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.

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.

Let R be a commutative ring and m, n be positive integers. We define a proper submodule N of an R-module M to be (m,n)-closed if for r∈R and b∈M, r^{m}b∈N implies rⁿ∈(N:_{R}M) or b∈N. This class of submodules lies properly between the classes of prime and primary submodules. Many characterizations, properties and supporting examples concerning this class of submodules are provided. The notion of (m,n)-modules is introduced and characterized. Furhermore, the (m,n)-closed avoidance theorem is proved. Finally, the (m,n)-closed submodules in amalgamated modules are studied.

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.

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.

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

Let  β= (((24!)!)!)!, and let {${\mathcal P}_{n^2+1}$} denote the set of all primes of the form {$n^2+1$}. Let ${\mathcal M}$ denote the set of all positive multiples of elements of the set {${\mathcal P}_{n^2+1} \cap (\beta,\infty)$}. The set {${\mathcal X}=\{0,\ldots,\beta\} \cup {\mathcal M}$} satisfies the following conditions: (1) ${\rm card}({\mathcal X})$ is greater than a huge positive integer and it is conjectured that ${\mathcal X}$ is infinite, (2)} we do not know any algorithm deciding the finiteness of ${\mathcal X}$, (3)~a~known and short algorithm for every {$n \in N$} decides whether or not {$n \in {\mathcal X}$}, (4) a known and short algorithm returns an integer~$n$ such that ${\mathcal X}$ is infinite if and only if ${\mathcal X}$ contains an element greater than $n$. The following problem is open: {\em simply define a set {${\mathcal X} \subseteq N$} such that ${\mathcal X}$ satisfies conditions (1)-(4), and \underline{we do not know any representation of~~${\mathcal X}$~~as a finite union of sets whose definitions are simpler than} \underline{the definition of ${\mathcal X}$}} {\tt (5)}. Let {$f(1)=2$}, {$f(2)=4$}, and let {$f(n+1)=f(n)!$} for every integer {$n \geqslant 2$}. For a positive integer $n$, let {$\Psi_n$} denote the following statement: {\em if a system of equations ${\mathcal S} \subseteq \Bigl\{x_i!=x_k: i,k \in \{1,\ldots,n\}\Bigr\} \cup \Bigl\{x_i \cdot x_j=x_k: i,j,k \in \{1,\ldots,n\}\Bigr\}$ has only finitely many solutions in positive integers \mbox{$x_1,\ldots,x_n$}, then each such solution \mbox{$(x_1,\ldots,x_n)$} satisfies {$x_1,\ldots,x_n \leqslant f(n)$}.} We prove that for every statement $\Psi_n$ the bound {$f(n)$} cannot be decreased. The author's guess is that the statements {$\Psi_1,\ldots,\Psi_9$} are true. We prove that the statement $\Psi_9$ implies that the set ${\mathcal X}$ of all {non-negative} integers $k$ whose number of digits belongs to {${\mathcal P}_{n^2+1}$} satisfies conditions {\tt (1)-(5)}.

An extensive thermodynamic study of N-methylformamide (CAS RN: 123-39-7) and N,N-dimethylformamide (CAS RN: 68-12-2), is presented in this work. The liquid heat capacities of N-methylformamide were measured by Tian–Calvet calorimetry in the temperature interval (250 – 300) K. The vapor pressures for N-methylformamide and N,N-dimethylformamide were measured using static method in the temperature range 238 K to 308 K. The ideal-gas thermo-dynamic properties were calculated using a combination of the density functional theory (DFT) and statistical thermodynamics. A consistent thermodynamic description was developed using the method of simultaneous correlation, where the experimental and selected titerature data for vapor pressures, vaporization enthalpies, and liquid phase heat capacities and calculated ide-al-gas heat capacities are treated together to ensure overall thermodynamic consistency of the results. Resulting vapor pressure equation is valid from the triple point to the normal boiling point temperature.

The aim of this paper is to investigate the amenability modulo an ideal of Banach algebras with emphasis on applications to homological algebras. In doing so, we show that amenability modulo an ideal of A^** implies amenability modulo an ideal of A. Finally, for a large class of semigroups, we prove that l¹(S)^** is amenable modulo Iσ^** if and only if an appropriate group homomorphic image of S is finite where Iσ is the closed ideal induced by the least group congruence σ.

Crop domestication and breeding considerably increased productivity over centuries, but simultaneously involved unconscious selection against ‘selfish plant behavior’. Paradoxically, modern-day crop breeding largely enhances individual plant-fitness. As agriculture relies on community performance, embracing an “Agroecological Genetics and Genomics” viewpoint might maximize communal yield by matching crop genotypes to target environments.

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.

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.

Materials based on platinum metals with very good catalytic activity were tested in the reduction of p–nitrophenol (pNP) to p–aminophenol (pAP). The majority of presented catalytic materials are based on the adsorption of p–nitrophenol on the surface of the catalyst simultaneously with molecular hydrogen, coming from sodium borohydride in an aqueous medium, which reduces it. In the present paper, a catalytic material based on osmium dispersed in n–decanol or n–dodecanol is presented, which also works as an emulsion membrane, for the absorption of p–nitrophenol and molecular hydrogen at the n–alcohol aqueous solution interface. The hydrogenation of p–nitrophenol is carried out in a reaction and separation column in which the acid receiving phase emulsion is dispersed in the osmium nanodispersion, in n–alcohols. This emulsion circulates from the base of the column to its upper part in co-current or counter-current with the source phase consisting of p–nitrophenol and sodium borohydride. Experiments show that the circulation of counter-current phases is superior to that in co-current, and the emulsion based on n–decanol is more efficient than the one based on n–dodecanol. The increase in the pH difference between the source and receiving phases leads to the increase in the conversion of p–nitrophenol to p–aminophenol. The efficiency of separation of the reaction product in the receiving phase is lower than the conversion at the same operating time. The apparent catalytic rate constant (kapp) of the new catalytic material based on the emulsion membrane with nanodispersion of osmium nanoparticles (0.1×10−3 for n–dodecanol and 0.9×10−3 for n-decanol) is lower by an order of magnitude compared to those based on adsorption on catalysts from platinum metal group. The advantage of the tested membrane catalytic material is that it extracts p–aminophenol in the acid receiving phase. The paper proposes a mechanism of the studied reduction system.

Wound healing is a multi-factorial response to tissue injury, aiming to restore tissue continuity. Numerous recent experimental and some clinical studies, clearly indicate that probiotics applied topically promote the wound healing process. However, the precise mechanism by which they contribute to healing is not yet clear. Each strain appears to exert a distinctive, even multi-factorial action on different phases of the healing process. Given that a multi-probiotic formula exerts better results than a single strain, the pharmaceutical industry has embarked on a race for the production of a formulation containing a combination of probiotics, capable of playing a role in all the phases of the healing process. Hence, the object of this review is to describe what is known to date of the distinctive mechanisms of each of the most studied probiotic strains in order to further facilitate research towards the development of combinations of strains and doses, covering the whole spectrum of healing. Eleven probiotic species have been analyzed, the only criterion of inclusion being a minimum of two published research articles.

We study the generalized χ and η cross helicities for non-ideal non-barotropic magnetohydrodynamics (MHD). χ and η, the additional label translation symmetry group, have been used to generalize the cross helicity in ideal flows. Both new helicities are additional topological invariants of ideal MHD. To study there behaviour in non-ideal MHD, we derive the time derivative of both helicities using the non-ideal MHD equations taking viscosity, finite resistivity and heat conduction into account. Physical variables are divided into ideal and non-ideal quantities separately during the mathematical analysis for simplification. The analytical results indicate that χ and η cross helicities are not strict constant of motion in the non-ideal MHD and show the rate of dissipation which is compared to the dissipation of other topological constants of motion.

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.

