In this study, we define new classes of convexity called of h-Godunova-Levin and h-Godunova-Levin preinvexity, through which some new inequalities of Hermite-Hadamard type were established. These new classes are the generalisation of several known convexity including the s-convex, P-function, Godunova-Levin. Further, the properties of h-Godunova-Levin function were also discussed. Meanwhile, the applications of h-Godunova-Levin Preinvex function are given

In this work, we introduce the class of h-MN-convex functions by generalizing the concept of MN-convexity and combining it with h-convexity. Namely, let M : [0, 1] → [a, b] be a Mean function given by M (t) = M (t; a, b); where by M (t; a, b) we mean one of the following functions: A_t (a, b) := (1 − t) a + tb, G_t (a, b) = a^1−tb^t and H_t (a, b) := $\frac{ab}{ta+\left(1-t\right)b}=\frac{1}{A_t\left(\frac{1}{a},\frac{1}{b}\right)}$ with the property that M (0; a, b) = a and M (1; a, b) = b. Let I, J be two intervals subset of (0, ∞) such that (0, 1) ⊆ J and [a, b] ⊆ I. Consider a non-negative function h : J → (0, ∞), a function f : I → (0, ∞) is said to be h-MN-convex (concave) if the inequality f (M (t; x, y)) ≤ (≥) N (h(t); f (x), f (y)), holds for all x, y ∈ I and t ∈ [0, 1]. In this way, nine classes of h-MN-convex functions are established, and therefore some analytic properties for each class of functions are explored and investigated. Characterizations of each type are given. Various Jensen’s type inequalities and their converses are proved.

In this work, several inequalities of Popoviciu type for h-MN-convex functions are proved, where M and N are denote to Arithmetic, Geometric and Harmonic means and h is a non-negative superadditive or subadditive function.

The closed forms of the non-resonant thermonuclear function in the Maxwell-Boltzmann and Tsallis case with depleted tail are obtained in generalized special functions. The results are written in terms of H-function of two variables. The importance of the results in this paper lies in the fact that the reaction rate probability integrals in Maxwell-Boltzmann and Tsallis cases are not obtained by the conventional method of approximation or by means of a single variable transform technique but by means of a two variable transform method. The Behaviour of the depleted non-resonant thermonuclear functions are examined using graphs. The results in the paper are of much interest to astrophysicists and statisticians in their further work in this area.

In this paper we obtain some inequalities of Hermite-Hadamard type for composite convex functions. Applications for AG, AH-h-convex functions, GA, GG, GH-h-convex functions and HA, HG, HH-h-convex function are given.

This paper aims to unify q-derivative/q-integral and h-derivative/h-integral in a single definition, this will be called q−h-derivative/q−h-integral. These notions are further extended on finite interval [a,b] in the form of left and right q−h-derivatives and q−h-integrals. Some inequalities are studied for q−h-integrals which are directly connected with well known results. In diverse fields of science and engineering the theory based on q-derivatives/q-integrals and h-derivatives/h-integrals can be unified by using the concept of q−h-derivative/q−h-integral.

It is argued that if the non-unitary measurement transition, as codified by Von Neumann, is a real physical process, then the ‘probability assumption’ needed to derive the Second Law of Thermodynamics naturally enters at that point. The existence of a real, indeterministic physical process underlying the measurement transition would therefore provide an ontological basis for Boltzmann’s Stosszahlansatz and thereby explain the unidirectional increase of entropy against a backdrop of otherwise time-reversible laws. It is noted that the Transactional Interpretation (TI) of quantum mechanics provides such a physical account of the non-unitary measurement transition, and TI is brought to bear in finding a physically complete, non-ad hoc grounding for the Second Law.

This paper introduces extensions H4,p and X8,p of Horn’s double hypergeometric function H4 and Exton’s triple hypergeometric function X8, taking into account recent extensions of Euler’s beta function, hypergeometric function, and confluent hypergeometric function. Among the numerous extended hypergeometric functions, the primary rationale for choosing H4 and X8 is their comparable extension type. Next, we present various integral representations of Euler and Laplace type, Mellin and inverse Mellin transforms, Laguerre polynomial representation, transformation formulae and a recurrence relation for the extended functions. In particular, we provide a generating function for the X8,p and several bounding inequalities for the H4,p and X8,p.

In this paper, a solenoid based linearly movable armature system is designed using robust control theory in order to improve the performance of the system. Reference track method is the best performance analysis for position control systems. Among the robust controllers, H infinity mixed-sensitivity and Mixed H 2 /H∞ with Regional Pole Placement Controllers are used to improve the performance of the system. Comparison of the proposed controllers for tracking a reference displacement signals (step and sine wave) and a promising simulation result have been obtained.

In the article, by applied the concept of strongly convex function and one known identity, we establish several Ostrowski type inequalities involving conformable fractional integrals. As applications, some new error estimations for the midpoint formula are provided as well.

This paper is devoted to the study of multi-dimensional integral transform with Fox H-function in the kernel in weighted spaces integrable functions in the domain R+n with positive coordinates. Mapping properties such as the boundedness, the range, the representations of the considered transformation are established.

The prim objective of commenced article is to determine q-sumudu transforms of a product of unified family of q-polynomials with basic (or q-) analogue of fox’s H-function and q-analog of I-functions. Specialized cases of the leading outcome are further evaluated as q-sumudu transform of general class of q-polynomials and q-sumudu transforms of the basic analogues of Fox’s H-function and I-functions.

In recent years, an interest in multimedia services has grown expeditiously where the main part is comprised of video. Firms as well as subscribers require higher resolutions, framerates and sampling precision which results to higher amount of data need for processing, storing and transmitting. Therefore, a big challenge arises for researchers to develop new compression standards which should reduce the huge amount of data and keep quality at the same level. This paper examines compression performance of the latest and currently most used video codecs, namely H.266/VVC, AV1, H265/HEVC and H.264/AVC. The test set consists of seven sequences with various content at 8K, Ultra HD and Full HD resolution and encoded to bitrates from 1 to 15 Mbps for Full HD and Ultra HD resolutions and from 5 to 50 Mbps for 8K resolution, respectively. Codec performance was measured using PSNR, SSIM and VMAF objective quality metrics. In terms of the Bjøntegaard-Delta (BD) model, the results showed that H.266/VVC outperforms all other codecs, namely H.264/AVC,H.265/HEVC and AV1, respectively. Averaged bitrate savings were approximately 78\% for H.266/VVC, 63\% for AV1 and 53\% for H.265/HEVC relative to H.264/AVC, 59\% for H.266/VVC, 22\% for AV1 compared to H.264/AVC and 46\% for H.266/VVC relative to AV1, all for 8K resolution. The results also showed that the performance varies depending on resolution – with higher resolution, the efficiency of newly developed codecs such as H.266/VVC and AV1 is greater, which confirmed the fact that the H.266/VVC and AV1 codecs have been primarily developed for videos at high resolutions as 8K and/or UHD.

Infections contribute to carcinogenesis through inflammation-related mechanisms. It is well established that H. pylori infection is an etiological factor in gastric carcinogenesis. However, the mechanism through which H. pylori infection contributes to the development of gastric cancer has not been fully elucidated. H. pylori-associated chronic inflammation is linked to genomic instability via reactive oxygen and nitrogen species (RONS). In this article, we summarize the current knowledge of H. pylori-induced double strand breaks (DSBs). Further, we will provide mechanistic insight into how processing of oxidative DNA damage via base excision repair (BER) leads to double strand breaks (DSBs). We review the recent progress how H. pylori infection triggers NF-kB /iNOS versus NF-kB/nucleotide excision repair (NER) axis mediated DSBs to drive genomic instability. Taken together, this review discusses current findings related to DSBs and their implications for the mechanisms of DSB repair.

Hippophae is a tree species with ecological, economic and social benefits. In this study, we assembled and annotated chloroplast genomes of sympatric Hippophae gyantsensis and H. rhamnoides subsp. yunnanensis. Their full-length are 155260 and 156415 bp, respectively. Each of them has 131 genes, comprising 85 protein-coding genes, 8 ribosomal RNA genes and 38 transfer RNA genes. After comparing the chloroplast genomes, we found 1302 base difference loci, and 63.29% are located in the intergenic region or intron sequences and 36.71% are located in the coding sequences. The SSC region has the highest mutation rate, followed by the LSC region; the IR regions have the lowest mutation rate. Among the protein-coding genes, three had a ratio of nonsynonymous to synonymous substitutions (Ka/Ks) >1 (but P values were non-significant) and 66 had Ka/Ks <1 (46 were significant). In general, the chloroplast protein-coding genes may be subject to purification selection. Among H. gyantsensis and H. rhamnoides subsp. yunnanensis chloroplast protein-coding genes, there are 20 and 16 optimal codons, respectively. Most of the optimal codons were ending with A or U, which indicates significant AT preference. It is an important reference for studies on the general characteristics and evolution of the Hippophae chloroplast genome.

