Length Contraction Research Articles

Webb's conjecture and generalised Harish‐Chandra theory

AbstractWebb's conjecture states that the orbit space of the Brown complex of a finite group at any given prime is contractible. This conjecture was proved by Symonds in 1998. In this paper, we suggest a generalisation of Webb's conjecture for finite reductive groups. This is done by associating to each irreducible character a new simplicial complex defined in terms of Deligne–Lusztig theory. We then show that our conjecture follows from a condition, called (‐HC‐conj) below, related to generalised Harish‐Chandra theory. In particular, using earlier results of the author, we prove our conjecture and recover Symonds result for finite reductive groups under mild restrictions on the prime . Finally, we show that the condition (‐HC‐conj) is implied by the contractibility of the orbit spaces associated to our newly defined complex offering an unexplored topological approach to proving the uniqueness of ‐cuspidal pairs up to conjugation.

Modular invariance and thermal effective field theory in CFT

We use thermal effective field theory to derive that the coefficient of the first subleading piece of the thermal free energy, c1, is equal to the coefficient of the subleading piece of the Casimir energy on S1 × Sd−2 for d ≥ 4. We conjecture that this coefficient obeys a sign constraint c1 ≥ 0 in CFT and collect some evidence for this bound. We discuss various applications of the thermal effective field theory, including placing the CFT on different spatial backgrounds and turning on chemical potentials for U(1) charge and angular momentum. Along the way, we derive the high-temperature partition function on a sphere with arbitrary angular velocities using only time dilation and length contraction.

Fixed points of two interpolative cyclic contractions in b-metric spaces.

The b-metric space happens to be one of the of most significant and non-trivial generalizations of metric spaces. In this paper, we introduce the concepts of Kannan type and Ćirić-Reich-Rus type cyclic contractions in b-metric spaces via interpolation. Existence and uniqueness of fixed points of these two newly introduced contraction mappings have been studied and validated with suitable examples. Our paper also generalizes, extends and provides improvements to the results in the recent paper by Edraoui et al. (2023) [11].

Kinematics of balls and light versus the theory of special relativity

The study of the emission, propagation, and reflection of balls leads to the mechanical ballistic law, which applies to both balls with and without mass. A natural extension of the ballistic law is to encompass massless entities such as light. According to the ballistic law, a ball or light emitted by a source inherits the velocity of the source in the absolute frame. The phenomenon described by the ballistic law works in the absolute frame which acts as the background of inertial frames and governs the kinematics of balls and light in each inertial frame. It explains why the light emitted, propagated, and reflected speed is the universal constant <mml:math display="inline"> <mml:mi>c</mml:mi> </mml:math> in any inertial frame when the sources and mirrors are at rest, why the laws of physics have the same form in any inertial frame, and why no experiment in such a frame can prove its motion. By understanding the kinematics of light, we can understand the multiple issues rooted in Lorentz’s transformation and Einstein’s special relativity. For example, the theory of special relativity misapplies the symmetry observed in some phenomena to two inertial frames. Thus, it duplicates a physical phenomenon from one inertial frame considered stationary to another. The Lorentz transformation imposes the speed of light <mml:math display="inline"> <mml:mi>c</mml:mi> </mml:math> in the moving and opposite directions of the inertial frame. Simultaneously, it varies in any other direction converging to infinite. The time contraction in the moving direction of the inertial frame is different from the time dilation in the opposite direction, and both times are different from those in any other direction. Thus, each direction requires a ruler and time synchronization. Lorentz’s transformation has no length contractions to support this fundamental concept of special relativity. These unacceptable conclusions prove that the theory of special relativity is self-negating.

Solving nonlinear fractional differential equations by common fixed point results for a pair of (α, Θ)-type contractions in metric spaces

Abstract The problem of common solutions for nonlinear equations has significant theoretical and practical value. In this article, we first introduce a new concept of a pair of ( α , Θ ) \left(\alpha ,\Theta ) -type contractions, and then, we present some common fixed point results for the contractions in complete metric spaces. Finally, our results are applied to consider the existence, uniqueness and approximation of common solutions for two classes of nonlinear fractional differential equations.

