This article aims to discuss, the stability and boundedness character of the solutions of the rational equation of the form \begin{equation}\label{eql21.1} y_{t+1}=\frac{\nu\epsilon^{-y_t}+\delta\epsilon^{-y_{t-1}}}{\mu+\nu y_t+\delta y_{t-1}},\quad t\in N(0). \end{equation} Here, $\epsilon>1, \nu,\delta,\mu\in (0,\infty)$ and $y_0, y_1$ are taken as arbitrary non-negative reals and $N(a)=\{a,a+1,a+2,\cdots \}$. Relevant examples are provided to validate our results. The exactness is tested using MATLAB.

A second order rational difference equation $$x_{n+1}=px_{n}+\frac{q}{x_{n-1}^2}$$ with the parameters $p$ and $q$ which lies in $(0,1)$, is studied. The dynamics of the equilibrium is characterized through the trichotomy of the parameter $p<\frac{1}{2}$, $p=\frac{1}{2}$ and $p>\frac{1}{2}$. It is found that there is no periodic solution of period $2$ and $3$ but there exists periodic solutions with only periodic solution $5$ and $10$ are achieved computationally.

Objective: To evaluate the status of receiving education on rational drug use, the criteria in medical drug selection, and level of knowledge of dentists working in a dentistry faculty in Turkey. Material and Methods: This was a descriptive study based on a questionnaire. One hundred seventeen (74%) dentists volunteered to participate in the study. The questionnaire consisted of 20 questions investigating sociodemographic features and rational drug use. Results: The mean age of the dentists was 30.8 ± 7.2 years, and 62.4% were men. The mean period of professional experience was 8.9±7.1 years. The most frequently used resources of references while prescribing medicine were Vademecum (medical drug guide) (61.5%), the internet (59.0%), and colleagues (49.6%). The most frequently reported condition described as ‘good’ was drug indications (43.6%). The dentists had a moderate level of information about posology, and administration route (48.7%), pharmacologic features (48.7%), and contraindications (46.2%). The number of dentists who stated that they considered cost while prescribing was low [always (6%), and frequently (15.4%)]. Rational drug use education had been received by 23.9% of the dentists. Conclusions: The dentists were found to have a lack of adequate and effective education on rational use of drugs. Regular and continuous education before and after graduation is a necessity for dentists and for their patients.

Let $f\left(1\right)=1$ , and let $f(n+1)=2^{2^{f\left(n\right)}}$ for every positive integer n. We consider the following hypothesis: if a system S ⊆ {x_i · x_j = x_k : i, j, k ∈ {1, . . . , n}} ∪ {x_i + 1 = x_k : i, k ∈{1, . . . , n}} has only finitely many solutions in non-negative integers x₁, . . . , x_n, then each such solution (x₁, . . . , x_n) satisfies x₁, . . . , x_n ≤ f (2n). We prove: (1) the hypothesisimplies that there exists an algorithm which takes as input a Diophantine equation, returns an integer, and this integer is greater than the heights of integer (non-negative integer, positive integer, rational) solutions, if the solution set is finite; (2) the hypothesis implies that there exists an algorithm for listing the Diophantine equations with infinitely many solutions in non-negative integers; (3) the hypothesis implies that the question whether or not a given Diophantine equation has only finitely many rational solutions is decidable by a single query to an oracle that decides whether or not a given Diophantine equation has a rational solution; (4) the hypothesis implies that the question whether or not a given Diophantine equation has only finitely many integer solutions is decidable by a single query to an oracle that decides whether or not a given Diophantine equation has an integer solution; (5) the hypothesis implies that if a set $\mathfrak{M}$ ⊆ has a finite-fold Diophantine representation, then $\mathfrak{M}$ is computable.

In this work, we consider the properties of the two-term Machin-like formula and develop an algorithm for computing digits of π by using its rational approximation. In this approximation, both terms are constructed by using a representation of 1/π in the binary form. This approach provides the squared convergence in computing digits of π without any trigonometric functions and surd numbers. The Mathematica codes showing some examples are presented.

Lipases have tremendous potential for industrial use, particularly, those mostly active against water-insoluble substrates, such as triglycerides composed of long-chain fatty acids. However, in most cases, mutants often need to be constructed to achieve optimal performance for such substrates. Protein engineering techniques have been reported as strategies for improving lipase characteristics by introducing specific mutations in the cap domain of esterases or in the lid domain of lipases, or through lid domain swapping. Here, we have improved the lipase character of a lipase, retrieved from the Marine Metagenomics MarRef Database and assigned to the Actinoalloteichus genus (WP_075743487.1), through site-directed mutagenesis and by substituting its lid domain (FRGTEITQIKDWLTDA) by the one of Rhizopus delemar (previously Rhizopus oryzae) lipase (FRGTNSFRSAITDIVF). Results demonstrated that the redesigned mutants gain activity against bulkier triglycerides such as glyceryl tridecanoate and tridodecanoate, olive oil, coconut oil, and palm oil. The absence of a residue in the new lid, present in the original lid, appears to be a key aspect to the increase in lipase character, although full activity recovery is only obtained with lid swapping.

