We have now identified two thermodynamically distinct types (A and B) of energetic processes naturally occurring on Earth. Type A energy processes such as the classical heat engines, apparently well follow the second law of thermodynamics; Type B energy processes, such as the newly discovered thermotrophic function that isothermally utilizes environmental heat energy to do useful work in driving ATP synthesis, which follows the first law of thermodynamics (conservation of mass and energy) but does not have to be constrained by the second law, owing to their special asymmetric functions. Several Type-B energy processes such as asymmetric-function-gated isothermal electricity and epicatalysis have been created through human efforts. The innovative efforts on Type-B processes to enable isothermally utilizing endless environmental heat energy could help to liberate all peoples from their dependence on fossil fuel energy, thus helping to reduce greenhouse gas CO2 emissions and control climate change towards a sustainable future for the humanity on Earth.

Accurate electricity price forecasting has become a substantial requirement since the liberalization of the electricity markets. Due to the challenging nature of the electricity prices, which includes high volatility, sharp price spikes and seasonality, various types of electricity price forecasting models still compete and can not outperform each other consistently. Neural Networks have been successfully used in machine learning problems and Recurrent Neural Networks (RNNs) have been proposed to address time-dependent learning problems. In particular, Long Short Term Memory and Gated Recurrent Units (GRU) are tailor-made for time series price estimation. In this paper, we propose to use Gated Recurrent Units as a new technique for electricity price forecasting. We have trained a variety of algorithms with rolling 3-year window and compared the results with the RNNs. In our experiments, 3-layered GRUs outperformed all other neural network structures and state of the art statistical techniques in a statistically significant manner in the Turkish day-ahead market.

The deepening of electricity reform results in increasingly frequent auctions and the surge of generators, it becomes difficult to analyze generators’ behaviors. Since it’s hard to find analytical market equilibriums, approximate equilibriums were obtained instead in previous studies by market simulations, which are strict to initial estimations and simulation results are chaotic in some cases. In this paper, a multi-unit power bidding model is proposed to reveal the bidding mechanism under clearing pricing rule by employing auction approach, for which initial estimations are non-essential. Normalized bidding price is introduced to construct generator's price-related bidding strategy. Nash equilibriums are derived depend on the marginal cost and the winning probability which are computed from bidding quantity, transmission cost and demand distribution. Furthermore, we propose a comparative analysis to explore the impact of uncertain elastic demand on the performance of the electricity market. The result indicates that, there exists market power among generators leading to social welfare decreases even under competitive conditions but elastic demand is an effective way to restrain generators’ market power. The feasibility of the models is verified by a case study. Our work provides decision support for generators and a direction for improving market efficiency.

Electricity demand forecasting plays a significant role in energy markets. Accurate prediction of electricity demand is the key factor to optimize power generation, consumption, saving energy resources, and determining the energy prices. However, integrating energy mix scenarios, including solar and wind power which are highly non-linear and seasonal, into an existing grid increases uncertainty in generation, adds the challenges for precise forecast. To tackle these challenges, state-of-the-art methods and algorithms have been implemented in literature. We have developed Artificial Intelligence (AI) based deep learning models that can effectively handle the information of long time-series data. Based on the pattern of dataset, four different scenarios were developed and two best scenarios were selected for prediction. Dozens of models were developed and tested in deep AI networks. In the first scenario (Scenario1), data for weekdays excluding holidays was taken and in the second scenario (Scenario2) all the data in the basket was taken. Remaining two scenarios, weekends and holidays were tested and neglected because of their high prediction error. To find the optimal configuration, models were trained and tested within a large space of alternatives called hyper-parameters. In this study, an Aritificial Neural Network (ANN) based Feed-forward Neural Network (FNN) showed the minimum prediction error for Scenario1 while a Recurrent Neural Network (RNN) based Gated Recurrent Network (GRU) showed the minimum prediction error for Scenario2. While comparing the accuracy, the lowest MAPE of 2.47% was obtained from FNN for Scenario1. When evaluating the same testing dataset (non-holidays) of Scenario2, the RNN-GRU model achieved the lowest MAPE of 2.71%. Therefore, we can conclude that grouping of weekdays as Senario1 prepared by excluding the holidays provides better forecasting accuracy compared to the single group approach used in Scenario2, where all the dataset is considered together. However, Scenario2 is equally important to predict the demand for weekends and holidays.

In this work we present a new unsupervised and language-independent methodology to detect relations of textual generality, for this, we introduce a particular case of textual entailment (TE), namely Textual Entailment by Generality (TEG). TE aims to capture primary semantic inference needs across applications in Natural Language Processing (NLP). Since 2005, in the TE recognition (RTE) task, systems are asked to automatically judge whether the meaning of a portion of the text, the Text - T, entails the meaning of another text, the Hypothesis - H. Several novel approaches and improvements in TE technologies demonstrated in RTE Challenges are signalling of renewed interest towards a more in-depth and better understanding of the core phenomena involved in TE. In line with this direction, in this work, we focus on a particular case of entailment, entailment by generality, to detect relations of textual generality. In-text, there are different kinds of entailment, yielded from different types of implicative reasoning (lexical, syntactical, common sense based), but here we focus just on TEG, which can be defined as an entailment from a specific statement towards a relatively more general one. Therefore, we have T→GH whenever the premise T entails the hypothesis H, being it also more general than the premise. We propose an unsupervised and language-independent method to recognize TEGs, from a pair ⟨T,H⟩ having an entailment relation. To this end, we introduce an Informative Asymmetric Measure (IAM) called Simplified Asymmetric InfoSimba (AISs), which we combine with different Asymmetric Association Measures (AAM). In this work, we hypothesize the existence of a particular mode of TE, namely TEG. Thus, the main contribution of our study is to highlight the importance of this inference mechanism. Consequently, the new annotation data seems to be a valuable resource for the community.

The fitting and modeling of skewed, complex, symmetric, and asymmetric datasets is an exciting research topic in many fields of applied sciences, notably lifetime, medical, and financial sciences. The Heavy tailed Nadarajah Haghighi model is introduced by compounding the heavy tailed family and Nadarajah Haghighi distribution in this paper. The so obtained model has three parameters accounting for the scale and shape of the distribution. The proposed distribution's fundamental characteristics such as probability density, cumulative distribution, hazard rate, and survival functions are provided, and several key statistical properties are established, and several entropy information measures are proposed. The estimation of model parameter is performed via the ML procedure. Further, different simulation experiments are conducted to demonstrate the performance of proposed estimator’s using some measure, like the average estimate, the average bias, and associated mean square error. Finally, we are applied our proposed model to analyze three different real datasets. In our illustration, we are compared the practicality of the recommended model with several well-known competing models.

Background: One of the most astounding discoveries of recent times is the recognition that cancer embodies a transition from a higher level of metazoan cell organization to a more foundational pre-metazoic state. This shift is steered by genes housed within the ancestral genome compartment, pervasive across all metazoan genomes, encompassing humans, and governed by a pre-metazoic gene regulatory mechanism (aGRN). This work aims to highlight the emerging field of evolutionary cancer cell biology (ECCB), which points to the deep homology between cancer and protist life cycles tracing back to the common ancestor of amoebozoans, metazoans, and fungi (AMF). The ECCB analysis reveals the essence of the non-gametogenic germline of the AMF ancestor, which serves as a blueprint for all metazoan germlines and stem cell lineages and controls the life cycle of cancer. Every germ and stem cell lineage of humans and metazoans traces its lineage back to this Urgermline, transmitting crucial processes such as asymmetric cell cycling, differentiation, stemness, and phenomena like GST and SGT (aka EMT and MET) to their subsequent evolutionary descendants. Oxygen-sensitive germline and stem cells suffer DNA-DSB due to stress and oxygen ranges reminiscent of ancestral hyperoxia, leading to cell senescence. Cells that can overcome senescence can proliferate as DSCD cells with defective symmetric cell division, paving the way for malignancy and PGCC cancers. Conclusions: Understanding cancer from its evolutionary origins may help break some of the logjams in cancer prevention and open up new therapeutic pathways.

Annotating training data is a time consuming and labor intensive process in deep learning, especially for images with many objects present. In this paper, we propose a method to allow deep networks to be trained on data with reduced numbers of annotations (per image) in heatmap regression tasks (e.g. object detection and counting), by applying an asymmetric loss function. In a real scenario, this reduction of annotations can be imposed by the researchers (e.g. ask the annotators to label only 50% of what they see in each image), or can potentially counteract unintentionally missing labels from the annotators. To demonstrate the effectiveness of our method, we conduct experiments in two domains, crowd counting and wheat spikelet detection, using different deep network architecture. We drop various percentages of instance annotations per image in training. Results show that an asymmetric loss function is effective across different models and datasets, even in very extreme cases with limited annotations provided (e.g. 90% of the original annotations reduced). Whilst tuning of the key parameters are required, we find that setting conservative parameter values can help more realistic situations, where only small amounts of data have been missed by annotators.

