In this article, the Legendre-Gould Hopper polynomials are combined with Sheffer sequences to introduce certain mixed type special polynomials. Generating functions, differential equations and certain other properties of Legendre-Gould Hopper based Sheffer polynomials are derived. Further, operational and integral representations providing connections between these polynomials and known special polynomials are established. Certain identities and results for some members of these new mixed polynomials are also obtained. Finally, the determinantal definitions of Legendre-Gould Hopper based Sheffer polynomials are also given.

Urban cycling is a sustainable transport mode that cities currently try to expand. However, cities still do not take advantage of geospatial technologies to understand cycling mobility based on the behavioural patterns and difficulties faced by cyclists. This study analyses a geospatial dataset crowdsourced by urban cyclists using an experimental geo-game. About 20 participants per city recorded bicycle trips during one week and, by aggregating them, we found not only the cyclists’ preferred streets but also the frictions faced during cycling. We successfully identified 284 places potentially having frictions: 71 in Münster, Germany; 70 in Castelló, Spain; and 143 in Valletta, Malta. At such places, Participants not only recorded bicycle trips but also segments at lower speeds indicating a deviation from an ideal cycling scenario. We described the potential frictions preventing from bicycle commuting based on the distance to bicycle paths, surrounding infrastructure, and location in the urban area.

Mitochondria are involved in many cellular processes and their main role is cellular energy production. They constantly undergo fission and fusion, and these counteracting processes are under strict balance. The cytosolic dynamin-related protein 1, Drp1 or dynamin-1-like protein (DNM1L) mediates mitochondrial and peroxisomal division. Defects in the DNM1L gene results in a complex neurodevelopmental disorder with heterogeneous symptoms affecting multiple organ systems. Currently there is no curative treatment available for this condition. We have previously described a patient with a de novo heterozygous c.1084G>A (p.G362S) DNM1L mutation and studied the effects of a small molecule, Bezafibrate, on mitochondrial functions in this patient’s fibroblasts compared to controls. Bezafibrate normalized growth on glucose-free medium, ATP production, oxygen consumption and s improved mitochondrial morphology in patient’s fibroblasts, albeit concomitantly causing a mild increase ROS production. Further studies would be needed to show the consistency of the response to Bezafibrate, possibly using fibroblasts from patients with different mutations in DNM1L, and this treatment should be confirmed in clinical trials. However, taking into account the favorable effects in our study, we suggest that Bezafibrate could be a possible treatment option for patients with certain DNM1L mutations.

Asymmetric lithium salts, such as Lithium (difluoromethanesulfonyl)(trifluoromethanesulfonyl)imide (LiDFTFSI), have been demonstrated to surpass traditional symmetric lithium salts with improved Li+ conductivity and the capacity to generate stable solid electrolyte interphase (SEI) while maintaining compatibility with aluminum (Al0) current collector. However, the intrinsic reductive mechanism through which LiDFTFSI influences battery performance remains unclear and under debate. Herein, the detailed SEI reactions of LiDFTFSI-based electrolytes were investigated by combining density functional theory and molecular dynamics, aiming to clarify the formation process and atomic structure of SEI. Our results show that asymmetric DFTFSI– weakens the interaction between carbonate solvents and Li+, and substantially alter the solvation structure, exhibiting a well-balanced coordination capacity to bis(trifluoromethanesulfonyl)imide (TFSI–). Nanoseconds hybrid molecular dynamics simulation further reveals that the preferential decomposition of LiDFTFSI produces sufficient LiF and Li2O to facilitate a robust SEI. Moreover, the abundant F– generated from LiDFTFSI decomposition accumulates on the Al surface and subsequently combines with Al3+ from the current collector to form AlF3, potentially inhibiting corrosion of the current collector. Overall, these findings elucidate how LiDFTFSI regulates the solvation sheath and SEI structure, advancing the development of high-performance electrolytes compatible with current collector.

This investigation explores the potential of enhancing aqueous zinc-ion batteries (AZIBs) through the introduction of a novel cathode material, NH4V4O10 (NVO), combined with reduced graphene oxide (rGO). Utilizing Density Functional Theory (DFT), it was hypothesized that the incorpora-tion of rGO would increase the interlayer spacing of NVO and diminish the charge transfer in-teractions, thus promoting enhanced diffusion of Zn2+ ions. These theoretical predictions were substantiated by experimental data acquired from hydrothermal synthesis, which indicated a marked increase in interlayer spacing. Significantly, the NVO-rGO composite exhibits remarkable cyclic durability, maintaining 95% of its initial specific capacity of 507 mAh g−1 after 600 cycles at a current density of 5 A g−1. The electrochemical performance of NVO-rGO not only surpasses that of pristine NVO but also outperforms the majority of existing vanadium oxide cathode materials reported in the literature. This study underscores the effective integration of theoretical insights and experimental validation, contributing to the advancement of high-performance energy storage technologies.

This study explores the enhancement of aqueous zinc-ion batteries (AZIBs) using ammonium-enhanced vanadium oxide cathodes. Density Functional Theory (DFT) calculations reveal that NH₄⁺ incorporation into V₆O₁₆ lattices significantly facilitates Zn²⁺ ion diffusion by reducing electrostatic interactions, acting as a structural lubricant. Subsequent experimental validation using (NH₄)₂V₆O₁₆ cathodes synthesized via a hydrothermal method corroborates the DFT findings, demonstrating remarkable electrochemical stability with a capacity retention of 90% after 2000 cycles at 5 A g⁻¹. These results underscore the potential of NH₄⁺ in improving the performance and longevity of AZIBs, providing a pathway for sustainable energy storage solutions.

This study presents the synthesis and electrochemical evaluation of nitrogen-doped vanadium oxide (N-V2O3/C) as a cathode material for aqueous zinc-ion batteries (AZIBs), using a hydrothermal method. Compared to undoped V2O3/C, N-V2O3/C exhibits enhanced electrical conductivity, capacity, and electrochemical kinetics, attributed to the incorporation of pyridinic and pyrrolic nitrogen. Initial charge-discharge cycles indicate phase transitions to amorphous vanadium oxides, enhancing conductivity. N-V2O3/C shows a high specific capacity of 168.4 mAh g−1 at 10 A g−1 and remarkable reversibility, highlighted by the transient existence of intermediate species during cycling. Optimal electrochemical performance is achieved with a vanadium to nitrogen molar ratio of 2:3, indicating the significant impact of nitrogen doping concentration on the material’s efficiency. This work underscores the potential of N-V2O3/C as a superior cathode material for AZIBs.

Using density functional theory (DFT), the density of states of NH4V3O8 (NVO) was analyzed pre and post-oxygen defects (Od) formation. The findings revealed a reduced bandgap in NVO after Od introduction, emphasizing the role of Od in enhancing conductivity of the material, thus improving its electrochemical attributes. Through the water bath method, both NVO and its oxygen-deficient counterpart, (NH4)2V10O25⸱8H2O (NVOd), were synthesized as potential cathode materials for aqueous zinc-ion batteries (AZIBs). Experimental outcomes resonated with DFT predictions, highlighting the beneficial role of oxygen defects in boosting electrical conductivity. Notably, the refined material displayed a remarkable capacity of 479.3 mAh g-1 at 0.1 A g-1, underscoring its promise for advanced energy storage solutions.

This study reports on the development of bio-based hydrophobic coatings for packaging papers through deposition of polyhydroxybutyrate (PHB) particles in combination with nanofibrillated cellulose (NFC) and plant wax. In a first approach, PHB particles in micrometer range (PHB-MP) were prepared through a phase-separation technique providing internally nanosized structures. The particles were transferred as a coating by dip-coating filter papers in the particle suspension, followed by sizing with a carnauba wax solution. This approach allowed partial to almost full surface coverage of PHB-MP over the paper surface resulting in static water contact angles of 105° to 122° and 129° to 144° after additional wax coating. In a second approach, PHB particles with submicron sizes (PHB-SP) were synthesized by an oil-in-emulsion (o/w) solvent evaporation method, and mixed in aqueous suspensions with 0 to 7 wt% NFC. After dip-coating filter papers in PHB-SP/NFC suspensions and sizing with a carnauba wax solution, static water contact angles of 112° to 152° were obtained. The intrinsic properties of the particles were analyzed by scanning electron microscopy, thermal analysis and infrared spectroscopy, indicating higher crystallinity for PHB-SP than PHB-MP. The chemical interactions between the more amorphous PHB-MP particles and paper fibers were identified as an esterification reaction, while the morphology of the NFC fibrillar network was playing a key role as binding agent in the retention of more crystalline PHB-SP at the paper surface, hence contributing to higher hydrophobicity.

