Let R be a commutative graded ring with unity, S be a multiplicative subset of homogeneous elements of R and P be a graded ideal of R such that P\bigcap S=\emptyset In this article, we introduce several results concerning graded S-prime ideals. Then we introduce the concept of graded weakly S-prime ideals which is a generalization of graded weakly prime ideals. We say that P is a graded weakly S-prime ideal of R if there exists s\in S such that for all x, y\in h(R), if 0\neq xy\in P, then sx\in P or sy\in P. We show that graded weakly S-prime ideals have many acquaintance properties to these of graded weakly prime ideals.

Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. The purpose of this paper is to introduce the concept of weakly S-primary ideals as a new generalization of weakly primary ideals. An ideal I of R disjoint with S is called a weakly S-primary ideal if there exists s∈S such that whenever 0≠ab∈I for a,b∈R, then sa∈√I or sb∈I. The relationships among S-prime, S-primary, weakly S-primary and S-n-ideals are investigated. For an element r in any general ZPI-ring, the (weakly) S_{r}-primary ideals are charctarized where S={1,r,r²,⋯}. Several properties, characterizations and examples concerning weakly S-primary ideals are presented. The stability of this new concept with respect to various ring-theoretic constructions such as the trivial ring extension and the amalgamation of rings along an ideal are studied. Furthermore, weakly S-decomposable ideals and S-weakly Laskerian rings which are generalizations of S-decomposable ideals and S-Laskerian rings are introduced.

This Paper intends to introduce the notion of prime ideals of Intuitionistic fuzzy normed Rings and to establish basic properties related to it. It investigates these notions and shown anew Result using intuinistic fuzzy points and non membership function incorparating with t-norm and s-norm to show aome results of fuzzy prime ideal.

This research paper aims to explicate the complex issue of the Riemann's Hypothesis and ultimately presents its elementary proof. The method implements one of the binomial coefficients, to demonstrate the maximal prime gaps bound. Maximal prime gaps bound constitutes a comprehensive improvement over the Bertrand's result, and becomes one of the key elements of the theory. Subsequently, implementing the theory of the primorial function and its error bounds, an improved version of the Gauss' offset logarithmic integral is developed. This integral serves as a Supremum bound of the prime counting function Pi(n). Due to its very high precision, it permits to verify the relationship between the prime counting function Pi(n) and the offset logarithmic integral of Carl Gauss. The collective mathematical theory, via the Niels F. Helge von Koch equation, enables to prove the RIemann's Hypothesis conclusively.

In this research first, a sequence of properties called delta is assigned to each prime number and then examined. Deltas are only dependent on the distribution of prime numbers, so the results obtained for the delta distribution can be considered as a proxy for the distribution of prime numbers. The first observation was that these properties are not unique and different prime numbers may have the same value of delta of a given order. It was found that a small number of deltas cover a large portion of prime numbers, so by recognizing repetitive deltas, the next prime numbers can be predicted with a certain probability, but the most important observation of this study is the normal distribution of deltas. This research has not tried to justify the obtained observations and instead of answering the questions, it seeks to ask the right question.

We developed some questions regarding twin prime conjecture by examining the bounded gaps between composite numbers and explained the relations between the formulas regarding composite numbers. Then we proved the twin prime conjecture to answer the new questions raised by proving the expression: \[ \liminf_{n\to\infty} (c_n_+_1 - c_n) \ge 10. \] In addition, we prove many different approaches have been and it has been proved that there must be a twin prime in the range $(p_k_2\cdot p_k_1, p^2_k_1)$, where $p \neq 2$.

In this paper, we study the symmetry between the supersingular prime number according to smallest sphenic number. With this symmetry, we show that the elements of sporadic group generates all prime numbers with the order by a simple application.

We talk about random when it is not possible to determine a pattern on the observed outcomes. A computer follows a sequence of fixed instructions to give any of its output, hence the difficulty of choosing numbers randomly from algorithmic approaches. However, some algorithms based on mathematical formulas like the Linear Congruential algorithm and the Lagged Fibonacci generator appear to produce "true" random sequences to anyone who does not know the secret initial input [1]. Up to now, we cannot rigorously answer the question on the randomness of prime numbers [2, page 1] and this highlights a connection between random number generator and the distribution of primes. From [3] and [4] one sees that it is quite naive to expect good random reproduction with prime numbers. We are, however, interested in the properties underlying the distribution of prime numbers, which emerge as sufficient or insufficient arguments to conclude a proof by contradiction which tends to show that prime numbers are not randomly distributed. To achieve this end, we use prime gap sequence variation. The algorithm that we produce makes possible to deduce, in the case of a binary choice, a uniform behavior in the individual consecutive occurrence of primes, and no uniformity trait when the occurrences are taken collectively.

I had previously developed an approach called Gocgen approach, which claimed to prove twin prime conjecture. In this paper, I processed the previously developed Gocgen approach with the zeta function and explained the relationship between the zeta function with some formulas to offer another perspective on the zeta function, and also created a new function that explains the Gocgen approach using the zeta function. Understanding the new function created will provide insight into the frequency of prime numbers.

In this paper, we present a new concept of the generalized core orthogonality (called the C-S orthogonality) for two generalized core invertible matrices $A$ and $B$. $A$ is said to be C-S orthogonal to $B$ if $A^{\tiny\textcircled{S}}B=0$ and $BA^{\tiny\textcircled{S}}=0$, where $A^{\tiny\textcircled{S}}$ is the generalized core inverse of $A$. The characterizations of C-S orthogonal matries and the C-S additivity are also provided. And the connection between the C-S orthogonality and C-S partial order has been given using their canonical form. Moreover, the concept of the strongly C-S orthogonality is defined and characterized.

Throughout this paper, we will establish a comprehensive theoretical foundation and rigorously develop the methodology to investigate the structure of quotient ring S/P under the influence of symmetric generalized n-derivations, where S represents an arbitrary ring, and P signifies a prime ideal of S satisfying certain algebraic identities acting on prime ideal P without relying on the assumption of primeness or semi-primeness of the ring.

A well-known result of Posner’s second theorem states that if the commutator of each element in a prime ring and its image under a nonzero derivation is central, then the ring is commutative. In the present paper, we extend this bluestocking theorem to an arbitrary ring with involution involving prime ideals. Further, apart from proving several other interesting and exciting results, we establish *-version of Vukman’s theorem [48, Theorem 1]. Precisely, we describe the structure of quotient ring A/L, where A is an arbitrary ring and L is a prime ideal of A. Further, by taking advantage of the *-version of Vukman’s theorem, we show that if a 2-trosion free semiprime ring A with involution admits a nonzero *-centralizing derivation, then A contains a nonzero central ideal. This result is in a spirit of the classical result due to Bell and Martindale [19, Theorem 3]. As the applications, we extends and unify several classical theorems proved in [6],[25,[42], and [48] . Finally, we conclude our paper with a direction for further research.

The Ramanujan primes are the least positive integers Rn having the property that if m ≥ Rn, then π_m − π_(m/2) ≥ n. This document develops several bounds related to the Ramanujan primes, sharpening the currently known results. The theory presented is by no means exhaustive, however it provides insights for future research work. Alternatively, we may say that it is a road map which may be followed to make further discoveries.

Twin prime numbers are two prime numbers which have the difference of 2 exactly. In other words, twin primes is a pair of prime that has a prime gap of two. Sometimes the part “twin prime” is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Up to date there is no any valid proof/disproof for twin prime conjecture. Through this research paper, my attempt is to provide a valid proof for twin prime conjecture.

The present study aims to show on the one hand how easily one can get confused when doing research on the internet. Different platforms, fora and homepages supply the visitor with different - and sometimes contradictory - information. On the other hand, we show how to overcome these contradictions and produce valuable research based on almost all sources. For our study, we use the example of the Feit-Thompson conjecture, which is - in opposite to the well-known Feit-Thompson theorem - not widely known. We try to clarify the scientific literature on this topic and we embed our own result into the present state of art. We prove that pq−1p−1 does not divide qp−1q−1 if p and q are twin primes, i.e. p=q+2. Thus we prove that the Feit-Thompson conjecture is true for twin prime numbers.

Topological indices have been used to modeling biological and chemical properties of molecules in quantitive structure property relationship studies and quantitive structure activity studies. All the degree based topological indices have been defined via classical degree concept. In this paper we define a novel degree concept for a vertex of a simple connected graph: S degree. And also we define S indices of a simple connected graph by using the S degree concept. We compute the S indices for well-known simple connected graphs such as paths, stars, complete graphs and cycles.

The Diophantine equation for which p is prime 2^n = p^2 + 7 and n is integers with p > 0, is examined in this work. It is demonstrated by examining the characteristics of the equation that the only solutions meeting these requirements are p = 3 with n = 5 and p = 5 with n = 7. In order to analyze the above equation, it is necessary to look at the properties of primes and how they relate to powers of two. These results advance our knowledge of prime numbers and how they behave in certain mathematical problems.

The Goldbach Conjecture, which is frequently termed as “1 + 1”, has been a fascinating goal for many mathematicians over centuries. A Chinese mathematician, Dr. Jingrun Chen, proved 1 + 2, which is a great success and the best result so far achieved. Although there were several attempts proving the conjecture, these attempts are either tediously long, complicated, or logically imperfect, thus not widely accepted. Taking advantage of the periodicity of primes, here the author provides a straight forward rigorous proof for the Conjecture.

