In this paper, it is proved that s-iteration with error and Picard-Mann iteration with error iterative processes converge strongly to the unique fixed point of Lipschitzian strongly pseudo-contractive map. This convergence is almost -stable and -stable. Applications of these results to the operator equations, where is a strongly accretive and accretive mappings of into itself.

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>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.

The paper introduces and describes the recent and still ongoing development activities performed in Luxembourg for In-Orbit Attach Mechanisms for (Drag) Sails Modules to be operated from Space Tugs. After some preparatory work aiming at understanding the possible operational aspects, three designs have been completed for their 3D (Metal and Plastic) Printing. The Plastic-printed prototype underwent a series of automated tests where a robotic arm, equipped with an advanced force sensor, replicated four docking scenarii in ideal and degraded modes. The observation of the forces and torques behaviors at and after impact allowed to characterize the typical patterns for the various contacts but also, to identify a type of impact potentially dramatic for the safety of the docking and its equipment: in case of off-axis approach, “point” contacts shall be avoided as they instantaneously transfer the total kinetic energy in a small area that could break.

This article begins with exploring fundamental limits in the universe. It examines key principles, such as the uniformity of physical laws and Energy conservation, that lead to maximum speed, locality, and maximum density. These universal limits govern physical phenomena, leading to very interesting results.I demonstrate that quarks and leptons comprise smaller entities named "Quantum Black Holes." These Quantum black holes are relativistically rotating miniature charged black holes consisting of a single core at the highest possible density. Quantum black holes are the only structures small enough in space-time capable of keeping all charges quantized (including gravitational charges.)By the end of the article, I prove that Quantum black holes explain the deficiencies of SM. They facilitate explanations of quantized gravity, the nature of Luminous and dark Matter, establishing the Mass, size, and (quantized) charges quantities of elementary particles, the nature of neutrino oscillations, and more. Elementary particles release their Energy outward, altering the curvature of nearby space-time and providing new insights into the nature of space-time curvature change. With this understanding, we can characterize movements and processes in local space-time using five sets of equations simultaneously: four representing the four charge types and one representing Dark Matter.

On the basis of the golden ratio and the compasseses, every angle was divided into three equal parts. In general, it has been proven that the problem of triangulation of an angle cannot be solved on the basis of the golden ratio and the expanding of the angle. The relationship of golden relativity with Pi number and Euler's number has not been investigated to solve impossible problems. According to the investigation of events in six-dimensional space-time, with the simultaneous movement of two arms of the compasses based on the golden ratio, every angle was divided into three equal parts. The growth rate based on the golden ratio is the key to solving the most intractable mathematical and physical problems.

We give a simple proof of the Chen inequality for the Chen invariant $\underbrace{\delta (2,...,2)}_{k\mbox{ terms}}$ of submanifolds in Riemannian space forms.

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.

A perirectal abscess, while typically considered benign, has the potential to invade extraperitoneal spaces, including the space of Retzius, resulting in complications with severe systemic illness. It is postulated that there is communication within adipose tissue between the pararectal spaces and the vesical extraperitoneal space anteriorly, secondary to the termination of the umbilical-vesical fascia at the reflection of the vesical peritoneum. While occurrences of perirectal abscess ex-tending to the extraperitoneal space are infrequent, a thorough understanding of the anatomical structure, physiology, and the subsequent therapeutic approach remains crucial. For assessment, a computed tomography scan with intravenous contrast is preferred for evaluation, given the probable insidious and nonspecific nature of the clinical presentation, physical exam signs, and even laboratory studies. Primary therapeutic modalities involve immediate resuscitation, intra-venous administration of broad-spectrum antibiotics, and percutaneous drainage. Surgical in-tervention may become necessary in cases where there is no prompt improvement in septic progression. Additionally, the underlying comorbidities and baseline illness could be indicative of unfavorable outcomes. If fever or sepsis is not efficiently controlled, a more comprehensive workup or intervention should be contemplated, considering the associated higher risks of complications and mortality rates. In this study, we presented the case of a 68-year-old male with diffuse pain located in the lower abdomen. Fortunately, an immediate computed tomography scan played a pivotal role in iden-tifying a perirectal abscess with upward extension to the space of Retzius, which was subse-quently treated appropriately. Above all, this rare case presentation underscores the anatomic complexity within pelvic compartments and emphasizes the importance of maintaining high-index suspicions and analyzing overall differential diagnosis.

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.

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.

