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.

The Nocturnal Bottleneck explains how mammals evolved from their reptilian ancestors after inverting the chronotype, form diurnal to nocturnal. Pre-mammals traded-off the excellent visual system of their ancestors for improvements in audition and in olfactory telencephalon, needed for efficient orientation in the dark. This was how the mammalian nocturnal telencephalic wakefulness was born. However, the modified visual system of those pre-mammals became sensitive to the dangerous diurnal light and the exposure would involve a high risk of blindness and death. Therefore, pre-mammals had to remain immobile with closed eyes hidden in lightproof burrows during light time. This was the birth of the mammalian sleep. Typical reptiles distribute their wake time cycling between Basking Behavior, to attain the preferred body temperature, and poikilothermic Goal Directed Behavior, to perform life sustaining tasks. These cycles persisted during the new mammalian sleep. However, as the behavioral output had to be blocked during light time, the paralyzed reptilian Basking Behavior and Goal Directed Behavior cycles became the NREM and REM cycles, respectively. This was how NREM and REM cycles remained incorporated within the mammalian sleep. After the Cretaceous-Paleogene extinction, the environmental pressure for nocturnal life was softened, allowing high variability in chronotype and sleeping patterns. This permitted some mammalian groups, e.g., primates, to begin the quest for diurnal wake.Concluding, sleep constituted an additional bottleneck in the mammalian evolution. The reduced population of pre-mammals that was able to develop sleep during light time, including NREM and REM, became full mammals and survived; the remainder perished.

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.

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.

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.

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.

In combustor systems, thermoacoustic instabilities may occur and must be avoided for reliable op-eration. An acoustic network model can be used to predict the eigenfrequencies of the instabilities and the growth rate by incorporating the combustion dynamics with a Flame Transfer Function (FTF). The FTF defines the interconnection between burner aerodynamics and the rate of combus-tion. In the current study, the method to measure the FTF in a pressurized combustor is explored. A siren unit, mounted in the fuel line, induced a fuel flow excitation of variable amplitude and high maximum frequency. This was done here for pressurized conditions at 1.5 bar and 3 bar and at thermal power of 125 kW and 250 kW. In addition to the experimental investigation, a 1-D acoustic network model approach is used. In the model, thermo viscous damping effects and reflection coefficients are incorporated. The model results compare well with experimental data, indicating the proposed method to determine the FTF is reliable. In the approach, a combination of a FTF with a band stop approach and a network modeling approach was applied. The method provides a good match between experimentally observed behavior and analytical approach and can be used for instability analysis.

Evidence suggests that COVID-19 infection can cause lasting health consequences. Multidiscipli-nary rehabilitation services have been recommended to reduce the sequalae. However, the effec-tiveness of physical exercise interventions remains insufficiently documented. The aim of this study was to develop and implement a specific and well tolerated protocol-based, intervention to reduce muscle weakness in older adults impacted by COVID-19. Forty six older adults random-ized into Intervention and Control Groups. Isometric and isokinetic strength assessments were conducted for selected muscle groups using JBA Staniak® torquemeter and Biodex System 3 dy-namometer. Functional abilities were evaluated with the Time Up and Go test and Chair Stand Tests. Men in intervention group demonstrated a significant improvement in static conditions for knee flexors (KF), trunk extensors (TE) and trunk flexors (TF) and in dynamic conditions for knee extensors (KE). Women in intervention group showed significant improvement in static condition for EF, KF, TE and TF and in dynamic for a KE and for a KF. The interaction GROUP x TESTING SESSION was significant for Chair test (s) and Chair test (n). Our results demonstrate the effec-tiveness of a well-tolerated, protocol-based approach that can be used to diminish long lasting functional deficits in post-covid survivors.

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.

We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals.

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.

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.

The function of sleep in mammal and other vertebrates is one of the great mysteries of biology. Many hypotheses have been proposed, but few of these have made even the slightest attempt to explain the essence of sleep - the uncompromising need for reversible unconsciousness. During sleep, epiphenomena - often of a somatic character - occur, but these cannot explain the core function of sleep. One answer could be hidden in the observations made for long periods of time of the function of the central nervous system (CNS). The CNS is faced with conflicting requirements on stability and excitability. A high level of excitability is desirable, and is also a prerequisite for sensitivity and quick reaction times; however, it can also lead to instability and the risk of feedback, with life-threatening epileptic seizures. Activity-dependent negative feedback in neuronal excitability improves stability in the short term, but not to the degree that is required. A hypothesis is presented here demonstrating how calibration of individual neurons - an activity which occurs only during sleep - can establish the balanced and highest possible excitability while also preserving stability in the CNS. One example of a possible mechanism is the observation of slow oscillations in EEGs made on birds and mammals during slow wave sleep. Calibration to a genetically determined level of excitability could take place in individual neurons during the slow oscillation, so that action potentials are generated during the oscillations “up-phase”. This can only take place offline, which explains the need for sleep. The hypothesis can explain phenomena such as the need for unconsciousness during sleep, with the disconnection of sensory stimuli, slow EEG oscillations, the relationship of sleep and epilepsy, age, the effects of sleep on neuronal firing rate and the effects of sleep deprivation and sleep homeostasis. This is with regard primarily to mammals, including humans, but also all other vertebrates.

