In this paper, the problem of predicting future failure times based on a jointly type-II censored sample from k exponential populations is considered. The Bayesian prediction intervals and point predictors were then obtained. Generalized Bayes is a Bayesian study based on a learning-rate parameter. This study investigated the effects of the learning rate parameters on the prediction results. The loss functions of squared error, Linex, and general entropy were used as point predictors. Monte Carlo simulations were performed to show the effectiveness of the learning rate parameter in improving the results of prediction intervals and point predictors.

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.

Due to the special characteristics of the shooting distance and angle of remote sensing satellites, the pixel area ratio of ship targets is small and the feature expression is insufficient, which leads to unsatisfactory ship detection performance and even situations such as missed detection and false detection. In this study, we propose an improved-YOLOv5 algorithm. The improvement strategies mainly include: (1) Add the Convolutional Block Attention Module (CBAM) into the Backbone to enhance the extraction of target-adaptive optimal features; (2) Introduce cross-layer connection channel and lightweight GSConv structure into the Neck to achieve higher-level multi-scale feature fusion and reduce the number of model parameters; (3) The Wise-IoU loss function is used to cal-culate the localization loss in the Output, and assign reasonable gradient gains to cope with dif-ferences in image quality. In addition, during the preprocessing stage of experimental data, a me-dian and bilateral filter method is used for noise reduction to reduce interference from ripples and waves and highlight the information of ship features. The experimental results show that Im-proved-YOLOv5 has a significant improvement in recognition accuracy compared to various mainstream target detection algorithms; Compared to the original YOLOv5s, the mean Average Precision (mAP) has improved by 3.2% and the Frames Per Second (FPN) has accelerated by 8.7%.

In the paper, by virtue of a Lévy–Khintchine representation and an alternative integral representation for the weighted geometric mean, the authors establish a Lévy–Khintchine representation and an alternative integral representation for the Toader–Qi mean. Moreover, the authors also collect an probabilistic interpretation and applications in engineering of the Toader–Qi mean.

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.

Purpose: This research compared the dissociated phoria at near and distance fixation in free space using three techniques: the Howell test, alternate Cover test, and Thorington test. Methods: 220 healthy Mexican children (age 5.06-17.11) participated in this study. Phorias were quantified at both distances using each test, from the least to the most disruptive. The stereopsis degree and near point of convergence (break/recovery) were analyzed to understand their role on the visual system's sensorimotor balance. Results: For the exophoria/esophoria at near, the alternate Cover and Thorington tests showed similar values. The exophoria at distance, was similar with the alternate Cover and Howell tests, while esophoria, with the alternate Cover and Thorington tests. The break value and near exophoria relates to each other and affect the stereopsis degree, whereas age is associated with the stereopsis degree and break value. Conclusions: The analysis revealed that alternate Cover and Thorington tests can substitute one another, but not with the Howell test. The test's specific dissociation method may explain these results. Analyzing the binocular visual system provides information about its sensorimotor balance and fragility when faced to the technique’s degree of dissociation.

Generalized Bayes is a Bayesian approach based on the learning rate parameter η. In this study, we examine the effect of parameter η on the estimation results considering joint type-I and type-II hybrid censored samples from k exponential populations. In addition to the learning rate parameter, we consider two loss functions, the Linex and general entropy loss functions in the Bayesian approach. Monte Carlo simulations are performed to compare the performances of the estimation results under losses and different values of η. An illustrative example is performed to study the effect of the learning rate parameter and the different losses with different parameters.

Experimental tests and numerical analyses were carried out on short, thin-walled channel columns with modified cross-sectional shape. The columns were loaded with an axial compressive force applied at the center of gravity of the cross section. Tests were carried out on a universal testing machine, while numerical analyses were performed in ANSYS software. The purpose of the tests was to determine the values of critical forces for the compressed columns and to determine the values of maximum forces at which failure of the columns occurs. Critical forces were determined based on the strain-averaged method. Based on the study, it was found that the strength and resistance to loss of stability of columns is primarily affected by their stiffness, and therefore by the shape of the cross-sections. In addition, for short columns, it seems more important to determine the value of maximum forces than the values of critical forces.

Keywords: Chemical Intolerance, Drug Intolerance, Food Intolerance, QEESI, BREESI, Multiple Chemical Sensitivity, Toxicant-induced Loss of Tolerance, Prevalence

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.

In the paper, the authors establish two identities to express the generating function of the Chebyshev polynomials of the second kind and its higher order derivatives in terms of the generating function and its derivatives each other, deduce an explicit formula and an identities for the Chebyshev polynomials of the second kind, derive the inverse of an integer, unit, and lower triangular matrix, present several identities of the Catalan numbers, and give some remarks on the closely related results including connections of the Catalan numbers respectively with the Chebyshev polynomials, the central Delannoy numbers, and the Fibonacci polynomials.

This article lays the foundation for Extended Relativity (ER) – a unified geometric approach to the electromagnetic and gravitational field and relativistic dynamics in them. We explain here the basic tenets of ER, including the influenced spacetime of an object and the Extended Principle of Inertia. These two new ideas enable a unified theory of these fields. We introduce local scaling functions for describing the geometry of a spacetime influenced by a field and construct a simple, universal local scaling function which unifies electromagnetism and gravity. We recover the full electromagnetic theory, including Maxwell’s equations. For gravitation, ER passes all of the tests of General Relativity. Despite the non-linearity of relativistic gravitation, we obtain a method of combining fields from multiple sources. Finally, we identify the differences in the relativistic treatment of the electromagnetic field by Special Relativity and of the gravitational field by General Relativity and indicate how these differences are resolved in ER.

Considering the spectrum shortage problem of IoT devices, we introduce a collaborative spectrum sensing (CSS) framework in this paper to identify available spectrum resources, so that IoT devices can access it and meanwhile avoid causing harmful interference to the normal communication of the primary user (PU). However, in the process of the PU’s signal detection in IoT devices, the issue about the stopping time and decision cost arises. To this end, we propose a distributed cognitive IoT model, which includes two IoT devices independently using sequential decision rules to detect the PU. On this basis, we define the stopping time and cost function for IoT devices, and formulate an average cost optimization problem in CSS. To solve this problem, we further regard the optimal stopping time problem as a finite horizon problem, and solve the threshold of the optimal decision rule by dynamic programming. At last, numerical simulation results demonstrate the correctness of our proposal in terms of the global false alarm and miss detection probability, and it always achieves minimal average cost under various cost of each observation taken and thresholds.

Brugada syndrome (BrS) is an inherited disease characterized by right precordial ST-segment elevation on electrocardiograms (ECGs), and a high risk of life-threatening ventricular arrhyth-mia and sudden cardiac death. In BrS patients, except for SCN5A, mutations in other responsible genes are poorly elucidated. We identified a new missense mutation, c.1189C>T (p.R397C), in the KCNH2 gene in asymptomatic male proband with diagnosed BrS. We performed patch-clamp analysis on I(Kr) reconstituted with this KCNH2 mutation in Chinese hamster ovary cells and compared the phenotype with the wild type. We found that the R397C mutation increased the I(Kr) density. In silico modeling demonstrated that this missense mutation potentially leads to the shortening of action potential in the heart.

Japan is experiencing a super-aging society faster than is anywhere else worldwide. Consequently, extending healthy life expectancy is an urgent social issue. To understand diet that supports the extension of healthy life expectancy, we studied the relationships among quality of life (QOL: SF-36 questionnaire), physical activity (number of steps and activity calculated using an accelerometer), physical function (muscle strength, movement function, agility, static balance, dynamic balance, and walking function) and dietary intake among 469 older adults living in the Tokyo metropolitan area (65–75 years old, men/women = 166/303) from February 23, 2017, to March 31, 2018. There was a significant positive association between physical QOL and steps, moderate-intensity activity, and high-intensity activity (p < 0.05), and a significant positive association (p < 0.05) between physical activity and movement, static balance, and walking functions, but no association with muscle strength. These three body functions were significantly positively correlated with intake of vegetables, seeds, fruits, and milk, and with magnesium, potassium, vitamin B6, and the dietary fibre/carbohydrate ratio and composition ratios (p < 0.05). Balancing food and nutrition may improve QOL in older adults through increased physical function and physical activity. Future verification of interventions is needed.