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 introduce the concept of Nano Beta Closure, Nano Beta Interior and study the relationship between them also study some of their properties. Based on these notions we introduced the topological Approach to Decision Making and Its Application in the Medical Field" which describes the use of topological methods in decision-making, specifically through the utilization of nano beta closure and nano beta interior. These mathematical tools are applied in the medical field to improve diagnostic accuracy and aid in treatment planning. The authors demonstrate the effectiveness of this approach through a case study on the diagnosis of Chronic Kidney. The results show that the topological approach using nano beta closure and nano beta interior provides a reliable and accurate method for medical decision-making. Finally, we introduce a medical application for disease groups patients of with chronic kidney. To identify the main causative agent of kidney disease. where using this approach, the medical team can identify the specific areas of the kidney that are affected by the infection, as well as the extent of damage and any potential complications. This information is used to create an individualized treatment strategy that is customized to meet the specific requirements of the patient. and medical history. We write an algorithm that can be a helpful tool for doctors to utilize in diagnosing infection disease Chronic Kidney infections. By utilizing this approach, clinicians can provide accurate diagnoses, develop effective treatment plans, and ultimately improve patient outcomes. finally, we show that fractals hold significant importance in future nano topological generation of the human factor. Their unique properties and self-similar patterns offer insights into the complex organization of biological systems and provide a foundation for designing advanced Nanosystems.

Evolutionary psychology theories propose that contact with green, natural environments may benefit physical health, but little comparable evidence exists for brown, natural environments, such as the desert. In this study, we examined the association between “brownness” and “greenness” with fasting glucose among young residents of El Paso, Texas. We defined brownness as the surface not covered by vegetation or impervious land within Euclidian buffers around participants’ homes. Fasting glucose along with demographic and behavioral data was obtained from the Nurse Engagement and Wellness Study (N = 517). We found that residential proximity to brownness was not associated with fasting glucose when modeled independently. In contrast, we found that residential greenness was associated with decreased levels of fasting glucose, despite the relatively low levels of greenness within the predominantly desert environment of El Paso. A difference between the top and bottom greenness exposure quartiles within a 250 m buffer was associated with a 3.5 mg/dL decrease in fasting glucose levels (95% confidence interval: -6.2, -0.8). Our results suggest that within the understudied context of the desert, green vegetation may be health-promoting to a degree that is similar to other, non-desert locations in the world that have higher baselines levels of green.

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”.

Immersive Unit Visualization is an emergent form of visualization that arose from Immersive Analytics where, unlike traditional visualizations, each data point is represented by an individual visual mark in an immersive virtual environment. This practice has focused almost exclusively on virtual reality, excluding augmented reality (AR). This article develops and tests a prototype of an immersive Unit Visualization (Floating Companies II) with two AR devices: head-mounted display (HMD) and hand-held display (HHD). Results from the testing sessions with 20 users were analyzed through qualitative research analysis and thematic coding indicating that, while the HHD enabled a first contact with AR visualization on a familiar device, HMD improved the perception of hybrid space by supporting greater stability of virtual content; wider field of view; improved spatial perception; increased sense of immersion; and more realistic simulation, which impacted on information reading and sense-making. The materialization of abstract quantitative values into concrete reality through its simulation in the real environment and the ludic dimension stand out as important opportunities of this type of visualization. This paper investigates the aspects distinguishing two experiences regarding data visualization in hybrid space; and characterizes ways of seeing information with AR, identifying opportunities to advance information design research.

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.

Space exploration presents vast prospects for scientific, industrial, and economic progress. This paper introduces the MeSat mission as a pioneering approach to Mars exploration. MeSat aims to deepen our understanding of Martian conditions and resources by employing an optimized Earth-to-Mars trajectory, enabling a comprehensive study of the Martian atmosphere and surface. The mission comprises a Cargo Microsatellite hosting three 6U CubeSats and two 3U CubeSats, deployed into four separate Mars orbits forming a constellation. Each CubeSat carries distinct payloads: a THz radiometer for water detection, a high-resolution surface camera, a top-tier spectrometer, and a Fourier Transform Spectrometer (FTS) for wind speed readings. This paper focuses on two pivotal innovations: the development of a 183GHz radiometer payload for detecting water on Mars and a optimal mission design algorithm that analyzes a fuel-efficient low-thrust trajectory from Earth to Mars. Regarding the THz payload for water detection, a subharmonic Schottky diode-based mixer is meticulously designed to efficiently down-convert radio signals. The down-converted signals are carefully analyzed using a customized Do-It-Yourself (DIY) spectrum meter, which facilitated the capture and processing of acquired data. To provide the necessary Local Oscillator signals for the mixer, a Tripler employing three-anode Schottky diodes is developed. Additionally, the Tripler requires a signal generator for its entry frequency, which is addressed by developing a DIY signal generator. Together, these components, comprising the Schottky diode mixer, Tripler, and DIY circuits, collectively form the complete THz payload, demonstrating exceptional power efficiency with a total consumption of only 3.7W. The study employs a dual-step hybrid optimization algorithm (PSO-Homotopy) to analyze fuel-efficient low-thrust trajectories from Earth to Mars, incorporating the Ephemeris dynamics model to account for gravitational perturbations in the entire solar system. In practical mission design, crucial factors like hyperbolic excess velocity, diverse opportunities for Earth launch and Mars rendezvous, varied propulsion systems, and Time of Flight (TOF) play vital roles in trajectory optimization.

