross total resection (GTR) Simpson II and III have a significantly worse outcome as compared to Simpson I. The absence of adjuvant treatment leads to significant worsening of the disease progression curve. Adjuvant radiotherapy, especially GKRS, provides good local control of the disease and should be considered as an adjuvant treatment in all cases where Simpson I resection is not possible. Full article

Biochar application can enhance soil health and alter soil bacterial community structure. However, knowledge relating to biochar on soil nutrients of mountainous apple orchards and then assessing its effect on soil health, especially on soil microorganisms, is still scanty. Therefore, we evaluated the responses of six biochar treatments [Ck (0), T1 (2), T2 (4), T3 (6), T4 (8), and T5 (10) Mg hm⁻²] with a basal dose of chemical fertilizer on the soil nutrients under potted apple trees across 3, 6, 9, and 12 months, and then investigated the responses of the rhizobacterial communities. Experimental findings demonstrated that: (i) Across the months, the biochar-applied treatment (T5) compared to the control significantly enhanced soil nutrients, including soil pH (2.12 to 2.29%), soil organic matter (35 to 40%), total nitrogen (59 to 65%), ammonium nitrogen (25 to 33%), nitrate nitrogen (163 to 169%), and the activities of urease (76 to 81%), alkaline phosphatase (30 to 33%), catalase (8.89 to 11.70%), and sucrase (23 to 29%). (ii) Compared to the control, the biochar-applied treatment (T5) had a more desirable relative abundance of the bacterial phylum Proteobacteria (35.47%), followed by Actinobacteria (8.59%), Firmicutes (5.74%), and Bacteroidota (2.77%). Similarly, the relative abundance of the bacterial genera in the T5 was Sphingomonas (8.23%) followed by RB41 (3.81%), Ellin6055 (3.42%), Lachnospiracea (1.61%), Bacillus (1.43%), Kineosporia (1.37%), Massilia (0.84%), and Odoribacter (0.34%) than the control. (iii) Among the alpha diversity, the biochar-applied treatment (T5) revealed the highest Chao1 (20%) and ACE (19.23%) indexes, while Shannon (1.63%) and Simpson (1.02%) had relatively lower indexes than the control. Furthermore, positive correlations were found between the soil nutrients and some of the abundant bacterial phyla. Overall, the findings of this research demonstrated that biochar application at 10 Mg hm⁻² (T5) along with the required chemical fertilizer is beneficial to improve soil health and pave the way for sustainable production in apple orchards of the northern loess plateau. Full article

Progression-free survival (PFS) and overall survival (OS) for WHO grade 2 and 3 intracranial meningiomas are poorly described, and long-term results and data evaluating the routine use of supplementary fractionated radiotherapy (RT) or stereotactic radiosurgery (SRS) has been inconclusive. The aim of this study was to determine the long-term PFS and OS at a center that does not employ routine adjuvant RT. For this purpose, a retrospective population-based cohort study was conducted of all WHO grade 2 and 3 meningiomas surgically treated between 2005 and 2013. The cohort was uniformly defined according to the WHO 2007 criteria to allow comparisons to previously published reports. Patient records were reviewed, and patients were then prospectively contacted for structured quality-of-life assessments. In total, 51 consecutive patients were included, of whom 43 were WHO grade 2 and 8 were grade 3. A Simpson grade 1–2 resection was achieved in 62%. The median PFS was 31 months for grade 2 tumors, and 3.4 months for grade 3. The median OS was 13 years for grade 2, and 1.4 years for grade 3. The MIB-1-index was significantly associated with an increased risk for recurrence (p = 0.018, OR 1.12). The median PFS was significantly shorter for high-risk tumors compared to the low-risk group (10 vs. 46 months; p = 0.018). The surviving meningioma patients showed HRQoL measures comparable to that of the general population, with the exception of significantly more anxiety and depression. All patients who worked before surgery returned to work after their treatment. In conclusion, we confirm dismal prognoses in patients with grade 2 and 3 meningiomas, with tumor-related deaths resulting in severely reduced OS. However, the cohort was heterogenous, and a large subgroup of both grade 2 and 3 meningiomas was alive at 10 years follow-up, suggesting that a cure is possible. In addition, fractionated radiotherapy and chemotherapy had little benefit when introduced for recurrent and progressive diseases. Full article

