PROJECTIVELY FLAT MATSUMOTO METRIC AND ITS APPROXIMATION

Abstract In this article, the author studies the projectively flat Matsumoto metric F=α^2/（α -β）, where α=√αijy^iy^j is a Riemannian metric and β =biy^i is 1-form. Theyconclude that α is locally projectively fiat and β is paralled with respect to α. And get the same result for the higher order approximate Matsumoto metric.

PROJECTIVELY FLAT FINSLER METRICS WITH ALMOST ISOTROPIC S-CURVATURE

This article characterizes projectively fiat Finsler metrics with almost isotropic S-curvature.

Projectively flat exponential Finsler metric

In this paper, we study a class of Finsler metric in the form F=αexp(β/α)+εβ, where α is a Riemannian metric and β is a 1-form, ε is a constant. We call F exponential Finsler metric. We proved that exponential Finsler metric F is locally projectively flat if and only if α is projectively flat and β is parallel with respect to α. Moreover, we proved that the Douglas tensor of expo-nential Finsler metric F vanishes if and only if β is parallel with respect to α. And from this fact, we get that if exponential Finsler metric F is the Douglas metric, then F is not only a Berwald metric, but also a Landsberg metric.

On some projectively flat polynomial (α,β)-metrics

In this paper, we consider some polynomial （a,fl）-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α＋α1β＋α2β^2/α＋α4β^4/α^3 to be projectively flat, where ai 0=1,2,4） are constants with a1≠0, a is a Riemannian metric and β is a 1-form. By analyzing the geodesic coefficients and the divisibility of certain polynomials, we obtain that there are only five projectively flat cases for metrics of this type. This gives a classification for such kind of Finsler metrics.

Projectively flat arctangent Finsler metric

In this work, we study a class of special Finsler metrics F called arctangent Finsler metric, which is a special （α, β）-metric, where a is a Riemannian metric and β is a 1-form, We obtain a sufficient and necessary condition that F is locally projectively fiat if and only if α and β satisfy two special equations. Furthermore we give the non-trivial solutions for F to be locally projectively fiat. Moreover, we prove that such projectively fiat Finsler metrics with constant flag curvature must be locally Minkowskian.

Projectively flat Asanov Finsler metric

In this work, we study the Asanov Finsler metric F=α（β^2/α^2＋gβ/α＋1）^1/2exp{（G/2）arctan[β/（hα）＋G/2]}, where α=（αijy^iy^i）^1/2 is a Riemannian metric and β=by^i is a 1-fom, g∈（-2,2）, h=（1-g^2/4）^1/2, G=g/h. We give the necessary and sufficient condition for Asanov metric to be locally projectively flat, i.e., α is projectively flat and ,Sis parallel with respect to α. Moreover, we proved that the Douglas tensor of Asanov Finsler metric vanishes if and only if β is parallel with respect to α.

Projectively Ricci-flat General(α,β)-metrics

In this paper,we study the projectively Ricci-flat general(α,β)-metrics within to a spray framework and also bring out the rich variety of behaviour displayed by an important projective invariant.Projective Ricci curvature is one of the essential projective invariant in Finsler geometry which has been introduced by Z.Shen.The projective Ricci curvature is defined as Ricci curvature of a projective spray associated with a given spray G on M^(n) with a volume form dV on M^(n).

Projecting Spring Consecutive Rainfall Events in the Three Gorges Reservoir Based on Triple-Nested Dynamical Downscaling

Spring consecutive rainfall events(CREs) are key triggers of geological hazards in the Three Gorges Reservoir area(TGR), China. However, previous projections of CREs based on the direct outputs of global climate models(GCMs) are subject to considerable uncertainties, largely caused by their coarse resolution. This study applies a triple-nested WRF(Weather Research and Forecasting) model dynamical downscaling, driven by a GCM, MIROC6(Model for Interdisciplinary Research on Climate, version 6), to improve the historical simulation and reduce the uncertainties in the future projection of CREs in the TGR. Results indicate that WRF has better performances in reproducing the observed rainfall in terms of the daily probability distribution, monthly evolution and duration of rainfall events, demonstrating the ability of WRF in simulating CREs. Thus, the triple-nested WRF is applied to project the future changes of CREs under the middle-of-the-road and fossil-fueled development scenarios. It is indicated that light and moderate rainfall and the duration of continuous rainfall spells will decrease in the TGR, leading to a decrease in the frequency of CREs. Meanwhile, the duration, rainfall amount, and intensity of CREs is projected to regional increase in the central-west TGR. These results are inconsistent with the raw projection of MIROC6. Observational diagnosis implies that CREs are mainly contributed by the vertical moisture advection. Such a synoptic contribution is captured well by WRF, which is not the case in MIROC6,indicating larger uncertainties in the CREs projected by MIROC6.