This paper studies the goodness of fit test for the bivariate Hermite distribution. Specifically, we propose and study a Cramér-von Mises-type test based on the empirical probability generation function. The bootstrap can be used to consistently estimate the null distribution of the test statistics. A simulation study investigates the goodness of the bootstrap approach for finite sample sizes.

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.

Internet of things security will be a big challenge for the enterprises working behind the build-up of the internet of things, and it’s application. With IoT, another buzzword is blockchain-based cryptocurrency bitcoin. Blockchain technology has proven itself as one of the most secured existing technology. In this paper, we have discussed the significant challenges that will come up in identity management due to the heterogeneity of devices. We have proposed a solution for privacy preservation using secure identity management and possible communication methodology by using public key-based cryptography used in the blockchain. We have taken the ecosystem of smart home management and smart health management. At last, we have concluded with the discussion of futuristic applications of blockchain in other applications of the internet of things.

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.

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.

In recent decades, the Variational AutoEncoder (VAE) model has shown good potential and capabilities in image generation and dimensionality reduction. The combination of VAE and various machine learning frameworks has also worked effectively in different daily life applications, however its possibility and effectiveness in modern game design has seldom been explored nor assessed. The use of its feature extractor for data clustering was minimally discussed in literature neither. This paper first attempts to explore different mathematical properties of the VAE model, in particular, the theoretical framework of the encoding and decoding processes, the possible achievable lower bound and loss functions of different applications; then applies the established VAE model into generating new game levels within two well-known game settings; as well as validating the effectiveness of its data clustering mechanism with the aid of the Modified National Institute of Standards and Technology (MNIST) database. Respective statistical metrics and assessments were also utilized for evaluating the performance of the proposed VAE model in aforementioned case studies. Based on the statistical and spatial results, several potential drawbacks and future enhancement of the established model were outlined, with the aim of maximizing the strengths and advantages of VAE for future game design tasks and relevant industrial missions.

Fruits and vegetable diagnosis and inspection is a crucial part of quality control and health safety. From harvesting to retailing, stakeholders encounter tons of food losses due to the lack of monitoring of the fruit condition in retail. The problem gets worse because it is being handled by many people, including retailers and customers. We propose a transparent fiberglass-made vertical fruit showcase, which provides 80 percent more visibility, takes lesser shop space, and prevents human contact. It is convenient for the retailer and customer to use. Moreover, the controlled fruit environment is easy to integrate with IoT, which will help to generate consensus data for fruit management decisions in machine learning.

The aim of this study was to evaluate the clinical and radiographic outcomes of the All-on-4 technique in fully edentulous maxilla using R2GATE software for flapless, computer-guided surgery and immediate loading. Ten adult patients with fully edentulous maxilla, aged between 35 and 60 years, were included in the study between April 2021 and April 2022. The surgical procedure was performed under local anesthesia and followed the All-on-4 approach with immediate loading of implants using a screw-retained provisional acrylic resin prosthesis on the same day. Final prosthesis was delivered four months after the surgery. Clinical and radiographic outcomes were evaluated at four- and twelve-months post-operation. The study reported a 95% implant survival rate using the All-on-4 technique. The mean marginal bone level was recorded at 0.35 mm and 0.66 mm during the 4 and 12-month follow-up periods, respectively. Fixed provisional prosthesis fracture, abutment, and prosthesis screw loosening were the most frequent mechanical complications reported. Within the limitations of this study, the use of computer-guided surgery in the All-on-4 technique seemed to be a promising treatment option with high implant survival rates that may help reduce post-surgical discomfort and mechanical complications in the rehabilitation of the edentulous maxilla.

Olfactory dysfunction affects often has severe consequences on patients’ quality of life. The most common complaint in these patients is their reduced enjoyment of food in both patients with olfactory loss and parosmia. How the different types of olfactory dysfunction differ in relation to food and cooking habits, sensory awareness, and food-related quality of life has not yet received much attention. By applying questionnaires on cooking, food, olfactory function, weight changes, sensory awareness, and food-related quality of life, we investigate how various aspects of eating differ between participants with olfactory loss (n=271), parosmia(n=251), and normosmic controls(n=166). Cooking habits in olfactory dysfunction revealed pronounced differences as compared with normosmic controls. Cooking with olfactory dysfunction was associated with e.g., a lack of comfort and inspiration for cooking and an inability to make new foods successfully. Significant differences in cooking were also found between olfactory loss and parosmia. Food items were less familiar in participants with olfactory loss and parosmia, while the ratings of liking food items differed between olfactory loss and parosmia, indicating the importance of adapting ingredients in meals separately for olfactory loss and parosmia. Parosmia was associated with a higher incidence of weight loss, but we found no difference in the food-related quality of life between participants with olfactory loss and parosmia. While olfactory loss and parosmia have wide-ranging consequences on patients’ cooking and food habits, adapting meals to include ‘safer food items’ and integrating multisensory stimulation may be a possible avenue for improving the enjoyment of food.

Rapeseed (Brassica napus) is one of the most important oil crops in the world; however, drought significantly curtails its growth and productivity. Identifying drought-tolerant germplasm is an efficient and low-cost strategy for addressing water shortages. Using water loss ratio (WLR) as an index of drought tolerance, we screened a panel of 265 B. napus lines. We identified eight low-WLR and six high-WLR accessions, which were regarded as drought-tolerant and drought-sensitive, respectively. Further validated these selected accessions at the seedling stage under drought-stress conditions. The drought-tolerant accessions had significantly greater fresh and dry weights under drought stress than the drought sensitive accessions. Using RT-qPCR, we showed that a set of previously reported drought-adaptive marker genes were expressed at higher levels in the drought-tolerant lines than in the drought-sensitive lines. These results indicated that the drought-tolerant genotypes could be identified from natural populations using WLR. Then, we performed a genome-wide association study to identify loci harboring single nucleotide polymorphisms (SNPs). A total of 139 SNPs were significantly associated with the WLR, of which chromosome A10 harbored the largest number. Furthermore, four putative candidate genes were selected by combining the SNP–WLR association results and transcriptional expression data with the changes in drought tolerance. Thus, we have identified two drought-tolerant B. napus cultivars and uncovered genome-wide variation differentiating B. napus lines related to WLR, in addition to providing insights for further research into WLR-related drought mechanisms.

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.

This research paper aims to explicate the complex issue of the Riemann's Hypothesis and ultimately presents its elementary proof. The method implements one of the binomial coefficients, to demonstrate the maximal prime gaps bound. Maximal prime gaps bound constitutes a comprehensive improvement over the Bertrand's result, and becomes one of the key elements of the theory. Subsequently, implementing the theory of the primorial function and its error bounds, an improved version of the Gauss' offset logarithmic integral is developed. This integral serves as a Supremum bound of the prime counting function Pi(n). Due to its very high precision, it permits to verify the relationship between the prime counting function Pi(n) and the offset logarithmic integral of Carl Gauss. The collective mathematical theory, via the Niels F. Helge von Koch equation, enables to prove the RIemann's Hypothesis conclusively.

Manipulating autophagy is a promising strategy for treating cancer as several autophagy inhibitors shown to induce autophagic cell death. One of these, autophagonizer (APZ), induces apoptosis-independent cell death by binding an unknown target via an unknown mechanism. To identify APZ targets we used a label-free drug affinity responsive target stability (DARTS) approach with a liquid chromatography/tandem mass spectrometry (LC-MS/MS) readout. Of 35 protein interactors, we identified Hsp70 as a key target protein of unmodified APZ in autophagy. Either APZ treatment or Hsp70 inhibition attenuates integrity of lysosomes, which leads to autophagic cell death exhibiting an excellent synergism with a clinical drug, temozolomide, in vitro, in vivo, and orthotropic glioma xenograft model. These findings demonstrate the potential of APZ to induce autophagic cell death and its development to combinational chemotherapeutic agent for glioma treatment. Collectively, our study demonstrated that APZ, a new autophagy inhibitor, can be used as a potent antitumor drug candidate to get over unassailable glioma and revealed a novel function of Hsp70 in lysosomal integrity regulation of autophagy.