One of the most concerning global environmental issues is the pollution of agricultural soils by heavy metals (HMs), especially cadmium (Cd), which not only affects human health by taking Cd-containing foods but also impacts the quality of rice. The soil's nitrification and denitrification processes, coupled with the release of volatile organic compounds by plants, raise substantial concerns. The understanding of three aspects of paddy soil under conditions of heavy-metal pollution and water management is currently limited. In this review, we summarized recent literature related to the deleterious effects of Cd on both soil processes related to the N cycle and rice quality, particularly aroma, in different water management practices. Under both continuous flooding (CF) and alternate wetting and drying (AWD) conditions, cadmium (Cd) has been observed to reduce both nitrification and denitrification processes. The adverse effects are more pronounced in continuous flooding (CF) compared to alternate wetting and drying (AWD). Similarly, the alteration in rice aroma is more significant in AWD than in CF. The precise modulation of volatile organic compounds (VOCs) by Cd, remains unclear based on the available literature. Nevertheless, HM accumulation is higher in AWD conditions compared to CF, leading to a detrimental impact on volatile organic compounds (VOCs). The literature concluded that AWD practices should be avoided in Cd contaminated fields to decrease accumulation and maintain the quality of rice. In the future, rhizospheric engineering and plant biotechnology can be used to decrease the transport of HMs from the soil to the plant’s edible parts.

TThe passion of bodybuilding athletes for a symmetric, lean, heavily muscled body leads them to carry out exhausting exercise programs and restrictive eating regimens, sometimes resulting in disordered eating behaviors. This study investigates potential exacerbators on the development of disordered eating in bodybuilding and strength athletes. The study involved 103 Cypriot bodybuilding athletes of both sexes, performing at three levels: professional, recreational and strength athletes. The Eating Attitude Test 26 (EAT-26) and The Three Factor Eating Question-naire (TFEQ-R21) were used to evaluate disordered eating and eating behaviors respectively. The current study was performed under the auspices of the Hellenic Center of Education & Treatment of Eating Disorders (KEADD). The degree of deviation between the perceived ideal body weight and the actual body weight was associated with increased risk of eating disorder. Athletes who desired a lower body weight recorded higher scores on EAT-26 overall, (p=0.001), and the subscales of dieting (p=0.01) and bulimia. (p=0.001). Cognitive restraint and emotional eating scales of TFEQ-R21 were more pronounced in the non-professional athletes. (p=0.01). The emotional eating score was higher in women. There is a need for appropriate sport-specific, gender-specific preventive intervention to deescalate the risk of eating disorder, in both profes-sional and non-professional bodybuilding athletes.

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.

A series of novel N-n-butyl-1,8-naphthalimide derivatives were synthesized via a three-step reaction involving nucleophilic substitution and acylation. All of the compounds were characterized by IR, ¹H NMR, ¹³C NMR, MS, and elemental analysis, and the crystal structure of N-n-butyl-4-[N’,N’-bis(2`,4`-dichlorobenzoyl)ethylamino]-1,8-naphthalimide was determined. The π-π stacking interactions and hydrogen bonds between the two molecular core planes (naphthalimide ring) and the van der Waals forces between the flexible n-butyl groups resulted in a 3D long-chain structure. The UV-vis and fluorescence properties of the title compounds were investigated. The results indicated that the monosubstituted 1,8-naphthalimide derivatives bearing an electron-donating group on the benzene ring or a structure with a larger conjugative effect exhibited enhanced fluorescence properties.

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.

The life and work of Ignacio Ellacuría, S.J. is of radical vision, and revolutionary change. His dynamic life and works accompanied El Salvador and the Universidad Centroamericana through perhaps the most tumultuous years of the country’s history, yet there has been limited work done to examine his contributions. This paper shows how Ellacuría viewed the role of a Christian intellectual, and a Christian university within his philosophical and theological framework. I argue that Ignacio Ellacuría held, similarly to his soteriological views, that the intellectual must also be willing to sacrifice all for the sake of his/her work in a pattern of discipleship/martyrdom prefigured by his exemplars Christ and Socrates. It was this dedication to praxis and theory that western theology and philosophy had respectfully lost since their foundations which he sought to restore to a central role. In conclusion, the Christian intellectual and institution, according to Ellacuría, must use its voice and life in service of the people even to the point of martyrdom; he would argue, the implicit reason for Christian martyrdom and the crucifixion of Christ himself.

Building on the Sustainable Happiness Model, this study examined how congruency between ideal self-image and brand image influence a sense of happiness. The findings show that when ideal self-image and ideal social self-image are congruent with brand image a sense of happiness can be enhanced through brand identification and positive emotions. This study contributes to literature as it reveals the mechanism of how congruency between ideal self-image and brand image positively affect happiness.

Nanocrystalline silicon oxide (nc-SiOx:H) is a multipurpose material with its varied application in solar cells as a transparent front contact, intermediate reflector, back reflector layer and even tunnel layer for passivating contacts, owing to easy tailoring of its optical properties. In this work, we systematically investigate the influence of gas mixture (SiH4, CO2, PH3 and H2), RF power and process pressure on the optical, structural and passivation properties of thin n-type nc-SiOx:H films prepared in an industrial, high throughput, plasma-enhanced chemical vapor deposition (PECVD) reactor. We provide a detailed description of the n-type nc-SiOx:H material develop-ment using various characterization techniques (SEM, EDX, Raman spectroscopy, and spectro-scopic ellipsometry) with a focus on the relationship between the material properties and the pas-sivation they provide to n-type c-Si wafers characterized by their effective carrier lifetime (τeff). Further, we also outline the parameters to be kept in mind while developing different n-type nc-SiOx:H layers for different solar cell applications. We report a tunable optical gap (1.8 – 2.3 eV) for our n-type nc-SiOx:H films as well as excellent passivation properties with τeff up to 3.5 ms (iVoc ~ 715 mV) before annealing. Oxygen content plays an important role in determining the crystallinity and hence passivation quality of the deposited nanocrystalline silicon oxide films.

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.

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

Mediterranean Diet (MD), rich in minimally processed plant foods and in monounsaturated fats, but low in saturated fats, meat and dairy products, represents one of the most studied diets for cardiovascular health. It has been shown, from both observational and randomized controlled trials, that MD reduces body weight, improves cardiovascular disease surrogates such as waist-to-hip ratio, lipids, and inflammation markers, and even prevents the development of fatal and non-fatal cardiovascular disease, diabetes, obesity, and other diseases. However, it is unclear whether it offers cardiovascular benefits from its individual components or as a whole. Furthermore, limitations in the methodology of studies and meta-analyses have raised some concerns on its potential cardiovascular benefits. MD is also associated with characteristic changes in the intestinal microbiota, mediated through its constituents. These include increased growth of species producing short-chain fatty acids, such as Clostridium leptum and Eubacterium rectale, increased growth of Bifidobacteria, Bacteroides and Faecalibacterium prausnitzii species, and reduced growth of Firmicutes and Blautia species. Such changes are known to be favorably associated with inflammation, oxidative status, and overall metabolic health. This review will focus on the effects of MD on cardiovascular health through its action on gut microbioma.

Canine Hemangiosarcoma (HSA) is a devastating cancer affecting blood vessels in numerous sites within the body that is primarily seen in middle to older aged dogs. It is marked by its rapid aggressive metastatic pathology that often results in a lack of apparent symptoms in early stages. In most cases, disease becomes apparent due to hemorrhagic events following the rupture of the malignant vascular cell structures that can capture and pool blood cells, resulting in necrosis of the affected tissues. The poor survival times in affected patients cause a hindrance to the ability to carry out large scale studies, leaving numerous knowledge gaps to be filled in future research. The pathologic similarities between this and human angiosarcoma (HA) provides the potential for translatable research to be carried out that would improve outcomes across species. Here, current knowledge is outlined in order to improve understanding HSA holistically and suggest future direction. Emphasis is placed on the potential to improve veterinary practices in ways that will improve the ability to quickly and accurately diagnose patients in order to establish better client communication and provide clarity in collaborating to create the best informed treatment plan possible.

