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.

A concise proof of the Riemann Hypothesis is presented by clarifying the Hadamard product expansion over the zeta zeros, demonstrating that the Riemann Hypothesis is true.

Relationships between the Farey sequence and the Riemann hypothesis other than the Franel-Landau theorem are discussed. Whether a function similar to Chebyshev’s second function is square-root close to a line having a slope different from 1 is discussed. The nontrivial zeros of the Riemann zeta function can be used to approximate many functions in analytic number theory. For example, it could be said that the nontrival zeta function zeros and the Möbius function generate in essence the same function - the Mertens function. A different approach is to start with a sequence that is analogous to the nontrivial zeros of the zeta function and follow the same procedure with both this sequence and the nontrivial zeros of the zeta function to generate in essence the same function. A procedure for generating such a function is given.

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

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

Primate vision is an active process that constructs a stable internal representation of the 3D world based on 2D sensory inputs that are inherently unstable due to incessant eye movements. We present here a mathematical framework for processing visual information for a biologically-mediated active vision stereo system with asymmetric conformal cameras. This model utilizes the geometric analysis on the Riemann sphere developed in the group-theoretic framework of the conformal camera, thus far only applicable in modeling monocular vision. The asymmetric conformal camera model constructed here includes the fovea’s asymmetric displacement on the retina and the eye’s natural crystalline lens tilt and decentration, as observed in ophthalmological diagnostics. We extend the group-theoretic framework underlying the conformal camera to the stereo system with asymmetric conformal cameras. Our numerical simulation shows that the 1 theoretical horopter curves in this stereo system are conics that well approximate the empirical longitudinal horopters of the primate vision system.

Here, applying the theory of the generalization of the Boltzmann constant in curved space-time, we will model the mechanism by which elementary particles are formed. We will determine the relationship between gravity and each of the elementary particles that form the standard model following analogies to that of stellar bodies. In order to achieve our goal, we will propose new models for photons, quarks and gluons; with this, we will demonstrate why there are stable and unstable elementary particles; why the first family of elementary particles forms hadrons and why the second and third families cannot form hadrons; why the fermions comply with the Pauli exclusion principle and why the bosons do not comply with the Pauli exclusion principle, etc. Finally, we will analyse the generalization of the ADS/CFT correspondence and propose a theory of everything (T.O.E.).

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

Fractional differential mathematical model unfolding the dynamics of the COVID-19 pandemic in India is presented and explored in this paper. The purpose of this study is to estimate the future outbreak of disease and potential control strategies using mathematical models in India as a whole country as well as in some of the states of the country. This model is calibrated based on reported cases of infections over the month of April 2020 in India. We have used iterative fractional complex transform method to find approximate solutions of the model having modified Riemann Liouville fractional differential operator. We have also carried out a comparative analysis between actual and estimated cumulative cases graphically, moreover, most sensitive parameters for basic reproduction number$(R_0)$ are computed and their effect on transmission dynamics of COVID-19 pandemic is investigated in detail.

The Hamiltonian of a quantum mechanical system has an affiliated spectrum. If this spectrum is the sequence of prime numbers, a connection between quantum mechanics and the nontrivial zeros of the Riemann zeta function can be made. In this case, the Riemann zeta function is analogous to chaotic quantum systems, as the harmonic oscillator is for integrable quantum systems. Such quantum Riemann zeta function analogies have led to the Bender-Brody-Müller (BBM) conjecture, which involves a non-Hermitian Hamiltonian that maps to the zeros of the Riemann zeta function. If the BBM Hamiltonian can be shown to be Hermitian, then the Riemann Hypothesis follows. As such, herein we perform a symmetrization procedure of the BBM Hamiltonian to obtain a unique Hermitian Hamiltonian that maps to the zeros of the analytic continuation of the Riemann zeta function, and provide an analytical expression for the eigenvalues of the results. The holomorphicity of the resulting eigenvalues is examined. Moreover, a second quantization of the resulting Schrödinger equation is performed, and a convergent solution for the nontrivial zeros of the analytic continuation of the Riemann zeta function is obtained. Finally, from the holomorphicity of the eigenvalues it is shown that the real part of every nontrivial zero of the Riemann zeta function converges at σ = 1/2.

In this paper we address some variants for the products of Hadamard and Patterson. We prove that all zeros of the Riemann $\Xi$--function are real. We also prove that the Riemann hypothesis is true. The equivalence theorems associated with the Riemann zeta--function are obtained in detail.

In this 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.

This work is divided into two parts. In the first one the combinatorics of a new class of randomly generated objects, exhibiting the same properties as the distribution of prime numbers, is solved and the probability distribution of the combinatorial counterpart of the n-th prime number is derived, together with an estimate of the prime-counting function π(x). A proposition equivalent to the Prime Number Theorem (PNT) is proved to hold, while the equivalent of the Riemann Hypothesis (RH) is proved to be false with probability 1 (w.p. 1) for this model. Many identities involving Stirling numbers of the second kind and harmonic numbers are found, some of which appear to be new. The second part is dedicated to generalizing the model to investigate the conditions enabling both PNT and RH. A model representing a general class of random integer sequences is found, for which RH holds w.p. 1. The prediction of the number of consecutive prime pairs, as a function of the gap d, is derived from this class of models and the results are in agreement with empirical data for large gaps. A heuristic version of the model, directly related to the sequence of primes, is discussed and new integral lower and upper bounds of π(x) are found.

Among all the active confinement techniques, the use of pre-tensioned stainless steel straps has recently gained much attention. The flexibility of the stainless steel straps allows us to bend and pass them through the thickness of the masonry, thus creating a three-dimensional strengthening system between the two opposite facings. The use of the same perforation for the passage of several straps closed in a loop generates a continuous strengthening system that prevents parts of the structure from falling and injuring the occupants during seismic events. However, the perforations can nullify the in-plane strengthening, as they act as cylindrical hinges and make the reinforcement system labile for certain strap arrangements. Diagonal compression tests on square masonry panels performed in the present study show that the straps improve neither strength nor ductility when running along the mortar head and bed joints, arranged in square meshes. Conversely, they improve both strength and ductility when the straps make angles of 45° with the mortar joints. Furthermore, the experimental results show that the straps exert an anisotropic effect that decreases the apparent in-plane Poisson ratio. They also provide new insights into the diagonal compression test and allow formulating a new proposal for the pseudo-ductility factor.

Let g be a strictly increasing function on $\left(a,b\right),$ having a continuous derivative g′ on $\left(a,b\right).$ For the Lebesgue integrable function $f:\left(a,b\right)\to \mathbb{C}$ , we define the k-g-left-sided fractional integral of f by $S_{k,g,a+}f\left(x\right)={\int }_a^{x}k\left(g\left(x\right)-g\left(t\right)\right)g^{\prime }\left(t\right)f\left(t\right)dt,x\in \left(a,b\right]$ and the k-g-right-sided fractional integral of f by $S_{k,g,b-}f\left(x\right)={\int }_x^{b}k\left(g\left(t\right)-g\left(x\right)\right)g^{\prime }\left(t\right)f\left(t\right)dt,x\in [a,b),$ where the kernel k is defined either on $\left(0,\infty \right)$ or on $\left[0,\infty \right)$ with complex values and integrable on any finite subinterval. In this paper we establish some Ostrowski and trapezoid type inequalities for the k-g-fractional integrals of functions of bounded variation. Applications for mid-point and trapezoid inequalities are provided as well. Some examples for a general exponential fractional integral are also given.

The introduction of anti-amyloid monoclonal antibodies against Alzheimer’s disease (AD) is of high importance. However, even though treated patients show very little amyloid pathology, there is only a modest effect on the rate of cognitive decline. Although this effect possibly can increase over time, there is still a need for alternative treatments that will improve the cognitive function in patients with AD. Therefore, the purpose of this study was to characterize the triazinetrione ACD856, a novel pan-Trk positive allosteric modulator, in multiple models to address its neuroprotective and potential disease modifying effects. The pharmacological effect of ACD856 was tested in recombinant cell lines, primary cortical neurons or animals. We demonstrate that ACD856 enhanced NGF-induced neurite outgrowth, increased the levels of the pre-synaptic protein SNAP25 in PC12 cells and increased the degree of phosphorylated TrkB in SH-SY5Y cells. In primary cortical neurons, ACD856 led to increased levels of phospho-ERK1/2, showed neuroprotective effect against amyloid-beta or energy-deprivation induced neurotoxicity, and increased the levels of brain derived neurotrophic factor (BDNF). Consequently, administration of ACD856 resulted in a significant increase of BDNF in the brains of 21-months old mice. Furthermore, repeated administration of ACD856 resulted in a sustained anti-depressant effect which lasted up to seven days, suggesting effects that go beyond merely symptomatic effects. In conclusion, the results confirm ACD856 as a cognitive enhancer, but more importantly, they provide substantial in vitro and in vivo evidence of neuroprotective and long-term effects that contribute to neurotrophic support and increased neuroplasticity. Presumably, the described effects of ACD856 may improve cognition, increase resilience, and promote neurorestorative processes, thereby leading to a healthier brain in patients with AD.

I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument by identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with.

This paper is the continuation of a previous study, which highlighted some inconsistencies in the RILEM guidelines for the interpretation of the diagonal compression test. Although improved compared to the ASTM guidelines, in fact, the RILEM guidelines underestimate the state of hydrostatic stress induced by the diagonal compression test at the center of the wallette. The new interpretation of the diagonal compression test proposed in this article shows that the RILEM guidelines actually underestimate both the hydrostatic and the deviatoric stress states at the center of the wallette. The new formulation complies with the linear elastic theory and allows us to use the the diagonal compression test to identify the three elastic coefficients of masonry. In particular, it allows the identification of the Poisson ratio, which instead takes on a conventional value in the RILEM and ASTM guidelines. The difference of one order of magnitude between the conventional and proposed Poisson’s ratio is in agreement with the experimental results on another brittle material, namely concrete. Finally, the new proposal fills the gap between the results provided by the two tests usually performed to identify the shear behavior of masonry: the diagonal compression test and the shear-compression test.