Formation of Fe- and Mg-rich smectite and zeolite under alkaline conditions is concerned as secondary minerals after alkaline alteration of bentonite in a repository of radioactive wastes. It might be crucial for safety assessment whether smectite will be formed or not as secondary minerals after alkaline alteration of bentonite. In present paper, Fe- and Mg-rich smectite which are currently interacting with hyperalkaline groundwater was found at Narra in Palawan, Philippines. Mineralogical and geochemical investigation was conducted to understand formation process of smectite and factors determined secondary mineral species. Our study revealed a certain amount of smectite may have been produced under hyperalkaline conditions, altered from amorphous or poorly crystalline material such as M-S-H and F-S-H. Key factor which decides smectite or zeolite as secondary minerals after alkaline alteration of bentonite might be whether nuclei of M-S-H and/or F-S-H will be formed or not. This might be decided by the presence of dissolved Mg2+ and Fe2+ in the system. Our suggested formation process of smectite under alkaline conditions is analogue with generally-accepted model of smectite formation that might have been occurred on early Mars.

In this paper, modelling designing and simulation of a simple voltage amplidyne system is done using robust control theory. In order to increase the performance of the voltage amplidyne system with H ∞ optimal control synthesis and H ∞ optimal control synthesis via ∞-iteration controllers are used. The open loop response of the voltage amplidyne system shows that the system can amplify the input 7 times. Comparison of the voltage amplidyne system with H ∞ optimal control synthesis and H ∞ optimal control synthesis via ∞-iteration controllers to track a desired step input have been done. Finally, the comparative simulation results prove the effectiveness of the proposed voltage amplidyne system with H ∞ optimal control synthesis controller in improving the percentage overshoot and the settling time.

In this paper, the design and performance investigation of the permanent magnet machines have been done to increase the mechanical and electrical outputs improvement of the systems. A permanent magnet Dc motor (PMDM) and generator (PMDG) have been modelled and designed to improve the angular position and generated current respectively. In this work, augmentation based H 2 optimal and H infinity synthesis controllers have been designed as a controller for the two systems and a comparison between the proposed controller for tracking a reference inputs and a promising results have been obtained.

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.

The two-parameter Wright special function is an interesting mathematical object that arises in the theory of the space and time-fractional diffusion equations. Moreover, many other special functions are particular instantiations of the Wright function. The article demonstrates finite representations of the Wright function in terms of sums of generalized hypergeometric functions, which in turn provide connections with the theory of the Gaussian, Airy, Bessel, and Error functions, etc. The main application of the presented results is envisioned in computer algebra for testing numerical algorithms for the evaluation of the Wright function.

This case study focuses on exploring the potential of biogas as a direct substitute for conventional fossil fuels in industrial applications. Instead of being limited to its common uses as a vehicle fuel or for power generation, this research aims to investigate how biogas can be integrated into industrial processes as an advanced and sustainable energy solution. By conducting a detailed analysis of the financial implications associated with the utilization of landfill gas and gas derived from biomass, a comprehensive understanding of their practical applications in the industrial sector can be obtained. This research goes beyond a superficial examination and delves into the intricate aspects of incorporating biogas as a viable alternative fuel source. When we say that utilizing biogas is technically feasible, it means that the necessary infrastructure and technologies are available to support its integration into industrial processes. This implies that there are existing methods and systems in place that can efficiently harness and utilize biogas for various industrial applications. These technologies ensure a seamless transition from conventional fossil fuels to renewable energy sources, leading to a more sustainable and environmentally friendly industrial landscape. Moreover, the statement that utilizing biogas is economically feasible emphasizes that the financial viability of employing biogas in industrial processes is advantageous. This research explores the potential cost savings and benefits associated with substituting conventional fuels with biogas. By carefully examining the economic aspects, such as initial investments, operational costs, and potential revenue streams, a comprehensive understanding of the financial impact of adopting biogas solutions in the industrial sector can be gained. By expanding and broadening the understanding of the technical and economic feasibility of biogas integration, this research aims to provide valuable insights into the potential of advanced biogas solutions for industrial applications. Indeed, to make biogas a viable and sustainable option as a raw material, it is necessary to establish farming subsidies and financial support specifically tailored for biogas production, similar to the existing support provided for food production. These subsidies and financial incentives play a crucial role in promoting and encouraging the growth of the biogas industry. By establishing such support systems, farmers and other stakeholders in the agricultural sector can be incentivized to participate in the production of biogas. This can involve the utilization of agricultural waste, organic residues, or dedicated energy crops for biogas generation. The financial assistance can help offset the initial investment costs, provide incentives for production, and ensure the economic viability of biogas projects. Moreover, when considering large-scale landfills or situations where industrial demands for energy are relatively low, landfill gas becomes a viable and practical option. Landfill gas, which is generated by the decomposition of organic waste in landfills, can be harnessed and utilized for various industrial purposes. This not only helps in managing waste but also provides a valuable source of renewable energy. In summary, while farming subsidies and financial support are crucial for promoting biogas production, landfill gas remains a viable option for large landfills or situations with minor industrial demands. The combination of these two approaches offers a comprehensive outlook on utilizing biogas as a renewable energy source for industrial applications.

A wave is an energy that can propagate with a medium, the propagation of a wave moves with respect to time by carrying energy that moves with velocity per unit of time. Sea waves are one of the propagating wave problems that are broken down to produce wave propagation with a relatively inhomogeneous minimum amplitude and speed of sea waves which have their own difficulties in solving them numerically. This study aims to analyze the stability of wave propagation of submerged breakwaters using the Boundary Element Method. This research will approximate the boundary discretization of the breakwater domain and then combine it with the Finite Element Method in determining the moving elements of the velocity of fluid flow through a porous submerged breakwater. This study varies the magnitude of the incoming propagation velocity and the influence of the breakwater distance. The results of this study indicate that the resulting minimal wave assuming v = 1 m/s and the breakwater distance of s = 20 m gives a wave reflection with a minimum wave speed and amplitude of 0.12515 m

In this paper, a horizontally moving suspended mass pendulum base is designed and controlled using robust control theory. H infinity optimal loop shaping with first and second order desired loop shaping function controllers are used to improve the performance of the system using Matlab/Simulink Toolbox. Comparison of the H infinity optimal loop shaping with first and second order desired loop shaping function controllers for the proposed system have been done to track the desired angular position of the pendulum using step and sine wave input signals and a promising result has been obtained succesfully.

In this paper, the design and analysis of coupled tank water level control system is done using robust control theory. The main aim of this work is to improve level controlling mechanisms in industries and household areas. In this paper, H ∞ and μ –synthesis controllers are designed to improve the level control system. The coupled tank water level control system is designed using the proposed controller’s comparison and tested for tracking a reference level signals (step, sine wave and random) and simulation results have been analyzed successfully. Finally the comparative simulation results prove the effectiveness of the proposed coupled tank water level control system with H ∞ controller for improving the tracking mechanism performance of the system.

Vehicle windshield wiper system increases the driving safety by contributing a clear shot viewing to the driver. In this paper, modelling, designing and simulation of a vehicle windshield wiper system with robust control theory is done successfully. H∞ loop shaping and robust pole placement controllers are used to improve the wiping speed by tracking a reference speed signals. The reference speed signals used in this paper are step and sine wave signals. Comparison of the H∞ loop shaping and robust pole placement controllers based on the two reference signals is done and convincing results have been obtained. Finally the comparative results prove the effectiveness of the proposed H∞ Loop Shaping controller to improve the wiping mechanism for the given two reference signals.

In this paper, the design and control of a hydraulic system based tire changer machine have been analyzed and simulated using Matlab/Simulink Toolbox successfully. The machine have a displacement input which is a leg pedal displacement in order to push the piston of the pump to fed the motor with a pressured hydraulic fluid to rotate the tire with an angular speed to mount and dismount it. Augmentation based H_∞ and H₂ optimal synthesis controllers have been used to improve the performance of the machine. Comparison of the proposed controllers for tracking a reference input speed have been done using two reference inputs (step and random) signals. Finally the comparative simulation results proved the effectiveness of the proposed tire changer with H synthesis controller in improving the settling time and percentage overshoot.