We use a recently proposed formulation of quantum mechanics based, not on potential functions but rather, on orthogonal energy polynomials. In this context, the most important building block of a quantum mechanical system, which is the wavefunction at a given energy, is expressed as pointwise convergent series of square integrable functions in configuration space. The expansion coefficients of the series are orthogonal polynomials in the energy; they contain all physical information about the system. No reference is made at all to the usual potential function. We consider, in this new formulation, few representative problems at the level of undergraduate students who took at least two courses in quantum mechanics and are familiar with the basics of orthogonal polynomials. The objective is to demonstrate the viability of this formulation of quantum mechanics and its power in generating rich energy spectra illustrating the physical significance of these energy polynomials in the description of a quantum system. To assist students, partial solutions are given in an appendix as tables and figures.

On-going intensification of rice production systems in Southeast Asia is causing devastating yield losses each year due to rice hoppers. Continuing development of immunity to resistant rice varieties and pesticide application further complicate this problem. Hence, there is a high demand for biological control agents. Egg parasitoid wasps are among the most important natural enemies of rice hoppers such as Nilaparvata lugens and Nephotettix spp. However, our knowledge on their diversity is still very limited due to their small size and the lack of available morphological information. Classifying these parasitoids is the first step to properly understand their role in the rice agroecosystem. We used traditional morphological identification as well as DNA sequencing of COI and 28S genes to investigate the diversity of four important hopper egg parasitoid genera in the Philippines. Parasitoids of the genera Anagrus spp., Oligosita spp., Gonatocerus spp. and Paracentrobia spp. were collected in eight study landscapes located in Luzon. We found discrepancies between the morphological and the molecular analysis. Morphological and molecular results were only valid for Paracentrobia spp. Anagrus spp. and Gonatocerus spp. showed more genetic diversity, than expected after the morphological analysis, indicating cryptic species. The sequences for Oligosita spp. revealed less variation than expected. This is the first study on molecular diversity of rice parasitoids in the Philippines. More research combining morphological, behavioural and genetic methods as well as the establishment of a comprehensive DNA database is urgently needed to assess the performance and suitability of these organisms as biocontrol agents.

In this paper, we proposed a high accurate and stable Legendre transform algorithm which can reduce the potential instability for very high order at a very small increase in the computational time. The error analysis of interpolative decomposition for Legendre transform is presented. By employing block partitioning of Legendre-Vandermonde matrix and butterfly algorithm, a new Legendre transform algorithm with computational complexity O(N(logN)^2/loglogN) in theory and less than O(N(logN)^4) in practical application is obtained. Numerical results are provided to demonstrate the efficiency and numerical stability of the new algorithm.

We used light, electron microscope and teased fiber autoradiography to show that myelinating Schwann cells synthesize phospholipids and proteins in perinuclear cytoplasm and superficial cytoplasmic channels or Cajal bands (SCC/CB). Neither phospholipid nor protein syntheses occur in paranodal loops, Schmidt-Lanterman incisures or adaxonal cytoplasm. Autoradiographic studies also show that in support of local protein synthesis, RNAs move from the nucleus into perinuclear cytoplasm and out along SCC/CB. Unlike other phospholipids, phosphatidylinositol synthesis occurs extensively in axons. This finding indicates differences in the distributions of phospholipid synthesizing enzymes in smooth endoplasmic reticulum of Schwann cell processes and axoplasm.Autoradiographs of nerves at longer survival times show that tritiated phosphatidylcholine and fucose-labeled glycoproteins move from synthetic sites to outermost myelin lamellae. From there, phosphatidylcholine spreads inward reaching innermost lamellae of thicker sheaths in days. Coupled with retention of fucose glycoproteins in outer myelin lamellae is the presence of fucose glycoprotein synthesized during early myelination in inner lamellae of thicker sheaths, a result consistent with growth of myelin sheaths from inner lamellae out. In this review, we revisit these studies because they provide temporal and spatial perspectives needed in understanding dynamic aspects of myelinogenesis and how myelinating cells respond to injury and from altered gene expression.

This work presents a novel approach for the study of the movement of droplets on inclined surfaces under the influence of gravity and chemical heterogeneities. The developed numerical methodology uses data-driven modeling to extend the applicability limits of an analytically derived reduced-order model for the contact line velocity. More specifically, while the reduced-order model is able to capture the effects of the chemical heterogeneities to a satisfactory degree, it does not account for gravity. To alleviate this shortcoming, datasets generated from direct numerical simulations are used to train a data-driven model for the contact line velocity, which is based on the Fourier neural operator and corrects the reduced-order model predictions to match the reference solutions. This hybrid surrogate model, which comprises of both analytical and data-driven components, is then integrated in time to simulate the droplet movement, offering a speedup of five orders of magnitude compared to direct numerical simulations. The performance of this hybrid model is quantified and assessed in different wetting scenarios, by considering various inclination angles and values for the Bond number, demonstrating the accuracy of the predictions as long as the adopted parameters lie within the ranges considered in the training dataset.

As a member of smart materials, electrorheological elastomers (EREs) formed by pre-treating active electrorheological particles are attracting more and more attention. In this work, four Mg-doped strontium titanate particles with spherical, dendritic, flake-like and pinecone-like morphorlogies were obtained by hydrothermal and low-temperature co-precipitation. XRD, SEM, Raman and FT-IR were used to characterize the obtained products. The results showed that the sizes of Mg-doped strontium titanates are about 1.5‒2.0 μm, and the phase structure are dominated by cubic crystal. These Mg-doped strontium titanates were dispersed in a hydrogel composite elastic medium. Then, Mg-doped strontium titanate/glycerol/gelatin electrorheological composite hydrophilic elastomers were obtained with or without electric field. The electric field response properties of Mg-doped strontium titanate composite elastomers were investigated. It concluded that dendritic Mg-doped strontium titanate composite elastomers is high-performance EREs. And the maximum value of energy storage modulus of Mg-doped strontium titanate composite elastomers has achieved 8.70 MPa. This high electrorheological performance of the products is helpful for their applications in vibration control, force transducers, smart structures, dampers, and other fields.

This paper numerically investigates a 3D mesh independency study of a straight blade horizontal axis tidal turbine modelled using Computational Fluid Dynamics (CFD). The solution was produced by employing two turbulence models, the standard k-ε model and Shear Stress Transport (SST) in ANSYS CFX. Three parameters were investigated: mesh resolution, turbulence model, and power coefficient in the initial CFD, analysis. It was found that the mesh resolution and the turbulence model affect the power coefficient results. The power coefficients obtained from the standard k-ε model are 15% to 20% lower than the accuracy of the SST model. It can also be demonstrated that the torque coefficient increases with the increasing Tip Speed Ratio (TSR), but drops drastically after TSR = 5 and k-ε model failing to capture the non-linearity in the torque coefficient with the increasing TSR.

Titania is one of the most comprehensively studied nanostructures due to its widespread applications in production of catalytic, gas- sensing and corrosion- resistance materials [1]. M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices which are numerical parameters capturing structural and chemical properties. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules are correlated with their structure like boiling point, stability, strain energy etc of chemical compounds. In this paper, we determine M-polynomials of single-walled titanium (SW TiO2) nanotubes and recover important topological degree based indices of them to theoretically judge these nanotubes. We also use Maple to plot surfaces associated to different types of single-walled titanium (SW TiO2) nanotubes.

In this paper, carbon nanotubes modified screen-printed electrode (CNTs/SPE) was prepared and the CNTs/SPE was employed for the electrochemical determination of antioxidant substance Chlorogenic acids (CGAs). A pair of well-defined redox peak of CGA was observed at the CNTs/SPE in 0.10 mol∙L^-1 acetic acid-sodium acetate buffer (pH 6.2) and electrode process is adsorption-controlled. Cyclic voltammetry (CV) and differential pulse voltammetry (DPV) method for the determination of CGA were proposed based on the CNTs/SPE. Under the optimal conditions, the proposed method exhibited linear ranges from 4.73×10^-7 to 4.45×10^-5 mol∙L^-1, the linear regression equation was Ipa(µA) = 4.1993 C (mol∙L^-1)+1.1039 (r = 0.9976) and the detection limit for CGA could reach 3.25×10^-6 mol∙L^-1. The recovery of matrine was 94.74~106.65% (RSD = 2.92%) in coffe beans. The proposed method is quick, sensitive, reliable, and can be used for the determination of CGA.