Since 1742, the year in which the Prussian Christian Goldbach wrote a letter to Leonhard Euler with his Conjecture in the weak version, mathematicians have been working on the problem. The tools in number theory become the most sophisticated thanks to the resolution solutions. Euler himself said he was unable to prove it. The weak guess in the modern version states the following: any odd number greater than 5 can be written as the sum of 3 primes. In response to Goldbach's letter, Euler reminded him of a conversation in which he proposed what is now known as Goldbach's strong conjecture: any even number greater than 2 can be written as a sum of 2 prime numbers. The most interesting result came in 2013, with proof of weak version by the Peruvian Mathematician Harald Helfgott, however the strong version remained without a definitive proof. The weak version can be demonstrated without major difficulties and will not be described in this article, as it becomes a corollary of the strong version. Despite the enormous intellectual baggage that great mathematicians have had over the centuries, the Conjecture in question has not been validated or refuted until today.

A twin prime numbers are two prime numbers which have the difference of 2 exactly. In other words, twin primes is a pair of prime that has a prime gap of two. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Up to date there is no any valid proof/disproof for twin prime conjecture. Through this research paper, my attempt is to provide a valid disproof for twin prime conjecture.

The maximal prime gaps upper bound problem is one of the major mathematical problems to date. The objective of the current research is to develop a standard which will aid in the understanding of the distribution of prime numbers. This paper presents theoretical results which originated with a researchin the subject of the maximal prime gaps. the document presents the sharpest upper bound for the maximal prime gaps ever developed. The result becomes the Supremum bound on the maximal prime gaps and subsequently culminates with the conclusive proof of the Firoozbakht's Hypothesis No 30. Firoozbakht's Hypothesis implies quite a bold conjecture concerning the maximal prime gaps. In fact it imposes one of the strongest maximal prime gaps bounds ever conjectured. Its truth implies the truth of a greater number of known prime gaps conjectures, simultaneously, the Firoozbakht's Hypothesis disproves a known heuristic argument of Granville and Maier. This paper is dedicated to a fellow mathematician, the late Farideh Firoozbakht.

The -blocker (S)-practolol ((S)-N-(4-(2-hydroxy (isopropylamino)propoxy)phenyl)acetamide) was synthesized with 96% enantiomeric excess (ee) from the chlorohydrin (R)-N-(4-(3-chloro-2 hydroxypropoxy)phenyl)acetamide, which was produced in 97% ee and with 27% yield. Racemic building block 1-((1H-indol-4-yl)oxy)-3-chloropropan-2-ol for the -blocker pindolol was produced in 53% yield and (R)-1-((1H-indol-4-yl)oxy)-3-chloropropan-2-ol was produced in 92% ee. The chlorohydrin 7-(3-chloro-2-hydroxypropoxy)-3,4-dihydroquinolin-2(1H)-one, a building block for a derivative of carteolol was produced in 77% yield. (R)-7-(3-chloro-2-hydroxypropoxy)-3,4-dihydroquinolin-2(1H)-one was obtained in 96% ee. The S-enantiomer of this carteolol derivative was produced in 97% ee in 87% yield. Racemic building block 5-(3-chloro-2-hydroxypropoxy)- 3,4-dihydroquinolin-2(1H)-one, building block for the drug carteolol was also produced in 53% yield, with 99% ee of the R-chlorohydrin (R)-5-(3-chloro-2-hydroxypropoxy)-3,4-dihydroquinolin-2(1H)-one. The yield of all four chlorohydrins increased by use of catalytic amounts of base. The reason for this was found to be less formation of the dimeric by-products compared to use of higher concentration of the base. An overall reduction of reagents and reaction time was also obtained compared to our previous reported data of similar compounds. The enantiomers of the chlorohydrin building blocks were obtained by kinetic resolution of the racemate in transesterification reactions catalyzed by Candida antarctica Lipase B (CALB) from SyncoZymes Co, Shanghai, China. Optical rotations confirmed the absolute configuration of the enantiopure drugs.

Bacillus Calmette-Guérin (BCG) is the only widely used prophylactic tuberculosis (TB) vaccine that can prevent severe TB in infants. However, it provides poor protection in adults, and therefore, there in ongoing research on new TB vaccines and immunization strategies with more durable immune effects. The recombinant BCG and BCG prime-protein booster are two important vaccine strategies that have recently been developed based on BCG and could improve immune responses. In this study, three immune strategies based on four protective antigens, namely, ESAT-6, CFP-10, nPPE18, and nPstS1, were applied to construct recombinant rBCG-EPCP009, EPCP009 subunit protein, and BCG prime-EPCP009 booster vaccine candidates. The short- and long-term immune effects after vaccination in Balb/c mice were evaluated based on humoral immunity, cellular immunity, and the ability of spleen cells to inhibit in vitro mycobacterial growth. At 8 and 12 weeks after the initial immunization, splenocytes from mice inoculated with the BCG prime-EPCP009 protein booster secreted higher levels of PPD- and EPCP009-specific IFN-γ, IL-2, TNF-α, IL-17, GM-CSF, and IL-12 and had a higher IFN-γ⁺CD4⁺ TEM:IL-2⁺CD8⁺ TCM cell ratio than splenocytes from mice inoculated with the rBCG-EPCP009 and EPCP009 proteins. In addition, the EPCPE009-specific IgG2a/IgG1 ratio was slightly higher in the BCG prime-EPCP009 protein booster group than in the other two groups. The in vitro mycobacterial inhibition assay showed that the splenocytes of mice from the BCG prime-EPCP009 protein booster group exhibited stronger inhibition of Mycobacterium tuberculosis （M. tuberculosis）growth than the splenocytes of mice from the other two groups. These results indicate that the BCG prime-EPCP009 protein booster exhibited superior immunogenicity and M. tuberculosis growth inhibition to the parental BCG, rBCG-EPCP009, and EPCP009 proteins under in vitro conditions. Thus, the BCG prime-EPCP009 protein booster may be important for the development of a more effective adult TB vaccine.

In this study, we define the concept of pseudo-prime subhypermodules of hypermodules as a generalization of the prime hyperideal of commutative hyperrings in [17]. Firstly we examine the spectrum of the Zariski topology, which we built on the element of the pseudo-prime subhypermodules of a class of hyper-modules, then we give some relevant properties of the hypermodule in this topological hyperspace.

Let G be a finite group. The prime graph Γ(G) of G is defined as follows: The set of vertices of Γ(G) is the set of prime divisors of |G| and two distinct vertices p and p' are connected in Γ(G), whenever G has an element of order pp'. A non-abelian simple group P is called recognizable by prime graph if for any finite group G with Γ(G)=Γ(P), G has a composition factor isomorphic to P. In [4] proved finite simple groups ²D_n(q), where n ≠ 4k are quasirecognizable by prime graph. Now in this paper we discuss the quasirecognizability by prime graph of the simple groups ²D_2k(q), where k ≥ 9 and q is a prime power less than 10⁵.

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.

This study aimed to delineate the longitudinal antibody responses to the Pfizer- BioNTech COVID-19 vaccine (BNT162b2) within the Ugandan subset of the Sub-Saharan African (SSA) demographic, filling a significant gap in global datasets. We enrolled 48 participants, collecting 320 specimens over 12 months after vaccination. A validated enzyme-linked immunosorbent assay (ELISA) was used to quantify SARS-CoV-2-specific IgG, IgM, and IgA concentrations (ng/ml) and optical densities (ODs). Statistical analyses included box plots, diverging bar graphs, and the Wilcoxon test with Bonferroni correction. We showed a robust SIgG response within 14 days of the primary vaccine dose, consistent with global data. Remarkably, we observed no significant surge in S-IgG levels following the booster, contrasting trends other global populations. The S-IgM response was transient, and predominantly established thresholds, reflecting its typical early emergence and subsequent decline. S-IgA increased initially but declined six months post-vaccination, in line with the temporal dynamics of mucosal immunity. Eleven breakthrough infections occurred; however, all were asymptomatic, indicating a protective effect from the vaccination regardless of the participants' initial S-IgG serostatus. The Pfizer-BioNTech COVID-19 vaccine elicited strong S-IgG responses in the SSA demographic. However, antibody dynamics distinctly differed from global data highlight the significance of region-specific research and the necessity for customized vaccination strategies.

Prime number-related issues can be viewed from drastically different perspectives by examining the close connections between prime numbers and composite numbers. We think that multiple perspectives are the pillars on the path to solutions so we have created this study. As a result of the study, we proposed two new formulas by presenting three theorems and one proof for each theorem, a total of three proofs. We proved that the formula p · n + p returns a composite number in the first of the theorems, which is the preliminary theorem. Our first theorem except the preliminary theorem is that the formula p · n + p returns all composite numbers, and we proved that too. Finally, we created Theorem II using Theorem I to use in our other work and proved that the formula 2 · n · p + p returns all odd composite numbers, which is Theorem II. Afterward, we presented the similarities of the 2 · n · p + p formula we put forth with another known formula.

Streptococcus mutans is a key bacterium in dental caries- one of the most prevalent chronic infectious diseases. Conventional treatment both fails to specifically target the pathogenic bacteria and at-tempts to eradicate commensal bacteria as well. Thus, caries remains one of most common and challenging diseases. The use of bacterial viruses as anti-bacterial agents, is gaining interest worldwide. Hardly any phages were described against S. mutans. The objective of this study was to isolate anti-S. mutans phages and to characterize their antimi-crobial properties. Human saliva samples were filtered and screened for potential phages. Standard double-layered agar method was used for isolation. Whole genome sequence analysis and morphology visualization by TEM, were used for anti-S. mutans phage identification. Antibacterial properties were evaluated using clinical strains and ATCC strains of S. mutans in various states. Antibacterial effect was also tested on human cariogenic dentin. One phage against S. mutans was isolated and termed SMHBZ8. This phage showed effective lytic activity in vitro against both planktonic and biofilm S. mutans cultures. Moreover, the phage showed antibacterial effect when used on cariogenic dentin. The isolation and characterization of SMHBZ8 may be the first step in developing a potential phage therapy for dental caries.

