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.

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

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.

The aim of this study was to investigate the physicochemical characterization and biological activities of chitosan (CH) based composite films with the incorporation of chestnut flower essential oil (CFEO). The composite films were prepared by casting method and characterized in terms of structural, morphological and mechanical properties via FT-IR, XRD, UV, SEM and TGA. The results proved the significantly increased water vapor permeability (WVP), heat resistance, antibacterial and antioxidant capabilities of CH-CFEO films. The incorporation of CH and CFEO enhanced the UV blocking, which made the film shield almost all UV light. Films with the tensile strength of 6.37 ± 0.41 MPa and elongation at break of 22.57 ± 0.35% were got with 6 mg mL-1 CFEO. Subsequently, the fruit preservation experiments also confirmed that the composite films could effectively extend the shelf life of bananas through their excellent water vapor and oxygen barrier. These desirable performances enable our newly developed composite films to be a remarkable packaging material to solve the fresh fruit preservation dilemma.

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

Plant cells' ability to withstand abiotic stress is strongly linked to modifications in their mechanical characteristics. Nevertheless, the lack of a workable method for consistently tracking plant cell mechanical properties severely restricts our comprehension of the mechanical alterations in plant cells under stress. With Polyethylene Glycol (PEG6000), we created a drought-like environment, and we used the Double Resonator Piezoelectric Cytometry (DRPC) method to dynamically and non-invasively track changes in the stress (ΔS) created and viscoelasticity (storage modulus G' and loss modulus G") of protoplasts and suspension cells of rice during drought stress. The findings demonstrate that, rice suspension cells and protoplasts react mechanically differently to 5%–15% PEG6000 stress, implying distinct resistance mechanisms. However, neither of them can withstand 25% PEG6000 stress, they respond mechanically similarly to 25% PEG6000 stress. The results of DRPC are further corroborated by the morphological alterations of rice cells and protoplasts observed under an optical microscope. To sum up, the DRPC technique functions as a precise cellular mechanical sensor and offers novel research tools for the evaluation of plant cell adversity and differentiating between the mechanical reactions of cells and protoplasts under abiotic stress.

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

In this paper, we provide alternative proofs to some results proposed in the article "New inequalities involving circular, inverse circular, hyperbolic, inverse hyperbolic and exponential functions" authored by Yogesh J. Bagul.

Proposed fundamental laws of biology and a model of health and disease underscore the importance of the lymphatic system. The lymphatics are responsible for two of the laws of biology and the fulcrum of health and disease balancing proliferation with regeneration through the immune system. It is responsible for protection from the environment and repair of senile and damaged tissue. Life is constantly bombarded by forces that increase entropy. Lymphatics provide negative entropy to maintain health. Lymphatics help maintain cellular homeostasis removing products of metabolism. Using these principles, the role of lymphatics is investigated in salt sensitivity hypertension, cardiorenal system, the new pillar of heart failure and kidney disease - Sodium-Glucose Transport Protein 2 (SGLT2) Inhibitors, and brain diseases. The realization of organ lymphatics in maintenance of health and disease opens the avenue to new therapeutics. This is the unrealized potential of lymphatic study.

A complete MAPLE procedure is designed to implement effectively an algorithm for approximating the trigonometric functions. The algorithm gives a piecewise polynomial approximation on an arbitrary interval, presenting a special partition that we can get its parts, subintervals with ending points of finite rational numbers, together with corresponding approximate polynomials. The procedure takes a sequence of pairs of interval-polynomial as its output that we can easily explore in some useful ways. Examples on calculating approximate values of the sine function with arbitrary accuracy for both of rational and irrational arguments as well as drawing the graph of the piecewise approximate functions will be presented. Moreover, from the approximate integration of integrands of the form $x^m\sin x$ on $[a,b]$, another MAPLE procedure is proposed to find the desired polynomial estimates in norm for the best $L^2$-approximation of the sine function in the vector space $\mathcal{P}_{\ell}$ of polynomials of degree at most $\ell$, a subspace of $L^2(a,b)$.

One of the most important unresolved mysteries in mathematics is the Riemann Hypothesis, which suggests a fundamental connection between the non-trivial zeros of the Riemann zeta function and the distribution of prime numbers. Here, we explore the fascinating union of trigonometric functions, prime numbers, and the Riemann zeta function through an examination of the zeros in the statement ln(sec(π·n log(n))). We demonstrate a strong mathematical connection between these components, providing information on the mysterious properties of prime numbers and their complex relationships to basic mathematical operations. Our thorough investigation adds to the current discussion of the Riemann Hypothesis by offering possible solutions and deepening our comprehension of the intricate relationship between number theory and analytic functions.

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

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

In this 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.

Although the empirical Kepler’s laws can be proven by applying Newton’s laws to the dynamics of two particles attracted due to the gravitational interaction, there is no explicit formula for the motion as a function of time. In this paper, a quasi-analytical solution for this problem is proposed. It approximates the real behavior of celestial bodies with an acceptable degree of accuracy. All calculations involved require a low computational cost. This problem is closely related to Kepler’s equation, since, the solution for the equations of motion as a function of time gives us the solution to Kepler’s equation as well. The results are presented for each planet of the solar system (including Pluto), and the solution is compared against the real orbits.

We monitored the water quality and hydrological conditions of a horizontal subsurface constructed wetland (HSSF-CW) in Beijing, China, for 2 years. We simulated the area rate constant and the temperature coefficient with the first-order kinetic model. We examined the relationships between the nitrogen (N) removal rate, N load, seasonal variations in the N removal rate, and environmental factors, such as the area rate constant, temperature, and dissolved oxygen (DO). The effluent ammonia (NH₄⁺-N) and nitrate (NO₃⁻-N) concentrations were significantly lower than the influent concentrations (p<0.01, n=38). The NO₃⁻-N load was significantly correlated with the removal rate (R²=0.9566, p<0.01), but the NH^₄+-N load was not correlated with the removal rate (R²=0.0187, p>0.01). The area rate constants of NO₃⁻-N and NH₄⁺-N at 20 °C were 27.01±26.49 and 16.63±10.58 m∙yr⁻¹, respectively. The temperature coefficients for NO₃⁻-N and NH₄⁺-N were estimated at 1.0042 and 0.9604, respectively. The area rate constants for NO₃⁻-N and NH₄⁺-N were not correlated with temperature (p>0.01). The NO₃⁻-N area rate constant was correlated with the corresponding load (R²=0.9625, p<0.01). The NH₄⁺-N area rate was correlated with DO (R²=0.6922, p<0.01), suggesting that the factors that influenced the N removal rate in this wetland met Liebig's law of the minimum.

Firstly, a new set of Quasi-Cubic Trigonometric Bernstein basis with two tension shape parameters is constructed, and we prove that it is an optimal normalized totally basis in the framework of Quasi Extended Chebyshev space. And the Quasi-Cubic Trigonometric Bézier curve is generated by the basis function and the cutting algorithm of the curve are given, the shape features (cusp, inflection point, loop and convexity) of the Quasi-Cubic Trigonometric Bézier curve are analyzed by using envelope theory and topological mapping; Next we construct the non-uniform Quasi-Cubic Trigonometric B-spline basis by assuming the linear combination of the optimal normalized totally positive basis have partition of unity and continuity, and its expression is obtained. And the non-uniform B-spline basis is proved to have totally positive and high-order continuity. Finally, the non-uniform Quasi Cubic Trigonometric B-spline curve and surface are defined, the shape features of the non-uniform Quasi-Cubic Trigonometric B-spline curve are discussed, and the curve and surface are proved to be continuous.

We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approxi- mation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical approximation using Sinc methods. The inverse Laplace transform converges exponentially and does not use Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions incorporating one, two, and three parameters. The three parameter Mittag-Leffler function represents Prabhakar’s function. The exact Sinc methods are used to solve fractional differential equations of constant and variable differentiation order.

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.

