Cardiac dynamics are traditionally linked to a left ventricle, right ventricle and septum morphology, a topography that differs from the heart’s 5-century-old anatomic description of containing a helix and circumferential wrap architectural configuration. Torrent Guasp’s helical ventricular myocardial band (HVMB) defines this anatomy and its structure, explains why the heart’s 6 dynamic actions of narrowing, shortening, lengthening, widening, twisting and uncoiling happen. This database raises questions about deductions behind “accepted cardiac mechanics”, and its functional aspects will challenge and overturn them. These suppositions include the LV, RV, and septum description, timing of mitral valve opening, isovolumic relaxation period, reasons for torsion/twisting, untwisting, reasons for longitudinal and circumferential strain, echocardiographic sub segmentation, resynchronization, RV function dynamics, and diastolic dysfunction’s cause and unrecognized septum impairment. Torrent Guasp’s revolutionary contributions may alter future understanding of the diagnosis and treatment of cardiac disease.

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.

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.

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.

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.

Hash tables are widely used. They rely on good quality hash functions. Popular data structure libraries either provide no hash functions or weak hash functions for sets or maps, making it impossible or impractical to use them as keys in other tables. This article presents three algorithms for hashing a set, two of which are simple to implement, practically fast, and can be combined. The quality evaluations follow the method of [1, chapter 2]. The insight that we are looking for commutative semigroups suggests that even better methods than symmetric polynomials may be found.

Using the method of the beta function, Sun has recently evaluated some series of the type $\sum_{k=0}^{\infty}(ak+b)x^k/\binom{mk}{nk}$. By factorization of the polynomial $t^{m-n}(1-t)^n-x$, we will give a general method to find new $\pi$-series.

We investigate the behavior of the partial derivative approach to the change of scale formula and prove relationships among the analytic Wiener integral and the analytic Feynman integral of the partial derivative for the function space integral.

A simple approach was developed to predict corn yields using the MoDerate Resolution Imaging Spectroradiometer (MODIS) data product from two geographically separate major corn crop production regions: Illinois, USA and Heilongjiang, China. The MOD09A1 data product, which are 8-day interval surface reflectance data, were obtained from day of the year (DOY) 89 to 337 to calculate the leaf area index (LAI). The sum of the LAI from early in the season to a given date in the season [end of DOY (EOD)] was well fitted to a logistic function and represented seasonal changes in leaf area duration (LAD). A simple phenology model was derived to estimate the dates of emergence and maturity using the logistic function parameters b1 and b2, which represented the rate of increase in LAI and the date of maximum LAI, respectively. The phenology model predicted emergence and maturity dates fairly well, with root mean square error (RMSE) values of 6.3 and 4.9 days for the validation dataset, respectively. Two simple linear regression models (YP and YF) were established using LAD as the variable to predict corn yield; the yield model (YP) used LAD from predicted emergence to maturity, and the yield model (YF) used LAD for a predetermined period from DOY 89 to a particular EOD. When state/province corn yields for the validation dataset were predicted at DOY 321, near completion of the corn harvest, the YP model performed much better than the YF model, with RMSE values of 0.68 t/ha and 0.66 t/ha for Illinois and Heilongjiang, respectively. The YP model showed a similar or better performance, even for the much earlier yield prediction at DOY 257, compared to that of the YF model. In conclusion, the phenology and yield models were developed based only on logistic changes in remote sensing-derived LAD, and predicted phenological dates and corn yields with considerable accuracy and precision for the two regions selected for this study. However, these models must be examined for spatial portability in more diverse agro-climatic regions.

This work investigates centered polygonal lacunary functions restricted from the unit disk onto symmetry angle space which is defined by the symmetry angles of a given centered polygonal lacunary function. This restriction allows for one to consider only the p-sequences of the centered polygonal lacunary functions which are bounded, but not convergent, at the natural boundary. The periodicity of the $p$-sequences naturally gives rise to a convergent subsequence, which can be used as a grounds for decomposition of the restricted centered polygonal lacunary functions. A mapping of the unit disk to the sphere allows for the study of the line integrals of restricted centered polygonal that includes analytic progress towards closed form representations. Obvious closures of the domain obtained from the spherical map lead to four distinct topological spaces of the "broom topology'' type.

Financial system is essentially chaotic and unstable if there is not any external inputs. By means of Lyapunov function method, design of switching law, novel fuzzy assumption, $L^p$ estimation technique and Laplace semigroup theory, the author presents the boundedness and LMI-based (globally) asymptotical input-to-state stability criteria of financial systems. Particularly, the globally asymptotical stability in the meaning of switching implies that when the time $t$ is big enough, the dynamic of any subsystem must approach its unique equilibrium point. Besides, the global financial crisis often erupts periodically, which illuminates that the global stability in the classical sense is actually meaningless. So the stability in the meaning of switching proposed in this paper is suitable and appropriate. Numerical examples illuminate the effectiveness of the obtained results.

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

Background: Upper extremities’ function impairments (UEFI) and gait impairment are frequently reported even in the early stages of Multiple Sclerosis (MS) disease. These motor deficits can negatively affect the quality of life (QOL) in MS patient. Exercise has been repeatedly introduced as a beneficial adjuvant therapy for MS, attenuating a wide range of physical and psychological symptoms without any side effects or increased risks of relapse or exacerbation in disease symptoms.Aim: This paper investigates the effect of multi-function swing suspension training (MFSST) program on upper and lower extremities’ function (ULEF), and QOL in MS women according to expanded disability status scale (EDSS) score.Design: Experimental method with a pre-test and post-test design with control group. Setting: The department of Sports Injuries and Corrective Exercise at the Shahid Bahonar University of Kerman.Population: Forty-seven MS women.Methods: Eligible subjects who matched the selection criteria were randomly assigned into three groups as follow: i. Intervention group A (EDSS of 2 – 4), ii. Intervention group B (EDSS of 4.5 – 6.5), and iii. Control group (EDSS of 2 – 6.5). The intervention groups have been trained by the SET program for a duration of 8 weeks. At baseline and after the intervention, the upper extremities’ function (UEF) and the lower extremities’ function (LEF) were assessed by 9-hole peg test (9HPT) and the timed 25-foot walk (T25FW) test, respectively. Moreover, participants’ QOL was measured using the Short Form questionnaire (SF-36).Results: A significant difference was found between the pre-test and post-test variables of walking speed and upper extremity endurance in intervention groups, and between the intervention groups and control group (P < 0.05). Compared to control group, both intervention groups showed improvements in all subscales of QOL, except emotional role limitation score.Conclusions: In summary, these results show that the present protocol of MFSST could be effective in improving ULEF and QOL in MS patients, showing the improvements after 4^th week. Moreover, this protocol was more useful for patients with an EDSS score of more than 4.5. Therefore, it seems that exercise therapy should be considered as a beneficial clinical intervention approach to improve ULEF and QOL in MS patients.