When discussing the Diophantine quintic equation $p(a^5 + b^5) = q(c^5 + d^5)$ where p is a prime and q is an integer, there is a clear gap between the mathematical literature and online forums. Because of the intrinsic complexity of parameterizing fifth-degree equations, this equation re- mains largely unexplored. In this work, we approach this quintic problem through algebraic methods with the goal of providing numerical solutions that illuminate its properties and behaviors.Our research uncovers in- triguing patterns and connections that shed light on the enigmatic nature of Diophantine quintic equations in this particular form.

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

This paper serves as a seamless continuation of the previous work titled "Special Spirals are Produced by the ROTASE Galactic Spiral Equations with the Sequential Prime Numbers." Upon revisiting the data, a noteworthy observation emerged: the special spirals can be meticulously aligned with the prime spiral on a point-by-point basis through careful scaling and rotation for the parameter ρ remaining a constant greater than one. As ρ increases, both the scaling factor and rotation angle exhibit a corresponding augmentation, albeit with an intriguing caveat—the rotation angle asymptotically approaches its limit of 90°. Notably, the galactic spiral can be perceived as a remarkably close approximation of the Archimedean spiral, with the degree of proximity increasing as ρ grows larger. Furthermore, an intriguing correspondence arises when ρ takes on a value of 1; at this value, the galactic spiral bears a striking resemblance to the Fermat spiral, the space between two consecutive spiral loops undergoes a continuous reduction as the loop's radius expands, yet it never diminishes to zero; simultaneously, the area between two successive loops experiences an augmentation with the value of ρ.

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 $x \geq 13.1$.

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

The biofilm is a conglomerate of cells surrounded by an extracellular matrix, which contributes to the persistence of infections. The difficulty in removing the biofilm drives the research for new therapeutic options. In this work, the effect of terpenes (-)-trans-Caryophyllene, (S)-cis-Verbenol, (S)-(-)-Limonene, (R)-(+)-Limonene, and linalool was evaluated, individually and in combinations on bacterial growth, by assay with resazurin; the formation of biofilm, by assay with violet crystal; and the expression of associated genes, by real-time PCR, in two clinical isolates of S. aureus, ST30-t019 and ST5-t311, responsible for more than 90% of pediatric infections by this pathogen in Paraguay. All combinations of terpenes can inhibit biofilm formation in more than 50% without affecting bacterial growth. The most effective combination was (-)-trans-Caryophyllene and linalool at a 500 μg/mL concentration for each, with an inhibition percentage of 88%. This combination decreased the expression levels of the sdrD, spa, agr, and hld genes associated with the initial cell adhesion stage and quorum sensing. At the same time, it increased the expression levels of the cap5B and cap5C genes related to the production of capsular polysaccharides. The combinations of compounds tested are promising alternatives to inhibit biofilm formation in S. aureus.

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).

Let {$\Gamma(k)$} denote {$(k-1)!$}, and let {$\Gamma_{n}(k)$} denote {$(k-1)!$}, where {$n \in \{3,\ldots,16\}$} and {$k \in \{2\} \cup [2^{\textstyle 2^{n-3}}+1,\infty) \cap \mathbb N$}. For an integer {$n \in \{3,\ldots,16\}$}, let $\Sigma_n$ denote the following statement: if a system of equations {${\mathcal S} \subseteq \{\Gamma_{n}(x_i)=x_k:~i,k \in \{1,\ldots,n\}\} \cup \{x_i \cdot x_j=x_k:~i,j,k \in \{1,\ldots,n\}\}$} with $\Gamma$ instead of $\Gamma_{n}$ has only finitely many solutions in positive integers {$x_1,\ldots,x_n$}, then every tuple {$(x_1,\ldots,x_n) \in (\mathbb N \setminus \{0\})^n$} that solves the original system ${\mathcal S}$ satisfies {$x_1,\ldots,x_n \leqslant 2^{\textstyle 2^{n-2}}$}. Our hypothesis claims that the statements {$\Sigma_{3},\ldots,\Sigma_{16}$} are true. The statement {$\Sigma_6$} proves the following implication: if the equation {$x(x+1)=y!$} has only finitely many solutions in positive integers $x$ and $y$, then each such solution {$(x,y)$} belongs to the set {$\{(1,2),(2,3)\}$}. The statement {$\Sigma_6$} proves the following implication: if the equation {$x!+1=y^2$} has only finitely many solutions in positive integers $x$ and $y$, then each such solution {$(x,y)$} belongs to the set {$\{(4,5),(5,11),(7,71)\}$}. The statement {$\Sigma_9$} implies the infinitude of primes of the form {$n^2+1$}. The statement {$\Sigma_9$} implies that any prime of the form {$n!+1$} with {$n \geqslant 2^{\textstyle 2^{9-3}}$} proves the infinitude of primes of the form {$n!+1$}. The statement {$\Sigma_{14}$} implies the infinitude of twin primes. The statement {$\Sigma_{16}$} implies the infinitude of Sophie Germain primes.

Formation of Fe- and Mg-rich smectite and zeolite under alkaline conditions is concerned as secondary minerals after alkaline alteration of bentonite in a repository of radioactive wastes. It might be crucial for safety assessment whether smectite will be formed or not as secondary minerals after alkaline alteration of bentonite. In present paper, Fe- and Mg-rich smectite which are currently interacting with hyperalkaline groundwater was found at Narra in Palawan, Philippines. Mineralogical and geochemical investigation was conducted to understand formation process of smectite and factors determined secondary mineral species. Our study revealed a certain amount of smectite may have been produced under hyperalkaline conditions, altered from amorphous or poorly crystalline material such as M-S-H and F-S-H. Key factor which decides smectite or zeolite as secondary minerals after alkaline alteration of bentonite might be whether nuclei of M-S-H and/or F-S-H will be formed or not. This might be decided by the presence of dissolved Mg2+ and Fe2+ in the system. Our suggested formation process of smectite under alkaline conditions is analogue with generally-accepted model of smectite formation that might have been occurred on early Mars.

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.

Genetic engineering in the field for designing crop improvement has become an essential element in responding to the increasing need for food safety, environmental sustainability, and climate-resilient crops. The latest molecular technology is used by many breeders today to achieve remarkable results. Fast genome editing is currently being seen in a variety of organisms, including plants, because to the high specificity, high effectiveness, and low production cost of CRISPR/Cas [Clustered regulatory interspaced short palindromic repeat (CRISPR)-associated protein (Cas)] technology. Its applications in developing higher-yielding, nutrition rich, disease resistance, stress-tolerant crops fruits, and vegetables. Therefore, this technology has the potential to revolutionize agriculture and contribute to global food security. The Cas protein provides the enzymatic machinery necessary for the acquisition of new cells that target invasion elements. Cas proteins such as Cas9, Cas12, Cas13, and Cas14, among others, have distinct architectures and have been used to create new genetic tools that improve features that are important for agriculture. The versatility of Cas has accelerated genomic analysis and facilitated the use of CRISPR/Cas to manipulate and alter nucleic acid sequences in cells of different organisms. This review provides the evolution of CRISPR technology exploring its mechanisms and contrasting it with traditional breeding and transgenic approaches to improve different stress tolerance. We will also discuss the CRISPR/Cas system and explore the workings of the three Cas proteins that are currently known to exist: Cas12, Cas13, and Cas14. The edited crops by this technology do not have foreign DNA inserted into their genome, therefore, they are considered as non-transgenic by the regulatory bodies in most countries.

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

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.

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.

For each non-prime odd number as F=pq , if we consider m/n as an approximation for q/p and choose k=mn , then by proving some lemmas and theorems, we can compute the values of m and n. Finally, by using Fermat’s factorization method for F and 4kF as difference of two non-consecutive natural numbers, we should be able to find the values of p and q. Then we introduce two new and powerful sieves for separating composite numbers from prime numbers.

Let $S=\left(s_1, \ldots, s_n\right)$ be a finite sequence of integers. Then $S$ is a Gilbreath sequence of length $n$, $S\in\mathbb{G}_n$, iff $s_1$ is even or odd and $s_2, \ldots, s_n$ are respectively odd or even and $\min\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\leq s_{m+1}\leq\max\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\forall m\in\left[\left.1, n\right)\right.$. This, applied to the order sequence of prime number $P$, defines Gilbreath polynomials and two integer sequences A347924 \cite{oeisA347924} and A347925 \cite{oeisA347925} which are used to prove that Gilbreath conjecture $GC$ is implied by $p_n-2^{n-1}\leqslant\mathcal{P}_{n-1}\left(1\right)$ where $\mathcal{P}_{n-1}\left(1\right)$ is the $n-1$-th Gilbreath polynomial at 1.

We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to Poisson process and upon arrival of a catastrophe all inventory in the system is instantly destroyed. But consumer customers in the system (in the server or in the buffer) continue still waiting for the replenishment of the stock. The arrivals of the consumer customers follow a Markovian Arrival Process (MAP) and they can be queued in an infinite buffer. Service time of a consumer customer follows a phase-type distribution. The system receives negative customers whose have Poisson flows to service facility and upon arrival of a negative customer one consumer customer is pushed out from the system, if any. One of two replenishment policies can be used in the system: either (s,S) or (s,Q). If upon arrival of the consumer customer, the inventory level is zero, then according to the Bernoulli scheme, this customer is either lost (lost sale scheme) or join the queue (backorder sale scheme). The system is formulated by a four-dimensional continuous-time Markov chain. Steady state distribution is obtained using the matrix-geometric method. A comprehensive numerical study is performed on the performance measures under various replenishment policies. Finally, an optimization study is presented.

