A series of novel substituted isoxazolidine derivatives was synthesized through 1,3-dipolar cycloaddition reactions of α-aryl-N-methyl nitrones with various ethylene moieties, resulting in the formation of isoxazolidine derivatives. The structures of the synthesized compounds were characterized using spectroscopic methods. The [3+2] cycloaddition (32CA) reactions of α-aryl-N-methyl nitrones with diverse ethylene substituents were computed employing Density Functional Theory (DFT) at the B3LYP/6–31G(d) level, upgrading bond parameters. An investigation of the electron localization function (ELF) unveiled the zwitterionic nature of α-aryl-N-methyl nitrones, devoid of pseudoradical or carbenoid centers. Utilization of CDFT indices enabled the prediction of global electronic flux from the strongly nucleophilic α-aryl-N-methyl nitrones to the varied electrophilic ethylene functionalities. Molecular docking and molecular dynamics simulations were conducted on the isoxazolidine derivatives against the EGFR receptor (PDB: 4ZAU). In silico assessment of the synthesized isoxazolidines involved molecular docking, wherein the compound with the highest docking score was subjected to molecular dynamics simulations. Compound 11a, out of the thirty isoxazolidine derivatives, displayed the most substantial binding energy, yielding a g score of -6.57 kcal/mol. These observations highlighted the functional role of amide NH2 and NO2 in the binding process with the target protein, influencing its activity. Furthermore, prediction of ADME drug-likeness properties was performed to identify a suitable candidate.

Pavement friction plays a crucial role in ensuring the safety of road networks. Accurately assessing friction levels is vital for effective pavement maintenance and management strategies employed by state highway agencies. Traditionally, friction evaluations have been conducted on a case-by-case basis, focusing on specific road sections. However, this approach fails to provide a comprehensive assessment of friction conditions across the entire road network. This paper introduces a hybrid clustering algorithm, namely the combination of density-based spatial clustering of applications with noise (DBSCAN) and Gaussian mixture model (GMM), to perform pavement friction performance rating across a statewide road network. A large, safety-oriented dataset is first generated by integrating network friction and vehicle crash data based on the attributes contributing possibly to friction related crashes. One-, two-, and multi-dimensional clustering analyses, respectively, are then performed to rate pavement friction. The Chi-square test is further employed to validate and identify the practical ratings. It is shown that by effectively capturing the hidden, intricate patterns within the integrated, complex dataset and prioritizing friction-related safety attributes, the hybrid clustering algorithm can produce pavement friction ratings that align effectively with the current practices of the Indiana Department of Transportation (INDOT) in friction management.

One of the most rapidly advancing areas of deep learning research aims at creating models that learn to disentangle the latent factors of variation from a data distribution. However, modeling joint probability mass functions is usually prohibitive, which motivates the use of conditional models assuming that some information is given as input. In the domain of numerical cognition, deep learning architectures have successfully demonstrated that approximate numerosity representations can emerge in multi-layer networks that build latent representations of a set of images with a varying number of items. However, existing models have focused on tasks requiring to conditionally estimate numerosity information from a given image. Here we focus on a set of much more challenging tasks, which require to conditionally generate synthetic images containing a given number of items. We show that attention-based architectures operating at the pixel level can learn to produce well-formed images approximately containing a specific number of items, even when the target numerosity was not present in the training distribution.

Addressing global environmental problem, water splitting to produce hydrogen fuel by solar energy is getting so much attention. In the water splitting, the essential problem to solve is the development of efficient　catalysts for oxygen production. In this paper, having the prospect for a practical application of photocatalysts to artificial photosynthesis, molecular mechanisms in the current literature are briefly reviewed. At first, recent progress in the function of Mn cluster at the natural photosystem II is briefly described. The kinds of devices in which oxygen evolution reaction (OER) catalysts are used were designated; water electrolyzers, photoelectrodes, and photocatalysts. Some methods for analyzing molecular mechanism in OER catalysis, emphasized by FTIR method, are shown briefly. After describing common OER mechanisms, the molecular mechanisms are discussed for TiO2 and BiVO4 photoelectrodes with our novel data, followed by presenting of co-catalysts IrO2, RuO2, NiO2, and other metal oxides for OER catalysts. Recent reports describing OER catalysts of perovskites, layered double hydroxides (LDH), metal-organic frameworks (MOF), single atom catalysts, as well as metal complexes are reviewed. Finally, by comparing with natural photosystem, the requiring factors to improve the activity of the catalysts for artificial photosynthesis will be discussed.

