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

In the paper, the author finds bounds of the sine and cosine along a circle on the complex plane in terms of two double inequalities for the norms of the sine and cosine along a circle on the complex plane.

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

Post-ovulatory aging (POA) is an inevitable factor during some assisted reproduction technology procedures, and results in poor fertilization rates and impaired embryo development. This study used RNA sequencing analysis and experimental validation to study the similarities and differences between in vivo- and in vitro-matured porcine oocytes before and after POA. Differentially expressed genes (DEGs) between fresh in vivo-matured oocyte (F_vivo) and aged in vivo-matured oocyte(A_vivo) and DEGs between fresh in vitro-matured oocyte (F_vitro) and aged in vitro-matured oocyte(A_vitro) were intersected to explore the co-effects of POA. It was found that "organelles", especially "mitochondria", were significantly enriched GO terms. The expression of genes related to the “electron transport chain” and “cell redox homeostasis” pathways related to mitochondrial function significantly showed low expression patterns in both A_vivo and A_vitro groups. WGCNA analysis to explore gene expression modules specific to A_vivo. Trait-modules association analysis showed that the red modules were most associated with in vivo aging. There are a total of 959 genes in the red module, which are mainly enriched in “RNA binding”, “mRNA metabolic process”, etc. GO terms, and “spliceosome” and “nucleotide excision repair” pathways. DNAJC7, IK, and DDX18 were at the hub of the gene regulatory network. And these genes were all expressed higher in A_vivo. In summary, POA affects the organelle function of oocytes. A_vivo oocytes have some unique gene expression patterns. These genes may be potential anti-aging targets. This study helps us understand the detailed mechanism of POA and provides strategies for researching oocyte aging.

The Mann-Whitney effect is a measure for comparing survival distributions between two groups. The Mann-Whitney effect is interpreted as the probability that a randomly selected subject in a group survives longer than a randomly selected subject in the other group. Under the independence assumption of two groups, the Mann-Whitney effect can be expressed as the traditional integral formula of survival functions. However, when the survival times in two groups are not independent each other, the traditional expression of the Mann-Whitney effect has to be modified. In this article, we propose a copula-based approach to compute the Mann-Witney effect with parametric survival models under dependence of two groups, which may arise in the potential outcome framework. In addition, we develop a Shiny web app that can implement the proposed method via simple commands (https://nkosuke.shinyapps.io/shiny_survival/). Through a simulation study, we show the correctness of the proposed calculator. We apply the proposed methods to two real datasets.

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

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

We show succinctly a natural origin of the beautiful Gamma function in light of the WJ distribution, linking to quite distinct fields.

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

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

Kim(2015) introduced the degenerate Cauchy numbers of the second kind and gave some identities of them. In this paper, by using the modified polyexponential functions which are introduced by Kim-Kim(2019), we define the degenerate poly-Cauchy polynomials of the second kind and investigate some properties of them. Furthermore, we consider the degenerate unipoly-Cauchy polynomials of the second kind and discuss some properties of them.

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

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

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

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

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

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

Spectral calibration consists of the calibration of wavelengths and the measurement of the instrument's spectral response function (SRF). Unlike conventional slits, the absorbed aerosol sensors (AAS) are used as a slit homogenizer, in which the spectral response function (SRF) is not a conventional Gaussian curve. To be more precise, the SRF is the convolution of the slit function of the spectrometer, the line spread function of the optical system, and the detector response function. The SRF of the slit homogenizer is a flat-topped multi-Gaussian function. Considering the convenience of fitting, a super-Gaussian function, which looks like a similar distribution to the flat-topped multi-Gaussian function, is used to fit the measured data in a spectral calibration. According to the results, the SRF’s shapes, due to the Earth port, resemble a Gaussian curve with a flatted top could be concluded, which contains an FWHM of 1.78–1.82 nm for the AAS. The results show that the correlation coefficients are about 0.99, which proves that the fitting function could better characterize the SRF of the instrument.

In this work, we investigate the behaviour of relativistic quantum oscillator under the effects of Lorentz symmetry violation determined by a tensor $(K_F)_{\mu\nu\alpha\beta}$ out of the Standard Model Extension. We analyze this relativistic system under an inverse radial electric field and a constant magnetic field induced by Lorentz symmetry violation. We see that the presence of Lorentz symmetry breaking terms modified the energy spectrum of the system, and a quantum effect arise due to the dependence of the linear charge density on the quantum numbers of the system

We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage of using special functions is their analytic continuation which widens the range of the parameters of the definite integral over which the formula is valid. We give as examples definite integrals of logarithmic functions times a trigonometric function. In various cases these generalizations evaluate to known mathematical constants such as Catalan’s constant and π

Let $f(t)$ be a characteristic function. The question on infinite divisibility of $g_{2k}(t)=f^{(2k)}(t)/f^{(2k)}(0)$ is considered. There are given the condition for that function not to be infinite divisible. Some examples of infinite divisibility of $g_{2k}(t)$ are given.

This paper addresses a variant of the product for the Dirichlet $L$--functions. We propose a completely detailed proof for the truth of the generalized Riemann conjecture for the Dirichlet $L$--functions, which states that the real part of the nontrivial zeros is $1/2$. The Wang and Hardy--Littlewood theorems are also discussed with removing the need for it. The results are applicable to show the truth of the Goldbach's conjecture.

This paper attempts to extend the Riemann Zeta function of a complex number to a function of a matrix and/or a tensor $A$, namely $$\zeta (A)=\sum _{n=1}^{\infty} \frac{1}{n^{A}}= \sum _{n=1}^{\infty} \sum_{k=1}^n\lambda_k A^k$$ and inverse $$A=\sum _{n=1}^{\infty} \sum_{k=1}^n \mu(n)\lambda_k \zeta(A^k)$$ where $\mu(n)$ is the M\"obius function, $A$ is a complex matrix or tensor with any order, and $\lambda_k$ is eigenvalue of the matri/tensor $A$. This kind of calculations on the Riemann Zeta function has never been seen in the literature. Some examples are provided.

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

Resveratrol is one of the most investigated natural polyphenolic compounds and is contained in more than 70 types of plants and in red wine. The widespread interest in this polyphenol derives from its antioxidant, anti-inflammatory and anti-aging properties. Several studies have established that resveratrol regulates animal reproduction. However, the mechanisms of action and the potential therapeutic effects are still unclear. This review aims to clarify the role of resveratrol in the male and female reproductive functions, with a focus on animals of veterinary interest. In the female, resveratrol has been considered a phytoestrogen due to its capacity to modulate ovarian function and steroidogenesis via sirtuins, SIRT1, in particular. Resveratrol has also been used to enhance aged oocyte quality, and as a gametes cryo-protectant with mainly antioxidant, and anti-apoptotic effects. In the male, resveratrol enhanced testes function and spermatogenesis through activation of AMPK pathway. Furthermore, resveratrol has been supplemented to semen extenders improving the preservation of sperm quality. In conclusion, resveratrol has potentially beneficial effects for ameliorating ovarian and testes function. However, due to unclear data, further studies are necessary to consolidate these findings.