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

Several studies suggests that ghrelin (GHRL) has neurobiological effects that extend beyond control of food intake. Our previous results confirmed that GHRL modulates the secretory activity of the pineal gland (PG) through nocturnal melatonin (MEL) secretion in sheep, the seasonally reproductive animals. Here we investigated the effects of GHRL (10 ng/ml) on the expression of enzymes limiting synthesis of MEL, including tryptophan 5-hydroxylase 1 (TPH1), serotonin N-acetyltransferase (AA-NAT) and its phosphorylated form p31T-AA-NAT in sheep PG explants (n = 72) during the 4-hour incubation in a gas-liquid interface, at a short (SD) and long (LD) photoperiods. After each hour of incubation selected explants were frozen in liquid nitrogen and stored at -80°C for subsequent analysis (real-time PCR, western-blotting, ELISA). Results show that GHRL regulates nightly MEL secretion in a TPH1-independent manner. The factor modulating GHRL activity was photoperiod. During SD photoperiod GHRL significantly reduced the expression of p31T-AA-NAT, AA-NAT and inhibited MEL secretion from PG explants. Whereas, during LD photoperiod no effect of GHRL on MEL secretion and expression of examined enzymes was noted. Studies indicate that GHRL directly affects PG under in vitro conditions and causes MEL secretion in animals which exhibit seasonality in reproductive and metabolic processes.

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 work, a novel heterojunction based on ZnSnO3/ZnO nanofibers was prepared using electrospinning method. The crystal, structural and surface compositional properties of sample based on ZnSnO3 and ZnSnO3/ZnO composite nanofibers were investigated by X-ray diffractometer (XRD), Scanning electron microscope (SEM), X-ray photoelectron spectrometer (XPS) and Brunauer-Emmett-Teller (BET). Compared to pure ZnSnO3 nanofibers, the ZnSnO3/ZnO heterostructure nanofibers display high sensitivity and selectivity response with fast response towards ethanol gas at low operational temperature. The sensitivity response of sensor based on ZnSnO3/ZnO composite nanofibers were 19.6 towards 50 ppm ethanol gas at 225°C, which was about 1.5 times superior than that of pure ZnSnO3 nanofibers, which can be owed mainly to the presence of oxygen vacancies and the synergistic effect between ZnSnO3 and ZnO.

Marine sponges, a well documented prolific source of natural products, harbors numerous microbial communities believed to possess N-acyl homoserine lactones (AHLs) mediated Quorum sensing (QS) as one of the mechanisms of interaction. Bacteria and eukaryotic organisms are known to produce molecules that can interfere with QS signaling, thus affecting microbial genetic regulation and function. In the present study, we established the potential for production of both QS signal molecules as well as QS interfering molecules (QSI) in the same sponge species Sarcotragus spinosulus. A total of eighteen saturated acyl chain AHLs were identified along with six putative unsaturated acyl chain AHLs. Bioassay guided purification led to the isolation of two brominated metabolites with QS-interfering activity. The structures of these compounds were elucidated by comparative spectral analysis of 1HNMR and HR-MS data and was identified as 3-Br-N-methyltyramine (1) and 5,6-dibromo-N,N-dimethyltryptamine (2). The QSI activity of compounds 1 and 2 were evaluated using reporter gene assays for long- and short-chain signals (E. coli pSB1075 and E. coli pSB401) and was confirmed by measuring dose dependent inhibition of proteolytic activity and pyocyanin production in P. aeruginosa PAO1. The obtained results showed the co-existence of QS and QSI in S. spinosulus, a complex network which may mediate the orchestrated function of the microbiome within the sponge holobiont.

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.

Concomitant neuropathological hallmarks of Alzheimer’s Disease (AD) are common in the brains of people with Parkinson’s disease (PD). Furthermore, AD biomarkers are associated with cognitive decline and dementia in PD patients during life. Here, we highlight the considerable overlap between AD and PD, emphasizing neuropathological, biomarker, and mechanistic studies. We suggest that precision medicine approaches may successfully identify PD patients most likely to develop concomitant AD. The ability to identify PD patients at high risk for future concomitant AD in turn provides an ideal cohort for trials of AD-directed therapies in PD patients, aimed at delaying or preventing cognitive symptoms.

This topical review describes the results of recent research into and development of silicon nitride, a ceramic material with unique properties. The outcome of this ongoing research strongly encourages the use of monolithic silicon nitride and coatings as contemporary and future biomaterial for a variety of medical applications. Crystallographic structure, synthesis and processing of monolithic structures and coatings, and examples of their medical applications are covered that relate to spinal, orthopedic and dental implants, bone grafts and scaffolds, platforms for intelligent synthetic neural circuits, antibacterial and antiviral particles and coatings, optical biosensors, and nano-photonic waveguides for sophisticated medical diagnostic devices. The examples provided show convincingly that silicon nitride is destined to become a leader to replace titanium and other entrenched biomaterials in many fields of medicine.

The first detection of gypsum (CaSO4.2H2O) by the Mars Science Laboratory (MSL) rover Curiosity in the Gale Crater, Mars created a profound impact on planetary science and exploration. The unique capability of plasma spectroscopy involving in situ elemental analysis in extraterrestrial environments, suggesting the presence of water in the red planet based on phase characterization and providing a clue to Martian paleoclimate. The key to gypsum as an ideal paleoclimate proxy lies in its textural variants, and in this study terrestrial gypsum samples from varied locations and textural types have been analyzed by Laser Induced Breakdown Spectroscopy (LIBS) technique. Petrographic, sub-microscopic and powder X-ray diffraction characterizations confirm the presence of gypsum (hydrated calcium sulphate; CaSO4.2H2O), bassanite (semi-hydrated calcium sulphate; CaSO4.1/2H2O) and anhydrite (anhydrous calcium sulphate; CaSO4) along with accessory phases (quartz and jarosite). The principal component analysis of LIBS spectra from texturally varied gypsums can be differentiated from one another because of the chemical variability in their elemental concentrations. The concentration of gypsum is determined from the partial least-square regressions model. Rapid characterization of gypsum samples with LIBS is expected to work well in extraterrestrial environments.

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.

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.

The plant Allium hookeri, belonging to the Allium genus, has a history of being used both as a common food ingredient and in herbal medicine. It has recently been reported to have anti-oxidant and anti-inflammatory effects. A. hookeri has been also shown to exhibit neuroprotective and anti-neuroinflammatory activities, but the active compounds responsible for these effects have not been identified in previous studies. This study aimed to perform a metabolite profiling using an HRESI-qTOF MS/MS-based molecular networking approach and identify the active compounds from A. hookeri that target senescent cell-associated secretory phenotype (SASP) inhibitory effects, which contribute to neuroprotective activities. As a result, ten compounds, including one new flavonoid (2) and nine known compounds (1 and 3–10), were identified, and their biological activity was tested. The most potent compound was N-trans-feruloyltyramine (7), which inhibited SASP markers and contributed to the senomorphic activities of A. hookeri. These findings suggest that the phenolamides from A. hookeri could be a promising source of bioactive compounds for preventing senescence-associated diseases.

Balanced nitrogen (N) and phosphorus (P) rates coupling with rational fertilization methodology could promote crop N accumulation, N use efficiency and yield production, particularly in semi-arid and arid regions. To test these characteristics, a two-year (2018 and 2019) pot experiment was therefore performed by growing summer maize in a rain-proof glass greenhouse, under 9 combined N (112, 150 and 187 kg ha-1, urea) and P (45, 60, 75 kg ha-1, calcium superphosphate) rates and three contrasting fertilizer placements. The fertilizers were placed by broadcast on soil surface (Broadcast), side band on 4 cm strip soil surface within 7 cm from sowing line (Side band) and deep band on 4 cm strip below 7 cm soil depth within 7 cm from sowing line (Deep band). Results from three maize growth stages (eight-leaf, 45 days after sowing, DAS; tasseling, 60 DAS; and harvest, 115 DAS) showed that leaf, stem, root N accumulation and total soil N were significantly increased under Deep band than under both Side band and Broadcast at N150P60, N187P60, N150P75 and N187P75, but not at N112P45, N150P45, N187P45, N112P60 and N112P75. Significantly greater leaf, stem, and root N accumulations were also displayed at N150 and N187 than at N112 for the same P60 or P75 under Deep band at 60 DAS and 115 DAS, while were for leaf and stem N accumulations at P75 and P60 than at P45 for the same N150 under Deep band at 45 DAS, 60 DAS and 115 DAS. Significantly greater agronomy N use efficiency, partial factor productivity and N use efficiency exhibited under Deep band than under Side band and Broadcast at N150P75 and N187P75, but at N150P60 and N187P60 for NUE only. In addition, leaf, stem, seed, root N concentrations positively correlated with their own N accumulations or soil N concentration at tasseling and harvest stages. Our results demonstrate that a synchronized N150P60, N187P60, N150P75 or N187P75 fertilization rate with Deep band placement can improve soil N availability and root N uptake, and hereby greater aboveground N accumulation, N use efficiency and yield production of maize particularly practical for small-holder farmers globally.