Fixed point results employing simulation functions in JS-metric spaces

This paper introduces a new class of contractions in JS-metric spaces and utilizes it to obtain fixed point results, which generalize several well-known results. Moreover, an example is given to illustrate the utility of the obtained results.

Contraction And 𝐂(𝛂)- Suboperator Classes

In this paper we characterize the generalisation of contraction in Hilbert space and 𝐶(𝛼)- Suboperator class and establish some new result in the class of 𝐶(𝛼)- Suboperator [1] and its contractive extensions of a 𝐶(𝛼)- Suboperator class in a complex Hilbert space. The characterizations include a quadratic form inequality. The bounded linear operator 𝑇 in complex Hilbert space which satisfy 𝑇 = 𝛽𝐼 +(1 −𝛽)𝑈 where 𝛽 ∈ (0,1) and 𝑈 is a contraction (‖𝑈‖ ≤ 1)

Humanitarian aid practices on the Thai-Myanmar border after the coup: beyond depoliticization and inequality

Since the military coup in Myanmar in February 2021, conflicts have escalated, leading to a contraction of humanitarian space. While local actors have increasingly played a crucial role in adapting to the crisis, they encounter significant constraints within the aid system. This study explores the complex dilemmas of humanitarian aid localization on the Thailand-Myanmar border, focusing on challenges related to unequal power dynamics and depoliticized bureaucratic practices. The research finds that bureaucratic and managerial approaches to depoliticization limit the autonomy of local actors, impair their decision-making capabilities, and reduce humanitarian issues to technical and administrative problems, neglecting the intricate political context of the border crisis. The tension between control and flexibility, intertwined with systemic inequalities, further marginalizes the political subjectivity of refugees, and hinders the effective advancement of the localization process. This paper argues that reforming the humanitarian aid system should shift beyond depoliticization and inequality, emphasizing the importance of respecting marginalized subjectivities to establish a genuine foundation of trust and achieve aid justice.

Fixed point and stability results for multi-valued nonlinear graph contractions in complete metric spaces

Fixed point and stability results for multi-valued nonlinear graph contractions in complete metric spaces

Some Innovative Results for Interpolative Reich–Rus–Ćirić-Type Contractions in Rectangular m-Metric Spaces

In this paper, we study the existence of fixed points for interpolative Reich–Rus–Ćirić-type contractions in the setting of rectangular m-metric spaces. The use of the rectangular inequality, in place of the conventional triangle inequality, introduces a higher level of complexity in the computations, requiring more careful and refined analysis. We consider two distinct cases based on the sum of the interpolative exponents: one where the sum is less than 1, and another where the sum exceeds 1. The results we present generalize several existing theorems in the literature, and each is supplemented with illustrative examples to demonstrate their applicability. Moreover, we deduce corresponding results on m-metric spaces from these results, which are new themselves. They are also validated through examples.

Real-Time CASSCF (Ehrenfest) Modeling of Electron Dynamics in Organic Semiconductors. Dynamics Reaction Paths Driven by Quantum Coherences. Application to a Radical Organic Semiconductor.