Loose Tangle is a concept in graph theory that has a dual relationship with branch-width which is well-known graph width parameter. Ultrafilter, a fundamental notion in mathematics, is similarly known to have a dual relationship with branch-width when extended to a connectivity system (X, f). In this compact paper, we revisit and contemplate the interplay between Loose Tangle and Filter through the lens of a submodular partition function.

Euler’s product formula over the primes and Euler’s zeta function equate to enshrine the Fundamental Theorem of Arithmetic that every integer > 1 is the product of a unique set of primes. The product formula has no zero, and with a domain ≤1 Euler’s zeta diverges. Dirichlet’s eta function η(s), negates alternate terms of zeta, permitting convergence when s∈C and Re(s) < 1, and its non-trivial zeros {ρ}, have a deep relationship with the distribution of the primes. The Riemann Hypothesis is that all the non-trivial zeros have Re(ρ) = 1/2. This work examines the symmetries in a partial Euler’s zeta series with a complex domain equating it to the difference between two finite vector series whose matched terms have mirror-image arguments, but whose magnitudes differ when Re(s) ≠ 1/2. Analytical continuation generates a modified eta series η_l(s), in which every l^th term is multiplied by (1-l). If the integer l is appropriately determined by the Im(s), similar paired finite vector series have a difference that closely follows η_l (s) and their terminal vectors intersect in a unique way permitting zeros only when Re(s) = 1/2. Furthermore, those vectors tracking the derivatives of the series, have a special relationship permitting zeros of the differential only when Re(s) > 1/2.

Diminished ovarian reserve can be regarded as a sentinel indicator to foreshadow severe follicular loss and, ultimately, systemic aging. The negative slope of human ovulatory fidelity begins with a robust follicular endowment which gradually declines over time. In contrast, the youthful ovarian phenotype requires the coordinated work of endothelial, granulosa, immune, perivascular, stromal and possibly germline stem cells. Such a diverse tissue matrix can, in general, be influenced by platelet (PLT)-derived factors but this has not yet been specifically confirmed in the ovary after platelet-rich plasma (PRP). How could a comparable response be validated? Here a prospective, experimental study is proposed whereby eligible patients already undergoing scheduled laparoscopy provide ovarian tissue via biopsy submitted for co-culture with autologous Ca⁺² activated PRP. Recognizing the interlocking, central roles of nuclear factor κB (NF-κB) and tumor necrosis factor-α (TNF-α), incubated samples would be assessed for these in vitro before vs. after PRP exposure, in addition to stereomicroscopy. A mathematical model is available to track NF-κB oscillations and estimate gene expression, cell development, growth, apoptosis, and key immune and inflammatory actions. Since NF-κB and TNF-α are discharged in activated PLT releasate (or react to its cargo proteins) this audit permits extraction of response markers observed post-stimulus, thus linking discrete signals to transcriptional output, cellular fitness, and ovarian cytoarchitecture. From this, a hypothesis could emerge where intraovarian PRP is found to make no direct impact on follicles, although modified ovarian field function and curtailed local entropy incidentally favor optimized oocyte competence as a secondary effect.

Social surveys are conducted to determine how annoyed people are in a certain noise situation. The results are typically presented as exposure-response curves showing the percentage of the area population that are highly annoyed as a function of the noise exposure level. It is a well-known fact that the survey results are not only dependent on the accumulated noise exposure, DNL, DENL, or similar, but also on various other factors such as maximum levels, exposure patterns, noise spectra, etc. A re-analysis of previously reported surveys shows that the results are also to a large extent dependent on survey-specific factors like wording of the annoyance questions, how the questionnaires are presented, response scales, methods of scoring highly annoyed, etc. This paper discusses and quantifies the influence of such factors and suggests ways of comparing results from surveys that have been conducted according to different protocols and different analysis methods.

This paper presents a theorem in factorial functions with the sum of any two nonnegative integers that is equal to multiple of the product of factorial of the same two nonnegative integers.

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

We present smooth approximations to $ \vert{x} \vert $ using sigmoid functions. In particular $ x\,erf(x/\mu) $ is proved to be better smooth approximation for $ \vert{x} \vert $ than $ x\,tanh(x/\mu) $ and $ \sqrt{x^2 + \mu} $ with respect to accuracy. To accomplish our goal we also provide sharp hyperbolic bounds for error function.

In this paper, we generalize the concept of I-statistical convergence, which is a recently introduced summability method, with an infinite matrix of complex numbers and a modulus function. Lacunary sequences will also be included in our definitions. The name of our new method will be A^{I}-lacunary statistical convergence with respect to a sequence of modulus functions. We also define strongly A^{I}-lacunary convergence and we give some inclusion relations between these methods.

The author demonstrates a stable Lagrangian solid modeling method, tracking the interactions of solid mass particles rather than using a meshed grid. This numerical method avoids the problem of tensile instability often seen with smooth particle applied mechanics by having the solid particles apply stresses expected with Hooke's law, as opposed to using a smoothing function for neighboring solid particles. This method has been tested successfully with a bar in tension, compression, and shear, as well as a disk compressed into a flat plate, and the numerical model consistently matched the analytical Hooke's law as well as Hertz contact theory for all examples. The solid modeling numerical method was then built into a 2-D model of a pressure vessel, which was tested with liquid water particles under pressure and simulated with smoothed particle hydrodynamics. This simulation was stable, and demonstrated the feasibility of Lagrangian specification modeling for fluid–solid interactions.

As known all physical properties of solids are described well by the system of quantum linear harmonic oscillators. It is shown in the present paper that the system consisting of classical linear harmonic oscillators having temperature dependent masses or (and) frequencies has the same partition function as the system consisting of quantum linear harmonic oscillators having temperature independent masses and frequencies while the means of the square displacements of the positions of the oscillators from their mean positions for the system consisting of classical linear harmonic oscillators having: the temperature dependent masses; temperature dependent frequencies; and temperature dependent masses and frequencies differ from each other and from that of the system consisting of quantum linear harmonic oscillators, and hence, the system consisting of classical linear harmonic oscillators describes well the thermodynamic properties of the system consisting of quantum linear harmonic oscillators and solids.

