We study different aspects of an exactly solvable master equation (ME). Its simplicity allows one direct access to the details of its workings, highlighting significant features and peculiarities. The existence of phase transitions is unveiled.

Limited understanding exists regarding the intricate dynamics between the levels of social inhi-bition exhibited by both wives and husbands concerning their perceived family support and de-pressive symptoms, particularly within couples who are parents of children diagnosed with au-tism spectrum disorder (ASD). This study used the actor-partner, interdependence mediation model to analyze data collected from 397 pairs of Chinese parents with children diagnosed with ASD. The findings of the study revealed significant indirect actor effects, indicating that the levels of social inhibition exhibited by both wives and husbands were associated with their own de-pressive symptoms through their respective perceptions of family support. In general, the study did not find significant partner effects, except for some indirect effect (IE) of wives on their hus-bands' depressive symptoms through the wives' perceived social support. This observation sug-gests that cultural norms and role expectations within the family context may influence these dy-namics. These results underscore the potential importance of interventions aimed at addressing social inhibition and enhancing perceived family support to alleviate depressive symptoms in this population. Additionally, interventions targeting fathers should emphasize the importance of their involvement in parenting and collaboration with their partners in caring for children with ASD. Such collaborative efforts may contribute to improved outcomes for both parents and chil-dren within families affected by ASD.

This paper focuses on environmental policies for mitigating the impacts of climate change on the Taj Mahal, an iconic structure built on the banks of the Yamuna River from 1632 to 1653 with a blend of Persian and Indian architectural styles. The Taj Mahal is threatened by damage caused by climate change, including air pollution resulting in acid rain and floods that lead to erosion and discoloration of the main marble material of the Taj Mahal. This study employs a Systematic Literature Review (SLR) of peer-reviewed journal articles with a primary focus on environmental policy, the impacts of climate change, and the preventive measures undertaken by the Indian government. Based on the analysis of 270 papers, it is concluded that out of the total, 30 papers specifically address objectives relevant to this research. The study period spans from 2014 to 2024. The research findings reveal that air pollution has a significantly adverse impact on the Taj Mahal. Furthermore, nine policies are generally identified from the journal literature review aimed at preserving and protecting the Taj Mahal from the negative effects caused by air pollution.

Sentiment analysis has become an important tool for understanding public opinion across languages and domains. Recently, there has been an increase in the number of studies on sentiment analysis in low-resource languages such as Kazakh. This is important to ensure that modern text analysis technologies are accessible to all users, regardless of their language background. The aim of the study is to create a sentiment analysis model for analyzing texts in Kazakh. As part of this work, we aim to use fine-tuning techniques on our own dataset for already existing models, thus improving their accuracy and efficiency for analyzing Kazakh language texts. This paper presents a manually collected dataset "KazIntTelCom" from the city information service 2GIS, consisting of user reviews, manually annotated by the authors taking into account the polarity of sentiment (i.e. negative positive or neutral). This dataset was used to fine-tune two pre-trained multi-lingual Transformer-based sentiment analysis models taken from the HuggingFace platform. The distillBERT and XLM-RoBERTa models were used for tuning. Also, the models were tested on the dataset "KazSAnDRA". The results show that accurate tuning even on a relatively small dataset gives a significant increase in performance, which is confirmed by an increase in the accuracy index by 20%-30%. In addition, false misses and false detections are analyzed, which allows us to identify directions for further improvement of the models. The contribution of this work, in addition to the dataset, is the analysis of model errors, which will help future developers to make more accurate settings of hyperparameters of training for sentiment analysis in Kazakh. These results are important for natural language processing and their adaptation to low-resource languages, promoting more inclusive and equitable access to modern analytical tools. Thus, this study demonstrates the effectiveness of the Transformers architecture for sentiment analysis in Kazakh and opens new opportunities for further model improvement.

The valorization of aquaculture/fisheries processing by-products, as well as unavoidable/unwanted catches and discards in Greece is currently an underutilized activity despite the fact that there are several best practices in Northern Europe and overseas. One of the main challenges is to determine whether the available quantities for processing are sufficient to warrant valorization of discards and fish side streams. This is the first attempt to systematically record and analyze the available quantities of fish by-products and discards in Greece in a spatial and temporal way in an effort to create a national exploitation Master Plan for the valorization of this unavoidable and unwanted biomass. A thorough survey conducted within the VIOAXIOPIO project unveiled a substantial biomass of around 19,000 tonnes annually that could be harnessed for valorization. Furthermore, the production of various High Added Value Biomolecules (HAVB) was investigated, and experimental trials were conducted to assess the potential yields and the collected data were used to formulate four valorization scenarios.

We investigated the dynamics of a simple master equation describing the evolution of a probability distribution between two states, \( p_1 \) and \( p_2 \) (with \( p_1 + p_2 = 1 \)). Our focus is on the behavior of the entropy \( S \), the distance \( D \) from the uniform distribution (\( p_1 = p_2 = 1/2 \)), and the free energy \( F \). We define two ratios, \( \eta_S = \frac{dS/dt}{dF/dt} \) and \( \eta_D = \frac{dD/dt}{dF/dt} \), and find that both diverge to plus-minus infinity as the system evolves towards the uniform distribution. This divergence marks a critical transition point where the master equation temporarily loses physical meaning. However, after this divergence, the system settles into a new, well-behaved regime where the solutions stabilize at finite values, representing a new equilibrium or steady state. This two-regime behavior underscores the intricate dynamics of simple probabilistic systems as they approach and surpass equilibrium, providing insights into the complex interplay of entropy, distance, and free energy in statistical mechanics.

Derelict asbestos mine sites in South Africa pose a considerable risk to human, environmental and socio-economic health. Comprehensive mineralogical and geochemical datasets for the existing hazardous geological materials still exposed in Southern African derelict asbestos mines remain largely non-existent, as very little published and up-to-date literature is available. In this study three representative types of asbestos mineral fibres from derelict asbestos mines in Southern Africa, namely chrysotile from Havelock mine, amosite from Penge mine and crocidolite from Prieska mine are characterized mineralogically and geochemically to critically evaluate real-life hazards in rural and asbestos-fibre contaminated regions. The samples were examined using polarising light microscopy, X-ray fluorescence (major and trace elemental analysis), X-ray diffraction (including Rietveld refinement), specific surface area analyses and bio-durability tests. Data are discussed in view of their potential toxicities on both human health and the environment in the context of developing countries. Finally, information on the mineralogical and geochemical status of asbestos mine waste and its importance as baseline data for rehabilitation considerations is also evaluated.

Infrastructure such as transport, electricity, telecommunications, and sanitation are indispensable drivers for improving the country’s social and economic development. The industrial, agricultural, fisheries and service sectors are also key tools for the country's economic growth. This study aims to analyze the influence of infrastructure development on Djibouti’s economic growth and determine the other economic sectors. This study employs multiple regression analyses from Eviews Software to establish a correlation between these variables and Djibouti’s economic growth, utilizing data spanning from the period 2013 to 2022. The results reveals that mobile cell phone subscriptions, and the people using the health service management, industry, and service have a positive and highly significant influence on Djibouti's economic growth. The study found that access to electricity has a positive influence on economic growth in Djibouti, but is not statistically significant. In addition, the study shows that agriculture, forestry, and fisheries have a negative influence on economic growth in Djibouti, but are statistically significant. Therefore, we recommend that the Government of Djibouti strengthen and ensure the benefit of developing electricity infrastructure in Djibouti and the agriculture, forestry, and fisheries sectors to achieve sustainable economic growth in the coming years.

Accurately predicting drug-drug interactions (DDIs) is crucial for preventing adverse drug events in clinical settings. However, existing methodologies often rely on complex models built from diverse data sources, posing challenges in computational drug discovery. To address the need for precise computational methods in predicting unknown DDIs, this study introduces a novel Deep Neural Network (DNN)-based approach. By leveraging a wide range of drug-related information, including substructure, targets, side effects, pathways, and indications, our method calculates multiple drug similarities. These similarities are then synthesized using a nonlinear fusion method to extract high-level features. Subsequently, a tailored neural network is deployed for interaction prediction. Comparative evaluation against three prominent machine learning classifiers—Extreme Gradient Boosting (XGBoost), Adaptive Gradient Boosting (AdaBoost), and Light Gradient-Boosting Machine (LGBM)—using three benchmark datasets demonstrates the superior performance of DNN. It achieves outstanding accuracy, precision, recall, and F1-score metrics, all reaching 94.6% in cross-validation. Additionally, case studies involving numerous drug pairs confirm the reliability of DNN in accurately predicting unknown DDIs. These findings underscore DNN as a potent and reliable method for DDI prediction, with promising implications for drug discovery and healthcare applications.

Context: As software industries, adopted different frameworks where Scrum is play a vital role in different software industries. Scrum basis the three main stakeholders i.e. Product Owner, Scrum Master and Development. Where Scrum Master is a very crucial role for any agile project. However, in the past Scrum Master Faces different challenges, which discovered in several studies. However, we need to measure the effectiveness of the Scrum master in Agile Projects, how presently Scrum Master are performing in Pakistani software industries. Objective: The main objective of this research to identify the effectiveness of the Scrum Master in agile projects in Pakistani software industries. Method: Research Method (Qualitative Research) For this purpose, we gathered the facts from Pakistani software industries by using the qualitative method. We conducted a survey from different software industries; almost 12 participants responded the survey as per their best knowledge as well as they agreed for face- to-face interviews. Results: The results indicated that, mostly organization compliance with the Scrum ceremonies. In addition, 65% Scrum Masters has a great effectiveness in any agile project. 21% of Scrum Master generates negative impact in agile project. Conclusion: The main highlights of this research, we have presented the compliance of the Scrum in different software organization. Further, we explore the both positive and negative impact of the Scrum master in Pakistani software organizations.

