Uniqueness Results Research Articles

Mean field games with major and minor agents: the limiting problem and Nash equilibrium

In this paper, we consider a mean field game (MFG) with a major and N minor agents. We first consider the limiting problem and allow the coefficients to vary with the conditional distribution in a nonlinear way. We use the stochastic maximum principle to transform the limiting control problem into a system of two coupled conditional distribution dependent forward–backward stochastic differential equations (FBSDEs), and prove the existence and uniqueness result of the FBSDEs when the dependence between major agent and minor agents is sufficiently weak. We then use the solution of the limiting problem to construct an O ( N − 1 2 ) -Nash equilibrium for the MFG with a major and N minor agents.

Uniqueness and modified Newton method for cracks from the far field patterns with a fixed incident direction

Abstract We consider the inverse cracks scattering problems from the far field patterns with a fixed incident direction. We firstly show that the sound-soft cracks can be uniquely determined by the multi-frequency far field patterns with a fixed incident direction. The proof is based on a low frequency asymptotic analysis of the scattered field. One important feature of the uniqueness result is that the background can even be an unknown inhomogeneous medium. A modified Newton method is then proposed for the numerical reconstruction of the shapes and locations of the cracks. Compared to the classical Newton method, the modified Newton method relaxes the dependence of a good initial guess and can be applied for multiple cracks. Numerical examples in two dimensions are presented to demonstrate the feasibility and effectiveness of the modified Newton method. In particular, the quality of the reconstructions can be greatly improved if we use the measurements properly with two frequencies or two incident directions.

Review of Some Modified Generalized Korteweg–De Vries–Kuramoto–Sivashinsky (mgKdV-KS) Equations

This paper reviews the results of existence and uniqueness of the solutions of these equations: the Korteweg–De Vries equation, the Kuramoto–Sivashinsky equation, the generalized Korteweg–De Vries–Kuramoto–Sivashinsky equation and the nonhomogeneous boundary value problem for the KdV-KS equation in quarter plane.

Deep Ultraviolet Excitation Photoluminescence Characteristics and Correlative Investigation of Al-Rich AlGaN Films on Sapphire.

AlGaN is attractive for fabricating deep ultraviolet (DUV) optoelectronic and electronic devices of light-emitting diodes (LEDs), photodetectors, high-electron-mobility field-effect transistors (HEMTs), etc. We investigated the quality and optical properties of AlxGa1-xN films with high Al fractions (60-87%) grown on sapphire substrates, including AlN nucleation and buffer layers, by metal-organic chemical vapor deposition (MOCVD). They were initially investigated by high-resolution X-ray diffraction (HR-XRD) and Raman scattering (RS). A set of formulas was deduced to precisely determine x(Al) from HR-XRD data. Screw dislocation densities in AlGaN and AlN layers were deduced. DUV (266 nm) excitation RS clearly exhibits AlGaN Raman features far superior to visible RS. The simulation on the AlGaN longitudinal optical (LO) phonon modes determined the carrier concentrations in the AlGaN layers. The spatial correlation model (SCM) analyses on E2(high) modes examined the AlGaN and AlN layer properties. These high-x(Al) AlxGa1-xN films possess large energy gaps Eg in the range of 5.0-5.6 eV and are excited by a DUV 213 nm (5.8 eV) laser for room temperature (RT) photoluminescence (PL) and temperature-dependent photoluminescence (TDPL) studies. The obtained RTPL bands were deconvoluted with two Gaussian bands, indicating cross-bandgap emission, phonon replicas, and variation with x(Al). TDPL spectra at 20-300 K of Al0.87Ga0.13N exhibit the T-dependences of the band-edge luminescence near 5.6 eV and the phonon replicas. According to the Arrhenius fitting diagram of the TDPL spectra, the activation energy (19.6 meV) associated with the luminescence process is acquired. In addition, the combined PL and time-resolved photoluminescence (TRPL) spectroscopic system with DUV 213 nm pulse excitation was applied to measure a typical AlGaN multiple-quantum well (MQW). The RT TRPL decay spectra were obtained at four wavelengths and fitted by two exponentials with fast and slow decay times of ~0.2 ns and 1-2 ns, respectively. Comprehensive studies on these Al-rich AlGaN epi-films and a typical AlGaN MQW are achieved with unique and significant results, which are useful to researchers in the field.