Amyloids are fibrillar protein aggregates that are associated with diseases such as Alzheimer’s disease, Parkinson’s disease, type II diabetes and Creutzfeldt–Jakob disease. The process of amyloid aggregation involves three pathological protein transformations; from natively-folded conformation to the cross-β conformation, from biophysically soluble to insoluble, and from biologically functional to non-functional. While amyloids share a similar cross-β conformation, the biophysical transformation can either take place spontaneously via a homogeneous nucleation mechanism (HON) or catalytically on an exogenous surface via a heterogeneous nucleation mechanism (HEN). Here, we postulate that the different nucleation pathways can serve as a mechanistic basis for an etiological classification of amyloidopathies, where hereditary forms generally follow the HON pathway, while sporadic forms follow surface-induced (including microbially-induced) HEN pathways. Furthermore, the conformational and biophysical amyloid transformation results in loss-of-function (LOF) of the original natively-folded and soluble protein. This LOF can, at least initially, be the mechanism of amyloid toxicity even before amyloid accumulation reaches toxic levels. By highlighting the important role of non-protein species in amyloid formation and LOF mechanisms of toxicity, we propose a generalized mechanistic framework that could help better understand the diverse etiology of amyloid diseases and offer new opportunities for therapeutic interventions including replacement therapies.

Studies show that executive functions and motor development are associated among each other and with learning ability. A more technological lifestyle, related with digital culture, should be considered an important component to stimulate children. In addition, digital games constitute an element of the digital culture in which children are inserted. The aim of this study is to present a systematic mapping of the literature involving executive functions, motor development and the use of digital games in intervention programs for elementary school children, from 6 to 11 years old. Four databases were searched: PubMed, Scielo, Science Direct and SCOPUS, including publications between 2012 and March 2021. The initial results indicated 4881 works. After the selection process, 15 investigations that presented the central theme of the study were selected. The main results indicate that intervention strategies are quite heterogeneous. Most of the studies demonstrated significant positive effects after intervention protocols and were conducted in Europe and 46% of the studies were conducted in a school environment. No researches were identified that involved technological solutions involving executive functions, motor development and digital games in an integrated manner, constituting a field of future scientific research.

There is no simple method to measure glomerular filtration rate (GFR) in swine, an established model to study renal disease. We developed a protocol to measure GFR in conscious swine with the plasma clearance of iohexol. We used two groups: testing and validation, of 8 animals each. Ten milliliters of iohexol (6.47 g) were injected by the marginal auricular vein and blood samples (3 ml) were collected from the orbital sinus at different points after injection. GFR was determined considering two models: two-compartments (CL2: all samples) and one-compartment (CL1: the last six samples). In the testing group, CL1 overestimated CL2 by ~30%: CL2=245±93 and CL1=308±123 ml/mn. This error was corrected by a first order polynomial quadratic equation to CL1, which was considered the simplified method: SM=-47.909+(1.176xCL1)–(0.00063968xCL1²). SM showed narrow limits of agreement with CL2, and a concordance correlation of 0.97 and a total deviation index of 14.73%. Similar results were obtained for the validation group. This protocol is reliable, reproducible, can be performed in conscious animals, uses a single dose of the marker, and requires a reduced number of samples avoiding urine collection. Finally, it portends a significant improvement in animal-welfare conditions and handling necessities in experimental trials.

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

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

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

The largest part of the image encryption algorithms operates on the pixel as a central element by implementing diffusion confusion and eventually a permutation. On the other side, a permutation applied at the bit level changes not only the pixel value, but also its location within the image. In this work, we will propose a new technology of medical and color image encryption, based on chaotic permutations acting at the bit level, and a diffusion confusion ensured by an application of the method of Vigenere largely improved and adapted to the subject. Simulations performed on a large number of images of different sizes and formats ensure that our method is not subject to any known attacks.

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

Cognitive rehabilitation is useful for many after traumatic brain injury (TBI), but we lack critical knowledge about which patients benefit the most from different approaches. Advanced neuroimaging techniques have provided important insight into brain pathology and systems plasticity after TBI and have potential to inform new practices in cognitive rehabilitation. In this study, we aimed to identify candidate structural brain measures with relevance for rehabilitation of cognitive control (executive) function after TBI. Twenty-eight patients (9 female, mean age 40.5 (SD = 13.04) years) with moderate/severe TBI (>21 months since injury) that participated in a randomized controlled cognitive rehabilitation trial (NCT02692352) were included in the analyses. Regional brain volume was extracted from T1-weighted MRI scans before treatment using tensor-based morphometry. Both positive and negative associations between treatment outcome (everyday cognitive control function) and regional brain volume were observed. The most robust structural brain measures with relevance for improvement in function were observed in midline fronto-parietal regions, including the anterior and posterior cingulate cortices. The study pro-vides proof of concept and valuable insight for planning future studies focusing on neuroimaging in cognitive rehabilitation after TBI.

Advances in next-generation sequencing have facilitated the discovery of a multitude of long non-coding RNAs (lncRNAs) with pleiotropic functions in cellular processes, disease and viral pathogenesis. It came as no surprise when viruses were also revealed to transcribe their own lncRNAs. Among them, gammaherpesviruses, one of the three subfamilies of the Herpesviridae, code their largest number. These structurally and functionally intricate non-coding (nc) transcripts modulate cellular and viral gene expression to maintain viral latency or prompt lytic reactivation. The lncRNAs allow the virus to escape cytosolic surveillance, sequester and re-localize essential cellular factors and modulate the cell cycle and proliferation. Some viral lncRNAs act as “messenger molecules”, transferring information about viral infection to neighboring cells. This broad range of lncRNA functions is achieved through lncRNA structure-mediated interactions with effector molecules of viral and host origin, including other RNAs, proteins and DNAs. In this review, we discuss examples of gammaherpesvirus-encoded lncRNAs, emphasize their unique structural attributes, and link them to viral life cycle, pathogenesis and disease progression. We will address their potential as novel targets for drug discovery and propose future directions to explore lncRNA structure and function relationship.