In this paper, we introduce a new class of Laguerre-based Hermite-Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we derive symmetric identities of Laguerre-based Hermite-Fubini numbers and polynomials by using generating functions.

The topological index is a numerical quantity based on the characteristics of various invariants or molecular graph. For ease of discussion, these indices are classified according to their logical derivation from topological invariants rather than their temporal development. Degree based topological indices depends upon the degree of vertices. This paper computes degree based topological indices of Bismuth Tri-Iodide chains and sheets with the help of M-polynomial.

In the study of QSAR/QSPR, due to high degree of predictability of pharmaceutical properties, the eccentric-connectivity index has very important place among the other topological descriptors, In this paper, we compute the exact formulas of eccentric-connectivity index and its corresponding polynomial, total eccentric-connectivity index and its corresponding polynomial, first Zagreb eccentricity index, augmented eccentric-connectivity index, modified eccentric-connectivity index and its corresponding polynomial for a class of phosphorus containing dendrimers.

M-polynomial of different molecular structures helps to calculate many topological indices. A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR) quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Zagreb indices, Randic index, Symmetric division index, Harmonic index, Inverse sum index, Augmented Zagreb index, multiple Zagreb indices etc. are correlated. In this report, we compute closed forms of M-polynomial, first Zagreb polynomial and second Zagreb polynomial of Octagonal network. From the M-polynomial we recover some degree-based topological indices for Octagonal network. Moreover, we give a graphical representation of our results.

In this article, a new class of $q$-Hermite based unified Apostol type polynomials is introduced by means of generating function and series representation. Several important formulas and recurrence relations for these polynomials are derived via different generating methods. We also introduce $q$-analog of Stirling numbers of second kind of order $\nu$ by which we construct a relation including aforementioned polynomials.

We introduce the Hermite based poly-Bernoulli polynomials with a q parameter and give someof their basic properties including not only addition property, but also derivative properties and integralrepresentations. We also de.ne the Hermite based λ -Stirling polynomials of the second kind, and thenprovide some relations. Moreover, we derive several correlations and identities including the Hermite-Kampéde Fériet (or Gould-Hopper) family of polynomials, the Hermite based poly-Bernoulli polynomials with a qparameter and the Hermite based λ -Stirling polynomials of the second kind.

Intrahepatic cholangiocarcinoma (ICCA) is a malignant epithelial neoplasm characterized by biliary differentiation within the liver. ICCA is molecularly heterogeneous and exhibits a broad spectrum of histopathological features. It is a highly aggressive carcinoma with high mortality and poor survival rates. ICCAs are classified into two main subtypes: small duct type and large duct types. These two tumor types have different cell origins and clinicopathological features. ICCAs are characterized by numerous molecular alterations, including mutations in KRAS, TP53, IDH1/2, ARID1A, BAP1, BRAF, SAMD4, and EGFR, and FGFR2 fusion. Two main molecular subtypes–inflammation and proliferation–have been proposed. Recent advances in high-throughput assays using next-generation sequencing have improved our understanding of ICCA pathogenesis and molecular genetics. The diagnosis of ICCA poses a significant challenge for pathologists because of its varied morphologies and phenotypes. Accurate diagnosis of ICCA is essential for effective patient management and prognostic determination. This article provides an updated overview of ICCA pathology, focusing particularly on molecular features, histological subtypes, and diagnostic approaches.

We prove that the Legendre coefficients associated with a function f(x) can be represented as the Fourier coefficients of a suitable Abel-type transform of the function itself. Thus, the computation of N Legendre coefficients can be performed efficiently in O(NlogN) operations by means of a single Fast Fourier Transform of the Abel-type transform of f(x). We also show how the symmetries associated with the Abel-type transform can be exploited to further reduce the computational complexity. The dual problem of calculating the sum of Legendre expansions is also considered. We prove that a Legendre series can be written as the Abel transform of a suitable Fourier series. This fact allows us to state an efficient algorithm for the evaluation of Legendre expansions. Finally, numerical tests are presented to exemplify and confirm the theoretical results.

In this paper, we study sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials and represent each of them in terms of Chebyshev polynomials of all kinds. Here the coefficients involve terminating hypergeometric functions ₂F₁ and these representations are obtained by explicit computations.

In this paper, a new class of q-Hermite based Frobenius type Eulerian polynomials is introduced by means of generating function and series representation. Several fundamental formulas and recurrence relations for these polynomials are derived via different generating methods. Furthermore, diverse correlations including the q-Apostol-Bernoulli polynomials, the q-Apostol-Euler poynoomials, the q-Apostol-Genocchi polynomials and the q-Stirling numbers of the second kind are also established by means of the their generating functions.

We introduce a new kind of extended Hermite-based Frobenius type Eulerian polynomials and then derive diverse explicit and implicit summation equations including some symmetric formulas by utilizing series manupulation method. Multifarious summation formulas and identities given earlier for some well known polynomials such as Eulerian polynomials and Frobenius type Eulerian polynomials are generalized.

Background: Circulating rare cells participate in breast cancer evolution as systemic components of the disease and thus, are a source of theranostic information. Exploration of cancer-associated rare cells is in its infancy. We determined the validity of a rare-cell detection platform and demonstrated the usefulness of a certain rare cell subset as a novel approach to characterize the breast cancer system. Methods: Linearity of the Rarmax® platform was established using a spike-in approach. The platform includes red blood cell lysis, leukocyte depletion and high-resolution fluorescence image recording. Rare cell analysis was conducted on 28 samples (before and after surgery) from 14 patients with breast cancer, 20 healthy volunteers and 9 non-cancer control volunteers. In-depth identification of rare cells, including circulating tumor cells, endothelial-like cells, erythroblasts and inflammation-associated cells, was performed using a phenotype and morphology-based classification system. Results: The platform performed linearly over a range of 5-950 spiked cells, with an average recovery of 84.6%. Circulating epithelial and endothelial-like cell subsets have been demonstrated to be associated with or independent of cancer with tumor presence. Furthermore, certain cell patterns may be associated with treatment-related adverse effects. The sensitivity in detecting tumor-presence and cancer-associated abnormality before surgery was 50% and 85.7%, respectively and the specificity was 100% and 96.6%, respectively. Conclusion: The present study supports the idea of a cancer-associated rare cell abnormality to represent tumor entities as well as systemic cancer. The latter is independent of the apparent clinical cancer.

This paper is concerned with representing sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials. Indeed, by explicit computations each of them is expressed as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer and Jacobi polynomials which involve the hypergeometric functions ${}_1 F_1$ and ${}_2 F_1$.

Prebiotic dietary fiber supplements are commonly consumed to help meet fiber recommendations and improve gastrointestinal health by stimulating beneficial bacteria and the production of short-chain fatty acids (SCFAs), molecules beneficial to host health. The objective of this research project was to compare potential prebiotic effects and fermentability of five commonly consumed fibers using an in vitro fermentation system measuring changes in fecal microbiota, total gas production and formation of common SCFAs. Fecal donations were collected from three healthy volunteers. Materials analyzed included: pure beta-glucan, Oatwell (commercially available oat-bran containing 22% oat β-glucan), xylooligosaccharides (XOS), WholeFiber (dried chicory root containing inulin, pectin, and hemi/celluloses), and pure inulin. Oatwell had the highest production of propionate at 12 h (4.76 μmol/mL) compared to inulin, WholeFiber and XOS samples (p<0.03). Oatwell’s effect was similar to those of the pure beta-glucan samples, both samples promoted the highest mean propionate production at 24 h. XOS resulted in a significant increase in the genus Bifidobacterium after 24 h of fermentation (0 h: 0.67 OTUs; 24 h: 5.22 OTUs; p = 0.038). Inulin and WholeFiber increased the beneficial genus Collinsella, consistent with findings in clinical studies. All analyzed compounds were fermentable and promoted the formation of beneficial SCFAs.