Paving blocks are concrete pieces placed in exposed places to the weather, which are sub-jected to loads and wear. Hence, quality control in the manufacture of paving blocks is es-sential to guarantee the properties and durability of the product in construction projects. In Ecuador, the requirements are described in the Ecuadorian technical standard "NTE INEN 3040", and tensile splitting strength is a fundamental requirement to guarantee product quality. It is analyzed using quality control measurements such as dimensions, the weight of the fresh paving block in the vibro-compacted process, and the percentage of water absorption in order to know how the variables influence and manage to predict the tensile splitting strength to avoid product non-conformity in advance, having a timely and better control of the manufacturing process. The data was obtained from a company that can produce 30 000 units per day of rectangular paving blocks with 6 cm thickness. Mul-tivariate models such as multiple linear regression, regression trees, random forests and neural networks are performed to predict the tensile splitting strength variable through two groups of predictors; the first group is the thickness mm, width mm, length mm, mass of fresh paving block g and percentage of water absorption %. The second group of pre-dictor variables is the density of the fresh paving block kg/m3 and the percentage of water absorption %. It is concluded that the multiple linear regression method performs better in predicting the first group of predictor variables with a mean square error (MSE) of 0.110086, followed by the neural network without hidden layers resulting in an MSE of 0.112198. The best method for the second set of predictors was the neural network with-out hidden layers with a mean square error ( MSE ) of 0.112402, closely followed by the multiple linear regression model with an MSE of 0.115044.

Fatigue-related subchondral bone injury of the third metacarpal/ metatarsal (McIII/ MtIII) bone is a common cause of wastage and welfare concern in racehorses. Better understanding of bone health and strength would improve animal welfare and be of benefit for the racing industry. Porosity index (PI) of bone is an indirect measure of osseous pore size and number and is therefore an interesting indicator of bone strength. MRI of compact bone using traditional methods even with short echo times fails to generate enough signal to assess bone architecture as the water protons are tightly bound. Ultrashort echo time (UTE) sequences aim to increase the amount of signal detected in the equine McIII/MtIII condyle. Cadaver specimens were imaged using a novel dual-echo UTE MRI technique and PI was calculated and validated against quantitative CT-derived bone mineral density (BMD). BMD and PI are inversely correlated in the equine distal Mc/ MtIII with a mean r value of -0.29. The r value is significantly different between fore- and hindlimbs. Further work is needed to assess how correlation patterns behave in different areas of the bone and to evaluate PI in horses with and without clinically relevant stress injury.

This study introduces a remote sensing application using satellite imagery to survey a network-scale aggregate stockpile inventory. First, a real scale aggregate quarry site was surveyed using a small Unmanned Aerial Vehicle (sUAV) to produce digital terrain models that enabled analysis of aggregate pile geometry. Second, a lab experiment was designed and performed to validate the applicability of close-range Structure from Motion (SfM) photogrammetry for measuring aggregate piles' physical properties such as volume and density. The other part of the lab experiment delved into direct measurement of aggregate density under varying compaction efforts. These experimental results, in conjunction with some simplifying assumptions, enabled the calculation of aggregate stockpile volumes and estimated weights from satellite imagery. We estimated that an inventory of 4.4 and 1.1 million metric tons of crushed aggregates and Reclaimed Asphalt Pavement (RAP), respectively, stockpiled in Washington State for asphalt production in 2017. The merit of producing such database was further showcased in an example on the economic and environmental impacts of material transportation. We approximated that hauling aggregates from quarry plants to construction sites within Washington State incurs a cost of about $50 thousand to over $4 million, consumes about 0.25 to 20 TJ of energy, and emits 20 to over 1,500 tons of CO₂-eq per asphalt plant annually.

The world is moving to the next phase of the energy transition with high penetrations of renewable energy. Flexible and scalable redox flow battery (RFB) technology is expected to play an important role in ensuring electricity network security and reliability. Continuous performance improvements will further enhance their value by reducing parasitic losses and maximizing available energy conversion over broader operating conditions. Concentration overpotentials from poor internal reactant distribution at high and low states of charge (SOC) limit power densities and are thus an important area of investigation. However, efforts to address these coupled electrochemical phenomena can compromise mechanical performance. Modelling and simulation of cell design innovations have shown it is possible to reduce losses from pump energy while increasing the availability of active species where required. The combination of wedge-shaped cells with static mixers investigated in this paper can reduce pressure drop and improve energy efficiency. Toroidal vanadium redox flow battery (VRB/VRFB) designs incorporating this innovation are presented for further development to improve community engagement with the technology.