In this paper a full state feedback control of a double inverted pendulum on a cart (DIPC) are designed and compared. Modeling is based on Euler-Lagrange equations derived by specifying a Lagrangian, difference between kinetic and potential energy of the DIPC system. A full state feedback control with H infinity and H 2 is addressed. Two approaches are tested: open loop impulse response and a double inverted pendulum on a cart with full state feedback H infinity and H 2 controllers. Simulations reveal superior performance of the double inverted pendulum on a cart with full state feedback H infinity controller.

In this paper, modelling designing and simulation of a Ward Leonard layout system is done using robust control theory. In order to increase the performance of the Ward Leonard layout system with H infinity optimal control synthesis and H infinity optimal control synthesis via gamma-iteration controllers are used. The open loop response of the Ward Leonard layout system shows that the system needs to be improved. Comparison of the Ward Leonard layout system with H∞ optimal control synthesis and H infinity optimal control synthesis via gamma-iteration controllers to track a desired step speed input have been done. Finally, the comparative simulation results prove the effectiveness of the proposed Ward Leonard layout system with H infinity optimal control synthesis controller in improving the percentage overshoot and the settling time.

This cross-sectional study evaluated the validity of three alternative methods compared to the gold standard 24-h urine collection for estimating dietary sodium intake, a modifiable risk factor for hypertension, among middle-aged and older adults with elevated blood pressure. These included spot urine collection (using Kawasaki, Tanaka, and INTERSALT equations), 24-h dietary recall, and food frequency questionnaire responses, compared against 24-h urine collection in a subset of 65 participants (aged 50–75 years, 58.5 % women, 61.6 % hypertensive) from the DePEC-Nutrition trial. The validity of the methods was assessed using bias, Spearman correlation coefficient (SCC), intraclass correlation coefficient (ICC), and Bland-Altman analysis. Among the alternative methods, spot urine collection using the Kawasaki equation showed the strongest correlation (SCC 0.238; ICC 0.119, 95 % CI -0.079 to 0.323) but it exhibited a significant bias (1414 mg/day, p-value < 0.001) relative to 24-h urine collection. Conversely, dietary surveys had a smaller bias but wider limits of agreement. These findings underscore the complexities of accurately estimating dietary sodium intake using spot urine collection or dietary surveys in this specific population, suggesting that a combination or refinement of existing methodologies might improve accuracy. Further research with larger samples is necessary to develop more reliable methods for assessing sodium intake in this high-risk group.

Low-sodium salt substitute (LSSS) has the potential in regulating sodium and potassium intake and has been available in China market for years. However, its real-world use and impact to sodium\potassium intake is unclear. Baseline data of 4000 adult participants who participated in three similar-designed randomized controlled trails were pooled together for this study. Self-reported awareness and use of LSSS were collected using the uniform questionnaire, and the 24-h urinary sodium and potassium excretion was used to estimate their dietary intake. Mixed-effects models were developed to assess the relationship between LSSS and 24-h urinary sodium and potassium excretion. 32.0% of the participants reported awareness of LSSS and 11.7% reported its current use. After adjusting location, sex, age, and education, compared with the group of participants unaware of LSSS, participants who were aware but not using LSSS and those who were using LSSS had a lower 24-h urinary sodium excretion by –356.1(95% CI: –503.9, –205.9) mg/d and –490.6(95% CI: –679.2, –293.7), respectively (p&lt;0.001). No significant difference was found for 24-h urinary potassium excretion and sodium-to-potassium ratio among the three groups (p&gt;0.05). In conclusion, although associated with lower sodium intake, the awareness and real-world use of LSSS are still very low in China.

The Mobius function is commonly used to define Euler's totient function and the Mangoldt function. Similarly, the summatory Mobius function (the Mertens function) can be used to define the summatory totient function and the summatory Mangoldt function (the second Chebyshev function).

The treatment of the bulky Rind-based dibromosilanes, (Rind)2SiBr2 (2) [Rind = 1,1,7,7-tetra-R1-3,3,5,5-tetra-R2-s-hydrindacen-4-yl: EMind (a: R1 = Et, R2 = Me) and Eind (b: R1 = R2 = Et)], with two equivalents of tBuLi in Et2O at low temperatures resulted in the formation of blue solutions derived from the diarylsilylenes, (Rind)2Si: (3). Upon warming the solutions above −20 °C, the blue color gradually faded, accompanying the decomposition of 3 and yielding the cyclic hydrosilanes (4) via intramolecular C−H bond insertion at the Si(II) center. The molecular structures of the bulky Eind-based 3b and 4b were confirmed by X-ray crystallography. Thus, at −20 °C, blue crystals were formed (Crystal-A), which were identified as mixed crystals of 3b and 4b. Additionally, colorless crystals of 4b as a singular component were isolated (Crystal-B), whose structure was also determined by an X-ray diffraction analysis. Although the isolation of 3 was difficult due to their thermally-labile nature, their structural characteristics and electronic properties were discussed based on the experimental findings complemented by computational results. We also examined the hydrolysis of 3b to afford the silanol, (Eind)2SiH(OH) (5b).

Glioblastoma, a deadly brain tumor, shows limited response to standard therapies like te-mozolomide (TMZ). Recent findings from the REGOMA trial underscore a significant survival improvement offered by regorafenib (REGO) in recurrent glioblastoma. Our study aimed to propose a 3D ex vivo drug response precision medicine approach to investigate recurrent glio-blastoma sensitivity to REGO and elucidate the underlying molecular mechanisms involved in tumor resistance or responsiveness to treatment. 3D glioblastoma organoids (GB-EXPs) obtained from 18 patients’ resected recurrent glioblastoma tumors were treated with TMZ and REGO. Drug responses were evaluated using NAD(P)H FLIM, stratifying tumors as responders (Resp) or non-responders (NR). Whole-exome sequencing was performed on 16 tissue samples, and whole-transcriptome analysis on 13 GB-EXPs treated and untreated. We found 35% (n=9) and 77% (n=20) of tumors responded to TMZ and REGO, respectively, with no instances of TMZ-Resp be-ing REGO-NR. Exome analysis revealed a unique mutational profile in REGO-Resp tumors compared to NR tumors. Transcriptome analysis identified distinct expression patterns in Resp and NR tumors, impacting Rho GTPase and NOTCH signaling, known to be involved in drug response. In conclusion, recurrent glioblastoma tumors were more responsive to REGO com-pared to TMZ treatment. Importantly, our approach enables a comprehensive longitudinal ex-ploration of the molecular changes induced by treatment, unveiling promising biomarkers in-dicative of drug response.

Hypsizygus marmoreus has become one of the most popular edible mushrooms due to its high nu-tritional and economic value. Previous researchers found that Serratia odorifera could promote the growth of H. marmoreus by producing and secreting some of its inducers. However, the specific mechanism of action was still unclear. In this study, we found that exogenous addition of sterile fermentation filtrate (HZSO-1), quorum sensing (QS signaling molecules, 3-oxo-C6-HSL, cy-clo(Pro-Leu), and cyclo(Tyr-Leu) could significantly promote the growth of H. marmoreus, increase the number of clamp junctions, and the diameter of mycelium (P < 0.05). In addition, non-targeted metabolomic analysis has revealed that 706 metabolites were detected in the treated group. Of these, 307 metabolites were significantly different (P < 0.05). Compared with the control, 54 and 86 metabolites were significantly increased and decreased in the HZSO-1 group, respec-tively (P < 0.05). We speculated that the sterile fermentation filtrate of S. odorifera could mediate the carbohydrate and amino acid metabolism of H. marmoreus by influencing the pentose phosphate pathway (PPP) to increase the energy supply for the growth and development of the mycelium. The above results will further reveal the growth-promoting mechanism of S. odorifera on H. mar-moreus.

Aim: To compare the effectiveness of conventional and rotary NiTi files for Gutta-Percha (GP) removal in straight roots during retreatment root canal treatment (RCT), using manual Hedstrom files and ProTaper Universal System, respectively. Methods: It was an in-vitro experimental study using non-probability consecutive sampling. Sixty extracted single rooted maxillary and mandibular permanent teeth with straight canals were selected for this study. Following preparation, the root canals were filled with GP along with a sealer and kept for two weeks in a moist environment at room temperature. Thirty teeth were randomly allocated to the study and control groups each. GP removal was accomplished with Hedstrom files and Pro Taper retreatment files in group 1 and group 2, respectively. Digital radiographs were obtained using Kodak RVG digital radiography system software version VER.6.10.8.3-A and analyzed for the difference of opacities indicating residual GP. AutoCAD 2006 software was used to outline the root canal and the residual root filling. Independent sample t test was used to compare the total residual GP in both groups. Results: No significant difference in the residual root filling was observed following removal with conventional Hedstrom files versus ProTaper universal retreatment files. In both groups, the residual GP was confined to the apical third of the roots. Conclusion: ProTaper Universal Retreatment files and manual Hedstrom files are equally effective in the removal of GP in straight canals.

Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same geometric means finally help to systematically derive handy formulas that approximate the inverse error function. Our approach can be used for applications in e.g. high-speed Monte Carlo simulations where this function is used extensively.

In this work we develop a new algorithm for efficient computation of the Voigt/complex error function. In particular, in this approach we propose a two-domain scheme where number of the grid-points is dependent on the input parameter $y$. The error analysis we performed shows that the MATLAB implementation meets the requirements for radiative transfer applications involving the HITRAN spectroscopic database. The run-time test shows that this MATLAB implementation provides rapid computation especially at smaller range of the parameter x.

The manuscript surveys the special functions of the Fox-Wright type. These functions are generalizations of the hypergeometric functions. Notable representatives of the type are the Mittag-Leffler functions and the Wright function. The integral representations of such functions are given and the conditions under which these function can be represented by simpler functions are demonstrated. The connection with generalized fractional differential and integral operators is demonstrated and discussed.

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

In this paper, we classify the function space of all real-valued functions on R denoted as F(R,R) into 28 distinct blocks. Each block contains elements that share common features in terms of the cardinality of their sets of continuity and differentiability. Alongside this classification, we introduce the concept of the Connection, which reveals a special relationship structure between four well-known real-valued functions in real analysis: the Cantor function, Dirichlet function, the Thomae function, and the Weierstrass function. Despite the significance of this field, several perspectives remain unexplored.

In this article, our main purpose is to establish a new extension of Mittag-Leffler function by using the known extended beta function $\mathbf{B}_{\omega}(a,b;p)$ introduced in [1]. It led to a novel extension of the applicability of Mittag-Leffler function that introduced them as distributions defined for a specific set of functions. We also, investigate some of its important properties, namely recursion relation, Mellin transform and differential formulas.

Licochalcone H (LCH), a regioisomer of licochalcone C derived from the root of Glycyrrhiza inflata. CRC treatment has always been challenged by the development of resistance. We investigated the antiproliferative activity of LCH in oxaliplatin (Ox)-sensitive and -resistant CRC cells. LCH significantly inhibited cell viability and colony growth in both Ox-sensitive and Ox-resistant CRC cells. We found that LCH decreased epidermal growth factor receptor (EGFR) and AKT kinase activities and related activating signaling proteins including phospho (p)-EGFR and pAKT. A computational docking model indicated that LCH may interact with EGFR, AKT1, and AKT2 at the ATP-binding sites. LCH induced ROS generation, as verified by N-acetyl-L-cysteine (NAC) treatment, and increased the expression of the ER stress markers. LCH treatment of CRC cells induced depolarization of MMP and increased. Multi-caspase activity was induced by LCH treatment and confirmed by Z-VAD-FMK treatment. LCH increased the number of subG1 cells and arrested the cell cycle at the G1 phase. LCH inhibits the growth of Ox-sensitive and Ox-resistant CRC cells by targeting EGFR and AKT, and inducing ROS generation and ER stress-mediated apoptosis. Therefore, LCH could be a potential therapeutic agent for improving not only Ox-sensitive but also Ox-resistant CRC treatment.

A fundamental tool in mathematical physics is the logarithmic Sobolev inequality. A quantitative version proven by Carlen with a remainder involving the Fourier-Wiener transform is equivalent to an entropic uncertainty principle more general than the Heisenberg uncertainty principle. In the stability, the remainder is in terms of an entropy, not a metric. Recently, a stability result for H¹ was obtained by Dolbeault, Esteban, Figalli, Frank, and Loss in terms of an L^p norm. Afterwards, Brigati, Dolbeault, and Simonov discussed the stability problem involving a stronger norm. A full characterization with a necessary and sufficient condition to have H¹ convergence is identified in this paper. Moreover, an explicit H¹ bound via a moment assumption is shown. Also, the L^p stability of Dolbeault, Esteban, Figalli, Frank, and Loss is proven to be sharp.

The ability of 2D hybrid structures formed by boron, nitrogen and carbon atoms (h-BNCs) as potential substrates for surface enhanced Raman spectroscopy (SERS) detection of dioxin-like pollutants is theoretically analyzed. The strong confinement and high tunability of the electromagnetic response of the carbon nanostructures embedded within the h-BNC sheets point out that these hybrid structures could be promising for applications in optical spectroscopies, such as SERS. In this work, two model dioxin-like pollutants, TCDD and TCDF, and a model h-BNC surface composed by a carbon nanodisk of ninety-six atoms surrounded by a string of borazine rings, BNC96, are employed for the simulation of the adsorption complexes and the static and pre-resonance Raman spectra of the adsorbed molecules. A large affinity of BNC96 by these pollutants is reflected on the large interaction energies obtained for the most stable stacking complexes, with dispersion being the most important contribution to their stability. The large vibrational coupling of some active modes of TCDF and, specially, of TCDD makes the Raman static spectra display a ‘pure’ chemical enhancement of one order of magnitude. On the other hand, due to the strong electromagnetic response of BNC96, confined within the carbon nanodisk, pre-resonance Raman spectra obtained for TCDD and TCDF display large enhancement factors of 108 and 107, respectively. Promisingly, laser excitation wavelengths frequently used in SERS experiments also provoke significant Raman enhancements, around 104, for the TCDD and TCDF signals. Both the strong confinement of the electromagnetic response within the carbon domains and the high modulation of the resonance wavelengths within the visible and/or UV ranges in h-BNCs should lead to a higher sensitivity than graphene and white graphene parent structures, solving one of the main disadvantages of using 2D substrates for SERS applications.

Antisense technologies consist of the utilization of oligonucleotides or oligonucleotide analogs to interfere with undesirable biological processes, commonly through inhibition of expression of selected genes. This field holds a lot of promise for the treatment of a very diverse group of diseases including viral and bacterial infections, genetic disorders, and cancer. To date, drugs approved for utilization in clinics or in clinical trials target diseases other than bacterial infections. Although several groups and companies are working on different strategies, the application of antisense technologies to prokaryotes still lags with respect to those that target other human diseases. In those cases where the focus is on bacterial pathogens, a subset of the research is dedicated to produce antisense compounds that silence or reduce expression of antibiotic resistance genes. Therefore, these compounds will be adjuvants administered with the antibiotic to which they reduce resistance levels. A varied group of oligonucleotide analogs like phosphorothioate or phosphorodiamidate morpholino residues, as well as peptide nucleic acids, locked nucleic acids and bridge nucleic acids, the latter two in gapmer configuration, have been utilized to reduce resistance levels. The major mechanisms of inhibition include eliciting cleavage of the target mRNA by the host’s RNase H or RNase P, and steric hindrance. The different approaches targeted resistance to β-lactams including carbapenems, aminoglycosides, chloramphenicol, macrolides, and fluoroquinolones.

Current therapeutic protocols for the treatment of HIV infection consist of the combination of diverse anti-retroviral drugs in order to reduce the selection of resistant mutants and to allow for the use of lower doses of each single agent to reduce toxicity. However, avoiding drugs interactions and patient compliance are issues not fully accomplished so far. In this respect the identification of single agents with multitarget potential might represent the ideal solution. Accordingly, a small library of biphenylhydrazo 4-arylthiazoles derivatives has been synthesised and evaluated to investigate the ability of the new derivatives to simultaneously inhibit both associated functions of HIV reverse transcriptase. All compounds were active towards the two functions, although at different concentrations. The substitution pattern on the biphenyl moiety appears relevant to determine the activity.

A Zn(II) perchlorate complex has been prepared and characterized by single X-ray crystallography, nuclear magnetic resonance spectroscopy, thermogravimetric analysis, infrared spectroscopy, elemental analysis, and UV-vis spectroscopy. The complex crystallizes in the monoclinic space group P21/c (Z = 4) with a pentacoordinated zinc center. Interestingly, the Zn complex was found be to a potential fluorophore that could sense acetone and other ketones with high selectivity and sensitivity.