An analysis of the textural properties of activated carbons obtained from biomass via the LBET, NLDFT and QSDFT methods

This article presents the unique research results of the comprehensive analysis of the porous structure of activated carbons obtained from biomass waste materials from the wood industry during activation in an air atmosphere. The porous structure was analysed on the basis of nitrogen and argon adsorption isotherms via complementary multi-method analysis, i.e. the new numerical clustering-based adsorption analysis, the non-local density functional theory and the quenched solid density functional theory methods. The analytical results for the prepared activated carbons were compared with analogous results obtained for commercial activated carbon. On the basis of the conducted studies it has been determined that the new numerical clustering-based adsorption analysis method gives credible and valuable information on the textural properties of activated carbons which are in strict correlation and mutually complement with the results of the analysis with the use of the quenched solid density functional theory method. The research results obtained in this paper, it has also been shown that from waste materials of the wood industry, in a relatively cheap and cleaner production process, it is possible not only to obtain carbonaceous materials almost comparable to commercial activated carbon, but also to manage the waste in accordance with the principles of a closed-loop economy and sustainable development. The paper pays also attention to the often overlooked economic and ecological aspects, which should nevertheless be taken into account when comparing different adsorbents, rather than their textural properties alone.

Quantitative and Qualitative Experimental Assessment of Water Vapor Condensation in Atmospheric Air Transonic Flows in Convergent–Divergent Nozzles

Atmospheric air, being also a moist gas, is present as a working medium in various areas of technology, including the areas of airframe aerodynamics and turbomachinery. Issues related to the condensation of water vapor contained in atmospheric air have been intensively studied analytically, experimentally and numerically since the 1950s. An effort is made in this paper to present new, unique and complementary results of the experimental testing of moist air expansion in the de Laval nozzle. The results of the measurements, apart from the static pressure distribution on the nozzle wall and the images obtained using the Schlieren technique, additionally contain information regarding the quantity and quality of the condensate formed due to spontaneous condensation at the transition from the subsonic to the supersonic flow in the nozzle. The liquid phase was identified using the light extinction method (LEM). The experiments were performed for three geometries of convergent–divergent nozzles with different expansion rates of 3000, 2500 and 2000 s−1. It is shown that as the expansion rate increases, the phenomenon of water vapor spontaneous condensation appears closer to the critical cross-section of the nozzle. A study was performed of the impact of the air relative humidity and pollution on the process of condensation of the water vapor contained in the air. As indicated by the results, both these parameters have a significant effect on the flow field and the pressure distribution in the nozzle. The results of the experimental analyses show that in the case of the atmospheric air flow, in addition to the pressure, temperature and velocity, other parameters must also be taken into account as boundary parameters for possible numerical analyses. Omitting information about the air humidity and pollution can lead to incorrect results in numerical simulations of transonic flows of atmospheric air. The presented results of the measurements of the moist air transonic flow field are original and fill the research gap in the field of experimental studies on the phenomenon of water vapor spontaneous condensation.

LiLnGeS4 (Ln=La-Nd): Designing High Performance Infrared Nonlinear Optical Sulfides through "Band Reformation of AGS".

AgGaS2 (AGS) is the most commonly used commercial infrared nonlinear optical (IR NLO) material. However, AGS has a narrow band gap (Eg=2.58 eV) and a low laser-induced damage threshold (LIDT), primarily attributed to its mobile liquid-like Ag+ constituent and the unstable Ag-S chemical bond. Herein, we propose a "band reformation of AGS" strategy, which leads to the successful syntheses of four lanthanide sulfides, LiLnGeS4 (Ln=La-Nd), crystalizing in an asymmetric Ama2 structure. LiLaGeS4 demonstrates that eliminating the presence of Ag-4d band increases the Eg to 3.32 eV and enhances the LIDT (14-29×AGS, measured by both powder and single crystal); while increasing the nonbonding density of states of the S-3p band enhances the 2nd-nonlinear optical coefficient (1.06×AGS). Besides, the bond length discrepancy between [LiS4], [GeS4] and [LaS8] units leads to a moderate birefringence (Δn=0.052). Such a unique structure further results in extremely small thermal expansion with αL=0.41-1.74×10-5 K-1, along different crystallographic axes. Our theoretical studies indicate that the synergy of the structure building units contribute to the second harmonic generation performance. These results suggest that the "band reformation of AGS" strategy provides effective guidance to discover new NLO crystals with optimized performance.