In the framework of a multiplicative metric space. We have discuss some Properties of convex structures in pseudo multiplicative metric space and have applied these properties toiobtain alfixed point results in complete pseudo. It would be interesting to prove some further results in such metric spaces with completeness property.

In this paper, we define Ulisse Dini-type helicoidal hypersurface with spacelike axis in Minkowski 4-space ${\mathbb{E}}_1^4$ . We compute the Gaussian and the mean curvature of the hypersurface. Moreover, we obtain some special symmetry to the curvatures when they are flat and maximal.

A model of space-time is presented, whose origin is set before the appearance of any universe. It uses concepts of previous work, a central one being that the information about the laws of nature is stored locally everywhere in space such that all physical processes obey them. Since information storage is bound to matter or energy, space is assumed to consist of dark energy (DE), which thus assumes an importance far beyond its function as a stopgap for an energy deficit in our universe (U). The primordial state (PS) is a timeless and relatively large space of 3 dimensions described by a Wheeler DeWitt (WDW) equation, whose solution is interpreted as an arrangement of very many space quanta and possesses all the characteristics of the time-honored concept of the unmoved mover. The comparison of WDW solutions belonging to different mass densities of the DE favors one in which the space quanta are mini black holes, and allows the space quanta to be imagined as mass points that are kept at a distance compatible with the quantum volume by the Pauli principle or something equivalent. Triggered by an increase in probability, the PS is followed by a time-dependent state of space expansion (ES). The concomitant emergence of time occurs in a lightning huge crash, consuming almost all DE of the PS. The subsequent expansion proceeds in quantum leaps, whose huge size emerges from a WDW equation novelly derived from the time-dependent classical expansion solution, and is also used as size of the PS. Information is assumed to be geometrically stored in arrangements of space quanta similar to how genetic information is stored in DNA molecules. During space expansion information must be transferred from already existing "information quanta" to new ones. This requires time, slows down the expansion and is taken into account by a friction term in the cosmological momentum equation. Sinc e the Friedmann-Lemaître (FL) equation remains fully valid, the model can exclusively be based on recognized equations, so that the assumptions used to build it can be understood as interpretations.

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.

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.

To support pathologists in breast tumor diagnosis, deep learning plays a crucial role in the development of histological whole slide image (WSI) classification methods. However, automatic classification is challenging due to the high-resolution data and the scarcity of representative training data. To tackle these limitations, we propose a deep learning-based breast tumor gigapixel histological image multi-classifier integrated with a high-resolution data augmentation model to process the entire slide by exploring its local and global information and generating its different synthetic versions. The key idea is to perform classification and augmentation in feature latent space, reducing the computational cost while preserving the class label of the input. We adopt a deep learning-based multi-classification method and evaluate the contribution given by a Conditional Generative Adversarial Network-based data augmentation model on the classifier’s performance for three tumor classes in the BRIGHT Challenge dataset. The proposed method has allowed us to achieve an average F1 equal to 69.5, considering only the WSI dataset of the Challenge. The results are comparable to those obtained by the Challenge winning method (71.6), also trained on the annotated tumor region dataset of the Challenge.

We prove Lp estimates of a class of generalized Marcinkiewicz integral operators with mixed homogeneity on product domains. By using these estimates along with an extrapolation argument we obtain the boundedness of our operators under very weak conditions on the kernel functions. Our results in this paper improve and extend several known results on both generalized Marcinkiewicz integrals and parabolic Marcinkiewicz integrals on product domains.

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.

