In this paper the problem of sampling from uniform probability distributions is approached by means of space-filling curves (SFCs), a topological concept that has found a number of important applications in recent years. Departing from the theoretical fact that they are surjective but not necessarilly injective, the investigation focused upon the structure of the distributions obtained when their domain is swept in a uniform and discrete manner, and the corresponding values used to build histograms, that are approximations of their true PDFs. This work concentrates on the real interval [0,1], and the Sierpinski space-filling curve was chosen because of its favorable computational properties. In order to validate the results, the Kullback-Leibler distance is used when comparing the obtained distributions in several levels of granularity with other already established sampling methods. In truth, the generation of uniform random numbers is a deterministic simulation of randomness using numerical operations. In this fashion, sequences resulting from this sort of process are not truly random.

This work addresses the problem of sampling from Gaussian probability distributions by means of uniform samples obtained deterministically and directly from space-filling curves (SFCs), a purely topological concept. To that end, the well-known inverse cumulative distribution function method is used, with the help of the probit function,which is the inverse of the cumulative distribution function of the standard normal distribution. Mainly due to the central limit theorem, the Gaussian distribution plays a fundamental role in probability theory and related areas, and that is why it has been chosen to be studied in the present paper. Numerical distributions (histograms) obtained with the proposed method, and in several levels of granularity, are compared to the theoretical normal PDF, along with other already established sampling methods, all using the cited probit function. Final results are validated with the Kullback-Leibler and two other divergence measures, and it will be possible to draw conclusions about the adequacy of the presented paradigm. As is amply known, the generation of uniform random numbers is a deterministic simulation of randomness using numerical operations. That said, sequences resulting from this kind of procedure are not truly random. Even so, and to be coherent with the literature, the expression ”random number” will be used along the text to mean ”pseudo-random number”.

We present a cyclic symmetry type II vacuum spacetime admitting closed timelike curves (CTCs) which appear after a certain instant of time, i.e., a time-machine spacetime. The various authors in past have considered the 2D and 4D flat generalization of Misner space, but in the present work, we have considered the curved spacetime generalzations of 4D Misner space, and is asymptotically flat radially

A bijective analysis is confirming, the expansion of universal space has never been directly observed, and this assumption is unproven thus far. The measurement of the gravitational redshift, which was confirmed using the Mossbauer experiment, proves only the gravitational redshift and nothing more because there is no causality between the gravitational redshift and hypothetical expansion. Thus, even if the universal space is assumed to expand, the gravitational redshift cannot be assumed to be proof of the expansion. In addition, the Doppler effect was never observed in an expanding space; thus, the claim that the cosmological redshift is partially caused by the Doppler effect, which is caused by the expansion of space, is an unproven assumption. Furthermore, the discovery of cosmic microwave background (CMB) radiation simply proves that the radiation is emitted by the entire universal space, but does not prove the existence of a recombination period. In evidence-based cosmology, every element in the model has a corresponding element in physical reality that is observed and measured. The evidence-based cosmology model is related to the real universe by a bijective function of set theory. Supermassive black holes in the centre of galaxies are rejuvenating systems of the universe. They rotate their local superfluid space which is the physical origin of galactic rotation curves.

The general theory of relativity (GR) is known to be invariant under smooth coordinate transformations (diffeomorphism). This group has a subgroup known as the Lorentz group of symmetry which is manifested in the weak field approximation to GR. The dominant operator in the weak field equation of GR is thus the d'Alembert (wave) operator which has a retarded potential solution. Galaxies are huge physical systems having dimensions of many tens of thousands of light years. Thus any change at the galactic center will be noticed at the rim only tens of thousands of years later. Those retardation effects are neglected in present day galactic modelling used to calculate rotational velocities of matter in the rims of the galaxy and surrounding gas. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper we will show that taking general relativity seriously without neglecting retardation effects one can explain the radial velocities of galactic matter in the M33 galaxy without postulating dark matter.

We propose a geographical time-space model extending time-space relief cartography introduced by Mathis and L’Hostis [,,,]. The novelty of the model resides in the use of cones to describe the terrestrial surface instead of graph faces, and in the use of curves instead of broken segments for edges. The approach lies a the intersection of two domains involving graphic representation: cartography, and three dimensional computer graphics. We implement the model on the Chinese space. The Chinese geographical time-space of the reference year 2006 is produced by the combination and the confrontation of the fast air transport system and of the 7.5 times slower road transport system. Slower, short range flights are represented as curved lines above the earth surface with longer length than the geodesic, in order to account for a slower speed. The very steep slope of cones expresses the relative difficulty of crossing terrestrial time-space, as well as the comparably extreme efficiency of long-range flights for moving between cities. Finally, the whole image proposes a coherent representation of the geographical time-space where fast city to city transport is combined with slow terrestrial systems that allow to reach any location.

In experimental physics, we understand time as the duration of material changes that run into space. This fact is the standpoint for our model of time-invariant space in which causality is only a principle and not a physical actuality, and entropy runs only in space and not in time. Time is merely a duration of entropy that is increasing in time-invariant space. Time is entering existence when measured by the observer. In time-invariant space, motion happens only in space and not in time which means that also in open timelike curves motion happens only in space and not in time.

The stability of the filling roof as an important bearing unit in the stope of the access stope in the filling mining method is of great significance to guarantee the safe and efficient production of the mine. Arrangement of mining approach in downward cemented filling stope is the key factor af-fecting stability of filling body roof. Based on combination of laboratory test, theoretical analysis and numerical simulation, the influence of different mining approach arrangement on stability of filling body roof is analyzed. The weak filling surface is formed between adjacent mining paths. The mechanical strength of the weak filling surface is significantly reduced by laboratory experiments. The relationship between distribution of the weak filling surface, azimuth angle and stability of filling roof is further studied by numerical simulation. The results show that the stability of the filler roof is the best when the upper and lower stratified mining approach is arranged vertically.

The continuous development in the field of industrial automation and electric mobility has led to the need for more efficient electrical machines with high power density. The improvement of electrical machines slot filling factors is one of the measures to satisfy these requirements. In recent years, this topic has aroused greater interest in the industrial sector, since the evolution of the winding technological manufacturing processes allows an economically sustainable realization of ordered winding arrangements, rather than random ones. Moreover, the manufacture of electrical machines windings must be preceded by an accurate design phase in which it is possible to evaluate the maximum slot filling factor obtainable for a given wire shape and for its dimensions. For this purpose, this paper presents an algorithmic approach for the evaluation of maximum slot filling factors in electrical machines under ideal geometric premise. In particular, this algorithm has a greater degree of flexibility with respect to the algorithm approaches found in the literature, since the study has been extended to round, rectangular and hexagonal wire sections. Furthermore, the slot filling factor calculation was carried out both for standard and non-standard slots. The algorithmic approach proposed can be considered as an additional useful tool for the fast design of electrical machine windings.

The grain filling rate (GFR) plays a crucial role in determining grain yield. However, the regulatory and molecular mechanism of grain filling rate (GFR) in foxtail millet remains unclear. In this study, we found the GFR of 'Changnong No.47' (CN47) was significantly higher at 14 days after flowering (DAF) and 21 DAF in comparison to 'Changsheng 13' (CS13). Furthermore, CN47 also exhibited higher thousand grain weight and yield than CS13. Therefore, we conducted transcriptomics and metabolomics to analyze the biological processes and functional genes associated with GFR during two stages of grain filling in both cultivars. A total of 765 differentially expressed genes (DEGs) and 246 differentially accumulated metabolites (DAMs) were identified at the 14 DAF stage, while at the 21 DAF stage, a total of 908 DEGs and 268 DAMs were identified. The integrated analysis of co-mapped DAMs and DEGs revealed enriched pathways, including flavonoid biosynthesis, plant hormone signal transduction, tyrosine metabolism, ATP-binding cassette (ABC) transporters, beta-alanine metabolism, as well as stilbenoid, diarylheptanoid and gingerol biosynthesis. In order to elucidate their potential functions in the context of GFR, we developed a gene-metabolite regulatory network for these metabolic pathways. Notably we found some genes associated with ABC transporters and plant hormone signal transduction pathway were implicated in auxin transport and signal transduction, highlighting the crucial role of auxin during grain filling. The results provide initial insights into the regulatory and molecular mechanisms underlying GFR in foxtail millet, as well as offer valuable genetic resources for further elucidation of GFR in future studies. The findings have established a theoretical basis for improving the efficiency of yield breeding in foxtail millet.

Hydrogen storage in high pressure tanks can occur with different filling strategies. Many studies have been carried out on supplies with increasing pressure rates. However, hydrogen filling with constant mass inflow rate have not received the same attention. The present work aims to carry out numerical simulations to study hydrogen flow, in a type 3 tank of 70 MPa NWP and constant inflow rate condition. From the analysis of the results, it was possible to verify that there is a linear relationship between the increase in the total equilibrium temperature and the final hydrogen temperature. There is also a linear increasing relationship between Inlet and final temperatures when the equilibrium temperature is fixed. Considering fully adiabatic walls results in significant increases in temperature. The difference between total and static temperatures found in the Inlet tube decreases with the decrease in mass flow rate. The choice of a polymer for the tank lining led to higher temperatures when compared to an aluminum lining.

Preoperative angiography in glioblastoma (GBM) often shows arteriovenous shunts and early venous filling (EVF). Here, we investigated the clinical implications of EVF in GBM as a prognostic and vascular mimicry biomarker. In this retrospective multicenter study, we consecutively enrolled patients who underwent angiography with a GBM diagnosis between April 1, 2013, and March 31, 2021. The primary and secondary endpoints were the differences in overall survival (OS) and progression-free survival (PFS), respectively, between cases with and without EVF. Of 133 initially enrolled patients, 91 newly diagnosed with GBM underwent preoperative angi-ography and became the study population. The 6-year OS and PFS were significantly worse in the EVF than in the non-EVF group. Moreover, 20 GBM cases (10 with EVF and 10 without EVF) were randomly selected and evaluated for histological vascular mimicry. Except for two cases that were difficult to evaluate, the EVF group had a significantly higher frequency of vascular mimicry than the non-EVF group (0/8 vs. 5/10, P = 0.04). EVF on preoperative angiography is a robust prognostic biomarker for GBM and may help detect cases with a high frequency of histological vascular mimicry.

Shell nacre from Pinctada species has been extensively researched for managing bone defects. However, there is a gap in the research on using shell nacre as cement with improved physico-chemical properties. To address this, the current study aimed to develop a chemical curable com-posite shell nacre cement (SNC) using shell nacre powder and an organically modified ceramic resin shell nacre containing ladder-structured siloxane methacrylate (SNLSM). Different amounts of shell nacre (24, 48, and 72 weight(wt)%) were added to the SNLSM resin matrix and the effect on the physicochemical properties of the cement was studied. The composite shell nacre cement SNC 72 containing 72 wt% shell nacre exhibited significantly higher mechanical properties (com-pressive strength >100 MPa, flexural strength > 35 MPa) and low linear polymerization shrinkage (0.4%) than other compositions. SNC 72 was radiopaque and the exotherm generated during the curing of the cement was minimal. Direct contact of cured SNC 72 with L929 cells revealed the non-cytotoxic nature of the cement. Overall, the results of the study proved that the composite SNC 72 would be a promising candidate for bone defect management.

: Our study aim to test the influence of RGB reflectance and chlorophyll content on grain fill and grain yield of 15 durum wheat cultivars sown under semi-arid conditions. the evolution of chlorophyll content during three stages showed a stability during the heading stage, the chlorophyll content begins at this degradation during grain filling. Boutaleb genotype which was the best yielding genotype was characterized by low values ​​of RGB reflectance and high values ​​of majority of grain filling parameters and thousand kernels weight. Grain filling follows a sigmoid curve. Chlorophyll content was positively correlated with reflectance under the green band and negatively with both Red and Blue bands. A positive correlation was recorded between thousand kernel weight and grain yield, maximum grain dry weight and grain filling duration. The duration of the grain filling was positively influenced by the maximum dry weight of the grain and negatively by the grain filling ratio, the grain filling ratio was positively affected by reflectance at blue band. The principal component analysis separated the cultivars considered into 3 principal components, the absorption/reflectance component, the profitability component and the component of grain filling rate to which the local landrace Boutaleb belongs in terms of grain yield.