In this paper, we introduce a general family of Lagrange-based Apostol-type Hermite polynomials thereby unifying the Lagrange-based Apostol Hermite-Bernoulli and the Lagrange-based Apostol Hermite-Genocchi polynomials. We also define Lagrange-based Apostol Hermite-Euler polynomials via the generating function. In terms of these generalizations, we find new and useful relations between the unified family and the Apostol Hermite-Euler polynomials. We also derive their explicit representations and list some basic properties of each of them. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions.

Partial differential equations (PDEs) are used to describe a wide range of phenomena, such as heat transfer, fluid dynamics, and quantum mechanics. By solving PDEs, we can ob- tain insights into the behavior of the system and make predictions about its future evolution. Conventional numerical methods for obtaining the approximate solutions of PDEs may re- quire extensive computational resources and time, especially for complex PDEs and large- scale problems. The recently developed physics-informed neural network (PINN) has shown promise in a variety of scientific and engineering fields by incorporating physical laws into the loss functions of the neural network (NN). In addition, the training of PINN does not require ground truth data, but it has poor generalization ability to unseen domains. On the other hand, a convolutional neural network (CNN) has fast inference and better generalization ability, but it requires a large amount of training data. Taking the advantages of PINN and CNN by using Legendre multiwavelets (LMWs) as basis functions, we introduce a new method to approach the PDEs in this paper, namely Physics-Informed Legendre Multiwavelets CNN (PiLMWs-CNN), in order to continuously approximate a grid-based state representation that can be handled by a CNN. PiLMWs-CNN enable us to train our models using only physics-informed loss functions without any pre- computed training data, simultaneously providing fast and continuous solutions that gener- alize to previously unknown domains. In particular, the LMWs can simultaneously possess compact support, orthogonality, symmetry, high smoothness, and high approximation order. Compared to orthonormal polynomial (OP) bases, the approximation accuracy can be greatly increased and computation costs can be significantly reduced by using LMWs. We applied PiLMWs-CNN to approximate the damped wave equation, incompressible Navier-Stokes (N- S) equation, and two-dimensional heat conduction equation. The experimental results show that this method provides more accurate, efficient, and fast convergence with better stability when approximating the solution of PDEs.

The recent resurgence of yellow fever virus (YFV) activity in the tropical regions of Africa and South America has sparked renewed interest in this infamous arboviral disease. YFV had been a human plague for centuries prior to the identification of its urban transmission vector, the Aedes aegypti mosquito species, and the development of an efficient live-attenuated vaccine, the YF-17D strain. The combination of vector-control measures and vaccination campaigns drastically reduced YFV incidence in humans on many occasions, but the virus never ceased to circulate in the forest, through its sylvatic invertebrate vector(s) and vertebrate host(s). Outbreaks recently reported in Central Africa (2015-2016) and Brazil (since late 2016), reached considerable proportions in terms of spatial distribution and total numbers of cases, with multiple exports, including to China. In turn, questions regarding the likeliness of occurrence of large urban YFV outbreaks in the Americas or of a successful import of YFV to Asia are currently resurfacing. This two-part review describes the current state of knowledge and gaps regarding the molecular biology and transmission dynamics of YFV, along with an overview of the tools that can be used to manage the disease at the individual, local and global levels.

In the present paper, the (p,q)-Hermite based Apostol type Frobenius-Euler polynomials and numbers are firstly considered and then diverse basic identities and properties for the mentioned polynomials and numbers, including addition theorems, difference equations, integral representations, derivative properties, recurrence relations. Moreover, we provide summation formulas and relations associated with the Stirling numbers of the second kind.

While lidar-based forest inventory methods have been widely demonstrated, prediction of tree diameters with lidar is not well understood. The performance metrics typically used in studies for prediction of diameters can be difficult to interpret and may not support comparative inferences between sampling designs or study areas. We evaluate a variety of lidar and k nearest neighbor (k-NN) strategies for prediction of tree diameter distributions using two indices which are easier to interpret and compare. The indices are based on the coefficient of determination (R²), and root mean square deviation (RMSD). These indices facilitate comparisons with alternative (non-lidar) inventory strategies, and with other project areas. We evaluate k nearest neighbors (k-NN) dbh density (relative frequency by dbh class) prediction strategies with lidar for 190 training plots distribute across the 800 km² Savannah River Site in South Carolina, USA. We evaluate the performance of k-NN with respect to distance metrics, number of neighbors, predictor sets, and response sets. Amongst the examined strategies we found Mahalanobis distance with k = 3 neighbors performed best according to a number of criteria.

In this work, we offer a novel and accurate method in order to find the solution of the linear differential equations over the intervals [0, 1) based on the generalization of Legendre wavelets. The mechanism is still upon workable implementation of the operational matrix of integration and its derivatives. This method reduces the problems into algebraic equations via the properties of generalized Legendre wavelet (GLW) together with the operational matrix of integration. The function approximation has been picked out in such a way so as to enumerate the connection coefficients in an facile manner. The proposed numerical technique, based on the GLW, has been examined on three linear problems as a consequence of this investigation. The outcomes have shown that this method, as opposed to some other existing numerical and analytical methods, is a very useful and advantageous for tackling such problems.

Enclosed public spaces are the hotspots for airborne disease transmission. To measure and maintain indoor air quality in terms of airborne transmission, an open source, low cost and distributed array of Particulate Matter Sensors has been developed and named as Dynamic Aerosol Transport for Indoor Ventilation or DATIV system. This system can use multiple Particulate Matter Sensors (PMS) simultaneously and can be remotely controlled using a Raspberry Pie based operating system. The data acquisition system can be easily operated using the GUI within any common browser installed on a remote device such as a PC or Smartphone with corresponding IP address. The software architecture and validation measurements are presented together with possible future developments.

Face shields (also referred to as visors), goggles and safety glasses have been worn during the COVID-19 pandemic as one measure to control transmission of the virus. However, their effectiveness in controlling facial exposure to cough droplets is not well established and standard tests for evaluating eye protection for this application are limited. A method was developed to evaluate face shields, goggles and safety glasses as a control measure to protect the wearer against cough droplets. The method uses a semi-quantitative assessment of facial droplet deposition. A cough simulator was developed to generate droplets comparable to those from a human cough. The droplets consisted of a UV fluorescent marker (fluorescein) in water. Fourteen face shields, four pairs of goggles and one pair of safety glasses were evaluated by mounting them on two different sizes of breathing manikin head and challenging them with the simulated cough. The manikin head was positioned in seven orientations relative to the cough simulator to represent various potential occupational exposure scenarios, for example, a nurse standing over a patient. Droplet deposition in the eyes, nose and mouth regions were visualised following three ‘coughs’. Face shields, goggles and safety glasses reduced, but did not eliminate exposure to the wearer from droplets such as those produced by a human cough. The level of protection differed based on the design of the personal protective equipment and the relative orientation of the wearer to the cough. For example, face shields and goggles offered the greatest protection when a cough challenge was face on or from above and the least protection when a cough challenge was from below. Face shields were also evaluated as source control to protect others from the wearer. Results suggested that if a coughing person wears a face shield, it can provide some protection from cough droplets to those standing directly in front of the wearer.

The amphibian chytrid fungus, Batrachochytrium dendrobatidis (Bd), is an infectious disease responsible for the worldwide decline of amphibian species. To mitigate these declines, it is necessary to identify the various vectors by which the fungus can be transmitted between individuals and populations. The objective of this study was to determine whether adult female mosquitoes can carry and transfer Bd fungal cells. Mosquitoes were exposed to net soaked in a live Bd zoospore suspension to determine whether they are able to externally acquire the fungus. Another group was placed into containers with a sterile and Bd-inoculated agar plate to determine whether mosquitoes could transfer Bd between these surfaces. Bd DNA was found to be present on mosquito legs exposed to inoculated netting and agar plates suggesting that Bd can be transmitted by the mosquito over short distances This is the first study to demonstrate that an insect host may be a mechanical vector of Bd and suggests that we should begin to consider the role of mosquitoes in the dissemination and control of the fungus.

The Bessel function of the first kind J_N(kx) is expanded in a Fourier-Legendre series, as is the modified Bessel functions of the first kind I_N(kx) . Known polynomial approximations for the range −3≤x≤3 (having five-digit accuracy) are compared with those arising from this Legendre series and substitute versions are given with twice the number of terms and range (with five-digit accuracy or having fifteen-digit accuracy over −3≤x≤3). It is shown that infinite series of like-powered contributors (involving _2F_3 hypergeometric functions) extracted from the Fourier-Legendre series may be summed, having values that are inverse powers of the first five primes 1/(2^i 3^j 5^k 7^l 11^mm) for powers of order x24.