In recent years, neural networks based on attention mechanisms have been increasingly widely used in speech recognition, separation, enhancement, and other fields. In particular, the convolution-augmented transformer has achieved good performance as it can combine the advantages of convolution and self-attention. Recently, the gated attention unit (GAU) has been proposed. Compared with the traditional multi-head self-attention, approaches with GAU are effective and computationally efficient. In this article, we propose a network for speech enhancement called CGA-MGAN, a kind of Metric GAN based on convolution-augmented gated attention. CGA-MGAN captures local and global correlations in speech signals at the same time through the fusion of convolution and gated attention units. Experiments on Voice Bank + DEMAND show that the CGA-MGAN we propose achieves an excellent performance (3.47 PESQ, 0.96 STOI, and 11.09dB SSNR) at a relatively small model size (1.14M).

Raman spectroscopy is a type of inelastic scattering that provides rich information about a sub-stance based on the coupling of the energy levels of their vibrational and rotational modes with incident light. It has been applied extensively in many fields. As there is an increasing need for remote detection of chemicals in planetary exploration and anti-terrorism, it is urgent to develop a compact and easily transportable fully automated remote Raman detection system for trace detection and identification of information with high-level confidence about the target’s compo-sition and conformation in real-time and for real field scenarios. Here, we present an unmanned vehicle-based remote Raman system, which includes a 266 nm air-cooling passive Q-switched nanosecond pulsed laser of high-repetition frequency, a gated ICMOS, and an unmanned vehicle. This system obtains good spectral signals from remote distances ranging from 3 m to 10 m for simulating realistic scenarios, such as aluminum plate, woodblock, paperboard, black cloth, and leaves, and even for detected amounts as low as 0.1 mg. Furthermore, a CNN-based algorithm is implemented and packaged into the recognition software to achieve fast and more accurate de-tection and identification. This prototype provides a proof-of-concept for an unmanned vehicle with accurate remote substance detection in real-time, which can be helpful for remote detection and identification of hazardous gas, explosives, their precursors, and so forth.

The rapid urbanization growth of Dubai has resulted in connectivity issues, considered tre-mendous development pressure. That leads the local authorities to set a vision for Dubai as a 15-20 minute city by 2040. The 15-minute city, where all services can be reached with minimum travel time using sustainable mobility means (walking, cycling, or electric bik-ing). This paper aims to assess the current walkability situation within 15 minutes in the most significant parts of Dubai. This study considered 13 communities; Bur-Dubai and Business Bay were selected to represent the ungated communities, and eleven major gated communities were considered to indicate the gated ones. Those neighborhoods are selected based on the developments' socio-economic status and population density. The assessment considered 14 essential services, categorized into five categories: educational, health, social, entertainment, and religious. The research methodology conducted desktop research, site visits, interviewing random residents to collect data, and then using ArcGIS to assess walk-ability. The results show (64.5%) of the ungated neighborhoods population which access essential services within 15 minutes, while most of the gated communities residents must use cars to access many services. Furthermore, services distribution patterns and walkability infrastructures outside these developments should be developed to obtain higher walkability indicators.

In this paper, a range-gated lidar system utilizing an LN crystal as the electro-optical switch and a SCMOS (Scientific Complementary Metal Oxide Semiconductor) imaging device is designed. To achieve range-gated, we utilize two polarizers and a LN (LiNbO3) crystal to form an electro-optical switch. The optical switch is realized by applying a pulse voltage at both ends of the crystal due to the crystal's conoscopic interference effect and electro-optical effect. The advantage of this system is that low-bandwidth detectors such as CMOS and CCD (Charge-coupled Device) can be used to replace conventional high-bandwidth detectors such as ICCD (Intensified Charge Coupled Device), and time it has better imaging performance under specific conditions at the same. However, after using an electro-optical crystal as an optical switch, a new inhomogeneity error will be introduced due to the conscopic interference effect of the electro-optical crystal, resulting in range error of the lidar system. To reduce the influence of inhomogeneity error on the system, this paper analyzes the sources of inhomogeneity error caused by the electro-optical crystal and gives the crystal inhomo-geneity mathematical expression. A compensation method is proposed based on the above inho-mogeneity mathematical expression. An experimental lidar system is constructed in this paper to verify the validity of the compensation method. The experimental results of the range-gated lidar system show that in a specific field of view (2.6mrad), the lidar system has a good imaging per-formance, its ranging standard deviation is 3.86cm and further decreased to 2.86cm after com-pensation, which verifies the accuracy of the compensation method.

Opening gated-communities (GCs) has been widely discussed for urban inclusion and revitalization. With the policies of opening GCs being promoted in China, quantitative and comprehensive evaluation of the potential benefits is heavily needed. Taking Shanghai as an example, this study quantifies and analyzes the accessibility benefits and risks of opening GCs with factors including GC types, opening levels, travel modes, and travel destinations considered. We found that (1) opening GCs can bring 50m+ accessibility gains to 17% and 52% of the residents in Moderately Opening (MO) and Completely Opening (CO) scenarios, respectively. (2) Cycling benefits more than walking in all cases and scenarios. (3) For different GCs, conventional GCs have fewer benefits in MO but more in CO than the newly-established one. For different facilities, trips to bus stations demonstrate the largest accessibility gains. (4) The accessibility benefit of a residential building is highly determined by its closeness to the gates and relative location in the block. (5) Only 1% and 5-7% of external trips may penetrate the opened communities in MO and CO scenarios, respectively, which are far less than both expectation and the benefits. These findings precipitate at least two policy implications in China.

The prediction of stock prices holds significant implications for researchers and investors in evaluating stock value and risk. In recent years, researchers have increasingly replaced traditional machine learning methods with deep learning approaches in this domain. However, the application of deep learning in forecasting stock prices is confronted with the challenge of overfitting. To address the issue of overfitting and enhance predictive accuracy, this study proposes a stock prediction model based on GRU (Gated Recurrent Unit) with reconstructed datasets. This model integrates data from other stocks within the same industry, thereby enriching the extracted features and mitigating the risk of overfitting. Additionally, an auxiliary module is employed to augment the volume of data through dataset reconstruction, thereby enhancing the model’s training comprehensiveness and generalization capabilities. Experimental results demonstrate a substantial improvement in prediction accuracy across various industries.

The new genus and the new edaphic species, Prokletijella montana gen. n., sp. n., from the Prokletije mountains in Montenegro is described and illustrated. This is the first genus in Leptodirini with an asymmetric median lobe of the aedeagus. The phylogenetic relationship with the genus Adelopsella Jeannel, 1908 is discussed. The genus Adelopsella is redescribed to be accurately compared with Prokletijella. The occurrence of asymmetric genitalia in Leptodirini is discussed in relation with the occurrence of such asymmetry in males and females in other tribes of Cholevinae. The geographic distribution of the two genera is discussed in connexion with their phylogenetic relationship and mapped. The synonymy of the two subspecies A. bosnica bosnica and A. bosnica jezerensis Jeannel, 1911 is confirmed.

Magnesium (Mg) alloy is a widely used lightweight metal structural material due to its high specific strength and stiffness, excellent damping performance, and recyclability. Wrought Mg alloys are widely favored in fields such as aerospace, transportation, and biomedical stents. However, most wrought Mg alloys with a hexagonal close-packed (HCP) crystal structure lack sufficient independent slip systems to meet the von Mises criterion for uniform plastic deformation at room temperature. This can result in the formation of strong basal texture during plastic deformation and poor room temperature plastic forming ability. Improving the room temperature forming performance is a crucial challenge that must be addressed to broaden the application of Mg alloy sheets. Our research group has comprehensively summarized significant work and latest research progress in improving the room temperature forming of Mg alloy sheets via extrusion technology in recent years. Specifically, we have developed a new type of asymmetric extrusion technology that combines material structure evolution, mechanical property, and forming behavior analysis. We have elucidated the extrusion process characteristics, texture control mechanism, and forming properties of Mg alloy sheets through plastic deformation mechanisms, mold design, and finite element numerical simulation. Our findings provide a novel extrusion technology for the fabrication of highly formable Mg alloy sheets, which can be utilized in various applications.

Viral infections inflict many serious human diseases, being responsible for remarkably high mortality rates. In this sense, both the academy and the pharmaceutical industry are continuously searching for new compounds with antiviral activity, and in addition, face the challenge of developing greener and more efficient methods to synthesize these compounds. This becomes even more important with drugs possessing stereogenic centers as highly enantioselective processes are required. In this minireview, the advances achieved to improve synthetic routes efficiency and sustainability of important commercially antiviral chiral drugs are discussed, highlighting the use of organocatalytic methods.

Deep neural networks (DNNs) have made a huge impact in the field of machine learning by providing unbeatable humanlike performance to solve real-world problems such as image processing and natural language processing (NLP). Convolutional neural network (CNN) and recurrent neural network (RNN) are two typical architectures that are widely used to solve such problems. Time sequence-dependent problems are generally very challenging, and RNN architectures have made an enormous improvement in a wide range of machine learning problems with sequential input involved. In this paper, different types of RNN architectures are compared. Special focus is put on two well-known gated-RNN’s Long Term Short Memory (LSTM) and Gated Recurrent Unit (GRU). We evaluated these models on the task of force estimation system in pouring. In this study, four different models including multi-layers LSTM, multi-layers GRU, single-layer LSTM and single-layer GRU) were created and trained. The result suggests that multi-layer GRU outperformed other three models.