Soil moisture plays a key role in the Earth’s water and carbon cycles, but acquisition of continuous (i.e., gap-free) soil moisture measurements across large regions is a challenging task due to limitations of currently available point measurements. Satellites offer critical information for soil moisture over large areas on a regular basis (e.g., ESA CCI, NASA SMAP), however, there are regions where satellite-derived soil moisture cannot be estimated because of certain circumstances such as high canopy density, frozen soil, or extreme dry conditions. We compared and tested two approaches--Ordinary Kriging (OK) interpolation and General Linear Models (GLM)--to model soil moisture and fill spatial data gaps from the European Space Agency Climate Change Initiative (ESA CCI) version 3.2 (and compared them with version 4.4) from January 2000 to September 2012, over a region of 465,777 km² across the Midwest of the USA. We tested our proposed methods to fill gaps in the original ESA CCI product, and two data subsets, removing 25% and 50% of the initially available valid pixels. We found a significant correlation coefficient (r = 0.523, RMSE = 0.092 m³m^-3) between the original satellite-derived soil moisture product with ground-truth data from the North American Soil Moisture Database (NASMD). Predicted soil moisture using OK also had significant correlation coefficients with NASMD data, when using 100% (r = 0.522, RMSE = 0.092 m³m^-3), 75% (r = 0.526, RMSE = 0.092 m³m^-3) and 50% (r = 0.53, RMSE = 0.092 m³m^-3) of available valid pixels for each month of the study period. GLM had lower but significant correlation coefficients with NASMD data (average r = 0.478, RMSE = 0.092 m³m^-3) when using the same subsets of available data (i.e., 100%, 75%, 50%). Our results provide support for OK as a technique to gap-fill spatial missing values of satellite-derived soil moisture products across the Midwest of the USA.

We have particularly investigated the correlation law of the effect of different carbon black fillings on the hyper-elastic mechanical behavior of natural rubber by conducting uniaxial tensile tests over a wide range of deformations with different volume fractions of carbon black fillings (0%, 4.7%, 8.9%, 12.8%, 16.4%, 19.7%, 22.7%, 25.2%). The results show that the stress-strain curve for carbon black filled rubber increases with the amount of filling, meaning that the rubber gradually becomes "harder". We explore the correlation between the carbon black filling volume and the parameters of the Yeoh constitutive model by examining the Yeoh constitutive model to characterize the hyper-elastic mechanical behavior of rubber with different carbon black fillings. A quantitative relationship between the material parameters and the carbon black filling volume in the Yeoh constitutive model is presented. A method for calculating the material parameters of the Yeoh constitutive model is developed and it predicts the correlation between the hyper-elastic properties of rubber and the volume fraction of carbon black filling.

There is a lack of information on vaccination for pregnant women in the Brazilian literature. Our aim was to evaluate the data on vaccines recorded on the pregnancy card and knowledge about the importance of vaccination for women admitted for labor in a reference public tertiary maternity unit in Presidente Prudente, São Paulo, Brazil. Vaccine data as prescribed by the National Immunization Program of Brazil (NIP) in prenatal cards for patients in labor from the 45 municipalities of the western region of São Paulo state were obtained. A questionnaire relating to knowledge about the types and importance of vaccination in pregnancy was applied. All vaccines indicated by the NIP were registered in only 12.0% of the prenatal cards, and 33.0% of cards registered any vaccines. In this group, 16.6% were aged between 14 and 21 years, and tetanus and COVID-19 were the most prevalent vaccines that they had heard of during prenatal care. Data on vaccines was poorly recorded in the cards, suggesting a lack of attention and unpreparedness of professionals working in primary care. Our study has countrywide and global relevance, and may be applied mainly in Latin American countries facing similar difficulties and limitations with low rates of vaccination during pregnancy.

Land Surface Temperature (LST) is a basic parameter in energy exchange between the land and atmosphere and is frequently used in many sciences such as climatology, hydrology, agriculture, ecology, etc. LST time series data have usually deficient, missing and unacceptable data caused by the presence of clouds in images, presence of dust in atmosphere and sensor failure. In this study, Singular Spectrum Analysis (SSA) algorithm was used to resolve the problem of missing and outlier data caused by cloud cover. The region studied in the present research included an image frame of MODIS with horizontal number 22 and vertical number 05 (h22v05). This image involved a large part of Iran and Turkmenistan and Caspian Sea. In this study, MODIS LST sensor (MOD11A1) was used during 2015 with 1×1 Km spatial resolution and day/night LST data (daily temporal resolution). The results of the data quality showed that cloud cover caused 36.37% of missing data in the studied time series with 730 day/night LST images. Further, the results of SSA algorithm in reconstruction of LST images indicated the Root Mean Square Error (RMSE) of 2.95 K between the original and reconstructed data in LST time series in the study region. In general, the findings showed that SSA algorithm using spatio-temporal interpolation in LST time series can be effectively used to resolve the problem of missing data caused by cloud cover.

Currently, in some domestic and foreign mines, the backfill drilling pipeline experience a rupture phenomenon even when the wear degree is low. This results in a delay in production due to the filling becoming 'sick'. This paper presents, for the first time, the damage mechanism from a mechanical perspective and re-derives the anti-extrusion strength model of the backfill drilling pipeline. We investigate the influence of law on the anti-extrusion strength of pipelines from the perspective of stratum and cement ring. We then verify the theoretical and simulation results through engineering examples. The results demonstrate that the Mises stress criterion is a suitable modification principle for the anti-extrusion strength model of the backfill drilling pipeline. The anti-extrusion strength of the pipeline is related to the elastic modulus and Poisson's ratio of the stratum, and the thickness of the cement ring. It is negatively affected by the depth of the stratum. For hard strata, a cement ring with a smaller elastic modulus is suitable, while for soft stratum, a cement ring with a larger elastic modulus is recommended. When the missing angle of the cement ring is less than 60°, the stress concentration factor increases up to 2.2. The stress unloading capacity of the cement ring ranges from 32.7% to 37.8%, and optimal performance of the cement ring is achieved when it has high strength and low rigidity. The backfill filling pipeline of a copper mine abroad was destroyed due to external extrusion force exceeding its anti-extrusion strength value. The modified pipeline anti-extrusion strength model is 18.2% higher than the casing API strength value. This finding can inform the design of the backfill filling pipeline for China's kilometer-deep wells in the future.

Optical motion capture is a mature contemporary technique for the acquisition of motion data, alas it is non-error-free. Due to technical limitations and occlusions of markers, gaps might occur in such recordings. The article reviews various neural network architectures applied for gap filling problem in motion capture sequences within FBM framework providing the representation for body kinematic structure. The results are compared with interpolation and matrix completion methods. We found out, that for longer sequences simple linear feedforward neural networks can outperform the other, sophisticated architectures. We were also able to identify, that acceleration and monotonicity of input sequence are the parameters that have a notable impact on the obtained results.

With the aim to investigate the effect of parameter and quenching process on the joint of hot stamping steel by laser welding, the BR1500HS boron steel was welded by filling-wire laser welding with ER70-G welding wire under different parameters. The welded specimens were heated to 900℃ and held for 5min before water quenching. The universal material test machine, Optical micro-scope, Vickers hardness tester, scanning electron microscope and electron backscatter diffraction (EBSD) were used to characterize. The results showed that the macroscopic morphology of fusion zone (FZ) becomes from funnelform to hyperbolic curve shape when heat input increases and from hyperbolic curve shape to funnelform when wire-feed speed increases. The strength after quenching is more than 1557Mpa at heat input of 1040J/cm, wire feeding speed of 1.6m/min~1.8m/min and welding speed of 1.5m/min. EBSD test showed that the FZ and fine grain zone (FGZ) have more retained austenite (RA) than coarse grain zone (CGZ) before quenching and RA in FZ and heat affect zone (HAZ) decreased and distributed uniformed after quenching. The grain diameter in FZ distribute unevenly, with the maximum grain diameter larger than 40μm before quenching. After quenching, the grain diameter of FZ, HAZ and BM is more even and coarse grains in the FZ was refined. Before quenching, the microhardness of FZ and HAZ is of 450HV~500HV at different heat input and wire-feed speed and all region of joint keeps at 450HV~550HV after quenching. Most dimple and little river pattern in the joint fracture mor-phology before quenching indicates a well plasticity and most cleavage facet is observed after quenching due to the joint combine with martensite.

Robotics and autonomous technologies enable space travel. Robotics change space colonization. We study space-based robotics. Human-centric missions need robotics. Vision, decision-making, movement, and manipulation follow. These developments influence resource utilization, extravehicular activities, planetary surface exploration, long-duration space missions, and colonization. Robots improve research, productivity, and astronaut safety but present problems. Highlighting research and knowledge gaps. Space ethics, human-robot interaction, and failure recovery are gaps. This extensive study showed how robots and autonomous systems may transform space exploration and colonization. Researchers, engineers, and mission planners may benefit. Robotics and autonomy will improve space exploration.

The paper examines the various uncertainties encountered in high-frequency trading (HFT) environments and delves into the multiple challenges faced by HFT firms in navigating the Dodd-Frank Wall Street Reform and Consumer Protection Act (referred to as the "Dodd-Frank Act"), particularly during the initial stages of its enactment. These challenges include the ambiguity surrounding the definition of HFT, the lack of clarity regarding regulatory requirements and boundaries, inconsistencies in enforcement resulting from deviations in understanding the content, and the absence of detailed descriptions of the Act’s provisions. These hurdles significantly impact not only the daily operations of HFT firms but also pose higher demands on their long-term strategic planning and risk management. Drawing upon the Data, Information, Knowledge, Wisdom, and Purpose (DIKWP) model, this study employs an innovative analytical framework. Through the comprehensive application of conceptual space, cognitive space, and semantic space, it provides a systematic methodology for identifying and analyzing the aforementioned issues. This approach not only aids firms in better comprehending and adhering to complex regulatory requirements but also enables them to explore new business opportunities and competitive advantages while ensuring compliance.

With the increase of mining range from shallow coal seam outcrops to deep With the increase of mining range from shallow coal seam outcrops to deep mining and the improvement of mining intensity in the mining area, there has been a phenomenon of no water inrush in shallow coal mines and abnormal water inrush in deep coal mines in karst landform areas of Guizhou.The project conducted a study on the water source of water inrush in the Xinhua mining area of Jinsha County, Guizhou Province. The research results indicate that the overlying Changxing Formation limestone of the Longtan Formation is a weak (conductive) aquifer, and there is no possibility of water inrush in normal stratigraphic blocks. The spatiotemporal distribution characteristics of the water inrush working face have verified that the Changxing Formation limestone in the shallow mined area has been damaged by mining activities, resulting in a large number of cracks in the rock mass and the formation of a large-scale water accumulation area, becoming a water source for the water inrush in the working face below and a fast supply channel for atmospheric precipitation. The analysis of surface water and mine water quality data shows that the water quality types of mine water and surface water are basically the same, and they are HCO3•SO4-Na type water. The correlation curve between mine water inflow and atmospheric precipitation verifies that the cycle of atmospheric precipitation supplying the mine in Jinyuan Coal Mine is about 10 months before pit closure, and 1 month after pit closure; The Changxing Formation limestone serves as a water-conducting channel, and atmospheric precipitation serves as a source of replenishment for mine water. The research results provide scientific basis for the treatment of atmospheric precipitation water damage in sudden water inrush mines (areas) under similar hydrogeological conditions.

