This research answers the knowledge gap regarding the explanation of the quantum jump of the electron. This scientific paper aims to complete Einstein’s research regarding general relativity and attempt to link general relativity to quantum laws.

This research answers the knowledge gap regarding the explanation of the quantum jump of the electron. This scientific paper aims to complete Einstein's research regarding general relativity and attempt to link general relativity to quantum laws.

This research answers the knowledge gap regarding the explanation of the quantum jump of the electron. This scientific paper aims to complete Einstein’s research regarding general relativity and attempt to link general relativity to quantum laws.

Three-dimensional quantized space model is newly introduced. Quantum mechanics and relativity theory are explained in terms of the warped three-dimensional quantized spaces with the quantum time width (Dt=t_q). The energy is newly defined as the 4-dimensional space-time volume of E = cDtDV in the present work. It is shown that the wave function of the quantum mechanics is closely related to the warped quantized space shape with the space time-volume. The quantum entanglement and quantum wave function collapse are explained additionally. The special relativity theory is separated into the energy transition associated with the space-time shape transition of the matter and the momentum transition associated with the space-time location transition. Then, the quantum mechanics and the general relativity theory are about the 4-dimensional space-time volume and the 4-dimensional space-time distance, respectively.

The inability to delineate a unified physical ontology that accounts simultaneously for the laws of special relativity and the results of quantum experiments has been a defining problem in physics for more than 100 years. This analysis addresses the problem by positing a novel mixed ontology composed of a “discrete” 4D spacetime and a physical, ultra-high dimensional (3 x N) “Planck Space.” Together, Planck Space and the three spatial dimensions of 4D spacetime form a tightly integrated ((3 x N) + 3) hyperspace (the “Dual Ontology”).Critically, the Dual Ontology’s structure replaces 1) the continuous, differentiable manifold of 4D spacetime with a discrete, background-independent 4D spacetime that is intrinsically curved and 2) mathematical spaces with a physical (3 x N) Planck Space. Moreover, the Dual Ontology is structurally and dynamically predicated on the one-to-one mapping and identity between the discrete spatial units that simultaneously form 4D spacetime and Planck Space. The one-to-one mapping and identity of the discrete spatial units support an integrated quantum dynamics based upon the dynamic evolution of single and N-body quantum states in 4D spacetime in full compliance with the laws of special relativity and the instantaneous collapse of all quantum states in an ontic Planck Space, where special and general relativity and more generally, 4D spacetime’s laws of physics, do not apply.

This research answers the knowledge gap regarding the explanation of the quantum jump of the electron. This scientific paper aims to complete Einstein’s research regarding general relativity and attempt to link general relativity to quantum laws.

This research answers the knowledge gap regarding the explanation of the quantum jump of the electron. This scientific paper aims to complete Einstein’s research regarding general relativity and attempt to link general relativity to quantum laws.

We study the effect of the generation of the mechanical transverse wave (MTW)　travelling in the opposite direction (OD) to a moving medium (MM) on the relativistic energy conservation law (RECL). From the viewpoint of the relativity of simultaneity (RS), the time on the coordinate coinciding with the advance end of the wave (AEW) travelling toward the rear of the MM passes faster than that on the coordinate coinciding with the wave source (WS). Then the AEW in the MM travels forward compared to that in the rest frame of reference (RFR) which is stationary relative to the medium when the time on the coordinate coinciding with the WS is same for each inertial frame of reference (IFR). Hence, the coordinate interval (CI) between the AEW and WS in the MM is observed to be larger than that between them in the RFR. We show that this difference holds true for the CI of any portion having transverse velocities mutually converted by the Lorentz transformation (LT). This difference in the CI leads to that in the rest mass (RM). We demonstrate that the RM included in wave motion (WM) in the MM is larger than one included in WM in the RFR when comparing the portions having transverse velocities mutually converted by the LT. This relation holds true for all portions in WM. Therefore, the total coordinate interval of the portion (CIP) and total RM (TRM) included in WM in the MM (WMMM) are large compared to them included in WM in the RFR. Furthermore, we compare the relativistic kinetic energy (RKE) of the MTW travelling in the OD to the MM (ODMM) with that of the MTW propagating in the direction vertical to the moving direction of the medium. We prove that the CIP and RM included in the former MTW are larger than them included in the latter MTW when comparing each portion with the same transverse velocity (TV). Moreover, the total CIP and TRM included in the former MTW are also large compared to them included in the latter MTW. The reason for these is that the latter CIP and RM are equal to them in the RFR when comparing the portions having transverse velocities mutually converted by the LT. On the other hand, the energy supplied to generate each MTW is the same. From these, we demonstrate that the RKE of the MTW travelling in the ODMM can be larger than the total relativistic energy (TRE) of the MTW propagating in the direction vertical to the moving direction of the medium. Consequently, we propose a violation of the RECL and Einstein’s principle of relativity (EPR) because the TRE is not necessarily conserved in the IFR in which the medium is moving.

We have shown that according to the predictions of the standard quantum theory, signaling is possible using a postponed compensation Hong-Ou-Mandel interferometer, although it violates Lorentz invariance. We argue that new physics is required to deal with such a paradox. Either quantum principles or relativity needs reassessment. We propose an experiment that can decide whether relativity rules over quantum or vice versa.

Similarly to his special theory of relativity, Einstein's special principle of relativity extends beyond the limits currently known to it. Up to now, the principle has not been suspected to have the potential to translate laws. However, the principle holds an inherent capacity to translate physical laws and, in so doing, speeds up our understanding and control of physical reality. Such a translation of laws leads to the faster discovery of other laws, such as the Laws of Electronic Motion, characterizing the motion of electrons around the atomic nucleus, and the Third Law of Biological Resistance, facilitating the successful control of drug resistance in medicine. The ability of the special principle of relativity to translate laws shines forth once the said principle is duly interpreted. This interpretation exposes a parallelism between experimental frames of reference and justifies the applicability of the laws of one frame of reference in other parallel frames of reference. This process opens the door to our faster discovery of the laws governing a multiplicity of frames parallel to a frame we already know the laws of. In practice, the interpretation of Einstein's special principle of relativity speeds up our understanding of the workings of physical reality and strengthens our capacity to subdue matter.

HIGHLIGHTS This paper is presenting an experiment based on Ehrenfest's paradox where an effect of special relativity was expected but not observed. The validity of special relativity in our macro world will be questioned and an alternative will be offered. Indeed, special relativity has been successful in describing the behaviour of particles (Rossi & Hall, 1941), but since particles obey quantum rules, there is no observation of special relativity in our everyday world. On the contrary, there are at least two paradoxes based on special relativity: the twin paradox (Langevin, 1911) and Ehrenfest's paradox (1909). ABSTRACT After presenting the history of special relativity, the non-simultaneity of special relativity is questioned in our macro world. In addition, some issues between light clocks and the application of Lorentz transformation are presented. All this indicates that special relativity appears to be correct only for particles and would be invalid in our macro world. A new hypothesis is presented based on an adaptation of special relativity; this new hypothesis solves the anomalies and could be a solution to the twin paradox. This new hypothesis has a prediction in disagreement with special relativity. To test that prediction, a new experiment has been carried out and the preliminary results support the new hypothesis. Previously, a lack of special relativistic effects has been observed in the universe (Davis et al., 2004); that second observation is also explained with the new hypothesis.

Potential dependent special relativity and Gauss's law for the electric field have been used for gravity by assuming vacuum energy to be generated when the energy is a minimum useful expression for vacuum energy has been found. This expression shows that elementary particles are generated by gravity vacuum filling their hollow balls; using Schrödinger equation for spherically symmetric particles vacuum energy is quantized. Treating mass as vibrating spheres thus solving Schrödinger, coordinate harmonic oscillator energy relation has been found.

Newton's kinetic energy equation delineates the laws of motion for objects travelling at speeds much less than the speed of light, an equation extensively validated at these lower velocities. Any new, more complete formulation of kinetic energy must approximate Newton's kinetic energy equation under these conditions. Einstein's special relativity, utilizing the Lorentz factor, introduces a new perspective on spacetime, adhering to the requirement that the Newtonian kinetic energy equation serves as an approximation at low velocities. In this paper, we identify all factor expressions satisfying the condition that their approximate solutions at low velocities align with Newton's kinetic energy equation. We introduce the Yuyunrui factor, incorporating two real number hyperparameters, $\alpha$ and $\beta$, encompassing all potentially correct factors, with the Lorentz factor as a specific instance where $(\alpha=0$, $\beta=1)$. We classify all potentially correct $(\alpha, \beta)$ combinations into six categories based on their distinct scaling effects and present the corresponding scaling effects. The combinations of $(\alpha, \beta)$ values applicable in the real world are necessarily included within these candidates, with the precise values requiring rigorous experimental validation. This work aims to refine our understanding of special relativity beyond the Lorentz factor.

In this research article, we are going to study the concept of the theory of relativity and after extracting the essential information, we will try to find a relation between the theory of relativity and the results we are obtaining through contemporary physics experiments. It has been investigated that traveling in time is not a dream anymore and time can pass at a different rate for some people.

The study of the emission, propagation, and reflection of balls in Newtonian mechanics, applying the laws of conservation of momentum and energy when the mass of the balls converges to zero, concludes that the kinematics of light are like those of massless balls. The kinematics of light explain why the speed of light is the constant c in each inertial frame in which the light source and reflective mirror are at rest, why the laws of physics have the same form in each inertial frame, and why any light experiment in an inertial frame cannot prove the motion of that inertial frame. The following law of mechanics governs the kinematics of balls and electromagnetic radiation: Each inertial frame drags at its velocity the balls and electromagnetic radiation emitted by bodies at rest in that inertial frame. The theory of special relativity misapplies the symmetry observed in phenomena to two inertial frames; therefore, it duplicates a physical phenomenon from one inertial frame, which is considered stationary, into another. There are multiple issues rooted in Lorentz's and Einstein's transformations. For example, transformations offer the speed of light at the constant c in the moving and opposite directions of the inertial frame. At the same time, it is variable in any other direction, converging to infinity. Time contraction in the moving direction of the inertial frame is different from time dilation in the opposite direction. It requires a ruler and time synchronization in each direction. There are no length contractions in Lorentz's and Einstein's transformations to support the fundamental concept of length contraction in special relativity. With these unacceptable conclusions, the theory of special relativity is self-negating.