Single-Anastomosis Duodeno-Ileal bypass with Sleeve Gastrectomy (SADI-S) is a modification of the duodenal switch in which only one anastomosis is performed, with a longer common limb and an expected less malabsorptive effect. The present study analyzes presentation and treatment of malnutrition after SADI-S. 258 consecutive patients undergoing SADI-S between May 2007 and September 2017 were included. The common limb length was 200 cm in 50 cases, 250 cm in 156 and 300 in 52. 30 patients were admitted for severe hypoalbuminemia and 16 patients were submitted to revisional surgery and constitute the series of our study. Mean weight before reoperation was 57 kg and mean body mass index (BMI) was 21 kg/m2. Mean number of daily bowel movements was 5,6. Mean time to reoperation was 56 months. Revisional surgery consisted mainly in elongation of the common limb. Mean weight regain was 14 kg and mean final BMI was 26 kg/m2. Daily bowel movements were decreased to 1,3. Factors related to hypoalbuminemia were hypertension, poor controlled diabetes, age over 55 years and a shorter common limb. Although SADI-S is expected to be less malabsorptive than previous biliopancreatic diversions, caution has to be taken with selected patients to avoid postoperative malnutrition.

Brain capillary endothelial cell(s) (BECs) have numerous functions including their semipermeable interface-barrier (transfer and diffusion of solutes), trophic (metabolic homeostasis), tonic (vascular hemodynamics), and trafficking (vascular permeability, coagulation, and leukocyte extravasation) functions to provide brain homeostasis. BECs also serve as the brain’s sentinel cell of the innate immune system and are capable of antigen presentation. In metabolic syndrome (MetS) there are two regions resulting in proinflammatory signaling of BECs. Namely, visceral adipose tissue depots supplying excessive peripheral cytokines/chemokines (pCC) and gut microbiota dysbiotic regions supplying excessive soluble lipopolysaccharide (sLPS), small LPS-enriched extracellular vesicle exosomes (lpsEVexos), and pCC. This dual signaling of BECs at their receptor sites results in BEC activation and dysfunction (BECact/dys) and neuroinflammation. sLPS and lpsEVexos signal BECs toll-like receptor four, which then signals translocated nuclear factor kappa B (NFkB). Translocated NFkB promotes the synthesis and secretion of BEC proinflammatory cytokines and chemokines. Specifically, the chemokine CCL5 (RANTES) is capable of attracting microglia cells to BECs. BEC neuroinflammation activates perivascular space(s) (PVS) resident macrophages. Excessive phagocytosis by reactive resident PVS macrophages results in a stagnation-like obstruction, which along with increased capillary permeability due to BECact/dys could expand the fluid volume within the PVS to result in enlarged PVS (EPVS). Importantly, this remodeling may result in pre- and post-capillary EPVS that would contribute to their identification on T2-weighted MRI, which are considered to be biomarkers for cerebral small vessel disease.

We demonstrate a new quantitative method to the sieve of Eratosthenes, which is an alternative to the sieve of Legendre. In this method, every element of a given set is sifted out once only, and therefore, this method is free of the Mobius function and of the parity barrier. Using this method, we prove that every sufficiently large even number is the sum of two primes, and that every even number is the difference of two primes in infinitely many ways.

Integer is either a composite number or a prime number. Therefore, detecting composite numbers is important for solving prime numbers. The study of prime numbers, apart from satisfying human curiosity, can be very important. In this article, the order of composite numbers has been detected. And explained with a simple method and a simple function. And, a method has been developed in which all composite numbers and therefore prime numbers can be determined by using the specified methods, functions and formulas.

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.

Background and objective: Symptoms of most neurodegenerative diseases, including Parkinson’s disease (PD), usually do not occur until substantial neuronal loss occurs. This makes the process of early diagnosis very challenging. Hence, this research used variant call format (VCF) analysis to detect variants and novel genes that could be used as prognostic indicators in the early diagnosis of prodromal PD. Materials and Methods: Data were obtained from the Parkinson’s Progression Markers Initiative (PPMI), and we analyzed prodromal patients with gVCF data collected in the 2021 cohort. A total of 304 participants were included, including 100 healthy controls, 146 prodromal genetic individuals, 21 prodromal hyposmia individuals, and 37 prodromal RBDs. A pipeline was developed to process the samples from gVCF to reach variant annotation and pathway and disease association analysis. Results: Novel variant percentages were detected in the analyzed prodromal subgroups. The prodromal subgroup analysis revealed novel variations of 1.0%, 1.2%, 0.6%, 0.3%, 0.5%, and 0.4% for the genetic male, genetic female, hyposmia male, hyposmia female, RBD male, and RBD female, respectively. Interestingly, 12 potentially novel loci (MTF2, PIK3CA, ADD1, SYBU, IRS2, USP8, PIGL, FASN, MYLK2, USP25, EP300 and PPP6R2) that were recently detected in PD patients were detected in the prodromal stage of PD. Conclusion: Genetic biomarkers are crucial for the early detection of Parkinson’s disease and its prodromal stage. The novel PD genes detected in prodromal patients could aid in the use of gene biomarkers for early diagnosis of the prodromal stage without relying only on phenotypic traits.

Dynamic virtual testing by Hardware in the Loop (HIL) real time simulation systems is common to minimize physical tests to validate and verify control algorithms, logics and software, under normal and emergency conditions. The accurate but costly HIL models setup activities could have an extended use to simulate faulty conditions that are seldom observable in the real system, yet they must be detected in advance and recognized. Data driven diagnostic methods have reached a mature development, in various sectors, proving effective in early detecting slowly varying deviations from nominal patterns of signals, even without a priori knowledge of their nature and behavior. These methods rely on vast amount of data logged from real systems that are ever and ever richer of monitoring telemetries that are worth being exploited. However, due to the usually reliable and safe systems being managed, it is often difficult to collect enough data on anomalous situations to validate fault detection and isolation and limit false positives. HIL model-based simulations allow generating and observing operational domains or transients rarely observed in real operations. This allows identifying the signals that are most correlated to faults and that could be selected to setup data-based diagnostic models of parts or subsystems, which are more suitable than the whole HIL model for online diagnostics, as well as to identify the features and trends that are most symptomatic of anomalous conditions.

The article proposes asymptotic methods for calculating Sommerfeld integrals, which enable us to calculate the integral using the expansion of a function into an infinite power series at the saddle point, where the role of a rapidly oscillating function under the integral can be fulfilled either by an exponential or by its product by the Hankel function. The proposed types of Sommerfeld integrals are generalized on the basis of integral representations of the Hertz radiator fields in the form of the inverse Hankel transform with the subsequent replacement of the Bessel function by the Hankel function. It is shown that the numerical values of the saddle point are complex. During integration, auxiliary or so-called standard integrals, which contain the main features of the integrand function, were used. As a demonstration of the accuracy of the technique, a previously known asymptotic formula for the Hankel functions was obtained in the form of an infinite series. The proposed method for calculating Sommerfeld integrals can be useful in solving the half-space Sommerfeld problem. An example is the expression in the form of an infinite series for the magnetic field of reflected waves, obtained directly through the Sommerfeld integral (SI).

The variation of the cationic composition in I2-II-IV-VI4 semiconductor compounds is an effective tool for altering their properties in a controlled manner. In particular, a partial substitution of Cu for Ag in kesterite Cu2ZnSnS4 was proposed to suppress Cu-Zn antisite defects and the improve photovoltaic performance. However, the efficiency of this approach may substantially depend on the fabrication route. Here, we report on the synthesis of (Cu,Ag)-Zn-Sn-S (CAZTS) and Ag-Zn-Sn-S (AZTS) nanocrystals (NCs) by means of "green" chemistry in aqueous solution and their detailed characterization by Raman spectroscopy and by several complementary techniques. Through a systematic variation of the nominal composition and quantification of the constituent elements in CAZTS and AZTS NCs by XPS, we identified the vibrational Raman and IR fingerprints of both the main AZTS phase and secondary phases of Ag-Zn-S and Ag-Sn-S compounds (for the first time). The formation of the secondary phases of Ag-S and Ag-Zn-S cannot be avoided entirely for this type of synthesis. The Ag-Zn-S phase, having its bandgap in near infrared range, is the reason of the non-monotonous dependence of the absorption edge of CAZTS NCs on the Ag content, with a trend to redshift even below the bandgaps of bulk AZTS and CZTS.

Recently, the conformable derivative and its properties have been introduced. In this paper, we propose and prove some new results on conformable Boundary Value Problems. First, we introduce a conformable version of classical Sturm´s separation, and comparison theorems. For a conformable Sturm-Liouville problem, Green's function is constructed, and its properties are also studied. In addition, we propose the applicability of the Green´s Function in solving conformable inhomogeneous linear differential equations with homogeneous boundary conditions, whose associated homogeneous boundary value problem has only trivial solution. Finally, we prove the generalized Hyers-Ulam stability of the conformable inhomogeneous boundary value problem.

Based on recent popular money priming research results, which conclude that money makes self-sufficient (e.g. less interest in other people), we assumed that people are less interested in finding out whether others are lying or telling the truth. In a laboratory experiment, 163 students (85 women, 78 men, M_Age = 23.08, ranging from 18 to 36 years) were primed by actively handling money (versus paper sheets). Afterwards, they classified 24 video statements as true or deceptive (senders describing their most/least favorite movie), rated their classification confidence for each decision and then answered control questions. Results revealed no influence of priming condition on judgmental bias, classification accuracy, and classification confidence. Also the level of self-reported motivation to find out who lied or told the truth did not differ between conditions. Higher motivation was correlated to higher classification confidence. Additionally, and in line with Reinhard (2010) and Reinhard et al. (2011), higher classification accuracy correlated to a higher use of verbal content cues for classification decisions. Thus, while we were able to replicate these findings, our results contradict the assumption of a money prime influence on lie detection ability. Concluding, our results make self-sufficiency in this context questionable and offer next steps for research.