In terrain analysis and hydrological modeling, surface depressions (or sinks) in a digital elevation model (DEM) are commonly treated as artifacts and thus filled and removed to create a depressionless DEM. Various algorithms have been developed to identify and fill depressions in DEMs during the past decades. However, few studies have attempted to delineate and quantify the nested hierarchy of actual depressions, which can provide crucial information for characterizing surface hydrologic connectivity and simulating the fill-merge-spill hydrological process. In this paper, we present an innovative and efficient algorithm for delineating and quantifying nested depressions in DEMs using the level-set method based on graph theory. The proposed level-set method emulates water level decreasing from the spill point along the depression boundary to the lowest point at the bottom of a depression. By tracing the dynamic topological changes (i.e., depression splitting/merging) within a compound depression, the level-set method can construct topological graphs and derive geometric properties of the nested depressions. The experimental results of two fine-resolution LiDAR-derived DEMs show that the raster-based level-set algorithm is much more efficient (~150 times faster) than the vector-based contour tree method. The proposed level-set algorithm has great potential for being applied to large-scale ecohydrological analysis and watershed modeling.

The idea of an extension of life for CubeSats is proposed to reduce space debris in a low-earth orbit. In this work, a gripper is designed for geometry-based grasping in berthing tasks. The grasping operation is outlined for square- and rectangle-profiled CubeSats. Equilibrium conditions are used to choose fingertips shape and parameters for grasping the CubeSat body. A design scheme is proposed to provide the required accuracy. A design concept is developed into a lab prototype by using low-cost 3D printing technique, and a mock-up grasping task that is representative of the berthing operation is evaluated with the lab prototype. Center-mass hanging setup for the prototype and grasped body is used to evaluate the impact of grasping, partially replicating the conditions in space by reducing the effect of gravity on the system.

In this paper, we address the energy eigenvalues of two-dimensional Dirac oscillator perturbed by dynamical noncommutative space. We derived the relativistic Hamiltonian of Dirac oscillator in dynamical noncommutative space ($\tau$-space), in which the space-space Heisenberg–like commutation relations and noncommutative parameter are position-dependent. Then used this Hamiltonian to calculate the first-order correction to the eigenvalues and eigenvectors, based on the second quantization and using the perturbation theory. It is shown that the energy shift depends on the dynamical noncommutative parameter $\tau$. Knowing that with a set of two-dimensional Bopp-shift transformation, we mapped the noncommutative problem to the standard commutative one.

Let $\mathcal{X}$ be a Banach space. Let $\{\tau_j\}_{j=1}^n, \{\omega_k\}_{k=1}^m\subseteq \mathcal{X}$ and $\{f_j\}_{j=1}^n$, $\{g_k\}_{k=1}^m\subseteq \mathcal{X}^*$ satisfy $ |f_j(\tau_j)|\geq 1$ for all $ 1\leq j \leq n$, $|g_k(\omega_k)|\geq 1 $ for all $1\leq k \leq m$. If $x \in \mathcal{X}\setminus \{0\}$ is such that $x=\theta_\tau\theta_f x=\theta_\omega\theta_g x$, then we show that \begin{align}\label{FKDB} \|\theta_fx\|_0\|\theta_gx\|_0\geq \frac{\bigg[1-(\|\theta_fx\|_0-1)\max\limits_{1\leq j,r \leq n,j\neq r}|f_j(\tau_r)|\bigg]^+\bigg[1-(\|\theta_g x\|_0-1)\max\limits_{1\leq k,s \leq m,k\neq s}|g_k(\omega_s)|\bigg]^+}{\left(\displaystyle\max_{1\leq j \leq n, 1\leq k \leq m}|f_j(\omega_k)|\right)\left(\displaystyle\max_{1\leq j \leq n, 1\leq k \leq m}|g_k(\tau_j)|\right)}. \end{align} We call Inequality (\ref{FKDB}) as \textbf{Functional Kuppinger-Durisi-B\"{o}lcskei Uncertainty Principle}. Inequality (\ref{FKDB}) improves the uncertainty principle obtained by Kuppinger, Durisi and B\"{o}lcskei \textit{[IEEE Trans. Inform. Theory (2012)]} (which improved the Donoho-Stark-Elad-Bruckstein uncertainty principle \textit{[SIAM J. Appl. Math. (1989), IEEE Trans. Inform. Theory (2002)]}). We also derive functional form of the uncertainity principle obtained by Studer, Kuppinger, Pope and B\"{o}lcskei \textit{[EEE Trans. Inform. Theory, (2012)]}.

In a hypothetical scenario where space travels outside the solar system is possible and affordable, I examine the possible implications of infinite resources and the universalization of freedom in the social and individual spheres. I argue that freedom is the figure of man's emancipation and the supreme end of history, which represents a theme affirming the infinite and indefinite progress of history and science. Also discussed is Bakunin's theory of the critique of contractualism, which denies the idea of a mythical and primordial natural freedom that existed before the constitution of society. Furthermore, I highlight the deep pathos of romantic culture that feeds into Bakunin's anarchist thought and emphasize the relevance of the notion of freedom in the context of future space travel.

Various approaches to Quantum Gravity suggest an existence of a minimal measurable length. The cost to have such minimal length could be modified uncertainty principle, modified dispersion relation, non-commutative geometry or breaking of continuous Lorentz symmetry. In this paper, we propose that minimal length can be obtained naturally through spin-orbit interaction. We consider Dresselhaus anisotropic spin-orbit interaction as the perturbative Hamiltonian. When applied to a particle, it implies that the space, which seizes this particle, should be quantized in terms of units that depend on particle’s mass. This suggests that all measurable lengths in the space are quantized in units depending on existent mass and the Dresselhaus coupling constant. On one side, this indicates a breakdown of the space continuum picture near the scale of tabletop experiments, and on the other side, it proposes that spin-orbit interaction is a possible quantum gravity effect at low energy scale that leads naturally to space quantization.

A physical model based on the mechanism observed in experimental investigations is introduced to describe the formation of negative leader steps. Starting with a small length of a space leader located at the periphery of the negative streamer system of the stepped leader the model simulates the growth and the subsequent formation of the leader step. Based on the model, the average step length, the average step forming time and the average stepped leader propagation speed is estimated as a function of prospective return stroke peak current. The results show that the average step length and the average leader speed increases with increasing prospective return stroke current. The results also show that the speed of the stepped leader increases as it approaches the ground. For a 30 kA prospective return stroke current the average leader speed obtained is about 5 x 10⁵ m/s and the average step length was about 10 m. The results obtained are in reasonable agreement with the experimental observations.

The construction of random fillings from the excavation of medium hardness rocks, with high particle sizes, presents limitations in compaction control. This research applies new control techniques with revised test procedures in the construction of the random fillings core, which constitutes the main part of the embankment, with the bigger volume and provides the geotechnical stability to the infrastructure. The maximum layer thickness researched was 800mm. As there are many types of rocks, this research is applied to metamorphic slates. Quality control has been carried out by applying new research associated with the revision of wheel impression test, topographic settlements and plate bearing test (PBT). A statistical analysis of the core of 16 slate random fillings has been carried out, with a total of 2250 in situ determination of density and moisture content, 75 wheel impression tests, 75 topographic settlement control and 75 PBT. The strong associations found between different tests have allowed to simplify the quality control.

The implementation of green roofs as sustainable urban drainage systems provides benefits for stormwater control and the environment and is always more encouraged. In this paper, the estimation of the probability of vegetation survival without irrigation has been proposed as a guide to choose the proper values for the design parameters; in particular the growing medium thickness has been related to the average return interval of the water content at the end of the dry period. Moreover the study represents an improvement of the analytical probabilistic approach since a chain of consecutive rainfall events has been considered, in order to take into account the possibility that the storage capacity is not completely available at the beginning of each event because of the pre-filling from more than one previous rainfall as typically happens for green roofs. Finally, developed equations have been validated by means of their application to two case studies, respectively in northern and southern Italy.

Currently, maritime traffic is increasing with economic growth in several regions worldwide. However, this growth in maritime traffic has led to increased risk of marine accidents. These accidents have a higher probability of occurring in regions where geographical features, such as islands, are present. Further, the positioning of rescue ships in a particular ocean region with a high level of maritime activity is critical for rescue operations. This paper proposes a method for determining an optimal set of locations for stationing rescue ships in an ocean region with numerous accident sites in the Wando islands of South Korea. The computational challenge in this problem is identified as the positioning of numerous islands of varying sizes located in the region. Thus, the proposed method combines a clustering-based optimization method and an image processing approach that incorporates flood filling to calculate the shortest distance between two points in the ocean that detours around the islands. Experimental results indicate that the proposed method reduces the distance from rescue ships and each accident site by 5.0 km compared to the original rescue ship locations. Thus, rescue time is reduced.

The effect of filling velocity on positive macrosegregations in large size steel ingots was studied. Macrosegregation and macro-/micro-structure were characterized on the hot-tops and a portion of the upper section of two ingots. The measurements revealed that segregation features in the two ingots varied as a function of the alloying elements, and that the severity of positive macrosegregation in the casting body was reduced when the filling rate was increased. It was also found that at the higher filling rate, grain morphologies in the first solidified zones of the ingot changed from columnar to equiaxe, and secondary dendrite arm spacing (SDAS) became slightly smaller in the intermediate and final solidified zones. The experimental findings were analyzed in the framework of diffusion and convection controlled solidification, as well as liquid metal flow theories. The solute dependence of segregation features was related to the difference in solid-liquid partition coefficient and diffusion capability of each element in the liquid iron. Calculation of Reynolds numbers (Re) during the filling process, for both ingots, showed that higher filling velocity caused more instable movement of the liquid metal in the initial solidification stage, resulting in the modification of grain morphology, as well as accelerated solidification rate.

We show that one of the two important uncertainty principles derived by Maccone and Pati \textit{[Phys. Rev. Lett., 2014]} can be derived for arbitrary maps defined on subsets of $\mathcal{L}^p$ spaces for $1< p<\infty$. Our main tool is the Clarkson inequalities. We also derive a nonlinear uncertainty principle for weak parallelogram spaces and Type-p Banach spaces.

The author introduces a novel theoretical framework that suggests matter and energy are both converted from curved space. In Space Theory, gravitation is generated by the flow of space, instead of being transmitted by the graviton as in String Theory. This theory also suggests that Newton's gravitational constant, denoted as G, may not be truly constant but could vary over time. The equivalent equation of space is S=Ec²=mc⁴, and the gravitation of hollow sphere space is S_μν=4πGm=(4/3)π((r+a)³-r³). The Space Theory also predicts that the surface gravitational acceleration of the neutron star Crab Pulsar (PSR B0531+21) is approximately 8.21924883×10⁶ m/s².

Space debris, which includes retired satellites, used rocket stages, and explosion- or collision-related bits, poses a serious threat to both ongoing and future space activity. Addressing the problem of space debris has become essential for the sustainability of space operations due to the exponential development in satellite deployments and space research. The development of technology and tactics aimed at reducing the debris problem and assuring a cleaner cosmos are the main topics of this abstract, which provides an outline of the idea of sustainable space debris management and removal. The paper opens by outlining the history of space debris and the major difficulties caused by space debris, such as the dangers to functioning satellites, the possibility of catastrophic collisions, and the production of more debris as a result of cascade occurrences. The paper then emphasized the guidelines of space debris mitigation. It emphasizes the pressing requirement for long-term fixes that tackle the issue at its root. The paper then discusses different methods for managing space debris, such as proactive measures, active debris removal (ADR). It talks about how important it is to use sustainable methods during every stage of a space mission's lifecycle, from design and operation to deorbiting and disposal. This paper concludes with a summary of sustainable space debris removal, noting the difficulties caused by debris and the demand for all-encompassing approaches and technology to address this issue. It emphasizes how crucial global collaboration, technological development, and institutional frameworks are to creating a sustainable and debris-free space environment.