In this article, the new Hermite–Hadamard type inequalities are studied via generalized s-convexity on fractal sets. These inequalities derived on fractal sets are shown to be the generalized s-convexity on fractal sets. We proved that the absolute values of the first and second derivatives for the new inequalities are the generalization of s-convexity on fractal sets.

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

Let's define $\delta(x) = (\sum_{{q\leq x}}{\frac{1}{q}}-\log \log x-B)$, where $B \approx 0.2614972128$ is the Meissel-Mertens constant. The Robin theorem states that $\delta(x)$ changes sign infinitely often. Let's also define $S(x) = \theta(x) - x$, where $\theta(x)$ is the Chebyshev function. It is known that $S(x)$ changes sign infinitely often. We define the another function $\varpi(x) = \left(\sum_{{q\leq x}}{\frac{1}{q}}-\log \log \theta(x)-B \right)$. We prove that when the inequality $\varpi(x) \leq 0$ is satisfied for some number $x \geq 3$, then the Riemann hypothesis should be false. The Riemann hypothesis is also false when the inequalities $\delta(x) \leq 0$ and $S(x)\geq 0$ are satisfied for some number $x \geq 3$ or when $\frac{3 \times \log x + 5}{8 \times \pi \times \sqrt{x} + 1.2 \times \log x + 2} + \frac{\log x}{\log \theta(x)} \leq 1$ is satisfied for some number $x \geq 13.1$.

This paper presents Chebyshev Type inequalities for the Riemann-Liouville variable-order fractional integral operator using two synchronous functions on the set of real numbers. It is the first result of its kind in the current literature using variable-order Riemann-Liouville fractional integral operator. Some special cases for the result obtained in the paper are discussed.

In this paper, we derive Von Koch's inequality without using the Riemann Hypothesis. As well known, Von Koch's inequality is equivalent to the Riemann Hypothesis. Namely, we show that the Riemann Hypothesis is true. Furthermore, we show that the upper limit of its can be lowered.

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

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

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

The dislocation density tensors of thin elastic shells have been formulated explicitly in terms of the Riemann curvature tensor. The formulation reveals that the dislocation density of the shells is proportional to KA3=2, where K is the Gauss curvature and A is the determinant of metric tensor of the middle surface.

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

In this article we propose the integral, series and product representations for the Ramanujan zeta-function. We suggest a variant for the Conrey-Ghosh product for the entire Ramanujan zeta-function. We present some variants for the product for the Ramanujan $\Xi$-function. We prove that all of its zeros are real. Along the way we obtain the truth of the Riemann-Hardy conjecture.

In this paper, we suggest an expansion of the Planck distribution function derived from the Boltzmann principle. Thereby, we consider expanding Planck's law with a new distribution function, and discuss fine structure constant. Furthermore, using ideas applied to the expansion of the Planck distribution function, we show that Von Koch's inequality can be derived without using the Riemann Hypothesis, that is, the Riemann Hypothesis is true, and that the abc conjecture is not true. Furthermore, we define a generalization of Entropy and discuss that Entropy is relevant to dynamical systems described by logistic function models, such as the growth of bacteria and populations.

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

In this paper we provide amongst others some simple error bounds in approximating the weighted Riemann-Stieltjes integral $\int_{a}^{b}f\left(t\right) g\left(t\right) dv\left(t\right) $ by the use of three points formula \begin{equation*} f\left(b\right) \int_{c}^{b}g\left(s\right) dv\left(s\right) +f\left(a\right) \int_{a}^{d}g\left( s\right) dv\left( s\right) -f\left(x\right) \int_{c}^{d}g\left(t\right) dv\left(t\right) \end{equation*} where $x,$ $c,$ $d\in \left[a,b\right],$ $g,$ $v:\left[a,b\right] \rightarrow \mathbb{C}$ under bounded variation and Lipschitzian assumptions for the function $f$ and such that the involved Riemann-Stieltjes integrals exist.

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

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

A generalization of the sum of divisors function involves a recursive definition. This leads to variants of superabundant numbers, colossally abundant numbers, and Gronwall's theorem (relevant to the Riemann hypothesis).

Chronic Fatigue Syndrome (CFS) can be triggered by different factors and create a complex health situation. In the last decades incidence has been increasing. This situation is a clear example of how humans, viruses, and the environment are all connected. In the 90s cases related to CFS, com-plaints about a feeling of chronic fatigue, inability for everyday tasks, dull pain, cephalalgia, de-pression, anxiety, poor concentration. Clinical tests for EBV, HHV, CMV, IgG, IgM, T4 and T8 subsets were tested, along with hormones and hemogram tests. Most of the cases were women. The timeline of the medical history showed also myomas, breast lumps, premenstrual syndrome previously to CFS development. The nature of these conditions promoted the idea of a possible common link among them and CFS. Some cases also suffered from allergies, food intolerances, candidiasis, intestinal impairment, thyroid implications, endometriosis. As an initial working hypothesis, The Liver Link (TLL) was proposed in order to understand those different conditions affecting body, mind and emotional wellbeing. Considering liver implication can make a differ-ence in treatment and recovery. Low grade inflammatory conditions are related to Th2 predom-inance and liver functions. Functional disharmonies are very important because they usually still do not appear in any conventional tests. In 2002, TLL was presented as a framework to explain the concomitance of CFS and other conditions and the relationship with some viruses such as EBV, HHV, CMV, as a lecture in a congress at the University of Westminster (London). When SARS-CoV-2 outbroke, TLL helped to warn about the post-covid syndrome more likely to occur in specific individuals.

In this paper we provide some bounds for the error in approximating the Riemann-Stieltjes integral $\int_{a}^{b}f (t) du (t)$ by the generalized trapezoidal rule \begin{equation*} \left[ u\left( b\right) -u\left( x\right) \right] f\left( b\right) +\left[ u\left( x\right) -u\left( a\right) \right] f\left( a\right) \end{equation*} under various assumptions for the integrand $f$ and the integrator $u$ for which the above integral exists. Applications for continuous functions of selfadjoint operators and unitary operators in Hilbert spaces are provided as well.

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

The nonlocal boundary value problem, dtρu(t)+Au(t)=f(t) (0&lt;ρ&lt;1, 0&lt;t≤T), u(ξ)=αu(0)+φ (α is a constant and 0&lt;ξ≤T), in an arbitrary separable Hilbert space H with the strongly positive selfadjoint operator A, is considered. The operator dt on the left hand side of the equation expresses either the Caputo derivative or the Riemann-Liouville derivative; naturally, in the case of the Riemann - Liouville derivatives, the nonlocal boundary condition should be slightly changed. Existence and uniqueness theorems for solutions of the problems under consideration are proved. The influence of the constant α on the existence of a solution to problems is investigated. Inequalities of coercivity type are obtained and it is shown that these inequalities differ depending on the considered type of fractional derivatives. The inverse problems of determining the right-hand side of the equation and the function φ in the boundary conditions are investigated.

Here we will electrically-quantum model the neutron and proton as a three-phase alternating current electric generator, for this, we will use the theory of three-phase electric generators and vector or phasor diagrams. We will use this model to hypothesize how the quarks that form neutrons and protons with a combined mass of 10 MeV/c², can generate, through quarks-antiquarks-gluon interactions, a mass of 939.56 MeV/c² for the neutron and a mass of 938.27 MeV/c² for the proton. Using quantum mechanics and the theory of the generalization of the Boltzmann constant in curved space-time we will calculate the number of quarks-antiquarks-gluons and gravitons inside a neutron. We will also analyse βˉ decay using vector diagrams, we will calculate the tension of the string T₀ and the length of the string ℓs between quarks-antiquark and finally, we will model a black hole using a neutron equivalent model. In version 2 of this article, we will update the vector diagrams of the βˉ decay and theoretically calculate the energy of the W⁻ boson, the Z⁰ boson, and the Θ angle, Θ = arc cos (W⁻/Z⁰). We will demonstrate, through vector diagrams, that quarks-antiquarks-gluon interactions are the cause of the origin of the W⁻ boson and the Z⁰ boson. We will also demonstrate how the fine structure constant α originates. It is important to make clear, in future updates, we will describe the relationship that exists between the theory described in this paper and the Isospin theory, flavour and colour theory

In this article, the new Hermite–Hadamard type inequalities are studied via generalized s-convexity on fractal sets. These inequalities derived on fractal sets are shown to be the generalized s-convexity on fractal sets. We proved that the absolute values of the first and second derivatives for the new inequalities are the generalization of s-convexity on fractal sets.

The human mandible's cancellous bone, which is characterized by its unique porosity and directional sensitivity to external forces, is crucial for sustaining biting stress. Traditional CAD models fail to fully represent bone's anisotropic structure and thus depend on simple isotropic assumptions. For our research, we use the latest versions of nTopology and Creo Parametric software to make biomimetic Voronoi lattice models that accurately reflect the complex geometry and mechanical properties of trabecular bone. The porosity of human cancellous bone is accurately modeled in this work using biomimetic Voronoi lattice models. The porosities range from 70% to 95%, which can be achieved by changing the pore sizes to 1.0 mm, 1.5 mm, 2.0 mm, and 2.5 mm. Finite element analysis (FEA) was used to examine the displacements, stresses, and strains acting on dental implants with a buttress thread, abutment, retaining screw, and biting load surface. The results show that the Voronoi model accurately depicts the complex anatomy of the trabecular bone in the human jaw, compared to standard solid block models. The ideal pore size for biomimetic Voronoi lattice trabecular bone models is 2 mm, taking into account both the von Mises stress distribution over the dental implant, screw retention, cortical bone, cancellous bone, and micromotions. This pore size displayed balanced performance by successfully matching natural bone's mechanical characteristics. Advanced finite element analysis (FEA) improves biomechanical understanding of how bones and implants interact by creating more accurate models of biological problems and dynamic loading situations. This makes biomechanical engineering better.