We introduce a full binary directed tree structure to represent the set of natural numbers, further categorizing them into three distinct subsets: pure odd numbers, pure even numbers, and mixed numbers. We adopt a binary string representation for natural numbers and elaborate on the composite methodology encompassing odd- and even-number functions. Our analysis focuses on examining the iteration sequence (or composition) of the Collatz function and its reduced variant, which serves as an analog to the inverse function, to scrutinize the validity of the Collatz conjecture. To substantiate this conjecture, we incorporate binary strings into an algebraic formula that captures the essence of the Collatz sequence. By this means, we transform discrete powers of 2 into continuous counterparts, ultimately culminating in the smallest natural number, 1. Consequently, the sequence generated through infinite iterations of the Collatz function emerges as an eventually periodic sequence, thereby validating an enduring 87-year-old conjecture.

Pure-compression shells have been the central topic in the form-finding of shells. This paper studies tension-compression mixed type shells by utilizing a NURBS-based isogeometric form-finding approach that analyzes Airy stress functions to expand the possible plan geometry. A complete set of smooth version graphic statics tools is provided to support the analyses. The method is validated using examples with known solutions, and a further example demonstrates the possible forms of shells that the proposed method permits. Additionally, a guideline to configure a proper set of boundary conditions is presented through the lens of asymptotic lines of the stress functions.

Based on some geometrical properties of the Rabinovich system the closed-form solutions of the equations has been established. Moreover the Rabinovich system is reduced to a nonlinear differential equation depending on an auxiliary unknown function. The approximate analytical solutions are built using the Optimal Auxiliary Functions Method (OAFM). A good agreement between the analytical and corresponding numerical results has been performed. The accuracy of the obtained results emphasizes that this procedure could be successfully applied for more dynamical systems with these geometrical properties.

By using Modified simple equation method, we study the Cahn Allen equation which arises in many scientific applications such as mathematical biology, quantum mechanics and plasma physics. As a result, the existence of solitary wave solutions of the Cahn Allen equation is obtained. Exact explicit solutions interms of hyperbolic solutions of the associated Cahn Allen equation are characterized with some free parameters. Finally, the variety of structure and graphical representation make the dynamics of the equations visible and provides the mathematical foundation in mathematical biology, quantum mechanics and plasma physics.

In this paper, we studied the problem of early detection of natural phenomena associated with the formation of severe floods and the possibility of constant monitoring of their occurrence. The test object for the study was severe floods on the Crimean Peninsula, which occurred due to heavy rainfall in the summer of 2021. Based on the selected satellite and other data related to this period, an analysis carried out and key atmospheric objects identified, according to the proposed algorithm for their identification and grouping. Based on the results of the work, a positive conclusion made on the issue of their use to identify the likelihood of natural disasters that could lead to floods. In addition, the authors proposed to develop a portal for collecting and processing a large amount of satellite data related to flood prevention and monitoring the development of such processes, and stressed the need to create it.

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

That form and function relates, is the maxim to anatomy and physiology. Yet form-function relations can be difficult to establish. Human subjects with excessive trabeculated myocardium in the left ventricle, for example, are diagnosed with non-compaction cardiomyopathy, but the extent of trabeculations may be without relation to ejection fraction. Rather than rejecting a relation between form and function, we may ask whether the salient function is assessed; is there a relation to electrical propagation, mean arterial blood pressure, propensity to form blood clots, or all? And how should extent of trabeculated muscle be assessed? While reviewing literature on trabeculated muscle, we applied Tinbergen’s four types of causation - how does it work, why does it work, how is it made, and why did it evolve - to better parse what is meant by form and function. The paper is structured around cases that highlight advantages and pitfalls of applying Tinbergen’s questions. It further uses the evolution of lunglessness in amphibians to argue lung reduction can impact on chamber septation, and it considers the evolution of an arterial outflow in fishes to argue that reductions in energy consumption may drive structural changes with little consequences to function. Concerning trabeculations, we argue they relate to pump function in the embryo in the couple of weeks before the onset of coronary circulation. In fetal and postnatal stages, a spectrum of trabeculated-to-compact myocardium makes no difference to cardiac function and in this period form and function may appear unrelated.

Let $\mathcal{\mathcal{S}}_{\cos}^{\ast}$ denote the class of normalized analytic functions $f$ in the open unit disk $\mathbb{D}$ satisfying the subordination $\dfrac{zf^{\prime}(z)}{f(z)}\prec\cos z$. In the second section of this article we find the sharp upper bounds for the initial coefficients $a_{3}$, $a_{4}$ and $a_{5}$ and the sharp upper bound for module of the Hankel determinant $|H_{2,3}(f)|$ for the functions from the class $\mathcal{S}_{\cos}^{\ast}$. The first result of the next section deals with the sharp upper bounds of the logarithmic coefficients $\gamma_{3}$ and $\gamma_{4}$ and we found in addition the sharp upper bound for $\left|H_{2,2}\left(F_{f}/2\right)\right|$. For obtaining these results we used the very useful and appropriate Lemma 2.4 of N.E. Cho et al. [Filomat 34(6) (2020), 2061--2072], and the technique for finding the maximum value of a three variable function on a closed cuboid. All the maximum found values were checked by using MAPLE\texttrademark{} computare software, and we also found the extremal functions in each cases. All of our present results are the best ones and give sharp versions of those recently published in [Hacet. J. Math. Stat. 52, 596--618, 2023].

Due to the continued deepening of today’s mining projects, there is a need to develop new or improved rockbolts that are strong and yielding and have high energy absorption when exposed to dynamic loading. Impact tests can provide useful information about the dynamic response of rockbolts but most laboratory tests involve high costs in preparation and result validation. Numerical modeling is an alternative that, in addition to complementing laboratory results, can be used to represent the process of deformation and energy absorption of support elements. In this paper the implementation and results obtained from a finite difference (FDM) numerical model are presented. The model functions as a simulation tool to illuminate all the elements that conform the large-scale (1:1) impact test and their behavior and influence on the dynamic response of a threadbar bolt (22 mm nominal diameter). The model was calibrated using published results and based on these results as well as parametric analysis, the response of each component (steel tube, grout, and bolt) could be identified and its behavior in terms of absorbed energy and displacement could be observed. Results show the model can provide important preliminary information to make design decisions about support elements design.

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

The design is described of a readily useable technology for routine paddock-scale soil porosity estimation. The method is non-contact (proximal) and typically from sensors mounted on a small farm vehicle around 1 m above the soil surface. Challenges arise from the need to have a compact low-power rigid structure and to allow for pasture cover and surface roughness. The high-frequency regime for acoustic reflections from a porous material is a function of the porosity , the tortuosity , and the angle of incidence . There is no dependence on frequency, so measurements must be conducted at two or more angles of incidence in order to obtain two or more equations in the unknown soil properties and . A system requiring a single transmitter/receiver pair to be moved from one angle to another is not viable for rapid sampling. Therefore, the design includes at least two transmitter/reflector pairs placed at identical distances from the ground so that they would respond identically to power reflected from a perfectly reflecting surface. A single 25 kHz frequency is a compromise which allows for the frequency-dependent signal loss from a natural rough agricultural soil surface. Multiple-transmitter and multiple-microphone arrays are described which give a good signal to noise ratio while maintaining a compact system design. The resulting arrays have a diameter of 100 mm. Pulsed ultrasound is used so that the reflected sound can be separated from sound travelling directly through the air horizontally from transmitter to receiver. The average porosity estimated for soil samples in the laboratory and in the field is found to be within around 0.04 of the porosity measured independently. This level of variation is consistent with uncertainties in setting the angle of incidence, although assumptions made in modelling the interaction of ultrasound with the rough surface no doubt also contribute.

We prove an analog of the removable singularity theorem for bounded harmonic functions on stratified sets. The harmonic functions are understood in the sense of the soft Laplacian. The result can become one of the main technical components for extending the well-known Poincaré–Perron’s method of proving the solvability of the Dirichlet problem for the soft Laplacian.

In this study, based on a new quantum integral identity, the authors establish some quantum estimates of Hermite-Hadamard type inequalities for convex functions. These results generalize and improve some known results given in literatures.