Infrared thermography has already been proven to be a significant method in non-destructive evaluation since it gives information with immediacy, rapidity and low cost. However, the thorniest issue for wider application of IRT is the quantification. In this work, we proposed a specific depth quantifying technique by employing the Gated Recurrent Units (GRU) in composite material samples via pulsed thermography (PT). Carbon Fiber Reinforced Polymer(CFRP) embedded with flat bottom holes were designed via Finite Element Method (FEM) modeling in order to precisely control the depth and geometrics of the defects. The GRU model automatically quantified the depth of defects presented in the CFRP material. The proposed method evaluated the accuracy and performance of synthetic CFRP data from FEM for defect depth predictions.

The conditions which allow sustained growth of a protocell population are investigated in the case of asymmetrical division. The results are compared to those of previous studies concerning models of symmetrical division, where synchronization (between duplication of the genetic material and fission of the lipid container) was found under a variety of different assumptions about the kinetic equations and about the place where molecular replication takes place. Such synchronization allows a sustained proliferation of the protocell population. In the asymmetrical case there can be no true synchronization, since the time to duplication may depend upon the initial size, but we introduce a notion of homogeneous growth which actually allows sustained reproduction of a population of protocells. We first analyze Surface Reaction Models, defined in the text, and we show that in many cases they undergo homogeneous growth under the same kinetic laws which lead to synchronization in the symmetrical case. This is the case also for Internal Reaction Models (IRMs), which however require a deeper understanding of what homogeneous growth actually means, as discussed below.

The study of the mechanisms underlying stem cell differentiation is under intensive research, and includes the contribution of a metabolic switch from glycolytic to oxidative metabolism. While mitochondrial biogenesis has been previously demonstrated in number of differentiation models, it is only recently that the role of mitochondrial dynamics has started to be explored. The discovery of asymmetric distribution of mitochondria in stem cell progeny has still strengthened the interest for the field. This review attempts to summarize the regulation of mitochondrial asymmetric apportioning by the mitochondrial fusion, fission and mitophagy processes, as well as to emphasize how asymmetric mitochondrial apportioning in stem cells affects their metabolism, and thus epigenetics, and determines cell fate.

Two region asymmetric polymers PR2F and PR1F with three repeat units of A-D-A, π-D-A, and π-D-π along the polymer backbone were attained by polymerizing different fluorinated benzothiadiazole-thiophene units, FBT-T and 2FBT-T units (A–π), with benzodithiophene unit (D), respectively. Here, the new region asymmetric polymers were in contrast to the traditional polymers featuring a D–A or D–π–A–π backbone. Both the region asymmetric polymers showed a low lying of HOMO energy level in relation to that of the PC61BM acceptor and then obtained the high open-circuit voltage of ~1 V in both PR2F and PR1F devices. Bulk-heterojunction devices based on PR2F with difluorinated BT exhibited an appreciable power conversion efficiency (PCE) of 4.73% due to the relatively high and balanced charge carrier mobilities, while the mono-fluorinated BT polymer PR1F-based devices gave a lower PCE of 2.92%. These results indicate that the region asymmetric conjugated polymer is a promising class of materials for polymer solar cell applications, and it is significant to further understand the influence of polymer structure on optoelectronic properties.

The two-parameter Wright special function is an interesting mathematical object that arises in the theory of the space and time-fractional diffusion equations. Moreover, many other special functions are particular instantiations of the Wright function. The article demonstrates finite representations of the Wright function in terms of sums of generalized hypergeometric functions, which in turn provide connections with the theory of the Gaussian, Airy, Bessel, and Error functions, etc. The main application of the presented results is envisioned in computer algebra for testing numerical algorithms for the evaluation of the Wright function.

Parallax processing and structure preservation has long been important and challenging tasks in image stitching. In this paper, an image stitching method based on sliding camera to eliminate perspective deformation and asymmetric optical flow to solve parallax is proposed. By maintaining the viewpoint of two input images in the mosaic non-overlapping area and creating a virtual camera by interpolation in the overlapping area, the viewpoint is gradually transformed from one to another image view-point so as to complete the smooth transition of the two image viewpoints and reduce perspective deformation. Two coarsely aligned warped images are generated with the help of a global projection plane. After that, the optical flow propagation and gradient descent method are used to quickly calculate the bidirectional asymmetric optical flow between the two warped images, and the optical flow-based method is used to further align the two warped images to reduce parallax. In the image blending, the softmax function and registration error are used to adjust the width of the blending area, further eliminating ghosting and reduce parallax. Finally, the comparative experiments show that our method can effectively eliminate perspective deformation, reduce misalignment, and save running time.

The valve controlled cylinder drive system is the most common type among hydraulic applications. The nonlinear behaviour in such system is inevitable when the valve spool around its null position [1] , Leaney [2] utilised component linking method to investigate the nonlinearities in a Moog valve controlled asymmetric cylinder drive system by simulation in Fortran, in which a generalised concept is introduced and validated by comparing to the experimental results. An factor is proposed in the generalised concepts to describe the asymmetric cylinder state, which is a constant when the cylinder in extending or retracting, but numerically calculated when the valve spool in the underlap region [2]. This paper utilises the component linking method to simulate the Moog valve controlled asymmetric cylinder drive system in Matlab Simulink, and proposed an analytical solution for factor when the valve spool in the underlap region.

Nonparametric density estimation for nonnegative data is considered in a situation where a random sample is not directly available but the data are instead observed from the length-biased sampling. Due to the boundary bias problem of the location-scale kernel, the approach in this paper is an application of asymmetric kernel. Two nonparametric density estimators are proposed. The mean integrated squared error, strong consistency, and asymptotic normality of the estimators are investigated. Some simulations illustrate the finite sample performance of the estimators.

A series of chiral complexes of the form Ir(NHC)2(aa)(H)(X) (NHC = N-heterocyclic carbene, aa = chelated amino acid, X = halide) was synthesized by oxidative addition of -amino acids to iridium(I) bis-NHC compounds and screened for asymmetric transfer hydrogenation of ketones. Following optimization of the reaction conditions, NHC, and amino acid ligands, high enantioselectivity was achieved when employing the Ir(IMe)2(l-Pro)(H)(I) catalyst (IMe = 1,3-dimethylimidazol-2-ylidene), which asymmetrically reduces a range of acetophenone derivatives in up to 95% enantiomeric excess.

In this work, anchoring of cinchona derivatives to trifunctional cores (hub approach) was demonstrated to obtain size-enlarged organocatalysts. By modifying the cinchona skeleton in different positions, we prepared four C3-symmetric size-enlarged cinchona derivatives (hub-cinchonas), which were tested as organocatalysts and their catalytic activities were compared with the parent cinchona (hydroquinine) catalyst. We showed that in the hydroxyalkylation reaction of indole, hydroquinine provides good enantioselectivities (up to 73% ee), while the four new size-enlarged derivatives gave significantly lower values (up to 29% ee) in this reaction. Anchoring cinchonas to trifunctional cores was found to facilitate nanofiltration-supported catalyst recovery using PolarClean alternative solvent. The C3-symmetric size-enlarged organocatalysts were completely rejected by all the applied membranes, whereas the separation of hydroquinine was found to be insufficient using organic solvent nanofiltration. Furthermore, the asymmetric catalysis was successfully demonstrated in the case of Michael reaction of 1,3-diketones and trans-β-nitrostyrene using Hub3-cinchona (up to 96% ee) as a result of the positive effect of the C3-symmetric structure using a bulkier substrate. This means an increased selectivity of the catalyst in comparison to hydroquinine in the latter Michael reaction.

This article introduces a novel approach, termed the Asymmetric Probabilistic Tsetlin (APT) Machine, which incorporates the Stochastic Point Location (SPL) algorithm with the Asymmetric Steps technique into the Tsetlin Machine (TM). APT introduces stochasticity into the state transitions of Tsetlin Automata (TA) by leveraging the SPL algorithm, thereby enhancing pattern recognition capabilities. To enhance random search processes, we introduced a decaying normal distribution into the procedure. Meanwhile, the Asymmetric Steps approach biases state transition probabilities towards specific input patterns, further elevating operational efficiency. The efficacy of the proposed approach is assessed across diverse benchmark datasets for classification tasks. The performance of APT is compared with traditional machine learning algorithms and other Tsetlin Machine models, including the Asymmetric Tsetlin (AT) Machine, characterized by deterministic rules for Asymmetric transitions, and the Classical Tsetlin (CT) Machine, employing deterministic rules for symmetric transitions. Strikingly, the introduced APT methodology demonstrates highly competitive outcomes compared to established machine learning methods. Notably, both APT and AT exhibit state-of-the-art performance, surpassing the Classical Tsetlin Machine, emphasizing the efficacy of asymmetric models for achieving superior outcomes. Remarkably, APT exhibits even better performance than AT, particularly in handling complex datasets.