This research aimed to compare the measurements recorded by a traditional PCI technology biometer (Partial Coherence Interferometry) and by a SS-OCT (Swept Source Optical Coherence Tomography) technology machine in preoperative screening of patients with age-related cataract. Optical biometry was performed with the IOLMaster 500 (version 5.5, Carl Zeiss Meditec, Germany) and the ANTERION (Heidelberg Engineering, Germany) in a total sample of 144 eyes, from 80 patients, (37 men and 43 women), with a mean age of 70.54 ± 0.739 years (range: 45-89 years) and the values of the Axial Length (AL), two meridians of the cornea (Kf, Kflat and Ks, Ksteep), astigmatism (Ast) as well as the Anterior Chamber Depth (ACD) were compared with the program IBM SPSS Statistics 27. The IOLMaster500 and ANTERION devices did not have statistically significant differences in terms of axial length and flat corneal meridian Kf, while they differed statistically significantly in terms of steep corneal meridian Ks, astigmatism and anterior chamber depth. This study suggests that a thorough pre-operative check must be performed, sometimes with more than one device, aiming at greater accuracy in the measurements of the ocular biometrics, so that we achieve more successful postoperative outcomes and ultimately more satisfied patients.

The orexin/hypocretin neuropeptide family has emerged as a focal point of neuroscientific research following the discovery that this family plays a crucial role in a variety of physiological and behavioral processes. These neuropeptides serve as powerful neuromodulators, intricately shaping autonomic, endocrine, and behavioral responses across species. Notably, they serve as master regulators of vigilance and stress responses; however, their role in complex processes such as food intake, metabolism, and thermoregulation warrant further investigation. This narrative review provides a journey through the evolution of our understanding of the orexin system, from its initial discovery to the promising progress made in developing orexin derivatives. It goes beyond conventional boundaries, striving to synthesize the multifaceted activities of orexins. Special emphasis is placed on domains such as stress response, fear, anxiety, and learning, in which the authors contributed to the literature with original publications. This article demonstrates the orchestrating role of the orexins in several intricate and integrative physiological processes. It also overviews the advancement of orexin pharmacology, which has already yielded some promising successes, particularly in the treatment of sleep disorders. This interdisciplinary approach to studying neuropeptides unveils their significance as vital connectors between transient functional changes and lasting structural adaptations. Ultimately, it advances our understanding of the intricate physiological and behavioral contributions of the orexin/hypocretin neuropeptide family.

By introducing environmental mediator, for avoiding randomness in selecting indicators and subjectivity in deciding interaction path coefficients to reveal interaction mechanism among forest industry, ecology and environmental capacity, structural Pressure–State–Impact–Response (PSIR) and quantitative Structural Equation Modeling (SEM) are utilized with data on thirty–one provinces of China. We can find that: (i) forest industry has a negative influence on ecology, whereas ecology has a positive influence on industry; (ii) the destructive influence that industry has on ecology is much greater than the positive effect ecology has on industry; and (iii) environmental capacity plays a partial mediating role between industry and ecology. According to these results we can conclude that: (i) forest industry and ecology are not in a symbiotic relationship and have not reached a level of ecological security; (ii) the interaction between industry and ecology is in a period of transition from antagonistic to beneficial; and (iii) industry dominates ecology. However, we prospect the following advice: (i) methods of forest industry should be changed; (ii) new modes of industrial integration and circular economy should be developed; and (iii) the ability of the environment to sustain itself should be enhanced. The level of forest ecological security to discuss the symbiotic mechanism of industry and ecology will propose to be measured in future.

Erythropoiesis is a complex process driving the production of red blood cells. During homeostasis, adult erythropoiesis takes place in the bone marrow and is tightly controlled by erythropoietin (EPO), a central hormone mainly produced in renal EPO-producing cells. The expression of EPO is strictly regulated by local changes in oxygen partial pressure (pO₂) as under deprived oxygen (hypoxia) the transcription factor Hypoxia Inducible Factor-2 induces EPO. However, erythropoiesis regulation extends beyond the well-established HIF-EPO axis, and involves processes modulated by other hypoxia pathway proteins (HPPs), including proteins involved in iron metabolism. The importance of a number of these factors is evident as their altered expression has been associated with various anemia-related disorders, including chronic kidney disease. Eventually, our emerging understanding of HPPs and their regulatory feedback will be instrumental in developing specific therapies for anemic patients and beyond.

The causal networks are important for understanding the signaling alterations in diseases. To reveal the network pathways affected in epithelial-mesenchymal transition (EMT) and cancer stem cells (CSCs), which are related to poor prognosis of cancer, the molecular networks and gene expression in diffuse- and intestinal-type gastric cancer (GC) have been analyzed. The network pathways in GC were analyzed in Ingenuity Pathway Analysis (IPA). The analysis of the probe sets of which gene expression has significant differences between diffuse- and intestinal-type GC in RNA Sequencing publicly available data identified 1099 causal networks in diffuse- and intestinal-type GC. Master regulators of the causal networks included lenvatinib, pyrotinib, histone deacetylase 1 (HDAC1), mir-196, and erb-b2 receptor tyrosine kinase 2 (ERBB2). The analysis of the HDAC1-interacting network identified the involvement of regulation of EMT by growth factors pathway, coronavirus pathogenesis pathway, and vorinostat. The network had RNA-RNA interactions with microRNAs such as mir-10, mir-15, mir-17, mir-19, mir-21, mir-217, mir-223, mir-25, mir-27, and mir-34. These molecular networks revealed in the study may lead to the identification of drug targets for GC.

We introduce two symmetric concepts to physics: “distance” (space and time in one) and “wavematter” (electromagnetic wave packet and matter in one). We claim that physics has chosen the wrong concept of time: It is not aware that the time of a moving object flows in a direction other than my time. We provide 15 proofs for our claim by solving 15 mysteries of physics graphically! For example, we prove that length contraction and time dilation are actually geometrical effects in a 4D manifold that we call “Euclidean spacetime” (ES). We prove that the discrepancy in calculating the Hubble constant stems from a systematic error in the redshift measurement. We prove that what I deem wave, deems itself matter, which solves wave–particle duality. We even untangle quantum entanglement without the issue of non-locality. We finally understand why alternative theories of Euclidean relativity have failed: They are all based on four dimensions of space rather than distance. A huge amount of energy was injected into ES at a point that we take as origin. Ever since has this energy been moving radially away at the speed of light. We live in the 3D hypersurface of an expanding 4D hypersphere. Hyperspherical coordinates have the great advantage that they reduce all that is ever happening to just one formula. So, it is the Theory of Everything in these coordinates: “Energy is covering radial distance which, divided by Euclidean time, is equal to the speed of light.” Acceleration and force like gravitation emerge from a rotation of objects in ES and a subsequent projection to 3D space. Matching the symmetry simplifies physics.

The fractional advection-dispersion equation FADE plays an important role, especially in explaining the process of solute-transport in natural porous media with different degrees of heterogeneity. However, studies of the flow and transport of contaminants in the underground environment are based on the knowledge of many functional parameters of the subsoil. The delay factor caused by nonlinear absorption is one of these parameters inheriting significant ambiguities in its estimation in heterogeneous media. In the study, a fractional advection-dispersion FADE model was developed by the implicit Euler method, based on a Grunwald and Caputo-Liousville approximation to explicitly evaluate and simulate the transport mechanism of contaminants in media with unsaturated porous materials subjected to a nonlinear sorption model. Better solute mass retention was observed for fractional advection-dispersion FADE model. Moreover, the absorption parameter of the retardation coefficient has a better impact on the motion of the solute in a saturated porous medium. In other words, it has a significant effect on the dispersion of pollutants in aquifers. This study highlights the need to characterize the aquifer to predict solute transport in porous media.

Background: Microscopic examination of acid-fast stained sputum smears for detecting mycobacterial acid-fast bacilli (AFB) remains the most economical and readily available method for laboratory diagnosis of tuberculosis (TB). However, this conventional approach has limitations, including low sensitivity and labor-intensive procedures. Methods: An automated microscopy system incorporating artificial intelligence (AI) and machine learning for AFB identification was evaluated. The study was conducted at an Infectious Disease Hospital in Jiangsu Province, China, utilizing an intelligent microscope system (TB-Scan, Wellgen Medical, Kaohsiung). A total of 1,000 sputum smears were included in the analysis, with the system capturing digital microscopic images and employing an image recognition model to automatically identify and classify AFB. Referee technicians provided the gold standard for discrepant results. Results: The automated system demonstrated an overall accuracy of 95.00% (950/1,000), sensitivity of 91.24% (177/194), and specificity of 95.91% (773/806). Notably, the system identified 21 smears as positive that were previously reported as negative, with referee technicians confirming 17 of these as true positive and retracting the test results accordingly. Recalculating the performance, the accuracy increased to 96.70% (967/1,000), sensitivity to 91.94% (194/211), and specificity to 97.97% (773/789), with a false negative rate of 8.06% (17/211) and a false positive rate of 2.03% (16/789). Conclusions: The incorporation of AI and machine learning into an automated microscopy system demonstrated the potential to enhance the sensitivity and efficiency of AFB detection in sputum smears compared to conventional manual microscopy. This approach holds promise for widespread application in TB diagnostics and potentially other fields requiring labor-intensive microscopic examination.