A rational decision is a systematic and logical way of making a resolution. It is needed in critical situation, especially the unavoidable ones such as annual floods. People affected by this natural disaster, continue living their lives if good rational decisions are made. The current research consists of two studies. The first identifies rational decisions based on age, education, socio-economic and gender, while the second is based on decisions associated with resilience, coping strategies and age. A total number of 354 participants from various cities in East Java were used as participants of the study. The results in the first study, 58% of the people made good rational decisions, with the remaining 42% making low decisions. Furthermore, education was found to significantly influence the decision making process. The second study found a significant relationship between the resilience, coping strategies, age with the rational decisions. Conclusion of the study will be used make better decisions for the community in order to minimize physical and psychological impacts.

This paper presents a non-perturbative method for solving eigenproblems. This method applies to almost all potentials and provides non-perturbative approximations for any energy level. The method converts an eigenproblem into a perturbation problem, obtains perturbation solutions through standard perturbation theory, and then analytically continues the perturbative solution into a non-perturbative solution.

In this paper we study a conjecture proposed by P.Duxbury , C.laror , L.Leduino de Salles Neto in 2021\cite{conjecture} on the Golumb Ruler Problem which is a classical optimization model in discrete case . In \cite{conjecture} the authors constucted a continuous model for the Golumb Ruler Problem associated to the discrete case and conjectured that the optimal value of both cases are equal . We deal with this conjecture via algebraic geometrical methods .

Antibiotic resistance (ABR) is an emerging global threat to public health. Substantial evidence has indicated that community pharmacists (CPs) can play a critical role in managing the ever-increasing threat of antibiotic resistance. The study aimed to determine the knowledge, attitude, and practices of CPs (n=180) towards antibiotics and antibiotic resistance as well as to improve the rational use of antibiotics. Two phases of mixed methods (quantitative and qualitative) online study were conducted in Pakistan from August 2019 to March 2020 by using validated questionnaires and semi-structured interview data. Different statistical methods were used to tabulate the quantitative data whereas inductive thematic analysis was conducted to categorize themes from the qualitative data and draw conclusions. Approximately 64.4% were male (mean: 29-33 years old). Overall, CPs had good knowledge of and were familiar with superbugs and their roles in ABR (65.6%, Median=1, IQR=1) although they were poor in differentiating some antibiotic groups with their respective ABR patterns (31.1%, Median=1, IQR=1). Most CPs have a positive attitude towards antibiotics with most (90.0%) having identified ABR as a critical issue in public health (Median=1, IQR=0). Overall, CPs' practices towards antibiotics were reasonable where they tend to educate patients about the rational use of antibiotics (52.8%, Median=1, IQR=1). Two main themes (antibiotics and counseling of patients) were related to self-medication with while educational interventions are the sub-theme. ABR is multifactorial where the subthemes related to budget, time constraints incompetent staff, the absence of CPs, the lack of training, enforcement of laws and regulations are the need of the hour in Pakistan. Effective antibiotic stewardship programs, patient education, and awareness campaigns about antibiotics and ABR along with training of the CPs are important factors that have to be addressed in a timely manner.

According to Indonesia’s result of Basic Health Research of 2013, prevalence of acute respiratory infection in 2007 and 2013 were not different (25.5% and 25.0%, respectively). Identifying the cause of acute pharyngitis is a key point in determining the optimal treatment. The main purpose is to evaluate the rational use of drugs and its irrational impact as well as the correlation of the drug use with the incidence and prevalence of acute pharyngitis. This study was a descriptive and observational study, carried out retrospectively and concurrently at two community health centers located in Bandung and Cimahi, Indonesia. There were 80.01% over prescription of antibiotics, with a total of 8.98% is non-treatment option, and 62.43% irrational used of corticosteroids. The incidence and prevalence of acute pharyngitis at one health center in Bandung were 2.45% and 2.31%, respectively, with irrationality rate of 83.82%. Those recorded at one health center in Cimahi were 2.11% of incidence and 2.00% of prevalence with irrational rate of 91.29%. It can be concluded that there were still irrational use of medicines in the treatment of acute pharyngitis in community health center. The higher incidence and prevalence might indicate the declining health services quality.

We consider a classial case of irrational integrals containing a square root of a quadratic polynomial. It is well known that they can be expressed in terms of elementary functions by one of three Euler’s substitutions. It is less known that the Euler substittutions have a beautiful geometric interpretation. In the framework of this interpretation one can see that the number 3 is not the most suitable. We show that it is natural to introduce the fourth Euler substitution. By the way, it is not clear who was the first to attribute these three substitutions to Euler. In his original treatise Leonhard Euler uses two substitutions which are sufficient to cover all cases.

The paper examines common elements between Lévai’s and Milson’s potentials obtained by Liouville transformations of two rational canonical Sturm-Liouville equations (RCSLEs) with even density functions which are exactly solvable via Jacobi polynomials in a real or accordingly imaginary argument. We refer to the polynomial numerators of the given rational density function as ‘tangent polynomial’ (TP) and thereby term the aforementioned potentials as ‘e-TP’ A special attention is given to the overlap between the two potentials along symmetric curves which represent two different forms of the Ginocchio potential exactly quantized via Gegenbauer and Masjed-Jamei polynomials respectively. Our analysis reveals that the actual interconnection between Lévai’s parameters for these two rational realizations of the Ginocchio potential is much more complicated than one could expect based on the striking resemblance between two quartic equations derived by Lévai for ‘averaged’ Jacobi indexes.