Smoker’s paradox usually refers to the common observation of a favourable outcome of smoker patients in acute myocardial infarction. The interpretation of this phenomenon is still controversial and not fully explained. We aimed at assessing whether smoking could be associated with mortality in a large cohort of prospectively enrolled patients with ST segment elevation myocardial infarction (STEMI) referred to primary percutaneous coronary intervention (pPCI). From April 2006 to December 2018 a population of 2456 STEMI patients treated with primary PCI were prospectively enrolled in the MATRIX registry. Ischemic time, clinical, demographics, angiographic data and 1-year follow-up were collected. Among 2546 patients admitted with STEMI 1007 (41%) were current smokers. Smokers were 10 years younger and had lower crude in-hospital and 1-year mortality (1.5% vs 6%, p&lt;0.0001 and 5% vs 11%, p&lt;0.0001), shorter ischemic time (203 [147-299] vs 220 [154-334] minutes, p=0.002) and shorter decision time (60 [30-135] vs 70 [36-170] minutes, p=0.0063). After propensity-matching, age, cardiogenic shock and low TIMI score were associated with in-hospital mortality, while smoking habit was still associated with reduced mortality. Smoking was also associated with reduced death rate at 1-year follow-up (HR 0.54, 95% CI [0.37 - 0.78]; p&lt;0.001). Our data show a protective link between smoking status and mortality in patients with STEMI, the so called “smoker’s paradox”. This could be explained not only by the shorter ischemic time and younger age of the smoking population but also by a specific pathogenetic effect of smoking underlying the onset of STEMI and response to therapies.

Neurodegeneration is a major problem in neuroscience and medicine as it causes and worsens many neurological and psychiatric disorders. It involves gradual loss of neurons at different levels of the brain, affecting cognition, emotion, behavior, consciousness, and attention. Understanding the causes and consequences of neurodegeneration is crucial for identifying the risk factors, biomarkers, and treatments. However, the current therapies are mostly symptomatic and ineffective. Therefore, new and innovative methods, such as noninvasive brain stimulation (NIBS), are needed to modulate brain activity and plasticity in a safe and reversible manner. This field is rapidly developing, with a focus on exploring new clinical applications, mechanisms, and combinations of NIBS and drugs. This special issue covers the latest progress and challenges in the study of neurodegeneration in cognitive impairment and mood disorders from the experimental, clinical, and translational perspectives. It addresses the complexity and diversity of these conditions, the lack of disease-modifying treatments, the ethical and practical issues of conducting research in vulnerable and diverse populations, the integration and interpretation of data from multiple sources and modalities, and the development and validation of novel methods such as NIBS, artificial intelligence, and drug repurposing. Collaborative efforts among various stakeholders are needed to improve our knowledge and treatment of neurodegeneration underlying cognitive impairment and mood disorders.

We study C*-algebraic versions of following conjectures/theorems: (1) Bieberbach conjecture (de Branges theorem) (2) Robertson conjecture (3) Lebedev-Milin conjecture (4) Zalcman conjecture (5) Krzyz conjecture (6) Corona conjecture (Carleson theorem). We prove that the C*-algebraic Bieberbach Conjecture for invertible coefficients is true for second degree C*-algebraic polynomials.

Alzheimer’s Disease (AD), a progressive and debilitating condition, is reported to be the most common type of dementia, with at least 55 million people believed to be currently affected. Many causation hypotheses of AD exist, yet the intriguing link between viral infection and its possible contribution to the known etiology of AD has become an attractive focal point of research for the field and a challenging study task. In this review, we will explore the historical perspective and milestones that led the field to investigate the viral connection to AD. Specifically, several viruses such as Herpes Simplex Virus 1 (HSV-1), Zika virus (ZIKV), and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), along with several others mentioned, include the various viruses presently considered within the field. We delve into the strong evidence implicating these viruses in the development of AD. We will also extend beyond these mere associations by carefully analyzing the potential mechanisms by which viruses may contribute to AD pathology. This includes but is not limited to direct neuronal infections, dysregulation of immune responses, and the impact on protein processing. Controversies and challenges of the viral-AD relationship emerge as we tease out these potential mechanisms considered. Looking forward, we emphasize the future directions the field should take to tackle the remaining unanswered questions and the glaring research gaps that persist. Overall, this review aims to provide a comprehensive survey of the past, present, and future of the potential link between viral infections and their association with AD development.

In this paper, I introduce a new concept of representing numbers in base ; in other words, I have found new series for any number similar to series that could be written according to the collatz sequence which is called zi(n) in this article. These series need to end with 1. Then, we use two sets of rules to make a diagram which then proves the existence of such series for any number.In this diagram, by branching numbers into different branches in accordance to the modularity of 4 and continuing branching to the point that their numbers have enough common terms in their collatz series, we could reduce zi(n) to zi(k) so that k<n in any branch by Rule Number One. This diagram shows that zi(n) exists for every number, in other words, this proves the theorem (A) or zi-existence theorem. The proof of zi-existence theorem leads to a proof of the collatz conjecture because the collatz series could be written as a linear combination of such series that all of them end with 1, so the collatz series for any number ends with 1.

This interdisciplinary work presents a novel patent pending method of inertial electrostatic confinement (IEC) fusion called the Nuclear Electromagnetic Shaping Accelerator Reactor (NESAR) that addresses all of the major failure problems with currently known methods of IEC fusion. A brief background of previous IEC methods that generate a negative potential well to accelerate ions for fusion will be reviewed and compared to the NESAR method of magnetic confinement. In addition, a direct comparison will be presented between the NESAR and the tokamak method of fusion. The NESAR method of fusion obtains the plasma oscillation and compression capabilities of a tokamak without producing the catastrophic magnetic reconnection disruptions that currently plague tokamaks. Since the NESAR can oscillate charged particles comparable to the tokamak, this work will briefly review the history of the tokamak, how sawtooth magnetic reconnection occurs, and how the NESAR precludes the occurrence of magnetic reconnection. This work will also review the beginnings of a novel theory that has obtained interest from the Defense Advanced Research Projects Agency (DARPA) which is currently interested in possibly supporting further research into the NESAR to explore this new theoretical concept. This novel theory is a unified field theory based upon the trajectory of charged particle movements within the NESAR. The NESAR is the only concept of magnetic confinement in the world that may have the capability to allow charge particles to collectively interact relatively to a solitary location. Due to this possible capability, there is a probability that the confined particles may experience curved trajectories that could allow them to experience the effects of curvature deviation. If curvature deviation occurs with these magnetically confined charged particles; then the deviated acceleration would allow for the electromagnet field to be propelled to a higher dimension that could influence spacetime. Finally, this work will review another theory that explains how pole reversals are observed by the National Aeronautics and Space Administration’s (NASA) coiled magnetic field detectors. This theory requires little to no postulations to be framed and it is purely based upon the trajectory of charged particles within the NESAR, Michael Faraday’s law of induction, and experimental observations of rotating plasmas.

Intrusion detection is generally carried out by matching network traffic patterns with known attack patterns or by identifying abnormal network traffic patterns. One statistical methodological approach used in intrusion detection is Statistical Process Control (SPC) by constructing a control chart. Hotelling’s T2 control chart is a multivariate control chart commonly used to monitor the mean process. The performance of the T2 chart in monitoring mean shifts can be increased if a robust estimator is utilized. Based on previous research, T2 based on the Fast-MCD estimator has good performance in monitoring low to medium outlier contaminated data. Therefore, the MRCD estimator can be used to detect intrusion. On the other hand, this research focuses on developing a bootstrap-based robust Hotelling’s T2 charts with Fast-MCD and MRCD estimators for evaluating performance in detecting intrusion on intrusion detection datasets. Based application of UNSW-NB15, the proposed chart has better performance than the conventional T2 and Fast-MCD-based T2 despite the longer execution time.

Background: Parkinson's disease (PD) is a global disease. However, there is a lack of research specifically focused on the AfrAbia population. Climate change, driven mainly by global warming, is linked to detrimental health impacts, including an increased frequency and intensity of heat waves. Neurological diseases, including neurodegenerative syndromes like Alzheimer's disease, Parkinson's disease, and motor neuron illnesses, have been increasingly seen and recorded in scientific literature. Although there is much literature demonstrating the growth in neurodegenerative disorders, the relationship between environmental variables such as global warming, air pollution, heavy metals, and pesticides and the higher occurrence of these illnesses is still unknown. Objective: The current article primarily aims to examine the relationship between climatic changes, air pollution, pesticides, heavy metals, and the occurrence of PD. Initially, we evaluate the influence of exposure to these variables on the cause or origin of Parkinson's disease. In addition, we will investigate how these variables disrupt processes such as excitotoxicity, oxidative stress, and neuroinflammation, all of which are strongly linked to Parkinson's disease (PD). Conclusions: This research presents a plausible rationale for the adverse effects of environmental influences on the brain, which are pivotal in the progression or onset of Parkinson's disease from an AfrAbian standpoint.

The mechanistic influences of dopamine (DA) signaling and impact on motor function is nearly always interpreted from changes in nigrostriatal neuron terminals in striatum. This is a standard practice in studies of human Parkinson’s disease (PD) and aging, and related animal models of PD and aging-related parkinsonism. However, despite dozens of studies indicating an ambiguous relationship between changes in striatal DA signaling and motor phenotype, this perseverating focus on striatum continues. Although DA release in substantia nigra (SN) was first reported almost 50 years ago. assessment of nigral DA signaling changes in relation to motor function is rarely considered. Whereas DA signaling has been well-characterized in striatum at all 5 steps of neurotransmission (biosynthesis and turnover, storage, release, reuptake, and post-synaptic binding) in the nigrostriatal pathway, the depth of such interrogations in the SN, outside of cell counts, is sparse. However, there is sufficient evidence that these steps in DA neurotransmission in the SN are operational and regulated autonomously from striatum, and are present in human PD and aging, and related animal models. To complete our understanding of how nigrostriatal DA signaling affects motor function, it is past time to include interrogation of nigral DA signaling. This brief review highlights evidence that changes in nigral DA signaling at each step in DA neurotransmission are autonomous from those in striatum and changes in the SN alone can influence locomotor function. Accordingly, for full characterization of how nigrostriatal DA signaling affects locomotor activity, interrogation of DA signaling in SN is essential.