During flux weakening operation time (FWOT), the total iron loss rises and affects the accuracy of loss prediction and efficiency especially if a large range of FWOT exists. Iron loss prediction is widely employed in investigations for a fast electrical machine analysis using 2-D FEA. This paper studies harmonic loss analytically by a steady-state equivalent circuit. Consideration of skin effects and iron saturation are utilized in order to examine the accuracy through the relative error distribution in the frequency domain of each model from 50 to 700 Hz. Additionally, this comparative study presents a torque-frequency-flux density calculation over each single term of the modified IEM-formula. The analytical calculation is performed using 2-D FEA for a classic and modified IEM-formula along with experimental verifications on a surface-mounted PMSG for a wind generation application.

The COVID-19 pandemic is one of the worst catastrophes that we have faced globally in recent years. It has not only taken its toll on the economic sector but also on the education sector. The social distancing norms that are in place as a direct response to the pandemic have turned conventional classroom teaching into a problematic minefield; as such, students all over the world have been forced into unprecedented situations that have served only to worsen the situation. The current pandemic has given rise to one of the worst crises the 21^st Century has ever seen, resulting in a surge of unemployment. Many companies have taken the route of firing employees or making redundancies, as they cannot afford the monthly reimbursement for staff. While this issue primarily concerns full-time workers, it also carries significant consequences for students – a considerable number of students are required to earn their daily living costs, and, without a job, they cannot pay their educational fees, accommodation costs, or living expenses. This comprehensive study briefly discusses the multitude of problems faced by students in the UK regarding higher education, as a direct result of the coronavirus pandemic. It contains six individual sections: a detailed introduction; the methodological procedures employed; educational disruptions, covering issues from hindrances in field research to examinations and student evaluations; personal problems experienced by students, such as accommodation and loss of income; concerns arising from the global pandemic; and finally, a conclusion and summary of the study’s findings.

We analyzed signal transduction of three constitutively activating mutants (M410T, L469R, and D590Y) and two inactivating mutants (D417N and Y558F) of the eel luteinizing hormone receptor (eel LHR), known to occur in human LHR. The objective of this study was to assess the functional effects of these mutations in signal transduction and cell surface loss of receptor. Mutant receptors were transiently expressed in Chinese hamster ovary (CHO-K1) cells. Eel LH-stimulated accumulation of cyclic adenosine monophosphate (cAMP) was measured by homogeneous time-resolved fluorescence (HTRF) assays. The loss of receptors from the cells surface was measured using an enzyme-linked immunosorbent assay (ELISA) in human embryonic kidney (HEK) 293 cells. The cAMP response in cells expressing the wild type eel LHR was increased in a dose-dependent manner using eel LH ligand stimulation. Compared with the wild type, cells expressing the activating mutants (M410T, L469R, and D590Y), exhibited a 4.0-, 19.1-, and 7.8-fold increase in basal cAMP response without agonist stimulation, respectively. Their maximal responses to agonist stimulation were approximately 65%, 52%, and 98%, respectively, of those of the wild type. The inactivating mutants (D417N and Y558F) did not completely impair signal transduction, and their maximal responses were only 33% and25 % of those of wild type. These data clearly showed that the eel LHR-L469R and D590Y, activating mutants enhanced the rate of the loss of cell surface receptors following treatment with eel LH. Thus, the loss of cell surface receptors in cells expressing mutant eel LHRs was consistent with the eel LH agonist-induced production of cAMP. Our results suggested that the activation of the eel LHR requires appropriate loss of LHR-ligand complexes from the cell surface.

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.

This paper investigated reliability modeling for systems subject to dependent competing risks considering that the variation of failure threshold is not considered in most studies on competing failure reliability. Firstly, the variation of degradation quantity under shocks was analyzed, and the variation of threshold was considered on this basis. Secondly, the cumulative degradation under the influence of the random shock process was analyzed. The attractive property of copula is symmetry. Then, A linear Wiener process model is applied to model performance degradation failure, and a multi-performance-degradation correlated-competition model based on a Copula function is constructed, which considers the correlated competition between multiperformance degradation failures. Lastly, the micromotor system is used to analyze the applicability of the proposed model for bivariate instances. demonstrating the rationality and effectiveness of the proposed model.

The affected upper limb in children with Unilateral Spastic Cerebral Palsy (US CP) has motor and somatosensory impairments, that contribute negatively to children’s bimanual performance and quality of life. Mirror Therapy (MT) is being studied to become an approachable intensive and home-based therapy, suitable for children with US CP. The aim of this study is to examine the feasibility of a 5-week home-based program of MT for children with US CP. Six children aged 8-12 years old performed the therapy, five days per week, 30 minutes per day. A minimum of an 80% of compliance was required. The evaluations included the feasibility of the therapy (compliance, total dosage, perceived difficulty of the exercises, and losses of follow-ups and evaluations), the bimanual performance, the somatosensory function and the quality of life at baseline, at the end of the intervention, and at 1-month follow-up. All children completed the therapy and were included in the analysis. The total accomplishment was 86.47 ± 7.67. The perceived difficulty of the exercises ranged from 2,37 to 4,51. As a conclusion, a home-based program of Mirror Therapy is suitable and feasible for children with US CP.

By defining a constant probabilistic orbit of and iterated functions, the stability dynamics of these functions in possible interactions through connectivity provides the formation of a dynamic fixed point as a metric space between both iterated functions. The presence of a dynamic fixed point identifies qualitatively phases of iteration time lengths and interaction orbits of the event. Qualitative results show that the greater the average distance from one of the functions to the fixed point of the other (all possible solutions), the higher the iteration expression on time (false asymptotic effect) of one of the functions and in the opposite hand, the lower the average distance, the higher orbit’s interactions proximity between iterated functions (stability). This feature reveals asymptotic (well-defined) behavior between functions f and g within a well-defined Lyapunov stability.

Ecological changes evoke many felt losses and types of grief. These affect sustainability efforts in profound ways. Scholarship on the topic is growing, but the relationship between general grief research and ecological grief has received surprisingly little attention. This interdisciplinary article applies theories of grief, loss, and bereavement to ecological grief. Special attention is given to research about “non-death loss” and other broad frameworks about grief. Dynamics related to both local and global ecological grief are discussed. Kinds of potential losses arising out of ecological issues are clarified with the frameworks of tangible/intangible loss, ambiguous loss, nonfinite loss, and shattered assumptions. Various possible types of ecological grief are illuminated by discussing the frameworks of chronic sorrow and anticipatory grief/mourning. Earlier scholarship about disenfranchised ecological grief is augmented by further distinctions about various forms it may take. The difficulties in defining complicated or prolonged grief in ecological context are discussed, and four types of “complicated ecological grief” are explored. Based on the findings, three special forms of ecological loss and grief are named and discussed: transitional loss and grief, lifeworld loss, and shattered dreams. The implications of the results for ecological grief scholarship, counselling and coping are briefly discussed. The results can be used by psychological and healthcare professionals and researchers, but also by members of the public who wish to reflect on their eco-emotions.

Family Phyllanthaceae is one of the largest segregates of the eudicot order Malpighiales and its species are herb, shrub, and tree, which are mostly distributed in tropical regions. Certain taxonomic discrepancies exist at genus and family level. Here, we report chloroplast genomes of three Phyllanthaceae species—Phyllanthus emblica, Flueggea virosa, and Leptopus cordifolius— and compare them with six others previously reported Phyllanthaceae chloroplast genomes. The species of Phyllanthaceae displayed quadripartite structure, comprising inverted repeat regions (IRa and IRb) that separate large single copy (LSC) and small single copy (SSC) regions. The length of complete chloroplast genome ranged from 154,707 bp to 161,093 bp; LSC from 83,627 bp to 89,932 bp; IRs from 23,921 bp to 27,128 bp; and SSC from 17,424 bp to 19,441 bp. Chloroplast genomes contained 111 to 112 unique genes, including 77 to 78 protein-coding, 30 transfer RNA (tRNA), and 4 ribosomal RNA (rRNA) that showed similarities in arrangement. The number of protein-coding genes varied due to deletion/pseudogenization of rps16 genes in Baccaurea ramiflora and Leptopus cordifolius. High variability was seen in number of oligonucleotide repeats while analysis of guanine-cytosine (GC) content, codon usage, amino acid frequency, simple sequence repeats analysis, synonymous and non-synonymous substitutions, and transition and transversion substitutions showed similarities in all Phyllanthaceae species. We detected a higher number of transition substitutions in the coding sequences than non-coding sequences. Moreover, the high number of transition substitutions was determined among the distantly related species in comparison to closely related species. Phylogenetic analysis shows the polyphyletic nature of the genus Phyllanthus which requires further verification. We also determined suitable polymorphic coding genes, including rpl22, ycf1, matK, ndhF, and rps15 which may be helpful for the reconstruction of the high-resolution phylogenetic tree of the family Phyllanthaceae using a large number of species in the future. Overall, the current study provides insight into chloroplast genome evolution in Phyllanthaceae.