We have developed deep learning models for automatic identification of the maternal heart rate (MHR) and, more generally, false signals (FSs) on fetal heart rate (FHR) recordings. The models can be used to preprocess FHR data prior to automated analysis or as a clinical alert system to assist the practitioner. Three models were developed and used to detect (i) FSs on the MHR channel (the FSMHR model), (ii) the MHR and FSs on the Doppler FHR sensor (the FSDop model), and (iii) FSs on the scalp ECG channel (the FSScalp model). The FSDop model was the most useful because FSs are far more frequent on the Doppler FHR channel. All three models were based on a multilayer, symmetric, GRU and were trained on data recorded during the first and second stages of delivery. The FSMHR and FSDop models were also trained on antepartum recordings. The training dataset contained 1030 expert-annotated periods (mean duration: 36 min) from 635 recordings. In an initial evaluation of routine clinical practice, 30 fully annotated recordings for each sensor type (mean duration: 5 h for MHR and Doppler sensors, and 3 h for the scalp ECG sensor) were analyzed. The sensitivity, positive predictive value (PPV) and accuracy were respectively 62.20%, 87.1% and 99.90% for the FSMHR model, 93.1%, 95.6% and 99.68% for the FSDop model, and 44.6%, 87.2% and 99.93% for the FSScalp model. We built a second test dataset with a more solid ground truth by selecting 45 periods (lasting 20 min, on average) on which the Doppler FHR and scalp ECG signals were recorded simultaneously. Using scalp ECG data, the experts estimated the true FHR value more reliably and thus annotated the Doppler FHR channel more precisely. The models achieved a sensitivity of 53.3%, a PPV of 62.4%, and an accuracy of 97.29%. In comparison, two experts (blinded to the scalp ECG data) respectively achieved a sensitivity of 15.7%, a PPV of 74.3%, and an accuracy of 96.91% and a sensitivity of 60.7%, a PPV of 83.5% and an accuracy of 98.24%. Hence, the models performed at expert level (better than one expert and worse than the other), although a well-trained expert with good knowledge of FSs could probably do better in some cases. The models and datasets have been included in the Fetal Heart Rate Morphological Analysis open-source MATLAB toolbox and can be used freely for research purposes.

Infrared thermography has already been proven to be a significant method in non-destructive evaluation since it gives information with immediacy, rapidity, and low cost. However, the thorniest issue for the wider application of IRT is quantification. In this work, we proposed a specific depth quantifying technique by employing the Gated Recurrent Units (GRU) in composite material samples via pulsed thermography (PT). Finite Element Method (FEM) modeling provides the economic examination of the response pulsed thermography. In this work, Carbon Fiber Reinforced Polymer (CFRP) specimens embedded with flat bottom holes are stimulated by a FEM modeling (COMSOL) with precisely controlled depth and geometrics of the defects. The GRU model automatically quantified the depth of defects presented in the stimulated CFRP material. The proposed method evaluated the accuracy and performance of synthetic CFRP data from FEM for defect depth predictions.

Quantitative determination of the critical size of inclined coal pillar in old goaf water affected area is of great significance for water damage prevention and safe mining. The critical size of inclined waterproof coal pillar is derived by using theoretical analysis, numerical calculation and field engineering practice for the stability of the waterproof coal pillar in old goaf water affected area of 1303 working face of Dananhu I mine in Xinjiang region. Firstly, a force model of inclined waterproof coal pillar was established to reveal the law that the critical size of the coal pillar increases with the increase of coal seam inclination under the action of asymmetric load. Then, numerical simulation was applied to reveal the dynamic evolution process of plastic deformation-destabilization-destruction of section coal pillar under the influence of mining and single-side water pressure, and the critical size of waterproof coal pillar in study area was determined to be 19.09m. Finally, measures such as pumping and pressure relief and slurry reinforcement were adopted to reduce the deformation rate of the roadway on side of waterproof coal pillar, which ensured the stability of the coal pillar and roadway and the safe recovery of the working face.

The oral administration of (R)-3-hydroxybutyl-(R)-3-hydroxybutyrate, allows inducing a beneficial level of blood ketone bodies without the adverse effects due to the adhesion to a ketogenic diet. Several studies documented the therapeutic effectiveness of the (R)-3-hydroxybutyl (R)-3-hydroxybutyrate in treating neurodegenerative diseases as well as its boosting activity of athletic and cognitive performances during prolonged physical exercises. Further studies considering this ketone body ester for therapy of other pathologies are also underway. In the present work, we describe the synthesis of (R)-3-hydroxybutyl-(R)-3-hydroxybutyrate through the enantioselective transesterification of racemic ethyl 3-hydroxybutyrate with (R)-1,3-butanediol catalyzed by immobilized Candida antarctica lipase B (CAL-B). The enantiopure (R)-1,3-butanediol was in turn obtained from the kinetic resolution of the racemate by CAL-B catalyzed acetylation with vinyl acetate. The economy of the synthetic procedure has been improved by recycling the unreacted (S) enantiomers of the ethyl 3-hydroxybutyrate and 1,3-buatnediol after stereochemical inversion achieved by tosylation and SN2 with ammonium acetate. The overall procedure allows to incorporate up to 70% of the starting racemic reagents into the final product.

Diaminomaleonitrile (DAMN) is an electron-rich ligand which is commonly used in the synthesis of purines, amides and Schiff base ligands. In the last case lies the interest in this molecule, given its symmetry and apparent facility to form various ligands and complexes of interest in fields such as organic solar cells and catalysis among others. Nevertheless, its bisubstitution with aldehydes displays certain difficulty due to the double conjugated presence of the nitrile group (C≡N) in its structure, which significantly affect its coordination behavior by modulating the chemical reactivity of its amines. In addition to presenting a practical resume of guidelines for the preparation of different bisubstituted compounds from DAMN, this paper reviews the possibility of attaining a precise characterization by simple spectroscopic techniques. We provide an additional discussion for one of these techniques (commonly reported but often overlooked), given its potential to provide both the symmetry and E/Z configuration of the product. We hope the comprehensive evidence discussed and shown in this review will be helpful to further develop and understand the products derived of this interesting molecule in their broad applications.

This study investigates the asymmetric impacts of oil price changes on inflation in Algeria, Angola, Libya and Nigeria. Three different oil price data were applied in this study; the specific spot oil price of individual countries, the OPEC reference basket oil price and an average of the Brent, WTI and Dubai oil price. The dynamic panels ARDL were used to estimate the short and the long-run impacts. Also, this study partitioned the oil price into positive and negative changes to capture asymmetric impacts and found both positive and negative oil price changes positively influenced inflation. However, the impact was found to be more significant when oil prices dropped. The results from the study also found that money supply, the exchange rate and GDP are positively related to inflation while food production is negatively related to inflation. Accordingly, policymakers should be cautious in formulating policies between the positive and negative changes in oil prices as it was shown that inflation increased when the oil price dropped. Additionally, the use of contractionary monetary policy would help to reduce the inflation rate, and lastly, it is proposed that the government should encourage domestic food production both in quantity and quality to reduce inflation.

The asymmetric bimodal exponential power (ABEP) distribution is an extension of the generalized gamma distribution to the real line via adding two parameters which fit the shape of peakedness in bimodality on real line. The special values of peakedness parameters of the distribution are combination of half Laplace and half normal distributions on real line. The distribution has two parameters fitting the height of bimodality, so capacity of bimodality is enhanced by using these parameters. Adding a skewness parameter is considered to model asymmetry in data. The location-scale form of this distribution is proposed. The Fisher information matrix of these parameters in ABEP is obtained explicitly. Properties of ABEP are examined. Real data examples are given to illustrate the modelling capacity of ABEP. The replicated artificial data from maximum likelihood estimates of parameters of ABEP and distributions having an algorithm for artificial data generation procedure are provided to test the similarity with real data.

Binarization of degraded documents is an important preprocessing task for various document analysis such as OCR and historical document analysis. Existing studies have applied various convolutional neural network (CNN) models and generative models for document binarization, but they do not show generalized performance for noise that the model has not seen and it suffers from extracting elaborate text strokes. In this paper, to overcome these challenges, we utilize latent diffusion model (LDM), which is known for high-quality image generation model, for the first time in document binarization. By utilizing the iterative diffusion-denoising process in latent space, it shows high-quality cleaned binarized image generation and high generalized performance through using both data distribution and time step while training. Additionally, we apply gated U-Net to the backbone network to preserve text strokes using trainable gating value. Gated convolution can extract elaborate text stroke by allowing the model to focus on text region by combining gating value and feature. Furthermore, we maximize the effectiveness of the proposed model by training it with a combination of LDM loss and pixel-level loss, which is suitable for the model structure. Experiments on H-DIBCO and DIBCO benchmark datasets show that the proposed model outperforms existing methods.

The Mobius function is commonly used to define Euler's totient function and the Mangoldt function. Similarly, the summatory Mobius function (the Mertens function) can be used to define the summatory totient function and the summatory Mangoldt function (the second Chebyshev function).

The asymmetric synthesis of polyunsaturated triene C18:3 n-3 and C18:3 n-6 methoxylated ether lipids (MEL) of the 1-O-alkyl-sn-glycerol type is described as possible structural candidates for a triene C18:3 MEL of an unknown identity found in a mixture of shark and dogfish liver oil. Their C18:3 hydrocarbon chains constitute an all-cis methylene skipped n-3 or n-6 triene framework, along with a methoxyl group at the 2'-position and R-configuration of the resulting stereogenic centre. The methoxylated polyenes are attached by an ether linkage to the pro-S hydroxymethyl group of the glycerol backbone. The syntheses were based on the polyacetylene approach that involves a semi-hydrogenation of the resulting triynes. Both syntheses were started from our previously described enantio- and diastereomerically pure isopropylidene-protected glyceryl glycidyl ether, a double-C3 building block that was designed as a head group synthon for synthesis of various types of MELs.