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

The paper aims to illustrate the different roles that social sciences can play in the study of the energy transition. To this end, a scheme is developed that frames the relative position of the social sciences with respect to other disciplines (metaframe). Secondly, socialization is identified as a charismatic category capable of providing an original, typically sociological contribution to the complex and hesitant energy transition (masterframe)

This paper presents a novel 3-degrees-of-freedom (3-DOF) haptic master with rubber bands for self-resetting. The mechanical design avoids coupling between three directions mechanically by using three perpendicular axis intersecting at one point. Bevel gear transmission is adopted to increase the compactness of the overall structure. VR-based interactive system is designed and built by incorporating the proposed haptic master. The proposed haptic device can generate force feedback along 3-degree-of-freedom motion using motors and provide command signals to the avatar in the virtual environment. In order to analyze the performance of the developed device in terms of haptic feedback operation, ergonomics assessments are designed and experimentally implemented. Preliminary studies on the influencing factor including the guidance force, the reset force, the speed of the avatar and the arm the length have been conducted. The results of this paper are of great significance for the design of the haptic master and interactive system.

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

The stability properties of the Hill equation are discussed, and especially those of the Mathieu equation that characterize ion motion in electrodynamic traps. The solutions of the Mathieu equation for a trapped ion are characterized by using the Floquet theory and Hill's Method solution, which yields an infinite system of linear and homogeneous equations whose coefficients are recursively determined. Stability is discussed for parameters $a$ and $q$ that are real. Characteristic curves are introduced naturally by the Sturm-Liouville problem for the well known even and odd Mathieu equations $ce_m(z,q)$ and $se_m(z,q)$. We illustrate the stability diagram for a combined (Paul and Penning) trap and represent the frontiers of the stability domains for axial and radial motion. In case of a Paul trap the stable solution corresponds to a superposition of harmonic motions. The problem of evaluating the maximum amplitudes of stable oscillations for the ideal conditions (taken into consideration) is also approached. Anharmonic corrections are discussed within the frame of the perturbation theory, while the frontiers of the modified stability domains are determined as a function of the chosen perturbation parameter. The results apply to 2D and 3D ion traps used for different applications in quantum engineering, among which optical clocks, quantum logic and quantum metrology, but not restricted only to these.

In this paper, we consider a fourth-order suspension bridge equation with nonlinear damping term |u_t|^m-2u_t and source term |u|^p-2u. We give necessary and sufficient condition for global existence and energy decay results without considering the relation between m and p. Moreover, when p>m, we give sufficient condition for finite time blow-up of solutions. The lower bound of the blow-up time T_max is also established. It worth to mention that our obtained results extend the recent results of Wang (J. Math. Anal. Appl., 2014) to the nonlinear damping case.

Publically available (own) transcriptomic data were re-analyzed to quantify the alteration of functional pathways in the thyroid cancer, establish the gene hierarchy, identify potential gene targets and predict the effects of their manipulation. The expression data were generated from one case of papillary thyroid carcinoma (PTC) and from genetically manipulated BCPAP (papillary) and 8505C (anaplastic) human thyroid cancer cell lines. The study used the genomic fabric perspective that considers the transcriptome as a multi-dimensional mathematical object based on the three independent characteristics that can be derived for each gene from the expression data. We found remarkable remodeling of the thyroid hormone synthesis, cell cycle, oxidative phosphorylation and apoptosis pathways. Serine peptidase inhibitor, Kunitz type, 2 (SPINT2) was identified as the Gene Master Regulator of the investigated PTC. The substantial increase of the expression synergism of SPINT2 with apoptosis genes in the cancer nodule with respect to the surrounding normal tissue (NOR) suggests that its experimental overexpression may force the PTC cells into apoptosis with negligible effect on the NOR cells. The predictive value of the expression coordination for the expression regulation was validated with data from 8505C and BCPAP cells before and after lentiviral transfection with DDX19B.

Modern physics is situated on the fine line between scientific research and an attempt to answer metaphysical questions. Contemporary scholars such as Henry Stapp and Roger Penrose attempt to create an ontological interpretation of Schrödinger's equation in superposition state and its reduction or collapse to classical state. In this short essay I will try to explore how Immanuel Kant's metaphysics and the concept of noumena can be possibly integrated with quantum physics and Schrödinger's equation.

This research paper is to analyze the planning and design techniques of the tourism complexes in the process of municipalities’ master planning. First, it explains the importance of the tourism industry with the help of theories of scholars and experts. Then, it emphasizes the link between the economic developments of cities/regions with the development of the tourism industry. The innovation of this work is to integrate tourism industry planning and comprehensive regional/ urban planning. The main way of doing this is to plan and design the tourism complexes in the early stages of the master planning of the municipality. Urban land-use policies and locating techniques are suggested through this research. Land-use policies and new urban design models for the regional/urban sustainable development are some of the other handouts in this paper. The outcome of this research is good assistance for engineers, planners, and students of urban and regional development.

The purpose of this case study was to evaluate the benefits that evidence-based nutritional and training recommendations could have on the time course of reconditioning following hip arthroplasty in a competitive master triathlete. Methods: During 38 weeks (from 6 weeks prior to surgery through to the return to competition), the athlete was provided with detailed training and nutritional recommendations based on the latest research evidence. Dietary intake (via the remote food photographic method), body composition (via DXA), peak oxygen uptake (VO2peak), peak power output (PPO) and cycling efficiency (GE) were assessed 6 weeks pre- and 8, 12, 18, 21 and 25-weeks post-surgery. Training load was quantified (TRIMP score) daily during the retraining. Results: Total body mass increased by 8.2 kg (attributable to a 3.5 and 4.6 kg increase in fat mass and lean mass, respectively) between week -6 and week 8 despite a reduction in carbohydrate (CHO) intake post-surgery (<3.0g/kg/day). This was accompanied with a decrease in VO2peak, PPO, and GE due to a drop in training load. From week 7, the athlete resumed training and was advised to gradually increase CHO intake according to the demands of training. Conclusions: Eventually the athlete was able to return to competition in week 32 with a higher PPO, improved VO2peak and GE. Throughout retraining, energy availability was maintained around 30 kcal/kg LBM/day, protein intake was high while CHO intake was periodised. Such dietary conditions allowed the athlete to maintain and even increase lean mass, which represents a major challenge with ageing.

We apply utilized the extended form of the auxiliary equation method to obtain extensively reliable exact travelling wave solutions of perturbed Gerdjikov–Ivanov equation (GIE) that is widely used as a model in the field theory of quanta and non-linear optics. The method is based on a simple first order second degree ODE. The new form of the approach gives more solutions to the governing equation efficiently.

A proof is given showing the Collatz Conjecture is true for all positive integers. The proof was possible once the perspective of the proof was changed from looking at the pattern of the positive integers to looking at the conjecture rules. The conjecture rule for even numbers organizes all positive integers into unique sets and the rule for odd numbers interconnects the unique sets into dendritic pathways to “1.” Infinite loops, other than the minor 4-2-1 loop after reaching “1,” and pathways to infinity are shown to be mathematically impossible. The proof predicted a general equation that shows all positive integers ultimately reach a final value of “1," and calculates the values and locations of the odd positive integers during the iterations for each tested positive integer.

In the framework of the self-consistent Maxwell-Pauli theory, the non-linear Pauli equation is obtained. Stationary and nonstationary solutions of the nonlinear Pauli equation for the hydrogen atom are studied. We show that spontaneous emission and the related rearrangement of the internal structure of an atom, which is traditionally called a spontaneous transition, have a simple and natural description in the framework of classical field theory without any quantization and additional hypotheses. The behavior of the intrinsic magnetic moment (spin) of an electron wave in an external magnetic field is considered. We show that, according to the self-consistent Maxwell-Pauli theory, in a weak magnetic field, the intrinsic magnetic moment of an electron wave is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector.

The seismic events of 2015 in Nepal exposed the challenges associated with constructing earthquake-resistant 2-story self-built stone masonry structures in high-elevation rural regions, especially post-disaster. The Department of Urban Development and Building Construction (DUDBC) provided designs that failed to preserve the local architectural landscape and craftsmanship while adding unfamiliar knowledge and technology. To address the challenges related to architecture, structure, and socio-economic concerns in designing and implementing post-earthquake houses, a need-based building development framework is required for standardized practice. This study presents a novel framework to assess, design, and implement a self-built house after a disaster, consisting of five stages: 1) post-disaster problem assessment, 2) need identification, 3) material selection, 4) design development, and 5) validation and implementation. Based on this framework, we proposed a novel gabions building construction technology for two-story stone masonry structures that effectively mitigate post-disaster challenges such as logistic, resilience, and socioeconomic aspects while improving disaster resiliency specifically in the high-elevation rural areas of Nepal. The proposed two-story gabion building preserves architectural values, enhances structural integrity, and provides cost-effectiveness when compared with its DUDBC peer models while providing much-needed relief to the vulnerable community. The proposed resilient house, G- 2.1, utilizes locally sourced materials and craftsmanship, and innovative gabion technology that ensures affordability and facilitates knowledge transfer. The contribution of this study includes a development framework and a two-story gabions house that is most suitable for self-built post-disaster reconstruction and resilient to local architecture and socio-economic conditions while providing structural integrity and safety.