Ferulic acid has numerous beneficial effects for human health, which are frequently attributed to its antioxidant behavior. In this report many of them are reviewed and 185 new ferulic acid derivatives are computationally designed, using the CADMA-Chem protocol. For the later, the chemical space was sampled and evaluated. To that purpose selection and elimination scores were used, which are built from a set of descriptors accounting for ADME properties, toxicity, and synthetic accessibility. After the first screening, 12 derivatives were selected and further investigated. Their potential role as antioxidants was predicted from reactivity indexes, directed related with the formal hydrogen atom transfer and the single electron transfer mechanisms. The best performing molecules were identified by comparisons with the parent molecule and two references: Trolox and alpha-tocopherol. Their potential as polygenic neuroprotectors was investigated through the interactions with enzymes directed related with the etiologies of Parkinson’s and Alzheimer’s diseases. They are acetylcholinesterase, catechol-O-methyltransferase, and monoamine oxidase B. Based on the obtained results, the most promising candidates (FA-26, FA-118, and FA-138) are proposed as multifunctional antioxidants with potential neuroprotective effects. The findings derived from this investigation are encouraging and might promote further investigations on these molecules.

Enzymes are in high demand for very diverse biotechnological applications. However, natural biocatalysts often need to be engineered for fine-tuning their properties towards the end applications, such as the activity, selectivity, stability to temperature or co-solvents, and solubility. Computational methods are increasingly used in this task, providing predictions that narrow down the space of possible mutations significantly and can enormously reduce the experimental burden. Many computational tools are available as web-based platforms, making them accessible to non-expert users. These platforms are typically user-friendly, contain walk-throughs, and do not require deep expertise and installations. Here we describe some of the most recent outstanding web-tools for enzyme engineering and formulate future perspectives in this field.

Ziyuan-3 (ZY-3) satellite is the first civilian stereo mapping satellite in China and was designed to achieve the 1: 50000 scale mapping for land and ocean. Rigorous sensor model (RSM) is required to build the relationship between the three-dimensional (3D) object space and two-dimensional (2D) image space of ZY-3 satellite imagery. However, each satellite sensor has its own imaging system with different physical sensor models, which increase the difficulty of geometric integration of multi-source images with different sensor models. Therefore, it is critical to generate generic model， especially rational polynomial coefficients (RPCs) of optical imagery. Recently, relatively a few researches have been conducted on RPCs generation to ZY-3 satellite. This paper proposes an approach to evaluate the performance of RPCs generation from RSM of ZY-3 imagery. Three scenarios experiments with different terrain features (such as ocean, city and grassland) are designed and conducted to comprehensively evaluate the replacement accuracies of this approach and analyze the RPCs fitting error. All the experimental results demonstrate that the proposed method achieved the encouraging accuracy of better than 1.946E-04 pixel in both x-axis direction and y-axis direction, and it indicates that the RPCs is suitable for ZY-3 imagery and can be used as a replacement for the RSM of ZY-3 imagery.

Vancomycin is one of the ‘last-line’ classes of antibiotics used in the treatment of life-threatening infections caused by Gram-positive bacteria. Even though vancomycin was discovered in 1950s it was widely used after 1980s for the treatment of infections caused by methicillin-resistant Staphylococci as prevalence of such strains were increased. However, currently it is evident that vancomycin resistant Staphylococcusaureusandvancomycin-resistant Enterococci have been developed as a result of various reasons including use of avaparcin, which is an analog of vancomycin, as feed additive in livestock. In present day context, more attention should be paid on prevention of emergence of resistance for the antibiotics in order to keep antibiotics effective. In order to prevent emergence of resistance, proper guidance for the responsible use of antimicrobials is indispensable. Therefore, almost all stakeholders who use antibiotics should have in depth understanding on the antibiotic they use. As such, it is imperative to be aware of the important aspects of vancomycin. In the present review, efforts have been made to discussthe pharmacokinetics and pharmacodynamics, indications, emergence of resistance, control of resistance, adverse effects and alternative therapy for vancomycin.

Compared with ordinary asphalt pavement, the application of modified asphalt will improve the performance of asphalt pavement. However, using the same modification method for the whole road section can cause modification waste or result in some parts not meeting performance standards. This paper proposes a whole road section modification method. First of all, a finite element model was established using Abqus according to the actual road pavement material to analyze the mechanical response of each layer under different working conditions and establish the grading standard under comprehensive working conditions. Secondly, different modification methods were analyzed according to investigation and their modification effects were graded through clustering analysis method. Finally, different working conditions and different modification methods were reasonably matched and a section of highway was selected for verification. The results show that before modification, the calculated rutting is 6.23mm and after modification, it is reduced to 2.45mm which indicates that reasonable modification has a better effect and can achieve the purpose of rutting equalization control on the whole road section. It is of great significance to carry out reasonable modification on different conditions to control rutting equalization of asphalt pavements.