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.

After the first release of synthalin B (dodecamethylenbiguanide) in 1928 and its later retraction in the 1940s in Germany and the retraction of phenformin (N-Phenethylbiguanide) because of the letal complication of acidosiss,metformin (1-1-dimethylbiguanide) was first released in France in 1959 and then in the USA in 1995 for oral treatment of diabetes type 2. Acute gastrointestinal side effects often lead to dose reduction and strongly limit adherence to therapy.Main long-term consequences are deficency of vitamin B12 and of iron and sometimes also acidosis development. Intravenously injected F18-labelled glucose in metformin-treated type 2 diabetics accumulates in the the small and even more in the large intestine.The densitometry picture observed in metformin-treated diabetics is similar to that observed in patients after bowel-cleansing or chronically taking different types of laxatives where the accumulated radioactivity can even reach values observed in colon cancer. The glucose-lowering mechanism of action of metformin is therefore not only due to inhibition of glucose uptake in the small intestine but also to „attraction“ of glucose from the hepatocyte to the intestine,possibly through its secretion into the bile.Metformin is not different from the other biguanides ,synthalin B and phenformin.The mechanism of action,and the side effects are comparable to those of laxatives.

Background: Tuberculosis (TB) continues to be a serious public health threat that affects the most vulnerable population. Patients who are LTFU after TB diagnosis still represent one of the biggest challenges to TB control. Method: In this prospective observational study, we aimed to identify and analyse the risk factors associated with LTFU among TB patients who started first-line TB treatment in the Sanatorium Hospital in Luanda. Result: A total of 113 patients with TB were included between August 2018 and September 2019. Seventy-six (67.3%) patients were cured, 27 (23.9%) were LTFU, 5 (4.4%) died, 4 (3.5%) were transferred and 1 (0.9%) presented a treatment failure. After excluding those dead, transferred or who failed to treatment, we observed that severe TB at the time of diagnosis (OR 9.24, 95% CI 2.18-39.04) and food insecurity were significantly associated with LTFU (OR 5.96, 95% CI 1.66-21.41). Conclusion: The findings of our study are of enormous value to understand the reasons for the LTFU of patients with TB and can guide polices and facilitate designing measures to allow better adherence, and therefore, greater treatment success

Hearing loss that arises from various causes at different stages of life has a direct impact on individuals' physical and mental well-being. This paper aimed to evaluate the employment, workplace adaptation, productivity, and professional success of individuals who have hearing loss and whose hearing loss is corrected with a cochlear implant. In this cross-sectional study, the data was collected between November 2022 and March 2023 with the participation of individuals with cochlear implants living in several settlements in all regions of Türkiye. A total of 142 participants with severe hearing loss who were corrected with a cochlear implant were included in this study. The survey method was used to collect data for the study. The questionnaire consisted of 32 questions and was distributed to the participants online. In the first part of the questionnaire (1-10 questions), general characteristics of implant patients were investigated. In the second part (11-32 questions), the positive or negative effects of implantation on the work life of the participants were evaluated. Almost half of the research group (49.3%, n = 70) consisted of women, and the mean age of the participants was determined to be 35.8 ± 14.8. There was no significant difference between gender, educational status, implanted side, working time, working style (physical, desk), and factors affecting work life (p > 0.05). Professional satisfaction and success at work increased significantly more in those with acquired hearing loss (p = 0.010). Post-implantation workplace compliance, success, and productivity were found to be higher in those with acquired hearing loss (p = 0.013). It was observed that hearing loss had a greater negative impact on the work life of married people (p = 0.006). Cochlear implantation greatly enhances workplace satisfaction, increases self-confidence, and has a positive impact on the future of profoundly deaf individuals.

Children with hearing loss have been found to have significantly more behavioral and emotional challenges than their typically hearing peers, though these outcomes are variable at the individual level. Working memory deficits have been found to relate to executive functioning and overall emotion regulation, leading to behavior challenges. Language development is essential for development of social relationships and communicating one’s needs - this may lead to distress when children cannot communicate effectively. Based on prior findings in children with hearing loss and their typically hearing peers, working memory and language skills were hypothesized to be related to parent and teacher report of socioemotional functioning. Participants were 35 children with hearing loss (66% female, M = 5.17 years old, SD = ±1.97) whose language, working memory, and socioemotional functioning were evaluated during the course of treatment and educational planning. Bivariate analyses indicated that working memory was related to a number of socioemotional domains (e.g., functional communication, atypicality, withdrawal), as were language scores (e.g., social skills, inattention). The direction of these associations was such that stronger working memory and language skills were related to more regulated socioemotional functioning. A call to action of the current study includes more education with regard to profiles and presentations of children with hearing loss, and an early focus on socioemotional learning to foster the development of regulatory skills.

Radiotherapy is a crucial treatment for head and neck malignancies, but it usually leads to sensorineural hearing loss (SNHL). Changes in the immune microenvironment and sensorial neuroepithelium of the inner ear after radiation exposure remain poorly understood. This study investigated cochlear morphology and macrophages in the inner ear after high-dose irradiation. The heads of 8-week-old Cx3cr1GFP/+ heterozygous male mice were irradiated with 30Gy X-rays and biological samples were taken on the 1st, 7th, and 10th days after irradiation. Auditory brainstem responses were used to assess auditory function in mice. The changes of basal membrane hair cells, spiral ganglion (SGN), and inner ear macrophages were observed using hematoxylin-eosin (HE) staining and immunofluorescence staining. The expression of inflammatory mediators in the inner ear was detected by reverse transcription-polymerase chain reaction (RT-PCR) in cochlear tissue. As a result, there was no significant hair cell loss after high doses of radiation, but the mice developed full-frequency hearing loss on day 10 when HE staining revealed SGN atrophy and immunofluorescence revealed decreased neurofilament expression. The number of macrophages in the inner ear decreased over time. RT-PCR showed that cochlear inflammatory factors and chemokines were briefly up-regulated on the first day after irradiation and then decreased over time. In summary, high-dose irradiation causes acute SNHL that does not involve hair cell loss and may be associated with SGN changes. Radiation-induced SNHL is accompanied by a reduction in cochlear macrophages and changes in the immune microenvironment, but the relationship between the two has yet to be explored.

Estimating age at death is essential to establish a biological profile from human skeletal remains in both forensic and archeological settings. Imaging studies of skeletal age changes in adults have described metamorphosis of trabecular bone structure and bone loss in the proximal femur , as well as changes in morphology during different stages of life. This study aims to assess the utility of a digital representation of conventional X-ray films of the proximal femur for the estimation of age at death in a sample of 91 adult individuals (47 females and 44 males) of the Coimbra Identified Skeletal Collection. The proposed approach showed a root mean squared error (RMSE) of 17.32 years (and mean absolute error of 13.47 years) for females and an RMSE of 14.06 years (mean absolute error of 11.08 years) for males. The main advantage of this approach is the consistency in the feature detection and extraction, as X-ray images projected on the femora space will always produce the same set features to be analyzed for age estimation while more traditional methods rely heavily on operator experience which can lead to inconsistent age estimates among experts.

This article presents a new design of supporting tethers through the concept of force distribution. The transmitted force applied on tethers will be distributed on the new tether design area resulting in low acoustic energy transferred to anchor boundaries and stored energy enhancement. This technique achieves an anchor quality factor of 175,000 compared to 58,000 obtained from con-ventional tether design representing 3-fold enhancement. Also, the unloaded quality factor of the proposed design improved from 23,750 to 27,442 representing 1.2-fold improvements.

Results of profile loss measurements, including trailing edge flow details, are presented for the flow of an organic vapor through a linear turbine cascade. The so-called VKI-I blade profile from the open literature was chosen for the cascade, and the working fluid was NOVEC 649. Pitot probes and hot wire anemometry were employed to measure the flow field up and downstream of the cascade. Details of the unsteady flow caused by the trailing edge of the blades and the turbulent spectrum were investigated using hot-wire anemometry. The new organic vapor flow results were compared with literature data obtained for air and with the prediction of conventional literature loss models. It was found that under certain thermodynamic conditions, specific traditional loss models can reasonably predict organic Rankine cycle (ORC) turbines' profile loss. Still, significant deviations between the loss models and the experimental data can also occur.