Distributed Nash Equilibrium Seeking Strategies Under Quantized Communication

This paper is concerned with distributed Nash equi librium seeking strategies under quantized communication. In the proposed seeking strategy, a projection operator is synthesized with a gradient search method to achieve the optimization o players' objective functions while restricting their actions within required non-empty, convex and compact domains. In addition, a leader-following consensus protocol, in which quantized informa tion flows are utilized, is employed for information sharing among players. More specifically, logarithmic quantizers and uniform quantizers are investigated under both undirected and connected communication graphs and strongly connected digraphs, respec tively. Through Lyapunov stability analysis, it is shown that play ers' actions can be steered to a neighborhood of the Nash equilib rium with logarithmic and uniform quantizers, and the quanti fied convergence error depends on the parameter of the quan tizer for both undirected and directed cases. A numerical exam ple is given to verify the theoretical results.

Future changes in precipitation and water availability over the Tibetan Plateau projected by CMIP6 models constrained by climate sensitivity

Precipitation projections over the Tibetan Plateau(TP)show diversity among existing studies,partly due to model uncertainty.How to develop a reliable projection remains inconclusive.Here,based on the IPCC AR6–assessed likely range of equilibrium climate sensitivity(ECS)and the climatological precipitation performance,the authors constrain the CMIP6(phase 6 of the Coupled Model Intercomparison Project)model projection of summer precipitation and water availability over the TP.The best estimates of precipitation changes are 0.24,0.25,and 0.45 mm d^(−1)(5.9%,6.1%,and 11.2%)under the Shared Socioeconomic Pathway(SSP)scenarios of SSP1–2.6,SSP2–4.5,and SSP5–8.5 from 2050–2099 relative to 1965–2014,respectively.The corresponding constrained projections of water availability measured by precipitation minus evaporation(P–E)are 0.10,0.09,and 0.22 mm d^(−1)(5.7%,4.9%,and 13.2%),respectively.The increase of precipitation and P–E projected by the high-ECS models,whose ECS values are higher than the upper limit of the likely range,are about 1.7 times larger than those estimated by constrained projections.Spatially,there is a larger increase in precipitation and P–E over the eastern TP,while the western part shows a relatively weak difference in precipitation and a drier trend in P–E.The wetter TP projected by the high-ECS models resulted from both an approximately 1.2–1.4 times stronger hydrological sensitivity and additional warming of 0.6℃–1.2℃ under all three scenarios during 2050–2099.This study emphasizes that selecting climate models with climate sensitivity within the likely range is crucial to reducing the uncertainty in the projection of TP precipitation and water availability changes.

Transcriptional regulation in the development and dysfunction of neocortical projection neurons

Glutamatergic projection neurons generate sophisticated excitatory circuits to integrate and transmit information among different cortical areas,and between the neocortex and other regions of the brain and spinal cord.Appropriate development of cortical projection neurons is regulated by certain essential events such as neural fate determination,proliferation,specification,differentiation,migration,survival,axonogenesis,and synaptogenesis.These processes are precisely regulated in a tempo-spatial manner by intrinsic factors,extrinsic signals,and neural activities.The generation of correct subtypes and precise connections of projection neurons is imperative not only to support the basic cortical functions(such as sensory information integration,motor coordination,and cognition)but also to prevent the onset and progression of neurodevelopmental disorders(such as intellectual disability,autism spectrum disorders,anxiety,and depression).This review mainly focuses on the recent progress of transcriptional regulations on the development and diversity of neocortical projection neurons and the clinical relevance of the failure of transcriptional modulations.

Some constructions of projectively flat Finsler metrics

In this paper, we find some solutions to a system of partial differential equations that characterize the projectively flat Finsler metrics. Further, we discover that some of these metrics actually have the zero flag curvature.

Some projectively flat (α,β)-metrics

In this paper, we study a class of Finsler metrics in the form , where is a Riemannian metric, form, and ∈ and k≠0 are constants. We obtain a sufficient and necessary condition for F to be locally projectively flat and give the non-trivial special solutions. Moreover, it is proved that such projectively flat Finsler metrics with the constant flag curvature must be locally Minkowskian.