In a particle swarm with a fixed kinetic energy, the constituent particles move randomly and their velocity magnitudes follow a Maxwell distribution characterized by specific parameters. Within a certain time frame, particles in a sub-swarm may exhibit a bias in their movement direction. Thus, the particles may exhibit a special characteristic (biased random motion), where the group velocity in a particular direction remains constant u. For this biased particle swarm, composed of randomly moving particles with a fixed average speed c, particles have a higher probability of moving in a specific direction. Conversely, their likelihood of moving in all other directions is equally reduced. This study starts from the perspective of biased random walks and using Mathematica software proves that the diffusion rate of particles (in the reference frame R_u observed from R₀) in all directions is slower than that of an unbiased particle swarm with the same average speed c. Specifically, the degree of reduction is determined by the Lorentz-like factor. Lastly, we present the Ito equation for this biased random motion and provide associated verification examples. This study aims to serve as a reference for comprehending the underlying principles of the special relativity effect.

In gravity theory, there is a well-known trans-Planckian problem, which is that general relativity theory leads to a shorter than Planck length and shorter than Planck time in relation to so-called black holes. However, there has been little focus on the fact that special relativity also leads to a trans-Planckian problem, something we will demonstrate here. According to special relativity, an object with mass must move slower than light, but special relativity has no limits on how close to the speed of light something with mass can move. This leads to a scenario where objects can undergo so much length contraction that they will become shorter than the Planck length as measured from another frame, and we can also have shorter time intervals than the Planck time. The trans-Planckian problem is easily solved by a small modication that assumes Haug's maximum velocity for matter is the ultimate speed limit for something with mass. This speed limit depends on the Planck length, which can be measured without any knowledge of Newton's gravitational constant or the Planck constant. After a long period of slow progress in theoretical physics, we are now in a Klondike "gold rush" period where many of the essential pieces are falling in place.

Loop quantum gravity (LQG) quantizes gravity through the quantization of the space-time. It begins with general relativity (GR) and brings some concepts from quantum field theory to quantize the space-time. The conceptual background of GR is necessary to comprehend the LQG framework. Therefore, in this paper, prerequisite concepts such as special relativity, general relativity, covariant electromagnetism, tensor analysis, Lagrangian formulation, Hamiltonian formulation and basics of quantum mechanics are briefly introduced; that, are needed to study loop quantum gravity(LQG).

Newton's classical dynamics accurately describes the motion of objects moving at speeds much less than the speed of light and has been extensively validated under these conditions. Any new dynamics formula must reduce to Newton's equations at low velocities. Einstein's theory of special relativity, which utilizes the Lorentz factor, provides a revised view of space-time and also conforms to Newton's equations for low speeds. However, the Lorentz factor assumes that the maximum anisotropy of the speed of light is zero, a condition not fully supported by experimental evidence. The Michelson-Morley Experiment, conducted at a speed far less than that of light, suggests that while the measured anisotropy is very small, it is not zero. This small value could imply the existence of undiscovered physical laws. To address this, we propose the Yuyunrui factor, which includes two hyperparameters, \(\alpha\) and \(\beta\), encompassing various possible models. In this framework, the Lorentz factor represents a special case with \((\alpha=0, \beta=1)\) and zero anisotropy. We categorize the \((\alpha, \beta)\) combinations into four broad types based on their scaling effects and describe these in detail. Future experiments at higher speeds will be essential to accurately determine the true value of the maximum anisotropy of the speed of light and to refine the proposed factor.

It is well known that the photon trajectories follow a curved path in a gravitational field. We explore here the gravitational bending of electric field lines. It seems that the electric field lines of a charge, supported in a gravitational field, follow exactly the trajectories of photons emitted isotropically from a source situated at the charge location. From a detailed examination of the electrostatic field of a charge accelerated uniformly in the instantaneous rest frame, exploiting the strong principle of equivalence, one can determine the bending of the electric field lines of a charge in a gravitational field. The fraction of electric field lines crossing a surface, stationary above or below the charge in the gravitational field, is shown to be exactly similar to the fraction of photon trajectories, emitted from a source placed at the charge location, intersecting that surface. On the other hand, for a freely falling charge in the gravitational field there is no such bending of electric field lines. The field lines continue to extend in radial straight lines from the instantaneous 'present' position of the charge, as do the trajectories of photons streaming away from the instantaneous position of a freely falling source in the gravitational field. The electric field configuration of a freely falling charge in the gravitational field is shown to be exactly the same as that of a charge moving uniformly in an inertial frame with velocity equal to the instantaneous ``present'' velocity of the freely falling charge.

The theory of special relativity has reexamined and reconstructed the concepts of space and time, which are indispensable for describing physical laws, consequently instigating a major revolution in physics in general. Although the correctness of the special theory of relativity has been con-firmed by many observations and experiments, it is unclear why the "principle of relativity" and the "principle of the constant speed of light," which form the basis of the idea, are valid. Moreo-ver, although special relativity has advanced our understanding of time, our understanding of the fundamental question, "What is time?" is still limited. The theory of special relativity regards space as a four-dimensional construct consisting of one-dimensional time and three-dimensional space. This paper proposes an alternative framework, wherein real space is uniform and isotropic four-dimensional space, and elementary particles are waves that propagate through this four-dimensional space at a constant speed. This new perspective provides evidence to support two of Einstein’s key principles—the "principle of relativity" and the "principle of the constant speed of light." Furthermore, this model clarifies what time is and why time flows at a constant rate from the past to the future.

n this article a first attempt at formalizing a new approach to the grand unified theory is introduced. This theory named NUVO is based primarily on considering two aspects of inertia. The first aspect is how a mass couples to space, introducing definitions to distinguish massive particles from massless particles. The second aspect is space’s availability to couple to massive particles. In essence these are the two contributions of inertia; mass and space. Postulates, clarifications, and a mathematical structure are introduced. Part 1 covers the physics of the very large (cos- mic), laying ground work for part two which applies the structure to the very small (quantum). The cosmic application of the theory will show a strong correlation to empirical data and correspondence to General Rela- tivity, including; time dilation, length contraction, and orbital advances. Departing from the canonical findings of General Relativity by predicting a quantization of physical units under the effect of acceleration and or gravity.

Since the creation of the first parallel electrical power systems around the world, the rotor angle stability of synchronously operating generators has been one of the most crucial and challenging problems. In modern electricity networks, involving Kazakhstani, where the renewable energy technologies are rapidly penetrating, and the issue of stability takes on even greater importance due to the technical shortcomings of inverter-based generation. In this framework, an analysis of rotor angle transient stability was carried out when replacing existing synchronous generators with doubly fed induction generators under a certain pre-emergency mode. A critical proportion of active power generation by DFIG units was identified at which transient stability can still be maintained due to the sufficient stored kinetic energy of the synchronous machines remaining in operation. In addition, 2 simple solutions were investigated to improve transient stability, such as an increased time of the automatic reclosure operation and the use of special load shedding automation. For the analysis, a real power system of Mangystau region in Kazakhstan was considered, and the PowerWorld software was used.

We study whether the center of relativistic energy (CRE) is always constant in an isolated frame of reference (IFR). First, we assume that two objects in a moving isolated frame of reference (MIFR) move parallel to and very close to a coordinate axis from opposite directions and with equal speed. Here each length in the direction of travel of the objects is much longer than that perpendicular to the direction of travel of them, and moreover the latter is negligibly extremely short. Hence, the location of the CRE (LCRE) of the objects is very close to the coordinate axis in initial condition. When they become perfectly symmetric with respect to the coordinate axis, the forces perpendicular to the direction of travel of the objects are applied to each CRE and thereby a perfectly inelastic collision between them occurs on the coordinate axis. The combined object (CO) resulting from the perfectly inelastic collision begins to rotate because each momentum of the objects before the combination between them acts like the moment of force on the CO. For simplicity, we examine the energy distribution of the CO when it becomes perpendicular to the coordinate axis due rotation. The magnitude of velocity of each minute portion (MP) symmetrical with respect to the coordinate axis are different depending on whether the direction of each rotational velocity is the same or opposite to the direction of travel of the MIFR. Then the energy of each MP is not the same. As a result, the LCRE of the CO moves to the direction perpendicular to the coordinate axis, and its LCRE becomes far from the coordinate axis since the length in such direction is long enough. Therefore, we conclude that the LCRE in the MIFR is not necessarily invariant. Second, we suppose a process in which a force causes a negative acceleration on a moving object (MO) and thereafter the MO eventually comes to rest. What is considered here is the LCRE when the MO comes to rest. We pay attention to the position of the force applied to the MO because the transmission time of force (TTF) inside the MO may vary depending on the position of the MO where the force is applied. As a result, we find that the position at which the MO comes to rest differs depending on the TTF inside the MO. Therefore, we conclude that the LCRE in an IFR differs depending on the position of the MO where the force is applied, in other words, it in an IFR is not necessarily uniquely determined.

In the energy-momentum density expressions for a relativistic perfect fluid with a bulk motion, one comes across a couple of pressure-dependent terms, which though well known, are to an extent, lacking in their conceptual basis and the ensuing physical interpretation. In the expression for the energy density, the rest mass density along with the kinetic energy density of the fluid constituents due to their random motion, which contributes to the pressure as well, are already included. However, in a fluid with a bulk motion, there are, in addition, a couple of explicit, pressure-dependent terms in the energy-momentum densities, whose presence to an extent, is shrouded in mystery, especially from a physical perspective. We show here that one such pressure-dependent term appearing in the energy density, represents the work done by the fluid pressure against the Lorentz contraction during transition from the rest frame of the fluid to another frame in which the fluid has a bulk motion. This applies equally to the electromagnetic energy density of electrically charged systems in motion and explains in a natural manner an apparently paradoxical result that the field energy of a charged capacitor system decreases with an increase in the system velocity. The momentum density includes another pressure-dependent term, that represents an energy flow across the system, due to the opposite signs of work being done by pressure on two opposite sides of the moving fluid. From Maxwell's stress tensor we demonstrate that in the expression for electromagnetic momentum of an electric charged particle, it is the presence of a similar pressure term, arising from electrical self-repulsion forces in the charged sphere, that yields a natural explanation for the famous, more than a century old, 4/3 factor in the electromagnetic mass.