This study investigates the impact of rotor spacing on the aerodynamic performance of a coaxialcopter. It has been observed that a small distance between two rotors can result in significant interaction between the propellers, consequently affecting the rotor's aerodynamic efficiency. Exploiting this characteristic, the present research introduces a coaxialcopter with variable rotor spacing. Employing finite element numerical simulations, we assess the aerodynamic behavior of this novel configuration. Through comprehensive measurements and analysis of its aerodynamic performance across varying rotor spacings from 0.1R to 1R, we validate the effectiveness of a rotor spacing control strategy for enhancing takeoff maneuvers. Our numerical simulation results reveal that the performance characteristics of both upper and lower rotor converges toward that of a single rotor as pitch ratio increases, along with the reduce of their thrust fluctuations and aerodynamic performance periodicity. Considering stable power consumption patterns and endurance performance, we analysis the interrelations binding of pitch distance of the rotors, rotational speed, and pitch angle, vis-à-vis the thrust coefficient and power coefficient. Through parameter optimization method, we demonstrate that adjusting rotor spacing offers a practical means to enhance payload capacity without increasing power input, thereby improving the efficiency, which validates the practicality and efficacy of the parameter optimization approach. Furthermore, optimizing rotor spacing for specific operational scenarios enhances overall aerodynamic performance, suggesting a viable flight control strategy for takeoff and landing conditions.

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.

Research has shown that hands-on projects promote stem education, namely, via problem-solving. CanSat, literally 'satellite in a can', is a stem educational project promoted by the European Space Agency. This paper addresses this issue by researching this STEM project, which demonstrates how problem-solving can be achieved in secondary-level students within the framework of the CanSat. We use qualitative techniques of data collection and analysis. The results showed that students use sophisticated thinking strategies to process information within this interdisciplinary project: (a) cognitive testing, cognitive organization, cognitive regulation, and monitoring, in addition to computer language and physical–mathematical calculations, are cognitive and metacognitive behavior strategies revealed in the CanSat; (b) problem-solving was suggested as a specific model, where students’ higher cognitive and metacognitive ordering processes deepen in project development; (c) computational, lateral, or divergent and convergent thinking were detected as thinking types of students associated with and mobilized in the course of problem-solving, The findings of this research have practical implications for STEM education in space science. Hands-on projects using problem-solving are an essential strategy to promote STEM education. Additionally, they are a starting point to promote meaningful learning and new thinking types.

Due to the advantages such as low power consumption and higher concealment, deceptive jamming against synthetic aperture radar (SAR) receives extensive attention during the past decades. However, the large scene deception jamming is still a challenge because of the huge computing burden. In this paper, we propose a new large scene deceptive jamming algorithm. First, the time-delay and frequency-shift (TDFS) algorithm is introduced to improve the jamming processing speed. The system function of jammer (JSF) for a fake scatter is simplified to the multiplication of the scattering coefficient, a time-delay term in range dimension and a frequency-shift term in azimuth dimension. Then, in order to solve the problem that the effective region of the TDFS algorithm is limited, the scene deceptive jamming template is divided into several blocks according to the SAR parameters and imaging quality control factor. The JSF of each block is calculated by the TDFS algorithm and added together to achieve the large scene jamming. Finally, the correction algorithm in squint mode is derived. The simplification and parallel block processing could improve the calculation efficiency significantly. The simulation results verified the validity of the algorithm.

In our previous papers [1,3], using only the concepts of the zero-point energy and quantized space–times, all the fields including gravity were explained. However, the previous papers had the following limitations: First, the concept of the quantized space-time must be experimentally confirmed. Second, we should clarify the meaning of the quantized Einstein’s gravity equation, which is derived in [1]. Moreover, in another paper [2], we succeeded in describing the neutrinos’ self-energy and their oscillations. However, this paper assumes the rest energy of 3-leptons in advance, which is why we needed to uncover the reason why leptons have 3-generations. As mentioned, using the concepts of the zero-point energy and quantized space–times, we derived the quantized Einstein’s gravity equation in our previous paper [1]. The paper provides an analytical solution of this equalized Einstein’s equation, which implies the conservation of angular momentum in terms of quantized space–times. Employing this solution and without the standard big bang model, a unique form of acceleration equation for the acceleration-expansion universe is derived. Moreover, the temperature of the cosmic microwave background (CMB) emission is also obtained. Further, this solution results in an analytical (not numerical) derivation of the gravity wave. Moreover, based on the configuration of quantized space–times in terms of both electric and magnetic fields, we analytically attempted to calculate every equation in terms of electromagnetic and gravity fields, using the solution of the quantized Einstein’s gravity equation. As a result of this theory, first the calculated acceleration and temperature of CMB emission agree with the measurements. Furthermore, the analytical solution of the quantized Einstein’s gravity equation resulted in all the laws of electromagnetic and gravity fields in addition to the analytically derived gravity wave, which agrees well with the recent measurements. Moreover, the calculations of the energies in the basic configuration of the quantized space–times resulted in all 3-leptons’ rest energies. Considering this basic configuration is uniformly distributed everywhere in the universe, we can conclude that τ-particles or static magnetic field energy derived from the basic configuration of the quantized space–times is the identity of dark energy, which also distributes uniformly in the universe.