Since late December 2021, the Hunga Tonga-Hunga Ha'apai underwater volcano has been erupting in a series of large explosions. On Friday, January 15th, 2022, a particularly significant explosion sent a massive ash cloud high into the atmosphere. This study depicts the modeling of the volcanic ash dispersion from the event while incorporating meteorological data assimilation within the inline Weather Research and Forecasting model coupled with chemistry (WRF-Chem). Two forecast scenarios: one with only meteorology and no chemistry (OMET) and one with gas, aerosol chemistry, and no assimilation (NODA) were undertaken and compared to the third forecast impacting data assimilation to distinguish the Flux Adjusting Surface Data Assimilation System (FASDAS)'s effects. Data assimilation, a process that combines real-time observations with numerical models, plays a pivotal role in enhancing the accuracy of various scientific simulations and predictions.Analysis of different scenarios reveals that the FASDAS result in lessening of planetary boundary layer height (PBLH), downward surface shortwave flux, and 2m temperature by up to 800m, 250 W.m-2 and 6°C on the land portion, respectively, while the opposite is observed nearby the eruption site. Model validation against the observations shows that the inclusion of FASDAS nudging in WRF-Chem significantly enhances the model performance in retrieving meteorological variables. The simulations also revealed significant biases in the concentration of volcanic ash around the ash cloud. Additionally, data analysis from the Copernicus TROPOspheric Monitoring Instrument Sentinel-5 Precursor (TROPOMI-S5P) indicates that total SO2 emissions traveled west. This work demonstrates the significant contribution of data assimilation on the results of operational air quality predictions during violent volcanic eruption events.

Parkinson’s disease (PD) is one of the most common neurodegenerative diseases. Recent data highlight similarities between neurodegenerative diseases including PD and type 2 diabetes mellitus (T2DM) suggesting a crucial interplay between the gut–brain axis. GLP-1R agonists, known for their use in T2DM treatment, are currently extensively studied as novel PD modifying agents. For this narrative review article, we searched PubMed and Scopus databases for peer-reviewed research, review articles and clinical trials regarding GLP-1R agonists and PD, published in the English language with no time restrictions. We also screened the references of the selected articles for possible additional articles in order to include most of the key recent evidence. Our research was conducted between February 2023 and February 2024. We used the terms “GLP-1”, “GLP-1 receptor”, “GLP-1R agonists”, “PD”, “T2DM”, “insulin”, “neurodegenerative disease”, “glucose”, “animal models”, “clinical trials” in different combinations. Many data on animal models and preclinical studies show that GLP1-R agonists can restore dopamine levels, inhibit dopaminergic loss, attenuate neuronal degeneration and alleviate motor and non-motor features of PD. Evidence from clinical studies are also very promising enhancing the possibility of adding GLP1-R agonists in the current armamentarium of drugs available for PD treatment.

Caused by age or trauma, collapsed connective tissue can cause nerve entrapment and damage within the tarsal tunnel. Tarsal tunnel syndrome is relatively underdiagnosed. This study presents an intervention targeting damaged tissues surrounding the nerves and replacing the structural cushioning with a Wharton’s jelly tissue allograft. The eight selected patients from four clinical sites had tarsal tunnel-related defects. Patient outcomes were tracked on a 90-day calendar utilizing the Numeric Pain Rating Scale (NPRS) and the Western Ontario and McMaster University Arthritis Index (WOMAC). All patients had failed standard care practices for at least six weeks. Each patient received a Wharton’s jelly tissue allograft to sites around the affected tarsal tunnel. No patients experienced adverse reactions. Percent change calculated from the initial application to the 90-day follow-up showed an improvement of 59.43% in NPRS and a 37.58% improvement in WOMAC. This study provides evidence that WJ allograft applications are safe, minimally invasive, and efficacious for patients who have failed standard care treatments for tissue defects associated with Tarsal Tunnel syndrome. Limitations include the small cohort size and nonblinded nature. The results of this study warrant further research to confirm the efficacy, optimal dose, protocol, and durability of Wharton's jelly.

Diabetic retinopathy (DR), a major complication of prolonged diabetes, poses a significant risk of vision loss. Early detection is critical for effective treatment, yet traditional diagnostic methods by ophthalmologists are time-consuming, costly, and subject to variability. This study introduces a novel approach employing a hybrid Convolutional Neural Network-Radial Basis Function (CNN-RBF) classifier integrated with Multi-Scale Discriminative Robust Local Binary Pattern (MS-DRLBP) features for enhanced DR detection. We implemented advanced image preprocessing techniques, including noise reduction, morphological operations, and Otsu’s thresholding, to optimize blood vessel segmentation from retinal images. Our method demonstrates exceptional performance in screening DR, achieving an average of 96.10% precision, 95.35% sensitivity, 97.06% specificity, and 96.10% accuracy. These results significantly outperform traditional methods and offer a promising tool for remote and efficient screening of DR. Applied to publicly available datasets, this research contributes to the development of accessible, accurate diagnostic methods in ophthalmology, potentially reducing the global burden of diabetic vision loss.

We investigated how Artificial Intelligence (AI) reveals factors shaping COVID-19 vaccine hesitancy among healthcare providers by examining their open-text comments. We conducted a longitudinal survey starting in spring of 2020 with 38,788 current and former female nurses in three national cohorts to assess how the pandemic has affected their livelihood. In January and March-April 2021 surveys, participants were invited to contribute open-text comments and answer specific questions about COVID-19 vaccine uptake. A closed-ended question in the survey identified vaccine-hesitant (VH) participants who either had no intention or were unsure of receiving a COVID-19 vaccine. We collected 1,970 comments from VH participants and trained two Machine Learning (ML) algorithms to identify behavioral factors related to VH. The first predictive model classified each comment into one of three Health Belief Model (HBM) constructs (barriers, severity, and susceptibility) related to adopting disease prevention activities. The second predictive model used the words in January comments to predict the vaccine status of VH in March-April 2021; vaccine status was correctly predicted 89% of the time. Our results showed that 35% of VH participants cited barriers, 17% severity, and 7% susceptibility to receiving a COVID-19 vaccine. Out of the HBM constructs, the VH participants citing a barrier, such as allergic reactions and side effects, had the most associated change in vaccine status from VH to later receiving a vaccine.

Many industrial processes, several natural processes involving non-living matter, and all the processes occurring within living organisms take place in solution. This means that the molecules playing active roles in the processes are present within another medium, called solvent. The solute molecules are surrounded by solvent molecules and interact with them. Understanding the nature and strength of these interactions, and the way in which they modify the properties of the solute molecules, is important for a better understanding of the chemical processes occurring in solution, including possible roles of the solvent in those processes. Computational studies can provide a wealth of information on solute-solvent interactions and their effects. Two major models have been developed to this purpose: a model viewing the solvent as a polarizable continuum surrounding the solute molecule, and a model considering a certain number of explicit solvent molecules around a solute molecule. Each of them has its advantages and challenges, and one selects the model that is more suitable for the type of information desired for the specific system under consideration. These studies are important in many areas of chemistry research, from the investigation of the processes occurring within a living organism to drug design and to the design of environmentally benign solvents meant to replace less benign ones in the chemical industry, as envisaged by the green chemistry principles. The paper presents a quick overview of the modelling approaches and an overview of concrete studies, with reference to selected crucial investigation themes.

We present a modified version of the Szilard Engine, demonstrating that an explicit measurement procedure is entirely unnecessary for its operation. By considering our modified engine, we are able to provide a new interpretation of Landauer’s original argument for the cost of erasure. From this view, we demonstrate that a reset operation is strictly impossible in a dynamical system with only conservative forces. Then, we prove that to approach a reset yields an unavoidable instability at the reset point. Finally, we present an original proof of Landauer’s principle that is completely independent from the Second Law of Thermodynamics.

Cassava mosaic disease (CMD) and cassava brown streak disease (CBSD) are endemic threats to cassava production. To fill the existing gaps in the understanding of the epidemiology of these diseases in Côte d’Ivoire, nationwide field surveys were conducted in 2016, 2017 and 2020. The leaf samples collected were analysed by PCR. CBSD was not detected in all fields visited. However, an increase of CMD incidence was observed from 45.95% in 2016 to 51.37% in 2020 while CMD severity remained moderate over the years with a mean value of 2.29. Low whiteflies number was observed in field and decreasing over the years. Molecular analysis allowed detection of East African cassava mosaic Cameroon virus (EACMCMV) in single as well as in mixed infection with African cassava mosaic virus (ACMV). Single EACMCMV infection, which was detected only in three agroecological zones of the eastern Côte d’Ivoire in 2016, spread throughout the country in 2017 and became more widespread in 2020 with a preponderance in the central and southern zones, whereas the ACMV+EACMCMV coinfection has spread to the entire zones studied. Knowing the dynamics of the evolution of these viruses across the country, better disease management strategies could be adopted to control the disease.

Neurological disorders have been reported in a large number of coronavirus disease 2019 (COVID-19) patients, suggesting that this disease may have long-term adverse neurological consequences. COVID-19 occurs from the infection by a positive-sense single-stranded RNA virus called severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The membrane fusion protein of SARS-CoV-2, the spike protein, binds to its human host receptor, angiotensin-converting enzyme 2 (ACE2), to initiate membrane fusion between the virus and host cell. The spike protein of SARS-CoV-2 contains the furin protease recognition site and its cleavage enhances the infectivity of this virus. The binding of SARS-CoV-2 to the ACE2 receptor has been shown to downregulate ACE2, thereby increasing the levels of pathogenic angiotensin II (Ang II). The furin protease cleaves between the S1 subunit of the spike protein with the binding domain toward ACE2 and the S2 subunit with the transmembrane domain that anchors to the viral membrane, and this activity releases the S1 subunit into the blood circulation. The released S1 subunit of the spike protein also binds to and downregulates ACE2, in turn, increasing the level of Ang II. Considering that a viral particle contains many spike protein molecules, furin-dependent cleavage would release many free S1 protein molecules each of which can downregulate ACE2, while the infection with a viral particle only affects one ACE2 molecule. Therefore, the furin-dependent release of S1 protein would dramatically amplify the ability to downregulate ACE2 and produce Ang II. We hypothesize that this amplification mechanism that the virus possesses, but not the infection per se, is the major driving force behind COVID-19 associated neurological disorders.

