Weak Conditions Research Articles

Modifications to The Alcubierre Warp Field Metric in Anisotropic Matter and Implications to Detection of Warp Fields

The Alcubierre warp drive concept demonstrates a designed spacetime metric which enables hyperfast travel within the framework of known physics and has become one of the most widely studied spacetimes in the community. However, there has always been a singular issue with practical realization of the “warp drive” in that a large amount of matter with unattainable properties (such as negative or “exotic” matter/energy densities) are required. The negative matter-energy or “exotic” mass-energy density requirements violating the Averaged Weak and Null Energy Conditions mainly arise from solutions to the Einstein equations with little consideration of the matter content and characteristics within the metric. Recent efforts have shown that investigating details of the matter characteristics might offer new insights to practical warp field design and might lead to realizable solutions. This paper gives analysis of an anisotropic matter field solution, hypothetical applied variations to the Einstein coupling constant (via a multiplier function), and a multilayered warp bubble approach to reducing the warp field mass requirements to realizable forms and quantities. A discussion on the detection of such an advanced warp field is also given. Keywords: Alcubierre, Warp Drive, Spacetime Metric, Negative Energy, Einstein Equations, Anisotropic Matter

Factors influencing subseasonal predictability of northern Eurasian cold spells

AbstractCold‐air outbreaks have significant impacts on human health, energy consumption, agriculture, and overall well‐being. This study aims to evaluate the effectiveness of Subseasonal‐to‐Seasonal (S2S) models in predicting cold conditions over northern Eurasia, defined here as the lower tercile of weekly mean 2‐metre temperature anomalies. To assess the predictability of these events we use ensemble hindcasts from five prediction systems from the S2S database. Our analysis focuses on identifying the conditions under which the models confidently predict cold temperatures with a high (>0.5) probability 3–4 weeks ahead, which potentially can represent windows of forecast opportunity. We compare the group of forecasts that correctly predicted the events to the group that forecasted events that did not occur in practice (false alarms). Most of the confident forecasts of cold spells, both correct and false alarms, have cold anomalies already in the initial conditions, often in conjunction with either a negative phase of the North Atlantic Oscillation, or Scandinavian Blocking. We find that S2S models tend to overpredict cold temperatures, with false alarms occurring more likely when the forecasts are initialized during a weak polar vortex. Furthermore, most of the confident false alarms receive the signal from the stratosphere rather than following internal tropospheric dynamics. False alarms initialized during the weak polar vortex conditions are more common when the vortex is in a recovery stage and, subsequently, the downward ‐propagating signal is short‐lived in the troposphere. The analysis of forecasts during different Madden–Julian Oscillation (MJO) phases shows that nearly half of all confident correct cold‐temperature forecasts are initialized during an active MJO in phases 6–8. On the other hand, most false alarms occur during phase 3, which we suggest is due to the presence of the Scandinavian Blocking regime in the initial conditions for this phase.

Origin of Grain-Coating Chlorite and Implications for Reservoir Quality in the Triassic Deep-Buried Volcaniclastic Sandstones, Central Junggar Basin, Northwestern China.

The occurrence and genesis of grain-coating chlorite were investigated in order to evaluate the impact of grain-coating chlorite on preserving porosity in the deep-buried Triassic Karamay volcaniclastic sandstones based on thin sections, scanning electron microscopy, and an electron probe. Grain-coating chlorite was formed during the eogenesis, originating from the precursor of smectite through the solid-state transformation (SST) mechanism. The hydration and dissolution of unstable, intermediately basic volcanic rock fragments provided essential Fe2+ and Mg2+ ions for the formation of grain-coating chlorite. Due to relatively high stability and low susceptibility to dissolution, acidic volcanic rock fragments could not promote chlorite formation but resulted in authigenic quartz and clays as pore-filling cements. This process would destroy reservoir properties. Under high hydraulic conditions, medium- to coarse-grained sandstone experienced saltation transport, creating significant velocity differentials and pressure differentials on grain surfaces. Subsequently, clay grains adhere to the surfaces, forming grain-coating chlorite during diagenesis with good continuity. In contrast, pebbly sandstone undergoes rolling transport, resulting in smaller velocity differentials on grain surfaces. This makes relatively ineffective clay adsorption and leads to discontinuous grain-coating chlorite in subsequent stages. Under weak hydraulic conditions, grains and clay particles in fine-grained sandstone undergo suspended transport, lacking mutual movement and velocity differentials. Clay particles cannot effectively cover particles but instead fill the pores between them. Therefore, continuous grain-coating chlorite is more commonly developed in the medium- to coarse-grained sandstones and is crucial for inhibiting quartz cementation with a coverage rate exceeding 80%. Inadequate coatings fail to inhibit quartz cementation effectively, while excessive coatings may block pore throats. Optimal protection of primary porosity could occur only when grain-coating chlorite is moderately developed.