We present a strategy for the modeling of charge carrier dynamics in organic semiconductors using conventional quantum chemistry methods, including the analytic gradient for nuclear motion. The theoretical approach uses real-time CASSCF (Ehrenfest) all-electron dynamics coupled to classical nuclear dynamics for the special case of a small number (4-8) of molecular units. The objective is to obtain mechanistic/atomistic insight at the electronic structure level, relating to spin density dynamics, to the effect of crystal structure (e.g., slippage between spin/charge carriers), and to ferromagnetic and antiferromagnetic effects. The initial conditions for our simulations use the equilibrium structures of all the molecular units. At this geometry, a localized hole on one of the units corresponds to a coherent superposition of adiabatic states. We thus generate a dynamics reaction path driven by quantum coherences. Our aim is to inform experiment and to compare with parametrized theoretical models. The methodology is demonstrated for a perfectly π-stacked ethylene model (up to 8 eclipsed molecular units) for both hole transfer and localized exciton transfer. An application for hole transfer is presented for bisdithiazolyl (S,S) and bisdiselenazolyl (Se,Se) radicals for the special case of ferromagnetic coupling. For these examples, the embedded pyridine radical model organic chromophore (up to 6 eclipsed π-stacked molecular units) has been studied on its own as well as the target bisdithiazolyl (S,S) and bisdiselenazolyl (Se,Se) systems. A significant difference between these systems and the ethylene and pyridine stacks is that the (S,S) and (Se,Se) systems exhibit molecular slippage rather than being perfectly eclipsed. This slippage may result from crystal defects or intermolecular vibrations. For the model systems, the electron dynamics is dominated by the initial and final molecular units, irrespective of the length of the chain. The intervening units act as a "superexchange bridge". Our simulations reveal that, in the presence of slippage, charge migration cannot propagate across the entire system; instead, the coherence length is limited to 3 molecular units. The results also suggest that the mechanism of charge transport is different for bisdiselenazolyl (Se,Se) (superexchange-like A -[B]→ C) and bisdithiazolyl (S,S) (direct A → C). An analysis of the spin density suggests that, in the charge carrier dynamics, the additional charge carried by the Se versus S in the "scaffold" is small. Since we use a small number of molecular units, the coupled nuclear dynamics is seen to be complementary to the electron dynamics (i.e., creating a hole causes bond length contraction while filling a hole with an electron lengthens the bond). In all the cases studied, the mechanism of charge mobility is wave-like, rather than hopping, because we use the time dependent Schrödinger equation to propagate the electronic wave function.

Effects of isometric contraction training on hypertensive patients：A Systematic Review

Introduction: Hypertension is one of the major threats to the health of the entire population in today's society. Poor blood pressure values represent health warnings and are also a risk factor for cardiovascular diseases such as stroke, heart disease, angina pectoris, and peripheral arterial disease. The National Cardiovascular Disease Center's "China Cardiovascular Health and Disease Report 2023" data shows that the prevalence of hypertension in adults has reached 31.6%, with a total of 245 million patients. Moreover, studies have shown that 43.1% of the population have normal high blood pressure, with an estimated number of 4.35. The same problem occurs not only in China, but also in the statistics of the Centers for Disease Control and Prevention in the United States. Nearly 47% of the American population has hypertension. Isometric contraction training is a type of resistance training that was often considered to be avoided by hypertensive patients in previous exercise guidance. However, in recent years, research has shown that under appropriate control, it can effectively lower blood pressure. This study explores the effects of isometric contraction training on blood pressure during acute and non acute interventions by searching and organizing relevant literature, and attempts to find new strategies as non pharmacological treatments for hypertension. Based on past research, it has been found that long-term isometric contraction training has a consistent effect on lowering blood pressure. Although there are immediate changes in acute intervention studies, the duration is very short. The use of equal length contraction training or ischemic preconditioning as a non pharmacological blood pressure improvement strategy has been proven to be safe and effective, with high process controllability, and may be a more feasible strategy in the future. Aim of the study: This study aims to evaluate the relevant literature on equal length contraction training as a strategy for reducing blood pressure, explore the correlation between experimental methods and the degree of blood pressure reduction, and attempt to find more effective ways in non pharmacological treatment strategies for hypertension. Material and methods: After conducting a systematic search of the following databases, this article identified potentially qualified grey literature from Pubmed, Web of Science, and Google Scholar, as well as journals in related fields. There are no restrictions on language or publishing timeline. The retrieval strategy uses keywords, medical keywords (MeSH), and Boolean conjunctions, including isometric contract or tension, AND (Contract, Isometric or Contracts, Isometric or Isometric Contracts), and AND (Blood Pressure, High or Blood Pressures, High or High Blood Pressure or High Blood Pressures。 In addition, a literature review was conducted to further identify randomized controlled trials that met the inclusion criteria. Conclusions: IHG can significantly reduce SBP、DBP and MAP in hypertensive patients. Therefore, we recommend that this type of exercise (especially wall squatting and grip strength exercises) is considered an effective therapy for reducing arterial hypertension. The efficiency of this intervention is limited to the short term. Therefore, long-term effects (at least 1 year) should be studied.