LiLnGeS4 (Ln=La−Nd): Designing High Performance Infrared Nonlinear Optical Sulfides through “Band Reformation of AGS”

AbstractAgGaS2 (AGS) is the most commonly used commercial infrared nonlinear optical (IR NLO) material. However, AGS has a narrow band gap (Eg=2.58 eV) and a low laser‐induced damage threshold (LIDT), primarily attributed to its mobile liquid‐like Ag+ constituent and the unstable Ag−S chemical bond. Herein, we propose a “band reformation of AGS” strategy, which leads to the successful syntheses of four lanthanide sulfides, LiLnGeS4 (Ln=La−Nd), crystalizing in an asymmetric Ama2 structure. LiLaGeS4 demonstrates that eliminating the presence of Ag‐4d band increases the Eg to 3.32 eV and enhances the LIDT (14–29×AGS, measured by both powder and single crystal); while increasing the nonbonding density of states of the S‐3p band enhances the 2nd‐nonlinear optical coefficient (1.06×AGS). Besides, the bond length discrepancy between [LiS4], [GeS4] and [LaS8] units leads to a moderate birefringence (Δn=0.052). Such a unique structure further results in extremely small thermal expansion with αL=0.41–1.74×10−5 K−1, along different crystallographic axes. Our theoretical studies indicate that the synergy of the structure building units contribute to the second harmonic generation performance. These results suggest that the “band reformation of AGS” strategy provides effective guidance to discover new NLO crystals with optimized performance.

Broadband spin-dependent anti-reflection in chiral time-varying metamaterials

Time-varying metamaterials have garnered significant attention for their ability to achieve anti-reflection in the time domain. However, current systems face limitations in spin-controlled manipulation, as most studies focus on non-chiral, time-varying metamaterials. Consequently, realizing spin-dependent broadband anti-reflection using time-varying chiral metamaterials remains underexplored. In this work, we propose a time-varying chiral structure composed of four temporal layers, each with distinct impedances and chiral parameters. By carefully adjusting these parameters across the layers, our structure enables broadband anti-reflection for both right- and left-circularly polarized (RCP and LCP) waves under small chiral conditions. Under large chiral parameters, the structure selectively achieves broadband anti-reflection for LCP waves, while consistently reflecting RCP waves across the bandwidth. This unique spin-dependent broadband anti-reflection results from significant phase delays between RCP and LCP waves, a feature not achievable by non-chiral, time-varying multilayer structures. Additionally, the proposed structure allows impedance matching between chiral and non-chiral dielectric spatial-temporal slabs in finite regions under small chiral parameters. These findings offer promising avenues for advanced wave manipulation in chiral metamaterials, with potential applications in broadband absorbers, filters, and quantum information processing systems.

Application of fractional differential transform method and Bell polynomial for solving system of fractional delay differential equations

In this article, a new numerical technique is presented to obtain numerical solution of a system of fractional delay differential equations (FDDE’s) involving proportional and time dependent delay terms. The fractional derivative is used in Caputo sense. The proposed technique is the combination of fractional differential transform and Bell polynomial. The existence and uniqueness results are discussed for FDDE’s. Three numerical problems are discussed to show reliability and efficiency of the method. Numerical results are compared with exact and Matlab DDENSD solution. The main advantage of the present method is handing effectively the nonlinear terms present in the FDDEs by using Bell polynomial. The present method can deal with both linear and nonlinear FDDEs. The convergence result is discussed, and error analysis is presented in detail.

Timing and geometry of the Chemehuevi Formation reveal a late Pleistocene sediment pulse into the Lower Colorado River