This study examines the prospective association of egg consumption with multiple domains of cognitive function in older, community-dwelling men and women followed 16.3 years. Participants were 617 men and 898 women from the Rancho Bernardo Cohort aged 60 and older who were surveyed about egg intake/week in 1972-74, and attended a 1988-91 research visit when cognitive function was assessed with 12 tests. Analyses showed that egg intake ranged from 0-24/week (means: men=4.23.2, women=3.52.7, p<0.0001). In men, covariate-adjusted regressions showed egg intake was associated with better performance on Buschke total (p=0.04), long-term (p=0.02) and short-term (p=0.05) recall. No significant associations were observed in women (p’s>0.05). Analyses in those <60y at in 1972-74 showed egg intake was positively associated with scores on Heaton copying(p<.04) and the Mini-Mental Status Exam(MMSE;p<.02) in men, and category fluency(p<0.05) in women. Egg intake was not significantly associated with odds of poor performance on MMSE, Trails B, or category fluency in either sex. These reassuring findings suggest there are no long-term detrimental effects of egg consumption on multiple cognitive function domains, and for men, there may be beneficial effects for verbal episodic memory. Egg consumption in middle-age may also be related to better cognitive performance later in life.

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

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

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

Abstract: Background: Of the many side effects suffered by cancer patients, those related to cognitive performance have become increasingly prominent in clinical practice. We know that chemotherapy generates a series of side effects, such as nausea and vomiting, alopecia, and so on, which can be counteracted by complementary medication. However, in the case of post-chemotherapy cognitive impairment, or chemo brain, these cannot be controlled with drug therapies. However, before any intervention can be considered, it is necessary to know exactly what cognitive impairment is being triggered. For this reason, we decided to study the cognitive status of breast cancer patients. Methods: analytical, prospective, three-measure longitudinal, intrasubject unifactorial, non-probabilistic and accidental assignment study. The sample came from the Medical Oncology Department at Hospital de Salamanca, in Spain. Cognitive function (Trail Making Test and Stroop Test) was established as the primary variable; the presence of sleep disorders (Insomnia Severity Index, ISI) and anaemia (haemoglobin levels in blood) were analysed as secondary variables, in addition to sociodemographic variables (age, stage, type of carcinoma, radiotherapy, menopause, social support network, marital status, years of schooling and employment status). Results: We recruited 151 individuals according to the selection criteria. We can confirm that factors including anaemia, menopause, patient support network and marital status, years of schooling, and employment status did affect the cognitive performance of the patients in active chemotherapy treatment in the study. In contrast, sleep disorders, age, radiotherapy treatment, stage of disease, and type of carcinoma did not affect the cognitive performance of the cancer patients. Conclusions: Chemotherapy does impact the cognitive performance of breast cancer patients.

Background: Of the many side effects suffered by cancer patients, those related to cognitive performance have become increasingly prominent in clinical practice. We know that chemotherapy generates a series of side effects, such as nausea and vomiting, alopecia, and so on, which can be counteracted by complementary medication. However, in the case of post-chemotherapy cognitive impairment, or chemo brain, these cannot be controlled with drug therapies. However, before any intervention can be considered, it is necessary to know exactly what cognitive impairment is being triggered. For this reason, we decided to study the cognitive status of breast cancer patients. Methods: analytical, prospective, three-measure longitudinal, intrasubject unifactorial, non-probabilistic and accidental assignment study. The sample came from the Medical Oncology Department at Hospital de Salamanca, in Spain. Cognitive function (Trail Making Test and Stroop Test) was established as the primary variable; the presence of sleep disorders (Insomnia Severity Index, ISI) and anaemia (haemoglobin levels in blood) were analysed as secondary variables, in addition to intervening variables (age, stage, type of carcinoma, radiotherapy, menopause, social support network, marital status, years of schooling and employment status). Results: We recruited 151 individuals according to the selection criteria. We can confirm that factors including anaemia, menopause, patient support network and marital status, years of schooling, and employment status did affect the cognitive performance of the patients in the study. In contrast, sleep disorders, age, radiotherapy treatment, stage of disease, and type of carcinoma did not affect the cognitive performance of the cancer patients. Conclusions: Chemotherapy does impact the cognitive performance of breast cancer patients.

Background: Of the many side effects suffered by cancer patients, those related to cognitive performance have become increasingly prominent in clinical practice. We know that chemotherapy generates a series of side effects, such as nausea and vomiting, alopecia, and so on, which can be counteracted by complementary medication. However, in the case of post-chemotherapy cognitive impairment, or chemo brain, these cannot be controlled with drug therapies. However, before any intervention can be considered, it is necessary to know exactly what cognitive impairment is being triggered. For this reason, we decided to study the cognitive status of breast cancer patients. Methods: analytical, prospective, three-measure longitudinal, intrasubject unifactorial, non-probabilistic and accidental assignment study. The sample came from the Medical Oncology Department at Hospital de Salamanca, in Spain. Cognitive function (Trail Making Test and Stroop Test) was established as the primary variable; the presence of sleep disorders (Insomnia Severity Index, ISI) and anaemia (haemoglobin levels in blood) were analysed as secondary variables, in addition to intervening variables (age, stage, type of carcinoma, radiotherapy, menopause, social support network, marital status, years of schooling and employment status). Results: We recruited 151 individuals according to the selection criteria. We can confirm that factors including anaemia, menopause, patient support network and marital status, years of schooling, and employment status did affect the cognitive performance of the patients in the study. In contrast, sleep disorders, age, radiotherapy treatment, stage of disease, and type of carcinoma did not affect the cognitive performance of the cancer patients. Conclusions: Chemotherapy does impact the cognitive performance of breast cancer patients.

In this article, it is demonstrated that if the zeta function does not have a sequence of zeros whose real part converges to 1, then it cannot have any zeros in the critical strip, showing that the Riemann Hypothesis is false.

In this paper, an analytical form of Rump Function is presented. This seminal function constitutes a fundamental concept of digital signal processing theory and is also involved in many other areas of applied mathematics. In particular, Rump Function is performed in a simple manner as the limit of a sequence of real functions letting ? tend to infinity. This limit is zero for strictly negative values of the real variable ? whereas it coincides with the independent variable ? for strictly positive values of the variable ?. The novelty of this work compared to other research studies concerning analytical expressions of the Ramp Function, is that the proposed formula is not exhibited in terms of miscellaneous special functions, e.g. Gamma Function, Biexponential Function or any other special functions such as Error Function, Hyperbolic Function, Orthogonal polynomials etc. Hence, this formula may be much more practical, flexible and useful in the computational procedures which are inserted into digital signal processing techniques and other engineering practices.

In this paper, a new identity for the generalized fractional integral is defined, through which new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. We derive trapezoid and mid-point type inequalities connected to these generalized Hermite-Hadamard inequality.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η- convex function. Moreover, our results include several new and known results as special cases.

House is the haven that keeps people from natural and human conditions, it gives them trust, safety, and steadiness. It is one of the most basic human needs this became a serious function which cities offer, and became one of the most important aspects which caught urban researchers interest, they take into consideration a wide range of architectural, social, and economic indicators. The study aims to provide an overall conception of Rwandz residential functions, using a collection of parameters and some GIS and statistical techniques, to help establish plans and future projects to improve the growth of this city and other towns and cities in that area. The study found that the old parts of Rwandz city which are located in the core, differ from the outer parts which are relatively newer in many properties, generally, the core is more densely populated than the outer, bigger family size, more illiteracy, and unemployment, few incomes, older houses, smaller houses, in the opposite of the outer parts. Besides, the study tested the correlation coefficient between the criteria; it found some strong statistical relationships between them, which reflected some real-life properties of the residential function. Lastly, the study designed a regression model to predict the main residential function criteria.