The present article addresses the long-standing problem of the polymer brush bilayers under stationary shear flow at non-linear response regime where the system gets a non-Newtonian fluid. The main idea behind this research would be the fact that the immense lubricity of the polymer brush bilayers originates from a global restructuring that takes place at large shear rates. It is shown here that physical quantities like, stress tensor, viscosity tensor, the friction coefficient and the chain extensions could become dependent on the shear rate at non-Newtonian regime. Apparently, the sub-linear scaling of the physical quantities at large shear rates is solely due to the fact that the chains stretch in the shear direction.

Information geometry (IG) seeks to characterize the structure of statistical geodesic models from a differential geometric point of view. By considering families of probability distributions as manifolds with coordinate charts determined by the parameters of each individual model, the tools of differential geometry, such as divergences and metric tensors, provide effective means of studying their characteristics. The research undertaken in this paper presents a novel approach to the modelling study of information geometrics of a queueing system. In this context, the manifold of a stable M/G/1queue is characterised from the viewpoint of IG. The Fisher Information matrix (FIM) as well as the inverse of (FIM), (IFIM) of stable M/G/1 queue manifold are devised. In addition to that, new results that uncovered the significant impact of stability of M/G/1 queue manifold on the existence of (IFIM) are obtained. The Kullback’s divergence (KD), and J-divergence (JD).New result has been devised on the significant impact of both server utilization and squared coefficient of variation of the underlying M/G/1 queue manifold on both (KD) and (KD) are devised. Also, it is revealed that stable M/G/1 QM is developable (i.e., has a zero Gaussian curvature) and has a non-zero Ricci Curvature Tensor (RCT). Novel stability dynamics of M/G/1 queue manifold is revealed by discovering the mutual dual impact between the behaviour of (RCT) and the stability and the instability phases of the underlying M/G/1 queue manifold. Furthermore, a new discovery that presents the significant impact of stability of M/G/1 queue manifold and the continuity of the unique representation between M/G/1 queue manifold and Ricci Curvature Tensor (RCT). The information matrix exponential (IME) is devised. It is also shown that the obtained (IME) is unstable. Also, it is shown that stability of the devised (IME) enforces the instability of M/G/1 queue manifold. Unifying IG with Queueing Theory enables the study of dynamics of queueing system from a novel Riemannian Geometric (RG) point of view, leading to the analysis of the stable M/G/1 queue, based on the Theory of Relativity (TR).Extending the study over two new additional divergence measures, namely and together with a complete illustrative numerical results for all these measures including KD, JD. This links Queueing theory, IG with deep machine learning and metric learning. Furthermore, this reveals the revolutionary approach of queue learning. Full analytic study of Gaussian curvatures subject to both Angular and Monge techniques together with the overall stability dynamics impact on these curvatures. Full analytic study of Einestein Tensor and Stress Energy Tensor together with the overall stability dynamics impact on these curvatures. The inclusion of the definitions of Gaussian and Ricci, Ricci scalar curvatures and Einstein Tensor together with their physical interpretations; The proposed novel approach for the pioneer visualization of queueing systems via computational information geometry. The determination of new important links between classical queueing theory and other mathematical disciplines, such as IG, matrix theory Riemannian geometry and the THEORY OF RELATIVITY by providing for first time i) The full detailed derivations of the Gaussian curvature ii) The Ricci curvature tensor and iii) The full physical as well as the geometric interpretation of these new results. The provision of a novel link between Ricci Curvature (RCT) and the stability analysis of the stable M/G/1 QM. The full investigation of the newly introduced QT-IG unifiers together with the impact of stability/ instability of the underlying M/G/1 QM on them. The full investigation of the newly introduced (QIGU) unifiers together with the impact of stability/ instability of the underlying M/G/1 QM on them.

We present a MATLAB-based, open source reconstruction software for Hybrid Imaging problem arising from Current Density Impedance Imaging (CDII) and Acoustic-Electrical Impedance Tomography (AEIT), utilizing mixed finite element method solver of Darcy toolbox {\tt DarcyLite}~. For a formulation of hybrid inverse problems in impedance tomography the successive substitution iterative schemes are adapted and an reconstruction algorithm is developed. The problem formulation is a class of hybrid imaging modality which is current density impedance imaging or Acoustic-Electrical Impedance Tomography. The proposed algorithm is implemented numerically in two dimensions.