In this paper, inspired by Jleli and Samet [journal of inequalities and applications 38 (2014) 2 1–8] we introduce two new classes of auxiliary functions and utilize the same to define (q, y)R-weak 3 contractions. Utilizing (q, y)R-weak contractions, we prove some fixed point theorems in the setting 4 of relational metric spaces. We employ some examples to substantiate the utility of our newly proved 5 results. Finally, we apply one of our newly proved results to ensure the existence and uniqueness of 6 solution of a Volterra-type integral equation.

Here we consider sums of finite products of Chebyshev polynomials of the third and fourth kinds. Then we represent each of those sums of finite products as linear combinations of the four kinds of Chebyshev polynomials which involve the hypergeometric function ₃F₂.

In the paper, using two inversion theorems for the Stirling numbers and binomial coecients, employing properties of the Bell polynomials of the second kind, and utilizing a higher order derivative formula for the ratio of two dierentiable functions, the authors present two explicit formulas, a determinantal expression, and a recursive relation for a sequence of unnamed polynomials, derive two identities connecting the sequence of unnamed polynomials with the Bell polynomials, and recover a known identity connecting the sequence of unnamed polynomials with the Bell polynomials.

Modern cryptographic protocols such as zero-knowledge proofs and secure multi-party computation have increased the demand for a novel category of symmetric primitives. These primitives are not optimized for traditional platforms such as servers, microcontrollers, and desktop computers but rather for their ability to be implemented in arithmetic circuits. To enable efficient arithmetic operations, they define operations over larger finite fields and use low-degree invertible functions to construct their non-linear layers. Grendel is an arithmetization-oriented permutation that leverages the Legendre Symbol to enhance the growth of algebraic degrees in its non-linear layer. In this paper, we present a preimage attack on the sponge hash function instantiated with the full rounds of the Grendel permutation using algebraic methods. We introduce a technique that allows us to eliminate two full rounds of substitution permutation networks (SPN) in the sponge hash function with minimal or no additional cost. This method can be combined with univariate root-finding techniques and Gröbner basis attacks to break the number of rounds claimed by the designers. By utilizing this strategy, our attack achieves an improvement of two additional rounds compared to the previous state-of-the-art attack. While not breaking its security margin, it allows us to further understand the design and analysis of such cryptographic primitives.

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

The Astyanax species complex has two morphs: a blind, depigmented morph which inhabits caves in México and an eyed, pigmented surface-dwelling morph. The eyed morph can also be found in caves, sometimes hybridizing with the cave morph. This species complex has arguably become the most prominent model system among cave organisms for the study of evolutionary development and genomics. Before this study, 32 caves were known to be inhabited by the cave morph, 30 of them within the El Abra region. The purpose of this study was to conduct new surveys of the area and to assess some unconfirmed reports of caves presumably inhabited by troglomorphic fish. We describe two new localities, Sótano del Toro #2 and Sótano de La Calera. These two caves make a single hydric system together with the previously described cave of Sótano del Toro. The system is inhabited by a mixed population of troglomorphic, epigeomorphic and presumably hybrid fish. Furthermore, Astyanax cavefish and the mysid shrimp Spelaeomysis quinterensis show a phylogeographic convergence that supports the notion that the central Sierra de El Abra is a biogeographical region that has influenced the evolutionary history of its aquatic community across species. The presumptive location of its boundaries, which may limit cave-to-cave or surface-to-cave gene flow, are identified.

In the paper, by a very simple approach, the author establishes an expression in terms of a lower Hessenberg determinant for the Euler polynomials. By the determinantal expression, the author finds a recurrence relation for the Euler polynomials. By the way, the author derives the corresponding expression and recurrence relation for the Euler numbers.

Level index was introduced in 2017 for rooted trees which is a component of Gini index. In the origin, Gini index is a tool for economical investigations but Balaji and Mahmoud defined the graph theoretical applications of this index for statistical analysis of graphs. Level index is an important component of Gini index. In this paper we define a new graph polynomial which is called level polynomial and calculate the level polynomial of some classes of trees. We obtain some interesting relations between the level polynomials and some integer sequences.

In this paper, we firstly consider extended degenerate central factorial numbers of the second kind and provide some properties of them. We then introduce unified degenerate central Bell polynomials and numbers and investigate many relations and formulas including summation formula, explicit formula and derivative property. Moreover, we derive several correlations for the fully degenerate central Bell polynomials associated with the degenerate Bernstein polynomials and the degenerate Bernoulli, Euler and Genocchi numbers.

In this paper, we represent the generating function of w-torsion Fubini polynomials by fermionic p-adic integral on Z_p. Then we consider a quotient of such fermionic p-adic integrals on Z_p, representing generating functions of three w-torsion Fubini polynomials and derive some new symmetric identities for the w-torsion Fubini and two variable w-torsion Fubini polynomials.

Hydrogen is the lightest atom and composes roughly half of the atomic content in macromolecules, yet their location can only be inferred or predicted in most macromolecular structures. This is because hydrogen can rarely be directly observed by the most common structure determination techniques (such as X-ray crystallography and electron cryo-microscopy). However, knowledge of hydrogen atom positions, especially for enzymes, can reveal protonation states of titratable active site residues, hydrogen bonding patterns, and the orientation of water molecules. Though we know they are present, this vital layer of information, which can inform a myriad of biological processes, is frustratingly invisible to us. The good news is that, even at modest resolution, neutron crystallography (NC) can reveal this layer and has emerged this century as a powerful tool for elucidating enzyme catalytic mechanisms. Due to its strong and coherent scattering of neutrons, incorporation of deuterium into the protein crystal amplifies the power of NC. This is especially true when solvation and the specific participation of key water molecules are crucial for catalysis. Neutron data allow the modeling of all three atoms in water molecules and have even revealed previously unobserved and unique species such as hydronium (D3O+) and deuteroxide (OD-) ions as well as lone deuterons (D+). Herein, we briefly review why neutrons are ideal probes for identifying catalytically important water molecules and these unique water-like species, limitations in interpretation, and four vignettes of enzyme success stories from disparate research groups. One of these groups was that of Dr. Chris G. Dealwis, who died unexpectedly in 2022. As a memorial appreciation of his scientific career, we will also highlight his interest and contributions to the neutron crystallography field. As both the authors were mentored by Chris, we feel we have a unique perspective on his love of molecular structure and admiration for neutrons as a tool to query those structures.

The Single Site Order – a policy restricting staff from working at multiple long-term care homes – was mandated by the Public Health Agency of Canada to control the spread of COVID-19 in long-term care homes, where nearly 70% of COVID-19-related deaths in Canada occurred. This mixed methods study assesses the impact of Single Site Order on long-term care residents in British Columbia. Interviews were conducted (residents (n=6), family members (n=9), staff (n=18), and leadership (n=10) from long-term care homes (n=4)) and analyzed using thematic analysis. Administrative data was collected between April 2019 – March 2020 and April 2020 – March 2021 and analyzed using descriptive statistics and data visualization. Qualitative and quantitative data were triangulated and demonstrate staffing challenges became worse during implementation of the SSO resulting in the mental and physical health deterioration of LTC residents. Qualitative data demonstrated decreased time for personalized and proactive care, increased communication challenges, and increased loneliness and isolation. Quantitative data showed a decline in activities of daily living, increased antipsychotic medication use, pressure ulcers, behavioural symptoms, and an increase in falls. Addressing staff workload and staffing shortages during SSO-related policy implementation is essential to avoid resident health deterioration.

In this paper, we introduce the partially degenerate Changhee-Genocchi polynomials and numbers and investigated some identities of these polynomials. Furthermore, we investigate some explicit identities and properties of the partially degenerate Changhee-Genocchi arising from the nonlinear dierential equations.