We study the propagation of a particular field that we call Gaussian-top-hat that presents self-focusing and maintains its shape for some propagation distances.

The owners of forests with water protection functions in Bulgaria do not receive compensation for their limited right to use wood and non-wood forest products from the forest areas they own. At the same time, the contribution derived from forests with water protection functions is received by water users and water consumers, whereas the costs of managing the forests are borne by their owners. The problem thus defined is not a forestry one, but an economic one, and the purpose of this paper ensues therefrom, namely to propose and test a methodology for valuating the produc-tion function of forest areas with water protection function in Bulgaria, allowing a fair distribu-tion of income between the forest owner and the user of forest ecosystem services. The methodol-ogy is based on the form of forest management and the analytical expression of the economic rela-tionship between a forest owner and a user of forest ecosystem services, constructed using Schen-rock’s formula. It has been tested with actual data on forest areas with water protection functions falling within the administrative and territorial scope of Velingrad municipality and based on the obtained results proposals have been made for the distribution of the contributions generated by forest ecosystems between the forest owner and the user of the forest ecosystem services.

We present a precise and universal method for anticipating the thermodynamic characteristics of polyatomic molecules. Unlike conventional computational approaches that rely on numerous experimental spectroscopy or calorimetry data, our model only utilizes a small number of molecular constants. We accurately predicted the values of entropy, enthalpy, specific heat, and Gibbs free energy for boron trifluoride, which were in excellent accordance with the available experimental data. This investigation introduces a new approach to deal with the anharmonic vibrations of polyatomic molecules

BACKGROUND: Knee osteoarthritis (OA) commonly causes increase in the patients’ disability and reduce their function because it causes pain, limitation in knee range of motion and decrease in muscle power.AIM: This study investigated the effect of three different physical therapy programs on knee range of motion , pain level, muscle strength and functional condition in patients with knee OA. DESIGN: Randomized comparative study.SETTING: Outpatient Rehabilitation clinic of Tongji Hospital (Wuhan, China).POPULATION: Seventy-two patients of Knee OA (aged 40-70) enrolled and randomly allocated into three groups. Group A (n=24) received physical agents and isometric quadriceps exercises, group B (n=24) received same physical agents as group A in addition to open kinetic chain exercises and group C (n=24) received physical agents as group A in addition to closed kinetic chain exercises.METHODS: knee range of motion (by electro goniometer), knee pain level (by VAS), quadriceps muscle strength (by isokinetic dynamometer) and functional condition (by WOMAC) were assessed before and after 5 weeks of treatment.RESULTS: In between group analysis, there were significant differences (P<0.05) between the three groups for all outcome measure. In within-group analysis, group C was the only group that showed significant differences (P<0.05) in all the outcomes. Group A and B showed significant differences (P<0.05) in quadriceps muscle strength and knee pain and no significant differences (P>0.05) in knee ROM and functional condition.CONCLUSIONS: After the study, our solid conclusion is that in physical therapy programs or protocols, closed kinematic chain exercise is very effective, it improves knee ROM, and help in reducing knee pain, muscle strength, function and disability for patients with knee osteoarthritis.CLINICAL REHABILITATION IMPACT: Comparison between different physical therapy programs provides the rehabilitation team with the best treatment intervention that is more effective in treating the problems associated with knee osteoarthritis.

In this paper, the functional variable method is used to establish solitary wave solutions and periodic wave solutions of the loaded quadratic non-linear Klein-Gordon equation, the loaded cubic non-linear Klein-Gordon equation and the loaded coupled non-linear Klein-Gordon equation. All solutions of these equations have been examined and three dimensional graphics of the obtained solutions have been drawn by using the Matlab software. The main advantage of the proposed functional variable method over other methods is that it provides more new exact traveling wave solutions along with additional free parameters. The graphical representations of the soliton solutions and the periodic wave solutions by using distinct values of random parameter are demonstrated to better understand their physical features. The exact solutions have its great importance to reveal the internal mechanism of the physical phenomena.

Prime period sequences can serve as the fundamental tool to construct arbitrary composite period sequences. This is a review study of prime period perfect Gaussian integer sequence (PGIS). When cyclic group {1,2,…,N−1} can be partitioned into k cosets, where N=kf+1 is an odd prime number, the construction of a degree-(k+1) PGIS can be derived from either matching the flat magnitude spectrum criterion or making the sequence with ideal periodic autocorrelation function (PACF). This is a systematic approach of prime period N=kf+1 PGIS construction, and is applied to construct PGISs with degrees 1, 2, 3 and 5. However, for degrees larger than 3, matching either the flat magnitude spectrum or achieving the ideal PACF encounters a great challenge of solving a system of nonlinear constraint equations. To deal with this problem, the correlation and convolution operations can be applied upon PGIS of lower degrees to generate new PGIS with degree-4 and other higher degrees, e.g., 6, 7, 10, 11, 12, 14, 20 and 21 in this paper. In this convolution based scheme, both degree and pattern of a PGIS vary and can be indeterminant, which is rather nonsystematic compared with the systematic approach. The combination of systematic and nonsystematic schemes contributes the great efficiency for constructing abundant PGISs with various degrees and patterns for the associated applications.

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

We know that the classical Mittag-Leffler function play an important role as solution of fractional order differential and integral equations. We introduce the j-generalized p - k Mittag-Leffler function. We evaluate the second order differential recurrence relation and four different integral representations and introduce a homogeneous linear differential equation whose one of the solution is the j-generalized p-k Mittag-Leffler function. Also we evaluate the certain relations that exist between j-generalized p - k Mittag-Leffler function and Riemann-Liouville fractional integrals and derivatives. We evaluate Mellin-Barnes integral representation of j-generalized p-k Mittag-Le er Function. The relationship of j-generalized p-k Mittag-Leffler Function with Fox H-Function and Wright hypergeometric function is also establish. we obtained its Euler transform, Laplace Transform and Mellin transform. Finally we derive some particular cases.

Neptunea cumingii is an economically important marine shellfish found in the Yellow Sea and Bohai Sea areas of China. However, due to environmental factors, such as global warming, Neptunea cumingii resources are in decline along the coast of China. In this study, samples of Neptunea cumingii were collected in Zhangzidao and Yantai during spring, summer， autumn, and winter to clarify the gene expression patterns and regulatory mechanisms in the gills in different seasons. Transcriptome analysis was conducted using Neptunea cumingii gill tissues and genes with significantly different expression levels were extracted for functional verification. The most genes with differences in expression（DEGs） were found in comparisons of the winter and summer samples. Gene enrichment analysis based on Gene Ontology and Kyoto Encyclopedia of Genes and Genomes terms showed that these DEGs were mainly involved in immune and metabolic pathways, and they had significant effects on oxidative stress, body metabolism, and protein synthesis in Neptunea cumingii. Further screening of DEGs identified 34 genes related to temperature regulation comprising 13 genes with roles in innate immunity in shellfish, 12 genes related to oxidative stress, and nine genes related to protein synthesis and energy metabolism. Eleven DEGs were randomly selected for qPCR verification and the results were consistent with the transcriptome analysis results. In summary, the transcriptome results differed significantly between seasons in the gill tissues of Neptunea cumingii. The expression levels of immune regulatory genes could be promoted in Neptunea cumingii during the high temperature season, whereas the expression of these genes may be inhibited in the low temperature season. The results obtained in this study provide insights into the molecular defense mechanisms that might allow Neptunea cumingii to adapt to climate change.

