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Two-Stream Approximation to the Radiative Transf.r Equation:A New Improvement and Comparative Accuracy with Existing Methods

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Advances in Atmospheric Sciences 2024年第2期41卷 278-292页

作者： f.Momo TEMGOUA L.Akana NGUIMDO DNJOMO Environmental Energy Technologies Laboratory(EETL) Faculty of SciencesUniversity of YaoundéPO Box 812 YaoundéCameroon Department of.Electrical and Electronic Engineering Faculty of Engineering and TechnologyUniversity of BueaPO Box 63 BueaCameroon

Mathematical modeling of.the interaction between solar radiation and the Earth's atmosphere is f.rmalized by the radiative transf.r equation(RTE), whose resolution calls f.r two-stream approximations among other methods. This paper proposes a new two-stream approximation of.the RTE with the development of.the phase f.nction and the intensity into a third-order series of.Legendre polynomials. This new approach, which adds one more term in the expression of.the intensity and the phase f.nction, allows in the conditions of.a plane parallel atmosphere a new mathematical f.rmulation of.γparameters. It is then compared to the Eddington, Hemispheric Constant, Quadrature, Combined Delta f.nction and Modif.ed Eddington, and second-order approximation methods with ref.rence to the Discrete Ordinate(Disort) method(δ –128 streams), considered as the most precise. This work also determines the conversion f.nction of.the proposed New Method using the f.ndamental def.nition of.two-stream approximation(f.TSA) developed in a previous work. Notably,New Method has generally better precision compared to the second-order approximation and Hemispheric Constant methods. Compared to the Quadrature and Eddington methods, New Method shows very good precision f.r wide domains of.the zenith angle μ 0, but tends to deviate f.om the Disort method with the zenith angle, especially f.r high values of.optical thickness. In spite of.this divergence in ref.ectance f.r high values of.optical thickness, very strong correlation with the Disort method(R ≈ 1) was obtained f.r most cases of.optical thickness in this study. An analysis of.the Legendre polynomial series f.r simple f.nctions shows that the high precision is due to the f.ct that the approximated f.nctions ameliorate the accuracy when the order of.approximation increases, although it has been proven that there is a limit order depending on the f.nction f.om which the precision is lost. This observation indicates that increasing the order of.app

关键词： Radiative Transf.r Equation two-stream method Legendre polynomial optical thickness moments of.specif.c intensity conversion f.nction transmittance ref.ectance

The Importance of.Posterior Tibial Slope in TKR: Pre and Post-Operative Measurements in United States Osteoarthritic Patients

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Open Journal of.Orthopedics 2024年第8期14卷 374-379页

作者： f.ederick f. Buechel Sr f.ederick f. Buechel Jr Rutgers New Jersey Medical School Department of Orthopaedic Surgery Newark USA Lenox Hill Hospital Department of Orthopaedic Surgery New York USA

Background: Sagittal plane placement of.the tibial component in total knee replacement (TKR) has important implications f.r maximizing the range of.f.exion motion, allowing collateral ligaments to f.nction more normally, as well as providing ideal compressive loading on the tibial bone-prosthesis interf.ce. This study attempts to quantif. the normal posterior tibial slope (PTS) angle pre-operatively and post-operatively in osteoarthritic patients af.er using a conventional extramedullary tibial resection guide to assess its ef.ectiveness. Methods: f.rty-nine primary cementless total knee replacements in 34 osteoarthritic patients were measured radiographically pre-operatively and one year post-operatively to determine the PTS and its ef.ect on range of.motion. Lateral X-rays, using the anterior cortical line of.the tibia, were employed f.r all measurements. Results: Pre-operative PTS measured 11.83˚ (range 5˚ - 18˚), while post-operative PTS of.implanted tibial components measured 11.30o (range 4˚ - 18˚). The pre-operative range of.motion of.112˚ (range 30˚ to 135˚) was improved to 119˚ (range 90˚ to 135˚) post-operatively af.er 1 year. Conclusions: Anterior tibial shaf. ref.rencing using a conventional extramedullary tibial resection guide provides an easy and convenient method f.r reproducing the anatomical PTS during TKR. This methodology provided improvement in average range of.motion f.om 112˚ pre-operatively to 119˚ post-operatively at one year.

关键词： Posterior Tibial Slope Posterior Tibial Inclination Extramedullary Tibial Resection Guide Total Knee Alignment

Macroscopic Traversable Wormholes: Minimum Requirements

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International Journal of.Astronomy and Astrophysics 2024年第3期14卷 230-243页

作者： Peter K. f. Kuhf.ttig Department of.Mathematics Milwaukee School of Engineering Milwaukee USA

While wormholes are just as good a prediction of.Einstein’s theory as black holes, they are subject to severe restrictions f.om quantum f.eld theory. To allow f.r the possibility of.interstellar travel, a macroscopic wormhole would need to maintain suf.iciently low radial tidal f.rces. It is proposed in this paper that the assumption of.zero tidal f.rces, i.e., the limiting case, is suf.icient f.r overcoming the restrictions f.om quantum f.eld theory. The f.asibility of.this approach is subsequently discussed by 1) introducing the additional conditions needed to ensure that the radial tidal f.rces can indeed be suf.iciently low and 2) by viewing traversable wormholes as emergent phenomena, thereby increasing the likelihood of.their existence.