Côte d’Ivoire has substantially neglected crop residues from farms in rural areas. This study aims to provide strategies for the sustainable conversion of crop residues to hydrogen. Using existing data and theoretical approaches, up to 16,801,306 tons of crop residues of 11 crop types were available in Côte d’Ivoire in 2019. A theoretical hydrogen potential of 1,296,424.84 tons was estimated from the crop residues. Technically, 907,497.39 tons of hydrogen is expected annually. Three scenarios of hydrogen project implementation developed indicated that the Ivorian industries can be supplied with 9,026,635 gigajoules of heat. Moreover, 17,910 cars and 4,732 buses can be supported in the transport sector. It is estimated that 817,293.95 tons of green ammonia for farmers can be supplied. Five million, seven hundred twenty-seven thousand, nine hundred ninety-two (5,727,992) households are expected to have access to 1,718.40 gigawatts of electricity. Due to these changes in transport, energy, industry, and agricultural sectors, a reduction of 1,644,722.08 tons of carbon dioxide per year can be achieved theoretically. With the scenarios, some 263,276.87 tons of hydrogen are exportable to other countries. Conversion of crop residues to hydrogen is a promising opportunity with environmental and socio-economic impact. Therefore, this study requires further extensive research.

This perspective discusses the ongoing real-world practice using nitazxoanide, NSAIDs and/or azithromycin (Kelleni’s protocol) to manage the evolving manifestations of SARS CoV-2 Omicron EG.5.1, its descendant HV.1 as well as BA.2.86 and its descendant JN.1 subvariants in Egypt. These subvariants are well-known for their highly evolved immune-evasive properties and the manifestations include some peculiar manifestations as persistent cough besides high fever in young children as well as high fever, persistent severe cough, change of voice, loss of taste and smell, epigastric pain, nausea, vomiting, diarrhea, generalized malaise and marked bone aches in adults including the high risk groups. It’s suggested that the ongoing SARS CoV-2 evolution is continuing to mostly affect the high risk groups of patients, to some of whom we’ve also successfully prescribed nitazoxanide and/or NSAIDs for post-exposure prophylaxis of all household contacts. We also continue to recommend starting the immune-modulatory antiviral Kelleni’s protocol as soon as possible in the course of infection and adjusting it in a personalized manner to be more aggressive from the beginning for the high risk patients, at least until the currently encountered surge of infections subsides.

In this study, a simple approach to solving the Riemann Hypothesis, one of the most prominent unsolved problems in the field of Number Theory in mathematics and one of the “Millenium Prize Problems”, is presented. The Riemann Hypothesis, a conjecture about distribution of prime numbers, has remained unsolved since it was first proposed by German mathematician, Bernhard Riemann in 1859. This paper introduces an analytic continuation of the Zeta Function as well as symmetric approach through integration by parts to address this hypothesis. The proposed solution is obtained through analytical continuation in the critical strip 0<Re(s)<1 to establish that Re(s)=1/2.

Neurological disorders are the leading cause of cognitive and physical disability worldwide, affecting 15% of the global population. Due to the demographics of aging, the prevalence of neurological disorders, including neurodegenerative diseases, will double over the next two decades. Unfortunately, while available therapies provide symptomatic relief for cognitive and motor impairment, there is an urgent unmet need to develop disease-modifying therapies that slow the rate of pathological progression. In that context, biomarkers could identify at-risk and prodromal patients, monitor disease progression, track response to therapy, and parse causality of molecular events to identify novel targets for further clinical investigation. Thus, identifying biomarkers that discriminate between diseases and reflect specific stages of pathology would catalyze the discovery and development of therapeutic targets. This review will describe the prevalence, known mechanisms, ongoing or recently concluded therapeutic clinical trials, and biomarkers of three of the most prevalent neurodegenerative diseases, including Alzheimer’s disease (AD), amyotrophic lateral sclerosis (ALS), and Parkinson’s disease (PD).

Human endogenous retroviruses (HERV) are remnants of ancient retroviral infections that, over millions of years, became integrated into the human genome. While normally inactive, environmental stimuli such as infections have contributed to the transcriptional reactivation of HERV promoting pathological conditions including the development of autoimmunity, neurodegenerative disease and cancer. What infections then trigger HERV activation? Mycobacterium avium subspecies paratuberculosis (MAP) is a pluripotent driver of human disease. Aside from granulomatous diseases Crohn’s, sarcoidosis and Blau syndrome, MAP is associated with autoimmune disease: type one diabetes (T1D), multiple sclerosis (MS), rheumatoid arthritis and autoimmune thyroiditis. MAP is also associated with Parkinson’s disease. Autoimmune diabetes, multiple sclerosis and rheumatoid arthritis are the diseases with the strongest MAP/HERV association. There are several other diseases associated with HERV activation including diseases whose epidemiology and/or pathology would prompt speculation for a causal role of MAP. These include non-solar uveal melanoma, colon cancer, glioblastoma and amyotrophic lateral sclerosis (ALS). This article further points to MAP infection as a contributor to autoimmunity, neurodegenerative disease and cancer via unsilencing of HERV. We examine the link between the ever-increasing number of MAP- associated diseases, the MAP/HERV intersection with these diverse medical conditions and propose treatment opportunities based upon this association.

In this article, we review some of the key results concerning the stress-energy-momentum tensor in general theory of relativty. First, we derive Einstein's field equation using analytic approach. Then, we discuss different properties of stress-energy-momentum tensor for physical and scalar fields.

Abstract The modified Bessel function (MBF) of the first kind is a fundamental special function in mathematics with applications in a large number of areas. When the order of this function is integer, it has an integral representation which includes the exponential of the cosine function. Here we generalize this MBF to include a fractional parameter, such that the exponential in the previously mentioned integral is replaced by a Mittag-Leffler function. The necessity for this generalization arises from a problem of communication in networks. We find the power series representation of the fractional MBF of the first kind, as well as some differential properties. We give some examples of its utility in graph/networks analysis and mention some fundamental open problems for further investigation.

Background:Caregiving for individuals with neurological disease involves providing physical, emotional, and social support, which can be a challenging and stressful experience. This study aims to compare the caregivers' burden, including the impact on mental and physical health, social support, and quality of life, in different neurodegenerative disorders. Methods:Fifty-five primary caregivers (F=41;mean age=53.07±12.29) of patients with Parkinson's Disease (PD=26), Multiple System Atrophy (MSA=16), and Amyotrophic Lateral Sclerosis (ALS=13), took part in the study. Standardized screening scales for the quality of life (EQ-5D/EQ-VAS and PQoL), levels of the caregiving burden (CBI and FSQ), and the assessment of the anxiety-depressive axis (HADS) were administered. Results: The mean CBI score was higher for caregivers of MSA patients (28.81±21.90) and ALS (25.15±16.23) than for caregivers of PD patients (16.08±10.34; p=0.036). Critical burden (cut-off>36) was present in the caregivers of MSA (31.3%), ALS (23.1%), and PD (19.2%) patients. Caregivers of patients with ALS had a worse perception of quality of life (EQ-5D total score) than caregivers of patients with MSA and PD (p

The response of building elements during earthquakes has been an area of concern for different researchers around the world. The NSEs are the first elements to attain failure, the buildings after damages in safety priority are classified as in “Life Safety” mode, but in reality, they are in “Collapse Safety” mode and the occupants inside the buildings are in a state of “Non-Life Safety” as a result of falling of the hazardous NSE’s like cladding's, partitions, hanging objects. In addition to the Life Cycle Cost Assessment (LCCA), the Social Life Cycle Assessment (SLCA) is overlooked by the majority of the researchers, the community must be prepared to respond to an event more efficiently without any major casualties or loss of life. It is expected that by the end of 2050, almost double the construction will take place, the embodied energy during the pre-construction, post-construction and demolition generates a lot of CO2s into the environment, hence sustainability should be given due importance, helping in the achievement of Sustainable Developmental Goals (SDGs).

The early detection of cognitive decline and timely non-pharmacological management or drug therapy are extremely important in providing care for Parkinson’s disease with dementia (PDD). In this study, we first conducted a discovery study to identify six plasma microRNAs that may allow for the differentiation of PD with or without mild cognitive impairment via NGS. A total of 120 participants were further recruited in a validation cohort and divided into four subgroups, namely, normal controls (HC), PD with no dementia (PDND), PD with mild cognitive impairment (PD-MCI) and PDD. Among the six candidates, miR-203a-3p was successfully detected in the plasma of the validation cohort using droplet digital PCR (ddPCR). Our results show that the ratio of miR-203a-3p/miR-16-5p observed in PDD was significantly increased compared to in PD-MCI (p < 0.001) and PDND (p = 0.041). Moreover, the ratio of miR-203a-3p/miR-16-5p showed a significant correlation with MoCA scores (r = -0.237, p = 0.024) in patients with PD (PwP). The ROC curve of the logistic regression model, consisting of the variables of age, the ratio of miR-203a-3p/miR-16-5p and the UPDRS III score, also demonstrated an average AUC of 0.883 via 5-fold cross-validation. In conclusion, the ratio of miR-203a-3p/miR-16-5p may serve as a potential biomarker for distinguishing cognitive dysfunction from PwP.

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

This paper identifies preschool teachers' sources of stress, the times they experience high stress, and their ways of coping with stress levels. The study was conducted using a phenomenological design, one of the qualitative research models. The data were collected through semi-structured interviews with 36 preschool teachers working with children aged 0-6 in state and private schools. As a result of the content analysis, stressors were identified primarily at both interpersonal (positive, and effective interactions), and organizational levels (school management, and leadership style). It was also found that intense stress was experienced when children were difficult to control, such as during sleeping, eating, and cleaning. Finally, these results confirmed that the teachers used active/active behavioral, and passive/avoidant coping strategies. However, it was understood that preschool teachers perceived stress negatively, and did not see stress as a personal development situation. These results are discussed in terms of their ramifications for preschool education.