In this paper, we establish the generalized Qi-type inequality involving conformable fractional integrals. The results presented here would provide extensions of those given in earlier works.

Time is a component quantity of various measurements and is also used on its own to sequence events, to compare the duration of events or the intervals between them, and to quantify rates of change of quantities in material reality or in the conscious experience [1]. The measuring equipment well might happen to be a clock. By making a presupposition that clock is Time, it is perceived experimentally that “Time exhibits wave-like properties”

This paper aims to describe and analyze a relativistic engine that uses a permanent magnet and an electrically charged device. According to Newton’s third law, every action is met with an equal and opposite reaction, meaning the total force in a system unaffected by external forces is zero. However, relativity principles state that signals cannot travel faster than the speed of light, so actions and reactions cannot occur simultaneously. As a result, the total force cannot be zero at any given moment. This implies that the system gains mechanical momentum and energy over a finite period. The question then arises about how to uphold the law of momentum and energy conservation. It has been shown that the momentum is balanced by an equal and opposite momentum in the field, while the energy gained by the engine is offset by a reduction in the field’s energy. Previous analyses assumed that the bodies involved were macroscopically neutral, meaning the number of electrons and ions was equal in every volume element. This paper relaxes that assumption and examines charged bodies interacting with magnetic currents from permanent magnetic materials, exploring the implications for a charged relativistic engine based on a permanent magnet.

We mathematically derived a comprehensive theoretic framework “Asymmetry Theory”, based solely on the well-established principle of “the constancy of the velocity of light” without any other assumptions, like the ether. This paper proves that Asymmetry Theory encompasses all results of Special Relativity (STR) as a special case when the observer moves perpendicularly to the “source-observer” line. It explains everything STR does but extends beyond it, offering novel and groundbreaking insights. The longstanding controversies surrounding STR arise from its application outside its intended special case, hence, they are all resolved in Asymmetry Theory. Asymmetry Theory is supported by all experiments supporting STR, like Kaufmann, Ives-Stilwell, muon lifetime, nuclear reaction…., and those contradicting STR, like the Lunar range and GPS tests of light speed and the lack of transverse Doppler shift. Despite its mathematical rigorousness and all experimental evidence, we propose two new experiments to decisively test predictions from both theories.The mathematically derived Asymmetry Theory is a more comprehensive theoretical framework covering STR as a special case. It is self-consistent and theoretically proved by Maxwell’s equations. It does not contradict any established physical observations but instead resolves century-old controversies by providing a unified, mathematical and paradox-free explanation of key phenomena. Furthermore, its groundbreaking results offer a unified perspective across various distinct laws of physics, including: A formula for light velocity mathematically explains the Sagnac effect, one-way light speed, stellar aberration, Michelson-Morley, Hafele-Keating and Optic clocks. Electrodynamics formulas encompass particle acceleration, Mass-Energy and matter wave. A unified formula for all cases of classical and transverse Doppler effects covers time-varying Doppler effect, cosmological redshift, and Cherenkov radiation. A generalized form of Maxwell's equations for moving observers directly derives the formulas for light speed, Doppler effect and Sagnac effect.

Ontological premises have profound theoretical implications. This analysis posits a single, universal structure composed of two ontic entities: discrete, quantized units of space ("Planck Spheres") and a State of Absolute Nothingness (the "SOAN"). Planck Spheres and the SOAN form a physical, ultra-high (3 x N) dimensional space ("Planck Space") and a discrete 3D space (or "4D spacetime"). Together, Planck Space and 4D spacetime form a tightly integrated ((3 x N) + 3) hyperspace (the "Dual Ontology"). Critically, a one-to-one mapping and identity exists between the Planck Spheres comprising 4D spacetime and Planck Space. The Dual Ontology conjecture supports radically simplified physical explanations for three distinct areas of theoretical physics: First, the conjecture reconciles fundamental issues in Special Relativity and quantum mechanics by explaining why single and N-body quantum states (a) dynamically evolve in 4D spacetime subject to the speed of light and (b) instantaneously collapse in a physical Planck Space that is not subject to Special Relativity. Second, the temporal and physical asymmetry between the dynamic evolution of quantum states in 4D spacetime subject to Special Relativity and the instantaneous collapse of quantum states in a Planck Space where Special Relativity is inapplicable explains quantum path irreversibility and the arrow of time. Third, at or near the heat death of 4D spacetime, the instantaneous collapse of the energy content of Planck Space and the simultaneous transition of 4D spacetime's extremely widely dispersed energy content to a non-singular, generally localized volume at t = 0 explains 4D spacetime's isotropy, homogeneity, extremely high energy, pressure, and temperature, flatness, and low gravitational entropy. It also explains the horizon and fine-tuning problems.

In physics, thought experiments are impressive heuristic tools. They are valuable instruments to help scientists find new results and to teach students the known ones. However, as we shall show, they should always be received with prudence, even when they are a shortcut to 'prove' well-established results. Here, we show that the most widely known thought experiments devised to derive the gravitational frequency shift from energy conservation are, in fact, problematic. When properly set and correctly read, those thought experiments reveal that the existence of the gravitational frequency shift is, in fact, at odds with energy conservation. We also propose two new simple thought experiments, one using the conservation of energy and the other the conservation of linear momentum, that corroborate that conclusion, showing that those conservation principles do not imply the gravitational frequency shift. We think that our results may be of some epistemological interest and could serve as a warning sign on how thought experiments should be received and trusted.

The dramatic outbreak of the coronavirus disease 2019 (COVID-19) pandemics and its ongoing progression boosted the scientific community's interest in epidemic modelling and forecasting. The SIR (Susceptible-Infected-Removed) model is a simple mathematical model of epidemic outbreaks, yet for decades it evaded the efforts of the community to derive explicit solution. The present work demonstrates that this is a non-trivial task. Notably, it is proven that the explicit solution of the model requires the introduction of a new transcendental special function, related to the Wright's Omega function. The present manuscript reports new analytical results and numerical routines suitable for parametric estimation of the SIR model. The manuscript introduces iterative algorithms approximating the incidence variable, which allows for estimation of the model parameters from the numbers of observed cases. The numerical approach is exemplified with data from the European Centre for Disease Prevention and Control (ECDC) for several European countries in the period Jan 2020 -- Jun 2020.

Rebar quantity estimation is pivotal for determining the cost of construction projects and essential for bidding purposes. A bar bending schedule plays a crucial role by providing rebar information and bending instructions, facilitating efficient procurement. Traditional methods of bar bending schedules, which involve manual extraction from 2D (two-dimensional) drawings, are error-prone and hinder construction productivity. This study proposes a Building Information Modeling (BIM)-based algorithm that automates the generation of a Bar Bending Schedule (BBS) directly from the 3D (three-dimensional) BIM models, ensuring accuracy and eliminating manual errors. The effectiveness of the algorithm was verified by comparing the rebar quantities generated by the model against those derived from optimization calculations. The results demonstrated a mean absolute error of 0.017 and a mean absolute percentage error of 1.13%, validating the algorithm’s precision. Additionally, it achieved a remarkable 33.33% reduction in the manpower required for preparing BBSs, highlighting its potential to revolutionize construction workflow efficiency and accuracy.

The nonlocality of entangled quantum mechanical systems is incompatible with the standard interpretation of special relativity as a single 4D Minkowskian metric spacetime. The difficulty is that the definition of a spacetime interval between any pair of events precludes any form of nonlocal interaction, even the relatively benign non-signaling correlations. By an application of the relativity principle, and the use of the space ←→ time symmetry of the Lorentz boost I propose here a reinterpretation of special relativistic spacetime. This new ontology consists of a set of coexisting 3+1D spaces (‘framespaces’), each containing unique content in the form of a complex density. These spaces are related by the Lorentz boost, and coupled pairwise in a manner dictated by the Lorentz transformation. The inter-space coupling acting on the spacetime content gives rise to a nonlocal wave phenomenon, which is identified as quantum wave mechanics. The interspace coupling strength is then inversely proportional to Planck’s constant. The coexistence of multiple spaces is interpreted as momentum superposition, implying that momentum is the fundamental physical basis of quantum superposition. This new spacetime interpretation of quantum mechanics has many consequences, including explanations of quantum non-locality, the spacetime role of Planck’s constant, quantum measurement as a symmetry-breaking process and the redundancy of description of gauge theory.

Educators' subject-matter knowledge and their understanding of the many ways in which technology may be used to enhance student learning can both benefit from the usage of pedagogical technology, which is the primary goal of this kind of technology. The goal of this study is to determine the extent to which kids with special needs might benefit academically by adopting various forms of technology into their daily routines. This work makes use of descriptive qualitative research together with the methodology and processes that come with case study research. The emphasis of this study was placed on three institutions that welcome students of all abilities. According to the results of the qualitative research, inclusive schools do not universally possess the resources necessary to successfully incorporate technology into the classroom. The results suggest that this teacher occupies a position that is about equivalent to the center of the acceptable range. This displays the instructor's existing proficiency in the use of technology to enhance the results for their students.

In this work, the conceptions of the electrodynamics of action-at-a-distance and of electromagnetic fields are reviewed and confronted, with the aim of clarifying whether it is possible to propose a Weberian theory of action-at-a-distance, which together with a renewed mechanics (both re-specting the existence of a limiting velocity c) could constitute a framework capable of yielding predictions equivalent to those of the conventional Maxwell-Lorentz and SRT framework. In this work, it is shown that, considering basic assumptions about the interaction process, understanding it as an action exchange process, it is possible to derive the expression of the electrodynamic Phipps’ potential energy between two interacting charges. It is also shown that, with the same assumptions and the additional hypothesis that the interaction is supported by a mediating agent (aether or field) which is perturbed by the transmission of action, this perturbation obeys the wave equation (one of the main drawbacks of Weberian electrodynamics). Another aim of the work is to confront the relational electrodynamic formulations (supported by Galilean transformations that assume a universal time) with the Maxwell-Lorentz formulation of electromagnetism (linked to Lorentz transformations that entail local times), in order to elucidate whether the space-time to which the SRT leads us is a mere mathematical artifice or an inescapable reality.