Background: obese pre-diabetics have altered expression of cytokines, and sirtuin-1, that might influence myocardial function via microRNAs (miRs) expression. Objectives: to evaluate inflammatory/oxidative stress, miRs’ expression and cardiovascular function in obese pre-diabetics randomly assigned to metformin therapy vs. placebo vs. normo-glycemics at 12 months of follow-up. Materials and methods: eighty-three obese patients enrolled for abdominoplastic surgery, were divided in pre-diabetics (n 55), normo-glycemics (n 28), and assigned to hypocaloric diet. Pre-diabetics were randomly assigned to metformin (n 23) or to placebo (n 22) plus hypocaloric diet. Results: at enrollment, pre-diabetics obese vs. normo-glycemic presented higher values of glucose, insulin resistance (HOMA-IR), inflammatory/oxidative stress markers, miR-195 and miR-27, and lower values of sirtuin-1 (p<0.05). At 12 months of follow up, obese pre-diabetics with metformin vs. placebo experienced significant reduction of glucose values, HOMA-IR, and inflammatory/oxidative stress markers, with significant reduction of intima-media thickness (IMT), septum and posterior wall thickness, and left ventricle mass (LVM), (p <0.05). At 12 months of follow-up, obese pre-diabetics with placebo vs. normo-glycemics had higher values of inflammatory/oxidative stress markers, higher values of IMT, septum and posterior wall thickness, LVM, and myocardial performance index (MPI), (p<0.05). Obese pre-diabetics in metformin vs. placebo, and obese pre-diabetics with placebo vs. normoglycemics, had significant differences about IMT, MPI, and LVM (p<0.05). Obese pre-diabetics in metformin vs. placebo showed significant reduction of serum miR-195 and miR-27 (p<0.05). Obese pre-diabetics in metformin vs. normoglycemics showed higher expression of serum miR-195 and miR-27 ( p<0.05). Finally, we found inverse relation between IMT and insulin (R -0.351), HOMA-IR (R -0.340), miR-195 (R -0.355), miR-27 (R -0.181); between LVEF and Insulin (R -0.332), HOMA-IR (R -0.142), miR-195 (R -0.297) and miR-27 (R -0.163). We found inverse correlation between LVM and sirtuin-1 (R -0.272), Insulin (R -0.810), HOMA-IR (R-0.183), miR-195 (R -0.446) and miR-27 (R-0.433), and direct correlation with interleukin-6 (R 0.195). MPI inversely linked to miR-195 (R -0.260) and miR-27 (R -0.591). Conclusion: in obese pre-diabetics metformin therapy significantly reduces inflammation/oxidative stress, circulating miR-195 and miR-27, causing reduction of LVM, IMT and amelioration of cardiac performance.

When training deep neural networks tasks, the most popular choices are cross-entropy loss. On the other hand, in general speaking, a decent loss function can take on shapes that are considerably more flexible and ought to be adapted for different activities and datasets. In most of the classification tasks, generally if the true class is not correctly recognized by the network (top1), that class is placed among the five classes with the highest probability (top5). This shows that the network does not necessarily recognize the correct class with a low probability, but a class similar to it (such as 3 vs. 8 in mnist) assigns a higher probability and this causes a mistake in that task. Accordingly, we proposed a loss function deals with the error of class that the neural network incorrectly recognized as correct, in addition to the correct class error. We call our proposed loss as False Positive Loss (FPL), with the intention of viewing and designing loss functions not only through the utilization of true class but also through the utilization of the value of false positive classes. One of the core properties of our proposed loss is full adaptability, which makes False Positive Loss be fully capable of getting reformulated by using other widely used loss functions formulas based on the task or the need of the users. Extensive experimental results demonstrate that our suggested loss function outperforms other well-known losses on a variety of tasks and datasets. As can be observed, the performance of our False Positive Loss is superior to that of the cross-entropy loss when it comes to tasks involving 2D picture classification. We have compared our loss with cross entropy as the most common classification loss function on some models (such as ResNet-18, ResNet-50 and Efficientnet-V2) through classification known as a basic computer vision task. with both random or pre-trained initial weights. As a result, in some cases the models with our loss outperform the same tasks with cross entropy from the viewpoint of some metric (i.e. accuracy and FP). For example, the resnet-50 on cifar-10 dataset with random initialization indicated a top1 accuracy of 94.93 with cross entropy and 95.25 with our loss, while for top5 accuracy the results are 99.86 and 99.87, respectively.

Evidence supports an association between low magnesium (Mg) intake and coronary heart disease and between Mg intake and endothelial function. The aim of this study was to assess the effect of one week of Mg supplementation on endothelial function, assessed by flow mediated dilatation (FMD). Nineteen healthy men and women completed this cross-over pilot study in which participants were randomised to take an over-the-counter magnesium supplement for one week or to follow their usual diet. Weight, FMD and blood pressure (BP) were taken on completion of each intervention and 24hour urine collections and blood samples were taken to assess compliance. Baseline serum Mg was within normal range for all participants. Urinary Mg and urinary magnesium-creatinine ratio (Mg/Cr) significantly increased between interventions, (p = 0.03, p = 0.005 respectively). No significant differences in FMD or BP were found between the interventions. A significant negative correlation was seen between age and FMD (r = -0.496, p = 0.031). When adjusted for age, saturated fat was negatively associated with FMD (p = 0.045). One week of Mg supplementation did not improve FMD in a healthy population.

Evidence supports an association between low magnesium (Mg) intake and coronary heart disease and between Mg intake and endothelial function. The aim of this study was to assess the effect of one week of Mg supplementation on endothelial function, assessed by flow mediated dilatation (FMD). Nineteen healthy men and women completed this cross-over pilot study in which participants were randomised to take an over-the-counter magnesium supplement for one week or to follow their usual diet. Weight, FMD and blood pressure (BP) were taken on completion of each intervention and 24hour urine collections and blood samples were taken to assess compliance. Baseline serum Mg was within normal range for all participants. Urinary Mg and urinary magnesium-creatinine ratio (Mg/Cr) significantly increased between interventions, (p = 0.03, p = 0.005 respectively). No significant differences in FMD or BP were found between the interventions. A significant negative correlation was seen between age and FMD (r = -0.496, p = 0.031). When adjusted for age, saturated fat was negatively associated with FMD (p = 0.045). One week of Mg supplementation did not improve FMD in a healthy population.

Magnesium (Mg) deficiency may be a catalyst in the process of endothelial dysfunction, an early event in the pathogenesis of atherosclerosis. The aim was to determine the acute effect of an oral Mg supplement compared to control on endothelieal function assessed by flow-mediated-dilatation (FMD). Nineteen participants (39 years, body mass index (BMI) 22.9kg/m2) completed this randomised cross-over study. Blood pressure (BP) and FMD were measured and blood samples taken before participants drank 200ml water with or without an over the counter Mg supplement (450mg and 300mg for men and women). Measurements were repeated at 60 and 120 minutes. There was a statistically significant two-way interaction between treatment and time on serum Mg (p = .037). A difference of -0.085mm in FMD was observed 60 minutes post drink in the control group compared to baseline FMD, and no difference was observed in the supplement group compared to baseline. Despite the non-significant interaction between treatment and time on FMD, the difference seen in the control group and the lack of change in the supplement group at 60 minutes post-drink suggests that Mg may attenuate the reduction in FMD post-prandially.