We emphasize the point that, standard model of cosmology is basically a model of classical general relativity and it seems inevitable to have a revision with reference to quantum model of cosmology. Utmost important point to be noted is that, ‘Spin’ is a basic property of quantum mechanics and ‘rotation’ is a very common experience. In this context, we propose five assumptions in line with Planck mass as the baby universe. We appeal that, 1) Universe can be modeled as a time-reversed black hole (a white hole) with rotation and light speed expansion, and 2) ‘Light speed expanding cosmic space’ can be called as ‘Flat space’. With reference to light speed expansion, if one is willing to re-define cosmic red shift as [z/(1+z)], without considering Lambda cosmology model of matter density fractions, light travel distances can be reproduced with a marginal error of +8.6% at z =1.2, (i.e. traditional light travel distance is 8.6% higher than our estimate), 0% at z = 11.5 and -5.5% at z = 1200.( i.e. traditional light travel distance is 5.5% lower than our estimate). Advantages of our model are, 1) A quantum model of cosmology can be developed with unification of general theory of relativity and quantum mechanics. 2) Tension in estimating the current Hubble parameter can be eliminated via scaled Hawking’s black hole temperature formula with great confidence. 3) Galactic dark matter and visible matter can be studied in a unified manner. 4) Galactic light travel distances can be estimated very easily without matter density fractions. 5) Big Bang and Inflation like non-general relativistic concepts can be relinquished with further study.

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.

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.

Extensive in-situ resource utilisation (ISRU) will be essential to enable long-duration stays on Luna and Mars and reduce reliance on resupply from Earth. Early development of ISRU technologies has focused on standalone capabilities for specific targets related to life support and ascent propellant. An unexplored opportunity remains for greatly expanding the scope of materials that can be supplied by ISRU, and for integrating various technology platforms into a larger system. Recent advances in power-to-X technology aimed at decarbonising the global economy have made it possible to drive key chemical processes using electricity with small-scale, modular reactor. This paper proposes a vision for an integrated system of ISRU processes based on power-to-X technology to produce oxygen, hydrogen, water, methane, polymers, metal alloys, and synthetic fertilisers, using Martian regolith, atmosphere, and ice. A ‘building block’ strategy is adopted to convert raw materials into versatile intermediaries, which can then be combined to form essential products. A wider range of raw materials are available on Mars compared to Luna, suggesting greater opportunity for ISRU deployment to compensate for the greater time and cost requirements for a Mars resupply mission.

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 .

The onset of coronavirus disease 2019 (COVID-19), an infectious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has sparked unprecedented change. Due to the public health guidelines imposed during the COVID-19 pandemic, there is no longer sufficient street traffic for remaining buskers to generate sufficient revenue, leading a majority of street musicians to pursue remote music production. However, real-time music production is notoriously difficult due to the excessively high latencies that current video call platforms such as Zoom and Google Meet harbor. In this paper, we propose an architecture for a platform with end-to-end, near-lossless audio transmission tailored specifically to online joint music production, called Latent Space. We discuss the usage of a recurrent autoencoder with sequence-aware encoding (RAES) and a 1D convolutional layer for audio compression, which we dub ClefNet, as well as propose a new evaluation metric for naive autoencoders (AEs), MSE-DTW loss, which combines the traditional mean square error (MSE) loss function with dynamic time warping (DTW) to prevent an increase in loss when the target sequence predicted by the AE is strictly a temporal variation of the source sequence. Moreover, we detail the logistics of a live system implementation which uses the Web Audio API to extract raw audio samples in real-time to feed into our client-side model before relaying the traffic using peer-to-peer WebRTC technology. The Latent Space platform can be accessed at https://latent-space.tech, and the code and data can be found under the MIT License at https://github.com/rvignav/ClefNet.

A model of a single-server queuing-inventory system (QIS) with catastrophes and a finite waiting room for consumer customers (c-customers) has been developed. When a catastrophe occurs, all inventory in the system's warehouse is destroyed, but c-customers in the system are still waiting for restocking. In addition to c-customers, negative customers (n-customers) are also taken into account, which displaces one c-customers (if any). The policy (?, ?) is used to replenish stocks. If upon arrival of the c-customer the inventory level is zero, then according to Bernoulli’s scheme this c-customer is either lost or joining the queue. The mathematical model of the studied QIS is constructed in the form of a two-dimensional continuous-time Markov chain (2D CTMC). Exact and approximate methods for calculating the steady-state probabilities of constructed 2D CTMCs are developed and closed-form expressions are derived for calculating the performance measures. The results of numerical experiments are presented, demonstrating the high accuracy of the developed approximate formulas, as well as the behavior of performance indicators depending on the reorder point. In addition, an optimization problem is solved to obtain the optimal reorder point to minimize the expected total cost.