Helicobacter pylori is a common human pathogen that causes gastroduodenal diseases. H. pylori genome consists of numerous restriction-modification (R-M) genes. It is established that N6-adenine methylation plays a crucial role in bacterial gene regulation and virulence, but not much is known about the role of C5-cytosine methylation. In this study, we examined the influence of an orphan cytosine methyltransferase, hpyAVIBM on gastric infection in mice and cultured cells. Histopathological staining showed that the deletion of hpyAVIBM in H. pylori strain SS1 had increased damaging hemorrhagic effects on the mice stomach. The gelatin-zymography result demonstrated that the mice infected with mutant SS1ΔhpyAVIBM had significantly up-regulated pro-MMP-9 than those infected with SS1. Additionally, ELISA results of pro-inflammatory cytokines proved that mutant strain caused significantly more inflammatory effect on mice stomach than its wild-type counterpart. The immunohistochemistry data showed that mutant strain caused attenuated epithelial cell damage. Co-culture studies of H. pylori with AGS (Human Gastric Adenocarcinoma cell line) cells revealed that SS1ΔhpyAVIBM instigated significantly more apoptotic death in the AGS cells compared to the wild-type strain. Our results indicated that DNA methylation by hpyAVIBM plays a crucial role in modulating virulence factors in bacterial cells and their interaction with the host cells.

The past two decades has seen a growing demand for high-power, high-voltage utility scale inverters mostly fueled by the integration of large solar PV and wind farms. Multilevel inverters have emerged as the industry choice for these megawatt range inverters because their reduced voltage stress, capable of generating an almost sinusoidal voltage, in-built redundancy, among others. This paper present a new Switched-Source Multilevel Inverter (SS MLI) architecture. The new inverter show superior over existing topologies. It has reduced voltage stress on the semiconductor, uses less number of switches –reduced size/weight/cost and increased efficiency. The new SSMLI is comprised of two voltage sources (V₁, V₂) and 6 switches. It is capable of generating 5-level output voltage in symmetric modes (i.e., V₁ = V₂), and 7-level output voltage in asymmetric modes (i.e., V₁ ≠ V₂). To demonstrate the validity of the proposed inverter, simulations results using MATLAB^® /Simulink^® for 5- and 7-level output voltages are presented . The simulations are also verified experimentally using a laboratory prototype.

In this part of the series of two papers, we extend the theorems discussed in part I for infinite series. We then use these theorems to develop distinct novel results involving the Hurwitz zeta function, Riemann zeta function, Polylogarithm and Fibonacci numbers. In continuation, we obtain some zeros of the newly developed zeta functions and explain their behaviour using plots in complex plane. Furthermore, we provide particular cases for the theorems and corollaries which show that our results generalise the currently available functions and series such as the Riemann zeta function and the geometric series. Finally, we provide four miscellaneous examples to showcase the vast scope of the developed theorems.

It is well known that the primes and prime powers have a deep relationship with the nontrivial zeros of Riemann’s zeta function. This is a reciprocal relationship. The zeros and the primes are encoded in each other and are reciprocally recoverable. Riemann’s zeta is an extended or continued version of Euler’s zeta function which in turn equates with Euler’s product formula over the primes. This paper shows that the zeros of the converging Dirichlet or Catalan beta function, which requires no continuation to be valid in the critical strip, can be easily determined. The imaginary parts of these zeros have a deep and reciprocal relationship with the odd primes and odd prime powers. This relationship separates the odd primes into those having either 1 or 3 as a remainder after division by 4. The vector pathway of the beta function is such that the real part of its zeros has to be a half.

In the paper, the authors discover several series identities involving the Catalan numbers, the Catalan function, the Riemanian zeta function, and the alternative Hurwitz zeta function.

Proof of the Riemann hypothesis is obtained using the properties of the Gamma function, the Bernoulli function, and limitations imposed by the rational relations of the complex roots of the Riemann zeta function, and the rational relations of the complex Gamma functions.

In a recent paper, Sarikaya et al. introduced a new analogue of the classical Gamma function which they called, the conformable Gamma function. Motivated by their results, this paper seeks to establish some inequalities for the conformable Gamma and Polygamma functions. Among other analytical tools, the procedure relies on the generalized forms of some classical inequalities.

The main objective of this present paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. Also, we give some results related to the newly defined fractional operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

In this paper we address some variants for the products of Hadamard and Patterson. We prove that all zeros of the Riemann $\Xi$--function are real. We also prove that the Riemann hypothesis is true. The equivalence theorems associated with the Riemann zeta--function are obtained in detail.

In this article we propose the integral, series and product representations for the Ramanujan zeta-function. We suggest a variant for the Conrey-Ghosh product for the entire Ramanujan zeta-function. We present some variants for the product for the Ramanujan $\Xi$-function. We prove that all of its zeros are real. Along the way we obtain the truth of the Riemann-Hardy conjecture.

The main objective of this paper is to introduce a further extension of extended (p, q)-beta function by considering two Mittag-Leffler function in the kernel. We investigate various properties of this newly defined beta function such as integral representations, summation formulas and Mellin transform. We define extended beta distribution and its mean, variance and moment generating function with the help of extension of beta function. Also, we establish an extension of extended (p, q)-hypergeometric and (p, q)-confluent hypergeometric functions by using the extension of beta function. Various properties of newly defined extended hypergeometric and confluent hypergeometric functions such as integral representations, Mellin transformations, differentiation formulas, transformation and summation formulas are investigated.

In the paper, the authors generalize the notion "k-Mittag-Leffler function'', establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function.

Biodiesel is one of the most popular biofuels as it is a promising substitute of the conventional diesel fuel, but for now it cannot be used as a stand-alone fuel due to its low oxidative stability. For this reason, the last years there have been efforts for its upgrading through the partial hydrogenation of the fatty acid methyl esters (FAMEs) that biodiesel consists of. This procedure succeeds in resolving the problem of low oxidative stability, but in some cases a new problem arises as the non-selective hydrogenation is deteriorating the fuel’s cold flow properties, which are crucial for its operation without damaging the vehicle’s engine. More specifically, the problem of deteriorated cold flow properties is caused by the formation of trans-monounsaturated FAMEs and fully saturated FAMEs while the hydrogenation reaction is taking place. The hydrogenated biodiesels are preferred to contain more cis-monounsaturated FAMEs, because these are considered to have the best combination between high oxidative stability and good cold flow properties. As a result, various systems and methods have been tested in order to achieve a selective partial hydrogenation of biodiesel’s FAMEs. In this review article, the catalytic systems and methods that stood out in various researches are presented and the factors that lead to the best possible outcome are investigated and discussed.

Aim. To study the processes of lipid peroxidation and the activity of antioxidant defense enzymes depending on the chemiluminescent activity of neutrophilic granulocytes in patients with gastric cancer associated with H. pylori infection, depending on the stage. Materials and methods. 39 patients with stage I-II gastric cancer and 30 patients with stage III-IV gastric cancer were examined. The study of the chemiluminescent activity of neutrophilic granulocytes was carried out, the parameters of the lipid peroxidation system and antioxidant protection in plasma were determined using the spectrophotometric method. Statistical data processing was performed using the Statistica 7.0 software package (StatSoft, USA). Results. In patients with gastric cancer associated with H. pylori infection, regardless of stage, the proportion of neutrophilic granulocytes with normal activity does not exceed 1/3 of the total number of patients, the remaining 2/3 of patients have an altered chemiluminescent activity of neutrophilic granulocytes: in patients with gastric cancer by I -II stage of the disease, the majority revealed a reduced function of neutrophilic granulocytes, and in patients with gastric cancer stage III-IV of the disease, the majority showed increased chemiluminescent activity of neutrophilic granulocytes. In all patients with gastric cancer associated with H. pylori infection, regardless of the stage of the disease, an increase in lipid peroxidation processes with activation of antioxidant defense enzymes was detected. Conclusion. In all patients with gastric cancer associated with H. pylori infection, regardless of the stage of the disease, an increase in lipid peroxidation processes with activation of antioxidant defense enzymes was detected. At the same time, there are no statistically significant differences between the indicators of the system lipid peroxidation - antioxidant protection depending on the stage of gastric cancer and the chemiluminescent activity of neutrophilic granulocytes, which probably indicates that all reactive oxygen species produced by neutrophilic granulocytes in the respiratory burst are consumed locally, minimally affecting the development of oxidative stress in the blood plasma.