Background and Aim: Zinc plays a pivotal role in various zinc enzymes, resulting in the maintenance of liver function. Patients with chronic liver diseases (CLDs) usually have lower concentrations of zinc, which decrease further as liver fibrosis progresses. It remains unknown whether long-term zinc supplementation improves liver function and reduces the risk of hepatocellular carcinoma (HCC) development. Patients and Methods: Two hundred sixty-seven patients with CLDs who received a zinc preparation (Zn-group; 196 patients), or who did not receive zinc (no Zn-treatment group; 71 patients) were retrospectively analyzed in this study. The Zn-group was divided into 4 groups according to their serum Zn concentrations at 6 months after the start of Zn treatment. Results: Liver function significantly deteriorated in the no Zn-treatment group, while no notable change was observed in the Zn-group. The cumulative incidence rates of events and HCC at 3 years were lower in the Zn-group (9.5%, 7.6%) than in the no Zn-treatment group (24.9%, 19.2%) (p<0.001). According to the serum Zn concentrations, the cumulative incidence rates of events and HCC were significantly decreased in patients with Zn concentrations ≥ 70 µg/dl (p<0.001). Conclusion: Zinc supplementation appears to be effective at maintaining liver function and suppressing events and HCC development, especially among patients whose Zn concentration is greater than 70 µg/dl.

In this study, we actually want to explore the time-fractional Phi-four equation via two methods, the exp _a function method and the hyperbolic function method. We transform a fractional order dierential equation into an ordinary differential equation using a wave transformation and the fractional derivative in conformable form. Then, the resulting equation has successfully been explored for new explicit exact solutions. The procured solutions are simply showed the effectiveness and plainness of the projected methods.

Development and engineering of protein crystals regarding mechanical stability and crystallizability occurs on a small scale. Later in the process chain of industrial production however, filtration properties are important to separate the crystals from mother liquor. Many protein crystals are sensitive to mechanical stress which is why it is important to know the filtration behavior early on. In this study we analyze settling and filtration behavior of isometric, rod-like and needle shaped lysozyme and rod-like alcohol dehydrogenase (ADH) crystals on a small scale using an optical analytical centrifuge. Needle shaped lysozyme and rod-like ADH crystals show compressible material behavior. With the results from settling and filtration experiments the flux density function is calculated and modeled which can be used to describe the whole settling and permeation process in dependency of the solids volume fraction. This is also an issue for simulations of industrial processes.

Modern forestry systems are based upon typologies of forest types (FT). Many proposals were developed in Argentina, but without following unified criteria. The objective was to compare different approaches based on (i) functional forests (phenoclusters), and (ii) forest canopy-cover composition by tree species. We employed data of National Forest Inventories, forest models and climate data, comparing the proposals using univariate analyses. We test the performance of phenoclusters to differentiate the variability of native forests (proxy: forest structure), biodiversity (proxy: indicator species) and environment (proxies: soil carbon stock, elevation, climate). We proposed a simple forest type classification methodology based on species composition, considering basal area of tree species. Finally, we compared the performance of both proposals. In regions where monospecific forests are predominant, the classifications based on forest canopy-cover composition are feasible, but phenoclusters allowing to increase the complexity at landscape level. In those regions were predominant multi-specific stands, the classifications based on forest canopy-cover composition are useless, and phenoclusters allowing to decrease the complexity at landscape level. These results allowing to harmonize national FT classifications by using criteria and indicators to achieve sustainable forest management and conservation proposals.

This research was aimed to study the chickpea (Cicer arietinum L.) production among smallholder farmers in Damot Gale and Humbo Woredas. A multi-stage sampling technique was used in order to determine the sample respondents. By using simple random sampling techniques four sample Kebeles were selected. Cross sectional data were collected from 182 farmer households who were chickpea producers in 2016 production season. Primary data were collected from sample households using structured questionnaire. Descriptive statistics and econometric model were employed to analyze the data. To identify the production function of chickpea crops Cobbe-Douglas production function was employed. The study suggest interventions such as intensification strategies which increase yields through proper management and use of inputs, rural infrastructure improvement increases the likelihood of production of chickpea.

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

In this paper, it is shown that the bivariate beta statistical manifold of the first kind with three parameters has a gradient system Hamiltonian and is completely integrable. It is shown that this system admits a Lax pair representation. The question here is how to construct a gradient system and show that it is completely integrable while determining the integrable curves on the three-parameter bivariate beta manifold of the first kind admitting a potential function?To do this, we prove the existence of the potential on the manifold using ovidiu in Ovidiu, then using Amari's theorems in Amari, we show that this coordinate system admits a dual coordinate system. This will allow us to determine the Riemannian metric on the variety and to construct the gradient system. We linearise this system using Nakamura's method. We prove that it is Hamiltonian and completely integrable using the theorem in \cite{mama-proceeding}. It is shown that the Bivariate Beta of the first kind with three parameters, is an exponential function. The gradient system is linearizable. It is proven that the associate gradient system is Hamiltonian with $ \mathcal{H} $ which is in involution and satisfying $d\mathcal{H}=0.$ Therefore, the gradient system obtained is a sub-dynamical system of a $4$-dimensional system and is a completely integrable system. We show that the gradient system on the statistical model has the following Lax pair representation: $ \dot{L}= \left[L, N\right] $ where $L$ is a symmetric matrix and $N$ is the diagonal matrix. The gradient system defined by the Bivariate Beta family of the first kind with three parameters odd-dimensional manifold is a completely integrable Hamiltonian system.

Abstract Aim: The study aimed to evaluate the clinical laboratory features of moderate and severe COVID-19 patients among a cohort of the Egyptian population. The study also aimed to assess the accuracy—sensitivity, specificity, and area under the curve (AUC) of various detected parameters in predicting the severity of COVID-19 infection. Patients and methods: One hundred diagnosed COVID-19 patients and fifty healthy participants in total were involved in current study. COVID-19 patients were categorized based on how severe their symptoms into two groups. Estimates were made for serum levels of alanine aminotransferase (ALT), aspartate aminotransferase (AST), albumin, lactate dehydrogenase (LDH) and C-reactive protein (CRP) as well as white blood cells (WBCs) count, lymphocytes count, and hemoglobin content (Hb) content. Results: COVID-19 patients displayed increased serum levels of liver enzymes and CRP as well as WBCs count when compared to healthy individuals. On the other hand, Hb content, lymphocytes count, and albumin level fell in all COVID-19 patients. The severe group showed a statistically significant rise in liver enzymes, WBCs, and CRP levels, compared with moderate group. WBCs and lymphocytes counts were closely correlated with age, ALT, LDH, and CRP in all cases. WBCs and lymphocytes counts also had a negative correlation with albumin Level. Additionally, WBCs count, lymphocytes count, LDH activity and CRP level have higher AUC in severe than in moderate cases. WBCs count, LDH activity and CRP level have AUC above 0.80 in the severe group. Conclusion: The current investigation found a significant correlation between WBCs count, lymphocytes count, CRP level and liver injury in COVID-19 patients. WBCs count, lymphocytes count, LDH activity and CRP level were effective indicators for determining the severity of COVID-19.