One mechanism by which fructose could exert deleterious effect in metabolism and inflammation is via its potency vis-à-vis de Maillard reaction. We employed simulated stomach and duodenum digestion of ovalbumin to test the hypothesis that indeed AGEs are formed by fructose during simulated digestion of an ubiquitous food protein with intrinsic allergenic potential and under model physiological conditions. Methods: OVA was subjected to simulated gastric and intestinal digestion using standard models, in presence of fructose or glucose (0-100 mM). Peptide fractions were analyzed by fluorescence spectroscopy and intensity at Excitation: λ370 nm, Emission: λ 440nm. Results: AGE adducts form between fructose and OVA which can be found in peptide fractions (< 5 kDa) at times (30 min) and concentration ranges (10 mM) plausibly found in the intestines, whereas no reaction occurs with glucose. The reaction is inhibited by chlorogenic acid at concentrations compatible with those found in the gut. The reaction is inhibited by AG, a specific antiglycation agent. Conclusion: Our proof of principle study shows that fructose-AGE formation on an ubiquitous allergenic protein indeed occurs in one hour and thereby may pave the way for the study of yet another mechanism by which the excess fructose in our Western diets is contributing to disease: intestinal AGE formation, absorption and RAGE engagement.

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

In this study, we introduce a new class of bi-univalent functions using q-Janowski Function. We derive the Fekete-Szegö functional problems for functions in this new subclass, as well as estimates for the Taylor-Maclaurin coefficients |α2| and |α3|. Furthermore, a collection of fresh outcomes are3 presented by customizing the parameters employed in our initial discoveries.

The golden ratio, also known as Phi (ϕ ≈ 1.618034), attracted the interest of mathematicians, artists, and intellectuals for many centuries, probably from when it was discovered in human anthropometry. Even in recent times, researchers found the presence of golden ratio in Renaissance paintings and aesthetic preferences. The reasons behind the fascination with the golden ratio remain unclear, but it has been suggested that stimuli containing this proportion are often perceived as beautiful. However, evidence is conflicting, and the literature struggles to establish the existence of individual preferences for golden ratio. To gain new insights into the nature of these preferences, one hundred participants completed an implicit association task, with either golden ratio or random stimuli presented with positive or negative words. Participants initially categorized the stimuli based on their assigned categories. Then, we assessed their explicit preferences by asking to rate the stimuli in terms of pleasantness and by completing a line bisection task and the Ultimate Game. The results revealed the typical effects observed in implicit association tasks, with improved response times and accuracy when golden ratio stimuli were associated with positive word categories. In contrast, explicit ratings yielded mixed results. We discuss our findings in relation to previous studies that have explored this issue, highlighting the ongoing debate surrounding preferences for the golden ratio.

The poly lactic acid (PLA) is one of the most used bio-derived thermoplastic polymers in 3D and 4D printing applications. The determination of PLA surface properties is of capital importance in 3D/4D printing technology. (1) Background: The surface thermodynamic properties of PLA polymer were determined by using the inverse gas chromatography (IGC) technique at infinite dilution. The determination of the retention volume of polar and non-polar molecules adsorbed on the PLA particles filling the column allowed us to obtain the dispersive, polar, and Lewis’s acid-base surface properties at different temperatures from 40 °C to 100 °C. (2) Methods: the applied surface method was based on our recent model that used the London dispersion equation and the new chromatographic parameter function of the deformation polarizability and the harmonic mean of the ionization energies of the PLA polymer and organic molecules. (3) Results: The application of this new method led to the determination of the dispersive and polar free surface energy of adsorption of molecules on the polymeric material, as well as the glass transition and the Lewis acid-base constants. (4) Conclusions: four interval temperatures were distinguished showing four zones of the variations of the surface properties of PLA as a function of the temperature before and after the glass transition.

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

For doctoral students, publishing in peer reviewed journals is a task many face with anxiety and trepidation. The world of publishing, from choosing a journal, negotiating editors and navigating reviewers’ responses is a bewildering place. Looking in from the outside, it seems that successful and productive academic writers have knowledge that is inaccessible to novice scholars. While there is a growing literature on writing for scholarly publication, many of these publications promote writing and publishing as a straight-forward activity that anyone can achieve if they follow the rules. We argue that the specific and situated contexts in which academic writers negotiate publishing practices is more complicated and messy. In this paper, we attempt to make explicit our publishing processes to highlight the complex nature of publishing. We use autoethnographic narratives to provide discussion points and insights into the challenges of publishing peer reviewed articles. One narrative is by a doctoral student at the beginning of her publishing career, who expresses her desires, concerns and anxieties about writing for publication. The other narrative focuses on the publishing practices of a more experienced academic writer. Both are international scholars working in the Canadian context. The purpose of this paper is to explore academic publishing through the juxtaposition of these two narratives to make explicit some of the more implicit processes. Four key themes emerge from these narratives. To publish successfully, academic writers need: 1) to be discourse analysts; 2) to have a critical competence; and 3) to have writing fluency and 4) to be emotionally intelligent.

Diet modification may be a potential contributor in the prevention of age-related cognitive decline. The association between dairy product consumption and cognitive function remains unknown in older people. We investigated whether cheese intake is associated with lower cognitive function (LCF) in community-dwelling older adults. This cross-sectional study included 1503 adults aged over 65 years. Analyzed data were obtained from face-to-face interviews and functional ability measurement. Cognitive function was assessed using mini-mental state examination (MMSE), and a score ≤ 23 was defined as LCF. The prevalence of LCF was 4.6% and this group had smaller calf circumference, slower usual walking speed, and more frequent history of anemia than subjects with MMSE scores ≥ 24. After adjusting for confounding factors, logistic regression analysis revealed cheese intake (odds ratio (OR) = 0.404, 95% confidence interval (CI) = 0.198-0.824), age (OR = 1.170, 95% CI = 1.089-1.256), usual walking speed (OR = 0.171, 95% CI = 0.062-0.472) and calf circumference (OR = 0.823, 95% CI = 0.747-0.908) as significant factors associated with LCF. Although the present study was an analysis of cross-sectional data of Japanese community-dwelling older adults, the results suggest that cheese intake is inversely associated with LCF.

In this paper we use the Mellin convolution theorem, which is related to Perron's formula. Also we introduce new explicit formulae for arithmetic function which generalize the explicit formulae of Weil for other arithmetic functions different from the Von-Mangoldt function.

Sepsis is a serious disease that can lead to mortality. The etiology of the disease is connected to how the body as a host reacts toward microbes such as bacteria, viruses, and fungi invasion. Current research shows that during sepsis, the reaction toward microbe attacks takes two main phases. The first is known as a cytokine storm, while the second is a vicious cycle of pro-inflammatory responses followed by a strict anti-inflammatory response led by CD4+ Tregs. Various immunomodulatory therapies have been proposed to break the cycle of pro- and anti-inflammatory reactions to sepsis. However, clinical trials did not show promising results, indicating further research into the mechanism that Treg uses to inhibit proinflammatory reactions. We used next-generation sequencing (NGS) analysis of bulk RNA-seq and single-cell RNA-seq data to examine the exact molecular pathways used by Treg to inhibit the immune response in sepsis. Our approach identified ACOD1 (Aconitate Decarboxylase 1) as a primary mediator of Treg suppression of immune cells. We identified and validated CD36 as a downstream target of ACOD1. CD36 is a known metabolite regulator in Tregs. Taken together, our results indicate that targeting ACOD1 could prove valuable in regulating Treg function during sepsis.