The purpose of this article is to conduct a bibliometric review of literary production in terms of market interdependence. We investigate the effect of contagion on agricultural commodities and identify the commodities and methods used in the most cited publications over the decades. For this, we used the SCOPUS database, sorting with Rayyan, Excel, and finally, the Bibliometrix/R-project. The results showed that corn, wheat, soybeans, cotton, and sugar are the most studied commodities. There is no uniqueness concerning the methods used to identify interdependence and the contagion effect. Also, it is possible to perceive the growing scientific interest concerning the subject, with a diversity of authors and magazines. However, there is a direction of the and magazines most cited articles for analyzing agricultural commodities and energy, demonstrated a worldwide trend of studies relating natural resources, biofuels, clean energy, and efficiency. In addition, countries like China and the United States stand out in this scientific scenario as the countries that produce the most articles.

"Hidden hunger", the deficiency of important mineral micronutrients, affects more than 2 billion people globally. Adolescence is unquestionably a period of nutritional risk, given the high nutritional requirements for growth and development, erratic or capricious diets and the increased consumption of snacks. This study applied the rational food design approach to obtain micronutrient-dense biscuits by combining chickpea and rice flours to achieve an optimal nutritional profile, crunchy texture and appealing flavour. The perception of 33 adolescents of the suitability of such biscuits as a mid-morning snack was examined. Four biscuits were formulated, with different ratios of chickpea and rice flours (CF:RF): G100:0, G75:25, G50:50 and G25:75. Nutritional content, baking loss, acoustic-texture and sensory analyses were carried out. On average, the mineral content of biscuits with the CF:RF ratio of 100:0 doubled compared with the 25:75 formula. The dietary reference values for iron, potassium and zinc reached 100% in the biscuits with CF:RF ratios of 50:50, 75:25 and 100:0, respectively. The analysis of mechanical properties revealed that samples G100:0 and G75:25 were harder than the others. Sample G100:0 showed the highest sound pressure level (Smax). Sensory analysis showed that increasing the proportion of CF in the formulation augments the grittiness, hardness, chewiness and crunchiness. Most of the adolescents (72.7%) were habitual snack consumers; 52% awarded scores ≥ 6 to biscuit G50:50 for its overall quality, 24% described its flavour as "biscuit" and 12% as "nutty". However, 55% of the participants could not pinpoint any dominant flavour. In conclusion, it is possible to design nutrient-dense snacks that meet the micronutrient requirements and sensory expectations of adolescents by combining flours naturally rich in micronutrients.

In the field of business environments, the integration of novel artificial intelligence (AI) techniques has been identified in the literature and theoretical discourse as an essential catalyst for enhancing the decision-making processes. In the contemporary landscape of digital transformation, the application of these techniques becomes essential, despite encountering various hurdles that impede their seamless integration into the rational decision-making process within e-government, which constitutes a critical component of digital government initiatives. This study explores whether similar advancements can be observed within the e-government sector and investigates the impact of using machine learning (ML) as a technique of artificial intelligence on rational decision-making (RDM). Employing an empirical research approach, the study utilized a quantitative methodology, relying on an electronically structured questionnaire survey administered to 163 employees in the e-government sector in Jordan through purposive random sampling. Data analysis was conducted using the SPSS v25 program, complemented by a media-tion analysis using AMOS v23 software. The research findings revealed a significant contribution of using machine learning to enhance rational decision-making and trust levels, with trust positively impacting RDM. Trust was identified as a beneficial mediator in the relationship between machine learning and rational decision-making. Despite certain limitations, this study's outcomes offer substantial insights for researchers and government policy-makers alike, contributing to the advancement of sustainable practices in the e-government domain.

The COVID-19 pandemic has significantly impacted global health and economies, necessitating the development of effective vaccines against the novel virus. Understanding the structure and function of SARS-CoV-2 is crucial for rational vaccine design. The virus consists of several key proteins, including the spike protein, envelope protein, membrane protein, and nucleocapsid protein. The spike protein plays a crucial role in host cell entry by binding to the angiotensin-converting enzyme 2 (ACE2) receptor on human cells. The replication of the virus within host cells is facilitated by various viral proteins, such as the RNA-dependent RNA polymerase (RdRp) and the main protease (Mpro). Rational vaccine design strategies for SARS-CoV-2 primarily focus on targeting the spike protein due to its role in host cell entry. However, developing vaccines against this protein is challenging due to its highly mutable nature and potential conformational changes. Alternative strategies involve using other viral proteins, such as the nucleocapsid protein, which is conserved and essential for viral replication. Considering T-cell responses in vaccine design is also vital as they play a vital role in controlling viral infections. Vaccines that elicit both antibody and T-cell responses are more likely to provide robust and durable immunity against SARS-CoV-2. Advancements in rational vaccine design for SARS-CoV-2 include mRNA-based vaccines, viral vector-based vaccines, and protein subunit vaccines. However, challenges remain in developing a universally effective vaccine, including the emergence of new SARS-CoV-2 variants and mutations that may affect the efficacy of existing vaccines. In conclusion, rational vaccine design for SARS-CoV-2 requires a comprehensive understanding of the virus's structure and function, targeting key viral proteins, and considering T-cell responses.