In this paper, the author derives an explicit form of Heaviside Step Function, which evidently constitutes a fundamental concept of Operational Calculus and is also involved in many other fields of applied and engineering mathematics.In particular, this special function is exhibited in a very simple manner as a summation of four inverse tangent functions. The novelty of this work is that the proposed exact formulae are not performed in terms of miscellaneous special functions, e.g. Bessel functions, Error function, Beta function etc and also are neither the limit of a function, nor the limit of a sequence of functions with point – wise or uniform convergence.Hence, this formula may be much more appropriate and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

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

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

Very poor oral health, common among older adults, is associated with cognitive decline.This study aimed to investigate the association between denture use, chewing ability, and cognitive function in Korean middle-aged adults using samples representing middle-aged people at the national level. This longitudinal study included 9,998 middle-aged adults via Korea Longitudinal Study of Aging 7th special survey data. Denture use, chewing ability, health-related factors, and general characteristics were assessed by the Computer Assisted Personal Interview. After controlling general characteristics using a generalized estimating equation model, the association of denture use and MMSE scores with chewing ability of those with or without dentures and MMSE scores were analysed. Twenty-four percent of participants wore dentures among them, 35.1% complained of difficulty chewing when wearing dentures. Among participants who did not wear dentures, 16.4% complained of difficulty chewing. MMSE scores were lower among denture-wearers than non-denture wearers (β = -0.026, p < 0.001). In both groups, MMSE scores decreased with chewing difficulty and were significantly reduced among non-denture wearers (p < 0.05). Chewing ability was closely associated with cognitive function. Given the negative effect of difficulty chewing on cognitive function, maintaining chewing ability should be of great concern.

In this paper, we have established some new bounds of Fejér type Hermite-Hadamard inequality for k−fractional integrals involving r−times differentiable preinvex functions. It is noteworthy that in the past there was no weighted version of left and right sides of the Hermite-Hadamard inequality for k-fractional integrals for generalized convex functions available in literature.

In this study, we investigate the performance of the saddlepoint approximation of the probability mass function and the cumulative distribution function for the weighted sum of independent Poisson random variables. The goal is to approximate the hazard rate function for this complicated model. The better performance of this method is shown by numerical simulations and comparison with a performance of other approximation methods.

Riemann’s method is one of the definitive ways of solving Cauchy’s problem for a second order linear hyperbolic partial differential equation in two variables. The first review of Riemann’s method was published by E. T. Copson in 1958. This study extends that work. Firstly, three solution methods were overlooked in Copson’s original paper. Secondly, several new approaches for finding Riemann functions have been developed since 1958. Those techniques are included here and placed in the context of Copson’s original study. There are also numerous equivalences between Riemann functions that have not previously been identified in the literature. Those links are clarified here by showing that many known Riemann functions are often equivalent due to the governing equation admitting a symmetry algebra isomorphic to $SL(2,R)$. Alternatively, the equation admits a Lie-Bäcklund symmetry algebra. Combining the results from several methods, a new class of Riemann functions is then derived which admits no symmetries whatsoever.

We study the existence or absence of non-Shannon inequalities for variables that are related by functional dependencies. Although the power-set on four variables is the smallest Boolean lattice with non-Shannon inequalities there exist lattices with many more variables without non-Shannon inequalities. We search for conditions that excludes the existence of non-Shannon inequalities. It is demonstrated that planar modular lattices cannot have non-Shannon inequalities. The existence of non-Shannon inequalities is related to the question of whether a lattice is isomorphic to a lattice of subgroups of a group.

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

In this research paper an algorithm for the derivation of methods based on theorems and axioms of fuzzy logic is presented, analyzed and applied. This new proposed procedure generates fuzzy methods and evaluates the value of fuzzy propositions through fuzzy implication. The new implications of the family should satisfy a number of axioms. Also, we denote the conditions in order to satisfy the maximum number of axioms. Moreover, authors state and prove theorems focusing on fuzzy implication, observing the rule: the fuzzy function of fuzzy implication is strong and that lead to fuzzy negation. In addition, the optimal number of repetitions is calculated according to the expected truth value. The formulas produced are verified through the use of temperature and humidity values over a certain period of time and in a certain geographical area in Greece. The basic steps of the methodology are the fuzzification of the data given ​​using four membership degree functions and the application of the membership degrees of temperature and humidity values on a new type of fuzzy implication. Finally, we observed that the isosceles trapezium gave the best results and the type of fuzzy implication can be effectively applied.

Depression is one of the psychiatric disorders characterized by anxiety, pessimism, and suicidal tendencies, which seriously affect the quality of life of patients and their families. In this paper, we used polynomial-based kernel Granger causality values as network node connectivity indicators to construct brain networks for 5 depressed patients and 11 healthy individuals’ magnetoencephalogram(MEG) under positive, neutral, and negative emotional stimuli, respectively, and found that depressed patients had closer information exchange between frontal and occipital regions compared to healthy individuals and other brain regions, and fewer causal connections in parietal and central regions. Further analysis of the topological properties of the network revealed that depressed patients had higher mean degrees under negative stimuli (p=0.008)and lower mean clustering coefficients than healthy individuals(p=0.034). Comparing the mean degree and mean clustering coefficient of the same sample under different emotional stimuli, we found that depressed patients had the greater mean degree and mean clustering coefficient under negative stimuli than neutral and positive stimuli. We also found that patients’ feature path lengths under negative and neutral stimuli significantly deviated from small-world attributes. The results suggest that analysis of nuclear Granger causality-based brain networks can effectively characterize depression pathology.

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

In this paper, we introduce the (ρ,q)-analogue of the p-adic factorial function. By utilizing some properties of (ρ,q)-numbers, we obtain several new and interesting identities and formulas. We then construct the p-adic (ρ,q)-gamma function by means of the mentioned factorial function. We investigate several properties and relationships belonging to the foregoing gamma function, some of which are given for the case p = 2. We also derive more representations of the p-adic (ρ,q)-gamma function in general case. Moreover, we consider the p-adic (ρ,q)-Euler constant derived from the derivation of p-adic (ρ,q)-gamma function at x = 1. Furthermore, we provide a limit representation of aforementioned Euler constant based on (ρ,q)-numbers. Finally, we consider (ρ,q)-extension of the p-adic beta function via the p-adic (ρ,q)-gamma function and we then investigate various formulas and identities.

Different notions of entropy can be identified in different communities: (i) the thermodynamic sense, (ii) the information sense, (iii) the statistical sense, (iv) the disorder sense, and (v) the homogeneity sense. Especially the “disorder sense” and the “homogeneity sense” relate to and require the notion of space and time. One of the few prominent examples relating entropy to geometry and to space is the Bekenstein-Hawking entropy of a Black Hole. Although being developed for the description of a physics object—a black hole—having a mass, a momentum, a temperature, a charge etc. absolutely no information about these attributes of this object can eventually be found in the final formula. In contrast, the Bekenstein-Hawking entropy in its dimensionless form is a positive quantity only comprising geometric attributes like an area A—which is the area of the event horizon of the black hole-, a length L_P—which is the Planck length - and a factor ¼. A purely geometric approach towards this formula will be presented. The approach is based on a continuous 3D extension of the Heaviside function, with this extension drawing on the phase-field concept of diffuse interfaces. Entropy enters into the local, statistical description of contrast respectively gradient distributions in the transition region of the extended Heaviside function definition. The structure of the Bekenstein-Hawking formula eventually is derived for a geometric sphere based on mere geometric-statistic considerations.

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

Changes in the atomic and electronic structure of silicon carbide 3C-SiC (β-SiC), resulting from lead adsorption, have been studied within the density functional theory. The tests were conducted for three representative surfaces with varying degrees of lead coverage. Results indicate that chemisorption occurs, with the strongest binding, found on the hexagonal surface (111) in interaction with three dangling bonds. The adsorption energy rises with increasing coverage, especially as the surface approaches saturation. Analysis of the data was focused on parameters important for corrosion processes such as bond distances, binding energies, Bader charges and charge density difference.