Elevated carbon dioxide (eCO₂) stimulates wheat grain yield, but simultaneously reduces protein (N) concentration. Also other essential nutrients are subject to change. This study is a comprehensive synthesis of wheat experiments with eCO₂, estimating effects on N, minerals (B, Ca, Cd, Fe, K, Mg, Mn, Na, P, S, Zn), and starch. Analysis was made by i) deriving response functions for the relative effect on element concentration in relation to CO₂ concentration, ii) meta-analysis to test the magnitude and significance of observed effects, and iii) relating CO₂ effects on minerals to effects on N and grain yield. Responses range from zero to strong negative effects of eCO₂ on mineral concentration, with largest reductions for the nutritionally important elements N, Fe, S, Zn and Mg. Together with the positive but small and non-significant effect on starch concentration, the large variation in effects suggests that CO₂-induced responses cannot be explained by a simple dilution model. To explain the observed pattern, uptake and transport mechanisms may have to be considered, along with the link of different elements to N uptake. Our study shows that eCO₂ has a significant effect on wheat grain stoichiometry, with implications for human nutrition in a world of rising CO₂.

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

In the present study, we derive a new B-spline technique namely trigonometric B-spline collocation algorithm to solve some initial boundary value problems for the nonlinear Klein-Gordon equation. In order to carry out the time integration with Crank-Nicolson implicit method, the order of the equation is reduced to give a coupled system of nonlinear partial differential equations. The collocation approximation based on trigonometric cubic B-splines for spatial discretization is followed by the linearization of the nonlinear term. The efficiency and accuracy of the present method are validated by measuring the error between the numerical and analytical solutions when exist. The conservation laws representing momentum and energy are also computed for all problems.

In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals.

In this work, Gaussian Tribonacci functions are defined and investigated on the set of real numbers $\mathbb{R},$ \textit{i.e}., functions $f_{G}$ $:$ $\mathbb{R}\rightarrow \mathbb{C}$ such that for all $% x\in \mathbb{R},$ $n\in \mathbb{Z},$ $f_{G}(x+n)=f(x+n)+if(x+n-1)$ where $f$ $:$ $\mathbb{R}\rightarrow \mathbb{R}$ is a Tribonacci function which is given as $f(x+3)=f(x+2)+f(x+1)+f(x)$ for all $x\in \mathbb{R}$. Then the concept of Gaussian Tribonacci functions by using the concept of $f$-even and $f$-odd functions is developed. Also, we present linear sum formulas of Gaussian Tribonacci functions. Moreover, it is showed that if $f_{G}$ is a Gaussian Tribonacci function with Tribonacci function $f$, then $% \lim\limits_{x\rightarrow \infty }\frac{f_{G}(x+1)}{f_{G}(x)}=\alpha \ $and\ $\lim\limits_{x\rightarrow \infty }\frac{f_{G}(x)}{f(x)}=\alpha +i,$ where $% \alpha $ is the positive real root of equation $x^{3}-x^{2}-x-1=0$ for which $\alpha >1$. Finally, matrix formulations of Tribonacci functions and Gaussian Tribonacci functions are given. In the literature, there are several studies on the functions of linear recurrent sequences such as Fibonacci functions and Tribonacci functions. However, there are no study on Gaussian functions of linear recurrent sequences such as Gaussian Tribonacci and Gaussian Tetranacci functions and they are waiting for the investigating. We also present linear sum formulas and matrix formulations of Tribonacci functions which have not been studied in the literature.

In the paper, the authors find two explicit formulas and recover a recursive formula for the generalized Motzkin numbers. Consequently, the authors deduce two explicit formulas and a recursive formula for the Motzkin numbers, the Catalan numbers, and the restricted hexagonal numbers respectively.

Here, using the theory of electrical-quantum modelling of the neutron and proton as a three-phase alternating current electrical generator, we will analyse the proton decay and the inverse neutron decay and determine the following subatomic particles, Dproton, Protoniu, Dneutron and Neutroniumd.

In this note we generalize the regularity concept for semigroups in two ways simultaneously: to higher regularity and to higher arity. We show that the one-relational and multi-relational formulations of higher regularity do not coincide, and each element has several inverses. The higher idempotents are introduced, and their commutation leads to unique inverses in the multi-relational formulation, and then further to the higher inverse semigroups. For polyadic semigroups we introduce several types of higher regularity which satisfy the arity invariance principle as introduced: the expressions should not depend of the numerical arity values, which allows us to provide natural and correct binary limits. In the first definition no idempotents can be defined, analogously to the binary semigroups, and therefore the uniqueness of inverses can be governed by shifts. In the second definition called sandwich higher regularity, we are able to introduce the higher polyadic idempotents, but their commutation does not provide uniqueness of inverses, because of the middle terms in the higher polyadic regularity conditions.

This article introduces the Theory of Inverse Discrete Dynamical Systems (TIDDS), a novel methodology for modeling and analyzing discrete dynamical systems via inverse algebraic models. Key concepts such as inverse modeling, structural analysis of inverse algebraic trees, and the establishment of topological equivalences for property transfer between a system and its inverse are elucidated. Central theorems on homeomorphic invariance and topological transport validate the transfer of cardinal attributes between dynamic representations, offering a fresh perspective on complex system analysis. A significant application presented is an alternative proof of the Collatz Conjecture, achieved by constructing an associated inverse model and leveraging analytical property transfers within the inverted tree structure. This work not only demonstrates the theory's capability to address and solve open problems in discrete dynamics but also suggests vast implications for expanding our understanding of such systems.

This paper addresses the Collatz Conjecture, an open question in mathematics that postulates all positive integers will eventually reach one when a pair of specific operations are repeatedly applied. Despite its apparent simplicity, the conjecture lacks a formal proof. To tackle this enigma, we introduce Algebraic Inverse Trees (AITs), data structures that trace inverse operations of the Collatz sequence. This new approach not only elaborates our unique methodology but also sheds light on the underlying complexities of the Collatz Conjecture.

Colombia is the world's leading producer of mild washed arabica coffee and produces 12.6 million bags of green coffee, but at the same time 784,000 tons of waste biomass are dumped in open fields, of which only 5% is recovered or used. The objective of this project was to evaluate the production of platform chemicals from these coffee wastes. To achieve this, biomass characterization was carried out using proximate analysis, ultimate analysis and structural analysis. Hydrothermal valorization was carried out at a temperature range of 120-180 °C (LHW) and 180-260 °C (HTC) for one hour, the platform chemicals obtained were quantified by HPLC-IR, monitored by pH and conductivity, and the solid fraction was characterized by monitoring the functional groups in IR spectroscopy, and elemental analysis. Hydrolysis processes were obtained from 150 °C, production of platform chemicals from 180 °C and maximum concentration at 180 °C-4h, over 200 °C degradation of the products in the liquid fraction starts to take place. Homogeneous basic and acid catalysts were used to improve the yields of the reaction. The kinetics of the hydrolysis of lignocellulosic structures to sugars were also analyzed and described, and reaction orders of 1 (LHW), 3 (HTC) and their respective reaction rate equations were reported.

As more end devices are getting connected, the Internet will become more congested. A variety of congestion control techniques have been developed either on transport or network layers. Active Queue Management (AQM) is a paradigm that aims at mitigating the congestion on the network layer by active buffer control to avoid overflow. However, finding the right parameters for an AQM scheme is challenging, due to the complexity and dynamics of the networks. On the other hand, the Explicit Congestion Notification (ECN) mechanism is a solution that makes visible incipient congestion on the network layer to the transport layer. In this work, we propose to exploit the ECN information to improve AQM algorithms by applying Machine Learning techniques. Our intelligent method uses an artificial neural network to predict congestion and an AQM parameter tuner based on reinforcement learning. The evaluation results show that our solution can enhance the performance of deployed AQM, using the existing TCP congestion control mechanisms.

This paper investigates the feasibility of a backend design for real-time, multiple-channel processing digital phased array system, particularly for high-performance embedded computing platforms constructed of using general purpose digital signal processors. Frist, we obtained the lab-scale backend performance benchmark from simulating beamforming, pulse compression, and Doppler filtering based on MicroTCA chassis using Serial RapidIO protocol in backplane communication. Next, a field-scale demonstrator of a multifunctional phased array radar is emulated by using the similar configuration. Interestingly, the performance of a barebone design is compared to that of emerging tools that systematically take advantage of parallelism and multicore capabilities, including Open Computing Language.