MicroRNAs (miRNAs) regulate plant growth and development and their responses to biotic and abiotic stresses. Although extensive studies show that miR159 family members regulate leaf and flower development in Arabidopsis thaliana, the roles of miRNAs in soybean (Glycine max) are poorly understood. Here, we identified six MIR159 genes in soybean, MIR159aMIR159f, and investigate their expression patterns in plants under low-phosphorus (low-P), NaCl, or abscisic acid (ABA) treatments. In soybean leaves, MIR159e and MIR159f expression was induced by low-P treatment, while in roots, MIR159b, MIR159c, MIR159e, and MIR159f expression was upregulated. In flowers, low-P led to upregulation of MIR159a, MIR159b, MIR159c, and MIR159f, but downregulation of MIR159d and MIR159e. In soybean nodules, MIR159b was upregulated but MIR159a, MIR159c, and MIR159d was downregulated under P deficiency. NaCl treatment induced MIR159a, MIR159b, MIR159c, and MIR159e expression in leaves, and MIR159aMIR159f expression in roots. ABA treatment upregulated MIR159a, MIR159b, and MIR159c but downregulated MIR159d, MIR159e, and MIR159f in leaves. These results suggest that miR159 family members function in plant abiotic stress responses. Moreover, total P content in leaves was significantly lower in plants overexpressing MIR159e than in the wild type, suggesting that miR159e may regulate P absorption and transport in soybean.

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

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

This article proposes a new photovoltaic (PV) solar tracker design based on the advantage that installation latitude offers according to efficiency in function of orientation (EFO) of PVs. First, is described a methodology to let incorporate a low-precision, low-cost and high-availability solar tracking mechanism and control system. The design methodology considers the installation location (latitude and azimuth) as a starting point for establishing an adequate angular range of EFO, simultaneity the aspects of available technology and the knowledge accords to developer. Finally, the design technique is experimentally validated by the implementation of a solar tracker at latitude of 28° longitude of 109° and evaluates the efficiency on a specific day. According to result the feasibility of this type of solar tracker for latitudes close to or greater than 30° is highlighted, given that this tracking system costs 30% less than traditional commercial systems as slew drive with its incorporation of lower-resolution azimuth tracking mechanisms. It also increases collection efficiency by 26%, just as continuous or time-based dual-axis solar trackers do, without the more complex controls and mechanisms of these designs.

This document introduces a new cryptosystem mixing two improvement standards generally used for text encryption, in order to give birth a new color image encryption algorithm capable of dealing with known attacks. Firstly, two substitution matrixes attached to a strong replacement function will be generated for advanced Vigenere technique application. At the end of this first round, the output vector is subdivided into size blocks according to the used chaotic map, for acting a single enhanced Hill circuit insured by a large inversible matrix. A detailed description of such a large involutive matrix constructed using Kronecker products will be given. accompanied by a dynamic translation vector to eliminate any linearity. A solid chaining is established between the encrypted block and the next clear block to avoid any differential attack. Simulations carried out on a large volume of images of different sizes and formats ensure that our approach is not exposed to any known attacks.

This review provides an overview of advancements in plant genomics, emphasizing key stages in genomics projects and addressing associated challenges. Long read sequencing enables the cost-effective sequencing of plant DNA and assembly of highly continuous genome sequences - often even separating haplophases. Incorporating external hints, such as cDNA sequences from RNA-seq or full length cDNA sequencing, enhances the identification of gene models. While these steps enable high-throughput exploration of numerous plant genomes, a significant bottleneck lies in elucidating gene functions. The classical approach based on wet lab methods is impractical when dealing with thousands of genes in a new genome sequence. To overcome this challenge, computational tools harnessing existing information for cross species knowledge transfer are essential for expediting the functional annotation process. In support of researchers entering the field of plant genomics, a collection of recommended tools has been curated and is accessible at https://github.com/bpucker/ToolOverview.

The coastal zone, situated at the sensitive interface between land and sea, serves as a pivotal area of extensive human economic activities. As one of China's economic special zones, Xiamen exemplifies the comprehensive trajectory of coastal governance in China. This research adopts an interdisciplinary approach grounded in historical geography and political ecology, employing data collection methods encompassing historical literature, field surveys, and interviews. The research findings indicate that:(1) The year 1994 witnessed the pivotal role played by the United Nations Convention on the Law of the Sea (UNCLOS) in connecting Jimei Peninsula from a local context to the international arena, thus signifying a momentous turning point in the process of scale reconstruction. However, the subsequent implementation of the Coastal Exclusion Policy in 2002 had detrimental consequences, leading to the disintegration of the local scale, the erosion of maritime culture, and the disregard for the livelihood security of displaced coastal populations.(2)The Coastal Exclusion Policy serves as an instrumental tool for implementing scale politics, while its functional realignment has had profound implications for the coastal zone, encompassing economic transformation, ecological degradation, and the marginalization of the socio-cultural fabric that intertwines humans and the coastal environment.

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

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

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

Acoustic emission (AE) is caused by the sudden release of energy by a material as a result of material degradation related to deformation, crack, or fault within a solid. The same situation also occurs in leaks caused by turbulence in the fluid around the leak. In this study, analytical modeling for AE due to leakage through a circular pinhole in a gas storage cylinder was performed. The displacement fields responsible for AE, excited by the concentrated force (CF) associated with the turbulent flow though the pinhole, were derived by solving the Navier-Lamé equation. The CF as an excitation source was formulated in terms of a fluctuating Reynolds stress (FRS) and spatial Green’s function. In particular, a series of experiments were conducted under different operating conditions to explore the characteristics of the AE signals due to leak in a gas cylinder. Finally, the simulation and experimental results were compared to verify the accuracy of the simulation results.

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.

This paper is a response to the EPR paper titled: "Can quantum-mechanical description of physical reality be considered complete?", published in Physical Review in 1935. A quantum-mechanical (QM) measurement function describes a distribution of local results, while each empirical measurement process produces one result as exact as allowed by a measuring instrument calibrated to a non-local unit standard. Repeating these empirical measurements produces a Gaussian distribution of measurement results. The QM and empirical measurement result distributions can be compared. To precisely compare a QM measurement function describing a distribution of eigenvectors to a distribution of repetitive empirical measurement results, it is necessary to determine, by calibration, the precision of the eigenvectors to the same standard as the empirical results, because each eigenvector evidences uncertainty relative to a standard. When the calibration process is recognized as formal as well as empirical, QM measurement function results and metrology measurement process results are unified.

Proteomics research has become one of the most important topics in the fields of life science and natural science. At present, research on protein–protein interaction networks (PPINs) mainly focuses on detecting protein complexes or function modules. However, existing approaches are either ineffective or incomplete. In this paper, we investigate function module detection mechanisms in PPIN, including open databases, existing detection algorithms and recent solutions. After that, we describe the proposed solution based on simplified swarm optimization (SSO) algorithm and gene ontology knowledge. The proposed solution implements SSO algorithm for clustering proteins with similar function, and imports biological gene ontology knowledge for further identifying function complexes and improving detection accuracy. Furthermore, we use four different categories of species dataset for experiment: Fruitfly, Mouse, Scere, and Human. The testing and analysis result show that the proposed solution is feasible, efficient and could achieve a higher accuracy of prediction than existing approaches.