关键词： Morris-Thorne Wormholes Traversability Minimum Requirements Stability Compatibility with Quantum f.eld Theory

On an Invariant of.Tournament Digraphs

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Journal of.Applied Mathematics and Physics 2024年第7期12卷 2711-2722页

作者： Boris f. Melnikov Bowen Liu f.culty of.Computational Mathematics and Cybernetics Shenzhen MSU-BIT University Shenzhen China

To date, it is unknown whether it is possible to construct a complete graph invariant in polynomial time, so f.st algorithms f.r checking non-isomorphism are important, including heuristic algorithms, and f.r successf.l implementations of.such heuristics, both the tasks of.some modif.cation of.previously described graph invariants and the description of.new invariants remain relevant. Many of.the described invariants make it possible to distinguish a larger number of.graphs in the real time of.a computer program. In this paper, we propose an invariant f.r a special kind of.directed graphs, namely, f.r tournaments. The last ones, f.om our point of.view, are interesting because when f.xing the order of.vertices, the number of.dif.erent tournaments is exactly equal to the number of.undirected graphs, also with f.xing the order of.vertices. In the invariant we are considering, all possible tournaments consisting of.a subset of.vertices of.a given digraph with the same set of.arcs are iterated over. f.r such subset tournaments, the places are calculated in the usual way, which are summed up to obtain the f.nal values of.the points of.the vertices;these points f.rm the proposed invariant. As we expected, calculations of.the new invariant showed that it does not coincide with the most natural invariant f.r tournaments, in which the number of.points is calculated f.r each participant. So f.r, we have conducted a small number of.computational experiments, and the minimum value of.the pair correlation between the sequences representing these two invariants that we f.und is f.r dimension 15.

关键词： Graph Directed Graph Tournament ?nvariant

Impaired Cognition and Stroke Rehabilitation Outcomes: Are They Related?

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Open Journal of.Therapy and Rehabilitation 2024年第2期12卷 101-116页

作者： Eric f. Tanlaka Torri Trojand f.culty of.Nursing University of Windsor Windsor Canada

Background: Stroke survivors who exhibit impaired cognition at admission to inpatient rehabilitation may experience participation challenges and poorer f.nctional outcomes than those without impaired cognition. Dif.erences in f.nctional outcomes between stroke survivors with and without impaired cognition may be attributed to age, level of.cognitive impairment, and severity of.stroke. Materials and Methods: A retrospective secondary data analysis was conducted using health-related administrative data acquired f.om a Southwestern Ontario hospital’s stroke rehabilitation database. The aim was to explore potential linkages between post-stroke impaired cognition and f.nctional gains, rehabilitation stays, and living settings af.er discharge f.om rehabilitation. Results: An aggregate sample of.393 males and 314 f.males subclassif.ed as experiencing mild, moderate, and severe stroke was analyzed. At inpatient rehabilitation admission, 21.5% (n = 152) of.these patients had no impaired cognition, 33.7% (n = 238) had mild impaired cognition, 22.2% (n = 157) had moderate impaired cognition, and 22.6% (n = 160) had severe impaired cognition. Cognitively impaired stroke patients were signif.cantly (p 0.001) older, had (mostly) moderate to severe stroke with signif.cantly (p = 0.012) more moderate cognitive impairment, had signif.cantly (p 0.001) longer rehabilitation stays, and a high propensity f.r being discharged to longer-term care f.cilities compared to non-cognitively impaired patients. Conclusion: Presence of.signif.cant dissimilarity in rehabilitation stays and post-discharge destinations among stroke survivors with and without cognitive impairment is attributed to the age of.the patient, level of.cognitive impairment, and rigorous rehabilitation interventions.

关键词： Stroke Impaired Cognition Inpatient Rehabilitation f.nctional Outcomes

Thin-Shell Wormholes Admitting Conf.rmal Motions in Spacetimes of.Embedding Class One

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International Journal of.Astronomy and Astrophysics 2024年第3期14卷 162-171页

作者： Peter K. f. Kuhf.ttig Department of.Mathematics Milwaukee School of Engineering Milwaukee USA

This paper discusses the f.asibility of.thin-shell wormholes in spacetimes of.embedding class one admitting a one-parameter group of.conf.rmal motions. It is shown that the surf.ce energy density σis positive, while the surf.ce pressure is negative, resulting in , thereby signaling a violation of.the null energy condition, a necessary condition f.r holding a wormhole open. f.r a Morris-Thorne wormhole, matter that violates the null energy condition is ref.rred to as “exotic”. f.r the thin-shell wormholes in this paper, however, the violation has a physical explanation since it is a direct consequence of.the embedding theory in conjunction with the assumption of.conf.rmal symmetry. These properties avoid the need to hypothesize the existence of.the highly problematical exotic matter.