The novel coronavirus 2019 (COVID-19) pandemic is rapidly advancing despite public health measures. Pharmaceutical prophylaxis is an established approach to potentially control infectious diseases and is one solution to the urgent public health challenge posed by COVID-19. Screening and development of new vaccines and antivirals is expensive and time consuming while the repositioning of available drugs should receive priority attention as well as international government and agency support. Here we propose an old drug chloroquine (CQ) to be urgently repositioned as an ideal antiviral prophylactic against COVID-19. CQ has ability to block viral attachment and entry to host cells. Its proven clinical efficacy against a variety of viruses including COVID-19 and its current deployment in COVID-19 therapeutic trials strengthens its potential candidacy as a prophylactic. Furthermore, CQ has a long safety record, is inexpensive and widely available. Here we reviewed CQ's antiviral mechanisms, its laboratory efficacy activity against COVID-19, as well as CQ's pharmacokinetics in its established use against malaria and autoimmune diseases to recommend safe and potentially efficacious dose regimens for protection against COVID-19: a pre-exposure prophylaxis of 250-500mg daily and post-exposure prophylaxis at 8mg/kg/day for 3 days. We recommend further urgent research on CQ for COVID-19 prevention and urge that the above regimens be investigated in parallel with mass deployment by relevant agencies in attempts to contain the pandemic without unnecessary regulatory delays as benefits far outweigh risks or costs.

3,4-Dihydroquinolin-2(1H)-ones represent a class of valuable bioactive compounds with six-membered nitrogen-containing heterocyclic structures. The development of simple, mild and efficient synthetic methods has been widely concerned by synthetic chemists. In this review, we have summarized a series of different synthetic strategies for the synthesis of dihydroquinoline-2(1H)-ones via catalytic annulation of α,β-unsaturated N-arylamides in the past decade, including covering electrophilic cyclization, radical initiated cyclization and photochemical cyclization reactions. Besides, the substrate scope and mechanistic details are also discussed. This paper will provide a useful reference for the development of diverse synthesis methodologies of 3,4-dihydroquinolin-2(1H)-ones.

Antibacterial bone cements (ABCs), such as antibiotic-loaded bone cements (ALBCs), have been widely utilized in clinical treatments. Currently, bone cements loaded with vancomycin, gentamicin, tobramycin, or clindamycin are approved by the US Food and Drug Administration. However, traditional ALBCs exhibit drawbacks like burst release and bacterial resistance. Therefore, there is a demand for the development of antibacterial bone cements containing novel agents. In this review, we summarize the latest advancements in ABCs. More importantly, we provide an overview and outlook on novel antibacterial agent-loaded bone cements, including metallic antibacterial agents, pH-switchable antibacterial agents, cationic polymers, N-halamines, non-leaching acrylic monomers, antimicrobial peptides, etc. Offering novel perspectives for designing ABCs and treating bone infections.

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.

As matrix representations of magic labelings of related hypergraphs, magic squares and their various variants have been applied to many domains. Among various subclasses, trimagic squares have been investigated for over a hundred years. The existence problem for trimagic squares with singly even orders and orders 16n has been solved completely. However, very little is known for the existence of trimagic squares with other even orders except for the only three examples and three families. We construct normal trimagic squares by using product constructions, row-square magic rectangles, and trimagic pairs of orthogonal diagonal Latin squares. We give a new product construction: For positive integers p, q, and r having the same parity other than 1, 2, 3, 6, if normal p × q and r × q row-square magic rectangles exist, then a normal trimagic square with order pqr exists. As its application, we construct normal trimagic squares of orders 8q^3 and 8pqr for all odd integers q not less than 7 and p,r ∈ {7, 11, 13, 17, 19, 23, 29, 31, 37}. Our construction can easily be extended to construct multimagic squares.

Background: When homeostasis is disturbed it can occur a pathological event named inflammation. The main drugs used in the treatment consist of the non-steroidal and steroidal anti-inflammatory drugs. However, the side effects remain an obstacle during the treatments. In this work we aimed to evaluate three new regioisomers analogues of naphthyl-N-acylhydrazone derivatives. Methods: Acute models of inflammation in vivo (formalin-induced licking and carrageenan-induced inflammation) as well as in vitro were used to evaluate the effects of LASSBio-2039, LASSBio-2040, and LASSBio-2041. Results: All three substances (at 1, 10 or 30 µmol/kg) presented significant effect in the in vivo model reducing leukocyte migration, nitric oxide (NO) and interleukin-1β production. It was observed that only LASSBio-2039 significantly reduced cell migration in vitro. None of the LASSBios did affect inducible nitric oxide synthase activity nor presented NO scavenger effect. It was not observed any toxic effect neither in vivo nor in vitro. The new regioisomers analogues of naphthyl-N-acylhydrazone derivatives presented a significant anti-inflammatory activity suggesting LASSBio-2039 with a direct effect in leukocytes migratory capacity. Conclusions: Taken together the data indicate that these substances present promising effect for de development a prototype for new drugs.

Metabolic-dysfunction associated steatotic liver disease (MASLD) is a chronic liver disease that affects more than a quarter of the global population, and is increasing worldwide, due to the pandemic of obesity. Insulin resistance is closely associated with the development and progression of MASLD. Hepatic entry of increased fatty acids (FA) released from adipose tissue, increase in FA synthesis and reduced FA oxidation in the liver, and hepatic overproduction of triglyceride (TG)-rich lipoproteins may induce the development of MASLD. Since insulin resistance also induces atherosclerosis, the leading cause for death in MASLD patients is cardiovascular disease (CVD). Considering that the development of CVD determines the prognosis of MASLD patients, the ideal therapeutic interventions for MASLD should reduce body weight, improve coronary risk factors, in addition to an improvement in liver functiom. Lifestyle modification such as diet and exercise and surgical interventions such as bariatric surgery and intragastric balloons have shown to improve MASLD by reducing body weight. Sodium glucose cotransporter 2 inhibitors (SGLT2i) and glucagon-like peptide-1 receptor agonists (GLP-1RA) have been shown to improve coronary risk factors and to suppress the occurrence of CVD. Both SGLT2i and GLP-1 have been reported to improve liver enzymes, hepatic steatosis and fibrosis. We recently reported that the selective peroxisome proliferator-activated receptor-alpha (PPARα) modulator, pemafibrate, improved liver function. PPARα agonists have multiple anti-atherogenic properties. Here, we consider the pathophysiology of MASLD and the mechanisms of action of such drugs, and consider whether such drugs and the combination therapy of such drugs could be the ideal treatments for MASLD.

The predatory mirids Macrolophus pygmaeus Ramber and Nesidiocoris tenuis Reuter (Heteroptera: Miridae) are used for the biological control of Tuta absoluta Meyrick (Lep.: Gelechiidae) and other pests in tomato greenhouses. The functional response of 1 (young) and 10 (old) days old adult females and males of M. pygmaeus and N. tenuis on eggs of T. absoluta, was determined on tomato at two temperatures (20° and 25°C) and LD 16:8 and found to be Type II. M. pygmaeus females exhibited higher predation efficiency, than males at both tested temperatures. Young M. pygmaeus females had a higher efficiency than old ones, whereas males had a low efficiency irrespective of age. The predation efficiency of N. tenuis was high (but lower than M. pygmaeus) in both young females and males, although old females had a higher efficiency than the respective males. Our results show that the two predatory species have different functional response characteristics to their prey depending mainly on sex and age which may affect their role as biological control agents.

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.