Cow’s Milk (CM) is a healthy food consumed worldwide by individuals of all ages. Unfortunately, 'lactase deficient' individuals cannot digest milk's carbohydrate lactose depriving themselves of highly beneficial milk proteins like casein, lactoalbumin and lactoglobulin, due to lactose intolerance (LI), while other individuals develop cow milk allergy specifically against these proteins (CMPA). The management of these conditions is distinctly different and an inappropriate diagnosis or treatment may have significant implications for the patients, especially if they are infants or very young children, resulting in unnecessary dietary restriction or avoidable adverse reactions. Omics technologies play a pivotal role in elucidating the intricate interactions between nutrients and the human body, spanning from genetic factors to the microbiota profile and metabolites. This comprehensive approach enables the precise delineation and identification of distinct cohorts of individuals with specific dietary requirements, so that tailored nutrition strategies can be developed. This is what is called personalized nutrition or precision nutrition (PN), the area of nutrition that focuses on the effects of the nutrients over the genome, proteome and metabolome, promoting well-being and health, preventing diseases, reducing chronic disease incidence, and so increasing life expectancy. Here, we report the scientific community opinion proposing to replace the approach “one size fits all” with tailor-made nutrition programs, designed by integrating nutrigenomic data together with clinical parameters and microbiota profiles, taking into account the individual lactose tolerance threshold and needs in terms of specific nutrients intake. This customized approach could help LI patients to improve their quality of life, overcoming depression or anxiety, often resulting from the individual perception of this condition as different from a normal state.

This study explores the intricate relationship between the angle of vehicle-to-vehicle (V2V) conflicts and the severity of conflicts at signalized intersections during traffic signal failures, leveraging the advanced capabilities of LiDAR sensor technology. The research delves into the impact of conflict angles on collision outcomes and introduces LiDAR as a novel and precise tool for capturing spatial dynamics during unregulated traffic movements. Findings reveal that as the angle of V2V conflicts increases, indicating a wider approach between vehicles, the severity of conflicts tends to decrease. This reduction in severity is attributed to the detailed spatial data provided by LiDAR, enabling the identification of glancing impacts rather than direct head-on collisions. The mitigation of forces involved in collisions at increased angles contributes to a decreased likelihood of severe consequences, such as extensive vehicle damage and serious injuries to occupants.Conversely, as the angle of V2V conflicts decreases, signifying a narrower approach between vehicles, the potential for severe collisions tends to increase. LiDAR technology facilitates precise measurements of spatial coordinates and temporal dynamics, revealing that collisions occurring at smaller angles involve more direct and concentrated impact forces. This heightened risk of extensive damage to vehicles and increased injury severity is crucially captured by LiDAR, providing valuable insights into the relationship between conflict angles and collision outcomes during traffic signal failures. This study underscores the efficacy of LiDAR sensor technology in understanding the nuanced dynamics of V2V conflicts and highlights its role in developing targeted safety interventions. The integration of LiDAR data into traffic safety analyses offers a sophisticated approach to mitigating the impact of conflicts and enhancing overall safety at signalized intersections during signal failures. The research also highlighted that as the angle of V2P conflicts widens, PET experiences a proportional increase. A larger conflict angle signifies a more complex interaction between vehicles and pedestrians, leading to prolonged PET values. Conversely, a decrease in the angle of V2P conflicts is associated with a reduction in PET during traffic signal failures.The study commences with an examination of traffic characteristics at the E Cold Spring Ln – Hillen Rd intersection in Baltimore City, MD, utilizing a deployed LiDAR sensor. When the signal at this intersection experienced a temporary malfunction on a regular working day in September 2023, the LiDAR captured data related to vehicle and pedestrian volumes, as well as V2V and V2P conflicts. The primary objective of the research is to evaluate the repercussions of traffic signal failures on both traffic flow and safety, specifically V2V and V2P conflicts, occurring during periods of improper signal functionality. Additionally, this investigation delves into various factors that impact traffic signal performance, encompassing traffic demand, geometric layout, pedestrian interactions, and the incorporation of emerging technologies.

Parkinson’s Disease (PD) is a debilitating neurodegenerative disease, causing loss of motor function, and in some instances, cognitive decline and dementia, in those affected. The quality of life can be improved, and disease progression delayed through early interventions, however, current methods of confirming a PD diagnosis are extremely invasive. This prevents their use as a screening tool for the early onset stages of PD. We propose a surface imprinted polymer (SIP) electroimpedance spectroscopy (EIS) biosensor for detecting α-Synuclein (αSyn) and its aggregates, a biomarker that appears in saliva and blood during the early stages of PD as the blood brain barrier degrades. The surface imprinted polymer stamp is fabricated by low temperature melt stamping polycaprolactone (PCL) on interdigitated EIS electrodes. The result is a low-cost, small footprint biosensor that is highly suitable for non-invasive monitoring of the disease biomarker. The sensors were tested with αSyn dilutions in deionized water, and in constant ionic concentration matrix solutions with decreasing concentrations of αSyn to remove the background effects of concentration. The device response confirmed the specificity of these devices to the target protein of monomeric αSyn. The sensor limit of detection was measured to be 5 pg/L and its linear detection range was 5 pg/L – 5 µg/L. This covers the physiological range of αSyn in saliva and makes this a highly promising method of quantifying αSyn monomers for PD patients in the future. The SIP surface was regenerated, and the sensor reused to demonstrate its capability for repeat sensing as a potential continuous monitoring tool for the disease biomarker.

This paper presented a two-dimensional, well-balanced hydrodynamic and sediment transport model based on the solutions of variable density shallow water equations (VDSWEs) for sediment-laden flows, and the Exner equation for bed changes. Those equations are solved in a coupled way by the first-order Godunov-type finite volume method. The Harten-Lax-van Leer-Contact (HLLC) Riemann solver is extended to find the local Riemann fluxes in order to maintain the exact balance between the momentum term and the bed slope term. The advantage of a well-balanced scheme over an unbalanced scheme is demonstrated by the synthetic standing contact-discontinuity test case. Then, the model is employed to simulate two laboratory experiments. At last, a field case, the 1996 Lake Ha! Ha! flood event (Canada), is simulated. Results of cross sectional geometries and profiles of longitudinal thalweg agree well with measurements. The accuracy and simplicity of the numerical model, together with the robust implementation, make the model a good candidate for practical engineering applications.

This paper presents an in-depth study of the stress wave behavior propagating in a Rayleigh–Love rod with a sudden cross-sectional area change. The analytical solutions of stress waves are derived for the reflection and transmission propagation behavior at the interface of the cross-sectional area change in the rod, considering inertia and Poisson’s effects. Examples solved by the finite element method are provided to verify the correctness of the analytical results. In addition to the forward analysis of Rayleigh–Love wave propagation in rods impacted by a striker rod, a nondestructive testing method is proposed to conduct the defect assessment in the rod type of the structure component with a sudden cross-sectional area change within a cover medium by using the measured signals at the measurable zone of the rod to be inspected.

Neurodegenerative diseases (NDs) are a set of progressive, chronic, and incurable diseases characterized by the gradual loss of neurons, culminating in the decline of cognitive and/or motor functions. Alzheimer’s disease (AD) and Parkinson’s disease (PD) are the most common NDs and represent an enormous burden both in terms of human suffering and economic cost. The available therapies for AD and PD only provide symptomatic and palliative relief for a limited period and are unable to modify the diseases’ progression. Over the last decades, research efforts have been focused on developing new pharmacological treatments for these NDs. However, to date, no breakthrough treatment has been discovered. Hence, the development of disease-modifying drugs able to halt or reverse the progression of NDs remains an unmet clinical need. This review summarizes the major hallmarks of AD and PD and the drugs available for pharmacological treatment. It also sheds light on potential directions that can be pursued to develop of new, disease-modifying drugs to treat AD and PD, thereby decreasing the social and economic burdens linked to these NDs.

Prime numbers are the atoms of mathematics and mathematics is needed to make sense of the real world. Finding the Prime number structure and eventually being able to crack their code is the ultimate goal in what is called Number Theory. From the evolution of species to cryptography, Nature finds help in Prime numbers. One of the most important advances in the study of Prime numbers was the paper by Bernhard Riemann in November 1859 called “Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse” (On the number of primes less than a given quantity). In that paper, Riemann gave a formula for the number of primes less than x in terms the integral of 1/log(x) and the roots (zeros) of the zeta function defined by: Where ζ(z) is a function of a complex variable z that analytically continues the Dirichlet series. Riemann also formulated a conjecture about the location of the zeros of RZF, which fall into two classes: the "trivial zeros" -2, -4, -6, etc., and those whose real part lies between 0 and 1. Riemann's conjecture Riemann hypothesis [RH] was formulated as this: [RH] The real part of every nontrivial zero z* of the RZF is 1/2. Proving the RH is, as of today, one of the most important problems in mathematics. In this paper we will provide a proof of the RH. The proof of the RH will be built following these five parts: PART 1: Description of the RZF PART 2: The C-transformation PART 3: Application of the C-transformation to in Re(z) 0 to obtain ζ(z)=X(z)-Y(z) PART 4: Analysis of the values of z such that X(z)=Y(z), and |X(z)|=|Y(z)|, that equates to ζ(z)=0 Proof that |X(z)|=|Y(z)| only if Re(z)=1/2 Conclude that ζ(z)=0 only if Re(z)=1/2 for Re(z) 0 PART 5: We will also prove that all non-trivial zeros of ζ(z) in the critical line of the form are not distributed randomly. There is a relationship between the values of those zeros and the Harmonic function that leads to an algebraic relationship between any two zeros.

This study aimed to investigate the relationship between sleep duration, dementia severity, age, and ANS regulation. This cross-sectional pilot study included 27 older patients with probable Alzheimer’s disease, hospitalized at a psychiatric center. We measured heart rate variability to assess ANS regulation at night, evaluated dementia severity using the Clinical Dementia Rating scale, and obtained sleep duration data from sleep diaries maintained by psychiatric nurses. The data were analyzed using repeated-measures generalized linear models with age, sex, dementia severity, and medication (antipsychotics) as covariates. A sleep duration of 7–8 h per night was associated with better ANS regulation than other sleep durations, as indicated by sympathovagal balance (p = 0.005). ANS dysregulation was characterized by a 20.7% increase in sympathetic nervous system activity and a 14.8% decrease in parasympathetic nervous system (PSNS) activity. We found a significant correlation between dementia severity and PSNS activity (p = 0.04) and observed an inverted U-shaped association between sleep duration and ANS regulation. This pilot study demonstrated that a sleep duration of 7–8 h per night may be critical in maintaining optimal ANS regulation. Bidirectional associations between sleep duration, inadequate sleep duration, aging, and ANS regulation warrant further investigation.