This paper proposes a method of extracting energy from zero-point energy and evaluates the amount of energy gained. In addition, this electric circuit-based approach exhibits the Meissner effect, suggesting a new type of superconductivity that does not require refrigeration. The proposed method can provide extremely large amounts of energy, which is more than a conventional power station, without consuming fossil fuels or emitting radiation. Thus, it has the potential to solve the global energy problem. It involves preparing two electric loops containing diodes and connecting the loops together with current sources. The diodes are oriented in the same direction within each loop but in opposite directions in different loops. With this setup, the currents from the current sources build iteratively within the loops, resulting in large output currents. Our numerical analysis indicates that extremely large electric potentials are produced, which in turn yield large output currents. In addition, we confirm numerically that the voltage is zero around a loop and show analytically that the Meissner effect is present, proving the existence of a new type of superconductivity. Furthermore, when we introduce induction coils to not break the loop’s symmetry, they store extremely large amounts of energy and we can thus obtain energy from them via discharge currents.

Rechargeable solid-state batteries (SSBs) offer enhanced safety, higher energy density, and longer cycle life compared with conventional lithium-ion batteries, making them a promising solution for electric vehicles, grid storage, and other high-demand applications. However, challenges such as interface stability, low ionic conductivity, and manufacturing scalability hinder their commercial viability. This research provides a comprehensive cross-sectional thematic and bibliometric analysis of recent SSB research, focusing on four key areas: electrolyte engineering, electrode engineering, battery architecture, and performance evaluation. By analyzing publications from major databases, this study highlights the latest innovations, including improved solid electrolytes, advanced electrode materials, and novel architectures that enhance both performance and manufacturability. The findings offer valuable insights for researchers, engineers, and industry stakeholders by identifying critical gaps in the field and highlighting future research directions. The work examines progress in interface optimization, ion transport improvements, and scalable production techniques, which are crucial for advancing SSB technology. By presenting a detailed review of key developments and challenges, this study contributes to a deeper understanding of SSB progress and its potential to revolutionize the energy storage industry. The results will guide researchers in targeting high-impact areas and help industry leaders and policymakers strategize the commercial deployment of SSBs in electric vehicles, stationary energy storage, and other applications requiring reliable and efficient energy solutions.

Cryptocurrencies have obtained a crucial position in the international financial landscape. The cryptocurrency market has been perceived as a highly volatile market since the inception of Bitcoin. This study investigates the relevant performance of extreme value models (EVM) in estimating the Value-at-Risk (VaR) of Bitcoin and Ethereum returns. The extreme value mixture models, GPD-Normal-GPD (GNG) and GPD-KDE-GPD models are fitted to the returns of Bitcoin and Ethereum and the Kupiec likelihood backtesting procedure is performed on the VaR estimates to assess the fits. Both models’ results showed that the fits were a much more decent representation of the observed data when compared to the Normal distribution. The backtesting results showed that the GPD-KDE-GPD model’s fit was superior to that of the GPD-Normal-GPD for both sets of returns at all VaR risk levels except at the 99% level. The results of this study may assist with understanding the dynamics and risks associated with cryptocurrencies and can serve as a beneficial tool for decision-making and risk management to investors, traders, financial institutions and many other participants in the cryptocurrency ecosystem.

We introduce the Symplectic Structure of Information Geometry based on Souriau’s Lie Group Thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical observables like energy, heat, and moment as pure geometrical objects. Using Geometric (Planck) Temperature of Souriau model and Symplectic cocycle notion, the Fisher metric is identified as a Souriau Geometric Heat Capacity. Souriau model is based on affine representation of Lie Group and Lie algebra that we compare with Koszul works on G/K homogeneous space and bijective correspondence between the set of G-invariant flat connections on G/K and the set of affine representations of the Lie algebra of G. In the framework of Lie Group Thermodynamics, an Euler-Poincaré equation is elaborated with respect to thermodynamic variables, and a new variational principal for thermodynamics is built through an invariant Poincaré-Cartan-Souriau integral. The Souriau-Fisher metric is linked to KKS (Kostant-Kirillov-Souriau) 2-form that associates a canonical homogeneous symplectic manifold to the co-adjoint orbits. We apply this model in the framework of Information Geometry for the action of an affine Group for exponentiel families, and provide some illustrations of use cases for multivariate Gaussian densities. Information Geometry is presented in the context of seminal work of Fréchet and his Clairaut-Legendre equation. Souriau model of Statistical Physics is validated as compatible with Balian gauge model of thermodynamics. We recall the precursor work of Casalis on affine group invariance for natural exponential families.