Let $(\{f_j\}_{j=1}^n, \{\tau_j\}_{j=1}^n)$ and $(\{g_k\}_{k=1}^n, \{\omega_k\}_{k=1}^n)$ be two p-orthonormal bases for a finite dimensional Banach space $\mathcal{X}$. If $ x \in \mathcal{X}\setminus\{0\}$ is such that $\theta_fx$ is $\varepsilon$-supported on $M\subseteq \{1,\dots, n\}$ w.r.t. p-norm and $\theta_gx$ is $\delta$-supported on $N\subseteq \{1,\dots, n\}$ w.r.t. p-norm, then we show that \begin{align}\label{ME} &o(M)^\frac{1}{p}o(N)^\frac{1}{q}\geq \frac{1}{\displaystyle \max_{1\leq j,k\leq n}|f_j(\omega_k) |}\max \{1-\varepsilon-\delta, 0\},\\ &o(M)^\frac{1}{q}o(N)^\frac{1}{p}\geq \frac{1}{\displaystyle \max_{1\leq j,k\leq n}|g_k(\tau_j) |}\max \{1-\varepsilon-\delta, 0\},\label{ME2} \end{align} where \begin{align*} \theta_f: \mathcal{X} \ni x \mapsto (f_j(x) )_{j=1}^n \in \ell^p([n]); \quad \theta_g: \mathcal{X} \ni x \mapsto (g_k(x) )_{k=1}^n \in \ell^p([n]) \end{align*} and $q$ is the conjugate index of $p$. We call Inequalities (\ref{ME}) and (\ref{ME2}) as \textbf{Functional Donoho-Stark Approximate Support Uncertainty Principle}. Inequalities (\ref{ME}) and (\ref{ME2}) improve the finite approximate support uncertainty principle obtained by Donoho and Stark \textit{[SIAM J. Appl. Math., 1989]}.

Let $(\{f_j\}_{j=1}^n, \{\tau_j\}_{j=1}^n)$ and $(\{g_k\}_{k=1}^n, \{\omega_k\}_{k=1}^n)$ be two p-orthonormal bases for a finite dimensional Banach space $\mathcal{X}$. Let $M,N\subseteq \{1, \dots, n\}$ be such that \begin{align*} o(M)^\frac{1}{q}o(N)^\frac{1}{p}< \frac{1}{\displaystyle \max_{1\leq j,k\leq n}|g_k(\tau_j) |}, \end{align*} where $q$ is the conjugate index of $p$. Then for all $x \in \mathcal{X}$, we show that \begin{align}\label{FGJU} (1) \quad \quad \quad \quad \|x\|\leq \left(1+\frac{1}{1-o(M)^\frac{1}{q}o(N)^\frac{1}{p}\displaystyle\max_{1\leq j,k\leq n}|g_k(\tau_j)|}\right)\left[\left(\sum_{j\in M^c}|f_j(x)|^p\right)^\frac{1}{p}+\left(\sum_{k\in N^c}|g_k(x) |^p\right)^\frac{1}{p}\right]. \end{align} We call Inequality (1) as \textbf{Functional Ghobber-Jaming Uncertainty Principle}. Inequality (1) improves the uncertainty principle obtained by Ghobber and Jaming \textit{[Linear Algebra Appl., 2011]}.

We develop the theory of Heyting small spaces and prove a new version of Esakia duality for such spaces. To do this, we notice that spectral spaces may be seen as sober small spaces with all smops compact and introduce the method of the standard spectralification. This helps to understand open continuous definable mappings between definable spaces over o-minimal structures.

In the paper we consider conformal mappings of Riemannian spaces onto Ricci-2-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-2-symmetric spaces. The main equations for the mappings are obtained as a closed system of differential equations of Cauchy-type in covariant derivatives. We have found the number of essential parameters which the solution of the system depends on. Similar approach was applied for the case of conformal mappings of Riemannian spaces onto Ricci-m-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-m-symmetric spaces.

Manned missions to Mars and other deep space exploration targets are expected to take place in the next 20 years. These missions will involve prolonged crew exposure to the unique space environment, increasing the risk that astronauts will experience additional physical and psychological health conditions beyond those that would be expected through normal aging on Earth. Thus, there is an acute need to develop therapeutic solutions that can withstand the harsh space environment, while maintaining astronaut health and maximizing crew capabilities to foster successful exploration-class missions. This review covers the nuanced and interdisciplinary challenge that is providing safe and effective pharmaceuticals for future deep space missions. First, the limitations of current pharmaceutical solutions are discussed; the impacts of the space environment on human health and chemical compound stability are covered, along with an evaluation of astronaut medication use on similar missions. Second, potential pharmaceutical solutions and concepts are presented for consideration. Future research should prioritize these and other potential innovations to ensure that our space programs are well equipped to maximize crew safety as astronauts explore deep space objectives.

The paper presents a method for estimating the inertia tensor components of a spacecraft that has expired its active life using measurement data of the Earth's magnetic field induction vector components. The implementation of this estimation method is supposed to be carried out when cleaning up space debris in the form of a clapped-out spacecraft with the help of a space tug. It is assumed that a three-component magnetometer and a transmitting device are attached on space debris. With the help of this measuring system, the parameters for the rotational motion of space debris are estimated. Then the known controlled action from the space tug is transferred to the space debris. Next, measurements for the rotational motion parameters are carried out once again. Based on the available measurement data and parameters of the controlled action, the space debris inertia tensor components are estimated. It is assumed that the measurements of the Earth's magnetic field induction vector components are made in a coordinate system which axes are parallel to the corresponding axes of the main body axis system. Such an estimation makes it possible to effectively solve the problem of cleaning up space debris, to calculate the costs of the space tug working body and the parameters of the space debris removal orbit. Examples of numerical simulation using the measurement data of the Earth's magnetic field induction vector components on the Aist-2D small spacecraft are given. The results of the work can be used in the development and implementation of missions to clean up space debris in the form of clapped-out spacecraft.

Space exploration is demanding longer lasting human missions and water resupply from Earth will become increasingly unrealistic. In a near future, the spacecraft water monitoring systems will require technological advances to promptly identify and counteract contingent events of waterborne microbial contamination, posing health risks to astronauts with lowered immune responsiveness. The search for bio-analytical approaches, alternative to those applied on Earth by cultivation-dependent methods, is pushed by the compelling need to limit waste disposal and avoid microbial regrowth from analytical carryovers. Prospective technologies will be selected only if first validated in a flight-like environment, by following basic principles, advantages, and limitations beyond their current applications on Earth. Starting from the water monitoring activities applied on the International Space Station, we provide a critical overview of the nucleic acid amplification-based approaches (i.e., loop-mediated isothermal amplification, quantitative PCR, and high-throughput sequencing) and early-warning methods for total microbial load assessments (i.e., ATP-metry, flow cytometry), already used at a high readiness level aboard crewed space vehicles. Our findings suggest that the forthcoming space applications of mature technologies will be necessarily bounded by a compromise between analytical performances (e.g., speed to results, identification depth, reproducibility, multiparametricity) and detrimental technical requirements (e.g., reagent usage, waste production, operator skills, crew time). As space exploration progresses toward extended missions to Moon and Mars, miniaturized systems that also minimize crew involvement in their end-to-end operation are likely applicable on the long-term and suitable for the in-flight water and microbiological research.

A sintered wick was formed in a heat pipe through the process of sintering a mixture of copper powder with particle sizes of 100㎛ and 200㎛, mixed with a pore-forming agent. On application to the heat pipes. The thermal resistance of heat pipes containing a sintered wick was calculated for different tilting angles (0°, 45°, and 90°) according to the type of powder, thickness of the sintered wick, and the filling ratio of the working fluid. The heat transfer efficiencies were evaluated through temperature tests. The capillary force, which is closely related to heat transfer efficiency, is determined by the effective pore radius resulting from the sintering of the copper powder. Furthermore, it was observed that the heat transfer performance of the heat pipe was at its best when the working fluid filling ratio was 30%. Additionally, the width of the wick was found to have a direct correlation with the heat transfer performance.

The Grand Ethiopian Renaissance Dam (GERD), formerly known as the Millennium Dam, is currently under construction and has been filling at a fast rate without sufficient known analysis on possible impacts on the body of the structure. The filling of GERD not only has an impact on the Blue Nile Basin hydrology, water storages and flow but also pose massive risks in case of collapse. Rosaries Dam located in Sudan at only 116 km downstream of GERD, along with the 20 million Sudanese benefiting from that dam, would be seriously threatened in case of the collapse of GERD. In this study, through the analysis of Sentinal-1 satellite imagery we show concerning deformation patterns associated with different sections of the GERD’s Main Dam (structure RCC Dam type) and the Saddle Dam (Embankment Dam type). We processed 109 descending mode scenes from Sentinel-1 SAR imagery, from December 2016 to July 2021, using the Differential Synthetic Aperture Radar Interferometry technique to demonstrate the deformation trends of both - the GERD’s Main and Saddle Dams. The time-series generated from the analysis clearly indicates different displacement trends at various sections of the GERD as well as the Saddle Dam. Results of the multi temporal data analysis on and around the project area show inconsistent subsidence at the extremities of the GERD Main Dam, especially the west side of the dam where we recorded varying displacements in the range of 10 mm to 90 mm at the crest of the dam. We conducted the current analysis after masking the images with a coherence value of 0.9 and hence, the subsequent results are extremely reliable and accurate. Further decomposition of the subsiding rate has revealed higher vertical displacement over the west side of the GERD’s Main Dam as compared to the east side. The local geological structures consisting of weak zones under the GERD’s accompanying Saddle Dam adds further instability to its structure. We identified seven critical nodes on the Saddle Dam that match the tectonic faults lying underneath it, and which display a varying degree of vertical displacements. In fact, the nodes located next to each other displayed varying displacement trends: one or more nodes displayed subsidence since 2017 while the other node in the same section displayed uplift. The geological weak zones underneath and the weight of the Saddle Dam itself may somewhat explain this inconsistency and the non-uniform vertical displacements. For the most affected cells, we observed a total displacement value of ~90 mm during the whole study period (~20 mm/year) for the Main Dam while the value of the total displacement for the Saddle dam is ~380 mm during the same period (~85 mm/year). Analysis through CoastSat tool also suggested a non-uniformity in trends of surface water-edge at the two extremities of the Main Dam.

Can physical objects be in time-symmetry? Physical objects can only exist in a medium that has physical attributes, which means this medium is a type of energy. Is time energy? This article will show that time is not energy and there is no possibility that physical objects could be in time-symmetry. Physical objects only can be in symmetry in the time-invariant space in which they exist. In this perspective time measured with clocks is the result of the observer’s measurement in the time-invariant space. The time-symmetry model is flawed.

Penrose’s singularity from 1965 predicted that in the center of the black hole space-time curvature is infinite and consequently gravity force there is infinite. In 2014 NASA measured universal space has Euclidean shape. This means that stellar objects cannot curve universal space and that the space-time singularity model has no physical existence. In the center of black holes energy density of superfluid space is so low that the electromagnetic properties of space are changed. This causes electromagnetic forces between the nucleus and orbiting electrons to become unstable. In the center of a black hole, atoms are falling apart into elementary particles. Black holes are rejuvenating systems of the universe, they transform old matter into fresh energy in the form of elementary particles. Astrophysical jets are the outcome of this process.

Measuring the Sun’s magnetic field is a key component of monitoring solar activity and forecasting space weather. The main goal of the research presented in this paper is to investigate the possibility of reducing the dimensions and weight of a solar magnetograph while preserving its optical quality. This article presents a range of different designs, along with their advantages and disadvantages, and an analysis of the optical performance of each. All proposed designs are based on the Magneto Optical Filter (MOF) technique. As a result of the design study, a miniaturised solar magnetograph is proposed with an ultra-compact layout. The dimensions are 345mm × 54mm × 54mm and the optical quality is almost at the diffraction limit. The design has an entrance focal-ratio of F/17.65, with a plate scale of 83.58 arcsec/mm at the telescope image focal plane and produces a magnification of 0.79. The field of view is 1920 arcsec diameter, equivalent to ±0.27degrees, sufficient to cover the entire solar disk.