In the paper, by virtue of the Faá di Bruno formula and two identities for the Bell polynomial of the second kind, the authors find a closed form for the Stirling polynomials in terms of the Stirling numbers of the first and second kinds.

In the paper, the author introduces the notions "multi-order logarithmic numbers" and "multi-order logarithmic polynomials", establishes an explicit formula, an identity, and two recurrence relations by virtue of the Faa di Bruno formula and two identities of the Bell polynomials of the second kind in terms of the Stirling numbers of the fi rst and second kinds, and constructs some determinantal inequalities, product inequalities, logarithmic convexity for multi-order logarithmic numbers and polynomials by virtue of some properties of completely monotonic functions.

The digital orthophoto is an image with geometric accuracy and no distortion. It is acquired through a top view of the scene and finds widespread applications in map creation, planning, and related fields.This paper classifies the algorithms for digital orthophoto generation into two groups: explicit methods and implicit methods. Explicit methods rely on traditional geometric methods, obtaining geometric structure presented by explicit parameters with Multi-View Stereo (MVS) theories, as seen in our proposed Top view constrained Dense Matching (TDM). Implicit methods rely on neural rendering, obtaining implicit neural representation of scenes through the training of neural networks, as exemplified by Neural Radiance Fields (NeRF). Both of them obtain digital orthophoto by rendering from a top view perspective. In addition, this paper conducts an in-depth comparative study between explicit and implicit methods. The experiments demonstrate that both algorithms meet the measurement accuracy requirements and exhibit a similar level of quality in terms of generated results. Importantly, the explicit method shows a significant advantage in terms of efficiency, with a time consumption reduction of two orders of magnitude under our latest CUDA version TDM algorithm. Although explicit and implicit methods differ significantly in their representation forms, they share commonalities in the implementation across algorithmic stages. These findings highlight the potential advantages of explicit methods in orthophoto generation, while also providing beneficial references and practical guidance for the fast digital orthophoto generation using implicit methods.

The temperature effect plays an important role for an accurate determination of the polar free energy, polar thermodynamic parameters, and enthalpic and entropic Lewis’s acid base properties of oxides, polymers and composites polymers/oxides. The adsorption of polymers on other solid surfaces is crucial in many industrial applications, coatings, paints, catalysis, colloids and adhesion processes. (1) Background: Inverse gas chromatography at infinite was used for the physico-chemical characterization of solid substrates by determining the thermodynamic parameters of adsorption of model organic solvents on solid surfaces such as polymers, metallic oxides, carbon fibers, pharmaceutical or 3D/4D printing substrates. (2) Methods: A new method based on the London dispersion equation was applied with a new parameter associating the deformation po-larizability and the harmonic mean of the ionization energies of solvent. More accurate values of the dispersive and polar interaction energies of the various organic solvents adsorbed on PMMA in bulk phase and PMMA/silica at different recovery fractions were obtained as well as the Lewis acid-base parameters and the transition temperatures of the different composites. (3) Results: This new methodology gave very interesting results on the behavior of PMMA adsorbed on silica. An important effect of the temperature and the recovery fraction on the various physicochemical and thermodynamic properties was highlighted. The variations of all interaction parameters showed the presence of three transition temperatures for the different PMMA adsorbed on silica with the various coverage rates with a shift of these temperatures for a recovery fraction of 31% (4) Con-clusions: An important variation of the polar enthalpy and entropy of adsorption, the Lewis ac-id-base parameters and the intermolecular separation distance as a function of the temperature and the recovery fraction of PMMA on silica.

Diarrhoea is a serious cause of mortality worldwide that can lead to dehydration, gut barrier function impairment, nutrient malabsorption, and alterations of the gut microbiota (dysbiosis). Current solutions for its management, such as oral rehydration salts (ORS), inhibitors of the gut motility, antibiotics, and living probiotics only partially counteract the mechanisms of the disease and do not provide a full coverage of the problem. Potential risks of the use of living probiotic strains, particularly in immunocompromised patients, can be eliminated with the use of tyndallized (heat-killed) postbiotic bacteria and yeast. ABB C22® is a postbiotic combination of three tyndallized yeasts, namely Saccharomyces boulardii, Saccharomyces cerevisiae, and Kluyveromyces marxianus. To assess the action of the postbiotic combination on diarrhoea, immune and gut epithelial cell signaling assays, gut barrier formation assay and rotavirus gene expression assay were performed. ABB C22® showed a strong anti-inflammatory effect, an induction of the build-up of the gut epithelium, and a degree of protection against rotavirus infection. These experimental studies support the use of the postbiotic ABB C22® as a solution for the management of diarrhoea and gastrointestinal conditions, alone or in combination with existing but incomplete treatments.

In recent experimental studies, we reported the aggravating effects of Asian sand dust (ASD) on male reproductive function in mice. However, the effects of fetal ASD exposure on male reproductive function have not been investigated. The present study investigated the effects of fetal ASD exposure on reproductive function in male offspring. Using pregnant CD-1 mice, ASD was administered intratracheally on days 7 and 14 of gestation, and the reproductive function of male offspring was determined at 5, 10, and 15 weeks after birth. The secondary sex ratio was significantly lower in the fetal ASD-exposed mice than in the controls. Histologic examination showed partial vacuolation of seminiferous tubules in immature mice. Moreover, daily sperm production (DSP) was significantly less in the fetal ASD-exposed mice than in the controls. DSP in the fetal ASD-exposed mice was approximately 10% less than the controls at both 5 and 10 weeks. However, both the histologic changes and the DSP decrease were reversed as the mice matured. These findings suggest that ASD exposure affects both the fetal development and the reproductive function of male offspring. In the future, it will be necessary to clarify the onset mechanisms of ASD-induced male fetus death and male reproductive disorders.

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

This paper presents a comprehensive bibliometric analysis of research on form and typology in architectural publications, spanning from 1999 to 2024. Utilizing the Web of Science database and the bibliometrix package in R, the study examines trends, influential works, and thematic evolution in the field. The findings reveal a progression from foundational themes such as "architecture," "culture," and "planning" to more specialized and diverse topics, including "sustainability," "parametric design," and "digital fabrication." Key influential works by authors like Jane Jacobs, Kevin Lynch, and Bill Hillier are highlighted. The study also underscores the collaborative nature of contemporary architectural research, with significant international co-authorship. While providing valuable insights into the research landscape, the study acknowledges limitations, such as database reliance and the need for qualitative analysis. The paper concludes with recommendations for future research, emphasizing the exploration of emerging technologies, interdisciplinary collaborations, and regional research dynamics.

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

In this paper, we gave an attack on RSA when Euler function has small multiplicative inverse modulo "e" and the prime sum p+q is of the form p+q=2^nk_0+k_1 where n is a given positive integer and k_0 and k_1 are two suitably small unknown integers using sublattice reduction techniques and Coppersmith's methods for finding small roots of modular polynomial equations. When we compare this method with an approach using lattice based techniques, this procedure slightly improves the bound and reduces the lattice dimension.

Diarrhoea is a serious cause of mortality worldwide that can lead to dehydration, gut barrier function impairment, nutrient malabsorption, and alterations of the gut microbiota (dysbiosis). Current solutions for its management, such as oral rehydration salts (ORS), inhibitors of the gut motility, antibiotics, and living probiotics only partially counteract the mechanisms of the disease and do not provide a full coverage of the problem. Potential risks of the use of living probiotic strains, particularly in immunocompromised patients, can be eliminated with the use of tyndallized (heat-killed) postbiotic bacteria and yeast. ABB C22® is a postbiotic combination of three tyndallized yeasts, namely Saccharomyces boulardii, Saccharomyces cerevisiae, and Kluyveromyces marxianus. To assess the action of the postbiotic combination on diarrhoea, immune and gut epithelial cell signaling assays, gut barrier formation assay and rotavirus gene expression assay were performed. ABB C22® showed a strong anti-inflammatory effect, an induction of the build-up of the gut epithelium, and a degree of protection against rotavirus infection. These experimental studies support the use of the postbiotic ABB C22® as a solution for the management of diarrhoea and gastrointestinal conditions, alone or in combination with existing but incomplete treatments.