Prostate cancer is the most common cancer among men in Poland. A significant proportion of prostate cancers can be cured, providing longer survival. Patients have the opportunity to undergo minimally invasive treatment methods like brachytherapy, while maintaining their previous quality of life. The disease itself, as well as treatment complications, primarily affect the functioning of the urinary and digestive systems and impact the sexual sphere. Aim: This study aims to assess the quality of life of patients after prostate brachytherapy. Methods: The research was conducted at the Lower Silesian Oncology Centre in Wroclaw. The study included fifty men aged between 51 and 85 years. The following questionnaires were used: EORTC QLQ-C30, QLQ-PR25. Scales: Katz, Mini-MAC, PSS-10. Moreover, the study used a self-designed survey covering socio-demographical factors. Results: Prostate brachytherapy has a significant impact on the degree of sexual dysfunction. Compared to sexually inactive individuals, sexually active individuals exhibit fewer negative psychological symptoms. Choosing a destructive coping strategy intensifies the occurrence of symptoms, lowers patients' level of independence, and negatively affects their quality of life. Conclusions: Brachytherapy contributes to worsening sexual function and temporarily affects urinary system function, which may lower the overall quality of life in patients.

Some p53 mutants lose their tumor suppressor activity and acquire new oncogenic functions, known as a gain of function. Recent studies have shown that p53 mutants can exert oncogenic effects through specific miRNAs. We identified the differentially expressed miRNA profiles of the three most frequent p53 mutants (p53R273C, p53R248Q, and p53R175H) in the Saos-2 cell line (null p53) transfected as compared with p53WT transfected cells. The association between these miRNAs and the signaling pathways in which they might participate was performed through the miRPath Software. QRT-PCR was employed to validate the miRNAs profiles. In addition, we explored if the induction of cell migration and invasion by the p53R48Q mutant was dependent on the miR-182-5p. We observed that p53 mutants have an overall negative effect on miRNA expression. Likewise, we found miRNAs differentially expressed associated with regulating Oncogenic signaling pathways. We found overexpression of miR-182-5p, which is associated with processes such as cell migration and invasion. Inhibition of mutant p53R248Q and miR-182-5p increased FOXF2-MTSS1 levels and decreased cell migration and invasion. Our results suggest that p53 mutants increase the expression of miR-182-5p, and this miRNA is also necessary to induce cell migration and invasion by the p53R248Q mutant in a cancer cell model.

The aim of this article is to introduce the new notion on a given graph. The notions of valued set, valued function, valued graph and valued quotient are introduced. The attributes of these new notions are studied. Valued set is about the set of vertices which have the maximum number of neighbors. The kind of partition of the vertex set to the vertices of the valued set is introduced and its attributes are studied. The behaviors of classes of graphs under these new notions are studied and the algebraic operations on these sets in the different situations get new result to understand the classes of graphs, these notions and the general graphs better and more.

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

This paper considers a nonlinear model for population dynamics with age structure. The fertility rate with respect to age is non constant and has the form proposed by . Moreover, its multiplicative structure and the multiplicative structure of mortality makes the model separable. In this setting it is shown that the number of births in unit time is given by a system of nonlinear ordinary differential equations. The steady state solution together with the equilibrium solution is found explicitly.

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

This paper attempts to propose a Riemann spring model via an analogy between the Riemann Zeta function of a complex number and the elastic spring in series.

In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers.

Robin criterion states that the Riemann Hypothesis is true if and only if the inequality $\sigma(n) < e^{\gamma } \times n \times \log \log n$ holds for all natural numbers $n > 5040$, where $\sigma(n)$ is the sum-of-divisors function and $\gamma \approx 0.57721$ is the Euler-Mascheroni constant. Let $q_{1} = 2, q_{2} = 3, \ldots, q_{m}$ denote the first $m$ consecutive primes, then an integer of the form $\prod_{i=1}^{m} q_{i}^{a_{i}}$ with $a_{1} \geq a_{2} \geq \cdots \geq a_{m} \geq 0$ is called an Hardy-Ramanujan integer. If the Riemann Hypothesis is false, then there are infinitely many Hardy-Ramanujan integers $n > 5040$ such that Robin inequality does not hold and $n < (4.48311)^{m} \times N_{m}$, where $N_{m} = \prod_{i = 1}^{m} q_{i}$ is the primorial number of order $m$.

The paper continues the study of efficient algorithms for the computation of zeta functions over the complex plane. We aim to apply the modifications of algorithms to the investigation of underlying fractal structures associated with the Riemann zeta function. We discuss the computational complexity and numerical aspects of the implemented algorithms based on series with binomial-like coefficients.

To address the problems of poor recognition, low detection accuracy, a large number of model parameters and computation, complex network structure, and unfavorable portability to embedded devices in traditional tennis ball detection algorithms, this study proposes a lightweight tennis ball detection algorithm YOLOv5s-Z based on Robomater EP. The main work is as follows: Firstly, constructing lightweight G-Backbone and G-Neck network layers to reduce the number of parameters and computation of the network structure. Secondly, the convolutional coordinate attention is incorporated in G-Backbnone to embed the location information into the channel attention, which makes the network obtain the location information in a larger area through multiple convolutions and enhances the expression ability of the mobile network learning features. In addition, the Concat module in the original feature fusion is modified into a weighted bi-directional feature pyramid W-BiFPN with settable learning weights to improve the feature fusion capability and achieve efficient weighted feature fusion and bi-directional cross-scale connectivity. The EIOU loss is introduced to split the influence factor of aspect ratio and calculate the length and width of the target frame and anchor frame respectively, combined with Focal-EIOU Loss to solve the problem of imbalance between difficult and easy samples. The activation function Meta-ACON is introduced to achieve an adaptive selection of whether to activate the neurons and improve the detection accuracy. Finally, the experimental results show that compared with the original algorithm, the YOLOv5s-Z algorithm reduces the number of parameters and computation by 42$\%$ and 44$\%$, the model size by 39$\%$, and 2$\%$ improvement in average accuracy mean value, which verifies the effectiveness of the improved algorithm and the light weight of the model to meet the deployment requirements of embedded devices, and adapts Robomaster EP for accurate detection and real-time recognition of tennis balls.

In this work, we investigate the behaviour of a relativistic scalar particle in the background of the Lorentz symmetry violation determined by a tensor (KF)µναβ out of the Standard Model Extension. A linear electric field and a uniform magnetic can be induced by the violation of the Lorentz symmetry breaking effects, and analyze the behaviour of the scalar particle. We see that the analytical solution to the KG-equation can be achieved, and a quantum effect characterized by the dependence of the magnetic field on the quantum numbers is observed

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

The Colebrook equation is a popular model for estimating friction loss coefficients in water and gas pipes. The model is implicit in the unknown flow friction factor . To date, the captured flow friction factor can be extracted from the logarithmic form analytically only in the term of the Lambert -function. The purpose of this study is to find an accurate and computationally efficient solution based on the shifted Lambert -function also known as the Wright -function. The Wright -function is more suitable because it overcomes the problem with the overflow error by switching the fast growing term of the Lambert -function to the series expansions that further can be easily evaluated in computers without causing overflow run-time errors. Although the Colebrook equation transformed through the Lambert -function is identical to the original expression in term of accuracy, a further evaluation of the Lambert -function can be only approximate. Very accurate explicit approximations of the Colebrook equation that contains only one or two logarithms are shown. The final result is an accurate explicit approximation of the Colebrook equation with the relative error of no more than 0.0096%. The presented approximations are in the form suitable for everyday engineering use, they are both accurate and computationally efficient.