Let $\{f_j\}_{j=1}^n$ and $\{g_k\}_{k=1}^m$ be Parseval p-frames for a finite dimensional Banach space $\mathcal{X}$. Then we show that \begin{align}\label{UE} \log (nm)\geq S_f (x)+S_g (x)\geq -p \log \left(\displaystyle\sup_{y \in \mathcal{X}_f\cap \mathcal{X}_g, \|y\|=1}\left(\max_{1\leq j\leq n, 1\leq k\leq m}|f_j(y)g_k(y)|\right)\right), \quad \forall x \in \mathcal{X}_f\cap \mathcal{X}_g, \end{align} where \begin{align*} &\mathcal{X}_f\coloneqq \{z\in \mathcal{X}: f_j(z)\neq 0, 1\leq j \leq n\}, \quad \mathcal{X}_g\coloneqq \{w\in \mathcal{X}: g_k(w)\neq 0, 1\leq k \leq m\},\\ &S_f (x)\coloneqq -\sum_{j=1}^{n}\left|f_j\left(\frac{x}{\|x\|}\right)\right|^p\log \left|f_j\left(\frac{x}{\|x\|}\right)\right|^p, \quad S_g (x)\coloneqq -\sum_{k=1}^{m}\left|g_k\left(\frac{x}{\|x\|}\right)\right|^p\log \left|g_k\left(\frac{x}{\|x\|}\right)\right|^p, \quad \forall x \in \mathcal{X}_g. \end{align*} We call Inequality (1) as \textbf{Functional Deutsch Uncertainty Principle}. For Hilbert spaces, we show that Inequality (1) reduces to the uncertainty principle obtained by Deutsch \textit{[Phys. Rev. Lett., 1983]}. We also derive a dual of Inequality (1).

We develop the theory of Heyting locally small spaces, including Stone-like dualities such as a new version of Esakia duality and a system of concrete isomorphisms and equivalences. In such a way, we continue building tame topology, realising Grothendieck's ideas. We use up-spectral spaces and define the standard up-spectralification of a Kolmogorov locally small space. This research gives more understanding of locally definable spaces over structures with topologies.

Let $(\{f_j\}_{j=1}^n, \{\tau_j\}_{j=1}^n)$ and $(\{g_k\}_{k=1}^m, \{\omega_k\}_{k=1}^m)$ be p-Schauder frames for a finite dimensional Banach space $\mathcal{X}$. Then for every $x \in \mathcal{X}\setminus\{0\}$, we show that \begin{align}\label{UE} \|\theta_f x\|_0^\frac{1}{p}\|\theta_g x\|_0^\frac{1}{q} \geq \frac{1}{\displaystyle\max_{1\leq j\leq n, 1\leq k\leq m}|f_j(\omega_k)|}\quad \text{and} \quad \|\theta_g x\|_0^\frac{1}{p}\|\theta_f x\|_0^\frac{1}{q}\geq \frac{1}{\displaystyle\max_{1\leq j\leq n, 1\leq k\leq m}|g_k(\tau_j)|}. \end{align} where \begin{align*} \theta_f: \mathcal{X} \ni x \mapsto (f_j(x) )_{j=1}^n \in \ell^p([n]); \quad \theta_g: \mathcal{X} \ni x \mapsto (g_k(x) )_{k=1}^m \in \ell^p([m]) \end{align*} and $q$ is the conjugate index of $p$. We call Inequality (\ref{UE}) as \textbf{Functional Donoho-Stark-Elad-Bruckstein-Ricaud-Torr\'{e}sani Uncertainty Principle}. Inequality (\ref{UE}) improves Ricaud-Torr\'{e}sani uncertainty principle \textit{[IEEE Trans. Inform. Theory, 2013]}. In particular, it improves Elad-Bruckstein uncertainty principle \textit{[IEEE Trans. Inform. Theory, 2002]} and Donoho-Stark uncertainty principle \textit{[SIAM J. Appl. Math., 1989]}.

In this article, rst we are going to review the concept of ordinary frames , in more general case in measure spaces, namely, gc-frames. We try to develop the use of measure space in describing frames. Then by means of the gc-frames, we shall introduce gn-operators, which we shall show that each trace class operator has a vector-valued integral representation and vice-versa.

After proposing the Principle of Minimum Gravitational Potential, in a pursuit to find the explanation behind the correction to Newton's gravitational potential that accounts for Mercury's orbit, by finding all the higher-order corrections it is shown that the consequences of the existence of speed of light for gravity are not yet fully explored.

The aim of this article is to make a multi-criteria analysis of various exhibition spaces of an originally non-exhibition character and to determine how these spaces affect the selection of works and the exhibition concept. The analysis is based on the exhibitions of art objects at collective exhibitions in unconventional architectural spaces: commercial, i.e. the modern office building of PBG Gallery Skalar Office Centre in Poznań, post-industrial i.e. in the former Zakłady Przemysłu Ziemniaczanego Lubanta S.A. and in the historic interior of the "U Jezuitów" Gallery of the Cultural Integration Centre in Poznań. The multi-criteria comparative analysis shows a variety of features of the studied spaces as well as the relationship between architecture and art and their mutual interaction. The participatory role of the non-exhibition space in the process of creating an exhibition and selecting works has been proven. It has also been confirmed that the presentation of works of art in originally non-exhibition spaces creates a new quality of the artwork. Unconventional architectural space, when used for the exhibition of works of art, expands and strengthens the area of ​​their influence through the interaction between the work and the architectural space. The specificity of the space adapted for exhibition needs, the presence and type of architectural details in the interior, the quantity and quality of light and its distribution in space, the volume and colour of the interior determine the exhibition space and influence the shape of the exhibitions organised and the reception of the artworks. The only condition for the change of the original function of an architectural space into that of an exhibition space is a coherent artistic vision of the creator. This should take into account the appropriate selection of the exhibited objects, where the process of searching for the relationship between architecture and art determines the features of the architectural space as integral components influencing the realisation of the exhibition .

While investigating the outcomes of balloon dilatation procedures in patients with congenital obstructive lesions of the heart, several parallel observations have been made. The purpose of this review is to present these observations/phenomena/innovations related to balloon dilatation of pulmonary stenosis (PS), aortic stenosis (AS), and aortic coarctation (AC). In subjects who had balloon pulmonary valvuloplasty (BPV), development of infundibular obstruction, electrocardiographic (ECG) changes, changes in right ventricular filling, role of balloon/annulus ratios on the results of BPV, and double balloon vs. single balloon BPV will be reviewed. In patients who had balloon aortic valvuloplasty (BAV), causes of aortic insufficiency and trans-umbilical venous approach for BAV will be tackled. In children who had balloon angioplasty (BA) of AC, aortic remodeling and biophysical response after BA of AC will be discussed.

Abstract: The two-dimensional Fuzzy Transform was applied in image compression. The quality of the image compressed with this methodis better than that obtained using methods based on fuzzy relation equations and comparable with that of the JPEG method, with better compression execution times. In this paper we propose a variation of the method based on the two-dimensional Fuzzy Transform of image compression, in which the image is first partitioned into blocks and then each block is compressed with the higher compression rate. The advantage of this method consistsinto a greater compression of the image, guaranteeing a high quality of the reconstructed image.The results show that our method is better than the Fuzzy Transform method improving also the quality of the reconstructed image.

Let $(\Omega, \mu)$, $(\Delta, \nu)$ be measure spaces and $\{\tau_\alpha\}_{\alpha\in \Omega}$, $\{\omega_\beta\}_{\beta \in \Delta}$ be 1-bounded continuous Parseval frames for a Hilbert space $\mathcal{H}$. Then we show that \begin{align}\label{UE} \log (\mu(\Omega)\nu(\Delta))\geq S_\tau(h)+S_\omega (h)\geq -2 \log \left(\frac{1+\displaystyle \sup_{\alpha \in \Omega, \beta \in \Delta}|\langle\tau_\alpha , \omega_\beta\rangle|}{2}\right) , \quad \forall h \in \mathcal{H}_\tau \cap \mathcal{H}_\omega, \end{align} where \begin{align*} &\mathcal{H}_\tau := \{h_1 \in \mathcal{H}: \langle h_1 , \tau_\alpha \rangle \neq 0, \alpha \in \Omega\}, \quad \mathcal{H}_\omega := \{h_2 \in \mathcal{H}: \langle h_2, \omega_\beta \rangle \neq 0, \beta \in \Delta\},\\ &S_\tau(h):= -\displaystyle\int\limits_{\Omega}\left|\left \langle \frac{h}{\|h\|}, \tau_\alpha\right\rangle \right|^2\log \left|\left \langle \frac{h}{\|h\|}, \tau_\alpha\right\rangle \right|^2\,d\mu(\alpha), \quad \forall h \in \mathcal{H}_\tau, \\ & S_\omega (h):= -\displaystyle\int\limits_{\Delta}\left|\left \langle \frac{h}{\|h\|}, \omega_\beta\right\rangle \right|^2\log \left|\left \langle \frac{h}{\|h\|}, \omega_\beta\right\rangle \right|^2\,d\nu(\beta), \quad \forall h \in \mathcal{H}_\omega. \end{align*} We call Inequality (\ref{UE}) as \textbf{Continuous Deutsch Uncertainty Principle}. Inequality (\ref{UE}) improves the uncertainty principle obtained by Deutsch \textit{[Phys. Rev. Lett., 1983]}. We formulate Kraus conjecture for 1-bounded continuous Parseval frames. We also derive continuous Deutsch uncertainty principles for Banach spaces.

As renewed interest in human space-exploration intensifies, a coherent and modernized strategy for mission-design and planning has become increasingly crucial. Biotechnology has emerged as a promising approach to increase mission resilience, flexibility, and efficiency by virtue of its ability to efficiently utilize in situ resources and reclaim resources from waste streams. Since its infancy during the Apollo years, biotechnology, and specifically biomanufacturing, have witnessed significant expansions of scope and scale. Here we outline four primary mission classes, on Luna and Mars, that drive a staged and accretive biomanufacturing strategy. Each class requires a unique approach to integrate biomanufacturing into the existing mission architecture and so faces unique challenges in technology development.These challenges stem directly from the resources available in a given mission class – the degree to which feedstocks are derived from cargo and in situ resources – and the degree to which loop-closure is necessary. We see that as mission duration and distance from Earth increase, the benefits of specialized sustainable biomanufacturing processes increases. Here we present a strategic approach, guided by technoeconomics, to development, testing, and deployment of these technologies serves to nucleate the larger effort of supporting a sustained human presence in space. The processes needed for each scenario spans the technical breadth of synthetic biology to design engineering, from sophisticated genetic tailoring of chassis-organisms to building scalable, automated, easily operable bioreactors and processing systems. As space-related technology development often does, these advancements are likely to have profound implications for the creation of a stable, resilient bioeconomy on Earth.

We explore the field equations in a 4-d complex space-time, in the same way, that general relativity does for our usual 4-d real space-time, forming this way, a new "general relativity" in C⁴ space-time, free of sources. Afterwards, by embedding our usual 4-d real space-time in C⁴ space-time, we describe geometrically the energy-momentum tensor T_μν as the lost geometric information of this embedding. We further give possible explanation of dark eld and dark energy.

Einstein’s publication of the Special Theory of Relativity in 1905 gave birth to the space-time model as a fundamental arena of the universe. Time has become 4th dimension of space and theoretically one could move backward and forward in time. Hypothetical time travel has been a hot topic of scientific discussion since Kurt Gödel published his article about closed time-like curves (CTC) in 1949. He was aware that his CTC model confirms that there is no physical time. Physicists understood his model as a theoretical frame for time travel. Recent research confirmed that universal space is time-invariant. Motion happens only in space and time is the duration of motion. Nobody can travel in time because time has no physical existence. Time as duration is an emergent physical quantity entering existence in the process of measurement of the duration of material change with clocks. The universal space is utterly timeless. There is no physical time in the universe.