The Chemehuevi Formation is a distinctive 50−150-m-thick wedge-shaped Pleistocene sedimentary unit deposited by the Colorado River. It lines the perimeters of the river’s floodplains and bedrock canyons for more than 600 km between the mouth of the Grand Canyon and the delta region in the Gulf of California. The formation is composed of a basal tan to light-yellowish-brown and pale-orange mud-dominated facies overlain and interbedded by a light-yellow-brown sand-dominated facies. The unit is one of two extensively exposed aggradational packages in the Lower Colorado River corridor, in addition to a series of other smaller alluvial terrace deposits. The Chemehuevi Formation appears to represent the response of a fully integrated Colorado River system to a significant perturbation, in contrast to the Bullhead Alluvium, which is likely a unique result of Pliocene river integration. The aggradation of the Chemehuevi Formation in the Lower Colorado River corridor may be similarly due to a unique event in the Colorado River system, or it may instead be a well-preserved sedimentary sequence recording typical behavior of the Colorado River below the Grand Canyon in the late Pleistocene. As such, multiple causal mechanisms have been proposed, but no study to date has conclusively explained the Chemehuevi Formation. To help resolve its timing, duration, and origin, we applied post-infrared infrared stimulated luminescence, carbonate U-Th series, and zircon sensitive high-resolution ion microprobe U-Th series geochronology to determine the ages of key exposures of the unit over a wide spatial area. These new data demonstrate that the Chemehuevi Formation was deposited ca. 110−90 ka. The depositional ages collectively overlap, suggesting that deposition occurred rapidly relative to the resolution of the geochronometers. The new depositional timing coincides with a shift from glacial to interglacial conditions after the marine isotope stage 5-6 transition. This observation is consistent with a climate-induced sediment pulse as a causal mechanism, yet correlations with similar deposits in the Colorado River headwaters or in neighboring catchments appear elusive. Potentially, climate transitions between glacial and interglacial periods induced a sediment pulse from hillslopes of the Colorado River system that resulted in the Chemehuevi Formation. An alternative or additional explanation is that the Chemehuevi Formation represents release of lava dam−impounded sediment in the Grand Canyon. The surface geometry of the Chemehuevi Formation projects upstream to the approximate location of lava dams, and the largest possible lava dam impoundment (the Upper Prospect dam) is comparable in volume to the formation. The lava dam hypothesis appears to be a possible explanation for the Chemehuevi Formation. However, tying deposition to a specific lava dam or series of lava dams remains challenging due to discrepancies in timing and volume. The combined effects of a series of lava dams may have led to the Chemehuevi Formation, as the last Pleistocene lava dam eruption coincides with the onset of deposition. Alternatively, the formation may result from the combined effects of both regional climate transitions and the lava dams that created a transient reservoir to compound a climate transition−driven sediment pulse. The geochronologic data presented here do not allow us to distinguish between the lava dam or climate transition hypotheses but will need to be reconciled with any future proposed depositional model.

Global existence of weak solutions to the two‐dimensional nematic liquid crystal flow with partially free boundary

AbstractWe consider a nematic liquid crystal flow with partially free boundary in a smooth bounded domain in . We prove regularity estimates and the global existence of weak solutions enjoying partial regularity properties, and a uniqueness result.

Parabolic logistic equation with harvesting involving the fractional Laplacian

This paper deals with a class of parabolic reaction-diffusion equations driven by the fractional Laplacian as the diffusion operator over a bounded domain with zero Dirichlet external condition. Using a comparison principle and monotone iteration method, we establish existence and uniqueness results. We apply the existence result to the logistic growth problems with constant yield harvesting by constructing an ordered pair of positive sub- and supersolution of the corresponding elliptic problem.

Existence, Uniqueness, and Stability of Solutions for Nabla Fractional Difference Equations

In this paper, we study a class of nabla fractional difference equations with multipoint summation boundary conditions. We obtain the exact expression of the corresponding Green’s function and deduce some of its properties. Then, we impose some sufficient conditions in order to ensure existence and uniqueness results. Also, we establish some conditions under which the solution to the considered problem is generalized Ulam–Hyers–Rassias stable. In the end, some examples are included in order to illustrate our main results.

On implicit fuzzy fractional differential equations with $\phi$-Caputo derivative: Existence, uniqueness and continuous dependence results

On implicit fuzzy fractional differential equations with $\phi$-Caputo derivative: Existence, uniqueness and continuous dependence results

Mathematical Analysis of a Navier–Stokes Model with a Mittag–Leffler Kernel

In this paper, we establish the existence and uniqueness results of the fractional Navier–Stokes (N-S) evolution equation using the Banach fixed-point theorem, where the fractional order β is in the form of the Atangana–Baleanu–Caputo fractional order. The iterative method combined with the Laplace transform and Sumudu transform is employed to find the exact and approximate solutions of the fractional Navier–Stokes equation of a one-dimensional problem of unsteady flow of a viscous fluid in a tube. In the domains of science and engineering, these methods work well for solving a wide range of linear and nonlinear fractional partial differential equations and provide numerical solutions in terms of power series, with terms that are simple to compute and that quickly converge to the exact solution. After obtaining the solutions using these methods, we use Mathematica software Version 13.0.1.0 to present them graphically. We create two- and three-dimensional plots of the obtained solutions at various values of β and manipulate other variables to visualize and model relationships between the variables. We observe that as the fractional order β becomes closer to the integer order 1, the solutions approach the exact solution. Lastly, we plot a 2D graph of the first-, second-, third-, and fourth-term approximations of the series solution and observe from the graph that as the number of iterations increases, the approximate solutions become close to the series solution of the fourth-term approximation.