Deviation inequalities for dependent sequences with applications to strong approximations

In this paper, we give precise rates of convergence in the strong invariance principle for stationary sequences of bounded real-valued random variables satisfying weak dependence conditions. One of the main ingredients is a new Fuk-Nagaev type inequality for a class of weakly dependent sequences. We describe also several classes of processes to which our results apply.

Heat kernel estimates on local and non-local Dirichlet spaces satisfying a weak chain condition

In this paper, we focus on the heat kernel estimates for diffusions and jump processes on metric measure spaces satisfying a weak chain condition, where the length of a nearly shortest ε-chain between two points x,y is comparable with a function of d(x,y) and ε. For a diffusion, the best estimate is already given by Grigor'yan and Telcs, and we make it explicit in our particular case. For jump processes, especially those where the scale of the process is different with that of the jump kernel, we improve the results by Bae, Kang, Kim and Lee. Uniformity of the coefficients (or parameters) in the known estimates and metric transforms play the key role in our proof. We also show by examples how the weak chain condition is valid in practice.

Space–time computations of exactly time-periodic flows past hydrofoils

The computation of periodic flows is typically conducted over multiple periods. First, a number of periods is used to develop periodic characteristics, and afterwards statistics are collected from averages over multiple periods. As a consequence, it is uncertain whether the numerical results are exactly time-periodic, and additionally, the time domain might be needlessly long. In this article, we circumvent these concerns by using a time-periodic function space. Consequently, the boundary conditions and solutions are exactly periodic. We employ the isogeometric analysis framework to achieve higher-order smoothness in both space and time. The discretization is performed using residual-based variational multiscale modeling and weak boundary conditions are adopted to enhance the accuracy near the moving boundaries of the computational domain. We enforce the time-periodic boundary condition within the isogeometric discretization spaces, which converts the two-dimensional time-dependent problem into a three-dimensional boundary value problem. Furthermore, we determine the boundary velocities of moving hydrofoils directly from the computational mesh and use a conservation methodology for force extraction. Application of the computational setup to heaving and pitching hydrofoils displays very accurate and exactly periodic results for lift and drag.

Anti‐nuclear matrix protein 2 antibody‐positive amyopathic dermatomyositis presenting in a patient with prostate cancer: A case report

Key Clinical MessageNuclear matrix protein (NXP‐2) positive amyopathic dermatomyositis (DM) may present without classic symptoms like muscle weakness, dysphagia, and edema, and mimic conditions like cutaneous lupus. Given DM's association with malignancy and interstitial lung disease, prompt and accurate diagnosis is important. Testing for myositis‐specific antibodies aids diagnosis in ambiguous cases.

Effect of Novel pH Regulators on Copper film Chemical Mechanical Polishing for Ruthenium-Based Copper Interconnect under Weak Alkalinity Conditions

For Ruthenium (Ru)-based copper (Cu) interconnects Cu film chemical mechanical polishing (CMP), it is crucial to select appropriate pH regulators in the slurry to ensure the chemical reactions and maintain the stability of the polishing chemical environment. In this study, the effects of inorganic pH regulator KOH, organic pH regulator diethanolamine (DEA), and 2-amino-2-methyl-1-propanol (AMP) on CMP and slurry properties of Cu film were compared. It was found when using AMP as a pH regulator, the Cu/Ru removal rate selectivity (RRS) can reach 598:1, the surface roughness of Cu film decreased to 0.76 nm, and the slurry can remain stable for at least 7 d. The performance order of the three pH regulators is AMP＞KOH＞DEA. Meanwhile, through experimental results and test analysis, it has been confirmed that AMP can also play a multifunctional role as a complexing agent, dispersant, and surfactant. Therefore, AMP can replace KOH as a new pH regulator in weak alkaline slurries. This result plays an important role in guiding the selection of organic pH regulators in the optimization of Cu film CMP slurry.