The main ideas of F-transform came from representing expert rules. It would be therefore re reasonable to expect that the more accurately the membership functions describe human reasoning, the more efficient will be the corresponding F-transform formulas. We know that an adequate description of our reasoning corresponds to complicated membership functions -- however, somewhat surprisingly, most efficient applications of F-transform use the simplest possible triangular membership functions. There exist some explanations for this phenomenon which are based on local behavior of the signal. In this paper, we supplement this local explanation by a global one: namely, we prove that triangular membership functions are the only one that provide the accurate description of appropriate global characteristics of the signal.

Experimental test facilities are generally characterised using linear transfer functions to relate the wavemaker forcing amplitude to wave elevation at a probe located in the wavetank. Second and third order correction methods are becoming available but are limited to certain ranges of waves in their applicability. Artificial intelligence has been shown to be a suitable tool to find even highly nonlinear functional relationships. This paper reports on a numerical wavetank implemented using the OpenFOAM software package which is characterised using artificial intelligence. The aim of the research is to train neural networks to represent non-linear transfer functions mapping a desired surface-elevation time-trace at a probe to the wavemaker input required to create it. These first results already demonstrate the viability of the approach and the suitability of a single setup to find solutions over a wide range of sea states and wave characteristics.

Mutations in the “guardian of the genome” TP53 predominate in solid tumors. In addition to loss of tumor suppressor activity, a specific subset of missense mutations confers additional oncogenic properties. These “gain-of-function” (GOF) mutations portend poor prognosis across cancer types regardless of treatment. Our objective in this study was to identify novel therapeutic opportunities to overcome the deleterious effects of GOF TP53 mutants. Using gynecologic cancer cell lines with known TP53 mutational status, we established that treatment with a proteasome inhibitor induced cell death in cells with two recurrent GOF TP53 mutations (R175H and R248Q), and addition of a histone deacetylase inhibitor (HDACi) enhanced this effect. By contrast, p53-null cancer cells were relatively resistant to the combination. Towards understanding the mechanism, we found that proteasome inhibition promotes apoptosis of cells with TP53 GOF mutations, potentially through induction of the unfolded protein response. In line with the reported hyperstabilization of GOF p53 protein, cells treated with HDACi exhibited reduced levels of p53 protein. Together, these data form the basis for future clinical studies examining therapeutic efficacy in a preselected patient population with GOF TP53 mutations.

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.

Cognitive function, arthrogryposis, obstetrics palsy, children, motor disorder

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.

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.

This paper is motivated by three main assumptions: (1) The currently dominant forms of knowledge representation (natural language text, formulas, graphics) are suboptimal to facilitate knowledge transfer between control engineering sub-fields and into potential application domains. (2) Formal knowledge representation (in general) is a promising supplementary approach, but (3) the established technologies so far have failed to be significantly adopted for formal representation of control engineering knowledge. Thus, after briefly reviewing existing representation methods, we introduce our own approach: The Python based imperative representation of knowledge (PyIRK) and its application to formulate the Ontology of Control Systems Engineering (OCSE). One of its main features is the possibility to represent the actual content of definitions and theorems as nodes and edges of a knowledge graph, which is demonstrated by selected elements from Lyapunov theory. While the approach is still experimental, the formalization already allows to apply methods of automated quality assurance and a semantic search mechanism. The current feature set of the framework is demonstrated on various examples before directions for further developments are discussed.

As the problem of light pollution becomes more serious, more and more scholars pay attention to this issue and carry out related research. In the perspective of cities, the measurements of light pollution mainly focus on the brightness of the sky or artificial lighting on the ground. However, there is lack of research on the whole urban space. With the two-dimensional brightness analyses, this paper processes the changes of the light environment of the whole urban space into image quantization. It gets the 3D and 2D light environment changes of luminance distribution, color temperature distribution and chromaticity in the three space layers, the ground layer, the urban canopy layer and the sky layer, from dusk with natural light to night with artificial lighting completely. It is found that the brightness difference between the light environments among the three city levels gradually reduces with the measuring time, and the final values maintain at 0.11~0.25 cd/m². In the ground layer, the light environment is mainly affected by the lighting facilities, and vegetation can prevent the light from scattering up. The light environment of the urban canopy layer is the brightest in the whole city space and has the largest influence on the sky layer. The color concentrates in the range of yellow and red. The color temperature near the ground distributes in 3000K~15000K, and near the sky distributes in 2300K~2700K which is warmer than the natural night sky. The sky brightness of Dalian city is about 951 times than the natural night sky.

We explore the use of inverse multiquadratic (IMQ) functions as basis functions when solving the vibrational Schrödinger equation with the rectangular collocation method. The quality of the vibrational spectrum of formaldehyde (in six dimensions) is compared to that obtained using Gaussian basis functions when using different numbers of width-optimized IMQ functions. The effects of the ratio of the number of collocation points to the number of basis functions and of the choice of the IMQ exponent are studied. We show that the IMQ basis can be used with parameters where the IMQ function is not integrable. We find that the quality of the spectrum with IMQ basis functions is somewhat lower that that with a Gaussian basis when the basis size is large and for a range of IMQ exponents. The IMQ functions are, however, advantageous when a small number of functions is used or with a small number of collocation points e.g. when using square collocation.

Recently, representation formulae and monotonicity properties of generalized k-Bessel functions, Wk v,c., were established and studied by SR Mondal [24]. In this paper, we pursue and investigate some of their image formulae. We then extract solutions for fractional kinetic equations, involving Wk v,c, by means of their Sumudu transforms. In the process, Important special cases are then revealed, and analyzed.

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.

Due to its time effective, joint friendly and highly customizable character whole-body-electromyostimulation (WB-EMS) is regarded as a feasible solution for a large variety of training issues particularly in the area of non-athletic application. To identify gaps in research and summarize prevalent evidence we conducted an evidence map on outcomes addressed by WB-EMS trials in middle-aged to older, non-athletic adults. Based on a comprehensive systematic search in five databases and two study registers according to PRISMA, 54 projects published in 80 articles were included. More than 90% of the studies reported outcomes related to the physical fitness or function domain. Body composition parameters were addressed by two thirds of the projects. Health-related outcomes addressed by WB-EMS included cancer/neoplasm (n=7), endocrine regulation (n=8), glucose metabolism (15), nervous system diseases (n=2), cardiovascular system diseases (n=22), non-specific chronic low back pain (n=4), osteopenia (n=5) and diseases of the renal system (n=12). Outcomes related to inflammation were addressed 18 times. Of importance, no studies reported clinically relevant adverse effects related to the WB-EMS intervention. In summary, while considerable evidence on outcomes related to fitness/function and body composition is prevalent, evidence gaps of WB-EMS research were particular evident for diseases of the nervous and cerebrovascular system.