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

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

This research was devoted to study the effect of the tacticity of PMMA on the surface physicochemical properties such as the London dispersive component of the surface energy of the polymer, the polar and dispersive free energies, the Lewis’s acid-base surface parameters, and the Lewis acid and base surface energies of atactic, isotactic and syndiotactic PMMAs as a function of the temperature. Inverse gas chromatography (IGC) at infinite dilution was used to determine the surface thermodynamic properties of PMMA at different tacticities. The experimental values of the net retention time and volume of model organic molecules adsorbed on the atactic, isotactic and syndiotactic PMMAs, were obtained by IGC technique at infinite dilution. The London dispersion interaction energy was used for the separation of the polar and dispersive energy of the different n-alkanes and polar solvents adsorbed on the different PMMA surfaces. The London dispersive surface energy γ_s^d (T) of PMMAs was determined by applying the Hamieh thermal model that took into account the effect of the temperature on the surface area of adsorbed molecules. The obtained results showed non-linear variations of γ_s^d (T) of atactic, isotactic, and syndiotactic PMMAs with three maxima characterizing the three transition temperatures of PMMAs, T_g, T_g and T_(liq-liq) with a shift of these temperatures with the isotactic and syndiotactic PMMAs. It was showed that the polar interaction free energy ∆G_a^p (T) also showed the presence of the three above transition temperatures of the polymers. The study showed an important non-linearity variation of the different acid-base parameters in the various polymer surfaces proving the highest effect of the temperature and the tacticity on these parameters. The determination of the enthalpic and entropic Lewis’s acid-base parameters showed an amphoteric character for the different PMMAs. The basicity of the atactic PMMA was about four times larger than its acidity outside the neighborhood of the transition temperatures of the polymer. Whereas, the isotactic PMMA was about 2 to 2.5 times more basic than acid, while the syndiotactic PMMA exhibited the highest basicity by showing a surface 5 to 8 times more basic than acid. However, the Lewis acid-base parameters strongly depended on the temperature and sudden variations of these surface parameters were observed around the transition temperatures largely depending on the PMMA tacticity. The determination of the polar acid and base surface energies of the three PMMAs led to the same previous transition temperatures with an important effect of the tacticity of PMMA on the values of these acid-base surface energies.

Computing the rotation tensor is vital in the analysis of deformable bodies. This paper describes an explicit expression for the SO(3) rotation tensor R of the deformation gradient F, and successfully establishes an intrinsic relation between the exponential mapping Q = exp A and the deformation F. As an application, Truesdell's simple shear deformation is revisited.

By using directed dimensional analysis and data fitting, an explicit universal scaling law for the speed of falling dominoes is formulated. The scaling law shows that domino propagational speed is linear proportional to the 3/2 power of domino separation, and -1/2 power of domino height and thickness.

This study investigates five-year-old learners’ vocabulary retention through case studies, on a one week, one month, three months, and five months basis. It concerns the vocabulary learning of kindergarten children learning English as a second language (L2). This study attempts to seek answers to the questions of to what extent the presentation of the three different sets of words more effective than the other two is, both on recall and recognition and whether the recall and recognition levels showed differences in the three sets of words in course of time. In the literature, some studies have favoured semantic mapping in which new words are presented and organized in terms of associated lexical meanings. Some other studies have disfavoured semantic mapping. This study has administered three different sets of vocabulary: semantically related, cognates and semantically unrelated words. This study indicated that all participants were more successful with semantically related words on word recall and with cognates on word recognition. The results of this study do not support those which claim that making semantic associations may cause interference and hinder vocabulary learning. This study further suggests that semantically related words should be taught thematically to facilitate vocabulary teaching, particularly on word recall.

Biological systems are highly regulated. They are also highly resistant to sudden perturbations enabling them to maintain the dynamic equilibrium essential for sustenance of life. This robustness is conferred by regulatory mechanisms that influence the activity of enzymes/proteins within their cellular context, to adapt to changing environmental conditions. However, the initial rules governing the study of enzyme kinetics were tested and implemented for mostly cytosolic enzyme systems that were easy to isolate and/or recombinantly express. Moreover, these enzymes lacked complex regulatory modalities. Now, with academic labs and pharmaceutical companies turning their attention to more complex systems (for instance, multi-protein complexes, oligomeric assemblies, membrane proteins and post-translationally modified proteins), the initial axioms defined by Michaelis-Menten (MM) kinetics are rendered inadequate and the development of a new kind of kinetic analysis to study these systems is required. The current review strives to present an overview of enzyme kinetic mechanisms that are atypical and, oftentimes, do not conform to the classical MM kinetics. Further, it presents initial ideas on the design and analysis of experiments in early drug-discovery for such systems, to enable effective screening and characterisation of small-molecule inhibitors with desirable physiological outcomes.

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

To advance probiotic research, a comprehensive understanding of bacterial interactions with human physiology at the molecular and cellular levels is fundamental. Lacticaseibacillus rhamnosus LGG® is a bacterial strain that has long been recognized for its beneficial effects on human health. Probiotic effector molecules derived from LGG®, including secreted proteins, surface-anchored proteins, polysaccharides, and lipoteichoic acids, that interact with host physiological processes have been identified. In vitro and animal studies have revealed that specific LGG® effector molecules stimulate epithelial cell survival, preserve intestinal barrier integrity, reduce oxidative stress, mitigate excessive mucosal inflammation, enhance IgA secretion, and provide long-term protection through epigenetic imprinting. Pili on the cell surface of LGG® promote adhesion to the intestinal mucosa and ensure close contact to host cells. Extracellular vesicles produced by LGG® recapitulate many of these effects through their cargo of effector molecules. Collectively, the effector molecules of LGG® exert a significant influence on both the gut mucosa and immune system, that promotes intestinal homeostasis and immune tolerance.

This article presents a new methodology for modeling and analyzing discrete dynamic systems through the construction of inverse algebraic models, giving rise to the Theory of Inverse Discrete Dynamical Systems. Key concepts such as inverse modeling, structural analysis in inverse algebraic trees, and the establishment of topological equivalences for the analytical transfer of properties between the canonical system and its inverted counterpart are introduced. Central theorems on homeomorphic invariance and topological transport are demonstrated, consolidating the validity of transferring cardinal attributes between both equivalent dynamic representations. As a concrete application, an alternative proof of the historic Collatz Conjecture is presented through the rigorous construction of the associated inverse model and the analytical transfer of properties exhibited in the inverted tree structure. Furthermore, evidence has been presented on Conway's Conjecture in the Game of Life through meticulous inverse modeling in bounded cases, overcoming initial limitations of the theory in combinatorial explosions. Although a complete proof of the conjecture is not achieved, this positively expands the modeling and analysis capacity of the methodology. The impact of properly applying this novel theory to expand understanding and solve open problems in discrete dynamical systems seems vast and profound.

Ultrafast pump-probe spectroscopic studies allow for deep insights into the mechanisms and timescales of photophysical and photochemical processes. Extracting valuable information from these studies, such as reactive intermediates' lifetimes and coherent oscillation frequencies, is an example of the inverse problems of chemical kinetics. This article describes a consistent approach for solving this inverse problem that avoids the common obstacles of simple least-squares fitting that can lead to unreliable results. The presented approach is based on the regularized Markov Chain Monte Carlo sampling for the strongly nonlinear parameters, allowing for a straightforward solution of the ill-posed nonlinear inverse problem. The software to implement the described fitting routine is introduced and the numerical examples of its application are given. We will also touch on critical experimental parameters, such as the temporal overlap of pulses and cross-correlation time and their connection to the minimal reachable time resolution.