Theoretical approaches were applied to study the effect of magnetic field and heat transfer on the flow of blood plasma through an asymmetric arterial segment. The plasma was considered to be unsteady, laminar and an incompressible fluid through non-uniform arterial segment in a two-dimensional flow. Axial velocity, pressure gradient, stream function and pressure shift per wavelength were evaluated in blood plasma flow in arteries by use of coupled linear partial differential equations, solved with the help of Finite difference method. The corresponding initial and boundary conditions were obtained by discretizing the flow channel. The effect of magnetic field on blood plasma in arteries was determined by creating a magnetic field gradient through the application of a varying strength of magnetic field on the flow. Heat transfer characteristics due to applied magnetic field and viscosity of blood was obtained by use of linear partial differential equations to determine varying temperature conditions in heat transfer characteristics. Numerical results for velocity profiles, magnetic profiles and temperature profiles were obtained to characterize blood plasma viscosity by use of various non-dimensional parameters. The results were graphically presented using MATLAB software. The results obtained helped in analyzing theoretically the effects of magnetic field and heat transfer in arterial plasma flow.

Background: After allogeneic hematopoietic stem cell transplantation (allo-HSCT), acute leukemia relapse is common, and asymmetric bone marrow recurrence hasn’t been reported. Because the anatomical distribution of acute leukemia clones in the bone marrow after allo-HSCT is presumed to be diffuse, bone marrow aspirations are performed in single site. Case presentation: We identified two acute leukemia patients, whose leukemic burden in bilateral bone marrow specimens differed significantly. The first case was a 20-year-old man who was diagnosed with acute myelomonocytic leukemia and received haploidentical allo-HSCT. He had been in complete remission for two years and off immunosuppressive medications for a year, with normal peripheral blood count. Routine bone marrow biopsy of his left posterior iliac bone marrow showed 52% leukemia blasts, while the right side had 0% blasts ten days later. Due to the discordant results, the patient refused further intervention and died of high leukocyte syndrome four months later. The second case was a 23-year-old woman who was diagnosed with acute B lymphoblastic leukemia and received HLA-identical sibling allo-HSCT. Although 62% of blasts were found in her left iliac marrow on day +122, 0 % of blasts were found on a sample obtained from the right iliac crest on day +128. Whole-body 18F-FDG PET/CT scans confirmed that the leukemic infiltration in her bone marrow was asymmetric. Considering the higher leukemic burden on the left, we chose the left posterior iliac crest aspiration for further response evaluation. After chemotherapy combined with donor lymphocyte infusion, she achieved transient hematologic complete remission. She died of septic shock with heart failure at +258 days after allo-HSCT before infusion of anti-CD19 donor chimeric antigen receptor T cells. Conclusions: To our knowledge, these are the first case reports of asymmetric bone marrow infiltration of blasts in acute leukemia patients after allo-HSCT. Bilateral posterior iliac crest aspirations or 18F-FDG-PET/CT scans may help distinguish such distribution. If discordant bone marrow specimens are observed, physicians should restrict future bone marrow studies to the more involved side.

Behavioral instability is a new concept used for indicating environmental stress based on behavioral traits. This study investigates the possibility of using behavioral instability as a tool for assessing personality in captive animals. The understanding of personality in captive animals can be a resourceful tool in the development of enrichment programs in order to improve animal welfare. In this study it is examined how an olfactory stimulus affects the behavior of two individuals of the species Ursus maritimus in captivity. When using continuous focal sampling throughout the day it was for many behaviors found that the individuals responded differently to stimuli, indicating that there was a difference in personality. This is shown using multiple approaches. One approach used traditional methods for behavioral analyses and the other approach used the concept of behavioral instability as a new quantitative method. This study proves use of behavioral instability as a new quantitative method for investigating personality, expanding the possibility of comparing personality between species. Moreover, it is shown that outliers, which cause asymmetric distributions, should not be removed in behavioral analysis without careful consideration.

Asymmetric reduction of enoates, imines and ketones are among the most important reactions in biocatalysis. These reactions are routinely conducted using enzymes that use nicotinamide cofactors as reductants. The deazaflavin cofactor F₄₂₀ also has electrochemical properties that make it suitable as an alternative to nicotinamide cofactors for use in asymmetric reduction reactions. However, cofactor F₄₂₀-dependent enzymes remain under-explored as a resource for biocatalysis. In this review, we consider the cofactor F₄₂₀-dependent enzyme families with greatest potential for the discovery of new biocatalysts: the flavin/deazaflavin-dependent oxidoreductases (FDORs) and the luciferase-like hydride transferases (LLHTs). We discuss characterized F₄₂₀-dependent reductions that have potential for adaptation for biocatalysis, and we consider the enzymes best suited for use in the reduction of oxidized cofactor F₄₂₀ to allow cofactor recycling in situ. We also discuss recent advances in the production of cofactor F₄₂₀ and its functional analog F_O-5’- phosphate, which remains an impediment to the adoption of this family of enzymes for industrial biocatalytic processes. Finally, we discuss the prospects for the use of this cofactor and dependent enzymes as a resource for industrial biocatalysis.

Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same geometric means finally help to systematically derive handy formulas that approximate the inverse error function. Our approach can be used for applications in e.g. high-speed Monte Carlo simulations where this function is used extensively.

In this work we develop a new algorithm for efficient computation of the Voigt/complex error function. In particular, in this approach we propose a two-domain scheme where number of the grid-points is dependent on the input parameter $y$. The error analysis we performed shows that the MATLAB implementation meets the requirements for radiative transfer applications involving the HITRAN spectroscopic database. The run-time test shows that this MATLAB implementation provides rapid computation especially at smaller range of the parameter x.

The manuscript surveys the special functions of the Fox-Wright type. These functions are generalizations of the hypergeometric functions. Notable representatives of the type are the Mittag-Leffler functions and the Wright function. The integral representations of such functions are given and the conditions under which these function can be represented by simpler functions are demonstrated. The connection with generalized fractional differential and integral operators is demonstrated and discussed.

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

The ejido system in Mexico based on communal land was transformed for private ownership due to neoliberal trends during 1990. This research describes the evolution of Mexican land policies that changed the ejido system into private development to answer why land tenure change is shaping urban growth. To demonstrate this, municipalities of San Andrés Cholula and Ocoyucan were selected as a case study. Within this context, we evaluated how much ejido land is being urbanized due to real estate market forces and what type of urbanization model is created. These two areas represent different development scales: S.A. Cholula where its ejidos were expropriated as part of a regional urban development plan; and Ocoyucan where its ejidos and rural land were reached by private developers without local planning. To analyze both municipalities, historical satellite images from Google Earth were used with GRASS GIS 7.4 and corrected with QGIS 2.18. We found that privatization of ejidos fragmented and segregated the rural world for the construction of massive gated-communities. Therefore, a disturbing land tenure change occurred during the last 30 years, hence this research questions the role of local authorities in permitting land use change without regulations or local planning. The resulting urbanization model is a private sector development that isolates rural communities in their own territories, for which we provide recommendations.

In this paper, we classify the function space of all real-valued functions on R denoted as F(R,R) into 28 distinct blocks. Each block contains elements that share common features in terms of the cardinality of their sets of continuity and differentiability. Alongside this classification, we introduce the concept of the Connection, which reveals a special relationship structure between four well-known real-valued functions in real analysis: the Cantor function, Dirichlet function, the Thomae function, and the Weierstrass function. Despite the significance of this field, several perspectives remain unexplored.

In this article, our main purpose is to establish a new extension of Mittag-Leffler function by using the known extended beta function $\mathbf{B}_{\omega}(a,b;p)$ introduced in [1]. It led to a novel extension of the applicability of Mittag-Leffler function that introduced them as distributions defined for a specific set of functions. We also, investigate some of its important properties, namely recursion relation, Mellin transform and differential formulas.

Deep eutectic solvents are a mixture of two or more components, that at a particular composition become liquids at room temperature. When the compounds that constitute the DES are primary metabolites, namely, amino acids, organic acids, sugars, or choline derivatives, the DES are so called natural deep eutectic solvents (NADES). NADES fully represent green chemistry principles. These solvents are highly welcome, as they are obtained from renewable resources, and gratifyingly biodegradable and biocompatible. They are an alternative to room temperature ionic liquids (RTILs). From the pharmaceutical industry point of view, they are highly desirable, but unfortunately have been rarely used despite their enormous potential. In this review, we will look at their impact on the asymmetric catalytic synthesis of key target molecules, via metal-based catalysis, biocatalysis and organocatalysis. In many cases the NADES that have been used are chiral and can even promote enantioselective reactions, this crucial and very exciting aspect will also be discussed and analysed.