Master Valentim’s fountain became an important historical patrimony for Brazil, being portrayed by famous artists among them Jean-Baptiste Debret. In 1938, it was registered as cultural heritage by the Brazilian National Historical and Artistic Heritage Institute (IPHAN), and in 1990 it was subjected to excavation and restoration works. The fountain was built in Gneiss and Lioz limestone, with metallic plates and mortar connecting the Gneiss blocks. Currently, deteriorations in the fountain stones can be observed such as light stains and some aesthetic modifications caused by inadequate restorations. Petrography, XRF, XRD, Physical Properties, Colorimetry, Electrical Conductivity, ICP-OES, SEM-EDX, and TGA were performed in order to characterize the Gneiss blocks, the metallic plates, the stones used in previous restorations, as well as light stains observed on the Gneiss blocks. The petrography and XRD analyses inferred that light stains may have been caused by the formation of an insoluble salt as a result of the association of the lead from the plates with other elements. The XRD analysis on the light staining area indicated presence of cerussite (PbCO₃), and anglesite (PbSO₄), which are the probable cause of the light stains. The SEM-EDX results suggested that sulfur is the main element associated to lead.

P-band radar remote sensing applied during the Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS) mission has shown great potential for estimation of root zone soil moisture. When retrieving the soil moisture profile (SMP) from P-band radar, a mathematical function describing the vertical moisture distribution is required. Because only a limited number of observations are available, the number of free parameters of the mathematical model must not exceed the number of observed data. For example, a second order polynomial that contains 3 free parameters was presumed based on in-situ SMP data. The polynomial is currently parameterized based on 3 backscatter observations provided by AirMOSS (i.e. one frequency at three polarizations of HH, VV and HV). In this paper, a more realistic, physically-based SMP model containing 3 free parameters is derived based on a solution to Richards’ equation for unsaturated flow in soils. Evaluation of the new SMP model based on both numerical simulations and measured data revealed that it exhibits greater flexibility for fitting measured and simulated SMPs than the currently applied polynomial. It is also demonstrated that the new SMP model can be reduced to a second order polynomial at the expense of fitting accuracy.

The study aimed to analyze thoracic and lumbar erector spinae muscle activations during 3D elongation exercises in individuals with adolescent idiopathic scoliosis (AIS). Participants included 24 adolescents, meeting specific criteria such as a Cobb angle between 10° and 20°, and not having undergone surgical or brace treatments. EMG data were collected to evaluate muscle activations. The study found no significant interaction between exercise type and the side of the curve, but a significant main effect of exercise type on muscle activation, irrespective of Cobb angle. Different exercise types significantly affected muscle activity, with the highest activations in the TheraBand exercise, followed by manual and without equipment conditions. This suggests that exercise type significantly impacts muscle engagement in AIS patients, providing valuable insights for targeted exercise program design. The study, however, focused on short-term muscle activation, not long-term Cobb angle progression, pointing to the need for further research in this area.

Supervised land-use/land-cover (LULC) classifications are typically conducted using class assignment rules derived from a set of multiclass training samples. Consequently, classification accuracy varies with the training data set and is thus associated with uncertainty. In this study, we propose a bootstrap resampling and reclassification approach that can be applied for assessing not only the uncertainty in classification results of the bootstrap-training data sets, but also the classification uncertainty of individual pixels in the study area. Two measures of pixel-specific classification uncertainty, namely the maximum class probability and Shannon entropy, were derived from the class probability vector of individual pixels and used for the identification of unclassified pixels. Unclassified pixels that are identified using the traditional chi-square threshold technique represent outliers of individual LULC classes, but they are not necessarily associated with higher classification uncertainty. By contrast, unclassified pixels identified using the equal-likelihood technique are associated with higher classification uncertainty and they mostly occur on or near the borders of different land-cover.

Current physiology attributes the mechanism of membrane potential generation to transmembrane ion transport, but ion adsorption could just as well play this fundamental role. The evidence shows that the ion adsorption mechanism accurately reproduces the experimentally measured membrane potential. The Goldman-Hodgkin-Katz equation (GHK eq.) and the Nernst equation (Nernst eq.) are the typical mathematical formulas representing the membrane potential in current physiology. However, the authors were able to show that the potential formulas by ion adsorption mechanism give identical results to GHK eq. and Nernst. eq. Our experimental and theoretical analyses suggest that there is a special relationship between the membrane potential and the membrane surface charge density, and this unique equation inevitably leads to the establishment of a GHK eq and/or a Nernst eq. The authors found that the unique equation is the foundation of thermodynamics “Boltzmann distribution”. Thus, the GHK eq. and the Nernst eq. are simply the natural consequence of thermodynamics from the view of the ion adsorption mechanism.

Considerable amounts of agro-industrial by-products are discarded or burnt as fuel every year. However, they can be utilized as a valuable source of fiber, phenolics and other useful compounds such as antioxidants. The profile of beneficial compounds can be affected by genotype, locality, orchard management and productive season, adding or decreasing the bioactive potential of by-products. In this study, hazelnut (Corylus avellana L.) and walnut (Juglans regia L.) nutshells were investigated for their fiber content and antioxidant capacity as valorized by-products for the industry. Determinations (ORAC, TPC and color asses) were performed in hazelnut and walnut orchards located in Southern Chile during three consecutive seasons (2020/21; 2021/22 and 2022/23). Analyses of oxygen radical absorbance capacity (ORAC) in nutshells showed the highest ORAC from both species in the season 2020/21 (3217 µmol TE g1DW for hazelnut shells and 4663 µmol TE g DW1 for walnut shells), while variability in the consecutive seasons was lower for hazelnut than in walnut. Total phenolic content in hazelnut shells was positively correlated with L* (R: 0.883) and E (R: 0.924) during 2020/21 season, also with L* for 2022/23 (R: 0.907). While ORAC was negatively correlated with L* (R: 0.922) in 2021/22. In addition, morphological and structural features of both nutshells examined by Scavenging Electron Microscopy (VP-SEM) and Confocal Scavenging Laser Microscopy (CSLM) revealed differential tissue distribution and accumulation patterns of both cellulose and lignin. On the other hand, photo-colorimetric values were determined for both shells and corresponding seasons, and non-significative differences were found both shells and among seasons Finally, these results provide insight into the physicochemical characteristics of two shell types which should be considered together with antioxidant capacity in their valorization as a residual material.

Currently, energy security and environmental degradation are the two biggest challenges before humanity that can be surmounted with the use of green and sustainable biofuels produced from lignocellulosic crops. In the future, to ensure adequate and cost-effective supply of biofuels, it requires a sufficient amount of amenable and quality lignocellulosic feedstocks. Therefore, agricultural yields of lignocellulosic biomass crops should be substantially increased by intense genetic maneuvering of key gene regulatory mechanisms and signaling pathways that control plant biomass yield. Recently, numerous miRNAs families are identified, characterized, and validated across the plant kingdom. Plant microRNAs (miRNAs) are 21 to 24 nucleotides long, non-coding small RNAs, act as regulators of their target genes via inducing modifications in transcription, translation, and epigenome. MiRNAs represent many hallmark characteristics like sequence-specific regulation, tissue, and species-specific expression, evolutionary conservation, and functional diversity. They coordinate well physiological and life cycle processes in plants under adverse environmental conditions. Hence, miRNAs offer accurate, precise, and efficient regulatory switches in the miRNA-targeted genetic networks. It is evident from the study of the miR156 family and its target SQUAMOSA PROMOTER BINDING PROTEIN-LIKE (SPL) genes network that controls highly significant agronomic traits in crop plants. The miR156/SPL module acts as a master circuit that synchronizes many intricate complex biological functions such as growth and development, and metabolic processes by sensing internal and external environmental signals in plants. Therefore, miR156 can prove a potential target for miRNAs based plant biotechnology to harmonize complex biofuel traits and improve biomass yield in lignocellulosic biomass crops.

In this paper, we revisit the two theoretical approaches for the formulation of the tachyonic Dirac equation. The first approach works within the theory of restricted relativity, starting from a Lorentz invariant Lagrangian consistent with a spacelike four-momentum. The second approach uses the theory of relativity extended to superluminal motions and works directly on the ordinary Dirac equation through superluminal Lorentz transformations. The equations resulting from the two approaches show mostly different, if not opposite, properties. In particular, the first equation violates the invariance under the action of the parity and charge conjugation operations. Although it is a good mathematical tool to describe the dynamics of a space-like particle, it also shows that the mean particle velocity is subluminal. In contrast, the second equation is invariant under the action of parity and charge conjugation symmetries, but the particle it describes is consistent with the classical dynamics of a tachyon. This study shows that it is not possible with the currently available theories to formulate a covariant equation that coherently describes the neutrino in the framework of the physics of tachyons, and depending on the experiment, one equation rather than the other should be used.

The effects on Raychaudhuri's equation of an intrinsically discrete or particle nature of spacetime are investigated, through consideration of null congruences emerging from, or converging to, a generic point of spacetime, i.e. in geometric circumstances somehow prototypical of singularity issues. This is done from an effective point of view, meaning through a (continuous) description of spacetime modified to embody the existence of an intrinsic discreteness on the small scale, adding to previous results for non-null congruences. Various expressions for the effective rate of change of expansion are derived. They in particular provide finite values for the limiting effective expansion and its rate of variation when approaching the focal point; this on top of resulting non vanishing the limiting cross-sectional area itself of the congruence.

In this paper, I investigate Hyers-Ulam-Rassias stabilities of the general quintic functional equation and the general sextic functional equation.