Outcomes of repeated decision--making processes may be affected by adversarial actors, without being noticed. Adversaries may try to gain knowledge about a particular decision--making process, identify its decision--makers, and guess which underlying decision support model is used. Then they can simulate the process, and craft different scenarios to affect its decision outcomes. Therefore, designers of decision support systems need to incorporate this in the decision modeling phase. The purpose of this study is to demonstrate this for the repeated decision--making in a patent application process. In this process, two sequential decision outcomes can be affected by adversarial actors: a company's decision to which type of patent office to send a patent request to, and the decision of a specialized patent officer to grant an application, or not. It is motivated that the company's decision--maker is \emph{bounded} rational. A theory for information--theoretic bounded rational decision--making under uncertainty proposed by Ortega et al.\ is adopted to model this type of decision--maker. A framework is provided to simulate a number of scenarios that adversaries may deploy to affect decision outcomes of a repeated patent application decision--making process. The framework is also utilized for statistically testing the presence of the scenarios, and to demonstrate how to discourage adversaries from deploying them.

The asymptotic dynamics of the classes of rational difference equations (RDEs) of third order defined over the positive real-line as $$\displaystyle{x_{n+1}=\frac{x_{n}}{ax_n+bx_{n-1}+cx_{n-2}}}, \displaystyle{x_{n+1}=\frac{x_{n-1}}{ax_n+bx_{n-1}+cx_{n-2}}}, \displaystyle{x_{n+1}=\frac{x_{n-2}}{ax_n+bx_{n-1}+cx_{n-2}}}$$ and $$\displaystyle{x_{n+1}=\frac{ax_n+bx_{n-1}+cx_{n-2}}{x_{n}}}, \displaystyle{x_{n+1}=\frac{ax_n+bx_{n-1}+cx_{n-2}}{x_{n-1}}}, \displaystyle{x_{n+1}=\frac{ax_n+bx_{n-1}+cx_{n-2}}{x_{n-2}}}$$ is investigated computationally with theoretical discussions and examples. It is noted that all the parameters $a, b, c$ and the initial values $x_{-2}, x_{-1}$ and $x_0$ are all positive real numbers such that the denominator is always positive. Several periodic solutions with high periods of the RDEs as well as their inter-intra dynamical behaviours are studied.

Ensuring fire safety is an important condition for the successful operation of industrial enterprises. It is necessary to detect the threat of fire before ignition. An indicator of danger is the appearance of gas, which occurs as a result of unauthorized heating of equipment. Gas sensors make it possible to detect the appearance of gases characteristic of the decomposition of materials at the stage of smouldering and pyrolysis, which cause a change in the composition of the atmosphere. This paper presents a mathematical method for the rational placement of gas analyzers for premises of potentially hazardous industries. It is the rational placement of gas sensors, which ensures safety, taking into account economic feasibility that determines the effectiveness of their use. For the first time, the analysis of gas accumulation during the movement of the flow from the source to the ceil-ing, then propagation to the location of the sensors, is used for the first time to select the placement of gas sensors. Depending on the permissible values of the gas volume, the placement and number of gas sensors are selected. The calculation of the conditions for the rational placement of gas sen-sors for the most common indicators, such as carbon monoxide and hydrogen at different sizes and heights of rooms, is carried out. The method of calculating the location of gas analyzers makes it possible to diagnose and predict fire hazard at technological facilities on the basis of gas control, and compare the obtained values with the maximum permissible values. This method provides cal-culation of the coordinates of the gas source from the coordinates of the triggered sensors. Knowing the coordinates of all sensors, the coordinates of the sensors that gave the alarm, and the formula for determining the volume of the gas cloud under these sensors, it is possible to assess the localization of the source of dangerous gas in the protected room. This increases the efficiency of the fire safety system. The method makes it possible to control the layout of sensors depending on the volume of protected premises, types of production, the creation of new sensors, changes in the composition of hazardous gas in different technological conditions.

Using number theory, a formula is obtained that describes the thermal conductivities of ZrC, UC, UN, ThN, ZrN and Th_xU_1-xN at x = 0.2 and 0.5 with temperature change. This formula contains the atomic numbers of the elements, the thermal conductivities of the individual elements of the substance, and the structural parameter. There is no direct dependence on temperature in the formula, since it is hidden in the thermal conductivities of each element and in the structure parameter. In some temperature ranges, the structural parameter is constant; therefore, the thermal conductivity of some carbides and nitrides is expressed through summing the thermal conductivities of individual elements.

Phthalate esters (PAEs) are a ubiquitous kind of environmental endocrine-disrupting chemicals, causing environmental and health issues. EstJ6 is an effective phthalate-degrading hydrolase, and its mutant with a combination of three non-conservative distal mutations has an improved activity against PAEs with unknown molecular mechanisms. Herein, we attempt to fill the significant gap between distal mutations and the activity of this enzyme using computational approaches. We find mutations result in a redistribution of enzyme’s preexisting conformational states and dynamics changes of key functional regions, especially the lid over the active site. The outward motion of the lid upon mutations should make it easier for substrates or products to enter or exit. Additionally, the stronger substrate binding affinity and conformational rearrangements of catalytic reaction-associated residues in mutant, accompanied by the strengthened communication within the protein, might contribute to the elevated catalytic efficiency. Finally, an attempt has been done to improve the thermostability of EstJ6 upon introducing a distal disulfide bond between residues A23 and A29, and the simulation results are as expected. Together, our work explored the allosteric effects caused by distal mutations, which could provide insights into the rational design of esterases for industrial applications in the future.