Chiral hydroxamic acid (HA) and bis-hydroxamic acid (BHA) ligands have made significant contributions to the field of asymmetric synthesis, particularly in the synthesis of natural products. These ligands possess unique molecular structures that allow for exceptional stereochemical control, leading to their widespread use in catalytic systems. This review highlights the advancements made in asymmetric synthesis using chiral hydroxamic acid and bis-hydroxamic acid ligands and their impact on the synthesis of complex natural products. The discussion encompasses their role in enantioselective C-C bond formation, the functionalization of C-H bonds, asymmetric transformations involving heteroatoms, and their application in the total synthesis of natural products. The versatility and efficiency of chiral hydroxamic acid ligands and bis-hydroxamic acid ligands make them invaluable tools for synthetic chemists working towards the efficient and selective synthesis of natural products. This review provides a comprehensive overview of their contributions, showcasing their potential to expand the boundaries of chemical synthesis and access the diverse array of natural product scaffolds.

The economic downturn caused by the financial crisis of 2008-2009 and the intensifying glob-al climate policy trends forced changes in the energy management of the European Union. The study examined how the most relevant energy economic variables affected the economic growth of the EU between 2010-2019. The study examined the relationship between GDP (dependent variable) and energy consumption, greenhouse gas emissions, the average energy price, and renewable energy use (independent variables) using the PSL-PM methodology. The results show an asymmetric picture because the independent variables influenced the eco-nomic growth of the EU in the examined period with different correlations and with different strengths. One of the significances of the study is that the presented and analyzed variables, as well as the results of the relationships between them, can contribute to the optimization of the EU's currently critical energy management and economic growth.

The pulsating flow is one of the techniques which can enhance heat transfer, therefore leading to energy saving in tubular heat exchangers. This paper investigates the heat transfer and flow characteristics in a two-dimensional in-line tube bundle with the pulsating flow by a numerical method using the Ansys Fluent. Numerical simulation is performed for Reynolds number Re = 500 with different frequencies and amplitude of pulsation. Heat transfer enhancement was estimated from the central tube of the tube bundle. Pulsation velocity had an asymmetrical character with a reciprocating flow. The technique developed by the authors to obtain asymmetric pulsations was used. This technique allows simulating an asymmetric flow in heat exchangers equipped with a pulsation generation system. Increase in both the amplitude and the frequency of the pulsations has a significant effect on heat transfer enhancement. Heat transfer enhancement is mainly observed in the front and back of the cylinder. At a steady flow in these areas, heat transfer is minimal due to the weak circulation of the flow. The increase in heat transfer in the front and back of the cylinder is associated with increased velocity and additional flow mixing in these areas.

Tropical storm Nate, which was a powerful hurricane prior to landfall along the Alabama coast, traversed north towards our instrumented site in Hunstville, AL. The rain bands lasted 18 h and the 2D-video disdrometer (2DVD) captured the event which was shallow and indicative of pure warm rain processes. Measurements of raindrop size, shape and velocity distributions are quite rare in pure warm rain and are expected to differ from cold rain processes. In particular, asymmetric shapes due to drop oscillations and their impact on polarimetric radar signatures in warm rain have not been studied so far. Recently, the 2DVD data has been used for 3D reconstruction of asymmetric raindrop shapes but their fraction (relative to the more common oblate shapes) in warm rain has yet to be ascertained. Here we compute the scattering matrix drop-by-drop using Computer Simulation Technology integral equation solver for drop sizes>2.5 mm. From the scattering matrix elements, the polarimetric radar observables are simulated by integrating over 1 minute consecutive segments of the event. These simulated values are compared with dual-polarized C-band radar data located at 15 km range from the 2DVD site to evaluate the contribution of the asymmetric drop shapes.

The enantioselective alpha-amination of 1,3-dicarbonyl compounds has been performed using a catalytic system based on deep eutectic solvents (DES) and chiral 2-amino benzimidazole-derived organocatalysts. This procedure avoids the use of toxic volatile organic compounds (VOCs) as a reaction medium, providing access to highly functionalized chiral molecules, which are important intermediates for the natural product synthesis, in a selective and efficient manner. Furthermore, the reaction can be performed on a large scale and recycling the catalytic system is possible for at least five times, leading to a clean, cheap, simple, and scalable procedure that meets most of the criteria required to be a green and sustainable process.

A reliability-based criterion to estimate strength amplification factors for buildings with asymmetric yielding located within a seismic region presenting different soil conditions is proposed and applied. The approach involves the calculation of the mean annual rate of exceedance of structural demands of systems with different levels of asymmetric yielding. Two simplified mathematical expressions are developed considering different soil conditions of the valley of Mexico. The mathematical expressions depend on the ductility of the structural systems, their level of asymmetric yielding, their fundamental vibration period and the dominant period of the soil. In addition, the proposed expressions are compared with that recommended by the current Mexico City Building Code (MCBC). Since the expressions are developed with the help of simplified structural systems, the validity of such expressions is corroborated by comparing the expected ductility demand of multi-degree of freedom (MDOF) structural systems with respect to that of their equivalent simplified systems. Both structural representations are associated with a given annual rate of exceedance value of an engineering demand parameter. The expressions proposed in this study will be incorporated in the new version of the MCBC.

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

It is well known that the primes and prime powers have a deep relationship with the nontrivial zeros of Riemann’s zeta function. This is a reciprocal relationship. The zeros and the primes are encoded in each other and are reciprocally recoverable. Riemann’s zeta is an extended or continued version of Euler’s zeta function which in turn equates with Euler’s product formula over the primes. This paper shows that the zeros of the converging Dirichlet or Catalan beta function, which requires no continuation to be valid in the critical strip, can be easily determined. The imaginary parts of these zeros have a deep and reciprocal relationship with the odd primes and odd prime powers. This relationship separates the odd primes into those having either 1 or 3 as a remainder after division by 4. The vector pathway of the beta function is such that the real part of its zeros has to be a half.

In recent years, unmanned aerial vehicles (UAVs) have become a valuable platform for many applications, including communication networks. UAV-enabled wireless communication faces challenges in complex urban and dynamic environments. UAVs can suffer from power limitations and path losses caused by non-line-of-sight connections, which may hamper better communication performance. To address these issues, reconfigurable intelligent surfaces (RIS) have been proposed as a helpful tool to enhance UAV communication networks. However, due to the high mobility of UAV, complex channel environments, and dynamic RIS configurations, it is challenging to estimate the link quality of ground users. In this paper, we propose a link quality estimation model using a gated recurrent unit (GRU) to assess the link quality of ground users for a multi-user RIS-assisted UAV-enabled wireless communication system. Our proposed framework uses a time series of user channel data and RIS phase shift information to estimate the quality of the link for each ground user. Simulation results showed that the proposed GRU model effectively and accurately estimates the link quality of the ground users in the RIS-assisted UAV-enabled wireless communication network.

For voltage-gated Ca2+ channel (VGCC), its α2δ subunits are traditionally considered to be auxiliary subunits that regulates VGCC trafficking to the plasma membrane. The antiepileptic, antinociceptive and anxiolytic gabapentin (GBP) has previously been shown to bind the VGCC α2δ subunits with high affinity to disrupt VGCC trafficking. Yet, the interaction between GBP and α2δ still remains poorly understood from a structural point of view. For instance, it is not clear yet what the structural implication is of α2δ-1-bound GBP against VGCC trafficking. With a set of experimental data-driven structural analysis of the VGCC α2δ-1 and its ligand GBP, this article postulates for the first time that: 1), α2δ-1 bound GBP stabilizes the α2δ-1-GBP complex structure; 2), α2δ-1 bound GBP restrains the conformational flexibility of α2δ-1; 3), α2δ-1-bound GBP establishes an electrostatic axis consisting of Q535 (Gln535)-R241 (Arg241)-GBP (gabapentin)-D452 (Asp452), which constitutes an energetically favourable contribution towards the structural stability of the α2δ-1-GBP complex and helps restrains the conformational flexibility and local structural rigidification of α2δ-1; and 4), GBP-induced local conformational inflexibility and structural rigidification of α2δ-1 is one key step in the pharmacological disruption of VGCC trafficking by GBP.

In the paper, the authors discover several series identities involving the Catalan numbers, the Catalan function, the Riemanian zeta function, and the alternative Hurwitz zeta function.

Proof of the Riemann hypothesis is obtained using the properties of the Gamma function, the Bernoulli function, and limitations imposed by the rational relations of the complex roots of the Riemann zeta function, and the rational relations of the complex Gamma functions.

In a recent paper, Sarikaya et al. introduced a new analogue of the classical Gamma function which they called, the conformable Gamma function. Motivated by their results, this paper seeks to establish some inequalities for the conformable Gamma and Polygamma functions. Among other analytical tools, the procedure relies on the generalized forms of some classical inequalities.