A simple undirected graph $\Gamma=(V_\Gamma,E_\Gamma)$ admits an $H$-covering if every edge in $E_\Gamma$ belongs to at least one subgraph of $\Gamma$ that isomorphic to a graph $H$. For any graph $\Gamma$ admitting $H$-covering, a total Labelling $\beta: V_\Gamma \cup E_\Gamma \longrightarrow \{1,2,\dots,p\}$ is called an $H$-irregular total $p$-labelling of $\Gamma$ if every two different subgraphs $H_1$ and $H_2$ of $\Gamma$ isomorphic to $H$ have distinct weights where the weight $w_\beta(K)$ of subgraph $K$ of $\Gamma$ is defined as $w_f(K):=\displaystyle \sum_{v\in V_K} f(v) + \sum_{e\in E_K} f(e)$. The smallest number $p$ for which a graph $\Gamma$ admits an $H$-irregular total $p$-labelling is called the total $H$-irregularity strength of $\Gamma$ and is denoted by $ths(\Gamma)$. In this paper, we determine the total $H$-irregularity strength of edge comb product of two graphs.

This article will briefly review the progress of h-BN based solid-state metal semiconductor metal (MSM) neutron detectors. In the last decade, several groups have been working on hexagonal boron nitride (h-BN) based solid-state neutron detectors. Recently, the detection efficiency of 59% has been reported. Efficient, low-cost neutron detectors made from readily available materials are essential for various applications. Neutron detectors are widely used to detect fissile materials and nuclear power plants for security applications. The most common and widely used neutron detectors are 3He based, which are sometimes bulky, difficult to transport, have high absorption length, need relatively high bias voltage (>1000 V), and have low Q-value (0.764 MeV). Also, 3He is not readily available material. Thus, there is a strong need to find an alternative detection material. 10B isotope has a high neutron absorption cross-section, and it has been tested as a coating on the semiconducting materials. Due to the two-step process, neutron capture through 10B, and then electron-hole pair generation in a typical semiconducting material, the efficiency of these devices is not up to the mark. The progress in h-BN based detectors requires a review to envision the further improvement in this technology.

Helicobacter pylori is the most common human gastric infection. H. pylori stool antigen lateral flow immunochromatography assay (HpSA-LFIA) is considered one of the most cost-effective and rapid non-invasive assays (active tests). The evaluation of this test is crucial for accuracy and utility assurance. This study aimed to evaluate the polyclonal antibody-based HpSA-LFIA in comparison to a monoclonal antibody-based ELISA kit. Methodology: Stool samples were collected from 200 gastric patients for HpSA-LFIA and semi-quantitative HpSA-ELISA. Statistical analysis of the diagnostic values was performed using MedCalc software. Chi-square tests were used to determine the effects of gender and age. Results: The obtained results found that HpSA-LFIA achieved promising sensitivity (93.75%) and NPV (98.00%). However, it had poor specificity, PPV, and accuracy, respectively, 59.76%, 31.25%, and 65.31%. LR+ & LR- were 2.33% & 0.1%, respectively. Gender had no significance on the di-agnostic parameters of HpSA-LFIA. Age groups had irrelevant sensitivity; however, specificity was significantly higher in patients over 45 years. Conclusion: It was concluded that HpSA-LFIA was not accurate enough to be the sole test for di-agnosis and needs other confirmatory tests in case of positive conditions

Most Acinetobacter baumannii strains are naturally competent. Although some information is available about factors that enhance or reduce the frequency of transformation of this bacterium, the regulatory elements and mechanisms are barely understood. In this article, we describe studies on the role of H-NS in the regulation of expression of genes related to natural competency and the ability to uptake foreign DNA. The expression levels of the natural transformation-related genes pilA, pilT, pilQ, comEA, comEC, comF, and drpA were significantly increased in a Δhns derivative of Acinetobacter baumannii A118. Complementation of the mutant with a recombinant plasmid harboring hns restored expression levels of six of these genes (pilT remained expressed at high levels) to those of the wild-type strain. The transformation frequency of the A. baumannii A118 Δhns strain was significantly higher than that of the wild-type. Similar, albeit not identical, effects occurred when hns was deleted from the hypervirulent A. baumannii AB5075 strain. Reduction of gene expression in a few cases was not as pronounced as to reach wild-type levels, and expression of comEA was enhanced further. In conclusion, the expression of all seven transformation-related genes was enhanced after deleting hns in A. baumannii A118 and AB5075, and these modifications are accompanied by an increase in the cells’ transformability. The results demonstrate a role of H-NS in A. baumannii’s natural competence.

Noise reduction is the major issue in the loudspeaker for the application of the musical instruments and related areas. In this paper, a noise disturbance control of a loudspeaker with optimal and robust controllers has been done successfully. The noise of the loudspeaker has been analyzed by simply track a reference cone displacement with the actual cone displacement. Static output feedback and H infinity optimal loop shaping controllers have been used to compare the actual and reference cone displacements by using a sine wave and random cone displacement signals and a promising results have been analyzed.

Morphogenesis remains a riddle, wrapped in a mystery, inside an enigma. It remains a formidable problem viewed from many different perspectives of morphology, genetics, and computational modelling. We propose a biochemical reductionist approach that shows how both internal and external physical forces contribute to plant morphogenesis via mechanical stress-strain transduction from the primary cell wall tethered to the plasma membrane by a specific arabinogalactan protein (AGP). The resulting stress vector with direction defined by Hechtian adhesion sites, has a magnitude of a few picoNewtons amplified by a hypothetical Hechtian growth oscillator. This paradigm shift involves stress activated plasma membrane Ca2+channels and auxin-activated H+-ATPase. The proton pump dissociates periplasmic AGP-glycomodules that bind Ca2+. Thus, as the immediate source of cytosolic Ca2+ an AGP-Ca2+ capacitor directs vectorial exocytosis of cell wall precursors and auxin efflux (PIN) proteins. In toto these components comprise the Hechtian Oscillator and also the gravisensor. Thus interdependent auxin and Ca2+ morphogen gradients account for the predominance of AGPs. The size and location of a cell surface AGP-Ca2+ capacitor is essential to differentiation and explains AGP correlation with all stages of morphogenetic patterning from embryogenesis to root and shoot. Finally, evolutionary origins of the Hechtian Oscillator in the unicellular Chlorophycean algae reflect the ubiquitous role of chemiosmotic proton pumps that preceded DNA at the dawn of life.

Jacobian theta function identities are related to the Addition formula for the Weierstrass 1 Sigma function. In this paper, from the Addition formula for Weierstrass Sigma function, new and 2 simple proofs of four square sums theorem are given. Using the addition formula of the theta func- 3 tions, we also give simple proofs of two square sums and eight square sums theorem.

In this paper, we introduce two subclasses of analytic and Spirallike functions and investigate convolution properties, the necessary and sufficient condition, coefficient estimates and inclusion properties for these classes .

A new generalization of extended beta function and its various properties, integral representations and distribution are given in this paper. In addition, we establish the generalization of extended hypergeometric and con uent hypergeometric functions using the newly extended beta function. The properties these extended and con uent hypergeometric functions such as integral representations, Mellin transformations, dif- ferentiation formulas, transformation and summation formulas are also investigated.

Abstract: Background: Restless Legs Syndrome /Willis-Ekbom disease (RLS/WED) has occasionally -but not consistently- been associated with cognitive, and most notably, language and executive impairment. The present study was conducted to investigate the cognitive trajectories of older individuals with RLS/WED. Methods: Participants were drawn from the randomly selected, older (>64 years), population-based HELIAD cohort. Individuals without dementia, with available neuropsychological evaluations at baseline and follow-up were considered for potential eligibility. A comprehensive assessment examining five principal components of cognition (memory, visuo-spatial ability, attention, executive function, and language) was administered to the partici-pants. Generalized estimating equations analysis was used to examine the unadjusted and adjusted (for critical factors and covariates) effects of RLS/WED on cognition over time. Results: A total of 1003 predominantly female, older (72.9 ±4.9 years) partici-pants, with follow-up evaluations after a mean of 3.09 ±0.85 years and without demen-tia at baseline and follow-up were included in the present study. Among them, 81 were diagnosed with RLS/WED at baseline. Global cognition, memory, attention, executive and visuo-perceptual skills did not differ between those with and without RLS/WED. However, the RLS/WED group performed worse on language at baseline by 0.249 of a standard deviation, while demonstrating a mitigated language decline over time, by 0.063 of a standard deviation. The unadjusted models yielded similar results. Conclu-sions: Our findings were indicative of a baseline language disadvantage among older individuals with RLS/WED, but the initial discrepancy tends to dissolve over time.