Spatial attentional biases can be observed during the processing of linguistic material. For example, we previously reported that healthy subjects overestimate the semantic distance between word stimuli in the right vs left space. Here we explored whether attentional biases are also observed in tasks requiring evaluation of phonological distance between words in the right and left hemispace. Forty-one healthy subjects were presented with triplets of words arranged in space and were asked to indicate the side of space in which the phonological distance between the middle word and an outer word was smaller. In Experiment 1 real words and pseudowords were used, while in Experiment 2 only pseudowords and consonant strings were used. Subjects overestimated the phonological distance between the middle and outer words in the right space. These findings were specific to word stimuli. These results are consistent with the idea that semantic and phonological information may be internally mapped onto spatial representations.

Heart failure with reduced ejection fraction (HFrEF) is considered a major healthcare problem with frequent decompensations, high hospitalization and mortality rates. In severe heart failure (HF), the symptoms are refractory to medical treatment and require advanced therapeutic strategies. Early recognition of HF sub- and decompensation is the cornerstone of the timely treatment intensification and, therefore, improvement of the prognosis. Echocardiography is the gold standard for the assessment of systolic and diastolic functions. It allows to obtain accurate and non-invasive measurements of the ventricular function in HF. In severely compromised HF patients, advanced cardiovascular ultrasound modalities may provide a better assessment of intracardiac hemodynamic changes and subclinical congestion. Particularly, cardiovascular and lung ultrasound allow to make a more accurate diagnosis of subclinical congestion in HFrEF. The aim of this review is to summarize the advantages and limitations of currently available ultrasound modalities in the ambulatory monitoring of patients with HFrEF.

Solar geoengineering (SG) solutions have many advantages compared to the difficulty of carbon removal (CR): SG produces fast results, is shown here to have much higher efficiency than CR, is not related to fossil fuel legislation, and is something we all can participate in brightening the Earth with cool roofs, and roads. SG requirements detailed previously to mitigate global warming (GW) have been concerning primarily because of overwhelming goals and climate circulation issues. In this paper, the advantages of annual solar geoengineering (ASG) to mitigate yearly global warming increases are explored and detailed as it provides higher feasibility in geoengineering applications. ASG area modification requirements found here are generally 50 to possibly higher than 150 times less compared to the challenge of full SG GW mitigation reducing circulation concerns. Results indicate that there are mixed technologies that can help meet annual mitigation Earth brightening goals. As well, results show much higher feasibility for L1 space shading compared to prior literature estimates for full GW mitigation. However, stratosphere injections appear challenging in the annual approach. Because ASG earth brightening area requirements are much smaller than those required for full mitigation, we have concerns that worldwide negative SG would interfere with making positive advances for several reasons. Negative SG currently dominates yearly practices with the application of dark asphalt roads and roofs. This issue is discussed.

There is an overall scientific consensus that public space and, mainly, space with a high ecological index – most notably experienced in green areas – positively affects individual and collective well-being and urban dwellers’ physical and mental health. However, the ‘reality check’ indicates difficulties in translating the assumed benefits of green space into implementable interventions in urban environments. To examine such an ‘implementation gap’ on the case of Zurich seems valid, given that the ‘green urban agenda’ debate has been embedded in numerous Swiss policies (from the federal to the municipal levels). In narrow terms, the research first focuses on Zurich’s district 9 consisting of two neighborhoods (Altstetten and Albisrieden) – the area under ongoing densification yet with a variety of green spaces, to then elucidate four green space clusters and their 400-meter catchment areas in the mentioned district. The mixed-method approach has been applied at three analytical levels: 1) documentary analysis of multi-scale national policy toolkits, to identify the critical tenets associated with the ‘green urban agenda’, 2) assessment of green spaces in Zurich’s district 9 based on online available quantitative data and on-site observation, to determine their provision, types, size and mutual connectivity, and 3) analysis of four green space clusters within the mentioned district through on-site observation, to identify green space attributes and main activities. Through critical mutual examination of the identified ‘green urban agenda’ principles in the national policies, on the one hand, and green space attributes, on the other, the research findings reveal the extent of the convergence and/or divergence between the ‘green urban agenda’ policy trends and their implementation in practice.

We present a cosmological model in which the Big Bang was not the beginning of space and time; there was a previous phase leading up to it, with multiple cycles of contraction and expansion that repeat indefinitely. In this paper we propose a unique property of Space-time, this particular and marvelous nature of space shows us that space can stretch, expand, and shrink. When matter comes closer to each other, the space also shrinking between them. As space shrunk it produced the pressure, which pressure stretching the Shrunk space. This property of space is causes the size of the Universe changed over time: growing or shrinking. The observed accelerated expansion, which relates the stretching of Shrunk space for the new theory, is derived. When space exponentially shrunk, it creates the pressure, which leads to stretching the shrink volume of space. As pressure of shrink space decreases, the stretching of shrunk space increases, that is although in general, decelerate in the pressure of shrink space leads to accelerate the expansion of space. The pressure of the shrunk space will cease at the certain cosmic scale, so the expansion of the Universe will eventually stop, after that a period of slow contraction will begin, thus bringing the universe back to contract to its initial state, ending in a Big Crunch. The universe will not continue to expand forever, no need however, for dark energy. The new definition of eternal space and its unique properties enables us to describe a sequence of events from the Big Bang to the Big Crunch.

We investigate the behavior of the partial derivative approach to the change of scale formula and prove relationships among the analytic Wiener integral and the analytic Feynman integral of the partial derivative for the function space integral.

Reinvigorated public interest in human space exploration has led to the need to address the science and engineering challenges described by NASA's Space Technology Grand Challenges (STGCs) for expanding the human presence in space. Here we define Space Bioprocess Engineering (SBE) as a multi-disciplinary approach to design, realize, and manage a biologically-driven space mission as it relates to addressing the STGCs for advancing technologies to support the nutritional, medical, and incidental material requirements that will sustain astronauts against the harsh conditions of interplanetary transit and habitation offworld. SBE combines synthetic biology and bioprocess engineering under extreme constraints to enable and sustain a biological presence in space. Here we argue that SBE is a critical strategic area enabling long-term human space exploration; specify the metrics and methods that guide SBE technology life-cycle and development; map an approach by which SBE technologies are matured on offworld testing platforms; and suggest a means to train the next generation spacefaring workforce on the SBE advantages and capabilities. In doing so, we outline aspects of the upcoming technical and policy hurdles to support space biomanufacturing and biotechnology. We outline a perspective marriage between space-based performance metrics and the synthetic biology Design-Build-Test-Learn cycle as they relate to advancing the readiness of SBE technologies. We call for a concerted effort to ensure the timely development of SBE to support long-term crewed missions using mission plans that are currently on the horizon.

Origins of the time, mass, electric charges and magnetic monopoles are explained. The energies, electric charges and magnetic charges of the particles are defined as E = cDtDV and |q| = cDt = E/DV, and |q_m| = c²Dt, respectively, for the 3-D quantized spaces warped along the time axis direction of ct in the 4-D Euclidean space. The energy (or mass) and charges (or electric charges and magnetic charges) are the vectors along the time axis of ct in the 4-D Euclidean space. This new concept is closely connected to the wave function of the quantum mechanics. The electric charges, magnetic charges and energies have the property of the space direction independence. Magnetic monopoles (charges) are the force carrying bosons with the inside electric field time loop. Electric monopoles are the elementary fermions. Photon space fluctuations are explained with the quantized magnetic charges.

The continuous flowing spacetime forms a spacetime group G, one of its fundamental groups is the Poincare group PO(1,3), and the matter and interaction fields are representations of its intrinsic spacetime group. As a kind of quantized space-time unit, space-time group elements generate both space-time manifolds and matter. Matter and fields are aggregates of the quantum space-time within them and determine their type: the Lorentz group SO(1,3) represents a rotating spacetime corresponding to visible matter and the translation group P^1,3 represents a translational spacetime corresponding to dark matter and dark energy. The aggregation mode of space-time degrees of freedom in matter reveals that charge conjugation symmetry is the inverse symmetry of internal time of charged particles, and the external parity breaking of neutrinos is also due to their internal spatial aggregation mode.

We define degree of dependence of two events A and B in a probability space by using Boltzmann-Shannon entropy function of an appropriate probability distribution produced by these events and depending on one parameter (the probability of intersection of A and B) varying within a closed interval I. The entropy function attains its global maximum when the events A and B are independent. The important particular case of discrete uniform probability space motivates this definition in the following way. The entropy function has a minimum at the left endpoint of I exactly when one of the events and the complement of the other are connected with the relation of inclusion (maximal negative dependence). It has a minimum at the right endpoint of I exactly when one of these events is included in the other (maximal positive dependence). Moreover, the deviation of the entropy from its maximum is equal to average information that carries one of the binary trials defined by A and B with respect to the other. As a consequence, the degree of dependence of A and B can be expressed in terms of information theory and is invariant with respect to the choice of unit of information. Using this formalism, we describe completely the screening tests and their reliability, measure efficacy of a vaccination, the impact of some events from the financial markets to other events, etc. A link is available for downloading an Excel program which calculates the degree of dependence of two events in a sample space with equally likely outcomes.

We give an exact mathematical construction of a spacelike order $<$, which is dual to the standard chronological order $\ll$ in the $n$-dimensional Minkowski space $M^n$ and we discuss its order-theoretic, geometrical as well as its topological implications, conjecturing a possible extension to curved spacetimes.

In estimating the maximum and minimum index void ratios for mixtures of sand and silt, the values of several empirical constants must be determined based on the type of sand and silt involved. These empirical constants are the filling coefficient, a, and embedment coefficient, b, both of which can be determined either through lab testing or correlations. These constants are then used in equations to predict the maximum and minimum index void ratios of the sand-silt mixtures. The study reported here developed simple correlations for estimating the filling and embedment coefficients using readily obtained laboratory data. These models were found to be excellent in developing filling and embedment coefficients that accurately (R2 values typically of 0.94 or greater.) predicted values of the index void ratios for sand and silt mixtures.

Let $(\{f_n\}_{n=1}^\infty, \{\tau_n\}_{n=1}^\infty)$ and $(\{g_n\}_{n=1}^\infty, \{\omega_n\}_{n=1}^\infty)$ be unbounded continuous p-Schauder frames ($0<p<1$) for a disc Banach space $\mathcal{X}$. Then for every $x \in ( \mathcal{D}(\theta_f) \cap\mathcal{D}(\theta_g))\setminus\{0\}$, we show that \begin{align}\label{UB} \|\theta_f x\|_0\|\theta_g x\|_0 \geq \frac{1}{\left(\displaystyle\sup_{n,m \in \mathbb{N} }|f_n(\omega_m)|\right)^p\left(\displaystyle\sup_{n, m \in \mathbb{N}}|g_m(\tau_n)|\right)^p}, \end{align} where \begin{align*} & \theta_f: \mathcal{D}(\theta_f) \ni x \mapsto \theta_fx \coloneqq \{f_n(x)\}_{n=1}^\infty\in \ell^p(\mathbb{N}), \quad \theta_g: \mathcal{D}(\theta_g) \ni x \mapsto \theta_gx \coloneqq \{g_n(x)\}_{n=1}^\infty\in \ell^p(\mathbb{N}). \end{align*} Inequality (1) is unexpectedly different from both bounded uncertainty principle \textit{[arXiv:2308.00312v1]} and unbounded uncertainty principle \textit{[arXiv:2312.00366v1]} for Banach spaces.