Phenotypic and Genomic Characterization of a Sulfate-Reducing Bacterium Pseudodesulfovibrio methanolicus sp. nov. Isolated from a Petroleum Reservoir in Russia.

The search for the microorganisms responsible for sulfide formation and corrosion of steel equipment in the oil fields of Tatarstan (Russia) resulted in the isolation of a new halotolerant strictly anaerobic sulfate-reducing bacterium, strain 5S69T. The cells were motile curved Gram-negative rods. Optimal growth was observed in the presence of 2.0-4.0% (w/v) NaCl, at pH 6.5, and at 23-28 °C under sulfate-reducing conditions. The isolate was capable of chemoorganotrophic growth with sulfate and other sulfoxides as electron acceptors, resulting in sulfide formation; and of pyruvate fermentation resulting in formation of H2 and acetate. The strain utilized lactate, pyruvate, ethanol, methanol, fumarate, and fructose, as well as H2/CO2/acetate for sulfate reduction. The genome size of the type strain 5S69T was 4.16 Mb with a G + C content of 63.0 mol%. On the basis of unique physiological properties and results of the 16S rRNA gene-based phylogenetic analysis, phylogenomic analysis of the 120 conserved single copy proteins and genomic indexes (ANI, AAI, and dDDH), assigning the type strain 5S69T ((VKM B-3653T = KCTC 25499T) to a new species within the genus Pseudodesulfovibrio, is suggested, with the proposed name Pseudodesulfovibrio methanolicus sp. nov. Genome analysis of the new isolate showed several genes involved in sulfate reduction and its sulfide-producing potential in oil fields with high saline formation water.

Geodesic connectivity and rooftop envelopes in the Cegrell classes

AbstractThis study examines geodesics and plurisubharmonic envelopes within the Cegrell classes on bounded hyperconvex domains in $$\mathbb {C}^n$$ C n . We establish that solutions possessing comparable singularities to the complex Monge–Ampère equation are identical, affirmatively addressing a longstanding open question raised by Cegrell. This achievement furnishes the most general form of the Bedford–Taylor comparison principle within the Cegrell classes. Building on this foundational result, we explore plurisubharmonic geodesics, broadening the criteria for geodesic connectivity among plurisubharmonic functions with connectable boundary values. Our investigation also delves into the notion of rooftop envelopes, revealing that the rooftop equality condition and the idempotency conjecture are valid under substantially weaker conditions than previously established, a finding made possible by our proven uniqueness result. The paper concludes by discussing the core open problems within the Cegrell classes related to the complex Monge–Ampère equation.

Employee Engagement Dynamics in High School Education: Investigating Influential Factors Across Contexts at a Ghanaian Institution

Employee engagement, a key element of organisational success, is influenced by various factors. However, there is limited clarity on how these factors impact employee engagement in high schools, particularly within the Ghanaian context. Hence, this study investigated perceived influential factors of employee engagement among high school teachers at Opoku Ware School in Ghana and their varying levels of influence across contexts using a structured survey administered to teachers (n = 75). Data analysis involving descriptive and inferential statistics, specifically ANOVA, was conducted to examine relationships between variables and test hypotheses. Key findings indicate that the employees have moderate engagement levels (M = 3.3), which are significantly impacted by leadership style, organisational culture, professional development, work-life balance, and recognition and rewards, with leadership style emerging as the most influential factor (M = 4.0). Furthermore, the analysis revealed significant differences in engagement factors across different departments (p < 0.05) and levels of seniority (p < 0.05), indicating that targeted interventions are required to address the diverse needs of teachers. However, unique results uncovered a consistency in leadership style (p = 0.33) across departments, and organisational culture (p = 0.81) and work-life balance (p = 0.76) across levels of seniority, suggesting the widespread potential impact of these specific factors. The study’s findings aligned with existing research and theories on employee engagement, emphasising the universal importance of the influential factors in driving engagement and offering valuable insights into ways high schools can enhance teacher engagement.

Backward Uniqueness for 3D Navier–Stokes Equations With Non-Trivial Final Data and Applications

Abstract Presented is a backward uniqueness result of bounded mild solutions of 3D Navier–Stokes Equations in the whole space with non-trivial final data. A direct consequence is that a solution must be axi-symmetric in $[0, T]$ if it is so at time $T$. The proof is based on a new weighted estimate that enables to treat terms involving Calderon–Zygmund operators. The new weighted estimate is expected to have certain applications in control theory when classical Carleman-type inequality is not applicable.