Wobbling motion as an exotic collective mode in nuclei without axial symmetry, was intensively discussed during the last few years. The observation of the newly proposed transverse wobbling, first reported in $^{135}$Pr and soon after in nuclei from other mass regions, was considered as a significant discovery in low-spin nuclear structure. However, both the reported experimental results and the proposed theoretical models were lively questioned in a series of works devoted to the investigation of the low-spin wobbling mode in the same nucleus. The electromagnetic properties of the $\Delta I=1$ transitions connecting the one- to zero-phonon and the two- to one-phonon wobbling bands in $^{135}$Pr were recently remeasured, demonstrating their predominant $M1$ magnetic character which is in contradiction with the wobbling motion interpretation. These new experimental observables being well reproduced by both quasiparticle-plus-triaxial-rotor model and interacting boson-fermion model calculations, are against the previously proposed wobbling characteristics of the low-spin bands in $^{135}$Pr. On the other hand, we obtained conclusive experimental evidence for the theoretically suggested transverse wobbling bands at medium spin in $^{136}$Nd. The comparison of the experimental data with calculations utilizing the triaxial projected shell model and a new developed particle-rotor model with frozen orthogonal geometry of the active nucleons, supports the description in terms of transverse wobbling of medium-spin bands in triaxial even-even nuclei.

In our paper, we develop the hypothesis of a general call for high mobility and discuss the consequences of it. First, we examine the contemporary social representations of mobility, looking for a definition of what is seen as being properly mobile. We will then show how intertwined social representations of space and time result in the prevalent vision of an inevitable and constant mobility. Next, we will thus discuss the importance of seeing mobility as much more than its material facet. Our third step will be to propose a formalisation of the contemporary requisite for mobility. Through four imperatives (activity, activation, participation, adaptation), the mobilitarian ideal requires each person and organisation to be constantly active, mobile, flexible, networking, etc. We argue that, today, we are all meant to be highly mobile. We will illustrate this point with the example of the parliamentary documents of the Belgian Prison Act (2005) in which prison is open and porous, good inmates are described as dynamic individuals on the move and the legitimate penitentiary system is a paradoxical mobilisation system. We will conclude by discussing the need to reshape our vision of the prison, considering its apparently paradoxical relation with mobility.

Using coherent optical detection and digital signal processing, laser phase noise and equalization enhanced phase noise can be effectively mitigated using the feed-forward and feed-back carrier phase recovery approaches. In this paper, theoretical analyses of feed-back and feed-forward carrier phase recovery methods have been carried out in the long-haul high-speed n-level phase shift keying (n-PSK) optical fiber communication systems, involving a one-tap normalized least-mean-square (LMS) algorithm, a block-wise average algorithm, and a Viterbi-Viterbi algorithm. The analytical expressions for evaluating the estimated carrier phase and for predicting the bit-error-rate (BER) performance (such as the BER floors) have been presented and discussed in the n-PSK coherent optical transmission systems by considering both the laser phase noise and the equalization enhanced phase noise. The results indicate that the Viterbi-Viterbi carrier phase recovery algorithm outperforms the one-tap normalized LMS and the block-wise average algorithms for small phase noise variance (or effective phase noise variance), while the one-tap normalized LMS algorithm shows a better performance than the other two algorithms for large phase noise variance (or effective phase noise variance). In addition, the one-tap normalized LMS algorithm is more sensitive to the level of modulation formats.

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.

The inherent value and use of hydrocarbon from waste plastics and solvents can be extended through open-loop chemical recycling as this process converts plastic to range of non-plastic materials. This process is enhanced by first creating plastic-solvent-combinations from multiple sources which are then streamlined through single process stream. We report on the relevant mechanics for streamlining industrially relevant polymers such as polystyrene (PS), polypropylene (PP), high-density polyethylene (HDPE) and acrylonitrile butadiene styrene (ABS) into chemical slurries mixed with various organic solvents such as toluene, xylene and cyclohexane. The miscibility of the polymer feedstock within the solvent was evaluated using the Relative Energy Difference method, and the dissolution process was evaluated using the “Molecular theories in a continuum framework” model. These models were used to design a batch process yielding 1 tonne/h slurry by setting appropriate assumptions including constant viscosity of solvents, disentanglement-controlled dissolution mechanism and linear increase of the dissolved polymer’s mass fraction over time. Solvent selection was found to be the most critical parameter for the dissolution process. The characteristics of the ideal solvent are high affinity to the desired polymer and low viscosity. This work serves as a universal technical guideline for open-loop chemical recycling of plastics avoiding the growth of waste plastic in a circular economy framework.

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.

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.

Considering increasingly ambitious pledges by countries, pressure from society, investors, and clients further up the supply chain, the question for companies is not so much whether to take decarbonisation action, but what action and by when. However, determining an ideal mix of measures to apply ‘decarbonisation efficiency’ requires more than knowledge of technically feasible measures and how to combine them to achieve the most economic outcome: In this paper, the author describes seven aspects which heavily influence the composition of an ‘ideal mix’ that executive leadership needs to take a (strategic) position on. These aspects consider underlying motivations and span across (socio-)economic, technical, regulatory, strategic, corporate culture and environmental factors and further underline the necessity of clarity of definitions. How these decisions influence the determination of the decarbonisation-efficient ideal mix of measures, both in principle but also in terms of specific impact is further explored by providing examples. What choices are taken by German manufacturers in several of the aspects is disclosed by insights from about 850 responses to the ‘Energy Efficiency Index of German Industry’. Knowledge of the status quo, and clarity in definitions, objectives, time frames and scope are key.

The present paper contains data on the density (ρ), sound velocity (u), specific heat capacity (c_p ) of the mixture of N,N-dimethylformamide + 1-butanol (DMF + BuOH) determined in the entire concentration range of solution and in the temperature range: (293.15–318.15) K. The analysis of thermodynamic functions such as isobaric molar expansion, isentropic and isothermal molar compression, isobaric and isochoric molar heat capacity, as well as their excess functions (〖 E〗_(p,m)^E,〖 K〗_(S,m)^E,〖 K〗_(T,m)^E,〖 C〗_"p,m" ^E,〖 C〗_"V,m" ^E) and also V_m^E was undertaken. The analysis of changes in the physicochemical quantities was based on consideration of the system in an aspect of intermolecular interactions with resulting changes in the mixture structure. The results available in the literature are confusing during the analysis and became the reason for our decision to thoroughly examine the system. What is more, for a system whose components are widely used, there is no information in the literature regarding the heat capacity of the tested mixture, which was also achieved and presented in this publication. The conclusions drawn from so many data allow us to approximate and understand the changes that occur in the structure of the system due to repeatability and consistency of the obtained results

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.

Liability to prevent consequences of an unhealthy situation due to accumulating toxic and hazardous emissions caused by open dumping of municipal solid waste with increasing urbanization has necessitated a renewed thinking on waste disposal. Grate fired incineration systems were adopted by urban managements in past and present but with criticisms due to formation of air borne emissions. Improved combustion methods like fluidized bed are now propagated because of current requirements like efficient energy recovery potential, stricter emission norms, adaptability with urban growth, adaptability to co-firing with other waste like biomass, edible oil wastes or industrial effluent and integration with conventional energy generation. Such a comprehensive and futuristic approach is more sustainable for the community. Multi-criteria decision-making tool is used to identify the best technology option among grate combustion and fluidized bed combustion for disposing and energy recovery from waste. Ten different collection and disposal options involving two combustion methods, namely, grate combustion and fluidized bed method are considered. Utilization of the energy is done for three end uses, namely, power generation, water distillation and district cooling. Two different regions in Saudi Arabia are considered for this study under two types of scenario, namely with recycling and without recycling. The different options are prioritized based on their overall ranking using five major performance factors.

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.

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.

In the present study we tested the effect of small molecular weight redox molecules on collagen-induced platelet aggregation. We used N-acetylcysteine amide (AD4), the amide form of N-acetylcysteine (NAC), a thiol antioxidant with improved lipophilicity and bio-availability compared to NAC, and the thioredoxin mimetics (TXM) peptides, TXM-CB3, TXM-CB13, and TXM-CB30. All compounds significantly inhibited platelet aggregation induced by collagen, with TXM-peptides and AD4 being more effective than NAC. The levels of TxB2 and 12-HETE, the main metabolites derived from the cyclooxygenase and lipoxygenase pathways following platelet activation, were significantly reduced in the presence of AD4, TXM-peptides, or NAC, when tested at the highest concentration (0.6 mM). The effect of AD4, TXM-peptides, and NAC was tested also on the clotting time (CT) of whole blood. TXM-CB3 and TXM-CB30 showed the highest increase of CT. Furthermore, two representative compounds, TXM-CB3, and NAC, showed an increase in the an-ti-oxidant free sulfhydryl groups of plasma detected by Ellman’s method, suggesting a contribution of plasma factors to the antiaggregating effects. Our results suggest that these small molecular weight redox peptides might become useful for the prevention and/or treatment of oxidative stress conditions associated with platelet activation.