Molten salt electrolysis stands as an indispensable technique for the production of rare earth metals, where the judicious distribution of the electric field within the electrolytic cell is paramount for ensuring the seamless operation of the electrolysis process. This study introduces a pioneering approach by integrating the Nernst-Planck equation with the Butler-Volmer equation, thereby devising a holographic electric field model tailored for the electrolysis of the NdF3-LiF molten salt system. The paper presents pioneering experimental measurements concerning the potential distribution and voltage drop characteristics within a 6kA rare earth electrolytic cell, elucidating the interplay between decomposition voltage and current density, which substantiates the model's precision. Our findings unveil that, under operational conditions of 4010 amperes, the 6kA electrolytic cell incurs a total voltage drop of 6.3 volts, delineating a melt voltage drop of 4.43 volts, an ohmic voltage drop of 0.248 volts, and an interfacial voltage drop of 1.622 volts at the electrode-electrolyte junction. The discrepancy in error is confined to within 0.3% of the actual measured voltage of 6.28 volts.The simulation outcomes from the holographic electric field model have been confirmed to precisely and comprehensively reflect the characteristics of the electric field distribution during the rare earth molten salt electrolysis process, offering valuable theoretical insights for practical manufacturing applications.

In the paper, the authors consider the generating functions of the Hermite polynomials and their squares, present explicit formulas for higher order derivatives of the generating functions of the Hermite polynomials and their squares, which can be viewed as ordinary differential equations or derivative polynomials, find differential equations that the generating functions of the Hermite polynomials and their squares satisfy, and derive explicit formulas and recurrence relations for the Hermite polynomials and their squares.

The eighty years old empirical Colebrook function widely used as an informal standard for hydraulic resistance relates implicitly the unknown flow friction factor , with the known Reynolds number and the known relative roughness of a pipe inner surface ; . It is based on logarithmic law in the form that captures the unknown flow friction factor in a way from which it cannot be extracted analytically. As an alternative to the explicit approximations or to the iterative procedures that require at least a few evaluations of computationally expensive logarithmic function or non-integer powers, this paper offers an accurate and computationally cheap iterative algorithm based on Padé polynomials with only one -call in total for the whole procedure (expensive -calls are substituted with Padé polynomials in each iteration with the exception of the first). The proposed modification is computationally less demanding compared with the standard approaches of engineering practice, but does not influence the accuracy or the number of iterations required to reach the final balanced solution.

Using an algebraic method for solving the wave equation in quantum mechanics, we encountered a new class of orthogonal polynomials on the real line. One of these is a four-parameter polynomial with a discrete spectrum. Another that appeared while solving a Heun-type equation has a mix of continuous and discrete spectra. Based on these results and on our recent study of the solution space of an ordinary differential equation of the second kind with four singular points, we introduce a modification of the hypergeometric polynomials in the Askey scheme. Up to now, all of these polynomials are defined only by their three-term recursion relations and initial values. However, their other properties like the weight function, generating function, orthogonality, Rodrigues-type formula, etc. are yet to be derived analytically. This is an open problem in orthogonal polynomials.

In the paper, by induction and recursively, the author proves that the generating function of multivariate logarithmic polynomials and its reciprocal are a Bernstein function and a completely monotonic function respectively, establishes a Lévy-Khintchine representation for the generating function of multivariate logarithmic polynomials, deduces an integral representation for multivariate logarithmic polynomials, presents an integral representation for the reciprocal of the generating function of multivariate logarithmic polynomials, computes real and imaginary parts for the generating function of multivariate logarithmic polynomials, derives two integral formulas, and denies the uniform convergence of a known integral representation for Bernstein functions.

In the paper, the author (1) presents an explicit formula and its inversion formula for higher order derivatives of generating functions of the Bell polynomials, with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem for the Stirling numbers of the first and second kinds; (2) recovers an explicit formula and its inversion formula for the Bell polynomials in terms of the Stirling numbers of the first and second kinds, with the aid of the above explicit formula and its inversion formula for higher order derivatives of generating functions of the Bell polynomials; (3) constructs some determinantal and product inequalities and deduces the logarithmic convexity of the Bell polynomials, with the assistance of the complete monotonicity of generating functions of the Bell polynomials. These inequalities are main results of the paper.

In this paper, we introduce a new class of degenerate Hermite-Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we derive symmetric identities of degenerate Hermite-Fubini numbers and polynomials by using generating functions.

The main purpose of this paper is to introduce a new class of $q$-Hermite-Fubini numbers and polynomials by combining the $q$-Hermite polynomials and $q$-Fubini polynomials. By using generating functions for these numbers and polynomials, we derive some alternative summation formulas including powers of consecutive $q$-integers. Also, we establish some relationships for $q$-Hermite-Fubini polynomials associated with $q$-Bernoulli polynomials, $q$-Euler polynomials and $q$-Genocchi polynomials and $q$-Stirling numbers of the second kind.

In this paper, we investigate a new $q$-analogue of the higher order degenerate Changhee polynomials and numbers, which are called the Witt-type formula for the $q$-analogue of degenerate Changhee polynomials of order $r$. We can derive some new interesting identities related to the degenerate $(h,q)$-Changhee polynomials and numbers.

In this paper, we investigate a new $q$-analogue of the higher order degenerate Changhee polynomials and numbers, which are called the Witt-type formula for the $q$-analogue of degenerate Changhee polynomials of order $r$. We can derive some new interesting identities related to the degenerate $(h,q)$-Changhee polynomials and numbers.

In this paper, we investigate the recently introduced degenerate Bernstein polynomials and operators and derive some of their properties. Also, we give some properties of the degenerate Euler numbers and polynomials and their connection with the degenerate Euler polynomials.

In the present paper, we introduce (p, q)-extension of Apostol type Frobenius-Euler polynomials and numbers and investigate some basic identities and properties for these polynomials and numbers, including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, explicit formulas and relations for these polynomials and numbers. Moreover, we discover (p, q)-extensions of Carlitz's result [L. Carlitz, Mat. Mag., 32 (1959), 247–260] and Srivastava and Pintér addition theorems in [H. M. Srivastava, A. Pinter, Appl. Math. Lett., 17 (2004), 375–380].

In the paper, by virtue of the Faá di Bruno formula and two identities for the Bell polynomial of the second kind, the authors find a closed form for the Stirling polynomials in terms of the Stirling numbers of the first and second kinds.

In the paper, the authors present unified generalizations for the Bell numbers and polynomials, establish explicit formulas and inversion formulas for these generalizations in terms of the Stirling numbers of the first and second kinds with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem connected with the Stirling numbers of the first and second kinds, construct determinantal and product inequalities for these generalizations with aid of properties of the completely monotonic functions, and derive the logarithmic convexity for the sequence of these generalizations.

Chronic obstructive pulmonary disease (COPD) is a condition that significantly impacts both patients and healthcare systems. The management of COPD involves various pharmacological intervention strategies, and addressing the issue of low adherence to these strategies has become a subject of significant interest. In response to this concern, there has been a shift towards utilizing telemedicine and mobile applications. The primary objective of this scoping review is to delineate the usage of mobile applications to enhance pharmacological therapeutic adherence in adult patients with COPD. The study involved a search of databases such as Medline, Google Scholar, Cochrane, and ClinicalTrial.gov, focusing on literature published in English and Spanish over the last decade. The selected studies assessed interventions involving mobile applications (mobile apps) designed to improve pharmacological adherence. Four digital aids were identified, available on online platforms, mobile apps, or both: m-PAC, myCOPD, Wellinks mHealth, and Propeller Health. Pro-peller Health, in particular, is an app that directly measures pharmacological adherence through electronic medication monitors attached to participants' inhalers. Opening the app was associated with higher odds of using control medications compared to participants who did not open the app. The findings suggest that these digital interventions serve as valuable tools to enhance patient adherence to treatment. Future research should focus on evaluating the effectiveness of different digital devices, such as digital inhalers and mobile applications, that directly measure pharmacological adherence.

Castration of stallions is traditionally performed after puberty around the age of 2 years old. No studies have focused on the effects of early castration on osteoarticular metabolism. Thus, we sought to compare early castration (3 days after birth) with traditional castration (18 months of age) in horses. Testosterone and estradiol levels were monitored from birth to 33 months in these two groups. We quantified the levels of biomarkers of cartilage and bone anabolism (CPII and N-MID) and catabolism (CTX-I and CTX-II), of osteoarthritis (HA and COMP) and inflammation (IL-6 and PGE2). We revealed a lack of parallelism between testosterone and estradiol syntheses after birth and during puberty in both groups. An extra-gonadal synthesis of steroids was observed around the 28 month-mark, regardless of the castration age. We found the expression of estrogen receptor (ESR1) in cartilage and bone, whereas androgen receptor (AR) expression appeared to be restricted to bone. Nevertheless, with regards to osteoarticular metabolism, steroid hormone deprivation resulting from early castration showed no discernable impact on the levels of biomarkers related to bone and cartilage metabolism, nor on those associated with OA and inflammation. Consequently, our research demonstrated that early castration does not disrupt bone and cartilage homeostasis.