This paper establishes a real integral representation of the reciprocal $\Gamma$ function in terms of a regularized hypersingular integral. The equivalence with the usual complex representation is demonstrated. A regularized complex representation along the usual Hankel path is derived.

Recently, different extensions of the fractional derivative operator are found in many research papers. The main aim of this paper is to establish an extension of the extended Caputo fractional derivative operator. The extension of an extended fractional derivative of some elementary functions derives by considering an extension of beta function which includes the Mittag-Leffler function in the kernel. Further, an extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and the generating relations for extension of extended hypergeometric functions also presented in this study.

The main objective of this present paper is to introduce further extension of extended Caputo fractional derivative operator and establish the extension of an extended fractional derivative of some known elementary functions. Also, we investigate the extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and generating relations for extension of extended hypergeometric functions.

We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the same order at certain arguments.

In the conservation of monumental heritage, the collection and utilization of information are of primary importance. The Heritage Building Information Modeling (HBIM) procedure harnesses the potential of three-dimensional models, offering significant advantages in accessing documentation, interoperability, multidimensionality of intervention design, cost evaluation and maintenance management. Attention here is focused on the Certosa di Pisa, a large historical complex built in the 14th century as a monastery of the Carthusian order, currently in a state of deterioration and in need of restoration and re-functionalization. The multifaceted nature of this monumental complex, with its intricate interplay of architectural elements spanning different historical periods and featuring diverse techniques, poses a significant challenge for structural safety assessment. This case study presents an opportunity to explore an HBIM approach to streamline the diagnostic process and facilitate the intervention design phase. The goal is achieved by utilizing an accurate 3D model enriched with data from multiple sources and automating certain operations for structural assessment. The usefulness of the HBIM methodology is highlighted as a valuable tool in the realm of Cultural Heritage structures for both technicians and scholars alike.

Glycosylation is a complex post-translational modification that conveys functional diversity to glycoconjugates. Cell surface glycosylation mediates several biological activities such as induction of intracellular signaling pathway and pathogen recognition. Red blood cell (RBC) membrane N-glycans determine blood type and influence cell lifespan. Although several proteomic studies were carried out, glycosylation of RBC membrane proteins has not been systematically investigated. This work aims at exploring the human RBC N-glycome by high-sensitivity MALDI-MS techniques to outline a fingerprint of RBC N-glycans. To this purpose, MALDI-TOF spectra of healthy subjects harboring different blood groups were acquired. Results showed the predominant occurrence of neutral and sialylated complex N-glycans with bisected N-acetylglucosamine, core- and/or an-tennary fucosylation. In the higher mass region these species presented with multiple N-acetyllactosamine repeating units. Amongst the detected glycoforms, the presence of glycans bearing ABO(H) antigens allowed us to define a distinctive spectrum for each blood group. For the first time, advanced glycomic techniques have been applied to a comprehensive exploration of human RBC N-glycosylation, providing a new tool for the early detection of distinct glycome changes associated with disease conditions as well as to understand pathogens molecular recognition.

Protein oligomerzation is key to countless physiological processes, but also to abnormal amyloid conformations implicated in over 25 mortal human diseases. Angiogenin (h-ANG), a ribonuclease A family member, produces RNA fragments that regulate ribosome formation, the creation of new blood vessels and stress granule function. Too little h-ANG activity leads abnormal protein oligomerization resulting in Amyotrophic Lateral Sclerosis (ALS) or Parkinson’s disease. While a score of disease linked h-ANG mutants has been studied by X-ray diffraction, some elude crystallization. There is also debate regarding the structure that RNA fragments adopt after cleavage by h-ANG. Here, to better understand the beginning of the process that leads to aberrant protein oligomerization, the solution secondary structure and residue-level dynamics of WT h-ANG and two mutants: H13A and R121C, are characterized by multidimensional heteronuclear NMR spectroscopy under near physiological conditions. All three variants are found to adopt well folded and highly rigid structures in solution, although the elements of secondary structure are somewhat shorter than those observed in cystallography studies. R121C alters the environment of nearby residues only. By constrast, the mutation H13A affects local residues as well as nearby active site residues residues K41 and H119. The conformation characterization by CD and 1D 1H NMR spectroscopies of tRNAAla before and after h-ANG cleavage reveals a retention of most duplex structure and little or no G-quadruplex formation.

The research paper presents a new approach towards constructing motion equations for structures with attached MTMDs (multiple tuned mass dampers). A primary system, with MDOF (multiple dynamic degrees of freedom) was reduced to an equivalent system with a SDOF (single degree of freedom) through the modal approach, and equations from additional MTMDs were added to a thus-created system. Optimization based on H2 and H∞ for the transfer function associated with the generalized displacement of an SDOF system. The research work utilized GA (genetic algorithms) and SA (simulated annealing method) optimization algorithms to determine the stiffness and damping parameters for individual TMDs. The effect of damping and stiffness (MTMD tuning) distribution depending on the number of TMDs was also analyzed. The paper also reviews the impact of primary system mass change on the efficiency of optimized MTMDs, as well as confirms the results of other authors involving greater MTMD effectiveness relative to a single TMD.

The sound field properties for non-cavitating marine propellers are studied using FW-H (Ffowcs William-Hawkings) acoustic analogy and BEM (Boundary Element Method) approach. For the first time, the FW-H formula to calculate acoustic pressure generated by the propeller wake sheet is proposed. The corresponding sound signal can be dominant up to several kilometres. Secondly, non-physical fictitious volume flux is observed when the permeable FW-H approach is used together with BEM. The reason is explained and a virtual source correction method is proposed to solve this problem. Furthermore, analytical analyse show that the second thickness term and the first two loading terms in Farassat 1A formula are important, and the others are negligible. The numerical studies show that the permeable FW-H approach produces underestimation when compared to the direct FW-H method, and the underestimation is severer for larger permeable surface and higher frequency. It is also found that the first loading term in Farassat 1A formula is the dominant source term in the direct FW-H method, while the first thickness term is dominant when the permeable FW-H approach is used.

Cotton is one of the most important economic crops in the world, whereas insect attacks is a prime cause of its losses on yield and quality. Despite it is important, little is known about the mechanism of cotton response to insect. In this study, we simulated insect feeding by applying insect oral secretions (OS) to wounds, and combined transcriptome and metabolome analysis to comprehensively investigate how OS from two major pest species (Helicoverpa armigera and Spodoptera litura) affect cotton defense responses. Obvious differences were observed that 12,668 and 13,379 genes differently expressed respectively in cotton after being treated with different OS when compared with wounding along. Upon the addition of OS, JA-signaling pathway were rapidly and strongly induced, however SA-biosynthesis related gens were significantly down-regulated. By constructing the co-expression gene network, we identified a hub gene which encoding a leucine-rich repeat receptor kinase may play important role in recognition and signal transduction at early stage. We also found that OS from different insect species altered abundance of flavonoid related compound with different patterns. Interestingly, Gossypol which is a well-known anti-insect compound was kept a relative low content after OS application relative to wounding which implied the existence of the suppression effects of OS to cotton defense response. This study illustrated the transcriptional and metabolic changes of cotton in responding to OS from two chewing insect species, identified potential key gene during the interaction process and finds the evidence for OS’s inhibition effects on cotton defense response.

The Koka gold deposit is located in the Elababu shear zone between the Nakfa terrane and the Adobha Abiy terrane, NW Eritrea. Based on the paragenetic study two main stages of gold mineralization were identified in the Koka gold deposit: 1) an early stage of pyrite-chalcopyrite-sphalerite-galena-gold-quartz vein; and 2) a second stage of pyrite-quartz veins. NaCl-aqueous inclusions, CO2-rich inclusions, and three-phase CO₂-H₂O inclusions occur in the quartz veins at Koka. The ore-bearing quartz veins formed at 268℃, from NaCl-CO₂-H₂O(-CH₄) fluids averaging 5 wt% NaCl eq. The ore-forming mechanisms include fluid immiscibility during stage I, and mixing with meteoric water during stage II. Oxygen, hydrogen and carbon isotopes suggest that the ore-forming fluids originated as mixtures of metamorphic water, meteoric water and magmatic water, whereas sulfur isotope suggest an igneous origin. Features of geology and ore-forming fluid at Koka deposit are similar to those of orogenic gold deposits, suggesting the Koka deposit might be an orogenic gold deposit related to granite.