: Crohn’s disease (CD) is a multifactorial chronic disorder that involves a combination of factors as genetic, immune response and gut microbiota. Actually, the therapy comprises salicylates, immunosuppressive agents, corticosteroids, biologic drugs. International guidelines don’t recommend the use of antibiotics except for septic complications of CD patients. The increased evidence of the implication of gut bacteria in this chronic disease support the rationale for using antibiotics as primary treatment of active CD. In the last decades several pathogens have been reported to be involved in the development of CD, but only Escherichia coli (E.coli) species and Mycobacterium avium paratubercolosis (MAP), aroused the interest due to their strong association with CD pathogenesis. Several meta-analyses have been published concerning antibiotic treatment in CD patients but randomized trials of antibiotic treatments against E.coli and MAP did not show prolonged benefits, and only generated conflicting results so much so that several questions are still unresolved regarding trial design, antibiotic dosing, the formulation used, the treatment course and the outcome measures. In this article we attempted to provide an overview and update of the trials on antibiotic treatment in active CD patients taking into account the role of pathogens, the mechanism by which the different antibiotics act on harmful pathogens, and antibiotic resistance. Finally, we also tried to draw new lines for future studies to use antibiotics to treat active CD patients

This study aimed at investigating the quality statuses of graduates’ sustainable core competences development and the causes behind the identified competence statuses by applying the core competencies’ model. The study employed case study design with thematic analysis involving seven interviewees. This study used tracer study findings and national exit exam results as exhibits. The study revealed “very good” and “excellent” quality statuses for the graduates’ core competence development of College of medicine and Health Sciences (CMHS). Similarly, this study identified “Good +” statuses for the quality of graduates’ core competence development in College of Agriculture and Environmental Sciences ( CAES) and College of Science (CS). Furthermore, the study identified "good" - and +” statuses for the quality of graduates’ competence development at the Faculty of Social Sciences (FSS) and Faculty of Humanities (FH). Improved instruction with a balance of theory and practice, task-oriented deans’ leadership behavior with fairness and shared vision- mission identity, handling internal conflicts, and external ethnic-based war influences were the major reasons for the identified higher competence quality statuses in CMHS, CAES, and CS, whereas the opposite direction decline of these factors were the causes for the low statuses of FSS and FH. Sustainable graduates’ core competence development leads to sustainable employability, labor force, and individual to nation-wide holistic sustainable development

Physical activity is especially important of children's everyday life with chronic disease. The aim of the study was to show whether asthma is a barrier to physical activity in our society. The correlation between the severity of the disease, body mass index, and physical activity were analyzed, and, parents' opinion whether children should participate in active sports was assessed. Physical activity of children with asthma was analyzed by questionnaires and activity-measuring armbands. 93 parents and their children were involved in the survey, while 20 children were wearing the armband. The age of children was 12.6±3.5 years (mean±SD), 69.9% were boys, 30.1% were girls. 93.4% of the respondents participated in physical education program and 56.5% also attended sporting activities on a regular basis. 61.2% of the children had mild, 37.6% moderate, and 1.2% severe asthma. 6.5% of the respondents stated that their illness had been consistently or frequently limiting the performance concerning their school or home duties over the past 4 weeks. Twelve percent of parents felt that physical activity was not appropriate in the context of this disease. We conclude, that fear of the consequences of physical activity depends largely on education which should involve their parents, teachers and coaches.

Changing the symmetry of spin from SU(2) to the quaternion group, $Q_8$, has many ramifications. In this paper we first summarize the properties of Q-spin and then discuss some of those resulting changes.

Crohn’s disease (CD) is a progressive, multifactorial, immune-mediated disease characterized by chronic inflammation of any part of the gastrointestinal (GI) tract. Pediatric patients present with a more extensive form of the disease, especially in the upper GI tract with various histopathological inflammatory patterns. Our study aims to analyze the endoscopic and histopathological findings in children with diagnosed CD and compare results on the initial and follow-up tests. Our study included 100 children and adolescents with CD, with performed endoscopic and histopathological (HP) procedures. The results of multiple biopsies performed in these 8 years were matched and compared. We found a statistically significant decrease in stool changes, weight loss, and abdominal pain as presenting symptoms, and in the fecal calprotectin levels. On esophagogastroduodenoscopy and ileo-colonoscopy 36.59% and 64.86% patients had specific findings, respectively. Non-caseating granulomas were found on 9% of oesophageal, 18% of gas-tric, and 12% of duodenal biopsies. In the lower GI tract, we have observed a disease progression in the rectum and descending colon between the first and second biopsies. Our study showed that more than a third of patients had specific endoscopic (36.59%) and histopathologic (32%) findings in the upper GI tract, and an additional 23% had HP findings highly suggestive of CD. We demonstrated the importance of regular endoscopic and histopathological assessments of pediatric CD patients.

Inflammatory bowel diseases, comprising Crohn’s disease (CD) and ulcerative colitis (UC), are chronic, relapsing and remitting immune-mediated inflammatory diseases affecting the gastrointestinal tract. Ustekinumab (UST) is a monoclonal antibody blocking the p40 subunit of the anti-interleukin (IL) 12/23. Pivotal trials (CERTIFI and UNITI-IM for CD, UNIFI for UC) established the efficacy of UST for the induction and maintenance of remission in both CD and UC, with the most favorable results in naïve patients to biologics. In recent years, a wealth of ‘real-world’ data has emerged supporting positive clinical, endoscopic, and histological outcomes in patients treated with UST, as well as reassuring safety data. More recently, the results of the first head-to-head trials of UST and tumor necrosis factor (TNF) antagonists have been reported. Moreover, a number of studies exploring the role of UST in specific clinical settings, such as perianal CD, postoperative complications and recurrence, extraintestinal manifestations, chronic antibiotic-refractory pouchitis, and pregnancy, have been reported. This review explores results reported to date on UST, including those from pivotal trials, real-world data, and emerging studies regarding therapeutic drug monitoring and immunogenicity. The safety profile of UST was also reviewed.

The conformity assessment of products or a measured value with the given standards is carried out based on the global risk of producers and consumers calculation. A product may conform to specifications but be falsely rejected as non-conforming. This is about the producer's risk. If a product doesn't meet the requirements but is falsely accepted as conforming, that poses a risk to the consumer. The conventional approach to risk assessment, which yields only a single numerical value for the global risk of producers and consumers, is naturally extended, and utilized for assessing risk in measurement models with linear regression. The outcomes of the two-dimensional extension, along a moderate scale, are the parabolas with an opening upwards. Risk surfaces were obtained through three-dimensional extension over the area limited by the moderate scale and guard band axes. Four models with different ranges of tolerance intervals were used to test this innovative method of risk assessment in linear regression. The corresponding standard measurement uncertainties are determined by applying a simplified measurement model with the use of comprehensive data on the measurement performance and by determining measurement uncertainty derived from consideration of the functional relationship obtained by linear regression analysis. Models that utilize information from linear regression analysis to determine measurement uncertainty are biased towards risks at the edges of the moderate scale. Testing the model's performances with metrics related to the confusion matrix, such as the F1 score, further substantiated this assertion. The diagnostic odds ratio has been proven to be extremely effective in identifying the curve along the guard band axis, along which the global risks of producers and consumers are at their lowest.

The primary purpose of this article is to deduce specific order estimates for the \textit{Mertens Function} $M(n)$, which facilitates us to analyze the location of zeros of the \textit{Riemann Zeta function} $\zeta(s)$. The paper also provides a brief overview about the notion of the \textit{Mertens Function} $M(n)$ and \textit{Redheffer Matrices} $\mathbb{A}_{n}$. In addition to learning about various \textit{spectral properties} of $ \mathbb{A}_{n}$, we shall also deduce the relation between these two, which, eventually would lead us to establish a necessary and sufficient condition for the \textit{Riemann Hypothesis} to hold true, as justified by \textit{Redheffer} himself. We shall also observe several numerical evidence as well as theoretical justification behind the falsity of the famous \textit{Mertens Hypothesis}, along with how researchers over the years have approached towards deriving an estimate of the smallest possible natural number $n$ for which the first such violation of the theorem occurs, utilizing numerous conjectures annotating about the order of $M(n)$. Readers who are highly motivated in pursuing research in any of the topics relevent to the contents of this paper will surely find the \texttt{References} section to be extremely resourceful.

Keywords: gender equality policy; initial teacher education; teacher educators’ perceptions; gender perspective; university teaching; sustainable development; SDG5; SDG4.

Any malocclusion can be associated with various face development patterns, including hyper, neutral and hypodivergent growth patterns. We measured face height ratios, angle formed by Y axis to SN and growth patterns in various malocclusions in a group of patients from Timis county. The pretreatment digital cephalograms of 350 participants were split into three groups based on Angle's classification of dentoalveolar malocclusion. Every cephalogram was digitally traced and analyzed using a composite cephalometric method analysis utilizing the WebCeph imaging cephalometric program, which included two linear and one angular. In general, patients from Timis county have a hypodivergent development pattern. Hypodivergent development pattern predominated in group I, II, and III. Group I hyperdivergent 5.14%, normodivergent 16.01%, hypodivergent 78.85%. Group II hyperdivergent 2.78%, normodivergent 14.44%, hypodivergent 82.78%. Group III hyperdivergent 10.53%, normodivergent 10.53%, hypodivergent 78.94%. In all three groups, the value of the angle formed by Y axis to SN is within normal limits group I 65.4 ±4.34°, group II 63.87± 3.86° and group III 64.66 ±5.28°. A strong negative correlation was found between angle: Y axis to SN and facial height ratio (r= -0,766; p &lt;0.001). In all kinds of malocclusion, patients from Timis county show primarily a hypodivergent development pattern.