Land use/land cover (LULC) changes have a substantial influence on ecosystem services. The objective of this study is to estimate LULC dynamics induced ecosystem service values (ESV) changes in Western Ethiopia. Data were acquired from Landsat images of the area for four periods (1990-2020), and 221 sample households. The areas of LULC classes and the improved ESV coefficients of Costanza et al (1997) were used estimate ESV changes in 1990-2020. Forest provides diverse provisions, regulatory, supportive and cultural services. Analysis of the Landsat images showed that forest, farmland, settlement, water body and bare-land were the major LULC classes in the study area. While forest ESV had accounted 46.1% (US$ 4.95 million) of the ESV of Wayu-Tuka district in 1990, farmland ESV constituted the largest share (63.3%, US$ 5.21 million) of the ESV of the area after 30 years (2020). The ESV of forest and bare-land showed decreasing trends in three decades (1990-2020) but the farmland service value revealed an increasing trend in the same periods. Forest ecosystem exhibited the largest service value loss (US$ 3.91 million) in 1990-2020; whereas, the service value gain of farmland was only US$ 2.2 million although farmland was responsible for the conversion of the largest area size (9,766.5 ha) from other land covers in 30 years. LULC change induced net ESV loss of the district in three decades (1990-2020) was 23.4% (US$ 2.51 million). Land conversion due to expansion of farmland (by 9,766.5 ha) and settlement (by 4,061.3 ha) was the main cause for the LULC dynamics and the significant ESV loss in 1990-2020. Thus, the government and local people should cooperate so as to curb the steady degradation of forest and its ecosystem services in Wayu-Tuka district, Western Ethiopia.

Vision loss can be avoided if diabetic retinopathy (DR) is diagnosed and treated promptly. Following are the main 5 DR stages: none, moderate, mild, proliferate, and severe. In this study, a deep learning (DL) model is presented that diagnoses all 5 stages of DR with more accuracy than previous methods. The suggested method presents two scenarios: case 1 with image enhancement using contrast limited adaptive histogram equalization (CLAHE) filtering algorithm in conjunction with an Enhanced Super-resolution generative adversarial network (ESRGAN), and case 2 without image enhancement; augmentation techniques are then performed to generate a balanced dataset utilizing the same parameters for both cases. Using Inception-V3 applied to the Asia Pacific Tele-Ophthalmology Society (APTOS) datasets, the developed model achieved an accuracy of 98.7% for case 1 and 80.87% for case 2, which is greater than existing methods for detecting the five stages of DR. It was demonstrated that using CLAHE and ESRGAN improves a model's performance and learning ability.

Stocks portfolio is a form of investment that can be used to minimize the risk of loss. In a stock portfolio, the value at risk (VaR) can be predicted through the portfolio return. If portfolio return variance is heteroscedastic risk prediction can be done by using VaR with ARIMA-GARCH or Ensemble ARIMA-GARCH model approach. Furthermore, the accuracy of VaR is tested through backtesting test. In this study, the portfolio formed from Astra Agro Lestari Ltd (AALI) and Indofood Ltd (INDF) stocks from 10/02/2012 to 10/01/2019. The results showed that the best model is ARIMA(0,0,[3])-GARCH(1,2) with AIC of -5.604 and MSE 1.874e-07.At confidence level of 95% and 1 day holding period, the VaR of the ARIMA(0,0,[3])-GARCH(1,2) was -0.3464. Based on the backtesting test, it is proven to be very accurate to predict the value of loss risk because the value of the violation ratio (VR) is equal to 0.

We study a localization of gravity through the matching point between non-inertial frames and local inertial frames. This localization of gravity is done through defining relative gravitational red-shift. This lead to an emergence of a timeless state in a mathematically consistent way. In this timeless state of gravity, we find a geometric interpretation of the speed of light and mass. The experimental support of the timeless state is the quantum entanglement and internal symmetries that are independent of time. Therefore gravity would be responsible for measurements independent of time including quantum entanglement. Timeless state in that sense explain why do we have gravity/gauge correspondence. We conjecture that the universe emerged from a black hole with a global $SU(3)\times SU(2)\times U(1)$ symmetry on its event horizon that produces gauge fields Electromagnetism, weak and strong nuclear force through localization of this global symmetry. Through the localization in the gravity field, the timeless measurements such as spin will be correlated with the varying of timeless measurement which is relative gravitational red-shift. We present a gravitational or geometric interpretation of spin-0, spin-1, and spin-1/2 states. We present an interpretation of why do we measure matter rather than anti-matter. We found that the Higgs scalar field is represented by the gravitational red-shift at every point in the space around the black hole. We derive the numerical value of the cosmological constant that agrees with experimental observations.

Background: Vitamin D was studied in regards to its possible impact on body mass reduction and metabolic changes in adults and children with obesity yet there were no studies assessing the impact of vitamin D supplementation during a weight management programme in children and adolescence. The aim of our study was to assess the influence of 26 weeks of vitamin D supplementation in overweight and obese children undergoing an integrated 12-months’ long weight loss programme on body mass reduction, body composition and bone mineral density. Methods: A double-blind randomized placebo-controlled trial. Vitamin D deficient patients ( <30 ng/ml level of vitamin D) aged 6-14, participating in multidisciplinary weight management programme were randomly allocated to receiving vitamin D (1200 IU) or placebo for the first 26 weeks of the intervention. Results: Out of the 152 qualified patients, 109 (72%) completed a full cycle of four visits scheduled in the programme. There were no difference in the level of BMI change. Although the reduction was greater in the vitamin D vs. placebo group (-4.28 ± 8.43 vs. -2.53 ±6.10) the difference was not statistically significant (p=0.319). Similarly the reduction in fat mass – assessed both using bioimpedance and DEXa was achieved, yet the differences between the groups were not statistically significant. Conclusions: Our study ads substantial results to support the thesis on no effect of vitamin D supplementation on body weight reduction in children and adolescents with vitamin D insufficiency undergoing a weight management programme. Trial registration no: NCT 02828228; trial registration date: 8 June 2016 registered in: ClinicalTrials.gov.

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.

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.

Variable-DOF (or kinematotropic) mechanisms are a class of reconfigurable mechanisms. The number of variable-DOF multi-loop planar mechanisms proposed so far is very limited. This paper proposes a novel 8-link variable-DOF planar mechanism with five motion modes. Firstly, a description of the 8-link variable-DOF planar mechanism is presented. Reconfiguration analysis of the 8-link mechanism is then carried out using an elimination and algebraic geometry hybrid approach. The analysis shows that the 8-link mechanism has one 2-DOF motion mode and four 1-DOF motion modes and can switch among three motion modes at four transition configurations and between two motion modes at the remaining four transition configurations. Geometric characteristics of the mechanism in different motion modes are also revealed. Unlike the variable-DOF planar mechanisms found in literature, the proposed 8-link mechanism has two inactive joints in one of its 1-DOF motion modes, and both 4R kinematic sub-chains of the mechanism must appear as parallelograms in a pair or anti-parallelograms in a pair in the same motion mode. As a by-product, a method for factoring trigonometric functions in two angles is proposed.

Taking care of stroke survivors can be taxing, however, it was understudied in Malaysia. This study aims to describe the burden of informal stroke caregivers within three months after hospital discharge. A longitudinal study design was conducted. Acute stroke survivors and their informal caregivers were recruited prior to hospital discharge, and the caregivers were interviewed by phone. Self-reported caregiver burdens were measured with Zarit Caregiver Burden Interview – Malay version (MZBI) and Caregiver Assessment of Function and Upset – Malay version (Malay-CAFU). The MZBI and Malay-CAFU scores were collected four times within three months. A total of 85 stroke survivors and 155 informal caregivers were recruited, with 58.1% of the caregivers were female. The stroke survivors had two caregivers on average. The mean (SD) scores for the three scales show a reduction, from 27.42 (12.73) in the first week to 17.77 (11.20) in the third month for MZBI, from 1.14 (0.94) to 0.62 (0.64) for instrumental activities of daily livings (IADL) of Malay-CAFU upset scale and 1.36 (1.00) to 0.78 (0.65) for activities of daily living (ADL) of Malay-CAFU upset scale in the same period. Stroke survivors may have several caregivers, usually their spouses or children. Within a short period, the caregiver’s burden was reduced. Early psychosocial support to alleviate the caregiver burden may be necessary.