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.

In this paper, two double Jordan-type inequalities are introduced based on the papers [1]-[5]. These inequalities generalize the inequalities obtained in [1]-[5]. As a result, some new upper and lower bounds of the sinc function are obtained. This extension of Jordan’s inequality is enabled by considering the corresponding inequalities through the concept of stratified families of functions elaborated in [6]. Based on this approach, some optimal approximations of the sinc function are derived by determining corresponding minimax approximants, also described in the paper [6].

Experimental evidence suggests that chronic intermittent hypoxia (CIH), a major hallmark of obstructive sleep apnea (OSA), boosts carotid body (CB) responsiveness, thereby causing in-creased sympathetic activity, arterial and pulmonary hypertension, and cardiovascular disease. An enhanced circulatory chemoreflex, oxidative stress, and NO signaling appear to play im-portant roles in these responses to CIH in rodents. Since the guinea pig has a hypofunctional CB (i.e., it is a natural CB knockout), in this study we used it as a model to investigate the CB de-pendence of the effects of CIH on pulmonary vascular responses, including those mediated by NO, by comparing them with those previously described in the rat. We have analyzed pulmonary artery pressure (PAP), the hypoxic pulmonary vasoconstriction (HPV) response, endothelial function both in vivo and in vitro, and vascular remodeling (intima-media thickness, collagen fiber content, and vessel lumen area). We demonstrate that 30 days of exposure of guinea pigs to CIH (FiO2, 5% for 40 s, 30 cycles/h) induces pulmonary artery remodeling but does not alter en-dothelial function or the contractile response to phenylephrine in these arteries. In contrast, CIH exposure increased the systemic arterial pressure, and enhanced the contractile response to phenylephrine while decreasing endothelium-dependent vasorelaxation to carbachol in the aorta, without causing its remodeling. We conclude that since all of these effects are independent of CB sensitization, there must be other oxygen sensors, beyond the CB, with the capacity to alter the autonomic control of the heart and vascular function and structure in CIH.

In this review, we outline our current understanding of the mechanisms involved in the absorption, storage, and transport of dietary vitamin A to the eye, the trafficking of rod opsin protein to the photoreceptor outer segments, which encompasses the logistical backbone required for visual function. Two key mechanisms of this process are emphasized in this manuscript: Ocular and systemic vitamin A membrane transporters, and rhodopsin transporters. Understanding the complementary mechanisms responsible for the generation and proper transport of the retinylidene opsin to the photoreceptor outer segment will eventually shed light on the importance of genes encoded by these proteins, and their relationship on normal visual function and in the pathophysiology of retinal degenerative diseases.

Despite the clinical significance of partial posttraumatic stress disorder (PTSD), research on its associated cognitive function profiles is notably lacking. This study aimed to identify distinct cognitive function profiles in patients with partial PTSD. Medical records of Vietnamese War Korean Veterans undergoing psychiatric assessments, including the Clinician-Administered PTSD Scale (CAPS) and neurocognitive tests on the same day, were retrospectively reviewed. The participants were divided into partial PTSD (N = 10) and non-PTSD (N = 36) groups based on the CAPS interview. Neurocognitive test score profiles of the partial PTSD and non-PTSD groups were compared. Covariance analysis adjusted for potential confounders in cognitive function. In cognitive profiles, executive function, mental flexibility (measured by Trail Making Test B), and concentration (measured by the Mini-Mental Status Exam) were significantly poorer in the partial PTSD group. When adjusted for age, depressive symptoms, and education level, no significant differences were observed in the cognitive profiles between the partial PTSD and non-PTSD groups. In the current study, executive function and concentration showed deficits in patients with partial PTSD compared with those without PTSD. Partial PTSD cognitive profiles displayed no significant differences from non-PTSD profiles when adjusted for possible confounders such as depressive symptoms.

In patients with schizophrenia, metabolic syndrome is associated with cognitive impairments. We carried out a second analysis of data from a longitudinal trial to examine the relationship between weight gain and cognitive function in patients with first-episode schizophrenia (FES) over the first 6-month antipsychotic treatment. Baseline and 6-month endpoint measurements were taken for both cognitive function and body weight. Linear and logistic regression analyses were applied to investigate the bidirectional relationship between weight gain and cognitive function. Clinically relevant weight gain (CRW) was defined as an increase in body weight ex-ceeding 7%. The final analysis included 337 participants. Lower baseline scores in processing speed (OR=0.837, p=0.007), working memory and attention (OR=0.889, p=0.043), and executive function (OR=0.863, p=0.006) domains were significantly associated with CRW at the 6-month endpoint. After adjusting for confounders, CRW was found to be associated with improvement in the Brief Visuospatial Memory Test (p=0.036). The findings suggest that patients with lower baseline cognitive performance experienced more substantial weight gain. Conversely, weight gain was correlated with cognitive improvements, particularly in the domain of visual learning and memory. This suggested a potential bidirectional relationship between weight gain and cog-nitive function in patients with first-episode schizophrenia.

Transformation formula under the action of a general linear fractional transformation for generalized Dedekind eta-function has been a subject of intensive study, Rademacher, Dieter, Meyer et al. However, the (Hecke) modular relation structure has not been recognized until the work of Goldstein-de la Torre, and streamlining the classical proofs in the modular relation will reveal the meaning hidden in those works. Our main aim is to elucidate the works of these researchers in the context of modular relations.