A Series Impedance Reshaping Control Method Considering PLL Dynamics for Grid-Connected Inverters Under Weak Grid Conditions

Grid-connected inverters are the key part in renewable energy power generation systems. Usually, phase-locked loop (PLL) is adopted in grid-connected inverters to achieve synchronization. However, prior-art works have revealed that the negative resistance behavior in the low-frequency band caused by PLLs may lead to system instability under weak grids. In this paper, first, a comprehensive small-signal output impedance modeling of the LCL-filtered single-phase grid-connected inverter is derived for stability analysis, where the digital control delays and PLL dynamics have been taken into account. Then, a simple but effective virtual series based impedance reshaping method is proposed. With that, the inverter system can operate stably even under a very weak grid (e.g., short-circuit ratio (SCR) is as low as 1.2). Compared with the traditional grid impedance compensation by virtually increasing grid resistance or reducing the grid inductance, the proposed method does not require grid impedance estimation and is robust against system parameter variations. Thus, its feasibility is improved. Finally, experimental tests are carried out on a single-phase 5-kW prototype, validating the effectiveness of the proposed scheme.

Local and 2-local Lie n-derivations of triangular algebras

Let R be a commutative ring with identity, and A , B be unital algebras over R . Let M be a unital ( A , B ) -bimodule, which is faithful as a left A -module and also as a right B -module. Let T = Tri ( A , M , B ) be an ( n − 1 ) -torsion free triangular algebra. In this note, we investigate the structure of local Lie n-derivations under certain mild conditions and 2-local Lie n-derivations under weaker conditions than that of local Lie n-derivations with n ≥ 3 on T . Under their corresponding conditions, we conclude that they are both standard on T .

An optimized approach to study nanoscale sarcomere structure utilizing super-resolution microscopy with nanobodies.

The sarcomere is the fundamental contractile unit in skeletal muscle, and the regularity of its structure is critical for function. Emerging data demonstrates that nanoscale changes to the regularity of sarcomere structure can affect the overall function of the protein dense ~2μm sarcomere. Further, sarcomere structure is implicated in many clinical conditions of muscle weakness. However, our understanding of how sarcomere structure changes in disease, especially at the nanoscale, has been limited in part due to the inability to robustly detect and measure at sub-sarcomere resolution. We optimized several methodological steps and developed a robust pipeline to analyze sarcomere structure using structured illumination super-resolution microscopy in conjunction with commercially-available and fluorescently-conjugated Variable Heavy-Chain only fragment secondary antibodies (nanobodies), and achieved a significant increase in resolution of z-disc width (353nm vs. 62nm) compared to confocal microscopy. The combination of these methods provides a unique approach to probe sarcomere protein localization at the nanoscale and may prove advantageous for analysis of other cellular structures.

Global attractivity for reaction–diffusion equations with periodic coefficients and time delays

In this paper, we provide sharp criteria of global attraction for a class of non-autonomous reaction–diffusion equations with delay and Neumann conditions. Our methodology is based on a subtle combination of some dynamical system tools and the maximum principle for parabolic equations. It is worth mentioning that our results are achieved under very weak and verifiable conditions. We apply our results to a wide variety of classical models, including the non-autonomous variants of Nicholson’s equation or the Mackey–Glass model. In some cases, our technique gives the optimal conditions for the global attraction.

Uniqueness of phase retrieval with short-time linear canonical transform

In this paper, we study the problem of phase retrieval with short-time linear canonical transform (STLCT). The relation between signal, window and their STLCT is provided through Fourier transform. Based on this theorem, a uniqueness result is established for all square integrable functions. For nonseparable real continuous signal, we prove the uniqueness theorems under some weaker conditions. In complex bandlimited and cardinal [Formula: see text]-spline spaces, uniqueness results are provided with magnitude-only STLCT.