This article reviews recent innovations in piezoelectric actuators, then indicates the future research targets. In the materials, the piezoelectric performances of relaxor-lead titanate (PZN-PT, PMN-PT) single crystals have been improved significantly by an AC electric poling technique. Also new loss characterization techniques facilitate developing high-power density piezoelectrics. The RMS vibration velocity reaches 0.6 m/s in the k₃₁ mode in lead zirconate titanate (PZT) nowadays, which corresponds to power density 30 W/cm³. Pb-free materials are urged due to the recent political regulation on toxic materials. In device designs, the original multilayer actuators (MLA) with Ag/Pd electrode have been switched to the ones with Cu or pure Ag, in order to suppress the heat generation, then to enhance the device power density. Piezoelectric micro-electro-mechanical-systems (MEMS’s) started to utilize the <1 0 0> oriented epitaxial films of rhombohedral PZT compositions, which exhibits enhanced piezoelectric properties. Also for higher-power applications, aero-sol deposition (AD) methods have been introduced to 10 -thick films. Regarding drive/control techniques in piezo-actuators, three developments are on-going, that is, “negative capacitance” power supplies for driving off-resonance (pseudo-DC) piezo-actuators, capacitive AC power supplies for efficiently driving resonance piezo-actuators, and DC/DC converters for harvesting electric energy from high-impedance piezoelectric devices under noise vibration. The applications of piezoelectric actuators in the 21^st century seem to be oriented toward “politico-engineering” with four keywords, “cooperation, protection, reduction, and continuation”. The sustainability technologies include the following piezoelectric items: (a) Pb-free piezoelectrics, (b) ultrasonic technology for decomposing hazardous materials, (c) reduction of contamination gas, (d) piezoelectric energy harvesting, and (e) device improvement with high energy-efficiency. On the other hand, the following crisis technologies have been developed with piezoelectrics: (a) detection and neutralization technologies of infectious/epidemic diseases such as anthrax, (b) autonomous unmanned underwater, aerial, and land vehicles with piezoelectric actuators, (c) pin-point target weapons, (d) high voltage supplies with piezoelectric transformers, and (e) compact energy sources for remote actuating/sensing systems.

In this paper we describe and exploit a geometric framework for Gibbs probability densities and the associated concepts in statistical mechanics, which unifies several earlier works on the subject, including Souriau's symplectic model of statistical mechanics, its polysymplectic extension, Koszul model, and approaches developed in quantum information geometry. We emphasize the role of equivariance with respect to Lie group actions and the role of several concepts from geometric mechanics, such as momentum maps, Casimir functions, coadjoint orbits, and Lie-Poisson brackets with cocycles, as unifying structures appearing in various applications of this framework to information geometry and machine learning. For instance, we discuss the expression of the Fisher metric in presence of equivariance and we exploit the property of the entropy of the Souriau model as a Casimir function to apply a geometric model for energy preserving entropy production. We illustrate this framework with several examples including multivariate Gaussian probability densities, and the Bogoliubov-Kubo-Mori metric as a quantum version of the Fisher metric for quantum information on coadjoint orbits. We exploit this geometric setting and Lie group equivariance to present symplectic and multisymplectic variational Lie group integration schemes for some of the equations associated to Souriau symplectic and polysymplectic models, such as the Lie-Poisson equation with cocycle.

Three-dimensional (3D) printing technologies are transforming the design and manufacture of components and products across a variety of disciplines, however their application in the construction industry is still limited. Material deposition processes can achieve infinite geometries and have advanced from rapid prototyping and model-scale markets to their application in fabricating functional products, large objects and the construction of full-scale buildings. Many international projects have recently been realized and the construction industry is beginning to utilise these dynamic technologies. The potential advantages for integrating 3D printing into house construction are significant, these include the capacity for mass customization of designs and parameters for functional and aesthetic purposes, reduction in construction waste from highly precise material placement, and the use of recycled waste products in layer deposition materials. With the ultimate goal of improving construction efficiency and decreasing building costs, applying Strand7 Finite Element Analysis software, a numerical model was designed specifically for 3D printing in a cement mix incorporated with recycled waste product High Density Polyethylene (HDPE) and found that construction of an arched truss-like roof was structurally feasible without the need for steel reinforcements. The lab sizes prototypes were manufactured based on the destined numerical model by using a 3D printing technology. Currently available 3D printing technologies can be adopted for building construction and this paper discusses the applications, advantages, limitations and future directions of 3D printing as an innovative and viable solution for affordable house construction.