In recent years, the exploration of space has expanded beyond the confines of our home planet, Earth, and has ignited a fervor for understanding the potential of sustaining life in extraterrestrial environments. One critical aspect of this endeavor is the cultivation of plants in microgravity—a unique environment that challenges traditional notions of plant growth and development. The Microgravity Plant Habitat, a cutting-edge apparatus designed to facilitate plant growth in space, stands at the forefront of scientific innovation in the quest for sustainable life beyond Earth.This research paper aims to explore into the complexities of the Microgravity Plant Habitat, exploring its design, functionality, and the profound implications it holds for future space exploration and colonization efforts. As humanity sets its sights on venturing further into the cosmos, the ability to cultivate plants in microgravity becomes paramount, not only for nutrition but also for the profound role plants play in maintaining life support systems and contributing to the psychological well-being of space travelers. Development of such plant habitat module will result in a bioregenerative life support system that will help in future deep space exploration and colonization of extraterrestrial planets. These modules can also cut the cost of space missions. The challenge of establishing outposts on the Moon or Mars requires thoughtful consideration of nourishment strategies. Space-based agriculture faces significant hurdles due to harsh conditions and limited resources. Researchers explore innovative solutions like hydroponics and aeroponics to meet nutritional needs and enhance well-being in extraterrestrial settlements. Beyond technological prowess, creating space bases demands a holistic approach, addressing biological and psychological aspects. Navigating deep space exploration emphasizes that food isn't just a logistical challenge but a symbol of our resilience and determination to thrive beyond Earth's confines.

Let $(\Omega, \mu)$, $(\Delta, \nu)$ be measure spaces. Let $(\{f_\alpha\}_{\alpha\in \Omega}, \{\tau_\alpha\}_{\alpha\in \Omega})$ and $(\{g_\beta\}_{\beta\in \Delta}, \{\omega_\beta\}_{\beta\in \Delta})$ be unbounded continuous 1-Schauder frames for a Banach space $\mathcal{X}$. Then for every $x \in ( \mathcal{D}(\theta_f) \cap\mathcal{D}(\theta_g))\setminus\{0\}$, we show that \begin{align}\label{UB} \mu(\operatorname{supp}(\theta_f x))\nu(\operatorname{supp}(\theta_g x)) \geq \frac{1}{\left(\displaystyle\sup_{\alpha \in \Omega, \beta \in \Delta}|f_\alpha(\omega_\beta)|\right)\left(\displaystyle\sup_{\alpha \in \Omega , \beta \in \Delta}|g_\beta(\tau_\alpha)|\right)}. \end{align} where \begin{align*} &\theta_f:\mathcal{D}(\theta_f) \ni x \mapsto \theta_fx \in \mathcal{L}^1(\Omega, \mu); \quad \theta_fx: \Omega \ni \alpha \mapsto (\theta_fx) (\alpha):= f_\alpha (x) \in \mathbb{K},\\ &\theta_g: \mathcal{D}(\theta_g) \ni x \mapsto \theta_gx \in \mathcal{L}^1(\Delta, \nu); \quad \theta_gx: \Delta \ni \beta \mapsto (\theta_gx) (\beta):= g_\beta (x) \in \mathbb{K}. \end{align*} We call Inequality (\ref{UB}) as \textbf{Unbounded Donoho-Stark-Elad-Bruckstein-Ricaud-Torr\'{e}sani Uncertainty Principle}. Along with recent \textbf{Functional Continuous Uncertainty Principle} (derived in [arXiv:2308.00312v1 [math.FA], 1 August 2023]), Inequality (\ref{UB}) also improves Ricaud-Torr\'{e}sani uncertainty principle \textit{[IEEE Trans. Inform. Theory, 2013]}. In particular, it improves Elad-Bruckstein uncertainty principle \textit{[IEEE Trans. Inform. Theory, 2002]} and Donoho-Stark uncertainty principle \textit{[SIAM J. Appl. Math., 1989]}.

Polar Mesospheric Summer Echoes (PMSEs) are radar echoes that are observed in the mesosphere during the Arctic summer months in the polar regions. By studying PMSE, researchers can gain insights into physical and chemical processes that occur in the upper atmosphere specifically in the 80 to 90 km altitude range. In this paper, we employ fully convolutional networks such as UNET and UNET++ for the purposes of segmenting PMSE from the EISCAT VHF dataset. First, experiments are performed to find suitable weights and hyperparameters for UNET and UNET++. Second, different loss functions are tested to find one suitable for our task. Third, as the number of PMSE samples used is relatively small that can lead to poor generalization. To address this, image-level and object-level augmentation methods are employed. Four, we briefly explain our findings by employing layerwise relevance propagation.

We studied generalization of a method for extending configurational studies to variables that are not exclusively geographical, in order to allow investigation of generic relationships in the built environment. We observed a number of limitations of the classical approach of configurational studies and we considered how a complex analytical method could be implemented in the study of non-topological variables, such as land use, noise pollution and financial or property rents. In order to do this we established a system of relationships based on a labeled primary graph. Categorization of the labels of the links was performed on a generic variable, specifically, the predominant use of roads. The graph was then contracted using an optimization algorithm, which we describe. The algorithm allows the network to be reduced to a more streamlined system that can better analyze the relationships between the different categories. Application of the method showed that it is faster to identify weaknesses in urban networks, and then take measures to resolve them. The case study concerns the pedestrianization of the Colosseum area in Rome.

Curriculum teaching is the basic unit to realize the cultivation and achievement of students’ ability in undergraduate colleges, and it is very important to investigate the influence mechanism of the curriculum system on the achievement states of students' ability. This paper first puts forward the theoretical system and framework of curriculum chains, and constructs a “double-energy and double-space” (DEDS) which consist of the curriculum energy efficiency space and student ability space respectively. Investigating the space-time transformation relationship of curriculum chains in the DEDS, the forward transformation model, inverse transformation model and the rheological model of the achievement states in the curriculum energy efficiency space and student ability space are established. Studying the dynamic evolution mechanism of curriculum chains within the DEDS, the dynamic evolution model, which presents the relationship between achievement states of curriculum energy efficiency/students' ability and curriculum/students' dynamic potential, are established; the control methods of courses/students' dynamic potential based on the proposed dynamic evolution model are developed to ensure the achievements of the graduates’ social ability; the evaluation and detection methods of achievement states of curriculum chains in DEDS are proposed to obtain the actual achievement states of curriculum energy efficiency and students’ ability, and this will provide effective input for the control of curriculums/students’ dynamic potential; the planning and design methods of curriculum chains facing social needs are presented, which can provide theoretical basis for the formulation of the talent training scheme and curriculum system in colleges and universities.

In this paper, we explore a new norm on L^p-space called r-norm, and hence producing a new normed space called r-normed space. Measure theoretic and functional analytic properties are covered such as the relation between r-norm and the classical p-norm. An application of r-normed space in probability theory and statsitics is also presented, notably, its role as a rigorous framework in describing the coefficient of determination.

We present a Quantum Space Model (QSM) of cosmic evolution based on the theory that space consists of energy quanta which participates in the evolution of the universe. It shows that Dark Energy is the energy of space which causes its accelerating expansion. We used the Friedmann equations to trace the history of the cosmos from a time before the Big Bang to its ultimate end. The universe started from a quantum size volume of space with high energy density.Quantum fluctuations triggered the release of energy in a Big Bang at very high temperature and pressure. It then expanded and cooled undergoing phase transitions to radiation, fundamental particles, and matter. Matter grew into galaxies, and was further consolidated by gravity into Dark Energy Stars/Black Holes, ending in a Big Crunch at about 1.380 trillion years, thus bringing the universe back to its initial state. It can stay in a Deep Feeeze inside a Black Hole and through fluctuations or other mechanism may start a new cycle in its life with a new Bang. If the Law of Conservation of Energy is universal, then the cosmos is eternal. Space and energy are equivalent just as matter and energy are. This is well founded in Planck’s energy equation. They are the two most fundamental quantities in the universe that govern cosmic evolution. The two principal long range forces are the gravitational force and the space force.The latter could be the fifth force in the universe. They may provide the clockwork mechanism that operates our eternal cyclic universe.

The article provides an overview of nanocomposites and microelectronic elements used in space electronics and radiation control systems of nuclear reactors. Only those nanocomposites and microelectronic elements are taken into account that improve their characteristics in radiation fields or remain indifferent when exposed to ionizing radiation. Considering the chemical composition of the materials of these nanocomposites and microelectronic elements, it is analyzed from which radioactive materials (RM) obtained by recycling radioactive waste (RW) such composites and microelectronic parts can be made. Thus, an alternative way of radioactive waste disposal is proposed, when these wastes are used in the form of microelectronic elements designed to operate under conditions of cosmic radiation.

Since the 21st century, China's urbanization process has been rapid development, the concept and function of urban public space in the city has been gradually paid attention to. In order to guarantee life and water, most urban construction relies on rivers, and Bridges are the most important way to communicate between urban areas. The main functional part of the bridge is the span structure, that is, the bearing structure of the bridge, and the lower part of the "gray" space formed by the bridge structure. Considering the social level, with the economic growth and urbanization development, people have brought a better living environment and quality of life, and also improved the requirements for urban public environment. In the increasingly tense urban space, how to use and transform the space under the bridge is a problem that needs to be considered and solved. In view of this problem, in this study, we try to solve the micro-transformation of space under Bridges in cities through public art from the perspective of "regional culture" and "art for all". This paper analyzes the micro-transformation of space art under Bridges in two large cities of Shanghai and Foshan, namely, the space under Bridges under Songhong Road in Shanghai, the space under Bridges under Central Of Suzhou River and the space under Bridges under Pingsheng Bridge in Foshan. This paper discusses the cultural intervention of "regional culture" in the micro-transformation of the space under the bridge, and the influence and effect of "art for all" on the public art space under the bridge after the transformation to the community and the public.

Urban green spaces provide a range of environmental and health benefits, which may become even more critical during times of crisis such as the current COVID-19 pandemic. However, with a radical shift in mobility, additional concerns over safety, and access temporarily restricted during the implementation of social distancing policies, the experience and use of urban green spaces may be reduced. This is particularly concerning for densely populated cities like New York, considered the first U.S. epicenter or vanguard of the outbreak. To better understand the impact of COVID-19 on the perception and use of urban green spaces, we conducted a social survey during the early months of the Covid-19 pandemic in New York City (May 13 - June 15, 2020). The results of the survey show respondents continued to use urban green spaces during the pandemic and consider them to be more important for mental and physical health than before the pandemic began. However, the study revealed a pattern of concerns residents have about green space accessibility and safety, and found key differences between the concerns and needs of different populations, suggesting a crucial role for inclusive decision-making, support for additional management strategies, and urban ecosystem governance that reflect the differential values, needs and concerns of communities across the City. As urban centers face looming budget cuts and reduced capacity, this study provides some empirical evidence to illustrate the value of urban green spaces as critical urban infrastructure, and may have implications for funding, policy, and management, of urban green spaces in NYC, with potential applications to other cities, particularly during times of crisis.

Information can be considered as the most fundamental, philosophical, physical and mathematical concept originating from the totality by means of physical and mathematical transcendentalism (the counterpart of philosophical transcendentalism). Classical and quantum information, particularly by their units, bit and qubit, correspond and unify the finite and infinite. As classical information is relevant to finite series and sets, as quantum information, to infinite ones. A fundamental joint relativity of the finite and infinite, of the external and internal is to be investigated. The corresponding invariance is able to define physical action and its quantity only on the basis of information and especially: on the relativity of classical and quantum information. The concept of transcendental time, an epoché in relation to the direction of time arrow can be defined. Its correlate is that information invariant to the finite and infinite, therefore unifying both classical and quantum information.

We derive an uncertainty principle for Lipschitz maps acting on subsets of Banach spaces. We show that this nonlinear uncertainty principle reduces to the Heisenberg-Robertson-Schrodinger uncertainty principle for linear operators acting on Hilbert spaces.