We bring a strength-based and socially-oriented lens to behaviors observed in profound autism. Social deficits are a defining characteristic of autism. Yet humans’ biological drive for social connection is sufficiently strong that is should be observable, in some form at least, in individuals with autism. We describe a case that validates this view. Mahad is a 20-year-old Pakistani-American male, with intellectual disability, and minimal verbal abilities. Mahad has an intense interest in food and the steps involved in food preparation. He employs and capitalizes on his family’s meal routines to ensure continual social attention from his mother. When not immersed in food, Mahad uses his limited capacities to pursue the additional biological needs of exploring his environment, seeking information, and developing his cognitive abilities.

This study centers on childcare facilities catering to children with moderate cerebral palsy, exploring a four-phase process: (1) cultivating an understanding and acceptance, (2) integrating specialized resources, (3) developing strategic plans, and (4) establishing stable collaboration. The case study demonstrates the profound impact of well-rounded support systems. Children with cerebral palsy showed marked improvements in development and emotional stability. Concurrently, their peers developed greater empathy and cooperative skills, smoothly adjusting to the inclusive setting. Additionally, the childcare staff refined their methods and attitudes, enhancing their ability to meet each child's specific needs and thus elevating the standard of integrated care.Concluding with three strategic recommendations, the paper proposes measures to augment the quality of care for children with special needs. These include defining clearer guidelines and policies for special needs care in childcare environments, emphasizing professional development and the amalgamation of diverse resources to cultivate a more skilled caregiving workforce, and encouraging robust partnerships between parents and childcare facilities. These recommendations are expected to significantly influence the domain of inclusive education, providing crucial insights for those engaged in early childhood care and education..

In this article, some notions about set, weight of set, number, number's position, special vertex are introduced. Some classes of graph under these new notions have been opted as if the study on the special attributes of these new notion when they've acted amid each other is considered. Internal and external relations amid these new notions have been obtained as if some classes of graphs in the matter of these notions are been pointed out.

Fires constitute a significant threat due to the pollutants emitted and the destruction they cause. People who take part in fire-fighting operations must be equipped with appropriate tools, including special clothing that will allow them to work and guarantee safety. One of the threats are compounds from the PAH group, which are characterized by high toxicity and carcinogenicity. Therefore, it is important that the materials used constitute a barrier to contamination. Various materials from which individual elements of special firefighter's clothing are made were tested. Additionally, the importance of height on the possibility of sorption of PAH compounds on a given type of material was analyzed. Based on the results obtained, it was found that the type of material and the zone in which the clothing items are used are important in the sorption processes of pollutants. Data in this area may be important for taking further actions regarding the modification of materials used in special fire brigade clothing and in their cleaning processes.

In this article, some notions about set, weight of set, number, number's position, special vertex are introduced. Some classes of graph under these new notions have been opted as if the study on the special attributes of these new notion when they've acted amid each other is considered. Internal and external relations amid these new notions have been obtained as if some classes of graphs in the matter of these notions are been pointed out.

The study aims to examine the effects of artificial intelligence (AI) on the consistency and analysis of financial statements in hotels in ASEZA, Jordan. This research is an exploratory, empirical study, which uses the methodology of data collection and interpretation to draw conclusions. The researchers used the arithmetic mean, standard deviation, T-test and ANOVA test to calculate the degree of significance of the study questions. The findings of a basic linear regression study of the impact of AI implemented in Jordanian hotels on the integration of accounting information systems and the association between AI and the integration of accounting information systems (R = 59.6%) also indicate that the fixed limit value amounted to (2.060) and the value of (Beta) for T-test

In the present paper, the so-called Einstein’s causality is scrutinized and proven to be an illusion, a sort of mathematical fallacy. Causality as a well-established universal principle was and is absolutely valid for subluminal, luminal and superluminal signals under any natural and/or artificial circumstances. It is also shown that conceptually special relativity theory (SRT) is inapplicable to superluminality of physical phenomena since SRThas the light speed in vacuum as an upper limiting speed in its own proper domain of applications, and also because SRT is crucially based on the concept of inertial reference frames (IRFs) which are related to each other by Lorentz transformations, that is why the relative velocity of any two IRFs must be smaller than light speed.

In this article it is shown, first, that a change of basis in Minkowski space is equivalent to a change of basis in Euclidean space if a basis element is replaced by its dual element, constituting a mixed basis set. Second, that such mixed bases can be interpreted as a measurement system used by local, flat observers whose direct distance measurements are restricted to an (n−1)-dimensional submanifold in an n-dimensional Euclidean space. Combining these steps, it is concluded that a local, flat observer in a four-dimensional Euclidean space measures a Minkowski spacetime. This interpretation could be useful for theories in special relativity and related fields that rely on spacetime concepts, as it offers a more intuitive geometric understanding of the Minkowski metric.

In this paper, a method of direct spinning is proposed for direct spinning of heterogeneous spun wire-blown holes standard parts and the motherboard mounted on the spin board assemblies. The standardization of the spinneret hole was conducive to improving the machining accuracy and efficiency of the pores, and the spinneret holes could be replaced in time when a hole in the spinneret fails. Moreover; on the other hand, according to the needs of the process of spinning, the spinnerets with various cross-sections were combined and installed on the same motherboard for spinning, and the spinning obtained different bionic new functional products. Based on the results, a finite element model of the standard part of the spinneret hole was developed, and the spinnability of the combinable spinnable spinneret board was verified by simulating the melt flow in the spinneret channel through POLYFLOW software. Further, by the processing of the spinneret, the motherboard was installed into a combined spinneret, and the spinneret assembly was installed on the spinning machine for the experiments. Furthermore, the tow section was observed using a microscope, and the results showed the feasibility of the proposed method.

Organizational diagnosis (OD) is a comprehensive review of an organization's objectives, re-source allocation, and utilization to achieve those objectives. This study employed OD to en-hance the effectiveness of the Department of Special Education within the Government of Punjab. A questionnaire based on Weisbord's six-box organizational model called the Organ-izational Diagnostic Questionnaire (ODQ), was administered to N=1200 participants, consist-ing of heads of top, middle, and bottom tiers at district and tehsil levels of special education schools, centers, and the main office. Out of these, 506 participants voluntarily completed the ODQ survey. The study findings indicated that the employees of the department possess a good understanding of the organization's objectives. However, there is a lack of opportunities for employee participation in departmental discussions, centralized decision-making, irra-tional task distribution, and unsupportive allocation of human resources. Additionally, there is poor communication, unsatisfactory promotions, incentives, and a lack of knowledge shar-ing among employees, as well as poor inter-relationships, conflicts, and ineffective help-seeking mechanisms. The study also revealed low readiness for change in the organization. Respondents' opinions differed significantly based on their qualifications, job experience, years served, and gender. To improve the department's capacity to absorb change, the study recommends enhancing collaboration and inter-departmental communication, soliciting comprehensive input from all tiers, and promoting employee participation, supportive supervision, and communication. The study contributes to the body of knowledge on OD and highlights the need for improved communication, collaboration, and employee participation, as well as a supportive and supervisory support system to enhance the effectiveness of organizations.

While adequate for English-speaking users in the United States, as well as many Commonwealth countries and other English-speaking jurisdictions (e.g., Canada, Australia, New Zealand or South Africa among others), typing in Romance Languages (Spanish, French, Portuguese and Italian) by using a standard US-QWERTY Keyboard is not easy since it is not adapted to special characters such as accented vowels, tildes and cedillas or ligatures, used in Romance Languages. With regard to the International Layout, intended to enable access to the most common diacritics used in Western European Languages, the problem comes from the fact that accented vowels are spread throughout the Keyboard layout, and their uppercase versions need chord combinations which can require good manual dexterity. This paper will analyze how the Spanish or Portuguese Keyboards are the best options for these users since they are QWERTY-based and the most compatible ones for the different character sets in Spanish, French, Portuguese and Italian Languages.

Automobile proving ground is important for the research of vehicles which is used for the vehicle dynamics, durability testing, braking testing, etc. However, the roads in automobile proving ground will inevitably be damaged with the extension of the service life. In most previous researches, equipment similar to laser cross-section was used to detect pavement quality, the principle of which was to reflect pavement quality by detecting road surface roughness. This method ignores the elastic deformation of the roads itself when the vehicle is traveling on it and hardly compensate for the amendment. Therefore, this article presents a new method based on force sensor to reduce the impact of elastic deformation such as wheel tyre deformation, pavement deformation, and wheel rim deformation. In which, force sensors mounted on the wheels collect the three-dimensional dynamic load of the wheel.The presented method has been tested with two sets of cobblestone road load data, and the results show that The　incentives imposed by the test vehicle on the target road are 88.3%, 91.0%, and 92.05% of the incentives imposed by the test vehicle on the standard road in three dimensions, respectively. It is clear that the proposed method has strong potential effectiveness to be applied for lose detection of the special road application.

In this work, we investigate the behaviour of relativistic quantum oscillator under the effects of Lorentz symmetry violation determined by a tensor $(K_F)_{\mu\nu\alpha\beta}$ out of the Standard Model Extension. We analyze this relativistic system under an inverse radial electric field and a constant magnetic field induced by Lorentz symmetry violation. We see that the presence of Lorentz symmetry breaking terms modified the energy spectrum of the system, and a quantum effect arise due to the dependence of the linear charge density on the quantum numbers of the system

Because imbalanced power will cause the loss of the propulsion motor of the railway vehicle, and the increase in temperature will shorten the service life of the electric vehicle. Not only this, but also increase the cost of electricity and maintenance. In the past, the industry only focused on methods to improve power quality such as load capacity, relay setting, and harmonic resolution. Now, the consider of three-phase unbalance rate (TPUR) must be applied. I propose special transformers wiring (STW) to improve the three unbalance rates and provide different transformer wiring methods. According to the IEEE Committee, in the future, power companies will need to install balanced relay stations to improve three-phase unbalance rate. the internal regulations of Taipower must be less than 4.5% (voltage unbalance rate (NPSUR)of 2.5% and motor temperature rise of 12.5%). the derivation of the transformer "three-phase unbalance rate" model is the focus of the railway system. This research is based on the model derivation of different wiring methods to improve the hot problem caused by the three-phase imbalance and improve the service life of the train. And pointed out that Scott, Le-Blanc, Modified-Woodbridge three wiring methods can be applied to future railway system routes to improve the three-phase unbalance rate, in line with the IEEE standard of less than 2%.