Biomimetic enhanced polarization orientation method for underwater scenes

Underwater polarization information can provide reliable autonomous heading feedback for underwater scenes in the presence of satellite denial and multi-source interference. A biologically inspired highly robust polarization orientation strategy is proposed to address the degradation caused by weak polarization and noisy patterns in underwater environments with poor illumination, turbidity, and cloud recession. This approach initially develops a biomimetic algorithm that enhances weak polarization information, based on the increased perception mechanism of the visual neural pathway of syrphid fly under weak light conditions. After overcoming restricting polarization transmission, it is further optimized with a non-local sparse coding denoising part that takes into account the similarity in the detailed structure of the polarized image's effective zenith region. Relying on the stable ∞ symmetric distribution of the angle of polarization, the ±π/2 feature point distribution is traversed and assigned, and polarization information is quantitatively assigned, compensated, and regulated along the solar meridian region, excluding invalid polarized pixels. The experiments demonstrate that the methodology effectively reconstructs the symmetry of the partially damaged angle of polarization distribution, eliminates external interference, autonomously solves the fitted heading correction problem, and improves the environmental adaptability of the bionic polarization compass. The data from underwater experiments indicate the orientation accuracy: the error in weakly polarized patterns is within 2°, and the accuracy in noisy patterns can be increased by over 50%.

Fluorescent α-Conotoxin [Q1G, ΔR14]LvIB Identifies the Distribution of α7 Nicotinic Acetylcholine Receptor in the Rat Brain.

α7 nicotinic acetylcholine receptors (nAChRs) are mainly distributed in the central nervous system (CNS), including the hippocampus, striatum, and cortex of the brain. The α7 nAChR has high Ca2+ permeability and can be quickly activated and desensitized, and is closely related to Alzheimer's disease (AD), epilepsy, schizophrenia, lung cancer, Parkinson's disease (PD), inflammation, and other diseases. α-conotoxins from marine cone snail venom are typically short, disulfide-rich neuropeptides targeting nAChRs and can distinguish various subtypes, providing vital pharmacological tools for the functional research of nAChRs. [Q1G, ΔR14]LvΙB is a rat α7 nAChRs selective antagonist, modified from α-conotoxin LvΙB. In this study, we utilized three types of fluorescein after N-Hydroxy succinimide (NHS) activation treatment: 6-TAMRA-SE, Cy3 NHS, and BODIPY-FL NHS, labeling the N-Terminal of [Q1G, ΔR14]LvΙB under weak alkaline conditions, obtaining three fluorescent analogs: LvIB-R, LvIB-C, and LvIB-B, respectively. The potency of [Q1G, ΔR14]LvΙB fluorescent analogs was evaluated at rat α7 nAChRs expressed in Xenopus laevis oocytes. Using a two-electrode voltage clamp (TEVC), the half-maximal inhibitory concentration (IC50) values of LvIB-R, LvIB-C, and LvIB-B were 643.3 nM, 298.0 nM, and 186.9 nM, respectively. The stability of cerebrospinal fluid analysis showed that after incubation for 12 h, the retention rates of the three fluorescent analogs were 52.2%, 22.1%, and 0%, respectively. [Q1G, ΔR14]LvΙB fluorescent analogs were applied to explore the distribution of α7 nAChRs in the hippocampus and striatum of rat brain tissue and it was found that Cy3- and BODIPY FL-labeled [Q1G, ΔR14]LvΙB exhibited better imaging characteristics than 6-TAMARA-. It was also found that α7 nAChRs are widely distributed in the cerebral cortex and cerebellar lobules. Taking into account potency, imaging, and stability, [Q1G, ΔR14]LvΙB -BODIPY FL is an ideal pharmacological tool to investigate the tissue distribution and function of α7 nAChRs. Our findings not only provide a foundation for the development of conotoxins as visual pharmacological probes, but also demonstrate the distribution of α7 nAChRs in the rat brain.