The forest regeneration phase in Sweden commonly involves mechanical soil preparation followed by planting of Scots pine or Norway spruce seedlings. The prepared soil offers planting positions with different properties, including decreased damage by pine weevil (Hylobius abietis L.). Nitrogen fertilization can be applied at the time of planting to aid establishment of the seedlings. In this study we compared the effect of organic nitrogen-fertilization for different planting positions, and seedling sizes on early survival and growth of Scots pine and Norway spruce seedlings. The main planting positions were capped mound, hinge, and mineral soil. Seedlings planted close to organic material were categorized as “low quality positions”, since proximity to organic material increase pine weevil attraction. Higher mortality rates related to pine weevil damage were recorded for seedlings planted in the low-quality positions, regardless of seedling size or N-fertilization. Pine weevil attack rates increased with increasing seedling size. Growth was in general lowest in mineral soil positions. The effect of organic N-fertilization on growth was positive for spruce regardless of planting positions and seedling size, while depending on planting position and seedling size for pine, indicating that effects of organic N-fertilization depend on seedling species, -size and planting position.

Ureaplasma species (Ureaplasma spp.) are commonly found as commensals in the human urogenital tracts , but their overgrowth can lead to infection in the urogenital tract and at distal sites. Treatment of Ureaplasma spp. infections is difficult. The lack of a cell wall confers resistance to all β-lactam and glycopeptide antibiotics whereas the lack of de novo synthesis of folic acid makes them resistant to sulfonamides and diaminopyrimidines. Thus, there is a need to search for new drugs effective against these bacteria. In the presented studies, the effect of N,N-diethyldithiocarbamate (DDC) at a concentration of 2 µg/ml, 20 µg/ml and 200 µg/ml on the growth and survival of Ureaplasma urealyticum and Ureaplasma parvum was tested. Our results indicated that all DDC concentrations used showed both bacteriostatic and bactericidal activity against both tested strains In brief, for the first time we showed the bacteriostatic and bactericidal activity of DDC against Ureplasma urealyticum and Ureaplasma parvum. Based on literature data, we conclude that this DDC activity is related to the inhibition of urease activity, which is an indispensable enzyme for these bacteria. Further research is needed and the results obtained in the present study should be verified in in vivo models of infection.

Optimizing the nitrogen (N) timings and rate can improve nutrient uptake, and nutrient-efficiencies, especially of N in wheat under the changing climate scenario. Climatic stress in the form of high temperature and drought resulted in the decreased crop physiology and, ultimately, grain yield. Taking the example of rainfed wheat, we quantified the impact of N application rates as full and split-dose at three variable sites of rainfed Pothwar, Pakistan by conducting field experiments for two years (2013-14 and 201-15). Treatments include, T1 = Control (No fertilizer applied), full dose of N applied at the time of crop sowing, i.e. T2 = 50 kg N ha^-1, T3 = 100 kg N ha^-1 and T4 = 150 kg N ha^-1 and split application of N at different timings during different stages of the crop called as split application of N, i.e. T5: Application of 50 kg N ha^-1 (15 kg N ha^-1 (Sowing) : 20 kg N ha^-1 (Tillering) :15 kg N ha^-1 (Anthesis), T6: Application of 100 kg N ha^-1 (30 kg N ha^-1 (Sowing): 40 kg N ha^-1 (Tillering) : 30 kg N ha^-1 (Anthesis) and T7: Application of 150 kg N ha^-1(45 kg N ha^-1 (Sowing) : 60 kg N ha^-1 (Tillering) : 45 kg N ha^-1 (Anthesis). Three study sites include viz. Islamabad (High rainfall with optimum temperature), University Research Farm (URF)-Koont (Medium rainfall with moderate temperature), and Talagang (low rainfall with high temperature). Results showed that the highest stomatal conductance (0.80 mole m^-2 sec^-1), net photosynthetic rate (20.07 μmole m^-2s^-1), transpiration rate (9.58 mmole m^-2s^-1), intercellular CO2 concentration (329.25 μmole CO₂ mol^-1 air), SPAD values (58.86 %) and proline contents (35.42 μg g^-1) were obtained for split application of N (T6 = Split N100) compared to control and full dose of N treatments. Among sites, these physiological traits remained highest at Islamabad and lowest at Talagang, while among years, maximum values of the measured parameters were obtained in 2013-14. A similar trend was observed for crop total N, N efficiencies, and agronomic traits of the crop. Our results suggest that optimum N application rate and its suitable timings can help to harvest real benefits of N as in our findings, split dose resulted in the maximum performance of the crop from physiological parameters to the agronomic traits of the rainfed wheat crop.

The objective of this study was to analyze the mental workload using EEG and eye tracking data and classify it using machine learning algorithms. The machine learning model was developed based on the simultaneous recording of eye tracking and EEG measurements during the experimental process. The experiments involved 15 university students, consisting of 7 women and 8 men. Throughout the experiments, the researchers utilized the n-back memory task and the NASA-Task Load Index (TLX) subjective rating scale to assess various levels of mental workload. The findings revealed that as the task difficulty increased, there was an increase in the diameter of both the right and left pupils, the number of fixations, the number and duration of saccades, and the number and duration of blinks. Conversely, variables related to fixation duration decreased. The EEG results indicated that theta power in the prefrontal, frontal, and front central regions increased with task difficulty. Additionally, alpha power increased in the frontal regions but decreased in the temporal, parietal, and occipital regions as the task became more challenging. Furthermore, low beta power significantly decreased in almost all brain regions as the task difficulty increased. In terms of the four-class classification problem, the mental workload level can be predicted with an accuracy rate of 76.59% using 34 selected features. This study has made a significant contribution to the literature by presenting a four-class mental workload estimation model that utilizes different machine learning algorithms.

Optimizing the nitrogen (N) timings and rate can improve nutrient uptake, and nutrient-efficiencies, especially of N in wheat under the changing climate scenario. Climatic stress in the form of high temperature and drought resulted in the decreased crop physiology and, ultimately, grain yield. Taking the example of rainfed wheat, we quantified the impact of N application rates as full and split-dose at three variable sites of rainfed Pothwar, Pakistan by conducting field experiments for two years (2013-14 and 201-15). Treatments include, T₁ = Control (No fertilizer applied), full dose of N applied at the time of crop sowing, i.e. T₂ = 50 kg N ha^-1, T₃ = 100 kg N ha^-1 and T₄ = 150 kg N ha^-1 and split application of N at different timings during different stages of the crop called as split application of N, i.e. T₅: Application of 50 kg N ha^-1 (15 kg N ha^-1 (Sowing) : 20 kg N ha^-1 (Tillering) :15 kg N ha^-1 (Anthesis), T₆: Application of 100 kg N ha^-1 (30 kg N ha^-1 (Sowing): 40 kg N ha^-1 (Tillering) : 30 kg N ha^-1 (Anthesis) and T₇: Application of 150 kg N ha^-1(45 kg N ha^-1 (Sowing) : 60 kg N ha^-1 (Tillering) : 45 kg N ha^-1 (Anthesis). Three study sites include viz. Islamabad (High rainfall with optimum temperature), University Research Farm (URF)-Koont (Medium rainfall with moderate temperature), and Talagang (low rainfall with high temperature). Results showed that the highest stomatal conductance (0.80 mole m^-2 sec^-1), net photosynthetic rate (20.07 μmole m^-2s^-1), transpiration rate (9.58 mmole m^-2s^-1), intercellular CO₂ concentration (329.25 μmole CO₂ mol^-1 air), SPAD values (58.86 %) and proline contents (35.42 μg g^-1) were obtained for split application of N (T₆ = Split N₁₀₀) compared to control and full dose of N treatments. Among sites, these physiological traits remained highest at Islamabad and lowest at Talagang, while among years, maximum values of the measured parameters were obtained in 2013-14. A similar trend was observed for crop total N, N efficiencies, and agronomic traits of the crop. Our results suggest that optimum N application rate and its suitable timings can help to harvest real benefits of N as in our findings, split dose resulted in the maximum performance of the crop from physiological parameters to the agronomic traits of the rainfed wheat crop.