The main aim of this paper is to investigate multifarious properties and relations for the gamma distribution. The approach to reach this purpose will be introducing a special polynomial including gamma distribution. Several formulas covering addition formula, derivative property, integral representation and explicit formula are derived by means of the series manipulation method. Furthermore, two correlations including Bernoulli and Euler polynomials for gamma distribution polynomials are provided by utilizing of their generating functions.

The aim of the present work is to explore a different non-traditional approach to higher dimensional spacetime which differs from the usual approaches such as large extra space dimensions, warped extra space dimensions and multiple extra time dimensions. This approach will be referred to as "Dynamic" higher dimensional spacetime. By this term will be introduced a new kind of higher dimensional spacetime (more than the usual 3+1 dimensions), which behaves dynamically in the sense that time is not a fixed dimension but is the extra plus one dimension to the spatial dimensions of the phenomenon we are studying. For a higher dimensional phenomenon, the lower dimensional time will behave as space and the new time will be a plus one dimension, meaning if we study a 3-dimensional phenomenon then time is the usual 4th dimension but if we are studying a 4-dimensional phenomenon then its time will be an extra 5th dimension and for this phenomenon the 4th dimension will behave as space. All spatial dimensions are indistinguishable from each other and behave in the exact same way, which means that the important parameter is not the dimension we are studying (for example the 4th or the 5th) but the number of dimensions in which a phenomenon can interact and how higher dimensional phenomena interact with lower ones. This non-traditional approach to higher dimensional spacetime may appear confusing at first but will become clearer in the rest of the paper. For this reason, we will first associate the time dimension with propagation relative to space dimensions and change orthogonal to them in order to give the reader a better intuition. Following that, we will describe how higher - dimensional phenomena would appear to us, the 3 - dimensional observer and try to set some guidelines on how we should mathematically model higher - dimensional phenomena in order for us to make accurate predictions of their behaviour. Then we will express the general framework of a "Dynamic" higher - dimensional spacetime and turn our gaze to 4+1 – dimensional phenomena. We will explore how a mass term arises for 4 – dimensional waves by generalizing the frequency – speed – wavelength relation of 3D waves and give a basic description on a possible way to describe a 4+1 – dimensional disturbance in a scalar Energy Field in order to make accurate predictions on our 3+1 dimensional plane. In this framework we will derive the Klein – Gordon equation by generalizing the wave equation and ignoring all lower than 4+1 - dimensional disturbances and compere our mass term findings with the Klein – Gordon equation mass term and with results from gravity – induced quantum interference experiments. Lastly, we will describe how a "Dynamic" 5 - dimensional spacetime would appear in a 3D observer and examine whether our findings are compatible with quantum mechanics and the special theory of relativity.

We present a new quadratic transformation identity for the confluent Heun function. This transformation is independent of the previously discovered quadratic transformation (Heliyon 10, e36535, 2024) and offers additional insights into the properties of this special function. Like the first transformation, this new identity involves two arbitrary parameters and has potential applications in both mathematical and physical contexts, particularly in quantum mechanics.

Microwave absorbers with lightweight, good stability and high efficiency have attracted much attention for their applications in many contemporary fields. In this work, the 3D porous (Ni@NO-C)n/NO-C composite absorber was prepared by a wet chemistry method with Ni chains and melamine as precursors, in which NO-C (N,O-doped carbon) encapsulated Ni particles are homogenously dispersed in the 3D porous networks of NO-C in the form of (Ni@NO-C)n chains. The special microstructure of the as-prepared material is proved to be benefit for the improvement of its microwave adsorption performance. The as-synthesized (Ni@NO-C)n/NO-C composite ab-sorber exhibited an effective absorption bandwidth of 4.1 GHz and an extremely large reflection loss of -72.3 dB. The excellent microwave absorbing performances can be ascribed to the coopera-tive consequence of dielectric loss and magnetic loss along with the balance between attenuation capability and impedance match.

We all have in mind Einstein's famous thought experiment in the elevator where we observe the free fall of a body and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation. We consider a uniformly accelerated reference frame in rectilinear translation and we show that the trajectories of the particles are ellipses centered on the horizon of the events. The frame of reference is non-inertial, the space-time is flat, the metric is non-Minkowskian and the computations are performed within the framework of special relativity. The deviation, compared to the classical case, is important close to the horizon, but small in the box, and the interest is above all theoretical and pedagogical. The study helps the student to become familiar with the concepts of metric, coordinate velocity, horizon, and, to do the analogy with the black hole.

Heritage conservation area designation is often resisted by communities due to concerns with overly strict regulations for property alterations and negative impacts on property values. This paper addresses these concerns by examining Freemans Bay and Onehunga – two Special Character Areas (SCAs) in Auckland, New Zealand. A property value analysis was used to assess the impact of SCA designation on property values and an online questionnaire survey gathered information on homeowners’ experiences and levels of satisfaction with living in an SCA. The results indicate that designated SCA properties have higher average values than non-designated properties and homeowners are overwhelmingly satisfied with living in a SCA. The main benefits are a sense of community and having certainty around the look and feel of their neighbourhood into the future. The main issue identified by respondents is the requirement for Resource Consent. The majority of people who had gone through the process found it to be a negative experience because of the high cost in terms of time and money. A historic urban landscape approach to the development of management plans and design guidelines is recommended to improve the implementation of the Special Character Areas in Auckland and beyond.

Leisure education has the potential to improve quality of life and prepares students for social par-ticipation after graduation. This study aimed to elucidate the perspectives of special education teachers regarding leisure instruction. This study surveyed 538 teachers from 10 special needs schools for students with intellectual disabilities in Prefecture A, a rural area of Japan. An online survey was conducted from October 21 to November 17, 2023. The survey items were based on 13 aspects of leisure instruction identified from a literature review related to leisure instruction in Japan and a qualitative analysis of interviews with high school teachers in special needs schools for stu-dents with intellectual disabilities. The results showed that “The ability to pass time during brief periods of free time,” “Various activity experiences that lead to leisure,” and “Knowing one’s strengths and weaknesses in activities” were significantly more important during school. Con-versely, “understanding the psychological importance of leisure,” “connecting with organizations that support leisure activities,” and “finding places to engage in leisure activities” were significantly more important after graduation. The results of this study will be used to identify gaps in percep-tions between special education teachers and vocational rehabilitation practitioners responsible for post-social participation support.

This study aimed to investigate Romanian physicians' awareness, recommendation practices, and opinions regarding using Foods for Special Medical Purposes (FSMPs) products. A total of ten physicians were interviewed using a structured questionnaire, and their responses were analysed using thematic content analysis. The study found that physicians were aware of FSMPs and recommended them to their patients based on nutritional deficits, weight loss, or deglutition impairments. In addition, disease stage, treatment scheme, taste, affordability, and availability were identified as factors influencing the recommendation and use of FSMPs. While physicians generally did not consult clinical trials, clinical experience was deemed essential for recommending FSMPs to patients. Patients' feedback regarding the usage and sourcing of FSMPs was generally positive, with some expressing concerns about the availability of different flavours and the costs of purchasing the products. The study concludes that physicians play a vital role in recommending FSMPs to patients and ensuring they have the necessary nutritional support during treatment. However, more patient education materials and collaboration with nutritionists may be required to improve patient outcomes and reduce patient financial burden.

This paper is mainly based on a stricter premise of the twin paradox and the assumption of inertial frame, discusses the properties of time and space under the premise of complete symmetry, and draws an interesting conclusion: the simultaneity of different reference frames is possible realized, and the space is relatively independent. And based on this, the twin paradox, cosmic inflation, ultra-distance action of quantum entanglement, microscopic space motion of particles, measurement problems and other phenomena are tentatively explained from a new angle. This interpretation is exploratory and new. At the same time, the author also proposes an experimental way to test the relative independence of space.At the same time, this paper attempts to strictly prove that Einstein's definition of simultaneity and spatial absoluteness in special relativity may be problematic.

On a rotating disk, two particles bounce at the vertices of a regular polygon in opposite directions. On the return to the entry point, a clock measures the time difference, called Sagnac effect. Due to Coriolis effects, the counterclockwise and clockwise paths are different. The particular case of the slow disk where the two trajectories are very close and almost polygonal is studied. The existence of a transition between a classical and a relativistic regime is proved. An experimental verification is proposed. Although the two Sagnac effects seem analogous, in detail their behavior is quite different.

In this paper, we present the definition, some properties, and solve a problem on special primes. These properties help in providing us with a better understanding of the problem posed related to special primes on the open problem garden website. The problem involves finding all the primes q, given a prime p such that q≡1(mod p) and 2^((q−1)/p)≡1(mod q). We prove that a prime number q is a special prime of p if and only if the order of 2 in U(q) divides q−1p. Also, we prove that a prime number q is not a special prime for any prime number if 2 is a generator of the group U(q) and that there exist infinitely many special primes for any given prime number.

For more than one hundred years, scientists dispute the correct interpretation of Lorentz transformations within the framework of the special theory of relativity of Albert Einstein. On the one hand, the changes in length, time and mass with increasing velocity are interpreted as apparent due to the observer dependence within special relativity. On the other hand, real changes are described corresponding to the experimental evidence of mass increase in particle accelerators or of clock delay. This ambiguity is accompanied by an ongoing controversy about valid Lorentz-transformed thermodynamic quantities such as entropy, pressure and temperature. In this paper is shown that the interpretation problem of the Lorentz transformations is genuinely anchored within the postulates of special relativity and can be solved on the basis of the thermodynamic approach of matter-energy equivalence, i.e. an energetic distinction between matter and mass. It is suggested that the velocity-dependent changes in state quantities are real in each case, in full agreement with the experimental evidence.

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators.