Human activities (e.g., exploitation, utilization, and conservation) exert substantial impact on forest ecological functions (FEF). The human influence on FEF significantly varies across developmental stages, which are attributed to the temporal and spatial in nature. This study evaluates some notable FEF indices (FEFI) in the 448 counties within the Yellow River basin (YRB) using panel data from the Seventh to Ninth National Forest Inventory. Data analysis involves employing the residual trends, geographical and temporal weighted regression. Results indicate that, firstly, the overall forest ecological function in the YRB is moderate to inferior, with superior FEF in counties endowed with more natural forest resources. Afforestation demonstrates a short-term improvement, but its effectiveness diminishes over time. Secondly, the positive spatial correlation is stronger among counties, characterized by both high-high and low-low agglomeration effects. Scattered planting, simple stand structure, and concentrated harvesting of forests at the identical stand ages hinder the formation of complex and large-scale FEF agglomerations. Thirdly, significant spatial-temporal differences exist in the impact of human activities on FEF. In the upper reaches of the basin, increased vegetation coverage through agricultural and forestry production benefited FEF, however, some over-exploitation of forests and grasslands is observed there. In the middle reaches, the economic development, expanding population and the greening activities help to improve FEF effectively, but excessive water using in agricultural production brought more difficulties to FEF improvement. In the lower reaches of the basin, improved wastelands and forest protection positively influence FEF. This study recommends that county governments should prioritize forest management with multi-species and multi-layered complex forests. Each county should define its position in regional development and ecological protection, considering the potential impacts on neighboring regions. This holistic approach promotes more effective integrated regional management.

The basic idea is to expand the completed zeta function $\xi(s)$ in MacLaurin series (infinite polynomial), which can be further expressed as infinite product (Hadamard product) by conjugate complex roots. Finally, the functional equation $\xi(s)=\xi(1-s)$ leads to $(s-\alpha_i)^2 = (1-s-\alpha_i)^2, i \in \mathbb{N}$ with solution $\alpha_i= \frac{1}{2}, i \in \mathbb{N}$, where $\alpha_i$ are the real parts of the zeros of $\xi(s)$, i.e., $s_i =\alpha_i\pm j\beta_i, i\in \mathbb{N}$. Therefore, a proof of the Riemann Hypothesis is achieved.

Chronic kidney disease patients treated by hemodialysis present a high cardio-vascular morbidity and mortality. There is an imperative need for novel biomarkers in identifying and to offer possible therapeutically intervention in these patients. We performed a prospective observational cohort study on 77 patients in the period October 2021 – October 2023. We measured serum plasma levels of Interleukin 1-Beta, Galectin 3, human suppression of tumorigenicity factor 2, bone morphogenetic protein 2 and fibroblastic growth factor 23 at the inclusion. We evaluated the correlations of these biomarkers with cardiac function and structure evaluated by echocardiography. Mean age was 61.02 (±11.81) years, 45 (56.2%) males and with a dialysis vintage of 4.95 (2.4-7.8) years. Median ejection fraction was 51 (43-54 %) and more than two thirds of the patients presented valvular calcifications. Overall mortality was 22%. Interleukin 1-Beta correlated positively with ejection fraction and global longitudinal strain and negatively with left atrium diameter and left ventricle tele systolic diameter. Galectin 3 values negatively correlated with aortic valve fibrosis and mitral valve calcifications and human suppression tumorigenity factor 2 negatively correlated with mitral valve calcifications. Some of these novel biomarkers could be used to better asses the cardio-vascular disease in patients on maintenance hemodialysis.

Background: Cardiovascular (CV) morbidity and mortality are many times higher in chronic kidney disease (CKD), as well as IgA nephropathy (IgAN), than in the general population. The occurrence of metabolic syndrome (MetS) and metabolic risk factors are independent risk factors for CV disease and renal progression. The study aimed to determine the prognostic role of metabolic profiles in a homogenous group of CKD patients. Methods: One hundred and forty-five IgA nephropathy patients (92 male, 53 female, age 54.7 ± 13 years) with CKD stage 1-4 were investigated and followed for a median of 190 months. The composite (CV and renal) endpoints included all-cause mortality and any CV event such as stroke, myocardial infarction, revascularization (CV), end-stage renal disease, and renal replacement therapy (renal). Results: Patients with MetS had significantly more endpoint events (16/27 patients vs. 15/98 patients, p = 0.001) compared to the nonMetS group. Of the secondary endpoints (CV or renal separately), the rate of the renal and CV endpoints was significantly higher in the MetS group (p = 0.001 and p = 0.029). The primary endpoint independent predictors of survival were dyslipidemia, eGFR, hemoglobin, urine albuminuria, and diabetes mellitus, as determined by Cox regression analysis. Independent predictors of secondary renal endpoint were dyslipidemia, hemoglobin, urine albumin, and eGFR. Predictors of secondary cardiovascular endpoints were gender, BMI, and diabetes. Kaplan-Meier curves showed significant differences in MetS and non-MetS when examined at the combined endpoints (CV and renal) or at each endpoint separately. The primary endpoint rate increased significantly with the increased number of MetS components (MetS comp. 0 vs. MetS comp. 2+, primary endpoints, p = 0.012). Conclusion: Our results showed that the metabolic profile has a prognostic role not only for renal endpoints but also for CV endpoints in IgAN. BMI, hyperuricemia, hypertension, and diabetes have a predictive value for the prognosis of IgA nephropathy.