An adequate representation of the water infiltration process in the soil allows improving the efficiency in application and the uniformity in surface irrigation. The Green and Ampt model has shown a good representation of the process, and researchers from the United States Department of Agriculture (USDA) determined the values of their parameters for soils of that country, which are shown in tables or through functional relationships and this information is used as reference in several parts of the world, although there is no certainty that they are representative of the soils in Mexico. In this study, the parameters of the Green & Ampt equation were determined and evaluated in some soils of agricultural importance in Mexico. The parameters were obtained in four ways: one of them applied a methodology adapted from Brooks and Corey to quantify the wetting front capillary pressure head and used an permeameter under constant hydraulic head to determine the saturated hydraulic conductivity, and the other three consisted in taking them from three studies reported by the USDA. The values of the parameters suggested in Mexico drastically underestimated the results with relative errors (RE) in a range of -49.0 to -94.0% and the most representative were those obtained with the methodology proposed in this research with RE of -15.0 to 6.0%.

Defining integrals over volume element in curved spacetime together with the mass and energy densities within that region of spacetime is apparently equivalent to the given energy and mass of that body or particle. With this in mind equations involving energies and mass can be rewritten in terms of their densities and the integral over the volume element. The idea find its place in the Hamiltonian formulations, and can be carried over into quantum mechanical frameworks systematically accounting for the effect of spacetime volume structures and gravity on dynamics of quantum systems. This article briefly explores this concept and runs through various frameworks and equations relevant to this idea, particularly the schrodinger-Newton equation and discusses the cosmological constant as a vacuum energy density.

In this paper, we introduce a way of representing a given mapping as the sum of odd and even mappings. Then, by using this representation, we investigate the stability of various forms for the general nonic functional equation.

Electrically charged particles such as Electrons and Protons carry electric, E, and magnetic, B, fields. In addition to these fields, Quantum Mechanics (QM) endows these particles with an `arcane and spooky' field --- the wavefunction. This wavefunction of QM is not only assumed to be separate but distinct from the electromagnetic field. We herein upend this view by demonstrating otherwise. That is, we demonstrate that the four components of the Dirac wavefunction, can be shown to not only be an intimate, but, a direct function of the electromagnetic field carried by the particle in question. Insofar as unity, depth in our understanding and insight into both Dirac and Maxwell's equations as major pillars of Modern Physics, we believe that this work may very well inch us one-step-closer to the truth.

In this short note we present a technique using which one attributes frequency and wavevector to (almost) arbitrary scalar fields. Our proposed definition is then applied to the classical wave equation to yield a novel nonlinear PDE.

Maxwell equation for the electric field has been solved for any medium by suggesting the wavenumber and angular frequency be complex quantities. This accounts for the field decay by interaction with the medium.This expression for the time and special decay of the electric field in a medium is used to construct a new wave function sensitive to the medium physical properties. This new wave function, unlike the conventional one, differentiates between a beam of particles in a vacuum and that enters a medium which is an attenuated due to the scattering effect.Another expression for time decaying electric field was obtained using Newton’s laws for frictional medium. This expression shows that the electric field diminishes due to friction.Fortunately, this time decaying part of the electric field is typical to that derived from Maxwell’s equations. Finally, a new Schrodinger equation sensitive to the medium properties was derived. This equation, fortunately, describes some scattering processes for Protein scattering, scattering of x-rays, opto-acoustic phonons, and Raman scattering for some materials successfully .

The dynamic and never exactly repeatable tumor transcriptomic profile of people affected by the same form of cancer requires a personalized and time-sensitive approach of the gene therapy. The Gene Master Regulators (GMRs) were defined as genes whose highly controlled expression by the homeostatic mechanisms commands the cell phenotype by modulating major functional pathways through expression correlation with their genes. The Gene Commanding Height (GCH), a measure that combines the expression control and expression correlation with all other genes, is used to establish the gene hierarchy in each cell phenotype. We developed the experimental protocol, the mathematical algorithm and the computer software to identify the GMRs from transcriptomic data in surgically removed tumors, biopsies or blood from cancer patients. The GMR approach is illustrated with applications to our microarray data on human kidney, thyroid and prostate cancer samples, and on thyroid, prostate and blood cancer cell lines. We proved experimentally that each patient has his/her own GMRs, that cancer nuclei and surrounding normal tissue are governed by different GMRs, and that manipulating the expression has larger consequences for genes with higher GCH. Therefore, we launch the hypothesis that silencing the GMR may selectively kill the cancer cells from a tissue.

Proposed in 1889 by Svante Arrhenius, the Arrhenius equation is an important result in physical chemistry which aims to find the relationship between temperature and reaction rates. It is also an essential equation for analytic chemistry which helps to determine the energy barrier for a given reaction. In this article, we will go through a detailed derivation of the exponential factor in the Arrhenius Equation based on the Boltzmann distribution of particle energy probability. Then, we will attempt to model the pre-exponential factor in accordance with the principles of collision theory for bi-molecular reaction with gaseous reactants. Understanding the basic principles of chemical reaction provides valuable tools to analyze complex reaction mechanisms in the perspective of optimizing existing industrial processes.

Recently quantum cosmology in tomographic representation was considered. as an important tool to analyze the quantum states of the early universe in relation with the subsequent classical evolution. Given a wave function the correspondent tomogram is defined proportional to the square modulus of its fractional Fourier transform. The classical limit obtained by taking the limit ℏ→0 can be compared with the classical tomogram obtained from the classical hamiltonian formalism. In this paper we show that a set of tomograms can be derived as exact solutions of a third order equation when a de Sitter quantum universe is considered. We finally discuss the limits of this approach to quantum cosmology because the extension to equations with arbitrary potentials can become extremely complicated for potentials given by algebraic polynomials of degree greater than two and therefore also for potentials expressible by arbitrary functions.

This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties we reformulate this equation using some ideas from the Lagrangian fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation and the corresponding Matlab code is provided with this article under an open source license.

Only two percent of Glioblastoma multiforme (GBM) patients respond to standard care and survive beyond 36 months (long-term survivors, LTS) while the majority survive less than 12 months (short-term survivors, STS). To understand the mechanism leading to poor survival, we analyzed publicly available datasets of 113 STS and 58 LTS. This analysis revealed 198 differentially expressed genes (DEGs) that characterize aggressive tumor growth and may be responsible for the poor prognosis. These genes belong largely to the GO-categories “epithelial to mesenchymal transition” and “response to hypoxia”. In this paper we applied upstream analysis approach which involves state-of-art promoter analysis and network analysis of the dysregulated genes potentially responsible for short survival in GBM. Binding sites for transcription factors associated with GBM pathology like NANOG, NF-κB, REST, FRA-1, PPARG and seven others were found enriched in the promoters of the dysregulated genes. We reconstructed the gene regulatory network with several positive feedback loops controlled by five master regulators – IGFBP2, VEGFA, VEGF165, PDGFA, AEBP1 and OSMR which can be proposed as biomarkers and as therapeutic targets for enhancing GBM prognosis. Critical analysis of this gene regulatory network gives insights on mechanism of gene regulation by IGFBP2 via several transcription factors including the key molecule of GBM tumor invasiveness and progression, FRA-1. All the observations are validated in independent cohorts and their impact on overall survival is studied.

The present work is concerned with the study of the generalized Langevin equation and its link to the physical theories of statistical mechanics and scale relativity. It is demonstrated that the form of the coefficients of Langevin equation depend critically on the assumption of continuity of the reconstructed trajectory. This in turn demands for the fluctuations of the diffusion term to be discontinuous in time. This paper further investigates the connection between the scale-relativistic and stochastic mechanics approaches, respectively, with the study of the Burgers equation, which in this case appears as a stochastic geodesic equation. By further demanding time reversibility of the drift the Langevin equation can also describe equivalent quantum-mechanical systems in a path-wise manner. The resulting statistical description obeys the Fokker-Plank equation of the probability density of the differential system, which can be readily estimated from Monte Carlo simulations of the random paths. Based on the Fokker-Plank formalism a new derivation of the transient probability densities is presented. Finally, stochastic simulations are compared to the theoretical results.

Abstract Introduction: In the last thirty years, brain neuromodulation techniques have been used as an alternative to pharmacological treatment of neurological disorders. Parkinson's disease (PD) is a neurodegenerative disorder leading to bradykinesia, rest tremor, postural changes, and non-motor symptoms such as depression, anxiety, sleep disorders, pain, and cognitive decline that compromises executive functions (EFs), responsible for the orderly execution of behaviors and tasks of daily life and intentional and directed actions. To this date, a few studies with transcranial direct current stimulation (tDCS) have shown beneficial effects in PD patients concerning specific motor and non-motor symptoms, targeting the motor cortex and/or prefrontal regions. Objective: The main objective of this study was to evaluate the effects of left prefrontal tDCS across a broad spectrum of motor and non-motor symptoms of PD using established validated scales. Method: Single-blind randomized clinical trial with 18 volunteers with PD, aged between 45 and 80 years (66.1 ± 9.65), who met inclusion and exclusion criteria. Participants were submitted to assessments of motor and non-motor functions employing psychometric scales and tests to evaluate EFs and were randomly divided into two groups: control (sham stimulation) and experimental (active stimulation). All participants were involved in three separate tDCS sessions. The anode was positioned over the left dorsolateral prefrontal cortex and the cathode over the right supraorbital region, with a direct current intensity of 2mA, lasting 20 minutes. At the end of the three sessions, all participants were reassessed. Results: Significant effects of tDCS on non-motor functions were observed for cognition (verbal fluency of actions, clock copy test, appointment by visual confrontation, and verbal memory with immediate free recall) and subjective assessment of sleep quality (overall restlessness and discomfort in the arms and legs at night, leg and arm cramps at night and distressing dreams). There was also an improvement in the rate of errors and successes for congruent and incongruent stimuli of the Stroop Test. The beneficial effects on motor function were decreased rigidity, improved gait, and greater agility in the finger-tapping test. Conclusion: Three tDCS sessions showed positive results for participants with PD, producing significant improvements in various motor and non-motor functions, including sleep quality, cognition, and EFs. Additionally, the present results indicate that tDCS neuromodulation of the left dorsolateral prefrontal cortex region is feasible, safe, and provides significant objective benefits for PD patients.