In this paper, the sequential prime numbers are used as variables for the galactic spiral equations which were developed from the ROTASE model. Special spiral patterns are produced when prime numbers are treated with the unit of radian. The special spiral patterns produced with the first 1000 prime numbers have 20 spirals arranged in two groups. The two groups have perfect central symmetry with each other and are separated with two spiral gaps. The special spiral pattern produced with natural numbers from 1 to 7919 shows 6 spirals in the central area and 44 spirals in the outer area. The whole 7919 spiral points can be plotted with either 6-spiral pattern or 44-spiral pattern. For the spirals only produced by the prime numbers in the 6-spiral pattern plotting, the spiral 2 and spiral 3 each has only one spiral point produced by prime number 2 and 3, respectively, all other spiral points produced by other prime numbers are located on the spiral 1 and spiral 5. The special spiral pattern is well explained with careful analysis, it is concluded that all prime numbers greater than 3 must meet one of the equations: P₁ = 1 + 6 * n (n > 0) P₅ = 5 + 6 * n (n ≥ 0) In other words, every prime number greater than 3 is either a P₁ prime number or a P₅ prime number, no exception. Matching one of the equations is a necessary condition for a number to be a prime number, not a sufficient condition. Hope such sufficient condition can be found in the future. The number of P₁ prime numbers roughly equal the number of P₅ prime number in the first 2 billion prime numbers. The galactic spiral equations with golden angle can duplicate Vogel’s result for the simulation of sunflower seed head pattern, and a pinwheel pattern can be produced also with galactic spiral equations and 1 degree more than golden angle.

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.

Hamman’s syndrome is a rare condition that mostly affects young males, often with a predisposition of asthma. It includes the presence of free air in the mediastinum and subcutaneous emfysema with no other underlying cause such as trauma or infection. It occurs spontanously and often in association with prolonged valsalva manouvre. This might explain why there are some cases of Hamman syndrome among young females giving birth. Here we present a case report of a 24-year- old primigravida with Hamman’s syndrome. She presented with symptoms a few hours after an uncomplicated vaginal delivery at 40+1 pregnancy week. The symptoms resolved spontanously after a few days of observation. We also give a systemic review of reported cases since 2000 to provide overview on pathomechanism, symptoms, diagnostics, treatment and management of this condition. Hamman’s syndrome is a rare, usually benign, but potentially serious complication that can occur during the second stage of labour. Diagnostics include inquiring about typical symptoms, clinical examination and chest x-ray or CT scan. Treatment is usually conservative with oxygen, bronchodilators and pain relief. The reccurence rate is low and there is no contraindication to vaginal delivery in future pregnancies. However, it is suggested that physicians and midwives be cautious and consider low threshold for instrumental delivery or caesarean section to avoid excessive valsalva manoeuvre.

Malocclusions have a continuously increasing prevalence from a generation to another as a result of climate changes, soil, atmosphere and water pollution. All of these aspects have unfavorable consequences on the nutritional scheme. Thus, nutrition together with other etiopathogenic factors contribute to complex alterations in the somatic development of the entire organism and, implicitly, of the cephalic extremity. The study group included 4147 children from randomly selected schools from Vâlcea County, Romania. The aim of this study is to determine the prevalence of malocclusions in schoolchildren from Vâlcea County, Romania, according to the three main classes of malocclusions (according to Angle’s classification), age groups (from 6 to 10 years old and from 11 to 14 years old), gender (male and female) and place of origin (rural and urban). For Angle class I malocclusions we recorded the highest prevalence (48,78% from the total number of schoolchildren with malocclusions), followed by Angle class II malocclusions (45,85% from the total number of schoolchildren with malocclusions) and for Angle class III malocclusions we found the lowest prevalence (5,37% from the total number of schoolchildren with malocclusions).According to gender, we found the highest prevalence in female gender (29,90% from the total number of female subjects), while in male gender we recorded a prevalence of 27,70% from the total number of male subjects. Regarding the place of origin, there is a higher prevalence of malocclusions in the urban areas (29,16%). The study subgroup included 140 children randomly selected from the total number of subjects from the study group. They were included in a more advanced study. The aim is to find potential associations between the presence of malocclusions and various oral variables. Categorical variables were expressed as numerical values and percentages, and their association was evaluated with either the Chi-square test of association or homogeneity, or the Fisher Exact test. The acquired data were incorporated into a binomial logistic regression model to assess the likelihood of developing malocclusions in relation to the following variables: defective phonation, bruxism, frequency of teeth brushing, onychophagia, oral respiration, infantile deglutition, placing objects between the maxillaries, thumb sucking and salivary aspects. It is also aimed to compare the results obtained with similar ones from the specialized literature.

Histone post-translational modification is one of the main mechanisms of epigenetic regulation, which plays a crucial role in the control of gene expression and various biological processes. However, whether or not it affects fungal virulence is not clear in Sclerotinia sclerotiorum. In this study, we identified and cloned the histone methyltransferase Defective in methylation 5 (Dim5) in S. sclerotiorum, which encodes a protein containing a typical SET domain. SsDim5 was found to be dynamically expressed during infection. Knockout experiment demonstrated that deletion of SsDim5 reduced the virulence in Ssdim5-1/Ssdim5-2 mutant strains, accompanied by a significant decrease in H3K9 trimethylation levels. Transcriptomic analysis further revealed the downregulation of genes associated with mycotoxins biosynthesis in SsDim5 deletion mutants. Additionally, the absence of SsDim5 affected the fungus's response to oxidative and osmotic, as well as cellular integrity. Together, our results indicate that the H3K9 methyltransferase SsDim5 is essential for H3K9 trimethylation, which regulating fungal virulence to host plants through impacting on mycotoxins biosynthesis, and the response to environmental stresses in S. sclerotiorum.

Coagulase negative Staphylococci (CoNS) are reported to be responsible for 50-60% of bloodstream infections in very preterm (&lt;1500 g) infants in Neonatal Intensive Care Units (NICU). Staphylococcus capitis is an increasingly prevalent pathogen in neonatal setting, frequently causing central-line associated bloodstream infections (CLABSI) that can be difficult to eradicate. CVC removal versus in situ treatment of CoNS CLABSIs is a matter of debate, with no clear consensus emerging in the existing literature. We revised all S. capitis CLABSIs in our NICU between 2019 and 2022, focusing on the role of catheter removal for eradication. Among 25 cases, 17 CVCs were removed after diagnosis, leading to a 76.5% eradication rate in this group. 3 infants had a persistently positive blood culture after CVC substitution. A new catheter was than inserted after a 48-hours washout period, resulting in resolution of the infection. Only 2 of 8 patients (25%) who retained the catheter after diagnosis, underwent infection eradication with antibiotic therapy alone. Catheter removal, when feasible, seems to be the most effective strategy to eradicate S. capitis CLABSIs, sometimes even requiring a 48-hours washout period before reinsertion. Further studies on this subject are needed to better standardize the management of this kind of infections.

S-adenosylmethionine (SAM) is considered to be a useful therapeutic agent for degenerative cartilage diseases, although its mechanism is not clear. We previously found that polyamines stimulate expression of differentiated phenotype of chondrocytes. We also found that cellular communication network factor 2 (CCN2) played a huge role in the proliferation and differentiation of chondrocytes. Therefore, we hypothesized that polyamines and CCN2 could be involved in the chondroprotective action of SAM. In this study, we initially found that exogenous SAM enhanced proteoglycan production but not cell proliferation in human chondrocyte-like cell line-2/8 (HCS-2/8) cells. Moreover, SAM enhanced gene expression of cartilage-specific matrix (aggrecan and type II collagen), Sry-Box transcription factor 9 (SOX9), CCN2 and chondroitin sulfate biosynthetic enzymes. Blockade of the methionine adenosyltransferase 2A (MAT2A) enzyme catalyzing intracellular SAM biosynthesis restrained the effect of SAM on chondrocytes. The polyamine level in chondrocytes was higher in SAM-treated culture than control culture. Additionally, alcian blue staining and RT-qPCR indicated that the effects of SAM on the production and gene expression of aggrecan were reduced by the inhibition of polyamine synthesis. These results suggest that the stimulation of polyamine synthesis and gene expression of chondrogenic differentiation factors, such as CCN2, account for the mechanism underlying the action of SAM on chondrocytes.

Cognitive impairment in patients with Parkinson’s disease (PD), which may occur in various severities, represents one of the commonest and most disabling non-motor manifestations during the course of the disease, causing a negative impact on patients’ quality of life. Eventually, it becomes a burden for the family members and/or the caregivers of patients, as it progresses to PD dementia. Current pharmacological treatments for cognitive impairment in PD exhibit partial efficacy, while novel effective therapeutic strategies are required. Accumulating preclinical and clinical evidence shows that several agents may provide beneficial effects on patients with PD and cognitive impairment, including ceftriaxone, ambroxol, intranasal insulin, nilotinib, atomoxetine, mevidalen, blarcamesine, prasinezumab, SYN120, ENT-01, NYX-458, GRF6021, fosgonimeton, INT-777, Neuropeptide S, silibinin, osmotin, cordycepin, huperzine A, fibroblast growth factor 21, Poloxamer 188, ginsenoside Rb1, thioredoxin-1, tangeretin, istradefylline, and Eugenia uniflora. Potential underlying mechanisms include the inhibition of a-synuclein aggregation, improvement of mitochondrial function, regulation of synaptic plasticity, impact on gut-brain axis, modulation of neuroinflammation, upregulation of neurotrophic factors, as well as cholinergic, dopaminergic, serotoninergic and norepinephrine neurotransmission. In this overview, we aim to cover the clinical aspects of PD associated cognitive impairment, highlighting recent evidence on emerging treatment approaches that are currently under investigation at a preclinical and clinical level.