An odd-dimensional sphere admits a killing vector field, induced by the transform of the unit normal by the complex structure of the ambiant Euclidean space. In this paper, we study orientable hypersurfaces in a Euclidean space those admit a unit Killing vector field and find two characterizations of odd-dimensional spheres. In first result, we show that a complete and simply connected hypersurface of Euclidean space Rn+1, n&gt;1 admits a unit Killing vector field ξ that leaves the shape operator S invariant and has sectional curvatures of plane sections containing ξ positive satisfies S(ξ)=αξ, α mean curvature if and only if n=2m−1, α is constant and the hypersurfaces is isometric to the sphere S2m−1(α2). Similarly, we find another characterization of unit sphere S2(α2) using the smooth function σ=g(S(ξ),ξ) on the hypersurface.

We prove that a diffeological space is diffeomorphic to the categorical join of any generating family of plots.

This paper presents a method for producing a gravity field through an electromagnetic field. The electromagnetic field can produce a positive or negative gravity field. The relationship between gravity force and electromagnetic is unknown. Former studies by theoretical physics predict the relationship between these two forces. Based on the general balance theory in six dimensions of space and time, the electromagnetic field was studied from this viewpoint. Three-dimensional waves oscillate in the fourth dimension and electromagnetic waves distort space-time. Aggregating these distortions can behave like a positive or negative gravity field. Consequently, the production of energy is possible from gravitational fields.

Let $(\Omega, \mu)$, $(\Delta, \nu)$ be measure spaces. Let $(\{f_\alpha\}_{\alpha\in \Omega}, \{\tau_\alpha\}_{\alpha\in \Omega})$ and $(\{g_\beta\}_{\beta\in \Delta}, \{\omega_\beta\}_{\beta\in \Delta})$ be continuous 1-Schauder frames for a Banach space $\mathcal{X}$. Then for every $x \in \mathcal{X}\setminus\{0\}$, we show that \begin{align*} \mu(\operatorname{supp}(\theta_f x)) \geq \frac{1}{\displaystyle\sup_{\alpha \in \Omega, \beta \in \Delta}|f_\alpha(\omega_\beta)|}, \quad \nu(\operatorname{supp}(\theta_g x))\geq \frac{1}{\displaystyle\sup_{\alpha \in \Omega , \beta \in \Delta}|g_\beta(\tau_\alpha)|}. \end{align*} where \begin{align*} &\theta_f: \mathcal{X} \ni x \mapsto \theta_fx \in \mathcal{L}^1(\Omega, \mu); \quad \theta_fx: \Omega \ni \alpha \mapsto (\theta_fx) (\alpha):= f_\alpha (x) \in \mathbb{K},\\ &\theta_g: \mathcal{X} \ni x \mapsto \theta_gx \in \mathcal{L}^1(\Delta, \nu); \quad \theta_gx: \Delta \ni \beta \mapsto (\theta_gx) (\beta):= g_\beta (x) \in \mathbb{K}. \end{align*} This solves a problem asked by K. M. Krishna in the paper 'Functional Continuous Uncertainty Principle' \textit{[arXiv:2308.00312v1]}.

Let $(\Omega, \mu)$, $(\Delta, \nu)$ be measure spaces. Let $(\{f_\alpha\}_{\alpha\in \Omega}, \{\tau_\alpha\}_{\alpha\in \Omega})$ and $(\{g_\beta\}_{\beta\in \Delta}, \{\omega_\beta\}_{\beta\in \Delta})$ be continuous p-Schauder frames for a Banach space $\mathcal{X}$. Then for every $x \in \mathcal{X}\setminus\{0\}$, we show that \begin{align}\label{CUE} \mu(\operatorname{supp}(\theta_f x))^\frac{1}{p} \nu(\operatorname{supp}(\theta_g x))^\frac{1}{q} \geq \frac{1}{\displaystyle\sup_{\alpha \in \Omega, \beta \in \Delta}|f_\alpha(\omega_\beta)|}, \quad \nu(\operatorname{supp}(\theta_g x))^\frac{1}{p} \mu(\operatorname{supp}(\theta_f x))^\frac{1}{q}\geq \frac{1}{\displaystyle\sup_{\alpha \in \Omega , \beta \in \Delta}|g_\beta(\tau_\alpha)|}. \end{align} where \begin{align*} &\theta_f: \mathcal{X} \ni x \mapsto \theta_fx \in \mathcal{L}^p(\Omega, \mu); \quad \theta_fx: \Omega \ni \alpha \mapsto (\theta_fx) (\alpha):= f_\alpha (x) \in \mathbb{K},\\ &\theta_g: \mathcal{X} \ni x \mapsto \theta_gx \in \mathcal{L}^p(\Delta, \nu); \quad \theta_gx: \Delta \ni \beta \mapsto (\theta_gx) (\beta):= g_\beta (x) \in \mathbb{K} \end{align*} and $q$ is the conjugate index of $p$. We call Inequality (\ref{CUE}) as \textbf{Functional Continuous Uncertainty Principle}. It improves the Functional Donoho-Stark-Elad-Bruckstein-Ricaud-Torr\'{e}sani Uncertainty Principle obtained by M. Krishna in \textit{[arXiv:2304.03324v1, 2023]}. It also answers a question asked by Prof. Philip B. Stark to the author.

In physics, symmetry is mostly about the symmetry between elementary particles, between matter and antimatter. In the universe, we have two fundamental types of energy: energy of matter and energy of space. These two energies have a symmetry that is not geometry type, not electric charge type, it is energy type. Every physical object with mass m symmetrically diminishes the energy density of space in its center exactly for the amount of its mass. This symmetry of matter and space energies is the physical source of gravity that is also valid in the centre of black holes.

Lunar seismology is a critical area of research, providing insights into the Moon's internal structure, composition, and thermal history, as well as informing the design of safe and resilient habitats for future human settlements. This paper presents the development of a state-of-the-art, three-axis broadband seismometer with a low frequency range of 0.001-1 Hz and a target sensitivity over an order of magnitude greater than previous Apollo-era instruments. The paper details the design, assembly, methodology and test results. We compare the acceleration noise of our prototype and commercial seismometers across all three axes. Increasing the test mass and reducing its natural frequency may further improve performance. These advancements in seismometer technology hold promise for enhancing our understanding of the Moon's and other celestial bodies' internal structures, and for informing the design of future landed missions to ocean worlds.

The G2 gas cloud motion data and the scarcity of observations on the event horizon-scale distances have challenged the comprehensiveness of the central supermassive black hole model. In addition, the Planck Legacy 2018 release has preferred a positively curved early Universe with a confidence level higher than 99%. This study investigates the impact of the background curvature and its evolution over the conformal time on the formation and morphological evolution of central compact objects and the consequent effect on their host galaxies. The formation of a galaxy from the collapse of a supermassive gas cloud in the early Universe is modeled based on interaction field equations as a 4D relativistic cloud-world that flows and spins through a 4D conformal bulk of a primordial positive curvature considering the preference of the Planck release. Owing to the curved background, this scenario of galaxy formation reveals that the core of the galaxy undergoes a forced vortex formation with a central event horizon leading to opposite vortices (traversable wormholes) that spatially shrink while evolving in the conformal time. It indicates that the galaxy and its core are formed in the same process whereas the surrounding gas clouds form the spiral arms due to the frame-dragging induced by the fast-rotating core. It demonstrates that the accretion flow onto the central supermassive compact object only occurs at the central event horizon of the two opposite vortices while their other ends eject the relativistic jets. This can elucidate the relativistic jet formation and explain the G2 gas cloud motion if its orbit is around one of the vortices but at a distance from the central event horizon. The gravitational potential of the early curved bulk could contribute to galaxy formation while the present spatial flatness deprives the potential of bulk which could lead to galaxy quenching. The formation of a galaxy and its core simultaneously could explain the growth of the supermassive compact galaxy core to a mass of ~10⁹ M_⊙ at just 6% of the current Universe age.

Indigenous knowledge is proven to be one of the foundations of sustainable land and marine management. While indigenous knowledge is acknowledged as of important factors on maintenance of biodiversity of the planet, it also ensures the sustenance of social and economic system of indigenous community. To facilitate the application of indigenous knowledge on management of customary forest in Indonesia, since 2012, the Government of Indonesia has been providing formal access for indigenous communities to their forests to maintain forest sustainability and to enhance the welfare of indigenous community. Nonetheless, the achievement of sustainable development goals in the scope of forest and conservation area management is threatened by various competing interests and power imbalance, which mostly leads to conversion of naturally vegetated area, as well as the inability of the community to integrate new economic opportunities to its institution. Moreover, the Government of Indonesia has not been regulating the involvement of indigenous community on the management of conservation area. Most importantly, such a program provides no reference on indigenous community, especially on the assessment of authenticity of indigenous community’s forest. Cultural space methodology may fill the aforementioned gaps. The methodology was developed based on the notion of cultural space and land administration, particularly the people-and-land/marine space relationship. Moreover, such a methodology was also constructed based on the experiences of agricultural and maritime communities in Indonesia on the administration of their territories. The methodology provides a procedure to convert information on the interrelation of indigenous community, its cultural space in forest and conservation area, and indigenous knowledge into geospatial information and data that represent the cultural space unit as a geographic feature. Therefore, such methodology may be utilised to assess the authenticity of a long-existing relationship between a community, especially an indigenous one, and its land, particularly that serves conservational function.

Dilation of contractions on Hilbert space and Banach space is classical. Recently, dilations theory has been put in the setting of sets, vector spaces, p-adic Hilbert spaces and modules. In this paper, we derive important dilation results for self-adjoint morphisms on indefinite inner product modules over *-rings of characteristic 2. More precisely, we prove indefinite inner product versions of Halmos dilation, Egervary N-dilation and Sz.-Nagy dilation.

Mathematical models across the applied sciences often utilize a standard methodological representation called a state variable formulation more commonly referred to as state space form. Recent research in unmanned underwater vehicle motor turbine blade thermal modeling for fatigue-life is generalized here permitting the proposed novel state space from to be applied to electrodynamics, motion mechanics, and many other disciplines. Proposed here is a very compact form inherently representing time variance, with a convenient presentation of dynamic variables applicable to all proper transfer functions, where all the distinct, real poles, zeros and gain of the transfer function appear as explicit components in the state space. The resulting manifestation simplifies utilization of the state space methods broadly across the applied sciences.

In recent years, urban planners and designers have paid attention to improve the creative factors in big and small cities in order to make the urban environment more attractive. It seems that improving desirable urban environmental qualities and walkability approaches such as flexibility, happiness, and vitality, provides the necessary background for creating creative urban spaces. The case study zone is urban walkways in Rasht that which has been completed four years ago. In this paper, after conceptualizing the nature of the creative city, as well as reviewing the views of the thinkers regarding the qualities of the environment, a conceptual model of creative urban space has been developed. Then, the indicators and criteria of creative urban space have been evaluated through the questionnaire and analysis through SPSS software and regression model, Pearson and Friedman. The result of the analyses of the five spatial, functional, social, perceptual, and environmental components and their relationship is expressed that factors such as paving streets, the development of local markets, the Suitability of urban walkways for physically and mentally handicapped people, the use of cultural elements, the use of diverse urban furniture and nightlife after building urban walkways play an important role in the realization of urban creative space in Rasht city.

The evolution of life on the planet Earth is happening primarily in the universe and secondary on the Earth. We will examine in this article evolution of life as the cosmic phenomena. In our model multidimensional time-invariant superfluid quantum space that is the fundamental arena of the universe and represents about 95% of the energy in the universe has stable entropy. The increase of entropy happens only by about 5% of the energy in the universe that is in the form of matter. The evolution of life in our model is a process of matter organization into living systems that tends to develop towards the constant entropy of the time-invariant multidimensional quantum space. This process runs in the entire universe. The development of life into intelligent organisms is the universal process running throughout the entire universe.