Background Some patients with mild cognitive impairment (MCI) experience gait disturbances. However, there are few reports on the relationship between gait disturbance and cognitive function in patients with MCI. Therefore, we investigated the neural correlates of gait characteristics related to cognitive dysfunction. Methods Eighty patients diagnosed with MCI from three dementia centres in Gangwon-do, Korea were recruited for this study. We defined MCI as a Clinical Dementia Rating global score of 0.5 or higher, with a memory domain score of 0.5 or greater. The patients were classified as having either early or late MCI based on their Mini Mental Status Examination z-scores. Multiple logistic regression analysis was performed to examine the association between the gait characteristics and cognitive impairment. Analyses included variables such as age, sex, years of education, number of comorbidities, body mass index and height. Results Gait velocity, step count, step length, heel-to-heel base support, swing and stance phase duration, and support time were associated with cognitive function. A decrease in gray matter volume in the right pericalcarine area was associated with gait characteristics related to cognitive dysfunction. An increase in the curvature of gray matter in the right entorhinal, right lateral orbitofrontal, right cuneus, and right and left pars opercularis areas was also associated with gait characteristics related to cognitive dysfunction. Conclusion Since gait impairment is an important factor in determining activities of daily living in patients with mild cognitive impairment, the evaluation of gait and cognitive functions in patients with mild cognitive impairment is important.

In this paper we introduce the New/Generalized two parameter Gamma function and Pochhammer symbol. We named them, as Generalized p - k Gamma Function and Generalized p - k Pochhammer symbol and denoted as $ _{p}^{a}\Gamma_{k}(x) $ and $ _{p}^{a}(x)_{n,k} $ respectively. We prove the several identities for $ _{p}^{a}\Gamma_{k}(x) $ and $ _{p}^{a}(x)_{n,k} $ those satisfied by the classical Gamma function. Also we provide the integral representation for the $ _{p}^{a}\Gamma_{k}(x) $

This paper presents a novel adaptive fault-tolerant neural-based control design for wind turbines with unknown dynamic and unknown wind speed. By utilizing the barrier Lyapunov function in the analysis of the Lyapunov direct method, the constrained behavior of the system is provided in which the rotor speed, its variation and generated power remain in the desired bounds. In addition, input saturation is also considered in terms of smooth pitch actuator bounding. Furthermore, by utilizing a Nussbaum-type function in designing the control algorithm, the unpredictable wind speed variation is captured without requiring accurate wind speed measurement, observation or estimation. Moreover, with the proposed adaptive analytic algorithms, together with the use of radial basis function neural networks, a robust adaptive and fault-tolerant control scheme is developed without the need for precise information about the wind turbine model nor the pitch actuator faults. Additionally, the computational cost of the resultant control law is reduced by utilizing a dynamic surface control technique. The effectiveness of the developed design is verified using theoretical analysis tools and illustrated by numerical simulations on a high-fidelity wind turbine benchmark model with different fault scenarios. Comparison of the achieved results to the ones that can be obtained via an available industrial controller shows the advantages of the proposed scheme.

We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer multicomponent mass is broken into fixed number of fragments and calculate the combinatorial multiplicity of all distributions in the set. We define random fragmentation by the condition that the probability of distribution be proportional to its multiplicity and obtain the partition function and the mean distribution in closed form. We then introduce a functional that biases the probability of distribution to produce in a systematic manner fragment distributions that deviate to any arbitrary degree from the random case. We corroborate the results of the theory by Monte Carlo simulation and demonstrate examples in which components in sieve cuts of the fragment distribution undergo preferential mixing or segregation relative to the parent particle.

If a clear and valid no-go for Einsteinian hidden parameters is real, it must in no way be possible to violate the CHSH with a local hidden variables based computer simulation. In the paper we show that with the use of a modied Glauber-Sudarshan method it is possible to violate the CHSH.The criterion value comes close to the quantum value and is approximately 2.4. The proof (POC) is presented with the use of an R computer program. The important snippets of the code are discussed and the complete code is presented in an appendix.

We establish certain modular equations of degree three based on some results of Ramanujan's theta functions.

In this article, we establish sharp trigonometric-polynomial bounds for unnormalized sinc function.

The occurrence of the COVID-19 pandemic has affected all aspects of our routine life. Here, we briefly reveal the less paid attention aspect, vocabulary. We extracted words from online news outlets during the first three months of the pandemic. The extracted words included many aspects, which we categorised into eight classes according to their functions and implications. We found out the top three dominant classes of vocabularies with the highest frequency compared to others, namely medical, economic and governance. The temporality in the pandemic timeline was vital in making sense of the predominant vocabulary. This paper is a rare preliminary report which provides a valuable insight into future articles with much more comprehensive data and analysis.

An approach to estimating the objective function value of minimization maximum lateness problem is proposed. It is shown how to use transformed instances to define a new continuous objective function. After that, using this new objective function, the approach itself is formulated. We calculate the objective function value for some polynomially solvable transformed instances and use them as interpolation nodes to estimate the objective function of the initial instance. What is more, two new polynomial cases, that are easy to use in the approach, are proposed. In the end of the paper numeric experiments are described and their results are provided.

In this study, we consider a Lambert series whose coefficients are the sum of divisors function. Utilizing the Lambert series in the sequel we introduce a normalized linear operator JR_(α,β) (z) by applying the convolution with Rabotnov function. We then, acquire sufficient conditions for JR_(α,β) (z) to be Univalent, Starlike and Convex respectively. In each component of this study, we expand the derived results by applying two Robin's inequalities, one of which is equivalent to the Riemann hypothesis.

Both lactic acid and short chain fatty acid (SCFA) play important roles in maintenance of intestinal epithelial structure and function. Trilactic glyceride (TLG) obtains both excellences of lactic acid and SCFA. This study was to investigate the effects of trilactic glyceride on growth performance, blood parameters, liver function, intestinal morphology and intestine function of piglets. Twelve weaned piglets (21±2 d) were randomly allocated to two treatment groups: 1) control group, piglets fed the basal diet; 2) TLG group, piglets fed the basal diet supplemented with 0.5 % TLG. On day 21 of the trial, D-xylose (0.1 g/kg·BW) was orally administrated to all piglets and blood samples were collected 1 h thereafter. Then, all the piglets were sacrificed to examine intestinal mucosal morphology and collect fatty tissue, liver and intestinal mucosa for further analysis. The results showed that: compared with the control group, TLG group decreased blood ALB and GGT on day 10 and 20, TLG group decreased blood TP and increased blood TG on day 20 of the trail (p < 0.05); TLG group decreased blood D-xylose and LDL, increased blood HDL (p < 0.05). These data suggested that supplementing trilactic glyceride had beneficial impacts on promoting nutrients’ metabolism, maintaining intestinal integrity, and alleviating oxidative stress and diarrhoea. Further research of molecular mechanisms showed changing expression levels of related proteins and genes, suggesting that these could be involved in the regulation of the impact. The community composition of the gut microbiota was also found to be altered in several operational taxonomic units within the genus, Prevotella (order Bacteroidales), and the order, Clostridiales.