By defining a constant probabilistic orbit of and iterated functions, the stability dynamics of these functions in possible interactions through connectivity provides the formation of a dynamic fixed point as a metric space between both iterated functions. The presence of a dynamic fixed point identifies qualitatively phases of iteration time lengths and interaction orbits of the event. Qualitative results show that the greater the average distance from one of the functions to the fixed point of the other (all possible solutions), the higher the iteration expression on time (false asymptotic effect) of one of the functions and in the opposite hand, the lower the average distance, the higher orbit’s interactions proximity between iterated functions (stability). This feature reveals asymptotic (well-defined) behavior between functions f and g within a well-defined Lyapunov stability.

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.

In the coded pulse scanning light detection and ranging (LIDAR) system, the number of laser pulses used at a given measurement point changes depending on the modulation and the method of spreading used in optical code-division multiple access (OCDMA). The number of laser pulses determines the pulse width, output power, and duration of the pulse transmission of a measurement point. These parameters determine the maximum measurement distance of the laser and the number of measurement points that can be employed per second. In this paper, we evaluate the performance and characteristics of combinations of modulation and spreading technology that can be used for OCDMA, and study optimal combinations according to varying operating environments.

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.

This paper is devoted to the study of multi-dimensional integral transform with Fox H-function in the kernel in weighted spaces integrable functions in the domain R+n with positive coordinates. Mapping properties such as the boundedness, the range, the representations of the considered transformation are established.

Is the amount of “greenness” within a 250-meter, 500-meter, 1000-meter or a 2000-meter buffer surrounding a person’s home a good predictor of their physical health? The evidence is inconclusive. We reviewed Web of Science articles that used geographic information systems buffer analyses to identify trends between physical health, greenness, and distance within which greenness is measured. Our inclusion criteria were: (1) use of buffers to estimate residential greenness; (2) statistical analyses that calculated significance of the greenness-physical health relationship; and (3) peer-reviewed articles published in English between 2007 and 2017. To capture multiple findings from a single article, we selected our unit of inquiry as the analysis, not the article. Our final sample included 260 analyses in 47 articles. All aspects of the review were in accordance with PRISMA guidelines. Analyses were independently judged as more, less, or least likely to be biased based on the inclusion of objective health measures and income/education controls. We found evidence that larger buffer sizes, up to 2,000m, better predicted physical health than smaller ones. We recommend that future analyses use nested rather than overlapping buffers to evaluate to what extent greenness not immediately around a person’s home (i.e., within 1,000-2,000m) predicts physical health.

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.

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.

In the modern power grid, characterized by the increased penetration of power electronics and extensive utilization of renewable energy, inverters-based power plants play a pivotal role as the principal interface of renewable energy sources (RESs) and the grid. Considering the stability characteristics of grid-following (GFL) inverters when the grid is relatively weak, the application of grid-forming (GFM) controls becomes imperative to enhance the stability of the entire power plant. Thus, there is an urgent need for suitable and effective models to study the interaction and stability of the paralleled inverters employing GFL and GFM controls. Thus, the small-signal modeling with full-order state space model and eigenvalues analysis is presented in this paper. First, the small-signal state-space model of the individual GFL and GFM inverters is obtained considering the control loop, interaction, reference frame, transmissions, and time delays. Then, the models of the individual inverter are extended to the hybrid inverters to study the effects of the GFM inverters on the small- signal stability of the entire system. And, the impacts of the inertia and damping are analyzed by the eigenvalues of the state-transition matrix. Case comprising three parallel GFL inverters and two GFL inverters with one GFM inverter, respectively, are studied to examine the effectiveness and accuracy of the model. Finally, the stability margin obtained from the eigenvalue analysis of the entire system is verified by time-domain simulations.

We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has connections with biased walks on digraphs. Within this framework, we introduce a space-time generalization of the Poisson process as a strictly increasing walk with discrete Mittag-Leffler jumps subordinated to a (continuous-time) fractional Poisson process. We call this process ‘space-time Mittag-Leffler process’. We derive explicit formulae for the state probabilities which solve a Cauchy problem with a Kolmogorov-Feller (forward) difference-differential equation of general fractional type. We analyze a “well-scaled” diffusion limit and obtain a Cauchy problem with a space-time convolution equation involving Mittag-Leffler densities. We deduce in this limit the ‘state density kernel’ solving this Cauchy problem. It turns out that the diffusion limit exhibits connections to Prabhakar general fractional calculus. We also analyze in this way a generalization of the space-time fractional Mittag-Leffler process. The approach of construction of good Laplacian generator functions has a large potential in applications of space-time generalizations of the Poisson process and in the field of continuous-time random walks on digraphs.