Cascading multi-segment rupture process of the 2023 Turkish earthquake doublet on a complex fault system revealed by teleseismic P wave back projection method

In this study,the vertical components of broadband teleseismic P wave data recorded by China Earthquake Network are used to image the rupture processes of the February 6th,2023 Turkish earthquake doublet via back projection analysis.Data in two frequency bands(0.5-2 Hz and 1-3 Hz)are used in the imaging processes.The results show that the rupture of the first event extends about 200 km to the northeast and about 150 km to the southwest,lasting~90 s in total.The southwestern rupture is triggered by the northeastern rupture,demonstrating a sequential bidirectional unilateral rupture pattern.The rupture of the second event extends approximately 80 km in both northeast and west directions,lasting~35 s in total and demonstrates a typical bilateral rupture feature.The cascading ruptures on both sides also reflect the occurrence of selective rupture behaviors on bifurcated faults.In addition,we observe super-shear ruptures on certain fault sections with relatively straight fault structures and sparse aftershocks.

Recent Ventures in Interdisciplinary Arctic Research:The ARCPATH Project

This paper celebrates Professor Yongqi GAO's significant achievement in the field of interdisciplinary studies within the context of his final research project Arctic Climate Predictions: Pathways to Resilient Sustainable Societies-ARCPATH(https://www.svs.is/en/projects/finished-projects/arcpath). The disciplines represented in the project are related to climatology, anthropology, marine biology, economics, and the broad spectrum of social-ecological studies. Team members were drawn from the Nordic countries, Russia, China, the United States, and Canada. The project was transdisciplinary as well as interdisciplinary as it included collaboration with local knowledge holders. ARCPATH made significant contributions to Arctic research through an improved understanding of the mechanisms that drive climate variability in the Arctic. In tandem with this research, a combination of historical investigations and social, economic, and marine biological fieldwork was carried out for the project study areas of Iceland, Greenland, Norway, and the surrounding seas, with a focus on the joint use of ocean and sea-ice data as well as social-ecological drivers. ARCPATH was able to provide an improved framework for predicting the near-term variation of Arctic climate on spatial scales relevant to society, as well as evaluating possible related changes in socioeconomic realms. In summary, through the integration of information from several different disciplines and research approaches, ARCPATH served to create new and valuable knowledge on crucial issues, thus providing new pathways to action for Arctic communities.

人工智能背景下Materials Project数据库在计算材料学课程教学中的应用

该文探讨了在人工智能背景下,Materials Project数据库在计算材料学课程教学中的应用和影响。Materials Project数据库是一个集成了AI和大数据技术的开放获取的材料库,能为学生提供海量的材料晶体结构和物性数据,使教学内容更为丰富,让学生能通过亲自操作获取和分析数据,深入理解微观结构与物性之间的关系。这一新兴的教学模式不仅提升了学生的科研能力和创新思维能力,还有助于培养具备计算材料专业知识和多学科交叉的复合型人才。总体来说,人工智能时代下,大数据的引入为计算材料学课程带来新的活力,并对未来教育改革和实践产生了积极影响。

On a Class of Two-Dimensional Projectively Flat Finsler Metrics with Constant Flag Curvature

In this paper, we study a special class of two-dimensional Finsler metrics defined by a Riemannian metric and 1-form. We classify those which are locally projectively flat with constant flag curvature.

Accelerated Primal-Dual Projection Neurodynamic Approach With Time Scaling for Linear and Set Constrained Convex Optimization Problems

The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.

Quantum block coherence with respect to projective measurements

Quantum coherence serves as a defining characteristic of quantum mechanics,finding extensive applications in quantum computing and quantum communication processing.This study explores quantum block coherence in the context of projective measurements,focusing on the quantification of such coherence.Firstly,we define the correlation function between the two general projective measurements P and Q,and analyze the connection between sets of block incoherent states related to two compatible projective measurements P and Q.Secondly,we discuss the measure of quantum block coherence with respect to projective measurements.Based on a given measure of quantum block coherence,we characterize the existence of maximal block coherent states through projective measurements.This research integrates the compatibility of projective measurements with the framework of quantum block coherence,contributing to the advancement of block coherence measurement theory.

REFINEMENTS OF THE NORM OF TWO ORTHOGONAL PROJECTIONS

In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.