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

Biological diversity (BD) explored by the biological systematics is a complexly organized natural phenomenon and can be partitioned in several aspects defined with references to various causal factors structuring biota. These BD aspects are studied by particular research programs based on specific taxonomic theories (TT). They provide in total a framework for comprehending the structure of the biological systematics and its multi-aspect relations to other fields of biology. General principles of individualizing BD aspects and construing TT as quasi-axiomatics are briefly considered. It stressed that each TT is characterized by a specific combination of interrelated ontological and epistemological premises most adequate to the BD aspect a TT deals with. The following contemporary research programs in systematics are recognized and characterized in brief: phenetic, rational (with several subprograms), numerical, typological (with several subprograms), biosystematic, biomorphic, phylogenetic (with several subprograms), evo-devo. From a scientific pluralism perspective, all these research programs related to particular naturally defined BD aspects are of the same biological and scientific significance and no one of them can pretend to take a privileged position. They elaborate “locally” natural classifications that can be united by a kind of generalized faceted classification.

By using the new recently proposed extended rational methods, we set some solitary and multi wave solutions of the coupled Higgs system in the present study. Some new families of hyperbolic and trigonometric solutions of the coupled Higgs equations are successfully obtained. Some solutions are real as some are complex valued functions. Particular forms of some solutions derived by choice of some parameters are demonstrated in three dimensional spaces. The complex valued solutions are also depicted by plotting both real and complex component.

Mode locked pulse generation has been reported using both active and passive mode locking schemes. Active mode locking technique has been proven to be an effective way to generate high-repetition-rate pulses by incorporating a modulator inside the laser cavity. Compared to actively mode locked lasers, passively mode locked lasers can generate pulse train at ultrashort pulse width but with relatively lower repetition rate. Thus, it is a brilliant idea to build a hybrid mode locked system combining both active and passive mode lockers. In this review, several hybrid mode locked fiber ring laser systems are discussed and summarized. Hybrid mode locking is a promising method to generate high speed ultrashort optical pulses for fiber-optic telecommunication system.

The variable-length arbitrary Lagrange-Euler (ALE)-ANCF finite element, which employ nonrational interpolating polynomials, cannot exactly describe the rational cubic Bezier curves such as conic and circular curves. The rational absolute nodal coordinate formulation (RANCF) finite element, whose reference length (undeformed length) is constant, can exactly represent the rational cubic Bezier curves. A new variable-length finite element called the ALE-RANCF finite element, which is capable of accurately describe the rational cubic Bezier curves, is proposed by combining the desirable features of the ALE-ANCF and RANCF finite element. In order to control the reference length of ALE-RANCF element within a suitable range, element segmentation and merging schemes are proposed. It is demonstrated that exact geometry and mechanic is maintained after the ALE-RANCF element is divided into two shorter ones, and compared with the ALE-ANCF elements, there are smaller deviations and oscillations after two ALE-RANCF elements are merged into a longer one. Numerical examples are presented and the feasibility and advantages of the ALE-RANCF finite element are demonstrated.

COVID-19 is characterized by an unprecedented abrupt increase in the viral transmission rate (SARS-CoV-2) relative to its pandemic evolutionary ancestor, SARS-CoV (2003). The complex molecular cascade of events related to the viral pathogenicity is triggered by the Spike protein upon interacting with the ACE2 receptor on human lung cells through its receptor binding domain (RBD_Spike). One potential therapeutic strategy to combat COVID-19 could thus be limiting the infection by blocking this key interaction. In this current study, we adopt a protein design approach to predict and propose non-virulent structural mimics of the RBD_Spike which can potentially serve as its competitive inhibitors in binding to ACE2. The RBD_Spike is an independently foldable protein domain, resilient to conformational changes upon mutations and therefore an attractive target for strategic re-design. Interestingly, in spite of displaying an optimal shape fit between their interacting surfaces (attributed to a consequently high mutual affinity), the RBD_Spike–ACE2 interaction appears to have a quasi-stable character due to a poor electrostatic match at their interface. Structural analyses of homologous protein complexes reveal that the ACE2 binding site of RBD_Spike has an unusually high degree of solvent-exposed hydrophobic residues, attributed to key evolutionary changes, making it inherently ‘reaction-prone’. The designed mimics aimed to block the viral entry by occupying the available binding sites on ACE2, are tested to have signatures of stable high-affinity binding with ACE2 (cross-validated by appropriate free energy estimates), overriding the native quasi-stable feature. The results show the apt of directly adapting natural examples in rational protein design, wherein, homology-based threading coupled with strategic ‘hydrophobic ↔ polar’ mutations serve as a potential breakthrough.

Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) have been utilised to forecast the foreign exchange market (Forex). However, such models usually exhibit unstable behaviour, as data perturbations often downgrade the functionality of the entire network due to their monolithic architecture. Hence, this study proposes a novel neuroscience-informed modular network applied to the closing prices and the sentiments retrieved from Yahoo Finance and Twitter APIs, aiming to anticipate better price fluctuations in Euro to British Pound Sterling (EUR/GBP) rather than monolithic methods. The proposed model is based on a new modular CNN, replacing pooling layers with orthogonal kernel initialisation RNNs coupled with Monte Carlo Dropout (MCD), namely MCoRNNMCD. It combines two modules: i) a convolutional simple RNN and ii) a convolutional Gated Recurrent Unit (GRU), where orthogonality and MCD are added to reduce the overfitting, assessing each module's uncertainty. These parallel feature extraction modules concatenate their outputs to a final three-layer Artificial Neural Network (ANN) decision-making module. A comprehensive comparison viewing objective evaluation metrics such as the Mean Square Error (MSE) proved that the proposed MCoRNNMCD-ANN outperformed single CNN, LSTM, GRU, and the state-of-the-art hybrid BiCuDNNLSTM, CLSTM, CNN-LSTM, and LSTM-GRU in forecasting hourly EUR/GBP closing price fluctuations.

Introduction Headache is a common public health problem, but its burden could be avoided by raising headache awareness and the appropriate use of acute medication and prophylactic medication. Few reports on raising headache awareness in the general public have been reported, and there are no reports on headache awareness campaigns through social networking services (SNS), or social media, in Japan. We prospectively performed a headache awareness campaign from March 2022 through 2 SNS, targeting nurse and wind instrumental musicians, because they are with high headache prevalence. Methods Through the 2 SNS, the article and video were distributed, respectively. The article and video described the 6 important topics for the general public about headaches, which were described in the Clinical Practice Guideline for Headache Disorders 2021. Just after reading or watching them as e-learning, we performed online questionnaire sheets to investigate the awareness of the 6 topics through the 2 SNS. The awareness of the 6 topics before and after the campaign was evaluated. Results In the SNS nurse-senka, we obtained 1191 responses. Women comprised 94.4%, and the median (range) age was 45 (20 to 71) years old. Headache sufferers were 63.8%, but only 35.1% had consulted doctors. In the SNS Creatone, we got the response from 134 professional musicians, with 77.3% of women. The largest number of respondents were in their 20s (range 18-60 years old). Headache sufferers were 87.9%. Of them, 36.4% had consulted doctors, 24.2% were medication-overuse headache. The ratios of individuals who were aware of the 6 topics significantly increased from 15.2%-47.0% to 80.4-98.7% after the online questionnaire in both SNS (p < 0.001, all). Conclusions We conducted this headache awareness campaign through e-learning and an online survey via 2 SNS. The ratios of individuals who were aware of the 6 topics about headaches significantly increased 1 month after e-learning. Our results suggest that e-learning and online survey can improve headache awareness. The materials in this campaign can be installed into smartphone applications and further spread on SNS, leading to strong influence. With rapid digital transformations such as online telemedicine and artificial intelligence diagnosis, raising awareness will be more efficient and effective and should be important.

(1) Background: Rational use of medicines (RUM) and their assessment is important to ensure optimal use of resources and patient care in hospitals. These assessments are essential to identifying practice gaps for quality improvement. (2) Methods: Assessment of adherence to WHO/ International Network for Rational Use of Drugs core prescribing indicators among out-patients in 2021 was conducted at the University Hospital of the Kwame Nkrumah University of Science and Technology in the Ashanti region of Ghana. We reviewed electronic medical records (EMR) of 110,280 patient encounters in the year which resulted in 336,087 medicines prescribed. (3) Results: The average number of medicines prescribed per encounter was 3 with generics being prescribed in 76% of prescriptions. Injections were prescribed in 7% of encounters while 90% of medicines were from Ghana’s Essential Medicines List 2017. (4) Conclusions: With the exception of patient encounters with injections, all prescribing indicators assessed in this study did not meet WHO optimum levels providing targets for quality improvement in RUM. Implementing prescribing guides and policies, regular audits and feedback as well as continuous professional development training may help to improve prescribing practices in the hospital.

The entropy of the partition generated by an n-tone music scale is proposed to quantify its regularity. The normalized entropy relative to a regular partition, and its complementary, here referred to as the bias, allow to analyze various conditions of similarity between an arbitrary scale and a regular scale. Interesting particular cases are scales having limited bias because their tones are distributed along interval fractions of a regular partition. The most typical case in music concerns partitions associated with well-formed scales generated by a single tone h. These scales are maximal even sets that combine two elementary intervals. Then, the normalized entropy depends on the number of tones as well as the relative size of both elementary intervals. When well-formed scales are refined, several nested families stand out with increasing regularity. It is proven that a scale of minimal bias, i.e. with less bias than those with fewer tones, is always a best rational approximation of log2h.