Badminton is one of the most popular racket sports played by children up to the elderly worldwide. Everyone can practice and play badminton as a leisure or competitive sport, regardless of age, experience, or skill level. It does not require physical contact among players and expensive equipment. Compared with closed-skill exercise (e.g., running, swimming), open-skill exercise (e.g., badminton, table tennis) has been reported to intervene more with cognitive function and prevent cognitive decline. In this review, we outline the characteristics of badminton’s beneficial effects on physical and cognitive aspects. The characteristics presented here indicate that intervention with regular badminton exercise could effectively improve cognitive function and prevent cognitive decline in the elderly.

Under the same seismic load, different local topography will have different effects, which is an important research field in seismic engineering. Hills are connected with valleys is a very typical terrain. Taking this terrain as an example, its response to the most destructive SH waves in the earthquake is studied. By simplifying and dividing the model, the wave functions satisfying the wave equation and boundary conditions in each region are constructed by using the complex function and moving coordinate method. The equations satisfying the boundary continuity conditions are established. With the help of calculation software, the numerical results are obtained. The influence of different parameters on ground motion is discussed.

In this paper, some convexity properties and some inequalities for the (p,k)-analogue of the Gamma function, Г_p,k(x) are given. In particular, a (p,k)-analogue of the celebrated Bohr-Mollerup theorem is given. Furthermore, a (p,k)-analogue of the Riemann zeta function, ζ_p,k(x) is introduced and some associated inequalities are derived. The established results provide the (p,k)-generalizations of some known results concerning the classical Gamma function.

The liver diseases are posing serious threat to human health associated with abusive use of allopathy medicines, especially in developing economies like Pakistan. The strengthening of detoxification system using natural products might be a suitable option to minimize the liver problems. In this current research, Zingiber officinale and Azadirachta indica were evaluated for their hepatoprotective role. For the purpose, 20 Sprague Dawley rats were equally divided into four groups i.e., negative control, paracetamol positive control, 2.5% ginger and 2% neem powder, respectively. During 42 days study, the levels of bilirubin and liver enzymes significantly elevated due to liver damage. Although, the values dropped (20-25%) in treatment group. Serum glucose and serum lipid profile increased in positive control group, but reduced (5-10%) in both ginger and neem groups. The serum protein profile declined in liver damage group, however, improved (~5%) in treatment groups. The hematological parameters slightly declined in liver damage group, but increased in ginger and neem groups. Moreover, the white blood cells differential count and renal parameters showed abnormal values in liver damage group, but improved after treatment. This study is promising and highlighted the hepato-protective role of neem and ginger that may open several avenues of research.

The two-parameter distribution introduced by Kumaraswamy (1980) is a very flexible alternative to the Beta distribution with the same (0,1) support. Originally proposed in the field of hydrology, it has subsequently received a good deal of positive attention in both the theoretical and applied statistics literatures. Interestingly, the problem of testing formally for the appropriateness of the Kumaraswamy distribution appears to have received little or no attention to date. To fill this gap, in this paper we apply the “biased transformation” methodology proposed by Raschke (2009) to several standard goodness-of-fit tests based on the empirical distribution function. A simulation study reveals that these (modified) tests perform well in the context of the Kumaraswamy distribution, in terms of both low size distortion, and respectable power. In particular, the “biased transformation” Anderson-Darling test dominates the other tests that are considered.

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 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.

We propose a neural-network-based watermarking method that introduces the quantized activation function that approximates the quantization of JPEG compression. Many neural-network-based watermarking methods have been proposed. Conventional methods have acquired robustness against various attacks by introducing an attack simulation layer between the embedding network and the extraction network. The quantization process of JPEG compression was replaced by the noise addition process in the attack layer of the conventional methods. In this paper, we propose a quantized activation function that can simulate the JPEG quantization standard as it is in order to improve the robustness against the JPEG compression. Our quantized activation function consists of several hyperbolic tangent functions and is applied as an activation function for neural networks. Our network was introduced in the attack layer of ReDMark proposed by Ahmadi et al. to compare it with their method. That is, the embedding and extraction networks had the same structure. We compared the usual JPEG compressed images and the images applying the quantized activation function. The results showed that a network with quantized activation functions can approximate JPEG compression with high accuracy. We also compared the bit error rate (BER) of estimated watermarks generated by our network with those generated by ReDMark. We found that our network was able to produce estimated watermarks with lower BERs than those of ReDMark. Therefore, our network outperformed the conventional method with respect to image quality and BER.

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.

This paper is concerned with a hydraulic cylinder directly controlled by a variable speed fixed displacement pump. The considered configuration is referred to as a one-motor-one-pump (1M1P) motor-controlled hydraulic cylinder (MCC). A 1M1P MCC with a hydraulically driven passive load-holding function enabled by controlled system pressures is proposed. The proposed load-holding functionality works if there is a standstill command, a loss of power supply, or a hose rupture. Additionally, this paper conducts a comprehensive analysis of the proposed system's operation and load-holding function across four quadrants. Simulation results demonstrate the four-quadrant operation and good load-holding performance under the aforementioned scenarios. In conclusion, the proposed 1M1P MCC can be successfully used on practical applications characterized by overrunning loads and four quadrant operation.