Enhancing photocatalytic performance in Bi₂WO₆ nanolayers via ultrasound-assisted oxygen vacancy engineering

High-quality two-dimensional Bi₂WO₆ nanolayers were synthesized via hydrothermal processes, with oxygen vacancies introduced through an ultrasound-assisted alkali etching treatment. Comprehensive characterization using Raman spectroscopy, X-ray absorption spectroscopy (XAS), transmission electron microscopy (TEM), X-ray photoelectron spectroscopy (XPS), and positron annihilation spectroscopy (PAS) confirmed the presence and effects of these vacancies on the structural and electronic properties of the nanolayers. Raman spectroscopy revealed shifts in vibrational modes, particularly a blue shift in the WO₆ octahedral vibration modes, indicative of oxygen vacancy formation. XPS analysis showed a reduction in the binding energies of the Bi 4f and W 4f orbitals, confirming an altered electronic environment. TEM images demonstrated significant lattice distortions in the oxygen-vacancy-rich regions, particularly disordered WO₆ octahedra and disrupted BiO bond lengths. These distortions are consistent with the structural disorder observed in XAS measurements, which highlighted a reduction in the coordination number of W atoms and a corresponding contraction of WO bond lengths. This charge redistribution between Bi and W atoms due to oxygen vacancies leads to localized structural perturbations, as further evidenced by PAS, which showed increased positron lifetimes associated with vacancy clusters, particularly around the Bi and W atoms. These vacancies create defective sites that trap photogenerated electrons, preventing their recombination with holes, thereby significantly enhancing photocatalytic performance. The enhanced photocatalytic activity was demonstrated by the nearly 98 % degradation of Rhodamine B dye under visible-light irradiation, a substantial improvement over the 70 % degradation achieved by the untreated sample. This work presents an innovative approach for generating stable oxygen vacancies in Bi₂WO₆ nanolayers and offers an in-depth understanding of the mechanisms that enhance photocatalytic performance, providing valuable insights for advancing photocatalysts designed for environmental remediation.

Some Fixed Point Results on Generalized Weak Contractions in Partial Metric Spaces With an Application

Some Fixed Point Results on Generalized Weak Contractions in Partial Metric Spaces With an Application

PENGEMBANGAN MICROLEARNING VIDEO 360° PADA FENOMENA KONTRAKSI PANJANG

Currently educators are faced with great challenges, where educators are required to develop human resources by utilizing technology, especially in modern physics learning in the era of Society 5.0. This research aims to design and develop a 360° video microlearning that is feasible to use as a learning media for modern physics courses on the topic of length contraction to support effective learning in class. This research is a type of development research using the ASSURE model. In this study, the sample used consisted of 60 respondents taken from 1 class of physics education students and 1 class of UNJ physics students. This study shows that the use of 360° videos significantly improves students' understanding of complex physics concepts and increases their involvement in the learning process. The impact can be seen from the improvement of learning quality that creates an interactive and engaging learning experience. The final product of this research is a 360° video presented using the YouTube platform and can be accessed easily by students using supporting electronic devices. The 360° video has gone through the feasibility test stage to media experts and material experts. The results of the product feasibility test by media experts with a percentage of 93.75% get the results of "Very Feasible", as well as by material experts with a percentage of 87.5% get the results of "Very Feasible".