The age of information (AoI) metric was proposed to measure the freshness of messages obtained at the terminal node of a status updating system. In this paper, the AoI of discrete time status updating system with probabilistic packet preemption is investigated by analyzing the steady state of a three-dimensional discrete stochastic process. Assuming the queue used in system is Ber/Geo/1/2*/η, which represents that the system size is 2 and the packet in buffer can be preempted by fresher packet with probability η. Instead of considering system’s AoI separately, we use a three-dimensional state vector (n,m,l) to simultaneously track the real time changes of the AoI, the age of packet in server, and the age of packet waiting in buffer. We give the explicit expression of system’s average AoI, and show that the average AoI of system without packet preemption is obtained by letting η=0. When η is set to 1, the mean of AoI of system having Ber/Geo/1/2* queue is obtained as well. Combining the results we have obtained and comparing them with corresponding average continuous AoIs, we propose a possible relationship between average discrete AoI with Ber/Geo/1/c queue and the average continuous AoI with M/M/1/c queue. For each of two extreme cases where η=0 and η=1, we also determine the stationary distribution of AoI using the probability generation function (PGF) method. The relations between average AoI and the packet preemption probability η, as well as AoI’s distribution curves in two extreme cases are illustrated by numerical simulations. Notice that the probabilistic packet preemption may occur, for example, in an energy harvest (EH) node of wireless sensor network, where the packet in buffer can be replaced only when the node collects enough energy. In particular, to exhibit the usefulness of our idea and methods and highlight the merits of considering discrete time systems, in this paper we give much more explanations showing that how the results about continuous AoI is derived by analyzing the corresponding discrete time system, and how the discrete age analysis is generalized to the system with multiple sources. In terms of packet service process, we also propose our idea to analyze system’s AoI when the service time distribution is relaxed to be arbitrary.

We study the connection between the phase and the amplitude of the wave function and the conditions under which this relationship exists. For this we use model of particle in a box. We have shown that the amplitude can be calculated from the phase and vice versa if the log Analytical uncertainty relations are satisfied.

Authors such as Schnoebelen (2012: 12) suggest that in some languages (cf. Navajo) certain dependent clauses are frequently used independently to “mark emotional evaluation and background information”. Evans (2007) uses the term insubordination to refer to this phenomenon. Our study focuses on a particular insubordinate construction introduced by the sequence ni que in Spanish, as in the example [¡Una carta cada día!] Ni que yo fuese Umbral. (CORPES 100), used as an independent clause with a sociopragmatic meaning which is different from that of its subordinate counterpart (cf. No escribiría una carta cada día ni que yo fuese Umbral). Our research questions ask about the potential for ni que to be used as a discourse marker fulfilling an expressive function when it introduces this type of construction, and the derived hypothesis is then oriented to test whether Schnoebelen's (2012) observation about insubordinate constructions applies also to this Spanish construction. In order to test this hypothesis, we performed a functional-discourse analysis of more than 2000 concordances (and their extended contexts) in Mark Davies' Corpus del Español and the Real Academia CORPES XXI. Our findings show that the insubordinate construction differs in function and meaning from its subordinate counterpart, the former fulfilling a stronger emotive function, often combined with other discourse-pragmatic functions, such as evaluation or the organization of discourse.

In this paper we analyze and propose new method and algorithm of selecting the optimal labor time as a function of skills following our main references Mirrlees (1971), Saez (2001) and Stancheva (2014). The optimal labor time is a situation when the utility function of individual reaches a maximum. One of the main differences with Saez (2001) is our algorithm for creation the skill distribution

In this paper we define a continuous wavelet transform of a Schwartz tempered distribution $f \in S^{'}(\mathbb R^n)$ with wavelet kernel $\psi \in S(\mathbb R^n)$ and derive the corresponding wavelet inversion formula interpreting convergence in the weak topology of $S^{'}(\mathbb R^n)$. It turns out that the wavelet transform of a constant distribution is zero and our wavelet inversion formula is not true for constant distribution, but it is true for a non-constant distribution which is not equal to the sum of a non-constant distribution with a non-zero constant distribution.

Suppose for n∈ ℕ, set A⊆ℝⁿ and function f∶A→ℝⁿ. If set A, using the Hausdorff outer measure, is measurable in the sense of Carathèodory; we want to find an extension of the expected value, w.r.t the Hausdorff measure, that's unique, finite and "natural" (defined on §2.3 & §2.4) for all f in a prevalent subset of ℝᴬ. The issue is current extensions of the expected value are finite for all functions in only a shy subset of ℝᴬ. The reason this issue wasn't resolved is mathematicians have not thought of the problem, focusing on application rather than generalization. Despite the lack of potential use, we'll attempt to solve the problem by defining a choice function---this shall choose a unique set of equivalent sequences of sets (Fₖ***) , where the set-theoretic limit of Fₖ*** is the graph of f; the measure Hʰ is the ℎ-Hausdorff measure, such for each k∈ℕ, 0 < Hʰ(Fₖ***) < +∞; and (fₖ*) is a sequence of functions where {(x,fₖ*(x))∶x∈ dom(Fₖ***)}=Fₖ***. Thus, the extended expected value of or E**[f,Fₖ***] is: ∀(ε>0)∃(N∈ℕ)∀(k∈N)(k≥N⇒1/Hʰ(dom(Fₖ***))∫dom(Fₖ*** )fₖ* dHʰ - E**[f,Fₖ***]<ε ) which should be unique, finite, and "natural" (defined on §2.3 & §2.4) for all f in a prevalent subset of ℝᴬ. Note we guessed the choice function using computer programming but we don’t use mathematical proofs due to the lack of expertise in the subject matter. Despite this, the biggest use of this research is the extension of the expected value is finite for "almost all" functions: this is easier to use in application when finding the "average" of functions covering an infinite expanse of space.

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.

The aim of this study is to obtain the Bayes estimators and the maximum likelihood estimators (MLEs) for the unknown parameters of the Rayleigh Weibull (RW) distribution based on progres-sive type-II censored samples. The approximate Bayes estimators are calculated using the idea of Lindley and Tierney-Kadane's approximation method under the squared-error loss function when the Bayes estimators are not handed in explicit forms. In this study, the approximate Bayes esti-mates are compared with the maximum likelihood estimates in the aspect of the estimated risks (ERs) using Monte Carlo simulation. In addition, the coverage probabilities of the parametric bootstrap estimates are calculated. Real lifetime data sets belonging to the cancer types as bladder cancer, head and neck cancer, and leukemia are used to illustrate the emprical results belonging to the approximate Bayes estimates, the maximum likelihood estimates, and the parametric bootstrap intervals.

This paper presents an approach to the two-dimensional analysis of elastic isotropic deep beams using the finite difference method (FDM). Deep beams are subjected to in-plane loading and present a shear span to height ratio of less than 2.50; consequently, Euler-Bernoulli beam theory and Timoshenko beam theory do not apply. Deep beams analysis is generally conducted using numerical methods such as the finite element method and to a lesser extent the FDM; the strut-and-tie model and the stress field method are also widely utilized. Analytical approaches usually make use of the Airy stress function, where stresses are formulated in terms of the stress function; however, the exact solution of this function satisfying all of the boundary conditions can hardly be found, even for simple cases. In this paper, deep beams were analyzed using the FDM. The FDM is an approximate method for solving problems described with differential equations. The FDM does not involve solving differential equations; equations are formulated with values at selected nodes of the structure. Therefore, the deep beam was discretized with a two-dimensional grid, and additional nodes were introduced at the boundaries and at positions of discontinuity (openings, brutal change of material properties, non-uniform grid spacing), the number of additional nodes corresponding to the number of boundary conditions at the node of interest. The introduction of additional nodes allowed us to apply the governing equations at boundary nodes and satisfy the boundary and continuity conditions. An Airy stress function approach and a displacement potential function approach were considered in this study whereby strong formulations of equations (equilibrium, kinematic, and constitutive) were set. Stress and stability analyses were carried out with this model; furthermore, deep beams of varying stiffness, layered beams, and beams having openings were analyzed. For slender beams, the results obtained with the Airy stress function approach showed good agreement with those of the Euler-Bernoulli beam theory, and for deep beams, the shapes of stress distributions were in good agreement with a proper understanding of the behavior of structures. On the other hand, the displacement potential function approach delivered unsatisfactory results, probably due to the use of an inefficient equation solver; a more powerful tool will be needed in future research for this purpose.