The uncertainty in the secondary path of an Active Noise Control (ANC) headphone affects the waterbed effect and stability of the feedback system. This study focuses on the uncertainty of the secondary path when real users wear headphones, and proposes a new uncertainty constraint based on the measured results of the secondary path transfer function under different wearing conditions of dummy head and limited subjects. This constraint and a cascaded second-order infinite impulse response filter with fixed coefficients are used to formulate a control strategic function, which is optimized by the Improved Grey Wolf Optimizer (IGWO) algorithm to obtain the optimal controller with better noise reduction performance. The proposed method and simulation model are validated based on the experimental test results. The results demonstrate that the safety factor and waterbed suppressing factor contained in the proposed uncertainty constraint ensures more stable noise reduction and effective suppression of the waterbed effect for new subjects without a priori data.

Although a growing number of evidence emphasizes superior of VATS over conventional thoracotomy, still is little known about early postoperative diaphragm muscle function after lobectomy via these two approahces. To fill the gap in existing literature, we conducted comparative study between VATS and conventional thoracotomy in terms of postoperative diaphragm muscle function, assessing its contractility, strength, magnitude of effort and potential risk of dysfunction such as: atrophy and paralysis. A total of 59 patients (30 after VATS), who underwent anatomical pulmonary resection at our institution, were enrolled into this study. The control group was consisted of 28 health subjects without medical condition could contribute to diaphragm dysfunction. Diaphragm muscle was assessed before and after surgery using ultrasonography. We found that both surgical approaches were associated with postoperative impairment of diaphragm muscle function - compared to baseline data. Postoperative reduction of diaphragm contraction was demonstrated in all of 59 patients. In case of control group, the differences between measurements were no observed. We noted that lobectomy via thoracotomy was linked with greater percentage of patients with diaphragm paralysis or/and atrophy that VATS. Similar findings were observed in refer to diaphragm magnitude effort, as well as, diaphragm contraction strength, where minimal invasive surgery was associated with better diaphragm function parameters - in comparison to thoracotomy. Disturbance of diaphragm work was reported both at operated and non-operated side. Upper right and left lobectomy was connected with greater diaphragm function impairment than other segments. In conclusion, VATS technique seems to be less invasive than conventional thoracotomy providing a better postoperative function of a main respiratory muscle.

Using only a limited number of computationally expensive functions, we show a way how to construct accurate and computationally efficient approximations of the Colebrook equation for flow friction. The presented approximations are based on the asymptotic series expansion of the Wright ω-function and symbolic regression. The results are verified with 8 million of Quasi-Monte Carlo points covering the domain of interest for engineers. In comparison with the built-in “wrightOmega” feature of Matlab R2016a, the herein introduced related approximations of the Wright ω-function significantly accelerate the computation. With only two logarithms and several basic arithmetic operations used, the presented approximations are not only computationally efficient but also extremely accurate. The maximal relative error of the most promising approximation which is given in the form suitable for engineers’ use is limited to 0.0012%, while for a little bit more complex variant is limited to 0.000024%.

The exact solutions of some conformable time fractional PDEs are presented explicitly. The modified Kudryashov method is applied to construct the solutions to the conformable time fractional Regularized Long Wave-Burgers (RLW-Burgers, potential Korteweg-de Vries (KdV) and clannish random walker's parabolic (CRWP) equations. Initially, the predicted solution in the finite series of a rational form of an exponential function is substituted to the ODE generated from the conformable time fractional PDE by using wave transformation. The coefficients used in the finite series are determined by solving the algebraic system derived from the coefficients of the powers of the predicted solution.

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

Classical methods for inverse problems are mainly based on regularization theory. In particular those which are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and great number of optimization algorithms have been proposed. When these two terms are distance or divergence measures, they can have a Bayesian Maximum A Posteriori (MAP) interpretation where these two terms correspond, respectively, to the likelihood and prior probability models.

Scientific progress is increasingly dependent on knowledge in computation-ready forms. In the life sciences, among others, many scientists carefully extract and structure knowledge from the scientific literature. In a process called manual curation, they enter knowledge into spreadsheets, or into databases where it serves their and many others' research. Valuable as these curation efforts are, the range and detail of what can practically be captured and shared remains limited, because of the constraints of current curation tools. Many important contextual aspects of observations described in literature simply do not fit in the form defined by these tools, and thus cannot be captured. Here we present the design of an easy-to-use, general-purpose method and interface, that enables the precise semantic capture of virtually unlimited types of information and details, using only a minimal set of building blocks. Scientists from any discipline can use this to convert any complex knowledge into a form that is easily readable and meaningful for both humans and computers. The method VSM forms a universal and high-level language for encoding ideas, and for interacting with digital knowledge.

We introduce a new generalized inverse which is a natural generalization of (pseudo) right core inverse in a Banach *-algebra. We characterize this generalized inverse by using right core and quasi-nilpotent decomposition. We then present its polar-like characterization and investigate related algebraic properties. Finally, the right core-EP inverse is characterized by certain new ways.

Seismic velocity inversion is one of the most critical issues in the field of seismic exploration and has long been the focus of numerous experts and scholars. In recent years, the advancement of machine learning technologies has infused new vitality into the research of seismic velocity inversion and yielded a wealth of research outcomes. Typically, seismic velocity inversion based on machine learning lacks control over physical processes and interpretability. Starting from wave theory and the physical processes of seismic data acquisition, this paper proposes a method for seismic velocity model inversion based on Physical Embedding Recurrent Neural Networks. Firstly, the wave equation is a mathematical representation of the physical process of acoustic waves propagating through a medium, and the finite difference method is an effective approach to solving the wave equation. With this in mind, we introduce the architecture of recurrent neural networks to describe the finite difference solution of the wave equation, realizing the embedding of physical processes into machine learning. Secondly, in seismic data acquisition, the propagation of acoustic waves from multiple sources through the medium represents a high-dimensional causal time series (wavefield snapshots), where the influential variable is the velocity model, and the received signals are the observations of the wavefield. This forms a forward modeling process as the forward simulation of the wavefield equation, and the use of error back-propagation between observations and calculations as the velocity inversion process. Through time-lapse inversion and incorporating the causal information of wavefield propagation, the non-uniqueness issue in velocity inversion is mitigated. Through mathematical derivations and theoretical model analyses, the effectiveness and rationality of the method are demonstrated. In conjunction with simulation results for complex models, the method proposed in this paper can achieve velocity inversion in complex geological structures.

In this paper, we introduce the notion of weighted generalized group inverse in a Banach algebra with proper involution. This is a natural generalization of weighted weak group inverse for a complex matrix and Hilbert space operator. We present several characterizations and representations of this generalized inverse. In addition, a new partial order on elements in a Banach *-algebra is investigated by using the weighted generalized group inverse and some known results are thus generalized.

Schrödinger dynamics is a nonlocal process. Not only does local perturbation affect instantaneously the entire space, but the effect decays slowly. When the wavefunction is spectrally bounded, the Schrödinger equation can be written as a universal set of ordinary differential equations, with universal coupling between them, which is related to Euler’s formula. Since every variable represents a different local value of the wave equation, the coupling represents the dynamics’ nonlocality. It is shown that the nonlocal coefficient is inversely proportional to the distance between the centers of these local areas. As far as we know, this is the first time that this inverse square law was formulated.

Exact and soliton type solutions have great importance in propagation of surface waves, fluid dynamics, optics, and many other elds of nonlinear sciences. In this study, the explicit and exact soliton type solutions for two space-time fractional Equal- Width (FEW) equations with conformable derivative are procured via the hyperbolic function approach. The wave type solutions are represented in some hyperbolic and trigonometric functions.