A general methodology for loan amortization under arbitrary discount functions is discussed. It is shown that it is always possible to uniquely define a scheme for constructing the loan amortization schedule with an arbitrary assigned discount function. It is also shown that even if the loan amortization is carried out from the sequence of principal payments and the sequence of accrued interest, the underlying discount function can be uniquely determined at the maturities corresponding to the installment payment dates. As a special case of the proposed approach, we derive the amortization method according to the law of simple interest.

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.

Background: 3D virtual reality (VR) Motionless Imagery Exercise through Avatar (MIEA) was developed to improve elderly’s psychological (cognitive and emotional) and physical health. This study observed the impact of this program on the cognitive functions and emotional well-being and the electrophysiological changes in older adults. Methods: This study was conducted using a randomized controlled trial design. The participants included 38 adults, 65 to 84 years of age, who were physically mobile and neurologically healthy. Among them, 19 participants were assigned to the experimental group, who underwent exercises using elderly avatars in a VR virtual exercise program. The other 19 participants were assigned to the control group who underwent the VR program. Both groups engaged in the VR intervention for 20 minutes three times a week, over six weeks. Results: The cognitive functions, including attention restraint, working memory, and phonemic fluency, of the experimental group showed significant improvements compared to the control group. Regarding emotional well-being, the experimental group showed greater self-efficacy. The electrophysiological changes revealed similar patterns to exercise-induced reactions in electromyography of the experimental group after intervention. Conclusions: These findings confirm that participation in 3D VR MIEA enhances cognitive functions and physical self-efficacy among the elderly. Therefore, 3D VR MIEA can be utilized in the rehabilitation therapy of patients or elderly with limited physical activity.

This paper concentrates on the general birth-death processes with two different types of catastrophes. The Laplace transform of transition probability function for birth-death processes with two-type catastrophes are is successfully expressed with the Laplace transform of transition probability function of the birth-death processes without catastrophe. The first effective catastrophe occurrence time is considered. The Laplace transform of its probability density function, expectation and variance are obtained.

Body-centered cubic bismuth (Bi) is considered an enticing pressure marker, and therefore it is highly desirable to command its accurate equation of state (EOS). However, significant discrepancies are noted among the previous experimental EOSs. In the present work, the EOS up to 300 GPa is theoretically obtained by direct solving the partition function via a direct integral approach (DIA). The calculated results nearly reproduce the hydrostatic experimental measurements below 75 GPa, and the deviations from the measurements gradually get larger with increasing pressure. Based on the ensemble theory of equilibrium state, DIA works with high precision particularly in high-pressure conditions, so the hydrostatic EOS presented in this work is expected to be a reliable pressure standard.

The fitting and modeling of skewed, complex, symmetric, and asymmetric datasets is an exciting research topic in many fields of applied sciences, notably lifetime, medical, and financial sciences. The Heavy tailed Nadarajah Haghighi model is introduced by compounding the heavy tailed family and Nadarajah Haghighi distribution in this paper. The so obtained model has three parameters accounting for the scale and shape of the distribution. The proposed distribution's fundamental characteristics such as probability density, cumulative distribution, hazard rate, and survival functions are provided, and several key statistical properties are established, and several entropy information measures are proposed. The estimation of model parameter is performed via the ML procedure. Further, different simulation experiments are conducted to demonstrate the performance of proposed estimator’s using some measure, like the average estimate, the average bias, and associated mean square error. Finally, we are applied our proposed model to analyze three different real datasets. In our illustration, we are compared the practicality of the recommended model with several well-known competing models.

In this paper the one-to-one correspondences and equivalences between ideals, primals, filters and grills are introduced. It is shown the local functions and the topological spaces induced by them are the same. From this point of view, the topological properties with respect to one topology can be derived from topological properties valid in the corresponding topology.

Traditional path planning algorithms have drawbacks in unmanned vehicle path planning, such as low efficiency, unsuitability for dynamic environments, and high computational complexity. To address these issues, this paper proposes a dynamic path planning method for unmanned vehicles that combines the A* algorithm with an improved Dynamic Window Approach (DWA). Firstly, a collision risk function is incorporated into the DWA algorithm to evaluate scores based on the braking distance corresponding to the current vehicle speed and the distance to obstacles, determining whether timely braking or obstacle avoidance is feasible. The earlier the braking or obstacle avoidance, the higher the score, thereby enhancing the evaluation algorithm of the DWA. Secondly, the key points extracted by the A* algorithm are used as temporary target points for the DWA algorithm, reducing the eight search directions to five. Finally, the key points of the A* algorithm’s path are set as the temporary end points for the DWA algorithm, integrating the two algorithms to plan a smoother curved path that can avoid unknown and dynamic obstacles. Simulation data demonstrates that compared to traditional artificial potential field methods, RRT, and Dijkstra’s algorithm, the new fusion algorithm reduces time by 11.71 seconds, a decrease of 6.9%, and shortens path length by 3.093 meters, a reduction of 4.16%, while increasing average linear velocity by 2.9%. The proposed algorithm ensures smoother paths while also making paths more rational and efficient

In the paper, the authors find closed forms for derangement numbers in terms of the Hessenberg determinants, discover a recurrence relation of derangement numbers, present a formula for any higher order derivative of the exponential generating function of derangement numbers, and compute some related Hessenberg and tridiagonal determinants.