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.

In the past few decades, probabilistic interpretations of brain functions have become widespread in cognitive science and neuroscience. In particular, the free energy principle and active inference are increasingly popular theories of cognitive functions that claim to offer a unified understanding of life and cognition within a general mathematical framework derived from information and control theory, and statistical mechanics. However, we argue that if the active inference proposal is to be taken as a general process theory for biological systems, it is necessary to understand how it relates to existing control theoretical approaches routinely used to study and explain biological systems. For example, recently, PID control has been shown to be implemented in simple molecular systems and is becoming a popular mechanistic explanation of behaviours such as chemotaxis in bacteria and amoebae, and robust adaptation in biochemical networks. In this work, we will show how PID controllers can fit a more general theory of life and cognition under the principle of (variational) free energy minimisation when using approximate linear generative models of the world. This more general interpretation provides also a new perspective on traditional problems of PID controllers such as parameter tuning as well as the need to balance performances and robustness conditions of a controller. Specifically, we then show how these problems can be understood in terms of the optimisation of the precisions (inverse variances) modulating different prediction errors in the free energy functional.

Given any sequence a = (an)n1 of positive real numbers and any set E of complex sequences, we write Ea for the set of all sequences y = (yn)n1 such that y=a = (yn=an)n1 2 E. In this paper, we use the spaces w1, w0 and w of strongly bounded, summable to zero and summable sequences, that are the sets of all sequences y such that ? n?1Pn k=1 jykj
n is bounded, tends to zero and such that y ? le 2 w0, for some scalar l, respectively, (cf. [24, 22]). These sets where used in the statistical convergence, (cf. [17, Chapter 4]). Then we deal with the solvability of each of the (SSIE) F
 E + F0x where E is a linear space of sequences, F = c0, c, `1, w0, w, or w1 and F0 = c0, c, or `1. For instance, the solvability of the (SSIE) w
 w0+s(c) x consists in determining the set of all sequences x = (xn)n1 2 U+ that satisfy the following statement. For every sequence y that satisfy the condition limn!1 n?1Pn k=1 jyk ? yk?1 ? lj = 0, there are two sequences u and v, with y = u+v such that limn!1 n?1Pn k=1 jukj = 0 and limn!1 (vn=xn) = L for some scalars l and L. These results extend those stated in [11, 12, 10].

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.

The Kwee van Woerden (KvW) method for the determination of eclipse minimum times has been a staple in eclipsing binary research for decades, due its simplicity and independence of external input parameters. However, its estimates of the timing error have been known to be of low reliability. During the analysis of very precise photometry of CM Draconis eclipses from TESS space mission data, KvW’s original equation for the timing error estimate produced numerical errors, which evidenced a fundamental problem in this equation. This contribution introduces an improved way to calculate the timing error with the KvW method. A code that implements this improved method, together with several further updates over the original method is presented as well. An example application on the CM Draconis light curves from TESS is given, where we show that its timing error estimates of about 1 second are in excellent agreement with error estimates obtained by other means.

In this paper, we introduced a generalized ∆-implicit locally contractive condition and give some examples to support it and to show its significance in fixed point theory. We prove that the mappings satisfying generalized ∆-implicit locally contractive condition admits a common fixed point, where, the ordered multiplicative GM−metric space is chosen as underlying space. The obtained fixed point theorems generalize many earlier fixed point theorems on implicit locally contractive mappings. In addition, some nontrivial and interesting examples are provided to support our findings. To demonstrate the originality of our new main result, we apply it to show existence of solutions to a system of nonlinear -Volterra type- integral equations.

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 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.

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.

An accurate flux measurement of low-energy charged particles trapped in the magnetosphere is necessary for space weather characterization and to study the coupling between the lithosphere and magnetosphere, which allows for the investigation of the correlations between seismic events and particle precipitation from Van Allen belts. In this work, the project of a CubeSat space spectrometer, the Low-Energy Module (LEM), is shown. The detector will be able to perform an event-based measurement of the energy, arrival direction, and composition of low-energy charged particles down to 0.1 MeV. Moreover, thanks to a CdZnTe mini-calorimeter, the LEM spectrometer also allows for photon detection in the sub-MeV range, joining the quest for the investigation of the nature of Gamma-ray bursts. The particle identification of the LEM relies on the ΔE−E technique performed by thin silicon detectors. This multipurpose spectrometer will fit within a 10 × 10 × 10 cm3 CubeSat frame, and it will be constructed as a joint project between the University of Trento, FBK, and INFN-TIFPA. To fulfil the size and mass requirements, an innovative approach, based on active particle collimation, was designed for the LEM; this avoids the heavy/bulky passive collimators of previous space detectors. In this paper, we will present the LEM geometry, its detection concept, the results from the developed GEANT4 simulation, and some characterisations of a candidate silicon detector for the instrument payload.