This study aimed to elucidate the perception gap regarding instructional matters between special education teachers and vocational rehabilitation practitioners involved in transition support in Japan. To this end, 126 vocational support providers affiliated with the Employment and Life Support Centers for persons with disabilities, which are vocational rehabilitation institutions in Japan, and 129 special education teachers from schools for students with intellectual disabilities in Prefecture X, Japan, were surveyed. They were asked to respond on the importance of teaching skills that constitute vocational readiness by means of a questionnaire comprising 25 items across five layers: vocational aptitude, basic work habits, interpersonal skills, daily living management, and health management, both during school and after graduation. The results revealed a perception gap in each of the first layer, vocational aptitude, and second layer, work habits. Additionally, only in the second layer, work habits, did special education teachers recognize the importance of instruction more during the school period than after graduation. Moving forward, it is necessary for both institutions involved in transition support to collaborate, focusing on students with disabilities based on the identified gap.

It is well known that a sequence of two non-collinear Lorentz boosts (pure Lorentz transformations) does not correspond to a Lorentz boost, but involves a spatial rotation, the Wigner or Thomas-Wigner rotation. We visualize the interrelation between this rotation and the relativity of distant simultaneity by moving a Born-rigid object on a closed trajectory in several steps of uniform proper acceleration. Born-rigidity implies that the stern of the boosted object accelerates faster than its bow. It is shown that at least five boost steps are required to return the object's center to its starting position, if in each step the center is assumed to accelerate uniformly and for the same proper time duration. With these assumptions, the Thomas-Wigner rotation angle depends on a single parameter only. Furthermore, it is illustrated that accelerated motion implies the formation of an event horizon. The event horizons associated with the five boosts constitute a natural boundary to the rotated Born-rigid object and ensure its finite size.

This paper presents an advanced and highly sophisticated model for hybrid electric special-purpose machines (HE-SPMs), specifically engineered to significantly enhance sustainability and efficiency in logistics operations. The primary objective of this model is centered around the optimization of energy flow, a feature that has undergone extensive testing and validation to ensure its reliability and effectiveness. The inclusion of auxiliary systems such as cutting-edge cooling and control systems further elevates the overall performance capabilities of the HE-SPMs, resulting in a seamless integration within various industries. By implementing these enhanced systems, substantial reductions in energy consumption and operational costs have been observed and well-documented through compelling case studies in both the construction and transportation sectors. The holistic nature of this approach impeccably aligns with the ongoing global efforts aimed at combating the pressing issue of climate change. By focusing on the development and utilization of eco-friendly technologies, this model actively contributes to the mitigation of harmful environmental impacts and promotes sustainable practices within the logistics industry. To further reinforce the efficacy of this remarkable model, future research endeavors will concentrate on expanding its applications to encompass other logistics domains.

The purpose of this evaluation is to determine the effect of intensive, interactive training on hospital workers’ preparedness for special pathogen cases by utilizing the Frontline Facility Special Pathogens Training Course created by New York

The urban museum has become a multi-functional institution that transcends the functional display of artifacts. The museum has become, in cities, a hybrid institution that keeps its doors open late to support a wide variety of special events. This study explored London’s ‘Museum Lates’ programs and event characteristics, using museums’ theoretical views as cultural tourism attractions. Furthermore, the study applied the contextual model of learning to understand visitor attendance motivations. Authors employed an interpretive approach using interviews with two types of participants, event visitors, and event coordinators. Findings suggested that attendees possess a complex of personal, physical, and socio-cultural motivations for participating in museum lates events. The characteristics of late events – extraordinary quality and evening time atmosphere – produce different effects than current museum exhibitions held during regular operating hours. Museum lates events can contribute to achieving cultural sustainability, adding cultural construct to the traditional three-pillars of sustainability. Keywords: Museums; special events; late opening; visitors' motivations; sustainability, touristic attractions

In this work, we investigate the behaviour of a relativistic scalar particle in the background of the Lorentz symmetry violation determined by a tensor (KF)µναβ out of the Standard Model Extension. A linear electric field and a uniform magnetic can be induced by the violation of the Lorentz symmetry breaking effects, and analyze the behaviour of the scalar particle. We see that the analytical solution to the KG-equation can be achieved, and a quantum effect characterized by the dependence of the magnetic field on the quantum numbers is observed

The construction industry generates significant CO2 emissions, and rebar is a major contributor to this environmental impact. Extensive research has been conducted to address this issue. Recent advancements have introduced algorithms to reduce rebar waste and consumption, demonstrating the feasibility of achieving near-zero rebar cutting waste (N0RCW) by considering special-length rebars. However, conventional lap splices, the most common rebar joint method, consistently consume excessive rebar quantities despite extending beyond their mandated zones. Conversely, couplers eliminate rebar lengths required for lapping splices, reducing the usage of rebar. Applying special lengths and couplers in heavily loaded structures like diaphragm walls can significantly reduce rebar usage and cutting waste, consequently reducing CO2 emissions and associated costs. This study aims to optimize rebar consumption and sustainability in diaphragm wall structures by integrating mechanical couplers with a special-length rebar approach. A case study confirmed a substantial reduction in purchased rebar usage (17.95% and 5.38%) and carbon emissions (15.24% and 2.25%) compared to the original design and previous study, respectively. Broadly implementing the proposed method across various buildings and infrastructure projects could further multiply these benefits, fostering the achievement of SDGs adopted by the United Nations for sustainable construction.

The paper covers the development of formulations and technology for low energy building materials based on the alkaline alumino-silicate binder and appropriate for special purposes. The microstructure of the binder was investigated using scanning electron microscopy and atomic force microscopy. The identification of the phase compositions was done by means of X-ray diffraction. By leach rate measurement and chemical analysis of pore liquid, the linkage of the alkali metal ions in water-insoluble composites was researched. The dependence of structure formation on mix design and curing conditions was investigated. Specific examples of manufacture and application of binder-based glues and adhesives have been considered, incl. ones for low-temperature insulating composite materials, heat insulation perlite-based materials, heat insulation of industrial boilers, and the fire resistant heat insulating system. The advantages of the binder-based temperature insulating composites compared to traditionally used ones are shown.

In this study, we investigate the behavior of randomly moving particles with a defined average energy, focusing on their biased motion around a specific point. These particles' velocity magnitudes follow a Maxwell distribution with a specific scale parameter. Our analysis derives the stochastic rotation rules for these particles and introduces the Ito equation conditions for biased stochastic rotation at a given curl value. We also consider the special relativistic-like effects in this context. The findings are validated through a representative example.

The special affine Fourier transform (SAFT) is a useful and powerful analyzing tool in signal processing, optics and communications. In this paper, we mainly discuss the randomized nonuniform sampling and reconstruction for random signals bandlimited in the SAFT domain. First, we show that the nonuniform sampling is identical to the uniform sampling after a pre-filter in the sense of second order statistic characters. Then, we propose an approximate reconstruction based on sinc interpolation for the nonuniform sampling of random signals bandlimited in the SAFT domain. Finally, we give the mean square error estimate for the proposed approximate recovery approach.

The non-inertial effects on spin-0 scalar particle that interacts with scalar potentials of Cornell-type in cylindrical system and Coulomb-type in the magnetic cosmic string space-time using Kaluza-Klein theory is analyzed. We show that the energy eigenvalue and eigenfunction depend on the global parameters characterizing the space-time, and the gravitational analogue of the Aharonov-Bohm effect for bound states is observed.

Number is based in special edges, is introduced. The kind of natural extension from edges toward vertex and the set of vertices in the way that, the final notion is number, is studied. The result is obtained which is about the study on the classes of graphs in the matter of new notions. There is the extended notion about having edge amid two vertices toward having some edges in the word of neighbor and in another stage going into the atmosphere of having consecutive edges in the terminology of path and in the upper vision going on the notion about path with jargon and buzzword of distance as if the minimal vertices has concluded the new notions with the word, number.

The existence of semantic inaccuracy §2 articles by A. Einstein “On the electrodynamics of moving bodies”, illustrating the principle of the relativity of simultaneity. In a sentence “The observers co-moving with the moving rod would thus find that the two clocks do not run synchronously while the observers in the system at rest would declare them synchronous”, the preposition “not” must be moved and placed before the word “synchronous”, at the end of the sentence. The criterion for synchronism of the clocks on the rod is the time it takes for the beam to travel from clock A to clock B and back, and for observers on the rod it will be the same both when the rod is at rest and when the rod is moving. Otherwise, observers on the rod would have had at their disposal an experiment that would allow them to determine whether the rod is moving or at rest, which contradicts the first postulate of the Special Theory of Relativity. The inaccuracy is found unchanged in modern editions in English and Russian, and can become a source of difficulties when teaching the basics of the Special Theory of Relativity based on primary sources, as well as make it difficult to understand the author’s logic when studying independently. Nobel laureate R. Feynman, having expanded and modified A. Einstein's thought experiment, eliminated the inaccuracy described in the article.

Special machinery engineering is of great importance to the manufacturing industry and makes a comparatively large contribution to many economies. Digital transformation is already well advanced in many producing industries, and modern ICT technologies such as agents, service orientation, digital twins and artificial intelligence are being used with increasing success. In addition to improving specific product characteristics such as reliability or flexibility, the adoption of modern ICT technologies to ensure sustainability is being intensively discussed. So far, however, there has been little uptake of these technologies in the special machinery industry; sustainability receives little attention. This article examines in detail the reasons for and impediments to the adoption of modern ICT technologies based on a study among special machinery manufacturers. Observations of existing challenges were gathered during daily work, described in detail, and used to derive conclusions about causal barriers. From this, detailed requirements are derived to promote the adoption of modern ICT technologies in the special machinery engineering sector and, ultimately, to bring sustainability more into focus.