A series of penta-1,4-dien-3-one containing a H-phosphonate scaffold were designed and synthesized. The structures of all title compounds were determined by 1H-NMR, 13C-NMR, 31P-NMR, and HRMS. Bioassay results showed that several of the title compounds exhibited remarkable antibacterial and antiviral activities. Among these, compounds 3c and 3o exhibited substantial antibacterial activities against Xanthomonas oryzae pv. Oryzae (Xoo) and Xanthomonas axonopodis pv. citri (Xac). In addition, compounds 3c, 3f, and 3r showed remarkable curative activities against tobacco mosaic virus (TMV), with 50% effective concentration (EC50) values of 290.0, 234.0, and 373.6 μg/mL, respectively. These were superior to that of ningnanmycin (386.2 μg/mL). Compound 3r exhibited comparative protective activity against TMV, with an EC50 value of 291.1 μg/mL, which was better than that of ningnanmycin (297.1 μg/mL). Notably, the solubility of all title compounds improved relative to the lead compound curcumin. These results suggest that penta-1,4-dien-3-one containing a H-phosphonate scaffold may be considered as an activator for antibacterial and antiviral agents.

The number of citations that a paper has received is the most commonly used indicator to measure the quality of research. Researchers, journals, and universities want to receive more citations for their scholarly publications to increase their h-index, impact factor, and ranking respectively. In this paper, we tried to analyses the effect of the number of available Google Scholar versions of a paper on citations count. We analyzed 10,162 papers which are published in Scopus database in year 2010 by Malaysian top five universities. Then we developed a software to collect the number of citations and versions of each paper from Google Scholar automatically. The result of spearman correlation coefficient revealed that there is positive significant association between the number of Google Scholar versions of a paper and the number of times a paper has been cited.

In this article, we present two topics related to mathematical economics. We offer an intriguing proposal for securing cost and production functions in the face of uncertainty and risk. We discuss the relationship between individual and social preferences. This is important because traditional revealed preference theory does not account for such factors.

To generate a probability density function (PDF) for fitting probability distributions of real data, this study proposes a deep learning method which consists of two stages: (1) a training stage for estimating the cumulative distribution function (CDF) and (2) a performing stage for predicting the corresponding PDF. The CDFs of common probability distributions can be adopted as activation functions in the hidden layers of the proposed deep learning model for learning actual cumulative probabilities, and the differential equation of trained deep learning model can be used to estimate the PDF. To evaluate the proposed method, numerical experiments with single and mixed distributions are performed. The experimental results show that the values of both CDF and PDF can be precisely estimated by the proposed method.

In this paper, we establish some inequalities bounding the ratio Г_p,k(x)/Г_p,k(y), where Г_p,k(.) is the (p,k)-analogue of the Gamma function. Consequently, some previous results are recovered from the obtained results.

According to the fact that the low convergence level on the complete elliptic integral of the first kind for the modulus which having values approach to one. In this paper we propose novelty of the complete elliptic integral consists of the new infinite series. We apply the scheme of iteration by substituting the common modulus with own modulus function into the new infinite series. We obtained so many new exact formulas of the complete elliptic integral derived from this method correspond to the number of iteration order. On the other hand, it has been also obtained a lot of new modulus functions rather than common used previously. The calculation results show that the number of significant figures of the new infinite series of the complete elliptic integral of the first kind is increased more and more. It means more fastly convergent would be obtained comparison values with the previous infinite series.

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.

The primary purpose of this article is to deduce specific order estimates for the \textit{Mertens Function} $M(n)$, which facilitates us to analyze the location of zeros of the \textit{Riemann Zeta function} $\zeta(s)$. The paper also provides a brief overview about the notion of the \textit{Mertens Function} $M(n)$ and \textit{Redheffer Matrices} $\mathbb{A}_{n}$. In addition to learning about various \textit{spectral properties} of $ \mathbb{A}_{n}$, we shall also deduce the relation between these two, which, eventually would lead us to establish a necessary and sufficient condition for the \textit{Riemann Hypothesis} to hold true, as justified by \textit{Redheffer} himself. We shall also observe several numerical evidence as well as theoretical justification behind the falsity of the famous \textit{Mertens Hypothesis}, along with how researchers over the years have approached towards deriving an estimate of the smallest possible natural number $n$ for which the first such violation of the theorem occurs, utilizing numerous conjectures annotating about the order of $M(n)$. Readers who are highly motivated in pursuing research in any of the topics relevent to the contents of this paper will surely find the \texttt{References} section to be extremely resourceful.

We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, inverse trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.

In history, theta function identities have been studied extensively and deeply. In this paper, applying the residue theorem of an elliptic function, we obtain a parameterized theta function identity. Then, by selecting the appropriate parameter, we derive some famous Jacobi identities, as well as other relatively simple theta function identities.

In this paper, an analytical form of the Unit Step Function (or Heaviside Step function) is presented. This important function constitutes a fundamental concept of Operational Calculus and is also involved in many other fields of applied and engineering mathematics. In particular, Heaviside Step Function is performed in a very simple manner by the use of a finite number of standard operations, as the summation of six inverse tangent functions. The novelty of this work when compared with other analytical expressions, is that the proposed exact formula contains two arbitrary single - valued continuous functions which satisfy only one restriction. In addition, the proposed representation is not exhibited in terms of miscellaneous special functions, e.g. Bessel functions, Beta function, Logistic function. Besides, it is neither the limit of a function, nor the limit of a sequence of functions with point – wise or uniform convergence. Hence, this formula may be much more practical, flexible and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

A new set of basis functions is presented. The foundation in mathematics is established. To reconstruct a signal, it is compared to the Fourier basis functions. The M-basis functions' potential applications are also presented.

I want to find an extension of the Hausdorff Measure and Fractal Measure which allows me to compute a unique, satisfying average for functions defined on non-fractal, measurable sets in the sense of Carathedory which has no gauge function.

We consider the inverse function $z=g(w)$ of a (normalized) starlike function $w=f(z)$ of order $\alpha$ on the unit disk of the complex plane with $0<\alpha<1.$ Krzy{\. z}, Libera and Z\l otkiewicz obtained sharp estimates of the second and the third coefficients of $g(w)$ in their 1979 paper. Prokhorov and Szynal gave sharp estimates of the fourth coefficient of $g(w)$ as a consequence of the solution to an extremal problem in 1981. We give a straightforward proof of the estimate of the fourth coefficient of $g(w)$ together with explicit forms of the extremal functions.

In this paper, the author obtains an analytic exact form of Heaviside function, which is also known as Unit Step function and constitutes a fundamental concept of the Operational Calculus.In particulat, this function is explicitly expressed in a very simple manner by the aid of purely algebraic representations. The novelty of this work is that the proposed explicit formula is not performed in terms of non – elementary special functions, e.g. Dirac delta function or Error function and also is neither the limit of a function, nor the limit of a sequence of functions with point wise or uniform convergence. Hence, it may be much more appropriate and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

Edible oils have commercial and nutritional value due to the presence of essential fatty acids. They can be consumed fresh in the form of capsules known as nutraceuticals. The quality of such products is of interest to the consumer. In this context, this study describes a method based on high resolution nuclear magnetic resonance (NMR) and Fourier transform mid-infrared spectroscopic analysis (FTIR), combined with statistical analyzes to differentiate different edible oils used as nutraceuticals in Brazil by fatty acid content. Through the analysis of 1H NMR spectra, the levels of saturated and unsaturated fatty acids in edible oils were characterized and quantified. Statistical analysis of the data confirmed the real distinction between nutraceutical raw materials, with emphasis on ω-9, ω-6 and ω-3 fatty acids. The analytical approach presented also demonstrated potential to identify the origin (animal or vegetable) of edible oils used as nutraceuticals.

Cutaneous T cell lymphoma (CTCL) is a devastating, potentially fatal T lymphocyte malignancy affecting the skin. Despite all efforts, the etiology of the disease remains unknown. Infectious agents have long been suspected as factors or co-factors in CTCL pathogenesis. This review deals with the panel of bacterial and viral pathogens that have been investigated so far in an attempt to establish a potential link between infection/carriage and CTCL development. A special focus is given to a recently discovered human protoparvovirus, namely the cutavirus (CutaV), which has emerged as a plausible CTCL etiological agent. Available evidence in support of this hypothesis as well as alternative interpretations and uncertainties raised by some conflicting data are discussed. The complexity and the multifacetedness of the Parvoviridae family of viruses are illustrated by presenting another protoparvovirus, the rat H-1 parvovirus (H-1PV). H-1PV belongs to the same genus as the CutaV but carries a considerable potential for therapeutic applications in cutaneous lymphoma.