Several studies have shown that tapering or stopping disease-modifying anti-rheumatic drugs (DMARDs) in rheumatoid arthritis (RA) patients in sustained remission is feasible. However, tapering/stopping bears the risk of decline in physical function as some patients may relapse and face increased disease activity. Here we analysed the impact of tapering or stopping DMARD treatment on the physical function of RA patients. The study was a posthoc analysis of physical functional worsening for 282 patients with RA in sustained remission tapering and stopping DMARD treatment in the prospective randomized RETRO study. HAQ and DAS-28 scores were determined in baseline samples of patients continuing DMARD (arm 1), tapering their dose by 50% (arm 2), or stopping after tapering (arm 3). Patients were followed over 1 year, and HAQ and DAS-28 scores were evaluated every 3 months. The effect of treatment reduction strategy on functional worsening was assessed in a recurrent-event Cox regression model with a study-group (control, taper, taper/stop) as the predictor. 282 patients were analysed. In 58 patients, functional worsening was observed. The incidences suggest a higher probability of functional worsening in patients tapering and/or stopping DMARDs, which is likely due to higher relapse rates in these individuals. At the end of the study, however, functional worsening was similar among the groups. Point estimates and survival curves show that functional decline after tapering or stopping DMARDs in RA patients with stable remission is small and related to relapses but to on overall functional decline.

Chloride (Cl-) is applied in coffee in rates as a “macronutrient” due that potassium (K+) is one of the most demanded nutrients by the coffee plant, and the potassium muriate (KCl) bases fertilizer is one the most used by the coffee growers. Does not exist scientific evidence that addresses the question regarding with which is the influences of the Cl- applied in the K fertilization base on MOP on coffee growth, nutrient uptake, and nitrogen use efficiency (NUE). Over four years, two trials were conducted on greenhouse and field conditions to address these questions. The trials set up were designed to test the influence of increased Cl- and reduced S rates on biomass accumulation, nutrient uptake, and NUE. A significant effect of the Cl- rates on growth was observed under greenhouse conditions but a non-significant effect on yield under field conditions. Cl- and S significantly influence the NUE in coffee. The result allows us to conclude that Cl- rates need to be balanced with S rates and that Cl- applied as a macronutrient can improve the NUE in coffee when those rates do not exceed 180 mg. L-1 Cl- and 80 mg.L-1 S in the greenhouse and 150 kg.ha-1.year-1 Cl- and 50 kg. ha-1.year-1 S in field conditions. In practical terms, coffee farmers need to balance the K base fertilizers sources to improve the nutrient use efficiency, especially the NUE.

INTRODUCTION: Superficial cutaneous bacterial infections have a high incidence in geriatric patients. The most implicated pathogens are gram-positive cocci (Staphylococcus aureus, Streptococcus pyogenes) while gram-negative germs are also implicated. Resistances to common topical antibiotics (mupirocin, fusidic acid) require alternatives to gram-positive and gram-negative microorganisms.Ozenoxacin cream for topical use (non-fluorinated bactericidal quinolone), in other countries and with other galenics, is indicated in children older than 6 months and in adults as a treatment of superficial bacterial infections, such as acne. In Spain, ozenoxacin cream is indicated only for non-bullous impetigo; scientific evidence show effectiveness also in other superficial skin bacterial infections.A cases series of clinical use of ozenoxacin in bacterial superficial skin infections in geriatric patients (institutionalized or community dwelling) is presented.METHODS: Multicenter case series (March-August 2022) of bacterial superficial skin infections treated with ozenoxacin cream (10mg/g every 12h, 5days); data from medical records (controls: 1-3-5 days), after obtaining informed consent (use of data and images).RESULTS: Series of 28 patients (mean age: 84,79) from nine nursing homes and one outpatient geriatric service, including acute and subacute/chronic cases.In all cases treatment was ozenoxacin 10mg/g topical cream applied every 12 hours for 5 days according to medical prescription (except for one case in which 3 days were enough for complete healing and another case treated for 10 days).Results showed complete healing in all 20 acute cases and significant clinical improvement in all subacute/chronic cases (with complete healing in one of them). Professionals scored the effectiveness in acute cases as a mean 4.5 points (maximum score: 5, p<.0001) and in subacute/chronic cases as 3.8 points (p=.010).There was no skin irritation or other adverse effects in anyone of the patients, and clinical improvement of pain, itching and other symptoms was observed, suggesting an anti-inflammatory effect. DISCUSSION AND CONCLUSIONS: Our results seem to demonstrate the effectiveness and tolerability of ozenozacin cream in bacterial infections other than non-bullous impetigo. Ozenoxacin cream is indicated only for the treatment of non-bullous impetigo; however, it is also shown to be effective, both in the scientific evidence and in our case series, for other superficial bacterial skin infections, both acute and subacute/chronic, suggesting the opportunity for clinical studies with an experimental design to evaluate the findings of clinical practice and to be able to have a therapeutic alternative to compensate for the complications of the appearance of resistance.

We have proposed a simple algorithm to retrieve the total ozone column and snow properties (spectral albedo and effective light absorption path) using the high spatial resolution single – view MSI/S-2 measurements over Antarctica.

This study was designed to assess the reliability of geographic information using satellite image information in ungauged basins. For this, this study constructed geographic information using actual gauged data and satellite information data and conducted runoff analysis through S-RAT, a rainfall–runoff model, and performed the comparison and analysis of geographic information and runoff data. For actual gauged data, the gauged geographic information of the Water Resources Management Information System (WAMIS) was collected, and for satellite information, the image information of moderate-resolution imaging spectroradiometer (MODIS) observation sensor loaded on Terra Satellite was collected. As analysis areas, three basins where mountains occupy more than 80% and another three basins where urban areas occupy more than 7% in the Han River basin were selected. According to the analysis result, the gauged information and satellite image information showed great difference in runoff, maximum 50% in peak flood and maximum 17% in total flood, in the rivers with many urban areas, while the runoff difference in the rivers with many mountains showed maximum 13% in peak flood and 4% in total flood. What showed the greatest difference in image information was land use, and it turned out that the MODIS satellite recognized the urban rivers as cities for more than maximum 60% compared to WAMIS-gauged data. Meanwhile, in the forest area, the MODIS satellite image showed error of less than 5% of the WAMIS-gauged data, which indicates that it has higher applicability in Mountain Rivers.

Family Fabaceae traditionally serves as food and herbal remedies source. Several plants are already used for menopausal symptoms treatment based on a presence of typical secondary metabolites, isoflavones. Beside soybean and clovers, isoflavones could be produced by other plants or in vitro cultures. This type of production can be further enhanced by elicitation that stimulates metabolites biosynthesis via stress reaction. Vanadium compounds have been already described as potential elicitors and the aim of this study was to determine an impact of NH₄VO₃ and VOSO₄ solutions on isoflavones production in Genista tinctoria L. cell cultures. The significant increase of isoflavones content such as genistin, genistein or formononetin was measured in a nutrient medium or dry mass after NH₄VO₃ treatment for 24 or 48 hours. The possible transport mechanism of isoflavones was also evaluated. An incubation with different transport inhibitors prior elicitation took effect on isoflavones content in the medium. However, there was non-ended result for particular metabolites such as genistein and daidzein, where ABC or alternatively MATE proteins can participate. Possible elicitation by some inhibitors was also discussed as result of their pleiotropic effect. Despite this outcome, the determining of transport mechanism is important step for identification of specific transporter.

In this paper, we propose an extension of the Planck distribution function derived from the Boltzmann principle. That is, we consider extending Planck's law with new distribution functions. In addition, using ideas applied to the expansion of the Planck distribution function, Von Koch's inequality is derived without using the Riemann hypothesis, showing that the abc conjecture is negated. We also describe some challenges for the future. Namely, we will discuss that Entropy is related to dynamical systems described by logistic function models, such as the bacterial and the population growth.

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.

In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.

Let a,b,c be positive integers such that a²+b²=c², 2|b,gcd(a,b)=1. In 1956, Jesmanowicz conjectured that for any positive integer w, the only solution of (aw)^x+(bw)^y=(cw)^z in positive integers is (x, y, z) = (2, 2, 2). In this paper, based on Gaussian integer ring, we show that Je$\acute{s}$manowicz' conjecture is true for any positive integer

VITEK MS PRIME (bioMerieux), a newly developed Matrix-assisted laser desorption ionization time-of-flight mass spectrometry (MALDI-TOF MS) system, alongside VITEK PICKME Pen (PICKME), offers easy sample preparation for bacteria and yeast. VITEK MS PRIME also offers two software platforms for filamentous fungi: the IVD database and the RUO database. Our study evaluated its identification agreement on 320 clinical isolates of bacteria and yeasts, comparing PICKME and traditional wooden toothpick sampling techniques against ASTA Mi-croIDSys Elite results. Additionally, we assessed the IVD (v3.2) and SARAMIS (v4.16) RUO data-bases on 289 filamentous fungi against molecular sequencing. The concordant rates for spe-cies-level identification of bacteria and yeasts were about 89.4% (286/320) between the PICKME and wooden toothpick, about 83.4-85.3% between VITEK MS PRIME and ASTA MicroIDSys Elite. Retesting with PICKME improved concordance to 91.9%. For filamentous fungi, species-level identification reached 71.3% with the IVD database and 85.8% with RUO, which significantly enhanced basidiomycetes' identification from 35.3% to 100%. Some strains in the IVD database, like Aspergillus vesicolor, Exophiala xenobiotica, and Nannizzia gypsea failed to be identified. VITEK MS PRIME with PICKME offers reliable and efficient microorganism identification. For fila-mentous fungi, combining the use of the RUO database can be beneficial, especially for basidi-omycetes.

In this paper for every number field K generated by a root α of a trinomial x⁷ + ax + b ∈ Z[x] and for every prime integer p, we calculate ν_p(i(K)), the highest power of p dividing the index i(K) of the field K. In particular, we calculate the index i(K). As application, when the index of K is not trivial, then K is not monogenic.