The construction of reinforced concrete (RC) structures inevitably consumes an excessive number of rebars, leading to significant cutting waste and carbon emissions. Extensive research has been conducted to minimize this issue and its consequences; however, these methods consistently consume a substantial number of rebars. This includes a previous study that utilizes the lap splice position optimization and special-length rebar concept without considering the lapping zone regulation. Moreover, conventional lap splices pose inherent drawbacks that could jeopardize the structural integrity of RC members. In contrast, mechanical couplers eliminate the need for rebar lapping, effectively reducing rebar consumption. This research aims to evaluate the impact of an integrated mechanical coupler and special-length-priority minimization algorithm on the reduction in rebar consumption and cutting waste in RC columns, achieving near-zero cutting waste. To validate the effectiveness of the proposed algorithm, it was applied to the column rebars of an RC building. The results revealed a significant reduction in ordered rebar consumption by 18.25%, accompanied by substantial reductions in cutting waste (8.93%), carbon emissions (12.99%), and total costs (10.81%) compared with a previous study. The outcomes provide the industry with insights into further reducing rebar consumption and its related consequences. Applying the proposed algorithm to various construction projects will further amplify the corresponding benefits.

Students with disabilities are often framed as “the problem” and have limited opportunities to engage in standards based mathematics, leading to persistent underachievement. In this paper, we investigate a research divide between mathematics educational research for students with and without disabilities, a divide with significant differences in the theoretical orientations and research methodologies used to understand learners. Based on an analysis of 149 mathematics educational research articles published between 2013 and 2015, we found significant differences between articles focused on learners with and without disabilities. For those with disabilities, mathematical problem solving was understood primarily from behavioral and information processing theoretical perspectives, while for those without disabilities, problem solving was understood primarily through constructivist and sociocultural perspectives. While 86% of research on problem-solving including students with disabilities was quantitative, only 35% of research on students without disabilities was quantitative. Fifty percent of problem-solving research on students without disabilities was qualitative, compared to only 6% of research on students with disabilities. Problem solving, then, is studied in very different ways for learners with and without disabilities. Students without disabilities are studied through close analysis of learning, often individual. Students with disabilities are most often studied quantitatively, in groups, with little analysis of individual thinking. By offering only a limited range of methods and theoretical orientations, this research divide reifies deficit constructions of students with disabilities.

The primary concept of time in special and general relativity (SR, GR) and quantum mechanics (QM) is coordinate time t. Here I show: SR and GR are mathematically correct, but physically t has an issue. It takes an observer as the center of time, just as the geocentric model takes Earth as the center of space. In Euclidean relativity (ER), the roles of t and proper time τ have switched. Time dilation is interpreted differently: In ER, an observed clock is slow with respect to an observer in his proper flow of time (not in its proper flow of time as in SR/GR). All energy is moving through 4D Euclidean space (ES) at the speed c. All four dimensions are distance, and “cosmic time” t is the total distance covered in ES divided by c. Unlike in previous ER models, an observer’s reality is only created by projecting ES orthogonally to his proper 3D space and to his proper flow of time. The Lorentz factor and gravitational time dilation are recovered in ER. So, ER predicts the same relativistic effects as SR and GR. Yet ER outperforms SR in solving time’s arrow and the c² in mc². ER also outperforms a GR-based cosmology in explaining the data from high-redshift supernovae while declaring cosmic inflation, expansion of space, dark energy, and quantum gravity redundant. ER even improves our understanding of QM: It solves the wave–particle duality and quantum entanglement while declaring non-locality redundant. I conclude: The true pillars of physics are ER and QM.

This paper uses a qualitative case study to investigate the experiences of Korean special education teachers who instruct children with disabilities from multicultural families. Through a purposive sampling method, study participants were chosen from a pool of individuals that the Korean multicultural support center recommended. These individuals are special teachers who are currently teaching children with disabilities from multicultural families. The qualitative case study approach used in this study seeks to elicit the participants’ experiences of teaching their students with special needs. The teachers’ experiences were analyzed and categorized into two main categories: 1) a mother's lack of Korean linguistic ability and 2) governmental and societal support for multicultural special education. Additionally, results also produced four sub-categories and seventeen minor categories. Such analyses lead to a greater understanding of the intricacies of educating children with special needs. Lastly, the implications of this study provide direction for future policy--including social welfare and educational support—that will meet the needs of multicultural families raising children with disabilities.

The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.

Inclusive education in Indonesia has evolved in recent years, in line with the government's commitment to provide equal education for all children, including those with special needs. This article reviews the philosophy of inclusive education and its implementation in Indonesian education. Through literature and policy analysis, it is found that although there is increasing awareness and support for inclusive education, there are still barriers that need to be overcome. These include the lack of accessibility and adequate facilities, limited teaching staff for children with special needs, and social stigma towards children with special needs. This review also identifies the characteristics of inclusive education and its implementation. In conclusion, inclusive education in Indonesia requires a holistic and collaborative approach between the government, communities, and educational institutions to create a truly inclusive and equal learning environment for all learners

Astragalus plants belong to the legume family and have obvious rhizosphere effect. The northwestern area of Yunnan China is the main distribution region of Astragalus plants with high application value, but low recognition and resource reserves. The aim of this research is to explore the species diversity of cultivable rhizosphere fungi derived from A. acaulis, A. forrestii, and A. ernestii growing in special high-cold environment of northwest Yunnan, and discover anti-infective components from these fungi. A total of 93 fungal strains belonging to 38 species in 18 genera were isolated and identified. Antibacterial and antimalarial screening yielded 10 target strains. Among them, the ethyl acetate crude extract of the fungus Aspergillus calidoustus AA12 from A. acaulis fermentation substance showed a broad antibacterial spectrum and the best antimalarial activity. Further chemical investigation led to the first discovery of seven compounds from the species of A. calidoustus, including a sesterterpine 6-epi-ophiobolin G (1), two sesquiterpenes penicisochroman A (2), pergillin (3) and 7-methyl-2-(1-methylethylethlidene)-furo[3,2-H]isoquinoline-3-one (4), and three polyketides trypacidin (5), 1,2-seco-trypacidin (6) and questin (7). Compound 1 exhibited moderate to strong antibacterial activity against six Gram-positive pathogens with the minimum inhibitory concentration (MIC) ranging from 25 to 6.25 μg/mL, and prominent inhibitory effect on the biofilm of Streptococcus agalactiae at MIC value of 3.125 μg/mL. This compound also displayed potent antimalarial activity against Plasmodium falciparum strains 3D7 and chloroquine-resistant Dd2 at the half maximal inhibitory concentration (IC50) values of 3.319 and 4.340 µmol/L at 72 h, respectively. This study contributed to our understanding of the cultivable rhizosphere fungi Astragalus-derived in special high-cold environment and further increased the library of fungi available for natural anti-infectious products screening.

In applied mathematics, statistics, operation research, physics, and engineering mathematics, confluent representations of hypergeometric functions in one and two variables are known to exist, and their occurrence in a variety of applications is also well recognised. In this article, we intend to present a new derivation of the extended Watson summation theorem for the Kim et al. given series 4F3. We assessed four attractive integrals involving generalized hypergeometric function as an application. With a few particular cases, this note will come to an end. In the results given above, symmetry appears on its own.

This work aims to introduce a novel concept: the Riesz-Dunkl fractional derivatives, within the context of Dunkl type operators. A particularly noteworthy revelation is that when a specific parameter $\kappa$ equals zero, the Riesz-Dunkl fractional derivative smoothly reduces to both the well-known Riesz fractional derivative and the fractional second-order derivative. Furthermore, we introduce a new concept: the fractional Sobolev space. This space is defined and characterized using the versatile framework of the Dunkl transform.

Over the last decade, the therapeutic scenario for advanced non-small-cell lung cancer (NSCLC) has undergone a major paradigm shift. Immune checkpoint inhibitors (ICIs) have shown a meaningful clinical and survival improvement in different settings of the disease. However, the real benefit of this therapeutic approach remains controversial in selected NSCLC subsets, such as those of the elderly with active brain metastases or oncogene-addicted mutations. This is mainly due to the exclusion or underrepresentation of these patient subpopulations in most of the pivotal phase III studies; this precludes the generalization of the ICI efficacy in this context. Moreover, no predictive biomarkers of ICI response exist that can help with patient selection for this therapeutic approach. Here, we critically summarize the current state of ICI efficacy in the most common “special” NSCLC subpopulations.

We propose a notion of a ternary skew-symmetric covariant tensor of 3rd order, consider it as a 3-dimensional matrix and study a ten-dimensional complex space of these tensors. We split this space into a direct sum of two five-dimensional subspaces and in each subspace there is an irreducible representation of the rotation group SO(3)↪SO(5). We find two independent SO(3)-invariants of ternary skew-symmetric tensors, where one of them is the Hermitian metric and the other is the quadratic form. We find the stabilizer of this quadratic form and its invariant properties. Making use of these invariant properties we define a SO(3)-irreducible geometric structure on a five-dimensional complex Hermitian manifold. We study a connection on a five-dimensional complex Hermitian manifold with a SO(3)-irreducible geometric structure, find its curvature and torsion. The structures proposed in this paper and their study are motivated by a ternary generalization of the Pauli’s principle proposed by R. Kerner.

Urinary and fecal incontinence as well as skin pressure injury are common healthcare problems in nursing home; however, these prevalence and related risk factors were not well understood in the Japanese special elderly nursing home settings. We surveyed the prevalence of urinary, fecal and double incontinence, and skin pressure injury among the elderly living in special elderly nursing home in Japan. A nationwide cross-sectional epidemiological survey was conducted with a total of 4,881 residents. The prevalence of urinary, fecal and double incontinence was 82.9%, 68.9% and 64.9%, respectively. Skin pressure injury was found in 283 residents (283/4881, 5.8%). Age, Care-Needs level, loss of voiding desire, and fecal incontinence were significant risk factors for urinary incontinence. Residential period, Care-Needs level, loss of voiding and defecation desires, and urinary incontinence were significant risk factors for fecal incontinence. Only male sex was a significant risk factor for skin pressure injury. Our study revealed continence status and the prevalence of pressure skin injury among older adult residents who receive an end-of-life care in special nursing homes in Japan. Further studies should be conducted to examine whether recovery of urinary and fecal sensations improves continence status.