As new vaccines reduce P. falciparum (Pf) cases, clinicians can focus on rescuing more children with cerebral malaria (CM). Adjunctive “therapeutically-rational exchange transfusion” (T-REX) refers to using special “Pf-resistant” donor red blood cells (RBCs) that secrete nano-sized RBC extracellular vesicles (EVs). Can some RBC EVs rapidly dislodge Pf-infected RBCs (iRBCs) sequestered in blood vessels and reduce inflammation? Does post-exchange “rebound parasitemia” reflect sequestration-reversal? We reviewed case-reports, EV and liposome studies, expert perspectives, and time-sequence data. In the AQUAMAT study, median coma-recovery time was 20 hours for artesunate. In contrast, a CM patient treated with type-O T-REX quickly began speaking (during the procedure). For other rapid-recovery CM patients, donor RBC variables had not been specified. Despite rapid Pf-killing, drugs need 20 hours to substantially reduce iRBC cytoadhesion while EVs can selectively bind distant inflamed tissues within 15 minutes. RBCs stressed by blood-bank storage and Pf infection secrete EVs. Post-exchange “rebound parasitemia” can occur within 60 minutes and may reflect release of sequestered iRBCs. Sequestration-reversal can be assessed by monitoring Pf parasitemia and total Pf biomass. New data suggest clinicians, working with transfusion- and laboratory-medicine physicians, can, and should, assess T-REX options and publish their findings to help clarify how RBC EVs may serve as therapeutic “decoy ligands.”

Knowledge is a property that measures the degree of awareness of an agent about a target in an environment. The goal in conventional intelligent and cognitive agent development is to build agents that can be trained to gain knowledge about a target. The definition and operations of this knowledge associated to the agent is not clear, whereas these are required for developing a reliable, scalable and flexible agent. In this paper, we provide a concise theoretical framework for the description and quantification of the knowledge property needed for an efficient design of cognitive and rational intelligent agents. We relate the quantification scheme to the epistemological description of knowledge and present many illustrative examples on the usefulness of the quantification scheme.

In present paper, spatial Minkowski Pythagorean Hodograph (MPH) curves are characterized with Rational Rotation Minimizing Frames (RRMFs). We define Euler-Rodrigues Frame (ERF) for MPH curves and by means of this concept, we reach the definition of MPH curves of type (n, m). Expressing the conditions provided by these curves in the form of Minkowski-Hopf map that we define, it is aimed to establish a connection with the Lorentz force which occurs during the process of Computer Numerical Control (CNC) type sinker Electronic Discharge Machines (EDMs). This approach is reinforced by split quaternion polynomials. Finally, we give conditons satisfied by MPH curves of low degree to be type (n, m) and construct illustrative examples.

The paper examines rational Darboux-Crum transforms (RDCTs) of the Jacobi-reference (JRef) potential on the line, with an emphasis on the transformations using only normalizable seed solutions. The Cooper-Ginocchio-Khare (CGK) potential constitutes the simplest example of this rich family of exactly solvable one-dimensional (1D) potentials. It was explicitly confirmed that that an arbitrary Darboux-Crum transformation (DCT) of the given Sturm-Liouville equation (SLE) can be represented as a chain of sequential Darboux deformations of the associated Liouville potentials. If the rational SLE (RSLE) under consideration is exactly solvable and the transformation function (TF) used at each step is nodeless then each RSLE constructed in such a way was proven being exactly solvable itself. The exact solvability of RDCTs of the JRef canonical SLE (CSLE) was also confirmed for the DCTs using pairs of juxtaposed eigenfunctions (an extension of the renowned Adler theorem to the RCSLEs of our interest). By re-expressing the reference polynomial fraction (RefPF) of the transformed CSLE in terms of the Krein determinant (KD), instead of Crum Wronskian (CW), it was shown that the eigenfunctions under consideration are expressible in terms of polynomial solutions of a generalized Heun equation with positions of the most poles dependent on the exponent parameters. The outlined technique was extended to two isospectral SUSY partners of the JRef potential (as well as to its third sibling with the inserted new lowest-energy level) which, by analogy with the CGK potential, are quantized by polynomial solutions of the 2-Heun equation with all four poles at some fixed positions on the real axis.

Tandem mass spectrometry (TMS) has emerged as a critical analytical tool in pharmaceutical sciences, playing a pivotal role in ensuring the rational use of medications. This article explores the applications of TMS across various stages of drug development, quality assurance, and patient care, highlighting its precision and reliability in advancing therapeutic efficacy. TMS facilitates the accurate identification and quantification of drug compounds, ensuring that pharmaceutical products meet high standards of purity and potency. By detecting even trace levels of impurities or contaminants, TMS strengthens the quality control processes critical to patient safety. In the realm of pharmacokinetics and pharmacodynamics, TMS enables detailed monitoring of drug absorption, distribution, metabolism, and excretion (ADME), allowing for a better understanding of drug behavior in the human body. It is also instrumental in therapeutic drug monitoring (TDM), ensuring that medication levels remain within therapeutic windows, thus optimizing dosing regimens and minimizing adverse effects. Additionally, TMS supports personalized medicine approaches by assessing drug interactions and tailoring treatments to individual patients. Through its application in drug discovery, development, and therapeutic monitoring, TMS serves as an indispensable tool for fostering rational medication use, contributing to more effective, safe, and personalized pharmaceutical care.