Algebraic dependences of meromorphic mappings sharing few moving hyperplanes with truncated multiplicity

In this article, we will prove an algebraic dependence theorem for meromorphic mappings into a complex projective space sharing few moving hyperplanes with different truncated multiplicity. Moreover, we also consider the weaker condition: \[\nu _{(f,{a_i}), \le k_i}\le \nu _{(g,{a_i}), \le k_i} \text{ instead of } \nu _{(f,{a_i}), \le k_i}= \nu_{(g,{a_i}), \le k_i}\] for some moving hyperplanes among the given moving hyperplanes. In order to implement this, besides using the technique reported by S. D. Quang in (Two meromorphic mappings having the same inverse images of some moving hyperplanes with truncated multiplicity, Rocky Mountain J. Math., vol. 52, no. 1, pp. 263–273, 2022) we have to separate the 2n + 2 moving hyperplanes from the given p+1 moving hyperplanes. After that, we count multiples of the intersection of the inverse images of the mappings f and g sharing these moving hyperplanes. Our result is an improvement of many previous results in this topic.

Weak alkaline flotation separation of galena from sphalerite with 6-butylamino-1,3,5-triazine-2(1H)-thione-4-thiol sodium

The reduction of lime usage in flotation separation of lead–zinc sulfide ores has an interesting topic for protecting environment and recovering valuable metal minerals. In this study, BN (6-butylamino-1,3,5-triazine-2(1H)-thione-4-thiol sodium) was introduced for the first time as a selective collector for galena flotation. The results of UV spectra, adsorption capacity, zeta potential and in-situ AFM manifested that BN exhibited the selective affinity towards Pb2+ over Zn2+ ions, and preferred to adsorb on galena surface, not on sphalerite. The FTIR and XPS further uncovered that BN assembled on galena via bonding its sulfur atoms with lead ions of galena to form the surface BN-Pb complexes. The micro-flotation findings revealed that BN returned the stronger collecting power and higher selectivity than isobutyl xanthate during flotation separation of galena from sphalerite, and achieved their effective separation at low alkaline conditions (pH ∼ 8.0). This study also offers an enlightenment for the design of chelating collectors suitable for use under weak alkaline conditions.

Orthogonal multi-peak solitons from the coupled fractional nonlinear Schrödinger equation

In this paper, we investigate the dynamics and stability of multi-peak solitons from the coupled nonlinear Schrödinger equation with the fractional dimension based on Lévy random flights. By implementing linear stability analysis and direct simulations, we demonstrate regions where the single and multi-peak modes are stable. Analysis of perturbed coupled solitons confirms the stability of higher-order modes compared to lower-order modes under the same configurations. The stability diagrams show that the force coupling, Lévy index, power, and the nonlinear intensity significantly influence the stability of high-order modes. Our findings indicate that stability is favored in self-defocusing systems with high Lévy indices under weak coupling conditions, with higher-order states exhibiting smaller stability regions.

Some new uniqueness and Ulam–Hyers type stability results for nonlinear fractional neutral hybrid differential equations with time-varying lags

Abstract This paper deals with some qualitative properties of solutions to nonlinear neutral hybrid differential equations connected to ψ-Caputo fractional derivative with time-varying lags. First, we demonstrate the problem possesses a mild solution uniquely where the source function may have temporal singularities. Second, in some cases, we indicate that the problem possesses a unique mild solution under some weaker conditions than the previous one. Third, we also obtain a result on a global mild solution for the problem. Finally, the results are further enriched by studying a new type of Ulam–Hyers stability for the main equation. The main results are obtained by applying the nice inequality, first proposed and proven in this paper. Some befit examples are given to justify the applicability of the main results.

CharacterizationofP SU(3,q)byitsorderandonespecialconjugacyclasssize

Suppose that G be a finite group, and let N (G)be the set of conjugacy class sizes of G. By Thompson’s conjecture, if H is a finite non abelian simple group, G is a finite group with a trivial center, and N (G) = N (H), then H and G are isomorphic. Chen et al. contributed interestingly to Thompsons conjecture under a weak condition. In this article, we investigate validity of Thompsons conjecture under a weak condition for the projective special unitary groups. This work implies that Thompsons conjecture holds for the PSU (3, q), where q is prime power.