The C-type lectin-like receptor 2 (CLEC-2) is expressed on platelets and mediates binding to podoplanin (PDPN) on various cell types. The binding to circulating tumor cells (CTCs) leads to platelet activation and promote metastatic spread. The increased level of soluble CLEC-2 (sCLEC-2), presumably, released from activated platelets was shown in patients with thromboinflammatory and malignant disease. However, the functional role of sCLEC-2 and the mechanism of sCLEC-2 release is not known. In this study, we focused on the effect of platelet activation on CLEC-2 expression and the sCLEC-2 plasma level in cancer patients. First, citrated blood from healthy volunteer donors (n=20) was used to measure the effect of platelet stimulation by classical agonists and PDPN on aggregation, CLEC-2 expression on platelets by flow cytometry, sCLEC-2 release to the plasma by ELISA and total CLEC-2 expression by Western blot analysis. Second, sCLEC-2 was determined in plasma samples from healthy donors (285) and patients with colorectal carcinoma (CRC; 194), melanoma (160), breast cancer (BC; 99) or glioblastoma (49). PDPN caused a significant increase of the aggregation response induced by classical agonists. ADP or PDPN stimulation of platelets caused a significant decrease of CLEC-2 on platelets and sCLEC-2 in the plasma, whereas, total CLEC-2 in platelet lysates remained the same. Thus, the increased plasma level of sCLEC-2 is not a suitable biomarker of platelet activation. In patients with CRC (median 0.9 ng/mL), melanoma (0.9 ng/mL) or BC (0.7 ng/mL) we found significantly lower sCLEC-2 levels (p&lt;0.0001), whereas, glioblastoma patients displayed higher levels (2.6 ng/mL; p=0.0233) compared to healthy controls (2.1 ng/mL). The low sCLEC-2 plasma level observed in most of the tumor entities of our study, presumably, results from the internalization of sCLEC-2 by activated platelets or binding of sCLEC-2 to CTC.

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.

Existing evidence suggest that lactoferrin might be beneficial for Alzheimer’s disease. We aimed to determine the effects of lactoferrin intervention on cognitive function from APP/PS1 mice, and possible mechanisms involved in. Both young and middle-aged male APP/PS1 mice were divided into control and lactoferrin group with 16 weeks’ intervention. Lactoferrin intervention had no effects on cognitive function from both young and middle-aged mice, and no key markers involved in Aβ, tau pathology, neuro-inflammation and synaptic plasticity were altered post lactoferrin intervention. In regards to gut microbiota profiles, in the young mice, lactoferrin elevated α diversity index including ACE and Chao 1, and reduced the relative abundance of the genera Bacteroides and Alistipes and elevated Oscillibacter, in addition, Oscillibacter, Anaerotruncus, EF096579_g, EU454405_g, Mollicutes_RF39, EU474361_g, EU774448_g, and EF096976_g were specifically abundant post Lf intervention via LEfSe analysis. In the middle-aged mice, the relative abundance of the phylum Proteobacteria, as well as the genera Oscillospira, Coprococcus and Ruminococcus was significantly reduced post Lf intervention, additionally, S24_7, Bacteroidia, Bacteroidetes and Methylobacterium were specific via LEfSe analysis post lactoferrin intervention. In conclusion, dietary lactoferrin might be beneficial for gut microbiota homeostasis although might have no effects on cognition.

A new formulation for a proposed solution to the 3D Navier-Stokes Equations in cylindrical co-ordinates coupled to the continuity and level set convection equation is presented in terms of an additive solution of the three principle directions in the radial, azimuthal and z directions of flow and a connection between the level set function and composite velocity vector for the additive solution is shown. For the case of a vertical tube configuration with small inclination angle, results are obtained for the level set function defining the interface in both the radial and azimuthal directions. It is found that the curvature dependent part of the problem alone induces sinusoidal azimuthal interfacial waves wheras when the curvature together with the equation for the composite velocity is considered oscillating radial interfacial waves occur. The implications of two extremes indicate the importance of looking at the full equations including curvature.

In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to get two new representations of the fundamental solution in form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed form formulas for particular cases of the fundamental solution are derived. In particular, we solve an open problem of representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.

Aluminum, a contentious trace element found in the environment, has been demonstrated to have harmful effects on both humans and animals. In contrast, Sempervivum tectorum, an evergreen plant, has been found to offer numerous beneficial effects for both humans and animals. Therefore, this study aims to assess the protective effect of S. tectorum on certain reproductive biomarkers in male rats exposed to aluminum. Thirty-five Wistar rats were randomly divided into five groups: NTC (no-treatment control) received distilled water; NC (negative control) received drinking water containing 1 mg/L aluminum sulfate (AS); E1 received 1 mg/L AS along with an 8% S. tectorum extract; PC (positive control) received only 8% S. tectorum extract; E2 received 1 mg/L AS for three months followed by 8% extract for one month. The study analyzed testosterone, LH, FSH, body weight, and the histological structure of the testis, epididymis, and prostate, as well as the levels of zinc, manganese, copper, and iron in these organs. Significant decreases in body weight, testis, and epididymis size were observed in the aluminum-exposed groups compared to the control, whereas these decreases were not significant in the S. tectorum-treated groups compared to the control. Aluminum exposure led to significant decreases in testosterone and LH levels, with FSH levels showing a non-significant decrease in males, which were mitigated significantly by the administration of the plant extract. Histological analysis revealed alterations in the testis, epididymis, and prostate of the AS-exposed groups, including necrosis of seminiferous tubule epithelium and Leydig cells in the testis, and basal epithelial necrosis in the epididymis and prostate. Aluminum levels increased in all organs studied, while levels of zinc, copper, iron, and manganese decreased, showing a negative and significant correlation with aluminum levels. The aqueous extract of S. tectorum demonstrated a protective effect on certain studied biomarkers in male rats affected by aluminum exposure.

In applied mathematics, statistics, operation research, physics, and engineering mathematics, confluent representations of hypergeometric functions in one and two variables are known to exist, and their occurrence in a variety of applications is also well recognised. In this article, we intend to present a new derivation of the extended Watson summation theorem for the Kim et al. given series 4F3. We assessed four attractive integrals involving generalized hypergeometric function as an application. With a few particular cases, this note will come to an end. In the results given above, symmetry appears on its own.