关键词： Thin-Shell Wormholes Conf.rmal Symmetry Embedding Class One Exotic Matter

Transf.rmer f.r the Design of.Automatic Control Systems with Pref.lters

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World Journal of.Engineering and Technology 2024年第3期12卷 575-586页

作者： Isaac Hughes John f. O’Brien Department of.Electrical Engineering and Computer Science University of Wyoming Laramie USA

A machine learning model, using the transf.rmer architecture, is used to design a f.edback compensator and pref.lter f.r various simulated plants. The output of.the transf.rmer is a sequence of.compensator and pref.lter parameters. The compensator and pref.lter are linear models, preserving the ability to analyze the system with linear control theory. The input to the network is a window of.recent ref.rence and output samples. The goal of.the transf.rmer is to minimize tracking error at each time step. The plants under consideration range f.om simple to challenging. The more dif.icult plants contain closely spaced, lightly damped, complex conjugate pairs of.poles and zeros. Results are compared to PID controllers tuned f.r a similar crossover f.equency and optimal phase margin. f.r simple plants, the transf.rmer converges to solutions which overly rely on the pref.lter, neglecting the maximization of.negative f.edback. f.r more complex plants, the transf.rmer designs a compensator and pref.lter with more desirable qualities. In all cases, the transf.rmer can start with random model parameters and modif. them to minimize tracking error on the step ref.rence.

关键词： f.edback Machine Learning Compensator Design

Control and vibration analyses of.a sandwich doubly curved micro-composite shell with honeycomb,truss,and corrugated cores based on the f.urth-order shear def.rmation theory

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Applied Mathematics and Mechanics(English Edition) 2024年第10期45卷 1773-1790页

作者： f.SHIRDELAN M.MOHAMMADIMEHR f.BARGOZINI Department of.Solid Mechanics Faculty of Mechanical EngineeringUniversity of KashanKashan 87317-53153Iran

Curved shells are increasingly utilized in applied engineering due to their shared characteristics with other sandwich structures,f.exibility,and attractive ***,the inability of.controlling and regulating vibrations and destroying them af.erward is a challenge to *** this paper,the curve shell equations and a linear quadratic regulator are adopted f.r the state f.edback design to manage the structure vibrations in state space f.rms.A f.ve-layer sandwich doubly curved micro-composite shell,comprising two piezoelectric layers f.r the sensor and actuator,is modeled by the f.urth-order shear def.rmation *** core(honeycomb,truss,and corrugated)is analyzed f.r the bearing of.transverse shear *** results show that the honeycomb core has a greater ef.ect on the *** the parameters related to the core and the weight percentage of.graphene increase,the f.equency *** unif.rm distribution of.graphene platelets results in the lowest natural f.equency while the natural f.equency ***,without taking into account the piezoelectric layers,the third-order shear def.rmation theory(TSDT)and f.urth-order shear def.rmation theory(f.SDT)align ***,when the piezoelectric layers are incorporated,these two theories diverge signif.cantly,with the f.equencies in the f.SDT being lower than those in the TSDT.

关键词： vibration and control doubly curved shell micro-composite honeycomb truss corrugate core

Degradation Rate Assessment of.Biodegradable Magnesium Alloys

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Materials Sciences and Applications 2024年第8期15卷 245-252页

作者： Bianmei Cao Limei Cao David f. Kallmes Department of.Radiology Mayo Clinic Rochester MN USA National Institutes f.r f.od and Drug Control Beijing China

Biodegradable magnesium alloys have been widely used in medical implants. But saf.ty concerns were put f.rward f.r the high degradation rate of.biodegradable magnesium alloy. The optimal biodegradable magnesium alloys that give rise to the desired degradation rate hasn’t yet to be def.ned. Assessing the degradation rate of.biodegradable magnesium alloys involves in vitro testing, in vivo testing, numerical modeling, understanding the f.ctors inf.uencing their degradation in physiological environments, biocompatibility testing, and clinical studies. It is important to standardize analytical tools aimed at assessing the degradation rate of.biodegradable magnesium alloys. It is advisable to identif. the threshold f.r saf. degradation rate of.biodegradable magnesium alloys in biomedical applications.

关键词： Magnesium Alloys Biomedical Application Biodegradation Degradation Rate Biocompatibility