Gifted students are usually known as students who have exceptional cognitive and learning abilities. This can be made clear through their learning performance or test scores. However, there are other students who have been identified as gifted and talented, yet have some learning and /or physical disabilities, and these are called twice-exceptional students. Identifying this population of gifted students is usually problematic because their disabilities and difficulties may mask their abilities and vice versa. It has been suggested that twice-exceptional students’ skills and abilities cannot be improved simply by working harder. Instead, these students need teachers to understand their strengths and weaknesses, use teaching strategies that fit their disabilities and serve their needs, and include their parents and educators in their learning process. Thus, this conceptual paper provides an extensive overview of the needs, challenges, and teaching strategies related to twice-exceptional students.

In this paper, we firstly consider extended degenerate central factorial numbers of the second kind and provide some properties of them. We then introduce unified degenerate central Bell polynomials and numbers and investigate many relations and formulas including summation formula, explicit formula and derivative property. Moreover, we derive several correlations for the fully degenerate central Bell polynomials associated with the degenerate Bernstein polynomials and the degenerate Bernoulli, Euler and Genocchi numbers.

Over the last three decades, special economic zones (SEZs) have given new impetus to the ever-growing export-oriented industrialization in developing countries. Where various economies have benefited from SEZs, many zones have ended up becoming enclaves with trifling advantage. The SEZs in Pakistan have experienced the same fate and failed to contribute to exports, employment and creating linkages with the domestic economy. Recently under China Pakistan Economic Corridor (CPEC), SEZs are proposed to be set up in Pakistan; with a hope to fuel the stuttering economy. However, it is pertinent to first understand the local context and device policies considering stakeholders' perspectives. This study aims to identify the factors for the successful implementation of SEZs derived from the regional context of Pakistan. In-depth interviews are conducted from most relevant stakeholders, who have been involved in the development of SEZs. The results pointed towards the removal of political influence over zones and government taking the lead role in deciding the types of industry to be invited in these zones. Each zone should have a clear vision of development based on its regional advantage. The zone promotions should be based on competitiveness rather than fiscal incentives. Joint ventures and PPP to be encouraged inside the zones for sustainable operations.

The water quality of the river is becoming deteriorated due to human interference. It is essential to understand the relationship between human activities and land-use types to assess the water quality of a region. GIS has the latest tool for analyzing the spatial correlation. Land use land cover and change detection is the best illustration to show the human interactions on land features. The study assessed water quality index of upper Ganga River near Haridwar, Uttarakhand and spatially correlated them with changing land use to reach a logical conclusion. At the upper course of Ganga along 78 Km long from Kaudiyala to Bhogpur, water samples were collected from five stations. For water quality index the physicochemical parameters like pH, EC, DO, TDS, CaCO3-, CaCO3, Cl¯, Ca++, Mg++, Na+, K+, F-, Fe2+ were considered. The result of the spatial analysis was evaluated through error estimation and spatial correlation. The root mean square error between spatial land use and water quality index of selected sampling sites was estimated as 0.1443. The spatial correlation between land-use change and site-wise differences in water quality index has also shown a high positive correlation with R² = 0.8455. The degree of positive correlation and root mean square error has strongly indicated that the water quality of the river at the upper course of Ganga is highly impacted through human activities.

Determining disability prevalence is an important area for population statistics, especially among young adolescents. The Washington Group on Disability Statistics is one source of reporting disabilities through functional difficulties. However, young adolescents self-reporting this measure is in its infancy. The purpose of this study was to carry out an intra-rater test-retest reliability study on a modified set of items for self-reporting functional difficulties. Young adolescents (n=74; boys=64%; age m=13.7, SD=1.8) completed a self-reported version of the child functioning module in a supervised classroom. The second administration took place two weeks later. Intraclass correlation coefficient (ICC) and Kappa (k) statistics were used to test reliability of the items, and interpretation through Landis & Koch, and Cohen, respectively. The majority of items had substantial or moderate agreement, although there was only fair agreement for self-care (ICC=0.59), concentration (ICC=0.50), and routine (ICC=0.54). Kappa statistics of behaviour were interpreted to be large (k=0.65), and seeing (k=0.49), walking (k=0.49), and speaking (k=0.49) difficulties were moderate. The majority of the items in the self-reported version of the child functioning module can be used in a scale format, although some caution may be required on items of self-care and concentration when used as a dichotomous variable.

The present paper introduces a method of basis transformation of vector fields that is specifically applicable to polynomials space and differential equations with certain polynomials solutions such as Hermite, Laguerre and Legendre polynomials. The method based on separated transformation of vector space basis by a set of operators that are equivalent to the formal basis transformation and connected to it by linear combination with projection operators. Applying the Forbenius covariants yields a general method that incorporates the Rodrigues formula as a special case in polynomial space. Using the Lie algebra modules, specifically , on polynomial space results in isomorphic algebras whose Cartan sub-algebras are Hermite, Laguerre and Legendre differential operators. Commutation relations of these algebras and Baker-Campbell-Hausdorff formula gives new formulas for special polynomials

Nowadays, it can be observed that all kinds of technology are gradually being incorporated to assist the human being in the performance of their frequent and daily tasks. Technological tools provide means to facilitate, improve, help and support any activity which, in itself, may be complicated, either because of the difficulty involved in carrying it out, or because the person carrying it out has limited capabilities due to the environment not being prepared for their abilities and skills. In this sense, Special Education is currently receiving special attention from researchers, especially those aimed at children. Although the proposals that have appeared recently provide perfect solutions to improve educational processes with ingenious didactic applications, there is still an interesting line of study on how to interact with these younger people in these educational processes. In this sense, haptic technologies can play a very important role, complementing all these solutions by incorporating tools that facilitate direct contact with people, especially in their initial stages, which are the most complicated. This paper aims to provide an overview of haptic technologies and how they present solutions that can be integrated into the aforementioned educational processes.

To embrace the special theory of relativity with classical thermodynamics correct Lorentz transformations of thermodynamic state functions are formulated. All of these Lorentz transformations of state functions equally support the time dilation phenomenon which is experimentally verified fact. Relativistic Boltzmann constant proves entropy to be the Lorentz variant. Twin paradox thought experiments for heat engines prove heat flux to be Lorentz variant. Lorentz transformation of entropy and heat flux proves temperature Lorentz invariant. All thermodynamic state functions are proved to be Lorentz variant which is shown in accord with Lorentz transformation of thermodynamic work.

When presenting special relativity, it is customary to single out the so-called paradoxes. One of these paradoxes is the formal occurrence of speeds exceeding the speed of light. An essential part of such paradoxes arises from the incompleteness of the relativistic calculus of velocities. In special relativity, the additive group is used for velocities. However, the use of only group operations imposes artificial restrictions on possible computations. Naive expansion to vector space is usually done by using non-relativistic operations. We propose to consider arithmetic operations in the special theory of relativity in the framework of the Cayley–Klein model for projective spaces. We show that such paradoxes do not arise in the framework of the proposed relativistic extension of algebraic operations.

The principle of the constancy of the velocity of light, which stated that the light velocity is invariant to the motion of the emitter, was well established and directly proven by experiments. Interestingly, the further assumption that the light velocity is independent of the motion of the observer was, arguably, never directly proven by any experiment for a century. This paper proposed the design of two experiments to directly test this assumption, which tried to address some perceived technical difficulty in such experiments. One is to directly measure the light speed as to moving sensors. The experiment setup is designed in such a way that the concerns of time synchronization and dilation can be avoided. Another experiment is to test the isotropy of the light speed to a moving particle in the electromagnetic accelerator by measuring the momentum to acceleration ratio. The experiment result, if positive, will provide direct and solid proof of the assumption. Otherwise, it may imply a need for further investigation. Since the light speed invariance to moving observers is a key assumption of some fundamental physical theory, either way, the experiments will have significant meanings.

We explore the possibility to form a physical theory in $C^4$. We argue that the expansion of our usual 4-d real space-time to a 4-d complex space-time, can serve us to describe geometrically electromagnetism and nuclear fields and unify it with gravity, in a different way that Kaluza-Klein theories do. Specifically, the electromagnetic field $A_\mu$, is included in the free geodesic equation of $C^4$. By embedding our usual 4-d real space-time in the symplectic 8-d real space-time (symplectic $R^8$ is algebraically isomorphic to $C^4$), we derive the usual geodesic equation of a charged particle in gravitational field, plus new information which is interpreted. Afterwards, we formulate and explore the extended special relativity and extended general relativity an $C^4$ or$R^8$. After embedding our usual 4-d space-time in $R^8$, two new phenomena rise naturally, that are interpreted as "dark matter" and "dark energy". A new cosmological model is presented, while the geometrical terms associated with "dark matter" and "dark energy" are investigated. Similarities, patterns and differences between "dark matter", "dark energy", ordinary matter and radiation are presented, where "dark energy" is a dynamic entity and "dark matter" reveal itself as a "mediator" betwen ordinary matter and "dark energy". Moreover, "dark matter" is deeply connected with "dark energy". Furthermore, the extended Hamilton-Jacobi equation of the extended space-time, is transformed naturally as an extended Klein-Gordon equation, in order to get in contact with quantum theories. By solving the Klein-Gordon equation analytically, we derive an eigenvalue for Higg's boson mass value at 125,173945 $Gev/c^{2}$. The extended Klein-Gordon equation, also connects Higg's boson (or vacuum) with Cosmology, due to the existence of our second "time" T (cosmological time), which serve us to connect quantum theories with Cosmology. Afterwards, in the general case, we explore the symmetries of the curved Hamilton-Jacobi equation locally, in order to investigate the consequences of a $C^4$ space-time in Standard Model. An extension to Standard Model is revealed, especially in the sector of strong nuclear field. The Stiefel manifold $SU(4)/SU(2)$ seems capable not only to describe the strong nuclear field but give us,as well, enough room to explore in the future, the possibility to explain quark confinment. Our extension, flavors firstly the unification of nuclear fields and afterwards the unification of nuclear fields with electromagnetic field. The desired grand unification, is achieved locally, through the symmetry group $GL(4,C)\simeq SO(4,4)\cap U(4)$ and we present a potential mechanism to reduce the existing particle numbers to just six. Afterwards,23 present the extended Dirac equation in $C^4$ space-time (Majorana-Weyl representation) plus a preliminary attempt to introduce a pure geometric structure for fermions. Finally, we consider a new geometric structure through n-linear forms in order to give geometric explanation for quantisation