We still do not have satisfactory answers about the inflationary and accelerating expansions of the universe, the missing mass problem, and the origins of the four fundamental forces and the quantum phenomena. Here, we introduce a new model of matter and space and a postulate on a constant of motion, and then show that an equation of motion derived from the constant of motion could provide new understandings of the above problems. For example, we show that there is a natural inflation scenario and that the co-moving distance to the closest accelerating supernova is clearly given as $c/(\sqrt{3} H)$ ($\sim$8.1 billion ly). In addition, we show that, in a system including a proton and an electron, the equation of motion has eight acceleration terms, some of which are suspected to be responsible for the four fundamental forces and the galaxy rotation anomaly. From further discussion, we conjecture that in order to understand the gravitational and strong interactions and the quantum phenomena, it is necessary to consider the expansion of the universe. The lensing mass distribution is explained, based on another postulate on a method of representing superposition.

Rough volatility models are popularized by \cite{gatheral2018volatility}, where they have shown that the empirical volatility in the financial market is extremely consistent with rough volatility. Fractional Riccati equation as a part of computation for the characteristic function of rough Heston model is not known in explicit form as of now and therefore, we must rely on numerical methods to obtain a solution. In this paper, we give a short introduction to option pricing theory and an overview of the current advancements on the rough Heston model.

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.

This paper secures the analytical soliton solutions of the perturbed NLSE gives to (1). The existence criteria have been demonstrated and the wave speed of the soliton befall out. To achieve all the results obtained we used the mathematical technique. In view of the results obtained, some new additional one have been reported in left-handed metamaterials.

Empowering women and promoting gender equality is crucial for accelerating sustainable development in fragile countries, including the Democratic Republic of Congo (DRC). However, there is scarce existing knowledge or understanding of the factors determining women’s empowerment in these contexts. We aimed to assess women's empowerment and determine its associated factors in Kinshasa, DRC. We analyzed data from the 2021 Performance Monitoring Assessment (PMA) survey. A sample of 1,365 women of childbearing age was retained for this study. Twenty empowerment items related to household decision-making, contraception use, and husband/partner influence were considered. We calculated the average women’s empowerment index (aWEI), identified the women empowerment variables using principal component analysis (PCA), and determined the associated factors for the first three principal components through the performance of multivariate binary logistic regression. In Kinshasa, the overall aWEI was estimated at 0.65. It was low for household decision-making (0.34) and high for husband/partner influence domains (0.93), respectively. Three principal components were identified and named, including the absence of threats, control of sexuality, and participation in decision-making. The factors associated with these components were having internet access, being in free union with a partner, being aged 40-49 years, and residing in a non-slum area. Increasing access to information would enable women in Kinshasa to make strategic decisions about their lives, benefiting themselves and others.

Physical processes are usually described using four-dimensional vector quantities - coordinate vector, momentum vector, current vector. But at the fundamental level they are characterized by spinors - coordinate spinors, impulse spinors, spinor wave functions. The propagation of fields and their interaction takes place at the spinor level, and since each spinor uniquely corresponds to a certain vector, the results of physical processes appear before us in vector form. For example, the relativistic Schrödinger equation and the Dirac equation are formulated by means of coordinate vectors, momentum vectors and quantum operators corresponding to them. In the Schrödinger equation the wave function is represented by a single complex quantity, in the Dirac equation a step forward is taken and the wave function is a spinor with complex components, but still coordinates and momentum are vectors. For a closed description of nature using only spinor quantities, it is necessary to have an equation similar to the Dirac equation in which momentum, coordinates and operators are spinors. It is such an equation that is presented in this paper. Using the example of the interaction between an electron and an electromagnetic field, we can see that the spinor equation contains more detailed information about the interaction than the vector equations. This is not new for quantum mechanics, since it describes interactions using complex wave functions, which cannot be observed directly, and only when measured goes to probabilities in the form of squares of the moduli of the wave functions. In the same way spinor quantities are not observable, but they completely determine observable vectors.In Section 2 of the paper, we analyze the quadratic form for an arbitrary four-component complex vector based on Pauli matrices. The form is invariant with respect to Lorentz transformations including any rotations and boosts. The invariance of the form allows us to construct on its basis an equation for a free particle combining the properties of the relativistic wave equation and the Dirac equation. For an electron in the presence of an electromagnetic potential it is shown that taking into account the commutation relations between the momentum and coordinate components allows us to obtain from this equation the known results describing the interactions of the electron spin with the electric and magnetic field. In section 3 of the paper this quadratic form is expressed through momentum spinors, which makes it possible to obtain an equation for the spinor wave function in spinor coordinate space by replacing the momentum spinor components by partial derivative operators on the corresponding coordinate spinor component. At the end of the paper the question on a possibility of second quantization of the electron field in the spinor coordinate space is touch upon. The statement that the electron and positron have the same, and exactly positive energy, and have opposite signs of charge and opposite signs of mass is also justified. Accordingly, in the process of annihilation their total energy, momentum, charge and mass do not change. It is shown that if we take as an axiom the conservation at interaction of the total mass of the system of particles taking into account its sign, then it is possible to explain the difference between bosons and fermions in the statistics to which they obey.

The integration of deep learning models into financial risk prediction and analysis has significantly transformed traditional approaches. While conventional quantitative methods often rely on simplistic metrics like maximum drawdown, the advent of deep learning necessitates a more nuanced evaluation, emphasizing the model's generalization ability, especially during market crises such as stock market crashes. This paper explores the critical aspects of evaluating deep learning models' risk control capabilities in finance, underscoring the importance of understanding both statistical metrics and generalization abilities, particularly in adverse market conditions. By examining deep learning models' performance in scenarios like stock market crashes and highlighting the significance of cross-validation techniques, this study aims to offer practitioners insights into constructing robust risk management systems. It advocates for a comprehensive approach integrating quantitative analysis with macroeconomic factors to enhance financial risk prediction and analysis in volatile markets. The experimentation reveals that different deep generative models excel in various aspects of financial time series analysis, with generative adversarial networks (GANs) demonstrating superior performance in predicting Value at Risk (VaR) and variational autoencoders (VAEs) excelling in return rate prediction. Moreover, integrating multiple models further enhances predictive performance, leveraging the strengths of each model to compensate for individual weaknesses. Overall, this paper underscores the potential and significance of deep generative models in financial time series analysis, offering a roadmap for improved risk management and decision-making in financial markets.

We show how the Poincar\'e--Riemann--Hilbert boundary-value problem enables us to construct effective estimates of the potential in the Schr\"odinger equation. The apparatus of the three-dimensional inverse problem of quantum scattering theory is developed for this. It is shown that the unitary scattering operator can be studied as a solution of the Poincar\'e--Riemann--Hilbert boundary-value problem. This allows us to go on to study the potential in the Schr\"odinger equation

Multi-parameter families of Lax pairs for the modified Korteweg-de Vries (mKdV) equation are defined by applying a direct method developed in the present study. The gauge transformations converting the defined Lax pairs to some simpler forms and reducing the variety of the Lax pairs this way are found. The direct method and its possible applications to other types of evolution equations are discussed.

(1) Background; limited research exists which considers master plots expressed by individuals with Stroke. The literature so far has focused on identified pre-established illness narrative types; (2). Methods: A narrative method was selected and a purposive sample of individuals with Stroke are identified. A categorical-form analysis was undertaken; (3) Results: A narrative master plot named overcoming the monster is identified and explored for its components and located temporally for each participant; (4) Conclusions: Health care professionals need to understand the importance of understanding the master plot overcoming the monster. This research supports the need for health care professionals to recognise and support narratives by listening in a non-directive way.

The ordinary 3D wave equation for nondissipative, homogeneous, isotropic media admits solutions where the point sources are permitted to move, but it does not admit solutions where the receiver is allowed to move. To overcome this limitation, the new wave equation is derived, permitting both the receiver and the source to move. This new wave equation is a generalization of the standard wave equation, and it reduces to the standard wave equation when the receiver is at rest. To derive this new wave equation, we first mathematically define a diverging spherical wave caused by the stationary point source. From this purely mathematical definition, the wave equation for the stationary source and the moving receiver is derived together with the corresponding free-space Green's function. Utilizing the derived Green's function, it was shown that this new wave equation also permits the solutions where both the receiver and the source are permitted to move. In conclusion, this paper demonstrates that, instead of an ordinary wave equation, the wave equation for the moving source and the moving receiver governs the waves emitted by the moving point sources and received by the moving receivers.

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.

Coupling the Maxwell tensor to the Riemann-Christoffel curvature tensor is shown to lead to a geometricized theory of electrodynamics. While this geometricized theory leads directly to the classical Maxwell equations, it also extends their physical interpretation by giving charge density, mass density and the four-velocity that describes their motions geometric definitions. Assuming the existence of a conserved energy-momentum tensor, all solutions to the geometricized theory of electrodynamics developed here are shown to be consistent with the emergence of gravity obeying the General Relativity field equation augmented by a term that mimics the properties of dark matter and/or dark energy. Finally, due to the symmetries of the theory, the properties and phenomenology of antimatter emerge in solutions.