In this work we looked for a stable and accurate procedure to perform feature selection in datasets with a much higher number of predictors than individuals, as in Genome-Wide Association Studies. Due to the instability in feature selection when many potential predictors are measured, a variable selection procedure is proposed that combines several replications of shrinkage regression models. A weighted formulation is used to define the final predictors. The procedure is applied to investigate Single Nucleotide Polymorphisms (SNPs) predictors associated to Alzheimer’s disease in the Alzheimer’s disease Neuroimaging Initiative (ADNI) dataset. Two data scenarios are investigated: one considering only the set of SNPs and another with the covariates age, sex, educational level and APOE4 genotype. The SNP rs2075650 and the APOE4 genotype are given as risk factors for AD, which is in line with the literature, and other four new SNPs are pointed, opening new hypotheses for in vivo analyses. These experiments demonstrate the potential of the new method for stable feature selection.

Adeno-associated viral (AAV) vectors can be used for gene delivery. AAV.CAP-Mac was recently developed; it can cross the blood-brain barrier and transduce cells throughout the CNS. However, some brain regions were not transduced in adult rhesus monkeys. Additionally, AAV vectors can only package 5 kb of DNA. Also, AAV vectors may be genotoxic and cytotoxic, especially at high doses. Finally, AAV vectors are very expensive to produce at sufficiently high titers for treatment. Off-the-shelf cell-based delivery systems wherein the cells can infiltrate the target tissue and be hyper-motile would be ideal. Also, mRNA-based gene editing would be a transient treatment, and thus be much safer.

Let R be a commutative ring with identity and m, n be positive integers. In this paper, we introduce the class of (m,n)-prime ideals which lies properly between the classes of prime and (m,n)-closed ideals. A proper ideal I of R is called (m,n)-prime if for a,b∈R, a^{m}b∈I implies either aⁿ∈I or b∈I. Several characterizations of this new class with many examples are given. Analougus to primary decomposition, we define the (m,n)-decomposition of ideals and show that every ideal in an n-Noetherian ring has an (m,n)-decomposition. Furthermore, the (m,n)-prime avoidance theorem is proved.

Abiotic stresses, including drought, salinity, cold, heat, and heavy metals, extensively reduce global agricultural production. Approaches such as conventional breeding and transgenic breeding have been widely used to cope with these environmental stresses. The clustered regularly interspaced short palindromic repeat- Cas (CRISPR/Cas) based gene-editing tool has revolutionized due to its simplicity, accessibility, adaptability, flexibility, and wide applicability. This system has a great potential to build up crop varieties with enhanced tolerance against abiotic stresses. In this review, we summarize the most recent findings on understanding the mechanism of abiotic stress response in plants and the application of CRISPR/Cas mediated gene-editing system towards enhanced tolerance to drought, salinity, cold, heat, and heavy metals stresses. Furthermore, in this review, we highlighted the recent advancements in prime editing and base editing tools for crop improvement.

Therapeutic vaccine studies should be designed to elicit durable, high magnitude, and efficacious T cell responses, all of which can be impacted by the choice of vaccination schedule. Here, we compare different prime-boost intervals (PBI) in a human papillomavirus (HPV) model using HPV16E6E7 Venezuelan equine encephalitis virus replicon particle (VRP) vaccination to address the optimal boosting schedule, quality of immune response, and overall in vivo efficacy. Six different vaccine regimens were tested with each group receiving booster vaccinations at different time intervals. Analysis of T-cell responses demonstrated a significant HPV16 E7 specific CD8+T cell response with minimally a one-week PBI between antigen re-exposure. Significant E7-specific in vivo cytotoxicity was also observed with longer PBIs. Additionally, longer PBIs led to an enhanced memory recall response to tumor challenge, which correlated with differential expansion of T cell memory subsets. Our findings imply that when using alphavirus vector platforms as a vaccination strategy, a one-week PBI is sufficient to induce high magnitude effector T cells with potent anti-tumor activity. However, longer PBIs lead to enhanced long-term protective anti-tumor immunity. These findings have implications for therapeutic vaccine clinical trials in which shorter intervals of prime-boost regimens may lead to suboptimal durable immune responses.

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.

In recent years, marine natural products have become one of the most important resources of novel lead compounds for critical diseases associated with age. Spirulina, a dietary supplement made from blue-green algae (cyanobacteria: scientific name Arthrospira platensis), is particularly rich in phycocyanin, a phycobiliprotein, which accounts for up to 20% of this cyanobacterium’s dry weight and is considered responsible for its anti-cancer, anti-inflammatory and antioxidant activities. Although the anti-aging activity of phycocyanin has been investigated, how exactly this compound works against aging remains elusive. Aim of our research is to use the yeast Saccharomyces cerevisiae as a model organism to investigate the anti-aging properties of phycocyanin from A. platensis. Our results show that phycocyanin has a powerful anti-aging effect, greatly extending the chronological life span of yeast cells in a dose-dependent way, being the effect pronounced also when cells were grown in SD medium under calorie restriction conditions (0.2% glucose). Both ROS and accumulation of dead cells were followed by staining chronologically aged cells with dihydrorhodamine 123 (DHR123) and propidium iodide (PI). Interestingly, we found that most of the aged phycocyanin treated cells, which were unable to form colonies, were actually ROS+/PI–. Finally, we show that the moment in which phycocyanin is added to the culture does not substantially influence its effectiveness in counteracting chronological aging.

ABSTRACTIntroduction and Purpose: Nurses are expected to be competent in practice based on the domain of standards and interpersonal soft skills (ISS). Nurses are faced with inadequate physical assessment 28%, formulating diagnoses 56%, plans 34%, implementation 31%, evaluation 37,5%, and communication skills 41%. Aims to develop an ISS learning model based on transformative learning theory and digitalization (TLTD) to improve nurses’ competencies. Method: Used Explanatory cross-sectional involved 190 practitioner nurses. Variables of individual characters (X1), facilities (X2), Social environment support/SES (X3), TLTD (X4), ISS (X5), and nursing competencies (Y) were measured. Data was collected using a checklist questionnaire, conducted on 6 June to 10 August 2022 at Dili, Baucau, and Maliana hospitals. Used descriptive and inferential analysis with SEM-PLS. Result: Five of the 11 hypotheses of statistical p-value < 0,05 and T-Test > 1,96, including X2>X4, X3>X5, X4>X5, and X5>y, to form ISS learning model. The characteristic of respondents were 81,8% young adults, 67,9% women, 57,8% undergraduates, judging the previous training 35% was unsuccessful, and 45,8% did not meet expectations. Learning facilities that are still lacking include policies 23,7%, curriculum 23,4%, guideline 22,7%, modules 27,9%, infrastructure 20,3%, social environment support 24,2% low, organizational support, 30,0% low peer support and 26,3% low family support. The average TLTD is 25,3% to 34,2%, ISS 22,1% to 30,5%, and nurse competence 25,3% to 30,5%.Suggestion: Result of the study become base to improve nurse’s competencies. Conclusion: Learning model was formed by facilities, SES, TLTD, ISS, and nurses’ competencies.

Background: Takayasu’s arteritis is a rare type of vasculitis, with severe complications like stroke, ischemic heart disease, pulmonary hypertension, secondary hypertension, aneurysms. Diagnosis is conducted by clinical and angiographic criteria. Treatment is medical and surgical, but unfortunately, the outcome is reserved. Case presentation: A 34- year- old Caucasian women had an ischemic stroke (2009). She was diagnosed with Takayasu’s arteritis and she received treatment with methotrexate, prednisolone, antiplatelet agents, with a mild improvement of clinical state. After 5 years (2014) she associated ascending aorta aneurysm, pulmonary hypertension, mild aortic regurgitation. The surgical treatment solved both ascending aorta aneurysm and left carotid artery stenosis (ultrasound in 2009 and computed tomography angiogram in 2014). Morphopathology revealed typical appearance for Takayasu’s arteritis. Tumor necrosis factor inhibitors (TNF-inhibitors) were associated to methotrexate. At 48 years (2023) she developed coronary heart disease (angina, electrocardiogram); echocardiography revealed severe pulmonary hypertension; angiography described normal coronary arteries, abdominal aorta pseudoaneurysm and arterial-venous fistula, with origin in right coronary artery and drainage on medium pulmonary artery. The patient refused surgical/ interventional treatment; she received again TNF- inhibitors, methotrexate, antiplatelet agents, statins. Conclusions: This case report presents us a severe form of Takayasu’s arteritis. We consider that morphopathology had a great importance in revealing to clinicians the typical appearance and the stadialization of inflammatory arterial process: acute or chronic. The verdict of morphopathologist was chronic phase, with acute relapses, so we decided that immunosuppressive treatment was still necessary.

Machine learning approaches are currently used to understand or model complex physical systems. In general, a substantial number of samples must be collected to create a model with reliable results. However, collecting numerous data is often relatively time-consuming or expensive. Moreover, the problems of industrial interest tend to be more and more complex and depending on a high number of parameters. High dimensional problems intrinsically involve the need of large data amount through the curse of dimensionality. That is why, new approaches based on smart sampling techniques are investigated to minimize the number of samples to be given to train the model, such as Active Learning methods. Here, we propose a technique based on a combination of Fisher information matrix and of Sparse Proper Generalized Decomposition that enables the definition of a new Active Learning informativeness criterion in high dimensions. We provide examples proving the performances of this technique on a theoretical 5D polynomial function and on an industrial crash simulation application. The results prove that the proposed strategy over-perform the usual ones.