The main objective of this present paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. Also, we give some results related to the newly defined fractional operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

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

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

This report demonstrates the first-time asymmetric synthesis of enantiopure structured triacylglycerols (TAGs) of the ABC type presenting three non-identical fatty acids, two of which unsaturated. The unsaturated fatty acids included the monounsaturated oleic acid (C18:1 n-9) and the polyunsaturated linoleic acid (C18:2 n-6). This was accomplished by a six-step chemoenzymatic approach starting from (R)- and (S)-solketals. The highly regioselective immobilized Candida antarctica lipase (CAL-B) played a crucial role in the regiocontrol of the synthesis. The synthesis also benefited from the use of the p-methoxybenzyl (PMB) ether protective group that enabled incorporation of two different unsaturated fatty acids to the glycerol skeleton. The total of six such TAGs were prepared, four constituting the unsaturated fatty acids in the sn-1 and sn-2 positions with a saturated fatty acid in the remaining sn-3 position of the glycerol backbone. In the two remaining TAGs the different unsaturated fatty acids accommodated the sn-1 and sn-3 end positions with the saturated fatty acid present in the sn-2 position. Enantiopure TAGs are urgently demanded as standards for enantiospecific analysis of intact TAGs in fats and oils.

The main objective of this paper is to introduce a further extension of extended (p, q)-beta function by considering two Mittag-Leffler function in the kernel. We investigate various properties of this newly defined beta function such as integral representations, summation formulas and Mellin transform. We define extended beta distribution and its mean, variance and moment generating function with the help of extension of beta function. Also, we establish an extension of extended (p, q)-hypergeometric and (p, q)-confluent hypergeometric functions by using the extension of beta function. Various properties of newly defined extended hypergeometric and confluent hypergeometric functions such as integral representations, Mellin transformations, differentiation formulas, transformation and summation formulas are investigated.

In the paper, the authors generalize the notion "k-Mittag-Leffler function'', establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function.

Chronic pain is a significant health problem worldwide. Recent evidence has suggested that dysfunctional states of the ventral hippocampus, including decreased neuronal excitability and connectivity with other brain regions, parallel pain chronicity and persistent nociceptive hypersensitivity in humans and rodents, respectively. But the molecular mechanisms underlying hippocampal modulation of pain remain poorly elucidated. In this study, we used ex vivo whole-cell patch-clamp recording, immunofluorescence staining and behavioral tests to examine whether hyperpolarization-activated cyclic nucleotide-gated channels 2 (HCN2) in the ventral hippocampal CA1 (vCA1) were involved in regulating nociceptive perception and CFA-induced inflammatory pain in mice. Reduced sag potential and firing rate of action potentials were observed in vCA1 pyramidal neurons from CFA-injected mice. Moreover, the expression of HCN2, but not HCN1, in vCA1 decreased in mice injected with CFA. HCN2 knockdown in vCA1 pyramidal neurons induced thermal hypersensitivity, whereas over-expression of HCN2 alleviated thermal hyperalgesia induced by intraplantar injection of CFA in mice. Our findings suggests that HCN2 in the vCA1 plays an active role in pain modulation and could be a promising target for the treatment of chronic pain.

Jacobian theta function identities are related to the Addition formula for the Weierstrass 1 Sigma function. In this paper, from the Addition formula for Weierstrass Sigma function, new and 2 simple proofs of four square sums theorem are given. Using the addition formula of the theta func- 3 tions, we also give simple proofs of two square sums and eight square sums theorem.

In this paper, we introduce two subclasses of analytic and Spirallike functions and investigate convolution properties, the necessary and sufficient condition, coefficient estimates and inclusion properties for these classes .

A new generalization of extended beta function and its various properties, integral representations and distribution are given in this paper. In addition, we establish the generalization of extended hypergeometric and con uent hypergeometric functions using the newly extended beta function. The properties these extended and con uent hypergeometric functions such as integral representations, Mellin transformations, dif- ferentiation formulas, transformation and summation formulas are also investigated.

Abstract: Background: Restless Legs Syndrome /Willis-Ekbom disease (RLS/WED) has occasionally -but not consistently- been associated with cognitive, and most notably, language and executive impairment. The present study was conducted to investigate the cognitive trajectories of older individuals with RLS/WED. Methods: Participants were drawn from the randomly selected, older (>64 years), population-based HELIAD cohort. Individuals without dementia, with available neuropsychological evaluations at baseline and follow-up were considered for potential eligibility. A comprehensive assessment examining five principal components of cognition (memory, visuo-spatial ability, attention, executive function, and language) was administered to the partici-pants. Generalized estimating equations analysis was used to examine the unadjusted and adjusted (for critical factors and covariates) effects of RLS/WED on cognition over time. Results: A total of 1003 predominantly female, older (72.9 ±4.9 years) partici-pants, with follow-up evaluations after a mean of 3.09 ±0.85 years and without demen-tia at baseline and follow-up were included in the present study. Among them, 81 were diagnosed with RLS/WED at baseline. Global cognition, memory, attention, executive and visuo-perceptual skills did not differ between those with and without RLS/WED. However, the RLS/WED group performed worse on language at baseline by 0.249 of a standard deviation, while demonstrating a mitigated language decline over time, by 0.063 of a standard deviation. The unadjusted models yielded similar results. Conclu-sions: Our findings were indicative of a baseline language disadvantage among older individuals with RLS/WED, but the initial discrepancy tends to dissolve over time.

This paper establishes a real integral representation of the reciprocal $\Gamma$ function in terms of a regularized hypersingular integral. The equivalence with the usual complex representation is demonstrated. A regularized complex representation along the usual Hankel path is derived.

Recently, different extensions of the fractional derivative operator are found in many research papers. The main aim of this paper is to establish an extension of the extended Caputo fractional derivative operator. The extension of an extended fractional derivative of some elementary functions derives by considering an extension of beta function which includes the Mittag-Leffler function in the kernel. Further, an extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and the generating relations for extension of extended hypergeometric functions also presented in this study.

The main objective of this present paper is to introduce further extension of extended Caputo fractional derivative operator and establish the extension of an extended fractional derivative of some known elementary functions. Also, we investigate the extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and generating relations for extension of extended hypergeometric functions.

We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the same order at certain arguments.

The endo- and exo-N-heterocyclic carbene precursors based on camphor were prepared diastereoselectively in five synthetic steps starting from (1S)-(+)-ketopinic acid. The obtained N-heterocyclic carbene precursors were investigated in an asymmetric benzoin reaction. All new compounds were fully characterized and the absolute configurations were determined by X-ray diffraction and NOESY measurements.

Evaluation of market connectedness and asymmetric volatility spillover has recently seen a surge in financial risk analytics and portfolio diversification. We carried out a meta-literature review on connectedness and spillovers, providing solid insight into the research field and robust guidelines for future investigation. The review consists of a quantitative bibliometric analysis of 594 papers and a qualitative content analysis of 77 papers covering 1991 to 2021. The results of the meta-citation analysis shows that Diebold's Spillover index (2007) is the predominant method in most works as far as market connectedness and spillover is concerned. With an extensive review, we answered the following objectives (1) Analyze the most influential authors, journals, and publications, (2) Understand the research streams and most studied streams, (3) Understand the theme structure and thematic evolution, and keyword trends, (4) Examine the pattern of collaboration, and most productive affiliations, (5) Explore future research directions and untapped areas. The content analysis revealed the following important research streams in the current literature (1) Asymmetries in the market connectedness, (2) Influence of Macro Factors in the market connectedness and spillover, (3) the Role of Oil in market spillovers and hedging portfolios, (4) Dynamic cross-market connectedness and spillovers. The ongoing financial turmoil and market advancements make market connectedness a vital research topic; thus, our work would significantly contribute to macroeconomic policymakers, researchers and hedging investors.

This study introduces session-aware recommendation models, leveraging GRU (Gated Recurrent Unit) and attention mechanisms for advanced latent interaction data integration. A primary ad-vancement is enhancing latent context, a critical factor for boosting recommendation accuracy. We address existing models' rigidity by dynamically blending short-term (most recent) and long-term (historical) preferences, moving beyond static period definitions. Our approaches, pre-combination (LCII-Pre) and post-combination (LCII-Post) with fixed (Fix) and flexible learning (LP) weight configurations, are thoroughly evaluated. We conducted extensive experiments to as-sess our models' performance on public datasets such as Amazon and MovieLens 1M. Notably, on the MovieLens 1M dataset, LCII-PreFix achieved a 1.85% and 2.54% higher Recall@20 than II-RNN and BERT4Rec+st+TSA, respectively. On the Steam dataset, LCII-PostLP outperformed these models by 18.66% and 5.5%. Furthermore, on the Amazon dataset, LCII showed a 2.59% and 1.89% improvement in Recall@20 over II-RNN and CAII. These results affirm the significant enhancement our models bring to session-aware recommendation systems, showcasing their po-tential for both academic and practical applications in the field.

The cardiac sodium ion channel (NaV1.5) is a protein with four domains (DI-DIV), each with six transmembrane segments. Its opening and subsequent inactivation results in the brief rapid influx of Na+ ions resulting in the depolarization of cardiomyocytes. The neurotoxin veratridine (VTD) inhibits NaV1.5 inactivation resulting in longer channel opening times, and potentially fatal action potential prolongation. VTD is predicted to bind at the channel pore, but alternative binding sites have not been ruled out. To determine the binding site of VTD on NaV1.5, we performed docking calculations and high-throughput electrophysiology experiments. The docking calculations identified two distinct binding regions. The first site was in the pore, close to the binding site of NaV1.4 and NaV1.5 blocking drugs in experimental structures. The second site was at the “mouth” of the pore at the cytosolic side, partly solvent-exposed. Mutations at this site (L409, E417, and I1466) had large effects on VTD binding, while residues deeper in the pore had no effect, consistent with VTD binding at the mouth site. Overall, our results suggest a VTD binding site close to the cytoplasmic mouth of the channel pore. Binding at this alternative site might indicate an allosteric inactivation mechanism for VTD at NaV1.5.