Spectral bounds on the entropy flow rate and Lyapunov exponents in differentiable dynamical systems

Abstract Some microscopic dynamics are also macroscopically irreversible, dissipating energy and producing entropy. For many-particle systems interacting with deterministic thermostats, the rate of thermodynamic entropy dissipated to the environment is the average rate at which phase space contracts. Here, we use this identity and the properties of a classical density matrix to derive upper and lower bounds on the entropy flow rate with the spectral properties of the local stability matrix. These bounds are an extension of more fundamental bounds on the Lyapunov exponents and phase space contraction rate of continuous-time dynamical systems. They are maximal and minimal rates of entropy production, heat transfer, and transport coefficients set by the underlying dynamics of the system and deterministic thermostat. Because these limits on the macroscopic dissipation derive from the density matrix and the local stability matrix, they are numerically computable from the molecular dynamics. As an illustration, we show that these bounds are on the electrical conductivity for a system of charged particles subject to an electric field.

Layered V10O24·nH2O as a new ammonium ion host material for aqueous and quasi-solid-state ammonium-ion hybrid capacitors

Aqueous ammonium-ion hybrid capacitors (AIHCs) emerge as a promising candidate for efficient and sustainable charge storage. Yet, a pivotal challenge lies in the development of an ammonium ion (NH4+) host material that possesses high capacity and prolonged cycle life. Herein, we explore the potential of layered V10O24·nH2O, synthesized via electrodeposition method, for use in high-capacity aqueous NH4+ storage. Our investigation, supported by both experimental observations and first-principles theoretical computations, has demonstrated that the layered V10O24·nH2O exhibits commendable electrochemical performance for aqueous NH4+ storage, which is attributed to the presence of certain amount of crystal water and unique nanowire network structure. This allows for a high specific capacity of 203.1 mAh g−1 at 0.3 A g−1, and the capacity retention is 97.6 % after 20,000 cycles. Ex-situ characterizations uncovered that the insertion and extraction of NH4+ in the V10O24·nH2O layers are reversible processes, accompanied by changes in the oxidation states of vanadium and the reversible contraction and expansion of the interlayer spacing. Furthermore, the as-assembled AIHCs device not only exhibits a voltage window of 1.8 V, surpassing other types of hybrid capacitors, but also retains 82.8 % capacitance after 10,000 cycles, showcasing its good flexibility and potential for series–parallel combinations. The study highlights the potential of layered V10O24·nH2O electrodes for sustainable energy storage applications and offers some insights for high-performance hybrid capacitors with non-metallic NH4+ as the charge carrier.

The Discovery of Accelerating Expansion of Universe 8.8 Billion Years after the Big Bang Vindicates M1 World One Out of the Six Solutions of Einstein’s General Theory of Relativity

This paper gives the mathematical methodology (Tensor mathematics) of describing the surfaces of our Universe in General Theory of Relativity. It expresses the mass energy equivalence formula. It introduces the concept of time dilation, length contraction and mass increment in high speed frame of reference. Minowski space time 4D manifold is illustrated for representing the flat spacetime fabric Reimannian Metric is enumerated. Schwarzschild metric and how mass is accounted for is given.

Some fixed point theorems in (3,2)-metric spaces

In this paper, we consider [Formula: see text]-metric spaces and prove several fixed point theorems for self-mappings on [Formula: see text]-metric spaces satisfying some conditions similar to contractions in ordinary metric spaces.

Kant's nutshell argument for idealism

AbstractThe significance or vacuity of the statement, “Everything has just doubled in size,” attracted considerable attention last century from scientists and philosophers. Presenting his conventionalism in geometry, Poincaré insisted on the emptiness of a hypothesis that all objects have doubled in size overnight. Such expansion could have meaning, he argued, “only for those who reason as if space were absolute … it would be better to say that space being relative, nothing at all has happened.” The logical empiricists concurred, viewing the universal doubling hypothesis as illustrating the intrinsic metrical amorphousness of continuous manifolds. It is striking, therefore, to find Kant invoking a universal contraction in space and time to support his famous doctrine of transcendental idealism. In one of several completely neglected passages, he writes: “The proof that the things in space and time are mere appearances can also be grounded on the fact that the whole world could be contained in a nutshell and the entirety of elapsed time in a second without the least difference being met with.” Kant's “also” may suggest an idealist argument distinct from any proposed in published works. Here I ask: What is the meaning of Kant's Nutshell Argument for Idealism?