Herein, two title compounds, N-Benzoyl-N’-4-cyanophenyl thiourea (I) and N-(4-nitrobenzoyl)-N’-4-cyanophenyl thiourea (II) were synthesized in high yield, via aroyl isocyanate and 4-aminobenzonitrile. The structure of the prepared compounds was characterized by elementary analysis and FT-IR, ¹H, ¹³C NMR spectroscopic methods. Cyclic voltammetric (CV) experiments were performed with glassy carbon electrode. The reduction potential values of different functional group such as nitro, cyano in title compounds were investigated using CV curves.

One of the ramifications of the COVID-19 pandemic is that it has lent urgency to ongoing discussions on mental well-being. While standard techniques are available to diagnose mental health disorders such as depression, anxiety, and stress, ambiguity persists regarding the emotional aspect of well-being. Emotional well-being (EWB) is a recently developed concept that seeks to understand the contribution of emotions to one’s well-being. Interactive approaches for such investigations are recommended to understand people’s contextual experiences. In this study, we use a qualitative approach to examine the psychological impact of the built environment on its residents to formulate the desiderata for an ideal place based on their perceptions. We use personal construct theory and the associated qualitative repertory grid technique. We recruited 15 students from the United Arab Emirates University and obtained information on their perceptions of three built environments they experienced. The findings revealed information on the students’ emotional constructs that were associated with a set of design-related factors, and the way the ideal hostel should be characterized in response to these associations. These findings enrich our knowledge of EWB within built environments and can inform their future design by considering the emotional aspect of the well-being of residents.

Background: The prognostic value of erythrocyte levels of the n-6 fatty acids (FAs) for total mortality and cardiovascular disease (CVD) outcomes remains an open question. Methods: We examined CV outcomes and death in 2500 individuals in the Framingham Heart Study Offspring cohort without prevalent CVD (mean age 66 years, 57% women) as a function of baseline levels of different length n-6 FAs (18 carbon, 20 carbon and 22 carbon) in the erythrocyte membranes. Clinical outcomes were monitored for up to 9.5 years (median follow up, 7.26 years). Cox proportional hazards models were adjusted for a variety of demographic characteristics, clinical status and RBC n-6 and long chain n-3 FA content. Results: There were 245 CV events, 119 CHD events, 105 ischemic strokes, 58 CVD deaths, and 350 deaths from all causes. Few associations between either mortality or CVD outcomes were observed for the n-6 FAs, with those that were observed becoming non-significant after adjusting for n-3 FA levels. Conclusions: Higher circulating levels of the marine n-3 FA levels are associated with reduced risk for incident CVD and ischemic stroke and for death from CHD and all-causes, however in the same sample, little evidence exists for association with n-6 FAs. Further work is needed to identify a full profile of FAs associated with cardiovascular risk and mortality.

Recently, many authors have been interested to introduce fuzzy implications over t-norms and t-conorms. In this paper, we introduce (S,N) and residuum fuzzy implication for Dubois t-norm and Hamacher's t-norm. Also, new concepts so-called (T,N) and residual fuzzy co-implication in dual Heyting Algebra are investigated. Some examples as well as application are discussed as well.

Heat emitters constitute the primary devices used in space heating and cover a fundamental role in the energy efficient use of buildings. In the search for an optimized design, heating devices should be compared with a benchmark emitter with maximum heat emission efficiency. However, such an ideal heater still needs to be defined. In this paper we perform an analysis of heat transfer in a European reference room, considering room side effects of thermal radiation and computing the induced operative temperature both analytically and numerically. By means of functional optimization, we analyse trends such as the variation of operative temperature with radiator panel dimensions, finding optimal configurations. In order to make our definitions as general as possible, we address panel radiators, convectors, underfloor (UFH) and ceiling heater. We obtain analytical formulas for the operative temperature induced by panel radiators and identify the 10-type as our ideal radiator, while the UFH provides the best performance overall. Regarding specifically UFH and ceiling heaters, we find optimal sizes that identify the according ideal emitters. The analytical method and quantitative results reported in this paper can be generalized and adopted in most studies concerning the efficiency of different heat emitter types in building enclosures.

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.

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 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.

This paper presents a theory on graph topological structure and graph coloring, proving that for any N-order graph structure (with a topological structure similar to ), the maximum number of colors required for coloring is less than or equal to . The Four Color Theorem is just one special case of this theory, with the maximum structure size for a four-color graph being a 4-order structure graph, hence requiring only a maximum of 4 colors for coloring.

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.

Let $G$ be a group with identity $e$ and $R$ be a commutative $G$-graded ring with nonzero unity $1$. Graded semi-primary and graded $1$-absorbing primary ideals have been investigated and examined by several authors as generalizations of graded primary ideals. However, these three concepts are different. In this article, we characterize graded rings over which every graded semi-primary ideal is graded $1$-absorbing primary and graded rings over which every graded $1$-absorbing primary ideal is graded primary.

Biochar application to the soil can improve soil quality and nutrient leaching loss. Recent studies have reported that surficial application of biochar to stored swine manure can reduce emissions of odorous compounds and reduce the volatilization loss of ammonia. Our working hypothesis was that the biochar-treated manure application to the soil would decrease nutrient leaching from manure and increase plant-available nutrients. The study objectives were to evaluate the impact of biochar-treated swine manure on soil total C, N, and other major and minor nutrients. Three biochars (i) neutral pH red-oak (RO), (ii) highly alkaline autothermal corn (Zea mays) stover (HAP), and (iii) mild acidic Fe-treated autothermal corn stover (HAPE) were incubated with swine manure for a month. The biochar-manure mixture was applied in triplicate to soil columns with application rate determined by the P₂O₅-P content in manure or manure-biochar mixtures after the incubation. The ammonium (NH₄⁺), nitrate (NO₃^-), and reactive P concentrations in soil column leachates were recorded for eight leaching events. Soil properties and plant-available nutrients were compared between treatments and control manure & soil. Manure-(HAP&HAPE) biochar treatments significantly increased soil organic matter (OM) and increased soil total C, N, and improved soil bulk density. Concentrations of KCl-extractable NH₄⁺ and NO₃^- significantly increased in HAPE column leachates during this 4-week study and in the soil after the experiment. A significant reduction in soil Mehlich3 Cu was also observed for the manure-HAPE mixture compared with the control. Overall, the manure-biochar incubation enabled biochar to sorb nutrients from manure, and the subsequent manure-biochar mixture application to soil improved soil quality and plant nutrient availability in comparison to conventional manure application to soil. This proof-of-the-concept study suggests that biochars could be used to solve both environmental and agronomic challenges and further improve the sustainability of animal and crop production agriculture.

(1) Background: The severity of malaria is associated with low bioavailability of antioxidants and high concentration of free radicals that induce oxidative damage in cerebral and pulmonary microcirculation. This can be prevented by the action of consumable antioxidants present in foods. Therefore, we investigated the protective role of lycopene (LYC) on the oxidative changes induced by Plasmodium berghei (Pb); (2) Methods: Mice were infected by intraperitoneal injection of 106 parasitized red blood cells and treated via gavage with LYC (3.11 mg/kg bw/day) or NAC (62 mg/kg bw/day). They were then evaluated for 1, 4, 8 or 12 days after infection. Levels of thiobarbituric acid reactive substances (TBARS), antioxidant capacity by inhibition of ABTS radicals (AC-ABTS) and DPPH (AC-DPPH), uric acid (UA), and nitric oxide (NO) were measured in brain and lung tissues; (3) Results: The infection caused oxidative stress confirmed by increased levels of TBARS, AC-ABTS, AC-DPPH, UA, and NO in the tissues leading to the death of the animals. LYC prevented the increase in TBARS, AU, and NO levels compared to Pb (p&lt; 0.0001) and NAC+Pb groups (p&lt;0.0001), reaching values similar to those of Sham animals; (4) Conclusions: These results are striking evidence of the beneficial effect of lycopene supplementation on oxidative stress in experimental malaria in vivo and emphasize the importance of antioxidant supplementation in the treatment of the disease.

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.