Partial shading on solar photovoltaic (PV) arrays is a prevalent problem in photovoltaic systems that impair the performance of PV modules and is responsible for reduced power output as compared to that in standard irradiance conditions thereby resulting in the appearance of multiple maximas on panel output power characteristics. These maxims contribute to mismatch power losses among PV modules. The mismatch losses depend on shading characteristics together with different interconnected configuration schemes of PV modules. The research presents a comparative analysis of partial shading effects on a 4 x4 PV array system connected in series(S), parallel (P), serries-parallel (SP),total-cross-tied (TCT),central-cross-tied(CCT),bridge-linked(BL),bridge-linked total cross-tied (BLTCT) ,honey-comb(HC), honey-comb total-cross-tied (HCTCT) and ladder (LD) configurations using MATLAB/Simulink. The PV module SPR-X20-250-BLK was used for modeling and simulation analysis. Each module is comprised of 72 number of PV cells and a combination of 16 PV modules was employed for the contextual analysis. Accurate mathematical modeling for the HCTCT configuration under partial shading conditions (PSCs) is provided for the first time and is verified from the simulation. The different configuration schemes were investigated under short-narrow,short-wide,long-narrow,long-wide, diagonal, entire row distribution, and entire column distribution partial shading condition patterns with mathematical implementation and simulation of passing clouds. The performance of array configurations is compared in terms of maximum power generated ), mismatch power loss (∆), relative power loss ) and the fill factor (FF). It was inferred that on average, TCT configuration yielded maximum power generation under all shading patterns among all PV modules interconnection configurations with minimum mismatch power losses followed by hybrid and conventional PV array configurations respectively.

Dry eye syndrome (DES) has become increasingly prevalent due to the prolonged use of digital devices in modern society. Individual supplementation with lutein or docosahexaenoic acid (DHA) demonstrated potential benefits for eye health. This study aimed to investigate the effects of lutein plus DHA complex supplementation on DES, visual function, and memory in healthy individuals. Thirty-four participants, aged 40~60 years, received lutein/DHA complex supplements (containing 10 mg free-form lutein, 200 mg DHA, 30 mg red algae extract (astaxanthin), phosphatidylserine, and vitamin A) for 12 weeks. Ophthalmological examinations and memory tests were carried out, and a questionnaire was administered at weeks 0, 6, and 12 of the study. After 12 weeks of the intervention, the tear break-up time had significantly increased, and intraocular pressure (IOP) had significantly decreased. This suggests that lutein/DHA complex supplementation may reduce the IOP and offer potential benefits for DES, as indicated by improved tear stability.

This work uses a new approach to investigate the Riemann hypothesis, drawing conclusions about its trueness. It is based on the more general method presented in a very recent publication, by the same author, showing in detail how to approach that very well-known and interesting problem. This is achieved by means of the theory of dynamical systems (Poincaré index associated to equilibria of 2-dimensional systems) and the study of the zeros of the Dirichlet eta function, defined by a Dirichlet series. By using the well-known fact that the zeros of the eta function include all zeros of the Riemann zeta function in the (open) critical strip, excluded the critical line, ((0,1/2) ∪ (1/2,1)) × (−∞,∞), the development proceeds using only the eta function. In addition, the open and simply connected region (1/2,1) × (0,∞) is used along the text, taking into account the symmetries of zeros of the functions under analysis in the critical strip. The basic line of proof is to find the mathematical expression for the Poincaré index of the vector field associated to the eta function, assuming the existence of a zero of the eta function outside the critical line (in (1/2,1) × (0,∞)), and investigating the resulting unfoldings. Eventually, an inconsistency occurs and the proof ends by contradiction.

This paper presents a novel algorithm, the multi-objective nonlinear interval PageRank (MONIPR) Algorithm. This algorithm extends the conventional PageRank (PR) algorithm, integrating nonlinear interval computation and multi-objective considerations into the computation process. The MONIPR algorithm bridges a research gap in integrating nonlinear interval approaches and multi-objective problems into the PR algorithm, which were traditionally treated separately. In addition, this research adopts the constrained interval arithmetic proposed to address the limitations of the conventional PR algorithm, which tends to overlook uncertainties and results in deterministic outcomes. In addition, we use a numerical example to demonstrate the proposed algorithm, contrasting it with the conventional approaches. A numerical example demonstrates the algorithm's performance by comparing the rank intervals obtained with the traditional crisp Markov chain and PR algorithm. The results highlight the ability of the proposed algorithm to provide a range of possible rank intervals, considering both uncertainty and multi-objectives. The findings suggest potential applications in decision-making, uncertainty quantification, and systems analysis.

The Marchenko method is a data-driven way which makes it possible to calculate Green's functions from virtual points in the subsurface by the reflection data at the surface, only requiring a macro velocity model. This method requires collocated sources and receivers. However, in practice, subsampling of sources or receivers will cause gaps and distortions in the obtained focusing functions and Green's functions. To solve this problem, this paper proposes to integrate sparse inversion into the iterative Marchenko scheme. Specifically, we add sparsity constraints to the Marchenko equations and apply sparse inversion during the iterative process. Our work not only reduces the strict requirements on acquisition geometries, but also avoids the complexity and instability of direct inversion for Marchenko equations. This new method is applied to a two-dimensional numerical example with irregular sampled data. The result shows that it can effectively fill gaps of the obtained focusing functions and Green's functions in the Marchenko method.

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, a complex-form ordinary differential equation (ODE) for the small symmetrical deformation of an elastic torus is successfully transformed into the well-known Heun's ODE, whose exact solution is obtained in terms of Heun's functions. To overcome the computational difficulties of the complex-form ODE in dealing with boundary conditions, a real-form ODE system is proposed. A general code of numerical solution of the real-form ODE is written by using Maple. Some numerical studies are carried out and verified by both finite element analysis and H. Reissner's formulation. Our investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell.

Kim-Kim (Russ. J. Math. Phys. 2017, 24, 241-248) defined the degenerate Laplace transform and investigated some of their certain properties. Motivated by this study, in this paper, we introduce the degenerate Sumudu transform and establish some properties and relations. We derive degenerate Sumudu transforms of power functions, degenerate sine, degenerate cosine, degenerate hyperbolic sine, degenerate hyperbolic cosine, degenerate exponential function, and function derivatives. We also acquire a relationship between degenerate Sumudu transform and degenerate gamma function. Moreover, we investigate a scale preserving theorem for the degenerate Sumudu transform. Furthermore, we show that the degenerate Sumudu transform is the theoretical dual transform to the degenerate Laplace transform.

The dramatic outbreak of the coronavirus disease 2019 (COVID-19) pandemics and its ongoing progression boosted the scientific community's interest in epidemic modelling and forecasting. The SIR (Susceptible-Infected-Removed) model is a simple mathematical model of epidemic outbreaks, yet for decades it evaded the efforts of the community to derive explicit solution. The present work demonstrates that this is a non-trivial task. Notably, it is proven that the explicit solution of the model requires the introduction of a new transcendental special function, related to the Wright's Omega function. The present manuscript reports new analytical results and numerical routines suitable for parametric estimation of the SIR model. The manuscript introduces iterative algorithms approximating the incidence variable, which allows for estimation of the model parameters from the numbers of observed cases. The numerical approach is exemplified with data from the European Centre for Disease Prevention and Control (ECDC) for several European countries in the period Jan 2020 -- Jun 2020.

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, the symmetrical deformation equation of elastic toroidal shells is successfully transferred into a well-known equation, namely Heun's equation of ordinary differential equation, whose exact solution is obtained in terms of Heun's functions. The computation of the problem can be carried out by symbolic software that is able to with the Heun's function, such as Maple. The Gauss curvature of the elastic toroidal shells shows that the internal portion of the toroidal shells has better bending capacity than the outer portion, which might be useful for the design of metamaterials with toroidal shells cells. Through numerical comparison study, the mechanics of elastic toroidal shells is sensitive to the radius ratio. By slightly adjustment of the ratio might get a desired high performance shell structure.