Motivated by Kim-Kim [19] introduced the new type of degenerate poly- Bernoulli polynomials by means of the degenerate polylogarithm function. In this paper, we define the degenerate poly-Frobenius-Euler polynomials, called the new type of degenerate poly-Frobenius-Euler polynomials, by means of the degenerate polylogarithm function. Then, we derive explicit expressions and some identities of those numbers and polynomials.

Recently, Kim-Kim [13] have introduced polyexponential functions as an inverse to the polylogarithm functions, and constructed type 2 poly-Bernoulli polynomials. They have also introduced unipoly functions attached to each suitable arithmetic function as a universal concept. Inspired by their work, in this paper, we introduce a new class of the Frobenius-Genocchi polynomials. We derive the diverse formulas and identities covering some summation formulas, derivative formula and correlations with Bernoulli polynomials and numbers, Stirling numbers of the both kinds, degenerate Frobenius-Genocchi polynomials and degenerate Frobenius-Euler polynomials. Moreover, by using the unipoly function as following Kim-Kim's work in <cite>Kim1</cite>, we consider degenerate unipoly-Frobenius-Genocchi polynomials and investigate some formulas and relationships with Daehee numbers, degenerate Frobenius-Genocchi numbers and Stirling numbers of the first kind. Finally, we obtain an Gaussian integral representation of the Frobenius-Genocchi polynomials in terms of the 2-variable Hermite polynomials.

In this paper, we derive multifarious relationships among the two types of higher order q-Daehee polynomials and p-adic gamma function via Mahler theorem. Also, we compute some weighted p-adic q-integrals of the derivative of p-adic gamma function related to the Stirling numbers of the both kinds and the q-Bernoulli polynomials of order k.

In this paper, we introduce a new class of Hermite-Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we derive symmetric identities of Hermite-Fubini numbers and polynomials by using generating functions.

In the paper, the authors establish two identities, which can be regarded as nonlinear differential equations, for the generating function of Eulerian polynomials, find two identities for the Stirling numbers of the second kind, and present two identities for Eulerian polynomials and higher order Eulerian polynomials, pose two open problems about summability of two finite sums involving the Stirling numbers of the second kind. Some of these conclusions meaningfully and significantly simplify several known results.

Discrete Double Hilbert Exponential sums along polynomials. This is preprint version (not peer reviewed) And we now check the proof of (ii) of Lemma 3.2 whether it is really true.

A unified presentation of a class of Humbert’s polynomials in two variables which generalizes the well known class of Gegenbauer, Humbert, Legendre, Chebycheff, Pincherle, Horadam, Kinnsy, Horadam-Pethe, Djordjević , Gould, Milovanović and Djordjević, Pathan and Khan polynomials and many not so called ’named’ polynomials has inspired the present paper and the authors define here generalized Humbert-Hermite polynomials of two variables. Several expansions of Humbert- Hermite polynomials, Hermite-Gegenbaurer (or ultraspherical) polynomials and Hermite- Chebyshev polynomials are proved.

The main aim of this paper is to investigate multifarious properties and relations for the gamma distribution. The approach to reach this purpose will be introducing a special polynomial including gamma distribution. Several formulas covering addition formula, derivative property, integral representation and explicit formula are derived by means of the series manipulation method. Furthermore, two correlations including Bernoulli and Euler polynomials for gamma distribution polynomials are provided by utilizing of their generating functions.

Rationale: Examining trends in patient characteristics, processes of care and outcomes, across an epidemic, provides important opportunities for learning. Objectives: To report and explore changes in admission rates, patient characteristics, processes of care and outcomes for all patients with COVID-19 admitted to intensive care units (ICUs) in England, Wales and Northern Ireland. Methods: Population cohort of 10,287 patients with COVID-19 in the Case Mix Programme national clinical audit from 1 February to 2 July, 2020. Analyses were stratified by time period (pre-peak, peak, post-peak) and geographical region. Multivariable logistic regression was used to estimate differences in 28-day mortality, adjusting for patient characteristics over time. Main results: Admissions to ICU peaked simultaneously across regions on 1 April, with ongoing admissions peaking ten days later. Compared with pre- and post-peak periods, patients admitted during the peak were slightly younger but had greater respiratory and renal dysfunction. Use of invasive ventilation and renal replacement reduced over time. Twenty-eight-day mortality reduced from 43.5% (95% CI 41.6% to 45.5%) pre-peak to 34.3% (95% CI 32.3% to 36.2%) post-peak; a difference of −8.8% (95% CI: −5.2%, −12.3%) after adjusting for patient characteristics. London experienced the highest admission rate and had higher mortality during the peak period but a greater reduction in post-peak mortality. Conclusion: This study highlights changes in patient characteristics, processes of care and outcomes, during the UK COVID-19 epidemic. After adjusting for the changes in patient characteristics and first 24-hour physiology, there was substantial improvement in 28-day mortality over the course of the epidemic.

As revealed by the recent resurgence of yellow fever virus (YFV) activity in the tropical regions of Africa and South America, YFV control measures need urgent rethinking. Over the last decade, most reported outbreaks occurred in, or eventually reached, areas of low vaccination coverage but suitable for virus transmission, with an unprecedented risk of expansion to densely populated territories in Africa, South America and Asia. As reflected in the World Health Organization’s initiative launched in 2017, it is high time to strengthen epidemiological surveillance to monitor accurately, viral dissemination and redefine vaccination recommendation areas. Vector-control and immunisation measures need to be adapted and vaccine manufacturing must be reconciled with an increasing demand. We will have to face more YF cases in the upcoming years hence, improving disease management through the development of efficient treatments will prove most beneficial. Undoubtedly, these developments will require in-depth descriptions of YFV biology at molecular, physiological and ecological levels. This second section of the two-part review describes the current state of knowledge and gaps regarding the molecular biology of YFV, along with an overview of the tools that can be used to manage the disease at the individual, local and global levels.

Objectives To develop and validate a prediction model for 28-day in-hospital mortality among adult patients critically ill with COVID-19 in the UK. Design Observational cohort study. Setting 287 adult critical care units in England, Wales and Northern Ireland, of which 260 admitted at least one eligible patient. Participants 10,933 patients with confirmed COVID-19 of whom 10,401 were eligible (excluding 532 patients with a duration of critical care less than 24 hours and 1 patient with unknown 28-day outcome): 8,666 development (March-April 2020) and 1,735 temporal validation (May-August 2020). Main outcome measures 28-day in-hospital mortality from start of critical care. Results Two models were developed using 14 patient level predictors selected from 30 candidate predictors, with and without adjustment for calendar time. In the temporal validation data, the model discrimination was maintained (c index 0.78) but calibration was poor, particularly for the model not adjusted for calendar time (ratio of observed to predicted mortality 0.74 versus 0.88 for the model adjusted for calendar time). Conclusions We developed and validated a prediction model for 28-day in-hospital mortality for patients critically ill with COVID-19. Although absolute predictions were inaccurate due to changing outcomes, the models will support risk-adjustment in analyses and monitoring changes in risk-adjusted outcome over time.

In this paper, we consider the zero distributions of q-shift monomi-als and difference polynomials of meromorphic functions with zero order, that extends the classical Hayman results on the zeros of differential poly-nomials to q-shift difference polynomials. We also investigate problem of q-shift difference polynomials that share a common value.

We introduce the lower chaos grade of a real-valued function F defined on the Markov triple (E,μ,Γ), where μ is a probability measure and Γ is the carré du champ operator. As an application of this concept, we obtain the better estimate of the four moments theorem for Markov diffusion generators worked by Bourguin et al (2019). For our purpose, we need to find the largest number except zero in the set of eigenvalues corresponding to its eigenfunction in the case where the square of a random variable F, coming from a Markov triple structure, can be expressed as a sum of eigenfunctions, We give some examples of eigenfunctions of the diffusion generators such as Ornstein-Uhlenbeck, Jacobi and Romanovski-Routh. In particular, two bounds, called the four moments theorem and fourth moment theorem respectively, will be provided for the normal approximation of the case where a random variable F comes from eigenfunctions of a Jacobi generator.