In light of Liu \emph{at el.}'s original works, this paper revisits the solution of Burgers's nonlinear equation $u_t=a(u_x)^2+bu_{xx} $. The study found two exact and explicit solutions for groups $G_4$ and $G_6$, as well as a general solution. A numerical simulation is carried out. In the appendix a Maple code is provided

The quiet-time solar wind electrons feature non-thermal characteristics when viewed from the perspective of their velocity distribution functions. They typically have an appearance of being composed of a denser thermal “core” population plus a tenuous energetic “halo” population. At first, such a feature was empirically fitted with the Kappa velocity space distribution function, but ever since the ground-breaking work by Tsallis, the space physics community has embraced the potential implication of the Kappa distribution as reflecting the non-extensive nature of the space plasma. From the viewpoint of microscopic plasma theory, the formation of non-thermal electron velocity distribution function can be interpreted in terms of the plasma being in a state of turbulent quasi equilibrium. Such a finding brings forth the possible existence of a profound inter-relationship between the non-extensive statistical state and the turbulent quasi-equilibrium state. The present paper further develops the idea of solar wind electrons being in the turbulent equilibrium, but unlike the previous model, which involves the electrostatic turbulence near the plasma oscillation frequency (i.e., Langmuir turbulence), the present paper considers the impact of transverse electromagnetic turbulence, particularly, the turbulence in the whistler-mode frequency range. It is found that the coupling of spontaneously-emitted thermal fluctuations and the background turbulence leads to the formation of non-thermal electron velocity distribution function of the type observed in the solar wind during quiet times. This demonstrates that the whistler-range turbulence represents an alternative mechanism for producing the Kappa-like non-thermal distribution, especially close to the Sun and in the near-Earth space environment.

This longitudinal study examined the development of executive function and calibration accuracy in pre-adolescents. Two hundred sixty two students(127 females) from grades 4 (n = 91), 5 (n = 89) and 6 (n = 82) took measures of executive function and performance calibration in a sport task, three times within a period of 20 months. A latent growth curve modeling analysis showed a significant relation between the rates of change of executive function and calibration. Further, the results showed a dynamic interplay in the development of executive function and calibration. There were significant inter-individual differences in the estimated population means both in executive function and calibration and in the rate of change of executive function, but not in the rate of change for calibration. The age of the participants had a positive effect only on the estimated population mean of executive function.

Stimulation of the alpha 7 nicotinic acetylcholine receptor (α7nAChR) has shown beneficial effects in several acute inflammatory disease models. This study aims to examine whether treatment with the selective α7nAChR agonist PHA 568487 can dampen inflammation and thereby improve cardiac function after myocardial infarction in mice. The possible anti-inflammatory properties of α7nAChR agonist PHA 568487 were tested in vivo using the air pouch model and in a permanent occlusion model of acute myocardial infarction in mice. Hematology parameters and cytokine levels were determined. Infarct size and cardiac function were assessed via echocardiography 24 h and one week after the infarction. Treatment with α7nAChR agonist PHA 568487 decreased 12 (CCL27, CXCL5, IL6, CXCL10, CXCL11, CXCL1, CCL2, MIP1a, MIP2, CXCL16, CXCL12 and CCL25) out of 33 cytokines in the air pouch model of acute inflammation. However, α7nAChR agonist PHA 568487 did not alter infarct size, ejection fraction, cardiac output or stroke volume at 24 h nor at 7 days after the myocardial infarction compared with control mice. In conclusion, despite promising immunomodulatory effects in the acute inflammatory air pouch model, α7nAChR agonist PHA 568487 did not affect infarct size or cardiac function after a permanent occlusion model of acute myocardial infarction in mice. Consequently, this study does not strengthen the hypothesis that stimulation of the α7nAChR is a future treatment strategy for acute myocardial infarction when reperfusion is lacking. However, whether other agonists of the α7nAChR can have different effects remains to be investigated.

The allosteric SERCA (Sarcoplasmic/Endoplasmic Reticulum Ca2+-ATPase) activator CDN1163 has been recently added to the group of pharmacological tools for probing SERCA function. We chose to investigate the effects of the compound on T lymphocyte Ca2+ stores, using the well-described Jurkat T lymphocyte as a reliable cell system for Ca2+ signaling pathways. Our study identified the lowest concentrations of the SERCA inhibitors thapsigargin (TG) and 2,5-di-(tert butyl)-1,4-benzohydroquinone (tBHQ) capable of releasing Ca2+, permitting the differentiation of the TG-sensitive SERCA 2b Ca2+ store from the tBHQ-sensitive SERCA 3 Ca2+ store. We proceeded to test the effects of CDN1163 on Ca2+ stores, examining specific actions on the SERCA 2b and SERCA 3 Ca2+ pools using our low dose SERCA blocker regimen. In contrast to previous work, we find CDN1163 exerts complex time-sensitive and SERCA isoform-specific actions on Ca2+ stores. Surprisingly, short-term exposure (0-30 minutes) to CDN1163 perturbs T cell Ca2+ stores by suppressing Ca2+ uptake with diminished Ca2+ release from the SERCA 2b-controlled store. Concomitantly, we find evidence for a SERCA-activating effect of CDN1163 on the SERCA 3 regulated store, given the observation of increased Ca2+ release inducible by low dose tBHQ. Intriguingly, longer-term (&gt;12 hours) CDN1163 exposure reversed this pattern, with increased Ca2+ release from SERCA 2b-regulated pools, yet decreased Ca2+ release responses from tBHQ-sensitive SERCA 3 pool. Our results reveal differential effects of CDN1163 on Ca2+ stores regulated by distinct SERCA isoforms, prompting the need for careful interpretation of the compound’s effects, particularly in cells expressing multiple SERCA isoforms.

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

It is proved that there exist two odd prime numbers, p_i and p_j , such that p_i + p_j = 2r + 2(r ⩾ 2), where p_n denote the n-th odd prime number, 1 ⩽ i, j ⩽ n. By the theory of generating functions, we prove that there exist two positive integers, h_i and h_j , such that h_i + h_j = r(r ⩾ 2), where h_n = (p_n − 1)/2，(p_n ⩾ 3).Then we complete the proof.

The Chromogranin A (CgA)-derived peptide Catestatin (CST: hCgA352-372) is highly conserved (>90% in 90% species) in mammalian species. The highest-evolved primates show 58.8% similarity with the lowest-evolved monotremes. CST was initially identified as a physiological brake in catecholamine secretion by inhibiting nicotinic-cholinergic signaling. CST also inhibits desensitization of catecholamine secretion, indicating that CST can act both as a cholinergic antagonist (short-term) and as a cholinergic agonist (long-term). The long-term effect sustains catecholamine secretion during stressful situations. CST is now established as a pleiotropic hormone: it affects the cardiovascular system by lowering blood pressure and cardiac contractility, enhancing baroreflex sensitivity, increasing heart rate variability, and promoting angiogenesis; and it increases insulin sensitivity by reducing inflammation, inhibiting hepatic glucose production, attenuating endoplasmic reticulum stress, and inducing glycogen production. The present review will highlight the important direct and indirect effects of CST, CST1-15 (aka cateslytin), D-CST1-15 (where L-amino acids were changed to D-amino acids), and human variants of CST (Gly364Ser-CST and Pro370Leu-CST) on microbial growth inhibition and their potential as therapy for antibiotic-resistant pathogenic microbes.

This study focuses on a new class of functions called sub-b-s-preinvex, that is a generalization of sub-b-s-convex and preinvex functions, and discusses some of their properties. A new sub-b-s-preinvex programming is introduced and the sufficient conditions of optimality under this type of function is established.

The spread of high-performance personal computers, frequently equipped with powerful Graphic Processing Units (GPU), raised the interest on a set of techniques able to extract models of electromagnetic phenomena (and devices) directly from available examples of the desired behavior. Such approaches are collectively referred to as Machine Learning (ML). A typical representative ML approach is the so called “Neural Network” (NN). Using such data-driven models allows evaluating the output in a much shorter time when a theoretical model is available, or allows predicting the behavior of the systems and devices when no theoretical model is available. With reference to a simple yet representative benchmark electromagnetic problem, some of the possibilities and the pitfalls of the use of NN for the interpretation of measurements (inverse problem) or to obtain the required measurements (optimal design problem) are discussed. The investigated aspects include the choice of the NN model; the generation of the dataset(s); the selection of hyperparameters (hidden layers, training paradigm). Finally, the capabilities in the handling of ill-posed problems are critically revised.

Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given for supporting the differential equations solving using inverse Sumudu transform.