This study was designed to extend the literature on multicomponent interventions for the children of deaf adults (CODA) population. This study used two evidence-based behavior intervention strategies: pre-session pairing (PSP) and independent group contingency (GC). These strategies have been successfully used to decrease off-task behavior in elementary school children with various abilities and diverse backgrounds. However, the research on multicomponent interventions has yet to examine their effects on the CODA population in inclusive classrooms. This study used a concurrent multiple baseline design across participants with an ABC sequence to examine teacher-implemented PSP with independent GC in reducing the off-task behavior of three CODAs in an inclusive classroom at a public elementary school. The results show that the intervention successfully decreased off-task behavior for all participating CODAs. The results suggest that CODAs can adapt to classroom rules and expectations when PSP and independent GC are systematically applied to them in classrooms.

The Internet of Medical Things (IoMT) is playing a pivotal role in the healthcare sector by allowing faster and more informed hospital care, personalized treatment, and medical solutions. A very effective and trustworthy solution for resource-constrained medical devices is provided by Physical Unclonable Functions (PUF) - based identity and authentication systems, however they are not yet entirely reliable. This paper proposes VXorPUF, a Vedic Principles - Based Hybrid XOR Arbiter PUF. Modeling attacks were performed on the proposed architecture and an accuracy of 49.80 % was achieved. Uniqueness, Reliability and Randomness were the figures of merit used to evaluate PUF.

The synchronous generator, as the main component of power systems, plays a key role in these system’s stability. Therefore, utilizing the most effective control strategy for modeling and control the synchronous generator results in the best outcomes in power systems’ performances. The advantage of using a powerful controller is to have the synchronous generator modeled and controlled as well as its main task i.e. stabilizing power systems. Since the synchronous generator is known as a complicated nonlinear system, modeling and control of it is a difficult task. This paper presents a sum of squares (SOS) approach to modeling and control the synchronous generator using polynomial fuzzy systems. This method as an efficacious control strategy has numerous superiorities to the well-known T–S fuzzy controller, due to the control framework is a polynomial fuzzy model, which is more general and effectual than the well-known T–S fuzzy model. In this case, a polynomial Lyapunov function is used for analyzing the stability of the polynomial fuzzy system. Then, the number of rules in a polynomial fuzzy model is less than in a T-S fuzzy model. Besides, derived stability conditions are represented in terms of the SOS approach, which can be numerically solved via the recently developed SOSTOOLS. This approach avoids the difficulty of solving LMI (Linear Matrix Inequality). The Effectiveness of the proposed control strategy is verified by using the third-part Matlab toolbox, SOSTOOLS.

The main purpose of this paper is to introduce and investigate degenerate Poisson distrib- ution which is a new extension of the Poisson distribution including the degenerate expo- nential function. We then provide several properties of the degenerate Poisson distribution such as the first and the second raw moments and di¤erence operator property. Moreover, we acquired the skewness and the kurtosis for the degenerate Poisson distribution. We also derive its moment generating function by which we define the degenerate Bell polynomials and give a connection for these polynomials related to the unsigned Stirling numbers of the …rst kind.

The complete-lattice approach to optimization problems with a vector- or even set-valued objective already produced a variety of new concepts and results and was successfully applied in finance, statistics and game theory. For example, the duality issue for multi-criteria and vector optimization problems could be solved using the complete-lattice approach, compare [11]. So far, it has been applied to set-valued dynamic risk measures (in the stochastic case), as discussed in Feinstein, Rudloff etc. (see [11], for example), but it has not been applied to deterministic calculus of variations and optimal control problems. In this paper, the following problem of set-valued optimization is considered: minimize the functional $$ \overline J_t[y]=\int_0^t \overline L(s,y(s),\dot y(s))\ ds + U_0(y(0)) $$ over all admissible arcs $y$, where $\overline L$ is the associated multifunction to a vector-valued Lagrangian $L$, the integral is in the Aumann sense and $U_0$ is the initial cost. A new concept of \emph{value function}, for which a Bellman's optimality principle holds, is introduced. Also the classical result of the Hopf-Lax formula holds for the generalized value function. Finally, a derivative with respect to the time $t$ and a directional derivative with respect to $x$ of the value function are defined, based on ideas close to the concepts in [12]. The value function is proved to be solution of a suitable Hamilton-Jacobi equation.

In this paper, we introduce a new generalization of the r-Stirling numbers of the second kind based on the q-numbers via an exponential generating function. We investigate their some properties and derive several relations among q-Bernoulli numbers and polynomials, and newly de…ned (q, r, w)-Stirling numbers of the second kind. We also obtain q-Bernstein polynomials as a linear combination of (q, r, w)-Stirling numbers of the second kind and q-Bernoulli polynomials in w.

Research indicates that brain region-specific synapse loss and dysfunction are early hallmarks and stronger neurobiological correlates of cognitive decline in Alzheimer’s disease (AD) than counts of amyloid plaques, neurofibrillary tangles, and neuronal loss. Even though the precise mechanisms underlying increased synaptic pruning in AD are still unknown, it has been confirmed that dysregulation of the balance between complement activation and inhibition is a crucial driver of pathology. The complement includes three distinct activation mechanisms, with activation products C3a and C5a, potent inflammatory effectors, and a membrane attack complex (MAC), leading to cell lysis. Besides pro-inflammatory cytokines, dysregulated complement proteins released by activated microglia bind to amyloid β at synaptic regions and cause microglia to engulf synapses. Additionally, research indicating that microglia-removed synapses are not always degenerating, and that suppression of synaptic engulfment can repair cognitive deficits point to an essential opportunity for intervention that can prevent the loss of intact synapses. In this study, we focus on the latest research on the role and mechanisms of complement-mediated microglial synaptic pruning at different stages of AD to find the right targets that could interfere with complement dysregulation and be relevant for therapeutic intervention at the early stages of the disease.

Background and objective: Obesity is a growing global epidemic. The composition of the intestinal microbiota can be influenced by several factors. Studies highlight the role of intestinal bacteria in the pathophysiology of obesity. So, the objective of this study was to investigate whether the use of probiotics, together with healthy lifestyle habits, contributes to weight reduction in obese indi-viduals by analyzing the intestinal microbiota profile. Methods: A prospective study was carried out with 45 adults with obesity. Participants underwent guidance on healthy lifestyle habits, re-ceived a probiotic component containing different microbiological strains and were followed for 60 days. Clinical parameters, body composition, biochemical analysis and intestinal microbiota assessment were performed before and after treatment. After 60 days, it was observed that the bacterial strains present in the probiotic were present in the patients' intestinal microbiota. Par-ticipants also showed improvements in physical activity, sleep quality, anxiety management, as well as changes in some eating habits, such as a reduction in the consumption of processed foods and a significant increase in water intake. Results: A reduction in BMI, fasting glucose, insulin, HOMA-IR, LDL cholesterol and triglycerides was observed, in addition to an increase in HDL cholesterol, improvement in bowel movement frequency and stool consistency. Analysis of the intestinal microbiota revealed an increase in microbial diversity and a better balance between the bacterial phyla Firmicutes and Bacteroidetes. Conclusions: The changes related to improving the composition of the intestinal microbiota, dietary habits, increased physical activity, reduced anxiety, and better sleep quality have significantly contributed to weight loss and improvements in physiological parameters in obese individuals.

Adolescents’ eating disorders and disordered eating behaviours appear to be a growing public health concern. The aetiology of these conditions is complex, as many different factors interact for their development. Among them, family factors such as parenting styles and comments regarding weight from family members are considered critical and are extensively researched. However, the impact of parental dieting has received less attention. A literature review was conducted in order to examine the relationship between parental engagement in weight-reduction dieting and their adolescent offspring’s disordered eating behaviours. The review was conducted in three databases (PubMed, Scopus and Google Scholar). A number of studies indicated that adolescents whose parents were engaged in dieting in order to lose weight are more likely to showcase disordered eating behaviours. However, research about this relationship is very scarce. More studies on the link between parental eating and dieting habits and the risk of disordered eating in adolescents are needed. Moreover, parents should be informed regarding the possible risks when they choose to follow weight-loss diets and the importance of adopting healthy eating and weight-control habits for the whole family.