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

In this paper, the new optical wave solutions of truncated M-fractional perturbed Kundu-Eckhaus model with full non-linearity are obtained by utilizing the expa function technique and modified extended tanh expansion function technique. The solutions are in the form of dark soliton, bright soliton, singular solitons and other form of solutions. The gained solutions are helpful for the further development of concerned model. The obtained results have also been presented graphically in both two-dimensional and three-dimensional formats to discuss the dynamical features as well as the parametric dependence of the constructed solutions. The study offers a highly spectacular and acceptable techniques to combine various intriguing wave demonstrations for more sophisticated models of the modern day.

Background Cytomegalovirus (CMV) is a major pathogen that cause remarkable rate of morbidity and mortality, especially in immunocompromised patients. It is important to find risk factors associated with CMV viremia. We studied the differences in CMV seropositivity in relation to liver function biomarkers in male and female Saudi population in an attempt to understand the variation in the CMV seroprevalence with sex and find the risk factor to develop liver dysfunction or hepatocellular carcinoma. Material and subjects: The CMV- IgG and IgM were screened in serum samples of 150 non- A-G hepatities patients with elevation of liver profiles (ALT, AST, ALP and GGT) and categorized as males and females. Samples were collected from different general hospitals and polyclinic in KSA from March 2014 to June 2015. A correlation between CMV seropositivity measured with both antibodies and liver enzymes were tested. Receiver operating characteristics (ROC) analysis and multiple regressions were done for the obtained data. Results: Our study shows that females had much higher IgG and IgM compared to age-matching males. A significant correlation between both antibodies and liver enzymes (AST, ALT) was recorded. Less significant correlation of both IgG and IgM with GGT was also observed. Receiver operating characteristics (ROC) analysis revealed that both IgG and IgM can be used as excellent predictive markers for CMV infection as both recorded 100% specificity and sensitivity together with area under the curve of 1 in males and females. Multiple regression analysis ascertain the correlation between both antibodies as dependent variables and liver enzymes as independent variables with ALT being the most affected enzyme with CMV seropositivity especially in females. Conclusion:he data discussed above This study shows that CMV is capable of initiating and accelerating liver dysfunction in both sexes. The high seroprevalence in females at reproductive age is especially important as they can transmit the virus to their developing fetus. Prevention of CMV infection in young girls 11-14 years old, through counseling on hygiene or possible future vaccination, may lead to a decrease of congenital CMV infections with the concomitant risk of developing liver dysfunction or hepatocellular carcinoma. Keywords: Cytomegalovirus, Alanine transaminase, Aspartate transaminase Alkaline phosphatase, γ-Glutamyltranspeptidase, liver function.

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

It is due to Littlewood that the truth of the Riemann theorem implies that of the Lindel\"{o}f conjecture. This paper aims to use the idea of Littlewood to prove the Lindel\"{o}f conjecture for the Riemann zeta function. The Lindel\"{o}f $\mu $ function at the critical line is zero, with use of the Riemann theorem for the entire Riemann zeta function, proved based on the work of Heath-Brown. Our result is given to show that the Lindel\"{o}f conjecture, connected with the proof of the moment conjecture, is true.

The main focus when developing software is to improve the reliability and stability of a software system. When software systems are introduced, these systems are used in field environments that are the same as or close to those used in the development-testing environment; however, they may also be used in many different locations that may differ from the environment in which they were developed and tested. In this paper, we propose a new software reliability model that takes into account the uncertainty of operating environments. The explicit mean value function solution for the proposed model is presented. Examples are presented to illustrate the goodness-of-fit of the proposed model and several existing non-homogeneous Poisson process (NHPP) models and confidence intervals of all models based on two sets of failure data collected from software applications. The results show that the proposed model fits the data more closely than other existing NHPP models to a significant extent.

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.

Fibre reinforced concrete (FRC) has been used for decades in certain applications of the construction industry, such as tunnel linings and precast elements, but has experienced an important progress in recent times, boosted by the inclusion of guidelines for their use in some national and international standards. Traditional steel fibres have been studied in depth and their performance is well known although in recent years new materials have been proposed as possible alternatives. Polyolefin macro-fibres, for instance, have proven to enhance the mechanical properties of concrete and the parameters that define their behaviour (fibre length, fibre proportion or casting method, for instance) have been identified. These fibres overcome certain traditional problems related to steel fibres, such as corrosion or their interaction with magnetic fields, which can limit the use of steel in some applications. The behaviour of polyolefin fibre reinforce concrete (PFRC) has been numerically reproduced with success through an embedded cohesive crack formulation that uses a trilinear softening diagram to describe the fracture behaviour of the material. Furthermore, concrete behaves well under high temperatures or fire events, especially when it is compared with other construction materials, but the behaviour of PFRC must be analysed if the use of these fibres is to be extended. To this end, the degradation of PFRC fracture properties has been recently experimentally analysed under a temperature range between 20ºC and 200ºC. As temperature increases, polyolefin fibres modify their mechanical properties and their shape, which reduce their performance as reinforcement of concrete. In this work, those experimental results, which include results of low (3 kg/m3) and high (10 kg/m3) proportion PFRC specimens, are used as reference to study the fracture behaviour of PFRC exposed to high temperatures from a numerical point of view. The experimental load-deflection diagrams are reproduced by modifying the trilinear diagram used in the cohesive model, which helps to understand how the trilinear diagram parameters are affected by high temperature exposure. Finally, some expressions are proposed to adapt the initial trilinear diagram (obtained with specimens not exposed to high temperature) in order to numerically reproduce the fracture behaviour of PFRC affected by high temperature exposure.

In this study we introduce the new classes $\mathcal{M}_{\alpha}(\sin)$ and $\mathcal{M}_{\alpha}(\cos)$ of $\alpha$-convex functions associated with sine and cosine functions. Also, we obtain the initial coefficient bounds for the first five coefficients of the functions that belong to these classes. Further, we determine the upper bound of Zalcman functional for the class $\mathcal{M}_{\alpha}(\cos)$ for the case $n=3$, showing that the Zalcman conjecture holds for this value. Moreover, the problem of the Fekete-Szeg\H{o} functional estimate for these classes is studied.