Culture signifies the customs, language, ceremonies, Indigenous Medical Knowledge (IMK) and other material objects of a tribe. These and many other features are a representation of identity for many Zambian communities. IMK practices are skills inherent by certain individuals in a tribal grouping who are chosen by the spirits (gods) or trained by those who practice. This intrinsic skill is in danger of diminishing as a result of modern medication. This article attempts to understand the role of traditional healers (also known as asing’anga in local language) in preservation of IMK in Chibombo District of Zambia. In so doing, the paper examined methods of preservation used by asing’anga and the challenges faced. Using hermeneutic phenomenology and linear snowball sampling, findings revealed that preservation was done through training. The study found unwillingness, expiration, and spirituality as challenges in the process of preserving IMK. The study recommended that the Lenje Cultural Association consider documenting and disseminating information to the local people by showcasing what is available in the Mukuni Culture Village Museum and Library. This was seen as a way through which many youths would be encouraged to appreciate the indigenous values in their culture.

In this research a neccessary and sufficient condition for the proof of the Binary Goldbach conjecture is established. It is established that the square of all natural numbers greater or equal to 2 have an additive partition equal to the sum of the square of a natural number greater or equal to zero and a Goldbach partition semiprime. All Goldbach partition semiprimes are odd except 4. This finding is in itself proof all composite even numbers have at least Goldbach partition. The result of the proof of the Binary Goldbach conjecture is used to prove the Andrica and Legendre conjectures. The Riemann hypothesis is examined and sources of non trivial zeroes outside the critical strip are discussed. An example example of a non-trivial zero outside the critical strip is given

Systemic lupus erythematosus (SLE) is a prevalent autoimmune condition, yet its alignment with a specific host immunological pathway remains unclear. The THαβ host immunological pathway, recognized for its defense against viruses and prions, has recently emerged as a response to DNA, RNA, and protein pathogens. SLE patients often produce anti-double strand DNA antibodies and anti-nuclear antibodies, suggesting a potential association with the THαβ host immune reaction. Throughout the course of SLE, elevated levels of type 1 interferons, type 3 interferons, interleukin-10, IgG1, and IgA1 are commonly observed. These cytokines and antibody isotypes are indicative of the THαβ host immunological pathway. Similarly, Myasthenia gravis, Grave’s disease, Graft versus host disease, autoimmune hemolytic anemia, immune thrombocytopenia, dermatomyositis, and Sjogren’s syndrome are also linked to THαβ-related type 2 hypersensitivities. Considering the potential association of these diseases with dysregulated THαβ immune responses, therapeutic strategies such as anti-interleukin-10 or anti-interferons α/β could be explored to manage these disorders effectively.

Damaged connective tissues between the bone and tendons or ligaments are common among adults regardless of activity level. Achilles tendinosis is one of the most common tissue defects and enthesopathies. The patient in this study is a 54-year-old female with chronic Achilles tendinosis from chronic enthesopathy at the Achilles tendon insertion with a retrocalcaneal exostosis for three years who has failed standard-of-care practices for over two years. The patient received extracorporeal pulsed-activated therapy (EPAT) before applying 2ml of CryoText, a Wharton’s jelly tissue allograft. The patient then received class IV laser therapy treatments twice weekly for three weeks. The patient started with a 10/10 VAS at the initial visit. At five weeks post-application, the patient’s score had improved by 80% at 2/10 VAS. By week 13, the patient rated her pain as 0/10 VAS. The improvement in patient-reported pain and functionality reported in this study after the application of Wharton’s Jelly, EPAT, and class IV laser therapy warrants future research studying the safety and efficacy of these patient care modalities together.

Synanthropic flora (weeds, spontaneously developed plants) are plants that accompany humans, appearing as a result of anthropopressure as well as after its cessation. The potential of synanthropic flora in shaping green areas usually brings many measurable benefits that depend on land management in cities. The study aimed to determine the preferences and attitudes of adults towards synanthropic flora in settlement units. The article presents survey results from 447 city residents. The obtained results were statistically analyzed using the k-means clustering method to identify segments of respondents with similar attitudes and preferences toward synanthropic flora. Mann-Whitney U tests were employed to determine statistical differences in the demographic variables among the analyzed clusters of respondents. Additionally, multiple regression analysis was performed to identify the opinions and attitudes towards synanthropic flora, that may influence their greater acceptance in the vicinity of residential areas. The results obtained in multiple regression allow for the statement that the respondent’s evaluation of the level of support for the introduction of more synanthropic vegetation into urban greenery (Yw) grows with the increase of acceptance of synanthropic plants occurrence in surroundings. Respondents’ opinions on the subject of the presence of synanthropic plants were studied using such variables concerning: synanthropic vegetation found in turfgrasses has a positive impact on the visual attractiveness of a site (X1), synanthropic plant communities present themselves better than others (X2), presence of synanthropic vegetation in an estate improves the quality of life in that location (X3), introduction of synanthropic flora into estate arrangements is a positive (X4), support for the use of synanthropic flora for educational purposes - as elements of playgrounds or in the form of environmental workshops (X5). Residents’ acceptance of synanthropic flora in green areas is at a relatively high level.

Neurodegeneration is becoming one of the leading causes of death worldwide as the population expands and grows older. There is a growing desire to understand the mechanisms behind prion proteins as well as the prion-like proteins that make up neurodegenerative diseases (NDs) including Alzheimer’s Disease (AD). Both amyloid β (Aβ) and hyperphosphorylated tau (p-tau) proteins behave in ways similar to that of the infectious form of the prion protein, PrPSc, such as aggregating, seeding, and replicating under not yet fully understood mechanisms, thus the designation of prion-like. This review aims to highlight the shared mechanisms between prion-like proteins and prion proteins in the structural variations associated with aggregation and disease development. These mechanisms are largely focusing on the dysregulation of protein homeostasis, self-replication, and protein aggregation, and how this knowledge could contribute to diagnoses and treatments for the given NDs.

The CACCC-box motif emerges as a pivotal cis-regulatory element implicated in diverse developmental processes and diseases, particularly cardiovascular diseases (CVDs). This study centers on the intricate interplay between the CACCC-box and its binding proteins such as: the Krüppel-like family (KLF) of transcription factors as primary effectors in the context of CVDs. Our analysis was through a bioinformatics approach, which reveal significant transcriptional activity among KLF subgroup 2, exhibiting the highest number of interactions focusing on the established roles: pluripotency, cancer, and cardiovascular development and diseases. Our analysis reveals KLF's interactions with GATA4, MEF2C, NKX2.5 and other ~ 90 potential genes that participate in the regulation of the hypertrophic environment (or CVD's Environment). Also, the GO analysis showed genes containing the motif CACCC were enriched for multiple CVD’s, in combination with STRING analysis these results pointed to a link between KLFs and these diseases. The analysis further identifies other potential CACCC-box binding factors, such as SP family members, WT1, VEZF1, and -SALL4, which are implicated in cardiac contraction, remodeling, and inflammation processes.

There is a great need to develop research-based models for supporting collaboration between educational institutions. Collaboration models are needed, for example, to assist the transition from lower educational level to higher education or from higher education to work life. In this research, collaboration was conducted through a joint upper-secondary school and university course that addressed global challenges by using a project-based learning approach. There is a shortage of research exploring students’ perceptions of collaboration. Therefore, the main purpose of this qualitative case study is to explore the relevance of the joint course for students and university students. The research was guided by the following research question: What kind of relevance did the students experience in the joint project-based learning course? The data was gathered using questionnaires, interviews, and reflective study reports. The data was analyzed via theory-based content analysis where research-oriented relevance model was used as the analysis framework. The analysis framework enabled categorizing experienced relevance on individual, vocational and societal dimensions. Altogether, the analysis produced 7 relevance categories for upper-secondary students and 9 for university students. According to the analysis, upper-secondary school students felt that the course offered the most on an individual relevance dimension whereas university students experienced the vocational relevance dimension most diverse. As the main conclusion, this research produced new insights on the experienced relevance of upper-secondary level and higher education cooperation from the students’ point of view. The acquired knowledge can be useful for everyone developing new cross-institutional cooperation models.

Recent research has implicated the gut microbiota in the development of lymphoma. Dysbiosis of the gut microbial community can disrupt the production of gut microbial metabolites, thereby impacting host physiology and potentially contributing to lymphoma. Dysbiosis-driven release of gut microbial metabolites such as lipopolysaccharides can promote chronic inflammation, potentially elevating the risk of lymphoma. In contrast, gut microbial metabolites, such as short-chain fatty acids, have shown promise in preclinical studies by promoting regulatory T-cell function, suppressing inflammation, and preventing lymphoma. Another metabolite, urolithin A, exhibited immunomodulatory and antiproliferative properties against lymphoma cell lines in vitro. While research on the role of gut microbial metabolites in lymphoma is limited, this article emphasizes the need to comprehend their significance, including therapeutic applications, molecular mechanisms of action, and interactions with standard chemotherapies. The article also suggests promising directions for future research in this emerging lymphoma and gut microbiome investigation field.

While providing safe water for the rural poor is considered a basic human right, there are numerous issues associated with existing technologies with shortcomings. Performance issues have continued to fail to meet the needs of impoverished families due to issues including high cost, difficulties with performance, and continuing needs for maintenance. These issues have severely interfered the safe water accessibility. Key aspects of the Guelph Water Filter (GWF) system can avoid/minimize many of these issues. The GWF as described herein enables delivery of low cost, long-term performance at 3Log removal of E.coli and can deliver 1 to 3 L of treated water per hour. The GWF is simple to operate, has an ability to provide sufficient water for a family, maintains longevity of performance, is easy to maintain and has protection against breakage during the cleaning process, is repairable at village level, and operates using a sizable reservoir of water to supply raw water, meaning the technology does not need to be refilled frequently. Hence, the capability of the novel GWF technology is shown to bypass many of the troublesome features of alternative low-tech water treatment technologies. The potential for the GWF to function for 2 days continuously avoids the need for young girls to fetch raw water frequently during a day, thereby enabling them to attend school. Hence, the GWF enhances the potential to result in ‘safe water and full schools’, providing the opportunity for girls to receive education and capture socio-economic benefits for the community.