Let $S=\left(s_1, \ldots, s_n\right)$ be a finite sequence of integers. Then $S$ is a Gilbreath sequence of length $n$, $S\in\mathbb{G}_n$, iff $s_1$ is even or odd and $s_2, \ldots, s_n$ are respectively odd or even and $\min\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\leq s_{m+1}\leq\max\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\forall m\in\left[\left.1, n\right)\right.$. This, applied to the order sequence of prime number $P$, defines Gilbreath polynomials and two integer sequences A347924 \cite{oeisA347924} and A347925 \cite{oeisA347925} which are used to prove that Gilbreath conjecture $GC$ is implied by $p_n-2^{n-1}\leqslant\mathcal{P}_{n-1}\left(1\right)$ where $\mathcal{P}_{n-1}\left(1\right)$ is the $n-1$-th Gilbreath polynomial at 1.

In this paper, we introduce a new type of degenerate poly-Fubini polynomials and numbers, are called degenerate poly-Fubini polynomials and numbers, by using the degenerate polylogarithm function and derive several properties on the degenerate poly-Fubini polynomials and numbers. In the last section, we also consider the degenerate unipoly-Fubini polynomials attached to an arithmetic function, by using the degenerate polylogarithm function and investigate some identities of those polynomials. In particular, we give some new explicit expressions and identities of degenerate unipoly polynomials related to special numbers and polynomials.

In this paper, we construct the degenerate poly-Fubini polynomials, called the type 2 degenerate poly-Fubini polynomials, by using the modified degenerate polyexponential function and derive several properties on the degenerate poly-Fubini polynomials and numbers. In the last section, we introduce type 2 degenerate unipoly- Fubini polynomials attached to an arithmetic function, by using the modified degenerate polyexponential function and investigate some identities for those polynomials. Furthermore, we give some new explicit expressions and identities of degenerate unipoly polynomials related to special numbers and polynomials.

We propose a correspondence between partition functions of ideal gases consisting of both bosons and fermions and algebraic bases of supersymmetric polynomials on the Banach space of absolutely summable two-sides sequences ℓ1(Z0). Such an approach allows us to interpret some combinatorial identities for supersymmetric polynomials from a physical point of view. We consider a relation of equivalence on ℓ1(Z0) induced by the supersymmetric polynomials, and semiring algebraic structures on the quotient set with respect to this relation. The quotient set is a natural model for the set of energy levels of a quantum system. We introduce two different topological semiring structures on this set and discuss their possible physical interpretations.

In this paper we consider Changhee polynomials of type two, which are motivated from the recent work of Kim and Kim. We investigate some symmetry identities for the Changhee polynomials of type two which are derived from the properties of symmtery for the fermionic p-adic integral on Zp.

We investigate the value distribution of dierence polynomials of entire and meromorphic functions, which can be viewed as the Hayman's conjecture. And we also study the uniqueness of dierence polynomials sharing a common value.

In this paper, we introduce a new generalization of the Hermite polynomials via (p, q)-exponential generating function and investigate several properties and relations for mentioned polynomials including derivative property, explicit formula, recurrence relation, integral representation. We also de…ne a (p, q)-analogue of the Bernstein polynomials and acquire their some formulas. We then provide some (p, q)-hyperbolic representations of the (p, q)-Bernstein polynomials. In addition, we obtain a correlation between (p, q)-Hermite polynomials and (p, q)-Bernstein polynomials.

In this paper, we investigate p-adic q-integral (q-Volkenborn integral) on Z_p of p-adic gamma function via their Mahler expansions. We also derived two q-Volkenborn integrals of p-adic gamma function in terms of q-Daehee polynomials and numbers and q-Daehee polynomials and numbers of the second kind. Moreover, we discover q-Volkenborn integral of the derivative of p-adic gamma function. We acquire the relationship between the p-adic gamma function and Stirling numbers of the first kind. We finally develop a novel and interesting representation for the p-adic Euler constant by means of the q-Daehee polynomials and numbers.

In the paper, the author introduces the notions "multi-order logarithmic numbers" and "multi-order logarithmic polynomials", establishes an explicit formula, an identity, and two recurrence relations by virtue of the Faa di Bruno formula and two identities of the Bell polynomials of the second kind in terms of the Stirling numbers of the first and second kinds, and constructs some determinantal inequalities, product inequalities, logarithmic convexity for multi-order logarithmic numbers and polynomials by virtue of some properties of completely monotonic functions.

Motivation by the definition of the type 2 poly-Bernoulli polynomials introduced by Kim-Kim [9], in the present paper, we consider a new class of new generating function for the Fubini polynomials, called the type 2 poly-Fubini polynomials by means of the polyexponential function. Then, we derive some useful relations and properties. We show that the type 2 poly-Fubini polynomials equal a linear combination of the classical of the Fubini polynomials and Stirling numbers of the first kind. In a special case, we give a relation between the type 2 poly-Fubini polynomials and Bernoulli polynomials of order r. Moreover, inspired by the definition of the unipoly-Bernoulli polynomials introduced by Kim-Kim [9]. We introduce the type 2 unipoly-Fubini polynomials by means of unipoly function and give multifarious properties including derivative and integral properties. Furthermore, we provide a correlation between the unipoly-Fubini polynomials and the classical Fubini polynomials.

In this paper, we consider a new class of polynomials which is called the multi-poly-Euler polynomials. Then, we investigate their some properties and relations. We provide that the type 2 degenerate multi-poly-Euler polynomials equals a linear combination of the degenerate Euler polynomials of higher order and the degenerate Stirling numbers of the first kind. Moreover, we provide an addition formula and a derivative formula. Furthermore, in a special case, we acquire a correlation between the type 2 degenerate multi-poly-Euler polynomials and degenerate Whitney numbers.

Inspired by the definition of degenerate multi-poly-Genocchi polynomials given by using the degenerate multi-polyexponential functions. In this paper, we consider a class of new generating function for the degenerate multi-poly-Bernoulli polynomials, called the type 2 degenerate multi-poly-Bernoulli polynomials by means of the degenerate multiple polyexponential functions. Then, we investigate their some properties and relations. We show that the type 2 degenerate multi-poly-Bernoulli polynomials equals a linear combination of the weighted degenerate Bernoulli polynomials and Stirling numbers of the first kind. Moreover, we provide an addition formula and a derivative formula. Furthermore, in a special case, we acquire a correlation between the type 2 degenerate multi-poly-Bernoulli numbers and degenerate Whitney numbers.

In this paper, we investigate p-adic q-integral (q-Volkenborn integral) on ℤ_{p} of p-adic gamma function via their Mahler expansions. We also derived two q-Volkenborn integrals of p-adic gamma function in terms of q-Daehee polynomials and numbers and q-Daehee polynomials and numbers of the second kind. Moreover, we discover q-Volkenborn integral of the derivative of p-adic gamma function. We acquire the relationship between the p-adic gamma function and Stirling numbers of the first kind. We finally develop a novel and interesting representation for the p-adic Euler constant by means of the q-Daehee polynomials and numbers.

In this paper, we introduce a new class of $(p,q)$-analogue type of Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we consider some relationships for $(p,q)$-Fubini polynomials associated with $(p,q)$-Bernoulli polynomials, $(p,q)$-Euler polynomials and $(p,q)$-Genocchi polynomials and $(p,q)$-Stirling numbers of the second kind.

In this paper, we investigate the new degenerate Daehee polynomials and numbers which are called the degenerate Daehee polynomials of the second kind, and derive some new and interesting identities and properties of those polynomials.

The main goal of the present paper is to construct some families of the Carlitz’s q-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz’s q-Bernoulli polynomials and numbers with weight (α, β) and investigate their some explicit properties and identities arising from the bosonic q-Volkenborn integral on ℤ_p. We then define the modified degenerate Carlitz’s q-Bernoulli polynomials and numbers with weight (α, β) and obtain some recurrence relations and other identities. Moreover, we derive some correlations with the modified Carlitz’s q-Bernoulli polynomials with weight (α, β), the modified degenerate Carlitz’s q-Bernoulli polynomials with weight (α, β), the Stirling numbers of the first kind and second kind.