Keywords: Parkinson’s disease; sleep disorders; GBA; Parkin

Hypsizygus marmoreus has become one of the most popular edible mushrooms due to its high nu-tritional and economic value. Previous researchers found that Serratia odorifera could promote the growth of H. marmoreus by producing and secreting some of its inducers. However, the specific mechanism of action was still unclear. In this study, we found that exogenous addition of sterile fermentation filtrate (HZSO-1), quorum sensing (QS signaling molecules, 3-oxo-C6-HSL, cy-clo(Pro-Leu), and cyclo(Tyr-Leu) could significantly promote the growth of H. marmoreus, increase the number of clamp junctions, and the diameter of mycelium (P < 0.05). In addition, non-targeted metabolomic analysis has revealed that 706 metabolites were detected in the treated group. Of these, 307 metabolites were significantly different (P < 0.05). Compared with the control, 54 and 86 metabolites were significantly increased and decreased in the HZSO-1 group, respec-tively (P < 0.05). We speculated that the sterile fermentation filtrate of S. odorifera could mediate the carbohydrate and amino acid metabolism of H. marmoreus by influencing the pentose phosphate pathway (PPP) to increase the energy supply for the growth and development of the mycelium. The above results will further reveal the growth-promoting mechanism of S. odorifera on H. mar-moreus.

Based on the high-precision quantitative measurement ability, the S-band subsystem of China's high- resolution aviation system carried out the agricultural application test for the first time in Jilin elm, China. The experiment is mainly carried out in combination with vegetation growth, soil moisture content inversion, wheat straw returning and ground feature classification. Through the design of quantitative measurement scheme, the results of different straw coverage and observation at different times are compared, which shows the prospect of S-band full polarization synthetic aperture radar system in the field of agricultural application.

A problem involving the government's inspection of coins in Lower Slobbovia is discussed in the \emph{American Mathematical Monthly}. It is desirable to classify and correct counterfeit coins by utilizing the fewest possible measures. However, previous article only proves the existence of the solution, which does not give a practical solution to the problem. This note provides effective methods to achieve the identification of coiners using dirac delta function and singularity function. Moreover, unit-order construction of continuum mappings and discretization of unique basis vectors with semi-expansion are established in S-base space.

Autophagy is a highly conserved catabolic process in eukaryotic cells. Reactive nitrogen species play roles as inductors and signaling molecules of autophagy. A key mechanism of NO-mediated signaling is S-nitrosylation, a posttranslational modification (PTM) of proteins at cysteine resi-dues. In the present work we analyzed the patterns of protein S-nitrosylation during the induc-tion of autophagy in Triticum aestivum roots. The accumulation of S-nitrosylated proteins in the cells during autophagy induced by KNO2 and antimycin A was visualized using monoclonal an-tibodies by Western blot analysis, and proteins were identified using a standard bottom-up pro-teomics approach. Protein S-nitrosylation is a labile and reversible PTM, and therefore SNO group can be lost during experimental procedures. Subsequent bioinformatic analysis using predictive algorithms and protein-ligand docking showed that identified proteins possess hypothetical S-nitrosylation sites. Analyzing protein-protein interaction networks enabled us to discover the targets that can directly interact with autophagic proteins, and those that can interact with them indirectly via key multifunctional regulatory proteins. In this study, we show that S-nitrosylation is a key mechanism of NO-mediated regulation of autophagy in wheat roots. A combination of in silico predictive algorithms with a mass spectrometry analysis provides a targeted approach for the identification of S-nitrosylated proteins.

Atherosclerosis (AS) is a chronic progressive disease caused by various factors, and causes various cerebrovascular and cardiovascular diseases (CVDs). Reducing the plasma levels of low-density lipoprotein-cholesterol (LDL-C) is the primary goal in preventing and treating AS. Proprotein Convertase Subtilisin/Kexin Type 9 (PCSK9) plays a crucial role in regulating LDL-C metabolism. Panax notoginseng has potent lipid-reducing effects and protects against CVDs, and its saponins induce vascular dilatation, inhibit thrombus formation, and are used in treating CVDs. However, the anti-AS effect of the secondary metabolite, 20(S) -protopanaxatriol (20(S)-PPT), remains unclear. In this study, the anti-AS effect and molecular mechanism of 20(S)-PPT were investigated in vivo and in vitro by western blotting, real time-polymerase chain reaction (RT-PCR), Enzyme-linked Immunosorbent Assay (ELISA), immunofluorescence staining, and other assays. The in vitro experiments revealed that 20(S)-PPT reduced the levels of PCSK9 in the supernatant of HepG2 cells, upregulated low density lipoprotein receptor (LDLR) protein levels, promoted LDL uptake by HepG2 cells, and reduced PCSK9 mRNA transcription by upregulating the levels of FoxO3 protein and mRNA and decreasing the levels of HNF1α protein and mRNA. The in vivo experiments revealed that 20(S)-PPT upregulated aortic αSMA expression, increased the stability of atherosclerotic plaques, and reduced aortic plaque formation induced by a high-cholesterol fed in ApoE-/- mice (HCF group). Additionally, 20(S)-PPT reduced the aortic expression of CD68, reduced inflammation in the aortic root, and alleviated the hepatic lesions in the HCF group. The study revealed that 20(S)-PPT inhibited LDLR degradation via PCSK9 to alleviate AS.

Sepsis is a serious and life-threatening medical emergency associated with dysregulated host immune responses to infection. Like cerebral vascular or acute cardiovascular incidents, sepsis is considered a time-dependent condition having severe and long-term consequences on human health. Apart from organ support, prompt administration of appropriate antimicrobial therapy is crucial to limit the burden of complications related to sepsis in ICU patients. The management of septic patients requires comprehensive and multi-disciplinary strategies for an adequate diagnosis. Most of the ICU population receives empirical antibiotic therapy without having a confirmed diagnosis. The misuse of antibiotics in intensive care units may increase the possibility of developing multidrug resistance along with considerable ecological side effects. The first doses of empirical anti-microbial therapy are slightly higher, regardless of the presence or absence of organ dysfunction, which may upregulate the production of circulating pro-and-anti-inflammatory mediators, having negative effects on the general well-being of the patients. This notion supports the introduction of individualized antimicrobial approaches based on local patterns of resistance to ensure the appropriate dosage of empirical therapy, as well as to limit the emergence of multidrug resistance in advanced-care patients. The adequacy and treatment duration must be viewed at regular intervals for effective de-escalation, and novel diagnostic approaches must be introduced to improve the quality of care in the ICU population.

Till date there are three full length COVID 19 virus genome sequences available from India. The earlier two were reported from Kerala, Southern India and the more recent one has been reported from Gujarat, western part of India. In this paper we report two novel mutations in the Spike protein sequence of Gujarat’s isolate. These mutations are based on comparison with the original Wuhan sequence. The two mutations have been found to be located just upstream and downstream of the receptor binding domain (RBD). Out of these two one has also been found to affect the secondary structure of the S1 domain. Since both of these mutations lie near the receptor binding domain, they might influence the spike receptor interactions by changing the conformation of the spike protein S1 domain. These mutations are uniquely placed and might be important in the context of vaccine engineering and therapeutic interventions.

Staphylococcus aureus (S. aureus) is recognized worldwide as one of the major agents of dairy cow intra-mammary infections. This microorganism can express a wide spectrum of pathogenic factors used to attach, colonize, invade and infect the host. The present study evaluated 120 isolates from eight different countries that were genotyped by RS-PCR and investigated for 26 different virulence factors to increase the knowledge on the circulating genetic lineages among the cow population with mastitis. New genotypes were observed for South African strains while for all the other countries new variants of existing genotypes were detected. For each country, a specific genotypic pattern was found. Among the virulence factors, fmtB, cna, clfA and leucocidins genes were the most frequent. The sea and sei genes were present in seven out of eight countries; seh showed high frequency in South American countries (Brazil, Colombia, Argentina), while sel was harboured especially in one Mediterranean country (Tunisia). The etb, seb and see genes were not detected in any of the isolates, while only two isolates were MRSA (Germany and Italy) confirming the low diffusion of methicillin resistance microorganism among bovine mastitis isolates. This work demonstrated the wide variety of S. aureus genotypes found in dairy cattle worldwide. This condition suggests that considering the region of interest might help to formulate strategies for reducing the infection spreading.

With the aim to develop novel scaffolds for sustained release of drugs, we initially developed an easy approach for the synthesis of α,ω-homobifunctional mercaptoacyl poly(alkyl oxide)s. This was based on the esterification of the terminal hydroxyl groups of poly(alkyl oxide)s with suitably S-4-methoxytrityl (Mmt) protected mercapto acids, followed by removal of the acid labile S-Mmt group. This method allowed the efficient synthesis of the title compounds in high yield and purity, which were further used in the development a thioether cross-linked liposome scaffold, by thia-Michael reaction of the terminal thiol groups with preformed nano-sized liposomes bearing maleimide groups on their surface. The reaction process was followed by 1H-NMR, using a Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion NMR experiment (1H-NMR CPMG), which allowed real-time monitoring and optimization of the reaction process. The thioether cross-linked liposomal scaffold that was synthesized was proven to preserve the nanosized characteristics of the initial liposomes and allowed sustained release of calcein (which was used as a chromophore), providing evidence for the efficient synthesis of a novel drug release scaffold consisted of nanoliposome building blocks.

The editorial explores the realm of emerging translational research in neurology and psychiatry, providing insights into various subjects, including neurodegenerative disorders and innovative therapeutic methods. The main objective is to study neurological and psychiatric disorders, such as Alzheimer's disease, with a particular emphasis on techniques for neural regeneration and repair. The editorial highlights the importance of taking a comprehensive approach to studying and treating complex neurological and psychiatric conditions. This involves thoroughly reviewing research papers on the causes, development, biomarkers, and treatment options for these conditions. The editorial emphasizes the necessity of using multidisciplinary and integrative methods to gain a deeper understanding and improve the treatment of these conditions. The development of an animal model for recurrent primary dysmenorrhea showcases the innovative techniques employed in the investigation of gynecological disorders, illustrating the capacity of translational research to connect fundamental scientific knowledge with practical medical applications. The cooperative endeavors of researchers and clinicians emphasized in this editorial lay the foundation for revolutionary advancements that hold the potential to enhance outcomes for individuals afflicted with neurological and psychiatric disorders globally.

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.

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.