This paper focuses on the problem of finite-time stabilization of homogeneous, non-Lipschitz systems with dilations. A key contribution of this paper is the design of a virtual recursive Hölder, non-Lipschitz state feedback which renders the non-Lipschitz systems in the special case dominated by a lower-triangular nonlinear system, finite-time stable. The proof is based on a recursive design algorithm developed recently, to construct the virtual Hölder continuous, finite-time stabilizer as well as a C¹ positive definite and proper Lyapunov function that guarantees finite-time stability of the non-Lipschitz non-linear systems.

In the paper, the author presents explicit and unified expressions for a sequence of improper integrals in terms of the beta functions and the Wallis ratios. Hereafter, the author derives integral representations for the Catalan numbers originating from combinatorics.

Radial basis function (RBF) networks are often viewed as instable when used in multi-layered architectures and therefore are mostly used in a single-layered manner. Universal approximation theorems for single-layered RBF networks further render deeper architectures useless. However, deep neural networks have proven their effectiveness on many different tasks. We show that deeper RBF architectures with multiple radial basis function layers are achievable and able to learn. We introduce an initialization scheme for deep RBF networks based on k-means clustering and covariance estimation. We further show how to make use of convolutions to speed up the calculation of a Mahalanobis distance in a partially-connected fashion, similar to convolutional neural networks (CNNs). Finally, we evaluate our approach on image classification as well as speech emotion recognition tasks. Our results show that deep RBF networks perform similar to simple CNNs.

Image stitching is a crucial aspect of image processing. However, factors like perspective and environment often lead to irregular shapes in stitched images. Cropping or completion methods typically result in substantial loss of information. This paper proposes a method for rectifying irregularly images into rectangles using deformable meshes and residual networks. The method utilizes a convolutional neural network to quantify rigid structures of images. Choosing the most suitable mesh structure based on the extraction results, offering options such as triangular, rectangular, and hexagonal. Subsequently, the irregularly image, predefined mesh structure, and predicted mesh structure are input into a wide residual neural network for regression. The loss function comprises local and global, aimed at minimizing the loss of image information within the mesh and global target. This method not only significantly reduces information loss during rectification but also adapting to different images with various rigid structures. Validation on the DIR-D dataset shows this method outperforms state-of-the-art methods in image rectification.

The aims of this study are to measure the technical efficiency (TE) of Cambodian household’s rice production and trying to determine its main influencing factors using the stochastic frontier production function. The study utilized primary data collected from 301 rice farmers in three selected districts of Battambang by structured questionnaires. The empirical results indicated the level of household rice output varied according to differences in the efficiency of production processes. The mean TE is 0.34 which means that famers produce 34% of rice at best practice at the current level of production inputs and technology, indicates that rice output has the potential of being increased further by 66% at the same level of inputs if farmers had been technically efficient. Furthermore, between 2013-2015 TE of household’s rice production recorded -14.3% decline rate due to highly affected of drought during dry season of 2015. Moreover, evidence reveals that land, fertilizer, and pesticide are the major influencing input factors of household’s rice production, while disaster, education of household head, family size and other crops’ cultivated area are core influencing factors decreasing TE. Conversely, the main influencing factors increasing TE are irrigated area, number of plot area and sex of household head.

The aims of this study are to measure the technical efficiency (TE) of Cambodian household’s rice production and trying to determine its main influencing factors using the stochastic frontier production function. The study utilized primary data collected from 301 rice farmers in three selected districts of Battambang by structured questionnaires. The empirical results indicated the level of household rice output varied according to differences in the efficiency of the production processes. The mean TE is 0.34 which means that famers produce 34% of rice at best practice at the current level of production inputs and technology, indicates that rice output has the potential of being increased further by 66% at the same level of inputs if farmers had been technically efficient. Furthermore, between 2013-2015, TE of household’s rice production recorded -14.3% decline rate due to highly affected of drought during dry season of 2015. Moreover, evidence reveals that land, fertilizer, and pesticide are the major influencing input factors of household’s rice production, while disaster, education of household head, family size and other crops’ cultivated area are core influencing factors decreasing TE. Conversely, the main influencing factors increasing TE are irrigated area, number of plot area and sex of household head.

This paper proposes training improvement methods of artificial neural networks (ANN) trajectory predictors. First, a dynamic power system time-series trajectory is split into several different segments to simplify the original ANN training problem. Moreover, the time-derivative of the trajectory is included to obtain an augmented loss function. Compared to previous studies which mainly focused on increasing the prediction accuracy, the aim of these novel techniques is to reduce the computational burden where the ANN output performance is still acceptable. The effectiveness of the developed methods is validated based on the WSCC three-machine nine-bus and IEEE 39-bus system models. The mean absolute error (MAE) and trajectory prediction results are analyzed, in which the numbers of neurons, hidden layers, and training epochs are constrained during the ANN training process. Rotor-angle difference between generators and the system frequency are investigated as the dynamic trajectories of the power system models. It is revealed that when the ANN architecture and epochs are constrained, the MAE results can be reduced, and the ANN training results can better reflect the original trajectory using the improvement approaches.