The purpose of this study was to investigate the effect of circuit training on β-amyloid, BDNF, and cognitive function in untrained obese elderly Korean women. The subjects for the study were aged 65–70 years, composed of the circuit training group(n=12) and control group(n=11). The 60-minute combined exercise was performed 3 times per week for 16 weeks. Exercise intensity was progressively increased from 40% HRR to 70% HRR. The test data were analyzed by paired t-test, independent t-test, and two-way repeated measures ANOVA, and the alpha level of .05 was set for all tests of significance. The findings of this study were as follows: β-amyloid significantly decreased after the exercise group had compared to before the exercise and BDNF and cognitive function significantly increased after the exercise group had compared to before the exercise. However, there were no significant changes in β-amyloid, BDNF, and cognitive function in the control group Therefore, it is suggested that the circuit training used in this study could be an effective exercise method for improving the risk factors of cognitive impairment in obese elderly Korean women.

The unsteady Ekman problem involves finding the response of the near-surface currents to wind stress forcing under linearized dynamics. Its solution can be conveniently framed in the frequency domain in terms of a quantity that is known as the transfer function, the Fourier transform of the impulse response function. In this paper, a theoretical investigation of a fairly general transfer function form is undertaken with the goal of paving the way for future observational studies. Building on earlier work, we consider in detail the transfer function arising from a linearly-varying profile of the vertical eddy viscosity, subject to a no-slip lower boundary condition at a finite depth. The linearized horizontal momentum equations are shown to transform to a modified Bessel’s equation for the transfer function. Two self-similarities, or rescalings that each effectively eliminate one independent variable, are identified, enabling the dependence of the transfer function on its parameters to be more readily assessed. A systematic investigation of asymptotic behaviors of the transfer function is then undertaken, yielding expressions appropriate for eighteen different regimes, and unifying the results from numerous earlier studies. A solution to a numerical overflow problem that arises in the computation of the transfer function is also found. All numerical code associated with this paper is distributed freely for use by the community.

In the paper, the authors present an explicit form for a family of inhomogeneous linear ordinary differential equations, find a more significant expression for all derivatives of a function related to the solution to the family of inhomogeneous linear ordinary differential equations in terms of the Lerch transcendent, establish an explicit formula for computing all derivatives of the solution to the family of inhomogeneous linear ordinary differential equations, acquire the absolute monotonicity, complete monotonicity, the Bernstein function property of several functions related to the solution to the family of inhomogeneous linear ordinary differential equations, discover a diagonal recurrence relation of the Stirling numbers of the first kind, and derive an inequality for bounding the logarithmic function.

The acute phase protein serum amyloid A (SAA) is associated with endothelial dysfunction and early-stage atherogenesis. Stimulation of vascular cells with SAA increases gene expression of pro-inflammation cytokines and tissue factor (TF). Activation of the transcription factor, nuclear factor kappa-B (NFkB), may be central to SAA-mediated endothelial cell inflammation, dysfunction and pro-thrombotic responses, while targeting NFkB with a pharmacologic inhibitor, BAY11-7082, may mitigate SAA activity. Human carotid artery endothelial cells (HCtAEC) were pre-incubated (1.5 h) with 10 µM BAY11-7082 or vehicle (control) followed by SAA (10 μg/mL; 4.5 h). Under these conditions gene expression for TF and TNF increased in SAA-treated HCtAEC and pre-treatment with BAY11-7082 significantly (TNF) and marginally (TF) reduced mRNA expression. Intracellular TNF and IL-6 protein also increased in HCtAEC supplemented with SAA and this expression was inhibited by BAY11-7082. Supplemented BAY11-7082 also significantly decreased SAA-mediated leukocyte adhesion to apolipoprotein E-deficient mouse aorta in ex vivo vascular flow studies. In vascular function studies, isolated aortic rings pre-treated with BAY11-7082 prior to incubation with SAA showed improved endothelium-dependent vasorelaxation and increased vascular cGMP content. Together these data suggest that inhibition of NFkB activation may protect endothelial function by inhibiting the pro-inflammatory and pro-thrombotic activities of SAA.

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

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

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

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

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

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

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

The Colony-Forming Unit (CFU) counting problem remains a complex issue without a universal solution in biomedical and food safety domains. A multitude of sophisticated heuristics and segmentation-driven approaches have been proposed by numerous researchers. Among those, U-Net is the most frequently cited and popular Deep Learning method. The latter approach provides a segmentation output map and requires an additional counting procedure which accounts for unique segmented regions and detected microbial colonies. However, because of pixel-based targets it tends to generate irrelevant artifacts or errant pixels, leading to inaccurate and mixed post-processing results. In response to these challenges, we propose a novel hybrid counting approach, incorporating a multi-loss U-Net reformulation and a post-processing Petri dish localization algorithm. First of all, our unique innovation lies in the multi-loss U-Net reformulation. We introduce an additional loss term at the bottleneck U-Net layer, focusing on delivering an auxiliary signal indicating where to look for distinct CFUs. Second, our novel localization algorithm accurately incorporates an agar plate and its bezel into the CFU counting routines. Finally, our proposition is further enhanced by the integration of a fully automated solution. This comprises a specially designed uniform Petri dish illumination system and a counting web application. The latter application is capable of directly receiving images from the camera, which are subsequently processed, and the segmentation results are sent back to the user. This feature provides an opportunity to correct the CFU counts, offering a feedback loop that contributes to the continued development of the Deep Learning model. Through extensive experimentation, we have found that all probed multi-loss U-Net architectures incorporated in our hybrid approach consistently outperform their single-loss counterparts which utilize exclusively the combination of Tversky and Cross-Entropy training losses at the output U-Net layer. We report further significant improvements by the means of our novel localization algorithm. This reaffirms the effectiveness of our proposed hybrid solution in addressing contemporary challenges of the precise in-vitro CFU counting.

Long-term safety of a nutraceutical combination based on agnus castus and magnolia extracts combined with soy isoflavones (SI) and lactobacilli, and effectiveness on vasomotor symptoms and sleep disorders in postmenopausal women, were assessed. A controlled study was carried-out in menopausal women comparing this nutraceutical combination (ESP group) with formulation containing isoflavones alone (C group), at the dosage recommended. Kuppermann index, PSQI, and SF-36 were determined at baseline, 3, 6 and 12 months. Endometrial thickness, mammary density and liver function were evaluated at baseline and after 12 months. 180 women (100 in ESP group and 80 in C group, mean age 55.5 years, in menopause for about 36 months) were enrolled in the study. At the treatment end, mammary density, endometrial thickness, and hepatic function did not show substantial differences between groups. Kuppermann index, and particularly hot flushes, were progressively and significantly decreased in frequency and severity during ESP versus C treatment. No adverse events were observed. Agnus castus and magnolia, combined with SI + lactobacilli, can effectively and safely be used in symptomatic postmenopausal women, mainly when quality of sleep is the most disturbing complaint. Endometrium, mammary glands and liver function, were unaffected after 12 months treatment.