New proposals for the equation of state of four- and five-dimensional hard-hypersphere mixtures in terms of the equation of state of the corresponding monocomponent hard-hypersphere fluid are introduced. Such proposals (which are constructed in such a way so as to yield the exact third virial coefficient) extend, on the one hand, recent similar formulations for hard-disk and (three-dimensional) hard-sphere mixtures and, on the other hand, two of our previous proposals also linking the mixture equation of state and the one of the monocomponent fluid but unable to reproduce the exact third virial coefficient. The old and new proposals are tested by comparison with published molecular dynamics and Monte Carlo simulation results and their relative merit is evaluated.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

Soil erosion and sediment transport are quite complex processes as they depend on physical, biological, mechanical, and chemical processes within a particular catchment. Therefore, it is highly essential to better explain engaged physical processes and means of accounting for site-specific conditions, for soil loss and sediment yield estimation. This paper mainly focuses on physical explanations behind soil erosion and common soil erosion models like Universal or Revised Universal Soil Loss Equation(USLE/RUSLE) and Modified Universal Soil Loss Equation(MUSLE). Based on the physical explanations and overall limitations, the MUSLE is selected for the application of sediment yield estimation. The main objective of this paper is to estimate the best exponent of the MUSLE, and to estimate the best combination of the exponent and topographic factor of the MUSLE under hydro-climatic conditions of Ethiopia. For the sake of calibration procedure, the main parameters of the MUSLE which directly affect soil erosion process such as cover, conservation practice, soil erodibility, and topographic factors are estimated based on the past experiences from literature and comparative approaches, whereas the other parameters which do not directly affect the erosion process or which have no any physical meaning (i.e coefficient a and exponent b) are estimated through calibration. It is verified that the best exponent of the MUSLE is 1 irrespective of the topographic factor, which results in the maximum performance of the MUSLE (i.e approximately 100\%). For the best combination of the exponent and topographic factor, the performance of the MUSLE is greater than or equal to 80\% for all four watersheds under our consideration, we expect the same for other watersheds of Ethiopia.

This paper presents the perturbation theory for the double–sine–Gordon equation. We obtain a system of differential equations that shows the amplitude and phase modulation of the approximate solution.. In the particular case λ = 0 we get the well-known perturbation theory for the sine–Gordon equation. For a special value λ=-1/8, we derive a phase-locked solution with the same frequency of the linear case. In general we obtain both coherent (solitary waves, lumps and so on) solutions as well as fractal solutions. We can demonstrate the existence of envelope wobbling solitary waves, because of the phase modulation depending on the solution amplitude and on the position. The main conclusion is that it is too reductive focus only on coherent solutions for the double sine-Gordon equation, because of the very rich behavior for the DSG nonlinear equation, including wobbling chaotic and fractal solutions.

Although there is a common physiological notion that the origin of the membrane potential is attributed to transmembrane ion transport, it is theoretically possible to explain its generation by the mechanism of ion adsorption. It was previously suggested that the ion adsorption mechanism led even to the potential formulas which are even identical to either the famous Nernst equation or Goldman-Hodgkin-Katz equation. Our further analysis shown in this paper indicates that the potential formula based on the ion adsorption mechanism leads to one equation which is the function of material surface charge density and the material surface potential. Furthermore, we confirmed that the equation holds in all the different experimental systems we studied. Although we have not succeeded in elucidating why such an equation is established, the equation appears to be the key equation governing the characteristics of the membrane potential regardless of the systems in question.

HU is the Hypergeometrical Universe Theory (HU)[1-8], proposed in 2006, where the Universe is a Lightspeed Expanding Hyperspherical Hypersurface and Gravitation is an absolute-velocity-dependent, epoch-dependent force. Here we introduce the Big Pop Cosmogenesis and show our calculations associated with the Equation of State of the Universe. This article is the first in a series of articles[9-22] supporting the paradigm shift.

A solution for the Prandtl-Blasius equation is essential to all kinds of boundary layer problems. This paper revisits this classic problem and presents a general Maple code as its numerical solution. The solutions were obtained from the Maple code, using the Runge-Kutta method. The study also considers convergence radius expanding and an approximate analytic solution is proposed by curve fitting. Similarly, the study resolves some boundary layer related problems and provide relevant Maple codes for these.

Recent astronomical observations with respect to measurements in distant supernovas, cosmic microwave background and weak gravitational lensing confirm that the Universe is undergoing a phase of accelerated expansion and it has been proposed that this cosmological behavior is caused by a hypothetical dark energy which has a strong negative pressure that allows explain the expanding universe. Several theoretical ideas and models related dark the energy includes the cosmological constant, quintessence, Chaplygin gas, braneworld and tachyonic scalar fields. In this paper, we have obtained new relativistic stellar configurations considering an anisotropic fluid distribution with a charge distribution which could represents a potential model of a dark energy star. In order to investigate the effect of a quadratic equation of state in this anisotropic model we specify particular forms for the gravitational potential that allow solving the Einstein-Maxwell field equations. For these new solutions we checked that the radial pressure, metric coefficients, energy density, anisotropy factor, charge density , mass function are well defined and are regular in the interior of the star. The solutions found can be used in the development of dark energy stars models satisfying all physical acceptability conditions but the causality condition and strong energy condition are violated. We expect that these models have multiple applications in astrophysics and cosmology.

In this paper we study the initial boundary value problem for logarithmic Higher Order Wave equation. Introducing the Logarithmic Sobolev inequality and using the combination of Galerkin method, we consider the theorem of existence of a global weak solution to problem for the initial boundary value problem of the logarithmic wave equation. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for logarithmic Higher Order Wave equation. The proof of the main theorem is given.

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

This study delves into the Schrödinger equation's new invariants, shedding light on their crucial implications for theoretical physics and beyond. Specifically, it explores the behavior of scattering amplitudes and bound states concerning the choice of coordinate systems. The research unveils that while the energy of bound states remains invariant under coordinate transformations, the phase of scattering amplitudes undergoes variations, underscoring its pivotal role in theories reliant on phase normalization. Moreover, these findings have played a pivotal role in constructing estimates for three-dimensional Navier-Stokes equations, enhancing our ability to model complex fluid dynamics with greater precision and reliability. Additionally, in seismic exploration, tomography, and ultrasound imaging, these properties allow researchers to optimize phase selection, facilitating the most effective interpretation of measurement results. This strategic phase manipulation ensures clearer insights into subsurface structures, tissue composition, and fluid dynamics, with the flexibility to seamlessly transition back to the original coordinate system post-interpretation. This interdisciplinary synergy underscores the profound impact of fundamental theoretical research on advancing practical applications across diverse scientific domains.

The mind-body problem is the central issue in both of philosophy and life science for several centuries. To date, there is still no conclusive theory to interpret the relation between the mind and the body, even just the mind alone. Here, we promote a novel model, a derived mathematic equation called the entropic system equation, to describe the innate characters of the mind and the mechanism of the mind-body coupling phenomenon. As the semi-open thermodynamic systems far from equilibrium, the living organisms could be logically considered as an entropic system. In the living organisms or the entropic systems, there also are three essential existing elements including mass, energy and information, in which the mind and the body are hypothetically coupled by free energy and entropic force.

An extension of the Stoney formula for the case of a back side metallized 8” silicon taiko wafer has been developed, in the elastic regime, within the frame of the theory of elasticity. A good correlation between the calculated warpage, determined by the stress released by a given back side metallization (BSM), and the corresponding experimental warpages of the same thick metal layers deposited on an 8” silicon taiko wafer provides evidences of the correctness of the developed theory. This development suggests the possibility to extend this approach to the case of 8” taiko wafers based on a wide band gap semiconductor such as silicon carbide (SiC).

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

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

With the digital transformation of the logistics industry, smart logistics algorithms have become a core technology to improve efficiency and reduce costs. This paper reviews the development history of traditional logistics technology and discusses the key role of technologies such as the Internet of Things, big data analysis, artificial intelligence, and automation in logistics technology innovation. It focuses on the application of intelligent logistics algorithms in path optimization, intelligent scheduling, data mining and prediction, and intelligent warehousing. To solve the problem of inconsistency between training and testing objectives, this paper proposes DRL4Route, a deep reinforcement learning-based path optimization framework, and designs the DRL4Route-GAE model. Validated through extensive offline experiments and online deployments, the model significantly outperforms existing optimal benchmark methods on real datasets, improving the location deviation squared metrics and the top-three location prediction accuracy metrics. These research results provide important support to further promote the intelligent development of the logistics industry.

In this paper, we analyze the generalized Ulam-Hyers stability of affine type AQ Functional Equation in various Banach Spaces using Direct and Fixed Methods

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.

Dual quaternions have wide applications in automatic differentiation, computer graphics, mechanics and others. Due to its application in control theory, the matrix equation AXB=C has been extensively studied. However, there is currently limited information on matrix equation AXB=C over the dual quaternion algebra. In this paper, we provide the necessary and sufficient conditions for the solvability of the dual quaternion matrix equation AXB=C, and present the expression for the general solution when it is solvable. As an application, we derive the ϕ-Hermitian solutions for the dual quaternion matrix equation AXAϕ=C, where the ϕ-Hermitian extends the concepts of Hermiticity and η-Hermiticity. Lastly, we present a numerical example to verify the main research results of this paper.