In recent decades, with the ever-growing scale of video data, near-duplicate videos continue to emerge. Data quality issue caused by near-duplicate videos is becoming more and more prominent, which has affected the application of normal videos. Although current studies on near-duplicate video detection can be helpful to uncover data quality issues for videos, they still lack a process of automatic merging for the video data represented by high-dimensional features, which are difficult to automatically clean the near-duplicate videos to improve data quality for video datasets. At present, there are few studies on near-duplicate video data cleaning. The existing studies have the sensitive problems of video data orderliness and clustering initial center under a condition that prior distribution is unknown, which seriously affect the accuracy of near-duplicate video data cleaning. To address the above issues, an automatic near-duplicate video data cleaning method based on a consistent feature hash ring is proposed in this paper. First, a residual network with convolutional block attention modules, a long short-term memory deep network, and an attention model are integrated to construct an RCLA deep network with the multi-headed attention mechanism to extract spatiotemporal features of video data. Then, a consistent feature hash ring is constructed, which can effectively alleviate the sensitivity of video data orderliness while providing a condition of near-duplicate video merging. To reduce the sensitivity of the initial cluster centers to results of near-duplicate video cleansing, an optimized feature distance-means clustering algorithm is constructed by utilizing a mountain peak function on a consistent feature hash ring, which can implement automatic cleaning of near-duplicate video data. Finally, experiments are conducted based on a commonly used dataset named CC_WEB_VIDEO and a coal mining video dataset. Compared with some existing works, simulation results demonstrate that the performance of the proposed method.

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

The 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.

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

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.

A reinforcement learning algorithm is proposed to improve the accuracy of short-term load forecasting (STLF) in this article. The proposed model integrates radial basis function neural network (RBFNN), support vector regression (SVR), and adaptive annealing learning algorithm (AALA). In the proposed methodology, firstly, the initial structure of RBFNN is determined by using SVR. Then, an AALA with time-varying learning rates is used to optimize the initial parameters of SVR-RBFNN (AALA-SVR-RBFNN). In order to overcome the stagnation for searching optimal RBFNN, a particle swarm optimization (PSO) is applied to simultaneously find promising learning rates in AALA. Finally, the short-term load demands are predicted by using the optimal RBFNN. The performance of the proposed methodology is verified on the actual load dataset from Taiwan Power Company (TPC). Simulation results reveal that the proposed AALA-SVR-RBFNN can achieve a better load forecasting precision as compared to various RBFNNs.

In order to solve the problem of feature extraction of underwater acoustic signals in complex ocean environment, a new method for feature extraction from ship radiated noise is presented based on empirical mode decomposition theory and permutation entropy. It analyzes the separability for permutation entropies of the intrinsic mode functions of three types of ship radiated noise signals, and discusses the permutation entropy of the intrinsic mode function with the highest energy. In this study, ship radiated noise signals measured from three types of ships are decomposed into a set of intrinsic mode functions with empirical mode decomposition method. Then, the permutation entropies of all intrinsic mode functions are calculated with appropriate parameters. The permutation entropies are obviously different in the intrinsic mode functions with the highest energy, thus, the permutation entropy of the intrinsic mode function with the highest energy is regarded as a new characteristic parameter to extract the feature of ship radiated noise. After that, the characteristic parameters, namely, the energy difference between high and low frequency, permutation entropy, and multi-scale permutation entropy, are compared with the permutation entropy of the intrinsic mode function with the highest energy. It is discovered that the four characteristic parameters are at the same level for similar ships, however, there are differences in the parameters for different types of ships. The results demonstrate that the permutation entropy of the intrinsic mode function with the highest energy is better in separability as the characteristic parameter than the other three parameters by comparing their fluctuation ranges and the average values of the four characteristic parameters. Hence, the feature of ship radiated noise can be extracted efficiently with the method.

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

In this paper, a new approach to the sliding-mode control of single-phase inverters under linear and non-linear loads is introduced. The main idea behind this approach is to utilize a non-linear, flexible and multi-slope function in controller structure. This non-linear function makes the controller possible to control the inverter by a non-linear multi-slope sliding surface. In general, this sliding surface has two parts with different slopes in each part and the flexibility of the sliding surface makes the multi-slope sliding-mode controller (MSSMC) possible to reduce the total harmonic distortion, to improve the tracking accuracy, and to prevent overshoots leading to undesirable transient-states in output voltage which are occurred when the load current sharply rises. In order to improve the tracking accuracy and to reduce the steady-state error, an integral term of the multi-slope function is also added to the sliding surface. The improved performance of the proposed controller is confirmed by simulations and finally, the results of the proposed approach are compared with a conventional SMC and a SRFPI controller.

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.

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 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.