In this article, we present two topics related to mathematical economics. We offer an intriguing proposal for securing cost and production functions in the face of uncertainty and risk. We discuss the relationship between individual and social preferences. This is important because traditional revealed preference theory does not account for such factors.

To generate a probability density function (PDF) for fitting probability distributions of real data, this study proposes a deep learning method which consists of two stages: (1) a training stage for estimating the cumulative distribution function (CDF) and (2) a performing stage for predicting the corresponding PDF. The CDFs of common probability distributions can be adopted as activation functions in the hidden layers of the proposed deep learning model for learning actual cumulative probabilities, and the differential equation of trained deep learning model can be used to estimate the PDF. To evaluate the proposed method, numerical experiments with single and mixed distributions are performed. The experimental results show that the values of both CDF and PDF can be precisely estimated by the proposed method.

In this paper, we establish some inequalities bounding the ratio Г_p,k(x)/Г_p,k(y), where Г_p,k(.) is the (p,k)-analogue of the Gamma function. Consequently, some previous results are recovered from the obtained results.

According to the fact that the low convergence level on the complete elliptic integral of the first kind for the modulus which having values approach to one. In this paper we propose novelty of the complete elliptic integral consists of the new infinite series. We apply the scheme of iteration by substituting the common modulus with own modulus function into the new infinite series. We obtained so many new exact formulas of the complete elliptic integral derived from this method correspond to the number of iteration order. On the other hand, it has been also obtained a lot of new modulus functions rather than common used previously. The calculation results show that the number of significant figures of the new infinite series of the complete elliptic integral of the first kind is increased more and more. It means more fastly convergent would be obtained comparison values with the previous infinite series.

Recently, Kim-Kim [13] have introduced polyexponential functions as an inverse to the polylogarithm functions, and constructed type 2 poly-Bernoulli polynomials. They have also introduced unipoly functions attached to each suitable arithmetic function as a universal concept. Inspired by their work, in this paper, we introduce a new class of the Frobenius-Genocchi polynomials. We derive the diverse formulas and identities covering some summation formulas, derivative formula and correlations with Bernoulli polynomials and numbers, Stirling numbers of the both kinds, degenerate Frobenius-Genocchi polynomials and degenerate Frobenius-Euler polynomials. Moreover, by using the unipoly function as following Kim-Kim's work in <cite>Kim1</cite>, we consider degenerate unipoly-Frobenius-Genocchi polynomials and investigate some formulas and relationships with Daehee numbers, degenerate Frobenius-Genocchi numbers and Stirling numbers of the first kind. Finally, we obtain an Gaussian integral representation of the Frobenius-Genocchi polynomials in terms of the 2-variable Hermite polynomials.

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

We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, inverse trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.

In this article, the main building of the former Uto City Hall, which was severely damaged in the 2016 Kumamoto earthquake, is investigated as a case study for the retrofitting of an irregular Reinforced Concrete building using the base-isolation technique. Its peak response is predicted via mode-adaptive bidirectional pushover analysis (MABPA), which was originally proposed by the authors. In the prediction step of MABPA, the peaks of the first and second modal responses are predicted considering the energy balance during a half cycle of the structural response. The numerical analysis results show that the peak relative displacement can be properly predicted by MABPA. The results also show that the performance of the retrofitted building models is satisfactory for the ground motion considered in this study, including the recorded motions in the 2016 Kumamoto earthquake.

The current report contributes to the understanding of the stereoselectivity of the chiral dirhodium(II) carboxylate catalysts derived from N-protected amino acid ligands. Investigating the possible effect of ligand stereo-purity on catalyst structure and enantioselectivity was carried out. This was justified through a new X-ray crystal structure for Rh2(S,S,S,R-PTTL)4 diastereomer.

Multilabel learning goes beyond standard supervised learning models by associating a sample with more than one class label. Among the many techniques developed in the last decade to handle multilabel learning best approaches are those harnessing the power of ensembles and deep learners. This work proposes merging both methods by combining a set of gated recurrent units, temporal convolutional neural networks, and long short-term memory networks trained with variants of the Adam optimization approach. We examine many Adam variants, each fundamentally based on the difference between present and past gradients, with step size adjusted for each parameter. We also combine Incorporating Multiple Clustering Centers and a bootstrap-aggregated decision trees ensemble, which is shown to further boost classification performance. In addition, we provide an ablation study for assessing the performance improvement that each module of our ensemble produces. Multiple experiments on a large set of datasets representing a wide variety of multilabel tasks demonstrate the robustness of our best ensemble, which is shown to outperform the state-of-the-art. The MATLAB code for generating the best ensembles in the experimental section will be made available at https://github.com/LorisNanni.

In history, theta function identities have been studied extensively and deeply. In this paper, applying the residue theorem of an elliptic function, we obtain a parameterized theta function identity. Then, by selecting the appropriate parameter, we derive some famous Jacobi identities, as well as other relatively simple theta function identities.

In this paper, an analytical form of the Unit Step Function (or Heaviside Step function) is presented. This important function constitutes a fundamental concept of Operational Calculus and is also involved in many other fields of applied and engineering mathematics. In particular, Heaviside Step Function is performed in a very simple manner by the use of a finite number of standard operations, as the summation of six inverse tangent functions. The novelty of this work when compared with other analytical expressions, is that the proposed exact formula contains two arbitrary single - valued continuous functions which satisfy only one restriction. In addition, the proposed representation is not exhibited in terms of miscellaneous special functions, e.g. Bessel functions, Beta function, Logistic function. Besides, it is neither the limit of a function, nor the limit of a sequence of functions with point – wise or uniform convergence. Hence, this formula may be much more practical, flexible and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

A new set of basis functions is presented. The foundation in mathematics is established. To reconstruct a signal, it is compared to the Fourier basis functions. The M-basis functions' potential applications are also presented.

I want to find an extension of the Hausdorff Measure and Fractal Measure which allows me to compute a unique, satisfying average for functions defined on non-fractal, measurable sets in the sense of Carathedory which has no gauge function.

We consider the inverse function $z=g(w)$ of a (normalized) starlike function $w=f(z)$ of order $\alpha$ on the unit disk of the complex plane with $0<\alpha<1.$ Krzy{\. z}, Libera and Z\l otkiewicz obtained sharp estimates of the second and the third coefficients of $g(w)$ in their 1979 paper. Prokhorov and Szynal gave sharp estimates of the fourth coefficient of $g(w)$ as a consequence of the solution to an extremal problem in 1981. We give a straightforward proof of the estimate of the fourth coefficient of $g(w)$ together with explicit forms of the extremal functions.

In this paper, the author obtains an analytic exact form of Heaviside function, which is also known as Unit Step function and constitutes a fundamental concept of the Operational Calculus.In particulat, this function is explicitly expressed in a very simple manner by the aid of purely algebraic representations. The novelty of this work is that the proposed explicit formula is not performed in terms of non – elementary special functions, e.g. Dirac delta function or Error function and also is neither the limit of a function, nor the limit of a sequence of functions with point wise or uniform convergence. Hence, it may be much more appropriate and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

Suppose for n∈ ℕ, set A⊆ℝⁿ and function f∶A→ℝⁿ. If set A, using the Hausdorff outer measure, is measurable in the sense of Carathèodory; we want to find an extension of the expected value, w.r.t the Hausdorff measure, that's unique, finite and "natural" (defined on §2.3 & §2.4) for all f in a prevalent subset of ℝᴬ. The issue is current extensions of the expected value are finite for all functions in only a shy subset of ℝᴬ. The reason this issue wasn't resolved is mathematicians have not thought of the problem, focusing on application rather than generalization. Despite the lack of potential use, we'll attempt to solve the problem by defining a choice function---this shall choose a unique set of equivalent sequences of sets (Fₖ***) , where the set-theoretic limit of Fₖ*** is the graph of f; the measure Hʰ is the ℎ-Hausdorff measure, such for each k∈ℕ, 0 < Hʰ(Fₖ***) < +∞; and (fₖ*) is a sequence of functions where {(x,fₖ*(x))∶x∈ dom(Fₖ***)}=Fₖ***. Thus, the extended expected value of or E**[f,Fₖ***] is: ∀(ε>0)∃(N∈ℕ)∀(k∈N)(k≥N⇒1/Hʰ(dom(Fₖ***))∫dom(Fₖ*** )fₖ* dHʰ - E**[f,Fₖ***]<ε ) which should be unique, finite, and "natural" (defined on §2.3 & §2.4) for all f in a prevalent subset of ℝᴬ. Note we guessed the choice function using computer programming but we don’t use mathematical proofs due to the lack of expertise in the subject matter. Despite this, the biggest use of this research is the extension of the expected value is finite for "almost all" functions: this is easier to use in application when finding the "average" of functions covering an infinite expanse of space.