A mixture of nonlabeled (14N2H4) and 15N labeled hydrazine (15N2H4) in an aqueous solution is oxidized to 15N2, 14N2, and 14N15N molecules, indicating the intermediate existence of the 14NH2-14NH-15NH-15NH2 with subsequent hydrogen transfers and splitting of side N-N bonds. Structures, thermodynamics, and electron characteristics of various N4H6 molecules in aqueous solutions are investigated using theoretical treatment at the CCSD/cc-pVTZ level of theory to explain the crucial part of the hydrazine oxidation reaction. Most N4H6 structures in aqueous solutions are decomposed during geometry optimization. Splitting the bond between central nitrogen atoms is the most frequent, but the breakaway of the side nitrogen is energetically the most preferred. The N-N fissions are enabled by suitable hydrogen rearrangements. Gibbs free energy data indicate the dominant abundance of NH3... N2... NH3 species. The side N atoms have very high negative charges, which should support hydrogen transfers in aqueous solutions. The only stable cyclo-(NH)4…H2 structure has a too high Gibbs energy and breaks the H2 molecule. The remaining initial cyclic structures are split into hydrazine and HN≡NH or H2N≡N species, and their relative abundance in aqueous solutions is vanishing.

The seasonal and vertical spatial variation characteristics of total N, NH4+—N and NO3-—N in the soil in Picea mongolica forest at different stand ages were studied. The results showed that: (1) NH4+ —N in the soil in Picea mongolica forest was positively correlated with sample date, soil NO3-—N and forest age (P <0.05), and negatively correlated with soil depth (P < 0.01). NO3-—N in the soil in Picea mongolica forest was negatively correlated with sample date and forest age (P < 0.05), and significantly negatively correlated with soil depth (P < 0.01); (2) the content of NH4+—N is greater than that of NO3-—N in each soil layer of Picea mongolica forest at three forest ages. The correlation analysis showed which had an impact on the content of NH4+—N and NO3-—N in the soil in Picea mongolica forest. The content was lower in February and November, and higher in May and August；(3) The contents of total N, NH4+—N and NO3-—N in the soil of Picea mongolica forest in the three forest ages increased with the depth of soil layer (0-50cm), and showed an overall downward trend. The contents of NH4+—N in the soil layer of young forest (0-10cm, 10-20cm and 20-30cm, 30-40cm and 40-50cm) were significantly different (P＜0.05), and the contents of NO3-—N were also significantly different (P＜0.05), while their contents of middle-aged forest and near mature forest increased with the depth of soil layer, There was no significant difference in the content of NH4+—N; (4) The content of NH4+—N in the soil in Picea mongolica forest generally showed the following change trend near mature forest > middle-aged forest > young forest. The change trend of soil NO3-—N content is consistent with that of the content of NH4+—N in the soil in Picea mongolica forest.

More than 110 countries including 500 cities worldwide have set the goal of reaching carbon neutrality. Heating contributes to most of the residential energy consumption and carbon emissions. The green energy transition of fossil-based heating systems is needed to reach the emission goals. However, the heating systems vary in energy source, heating technology, equipment location, and these complexities make it challenging for households to compare heating systems and make decisions. Hence, a decision support tool that provides a generalized ranking of individual heating alternatives is proposed for households as decision-makers to identify the optimal choice. This paper presents an analysis of 13 heating alternatives and 19 quantitative criteria in technological, environmental, and financial aspects, combines ideal solution based Multi-Criteria Decision Making with 6 weighting methods and 4 normalization methods, and introduces ensemble learning with a fuzzy membership function derived from Cauchy distribution to finalize the final ranking. The robustness of the proposed method is verified by 3 sensitive analyses from different aspects. Air to water heat pump, solar heating and direct district heating are the top three rankings in the final result under Danish national average data. A framework is designed to guide the decision-makers apply this ranking guideline with their practical feasible situations.

We assume that the current mathematical knowledge K is a finite set of statements from both formal and constructive mathematics, which is time-dependent and publicly available. Any theorem of any mathematician from past or present belongs to K. The set K exists only theoretically. Ignoring K and its subsets, sets exist formally in ZFC theory although their properties can be time-dependent (when they depend on K) or informal. In every branch of mathematics, the set of all knowable truths is the set of all theorems. This set exists independently of K. Algorithms always terminate. We explain the distinction between algorithms whose existence is provable in ZFC and constructively defined algorithms which are currently known. By using this distinction, we obtain non-trivial statements on decidable sets X⊆N that belong to constructive and informal mathematics and refer to the current mathematical knowledge on X. This and the next sentence justify the article title. For any empirical science, we can identify the current knowledge with that science because truths from the empirical sciences are not necessary truths but working models of truth about particular real phenomena.

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 $m$.

Inappropriate use of fertilizers is one of the major production constraints in sesame. Studies to optimize the use of N fertilizer on sesame were conducted at Humera Agricultural Research Center (HuARC) under rain fed and irrigation conditions. Thirteen (13) N doses were evaluated in a Randomized Complete Block Design (RCBD) during 2016, 2017 and 2018. In the rain fed condition; results showed higher number of days to 50% flowering on the higher N application. The 31-121.5 kg N ha-1 have scored higher seed yield, where the lower (18 kg N ha-1) and higher (156 kg N ha-1) N doses scored lower seed yield. In the irrigation condition; higher N application rate prolonged the flowering time to some extent and days to 90% maturity was reduced as N rate increased. Heavier seed weights and maximum seed yield were recorded on 64 and 75 kg N ha-1 and the lower N doses scored low seed yield. Agronomic efficiency of N fertilizer (N-AE) was higher on 64 kg N ha-1 under both growing conditions. The partial budget analysis revealed that 64 kg N ha-1 (rain fed) and 75 kg N ha-1 (irrigation) had the higher net profit, MRR and residual ranking. Therefore, for the greater sesame productivity 64 kg N ha-1 has to be recommended for rain fed and 64 to 75 kg N ha-1 for the irrigated sesame.

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

In order to understand the effect of Pb-CuI co-doping on the thermoelectric performance of Bi₂Te₃, n-type Bi₂Te₃ co-doped with x at% CuI and 1/2x at% Pb (x = 0, 0.01, 0.03, 0.05, 0.07, and 0.10) were prepared via high temperature solid state reaction and consolidated using spark plasma sintering. Electron and thermal transport properties, i.e., electrical conductivity, carrier concentration, Hall mobility, Seebeck coefficient, and thermal conductivity, of CuI-Pb co-doped Bi₂Te₃ were measured in the temperature range from 300 K to 523 K and compared to corresponding x% of CuI-doped Bi₂Te₃ and undoped Bi₂Te₃. The addition of a small amount of Pb significantly decreased the carrier concentration, which could be attributed to the holes from Pb atoms, thus the CuI-Pb co-doped samples show a lower electrical conductivity and a higher Seebeck coefficient compared to CuI-doped samples with similar x values. The incorporation of Pb into CuI-doped Bi₂Te₃ rarely changed the power factor because of the trade-off relationship between the electrical conductivity and the Seebeck coefficient. The total thermal conductivity(κ_tot) of co-doped samples (κ_tot ~1.4 W/m∙K at 300 K) is slightly lower than that of 1% CuI-doped Bi₂Te₃ (κ_tot~1.5 W/m∙K at 300 K) and undoped Bi₂Te₃ (κ_tot ~1.6 W/m∙K at 300 K) due to the alloy scattering. The 1% CuI-Pb co-doped Bi₂Te₃ sample shows the highest ZT value of 0.96 at 370 K. All data on electrical and thermal transport properties suggest that the thermoelectric properties of Bi₂Te₃ and its operating temperature can be controlled by co-doping.

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.

La reflexión sobre la formación que necesitan los docentes panameños tiene poca tradición investigativa, aunque recientemente se han desarrollado programas de formación de docentes para enseñar matemáticas de acuerdo con las tendencias actuales en la enseñanza de esta materia. Este artículo explica uno de estos programas de formación de posgrado. Específicamente, se discuten los lineamientos para su diseño y algunos resultados de su segunda implementación. Entre los resultados más importantes para este artículo tenemos a) la creación de la plataforma así como el conjunto de tareas diseñadas, las cuales han sido utilizadas para la formación de posteriores promociones de docentes; b) Destaca el cambio en los criterios que orientan la práctica docente al final del programa, en relación con los criterios utilizados antes de la formación, destacando particularmente la relevancia que adquieren los aspectos emocionales y los relacionados con la interacción en este proceso.