The objective of this study is to evaluate the effect of constitutive equations on the prediction accuracy for springback in cold stamping with various deformation modes. In this study, two types of yield functions—Hill’48 and Yld2000-2d—were considered to describe yield behavior. Isotropic and kinematic hardening models based on the Yoshida–Uemori model were also adopted to describe hardening behavior. Various material tests (such as uniaxial tension, tension- compression, loading-unloading, and hydraulic bulging tests) were carried out to determine the material parameters of the models. The obtained parameters were implemented in the finite element (FE) simulation to predict springback, and the results were compared with experimental data. U-bending and T-shape drawing were employed to evaluate the springback prediction accuracy. Obviously, the springback prediction accuracy was greatly influenced by constitutive equations. Therefore, it is important to choose appropriate constitutive equations for accurate description of material behaviors in FE simulation.

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.

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 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.

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.

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.

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.

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.

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 .

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.

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.

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 present study aims to develop an efficient numerical method for computing the diffraction and radiation of water waves with horizontal long cylindrical structures, such as floating breakwaters. A higher-order scheme is used to discretize geometry of the structure as well as the relevant physical quantities. As the kernel of this method, Wehausen’s free-surface Green function is calculated by a newly-developed Gauss-Kronrod adaptive quadrature algorithm after elimination of its Cauchy-type singularities. To improve computational efficiency, a Chebyshev approximation approach is applied to a fast calculation of the Green function that needs evaluation thousands of times. In addition, OpenMP parallel technique is used to the formation of influence coefficient matrix, which significantly reduces CPU time. Finally, computations are performed on wave exciting forces and hydrodynamic coefficients for the long cylindrical structures, either floating or submerged. Comparison with other numerical and analytical methods demonstrates good performance of the present method.

This work is the first in literature to tackle the difficult open problem of determining the upper bound and threshold theorem for the TDCDP (time-dependent controller parameter) of the (Fokker Planck Kolmogorov) probability density function. This revolutionary exposition will put control theory and other related inter-disciplinary fields to a higher level towards contemporary control theory. Notably, based on the influential role of control theory in both engineering and industry, this paper will be of great value to all engineering and industry professionals who seek to know more about advanced trends within control theory settings. On the other remit of the spectrum, Fokker Planck Kolmogorov(FPK) equations are of high importance to physicists as well as mathematicians, based on their multiple applicability to information theory, graph theory, data science, finance, economics, and beyond. So, this by default adds more taste and credibility to this study. This leads by nature to introducing a different flavor to this ground-breaking research by highlighting the impact of Fokker Planck Kolmogorov(FPK) to revolutionize crypocurrency,which have received its name because it uses encryption to verify transactions, a new debatable digital payment system that doesn't rely on banks to verify transactions. It’s a peer-to-peer system that can enable anyone anywhere to send and receive payments. The paper ends with closing remarks combined with some challenging open problems and the next phase of research.

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.

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.

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

In this 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.

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.

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.

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.

Recently, we have applied the generalized Littlewood theorem concerning contour integrals of the logarithm of analytical function to find the sums over inverse powers of zeroes for the incomplete Gamma- and Riemann zeta- functions, polygamma functions, and elliptical functions. Here, the same theorem is applied to study such sums for the zeroes of the Hurwitz zeta-function , including the sum over the inverse first power of its appropriately defined non-trivial zeroes. We also study some related properties of the Hurwitz zeta-function zeroes. In particular, we show that for any natural N and small real epsilon, when z tends to n=0, -1, -2… we can find at least N zeroes of zeta in the - vicinity of 0 for sufficiently small epsilon, as well as one simple zero tending to 1, etc.

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.

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.

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.

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.

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.

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.

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.

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.

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

In the paper, by virtue of some properties for the Riemann zeta function, the author finds a double inequality for the ratio of two consecutive Bernoulli numbers with even indexes and analyzes the approximating accuracy of the double inequality.

The objective of this study is to examine a nonparametric estimate , using the kernel approach, of the conditional distribution function of a scalar response variable that is given a random variable whose values take place in a separable real Hilbert space. The observations will be dependent on one another in a quasi-associated fashion. The pointwise practically perfect consistencies with rates of this estimator are established by us under some broad conditions. The study’s major objective is to investigate the convergence rate of the proposed estimator and its application in the convergence rate and asymptotic normality of the hazard function. The asymptotic normality of the developed estimator is established precisely. Simulation studies were conducted to investigate the behavior of the asymptotic property in the context of finite sample data.

The paper explores the Kullback-Leibler divergence formalism (KLDF) applied to the stable MG1 queue manifold. More potentially, both service time probability and cumulative functions which make KLDF exact are obtained. The credibility of KLDF is justified through consistency axioms. Some potential applications of Kullback-Leibler divergence to Biometry are presented. The paper concludes with closing remarks combined with some challenging open problems and the next phase of research.

We developed a novel hybrid approach for solving global optimization, computer science, bio-medical and engineering real life applications that is based on the coupling of the Whale Optimizer and Sine Cosine Algorithms via a surrogate model. We relate the whale optimizer algorithm to balance between the exploitation and the exploration process in the proposed method. There exist confirmed techniques for searching approximate best optimal solutions, but our algorithm will further guarantee that such numerical and statistical solutions satisfy physical bounds of the standard and real life functions. Our experiments with the benchmark, bio-medical, computer science and engineering real life problems have illustrated the advantages of using a newly hybrid approach based on mixing Whale Optimizer and Sine Cosine algorithms. It holds considerable potential for reducing execution time for solving standard and real life problems and at the same time improving the quality of the solution.

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.