The restoration of vegetation on coal gangue mountains has always been an area of concern, and therefore, an important area of research. Liupanshui city in Guizhou province, China, has a large number of coal gangue mountains, and for this reason, was chosen for studying vegetation succession on these sites. Vetiveria zizanioides is known to accelerate the restoration of vegetation on coal gangue mountains and to shorten community succession timeframes. Because of this, we investigated different successional stages after the planting of V. zizanioides on coal gangue mountains in the Dahe coal mine comprehensive environmental governance project area in Liupanshui city. Through field community surveys and model prediction, the effects of planted V. zizanioides on the species composition, species diversity, and community succession of gangue mountains 3, 6, 8, 10, and 13 years after planting were explored. In total, 35 plant species belonging to 17 families and 32 genera were recorded across the five different coal gangue mountains. With more time after planting, the height, coverage, density, and biomass of V. zizanioides all decreased, but increased for Miscanthus floridulus. The Simpson diversity index, Shannon–Wiener diversity index, and Pielou evenness index all first increased before decreasing over time; maximum values were recorded for the coal gangue mountain 8 years after planting of V. zizanioides. According to different similarity and dissimilarity indices, the successional stages became more similar with increasing time after planting. According to biomass fitting and prediction curves, the succession process of coal gangue mountain plant communities could be divided into a V. zizanioides community stage, a M. floridulus community stage, and a woody plant stage, that starts to approach the natural community of evergreen broad-leaved forests, with durations of 0–5.62 years, 5.62–17.48 years, and over 17.48 years, respectively. Full article

In this paper, we give some correct quantum type Simpson’s inequalities via the application of q-Hölder’s inequality. The inequalities of this study are compatible with famous Simpson’s $1/8$ and $3/8$ quadrature rules for four and six panels, respectively. Several special cases from our results are discussed in detail. A counter example is presented to explain the limitation of Hölder’s inequality in the quantum framework. Full article

Inequality theory has attracted considerable attention from scientists because it can be used in many fields. In particular, Hermite–Hadamard and Simpson inequalities based on convex functions have become a cornerstone in pure and applied mathematics. We deal with Simpson’s second-type inequalities based on coordinated convex functions in this work. In this paper, we first introduce Simpson’s second-type integral inequalities for two-variable functions whose second-order partial derivatives in modulus are convex on the coordinates. In addition, similar results are acquired by considering that powers of the absolute value of second-order partial derivatives of these two-variable functions are convex on the coordinates. Finally, some applications for Simpson’s $3/8$ cubature formula are given. Full article

Numerical approximations of definite integrals and related error estimations can be made using Simpson’s rules (inequalities). There are two well-known rules: Simpson’s $\frac{1}{3}$ rule or Simpson’s quadrature formula and Simpson’s $\frac{3}{8}$ rule or Simpson’s second formula. The aim of the present paper is to extend several inequalities that hold for Simpson’s $\frac{1}{3}$ rule to Simpson’s $\frac{3}{8}$ rule. More precisely, we prove a weighted version of Simpson’s second type inequality and some Simpson’s second type inequalities for Lipschitzian, bounded variations, convex functions and the functions that belong to $L^q$. Some applications of the second type Simpson’s inequalities relate to approximations of special means and Simpson’s $\frac{3}{8}$ formula, and moments of random variables are made. Full article

This study was carried out at Ny-Ålesund on Spitsbergen in Svalbard (High Arctic). Eight study sites were established along a transect from the fjord to the snout of the glacier. The sites differed from each other by the type of vegetation cover and soil characteristics. Soil samples were collected and placed in Tullgren funnels. Extracted arthropods were represented by two groups of mites (Mesostigmata and Oribatida) and springtails (Collembola). The pioneer species that occurred first after retreat of the glacier were representatives of the Collembola (Agrenia bidenticulata and Hypogastrura concolor). Later, other springtails appeared including Folsomia alpha, Folsomia quadrioculata, Hypogastrura concolor, Isotoma anglicana, Sminthurinus concolor and the first species of oribatid mites; Camisia foveolata and Tectocepheus velatus velatus. Arthropod communities recorded along the transect were characterized by large variations in both species composition and abundance of individuals. The greater the distance from the glacier snout, the greater the species richness (2 to 22 species). The mean number of species per sample was the lowest at site 8 (1 ± 0.71) (the closest to the glacier) and greatest at site 1 (14 ± 1.41) (furthest from the glacier). The Simpson’s diversity index (D) was distinctly greater at sites 1 (4.61 ± 0.06) and 3 (3.94 ± 0.11) than at other sites, especially site 8 (1.07 ± 0.06). Densities were least in the samples closest to the glacier (30 to 101 individuals; density 3000–10,100 individuals/m2). At the other locations, abundance was highly variable (905 to 7432 individuals; density 90,500–743,200 individuals/m2). The mean abundances were greatest at sites 2 and 3. The great variations in total abundances observed were often due to the presence or absence of one or more dominant species exhibiting extreme abundance variability between sites. The microarthropod community of the High Arctic is composed of heterogeneous circumpolar species, yet on a landscape scale is extremely dependent on local environmental conditions which may be subject to rapid change. Full article