We present set-theoretical solutions of the Yang-Baxter equation in BCK–algebras. Some solutions in BCK−algebras are not solutions in other structures (such as MV −algebras). Related to our investigations we also consider some new structures: Boolean coalgebras and a unified braid condition – quantum Yang-Baxter equation. Finally, we will see how poetry has accompanied the development / history of the Yang–Baxter equation.

We give an operator solution to an advanced-retarded differential equation. The application of the operators involved produces a solution in terms of Bessel functions.

The generalized Kuramoto–Sivashinsky equation is investigated using the modified Kudrayshov method for the exact analytical solution. The modified Kudrayshov method converts the nonlinear partial differential equation to algebraic equations, as a result of various steps, which on solving the so obtained equation systems yields the analytical solution. By this way various exact solutions including complex structures are found and drawn their behaviour in complex plane by Maple to compare the uniqueness of solutions.

The current study compared the goodness of fit and estimation precision of Bayes and maximum likelihood (ML) structural equation modeling across sample sizes. Data consisted of Markov Chain Monte Carlo generated samples of 50, 75, 100, 125, 150, 200, 250, 500, 750, 1000, and 1500 observations. The Bayes and ML methods were used to estimate a structural equation model with 40 parameters, including 12 continuous observed indicators, four latent variables, and three structural paths. Analyses were conducted with the Mplus 8.0 statistical software and were replicated 500 times with each of the 22 conditions (11 sample sizes x 2 estimation methods). Indices of model fit were the Bayes information criterion, the Tucker-Lewis index, the comparative fit index, the root mean square error of approximation, the posterior predictive p-value (for Bayes models), and the ꭓ2 test (for ML models). Results showed that as the sample size increased, both estimation methods exhibited improved model fit and enhanced estimation precision, and both methods performed well with samples of 200 or larger; however, ML demonstrated a marginally superior fit with smaller samples. These findings were not consistent with previous research and suggest that ML remains a better choice with continuous data and small samples.

This study derives space travel pricing by Walrasian Equilibrium, which is logical reasoning from the general relativity theory (GRT), the accounting equation, and economic supply and demand functions. The Cobb-Douglas functions embed the endogenous space factor as new capital to form the space travel firm's production function, which is also transformed into the consumer's utility function. Thus, the market equilibrium occurs at the equivalence of supply and demand functions, like the GRT presents the equivalence between the spatial geometric tensor and the energy-momentum tensor, which explains the principles of gravity and the motion of space matter in the spacetime framework. The mathematical axiomatic set theory of the accounting equation explains the equity premium effect that causes a short-term accounting equation inequality, then reaches the equivalence by suppliers' incremental equity through the closing accounts process of the accounting cycle. On the demand side, the consumption of space travel can be assumed as a value at risk (VaR) investment to attain the specific spacetime curvature in an expected orbit. Spacetime market equilibrium is then achieved to construct the space travel pricing model. The methodology of econophysics and analogy method was applied to infer the space travel pricing by the model of profit maximization, single-minded, and envy-free pricing in unit-demand markets. A case study with simulation was conducted for empirical verification of the math models and algorithm. Results show that space travel pricing remains the principle of market equilibrium but needs to be extended to the spacetime tensor of GRT.

We propose a generalization of Nambu-Hamilton equation in superspace $\mathbb R^{3|2}$ with three real and two Grassmann coordinates. We construct the even degree vector field in the superspace $\mathbb R^{3|2}$ by means of the right-hand sides of proposed generalization of Nambu-Hamilton equation and show that this vector field is divergenceless in superspace. Then we show that our generalization of Nambu-Hamilton equation in superspace leads to family of ternary brackets of even degree functions defined with the help of Berezinian. This family of ternary brackets is parametrized by the infinite dimensional group of invertible second order matrices, whose entries are differentiable functions on the space $\mathbb R^{3}$. We study the structure of ternary bracket in a more general case of a superspace $\mathbb R^{n|2}$ with $n$ real and two Grassmann coordinates and show that for any invertible second order functional matrix it splits into the sum of two ternary brackets, where one is usual Nambu-Poisson bracket, extended in a natural way to even degree functions in a superspace $\mathbb R^{n|2}$, and the second is a new ternary bracket, which we call $\Psi$-bracket, where $\Psi$ can be identified with invertible second order functional matrix. We prove that ternary $\Psi$-bracket as well as the whole ternary bracket (the sum of $\Psi$-bracket with usual Nambu-Poisson bracket) is totally skew-symmetric, satisfies the Leibniz rule and the Filippov-Jacobi identity (Fundamental Identity).

Hazelnut (Corylus avellana L.) is of great agroeconomic importance, prized for its nutritional value and antioxidant properties. Its yield and quality may differ due to factors such as season (S), locality (L) and cultivar (C). Our objective was to determine the dynamics of morphological features and antioxidant properties in nuts of Barcelona and Tonda di Giffoni (TDG) cultivars planted at two localities (Cunco and Perquenco) during three productive seasons (S1, S2 and S3). Barcelona grown in Perquenco in S1 and S3 (less precipitation, more solar radiation), performed better than in Cunco with respect to most morphological nut, kernel and shell features, and the same parameters generally had the same trends for TDG in S2 and S3. Among the seasons at the same localities, the differences between the predominant condition defects for both cultivars were in the decreasing order wrinkled/deformed kernels, double kernels, blank and mold ker-nels, with about 75% of hazelnuts without defect. In both cultivars, the shell had higher antioxi-dant properties that increased in S1 and S3 at both localities, and were consistently higher than in the kernels. Lipid peroxidation was higher in the kernel than shell in both cultivars and local-ities for S1 and S3. The results of this study suggest that the different hazelnut cultivar features including physical and chemical components depend on season and locality, which offers im-portant clues for all those interested in the hazelnut industry.

In this study, a new empirical equation was established to predict the sedimentation volume resulting from the construction of a multipurpose weir or low-head dam. The study employed a one-dimensional numerical model (STAFF) to investigate the key parameters affecting sedimentation volume. Short-term predictions were conducted through laboratory experiments with movable bed, and the results indicated that dimensionless unit stream power and the Shields parameter exhibited the most significant correlation with dimensionless deposition volume. Using a multiple regression approach, an empirical equation was formulated and validated for predicting sedimentation in the upstream reservoir of the weir.

In this paper, we propose a partial differential equation model based on phase-field for sentiment analysis in the field of hotel comment texts. The comment texts are converted into word vectors using the Word2Vec tool, and then we utilize the multifractal detrended fluctuation analysis (MF-DFA) model to extract the generalized Hurst exponent of the word vector time series to achieve dimensionality reduction of the word vector data. The dimensionality reduced data is represented in a two-dimensional computational domain, and the modified Allen-Cahn (AC) function is used to evolve the phase values of the data to obtain a stable nonlinear boundary, thereby achieving automatic classification of hotel comment texts. The experimental results show that the proposed method can effectively classify positive and negative samples and achieve excellent results in classification indicators. We compared our proposed classifier with traditional machine learning models and the results indicate that our method possesses a better performance.

In this study, we actually want to explore the time-fractional Phi-four equation via two methods, the exp _a function method and the hyperbolic function method. We transform a fractional order dierential equation into an ordinary differential equation using a wave transformation and the fractional derivative in conformable form. Then, the resulting equation has successfully been explored for new explicit exact solutions. The procured solutions are simply showed the effectiveness and plainness of the projected methods.

Here is shown method for the hydraulic solution of a looped gas-pipeline networks. Calculation of presented network is done according to principles of Hardy Cross method. The optimization was carried out by iteration of the pipes diameters, node consumptions are known and flow velocities through pipes have to stand below certain values. Accent is on determination of appropriate friction factor, and on selection of representative equation for natural gas flow under presented conditions in the network. Inappropriate usage of friction factor, equally as inappropriate usage of gas flow equation can lead to inaccurate final results. Here is shown new facts in comparison to previous calculation of gas distribution network in Kragujevac, Serbia which is done in 1994. After the implementation, measurements in situ have performed, and real measured values deviate from calculated. Causes for these errors are investigated, and improved and more accurate procedure is shown.

In this paper after introducing a model of binary data matrix for physical measurements of an evolving system (of particles), we develop a Hilbert space as an ambient space to derive induced metric tensor on embedded parametric manifold identified by associated joint probabilities of particles observables (parameters). Parameter manifold assumed as space-like hypersurface evolving along time axis, an approach that resembles 3+1 formalism of ADM and numerical relativity. We show the relation of endowed metric with related density matrix. Identification of system density matrix by this metric tensor, leads to the equivalence of quantum Liouville equation and metric compatibility condition ∇₀g_ij = 0 while covariant derivative of metric tensor has been calculated respect to Wick rotated time coordinate. After deriving a formula for expected energy of the particles and imposing the normalized Ricci flow as governing dynamics, we prove the equality of this expected energy with local scalar curvature of related manifold. Consistency of these results with Einstein tensor, field equations and Einstein-Hilbert action has been verified. Given examples clarify the compatibility of the results with well-known principles. This model provides a background for geometrization of quantum mechanics compatible with curved manifolds and information geometry.

Uncertain fractional differential equation (UFDE) is an excellent tool for describing complicated dynamic systems. This paper analyzes the valuation problems of currency option based on UFDE under optimistic value criterion. Firstly, an uncertain fractional currency model is formulated to describe the dynamics of foreign exchange rate. Then, the pricing formulae of European, American and Asian currency option are obtained under optimistic value criterion, respectively. Finally, numerical simulations are provided to illustrate the validity of our theoretical results.