The reported study was devoted to the investigation of viscoelastic behavior for solid and porous ultra-high-molecular-weight polyethylene (UHMWPE) under compression. The obtained experimental stress curves were interpreted using a two-term Prony series to represent the superposition of two coexisting activation processes corresponding to long molecular (~160 s) and short structural (~20 s) time scales, respectively, leading to good statistical correlation with the observations. In the case of porous polymer, the internal strain redistribution during relaxation was quantified using Digital Image Correlation (DIC) analysis. The strongly inhomogeneous deformation of the porous polymer was found not to affect the relaxation times. In order to generalize the results to three dimensions, X-ray tomography was used to examine the porous structure at the macro- and micro-scale levels. DIC analysis revealed positive correlation between the applied force and relative density. The apparent stiffness variation for UHMWPE foams with mixed open and closed cells was described using a newly proposed three-term expression. Furthermore, the in situ tensile loading and X-ray scattering study was applied for isotropic solid UHMWPE specimens to investigate their parameters of internal structure during orientation and stress relaxation process at another mode.

The Mediterranean basin is a hot spot of climate change where the Posidonia oceanica (L.) Delile (PO) and other seagrass are under stress due to its effect on marine habitats and the rising influence of anthropogenic activities (tourism, fishery). The PO and seabed ecosystems, in the coastal environments of Pantelleria and Lampedusa, suffer additional growing impacts from tourism in synergy with specific stress factors due to increasing vessel traffic for supplying potable water, fossil fuels for electrical power generation. Earth Observation (EO) data, provided by high resolution (HR) multi/hyperspectral operative satellite sensors of the last generation (i.e. Sentinel 2 MSI and PRISMA) have been successfully tested, using innovative calibration and sea truth collecting methods, for monitoring and mapping of PO meadows under stress, in the coastal waters of these islands, located in the Sicily Channel, to better support the sustainable management of these vulnerable ecosystems. The area of interest in Pantelleria was where the first prototype of the Italian Inertial Sea Wave Energy Converter (ISWEC) for renewable energy production was installed in 2015, and sea truth campaigns on the PO meadows were conducted. The PO of Lampedusa coastal areas, impacted by ship traffic linked to the previous factors and tropicalization effects of Italy southernmost climate change transitional zone, was mapped through a multi/hyper spectral EO-based approach, using training/testing data provided by side scan sonar data, previously acquired. Some advanced machine learning algorithms (MLA) were successfully evaluated with different supervised regression/classification models to map seabed and PO meadow classes and related Leaf Area Index (LAI) distributions in the areas of interest, using multi/hyperspectral data atmospherically corrected via different advanced approaches.

This study purposes the use of plug-in electric vehicles for demand side management (DSM) considering uncertainties in demand as well as uncertainties due to mobility of PEV to mitigate peak demand. The solution also seeks to reduce electric cost in addition to reducing the effects of greenhouse gases. In recent years DSM using distributed storage system such as battery energy management system (BESS) and plugged-in electric vehicles (PEV) have become very prevalent with most implementations resorting to deterministic load forecast. These methods do not consider the potential growth in demand making their solutions less robust. In this study we propose a real-time density demand forecast and stochastic optimization for robust operation of PEV for a building. This method accounts for demand uncertainties in addition to uncertainties in mobile energy storage as found in PEV, making the resulting solution robust as compared to the deterministic case. A case study on a real site in South Korea is used for verification and testing. The proposed study is verified and tested against existing algorithms. The result verifies the effectiveness of the proposed approach

Formalism proofing general derivation, applying matrix properties operations, showing fundamental relationships with inner product to outer product has been advanced here. This general proof formalism has direct application with physics to quantify quantum density at micro scale level to time commutator at macro scale level. System of operator algebraic equations have been rigorously derived to obtain analytic solutions which are physically acceptable. Extended physics application will include metricizing towards unitarization to achieve gaging Hamiltonian mechanics to electromagnetic gravitational strong theory, towards grand unifying physics atomistic to astrophysics or vice versa via quantum relativistic general physics thereby patching to classical physics fields energy.