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.

Within an Internet of Multimedia Things, the risk of disclosing streamed video content, such as arising from video surveillance, is of heightened concern. This leads to the encryption of that content. To reduce the overhead and lack of flexibility arising from full encryption of the content, a good number of selective-encryption algorithms have been proposed in the last decade. Some of them have limitations, in terms of significant delay due to computational cost, or excess memory utilization, or, despite being energy efficient, do not provide a satisfactory level of confidentiality, due to their simplicity. To address such issues, this paper presents a lightweight selective encryption scheme, in which encoder syntax elements are encrypted with the innovative EXPer (EXtended Permutation with exclusive OR). The selected syntax elements are taken from the final stage of video encoding that is during entropy coding. As a diagnostic tool, the Encryption Space Ratio measures encoding complexity of the video relative to the level of encryption so as to judge the success of the encryption process, according to entropy coder. A detailed comparative analysis of EXPer with state-of-the-art algorithms confirms that the EXPer provides significant confidentiality with a small computational cost and negligible encryption bitrate overhead. Thus, the results demonstrate that the proposed security scheme is a suitable choice for constrained devices in an Internet of Multimedia Things environment.

The present analysis deals with the study of the $f(Q, T )$ theory of gravity which was recently considered by many cosmologists. In this theory of gravity, the action is taken as an arbitrary function $f(Q, T )$ where $Q$ is non-metricity and $T$ is the trace of energy-momentum tensor for matter fluid. In this study, we have taken three different forms of the function $f(Q, T )$ as $f(Q,T)=a_1Q+a_2 T$ and $f(Q,T)=a_3 Q^2+a_4 T$ and discussed some physical properties of the same. Also, we have obtained the various cosmological parameters towards Friedmann-Lemaitre-Robertson-walker (FLRW) Universe by defining the transit form of scale factor which yields the Hubble parameter in redshift form as $H(z)=\frac{H_{0}}{(\lambda+1)} \left(\lambda+ (1+z)^{\delta}\right)$. %We have obtained the approx best-fit values of model parameters using the least square method for observational constraints on available datasets like Hubble dataset $H(z)$, Supernova dataset SNe-Ia, etc., by applying the Root Mean Squared Error formula (RMSE). By applying the Root Mean Squared Error formula (RMSE), we were able to determine the approximate best-fit values of model parameters using the least square approach for observational constraints on the datasets Hubble dataset $H(z)$, Supernova dataset SNe-Ia, etc. We have observed that the deceleration parameter $q(z)$ exhibits a signature-flipping (transition) point within the range $0.623 \le z_{0} \le 1.668$ through which it changes its phase from the decelerated to the accelerated expanding universe with $\omega = -1$ at $z=-1$ for the approximate best-fit values of the model parameters. %For obtained approx best-fit values of model parameters we have observed that the deceleration parameter $q(z)$ shows a signature-flipping (transition) point within the range $0.623 \le z_{0} \le 1.668$ through which it changes its phase from decelerated to the accelerated expanding universe with $\omega = -1$ at $z=-1$.

The ubiquitous connectivity for the space-air-ground integrated network (SAGIN) of the beyond fifth generation of communication and sixth generation of communication (B5G/6G) is envisaged to meet the needs for the demanded quality of service (QoS), green communication, and "dual carbon" target. However, the offloading and computation of massive latency-sensitive tasks dramatically increases the energy consumption of the network. Furthermore, the traditional power supply technology of the network base stations (BSs) enhances the carbon emission. To address these issues, we first propose a SAGIN architecture with energy harvesting devices, where the BS is powered by both renewable energy (RE) and the conventional grid. The BS explores wireless power transfer (WPT) technology to power the unmanned aerial vehicle (UAV) for stable network operation. RE sharing between neighbouring BSs is designed to fully utilize RE for reduce carbon emission. Secondly, on the basis of task offloading decision, UAV trajectory, and RE sharing ratio, we construct cost functions with joint latency-oriented, energy consumption, and carbon emission. Then, we develop a twin delayed deep deterministic policy gradient (TD3PG) algorithm based on deep reinforcement learning to minimize the cost function. Finally, simulation results demonstrate that the proposed algorithm outperforms the benchmark algorithm in terms of reducing latency, energy saving, and lower carbon emission.

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.

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.