High Order ADER-IPDG Methods for the Unsteady Advection-Diffusion Equation

We present a high-order Galerkin method in both space and time for the 1D unsteady linear advection-diffusion equation. Three Interior Penalty Discontinuous Galerkin (IPDG) schemes are detailed for the space discretization, while the time integration is performed at the same order of accuracy thanks to an Arbitrary high order DERivatives (ADER) method. The orders of convergence of the three ADER-IPDG methods are carefully examined through numerical illustrations, showing that the approach is consistent, accurate, and efficient. The numerical results indicate that the symmetric version of IPDG is typically more accurate and more efficient compared to the other approaches.

An Unconventional Divergence Preserving Finite-Volume Discretization of Lagrangian Ideal MHD

We construct an unconventional divergence preserving discretization of updated Lagrangian ideal magnetohydrodynamics(MHD)over simplicial grids.The cell-centered finite-volume(FV)method employed to discretize the conservation laws of volume,momentum,and total energy is rigorously the same as the one developed to simulate hyperelasticity equations.By construction this moving mesh method ensures the compatibility between the mesh displacement and the approximation of the volume flux by means of the nodal velocity and the attached unit corner normal vector which is nothing but the partial derivative of the cell volume with respect to the node coordinate under consideration.This is precisely the definition of the compatibility with the Geometrical Conservation Law which is the cornerstone of any proper multi-dimensional moving mesh FV discretization.The momentum and the total energy fluxes are approximated utilizing the partition of cell faces into sub-faces and the concept of sub-face force which is the traction force attached to each sub-face impinging at a node.We observe that the time evolution of the magnetic field might be simply expressed in terms of the deformation gradient which characterizes the Lagrange-to-Euler mapping.In this framework,the divergence of the magnetic field is conserved with respect to time thanks to the Piola formula.Therefore,we solve the fully compatible updated Lagrangian discretization of the deformation gradient tensor for updating in a simple manner the cell-centered value of the magnetic field.Finally,the sub-face traction force is expressed in terms of the nodal velocity to ensure a semi-discrete entropy inequality within each cell.The conservation of momentum and total energy is recovered prescribing the balance of all the sub-face forces attached to the sub-faces impinging at a given node.This balance corresponds to a vectorial system satisfied by the nodal velocity.It always admits a unique solution which provides the nodal velocity.The robustness and the accuracy of this unconventional FV scheme have been demonstrated by employing various representative test cases.Finally,it is worth emphasizing that once you have an updated Lagrangian code for solving hyperelasticity you also get an almost free updated Lagrangian code for solving ideal MHD ensuring exactly the compatibility with the involution constraint for the magnetic field at the discrete level.

Preface

This focused issue of the Communications on Applied Mathematics and Computation is in Honour of Prof.Rémi Abgrall on the Occasion of His 61th Birthday.Rémi Abgrall has been a student in mathematics(1981–1985)of Ecole Normale Supérieure de Saint Cloud(now part of ENS Lyon).After his studies in pure mathematics,he changed orientation tofluid mechanics.He did his PhD at the Laboratoire de Météorologie Dynamique(LMD)at Ecole Normale Supérieure under the supervision of Claude Basdevant.He graduated in December 1987 with a thesis on a semi-Lagrangian model of 2D turbulence,refereed by Olivier Pironneau and Marcel Lesieur.

Fermat and Pythagoras Divisors for a New Explicit Proof of Fermat’s Theorem:a4 + b4 = c4. Part I

In this paper we prove in a new way, the well known result, that Fermat’s equation a4 + b4 = c4, is not solvable in ℕ , when abc≠0 . To show this result, it suffices to prove that: ( F 0 ): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is not solvable in ℕ , (where a 1 , b 1 , c 1 ∈2ℕ+1 , pairwise primes, with necessarly 2≤s∈ℕ ). The key idea of our proof is to show that if (F0) holds, then there exist α 2 , β 2 , γ 2 ∈2ℕ+1 , such that ( F 1 ): α 2 4 + ( 2 s−1 β 2 ) 4 = γ 2 4 , holds too. From where, one conclude that it is not possible, because if we choose the quantity 2 ≤ s, as minimal in value among all the solutions of ( F 0 ) , then ( α 2 ,2 s−1 β 2 , γ 2 ) is also a solution of Fermat’s type, but with 2≤s−10) is solvable in ( a 1 ,2 s b 1 , c 1 ) , s ≥ 2 like above;afterwards, proceeding with “Pythagorician divisors”, we creat the notions of “Fermat’s b-absolute divisors”: ( d b , d ′ b ) which it uses hereafter. Then to conclude our proof, we establish the following main theorem: there is an equivalence between (i) and (ii): (i) (F0): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is solvable in ℕ , with 2≤s∈ℕ , ( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs. (ii) ∃( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs, for wich: ∃( b ′ 2 , b 2 , b ″ 2 )∈ ( 2ℕ+1 ) 3 coprime in pairs, and 2≤s∈ℕ , checking b 1 = b ′ 2 b 2 b ″ 2 , and such that for notations: S=s−λ( s−1 ) , with λ∈{ 0,1 } defined by c 1 − a 1 2 ≡λ( mod2 ) , d b =gcd( 2 s b 1 , c 1 − a 1 )= 2 S b 2 and d ′ b = 2 s−S b ′ 2 = 2 s B 2 d b , where ( 2 s B 2 ) 2 =gcd( b 1 2 , c 1 2 − a 1 2 ) , the following system is checked: { c 1 − a 1 = d b 4 2 2+λ = 2 2−λ ( 2 S−1 b 2 ) 4 c 1 + a 1 = 2 1+λ d ′ b 4 = 2 1+λ ( 2 s−S b ′ 2 ) 4 c 1 2 + a 1 2 =2 b ″ 2 4;and this system implies: ( b 1−λ,2 4 ) 2 + ( 2 4s−3 b λ,2 4 ) 2 = ( b ″ 2 2 ) 2;where: ( b 1−λ,2 , b λ,2 , b ″ 2 )={ ( b ′ 2 , b 2 , b ″ 2 ) if λ=0 ( b 2 , b ′ 2 , b ″ 2 ) if λ=1;From where, it is quite easy to conclude, following the method explained above, and which thus closes, part I, of this article. .

The Relation between Mental Workload and Face Temperature in Flight Simulation

In this research, we study the relationship between mental workload and facial temperature of aircraft participants during a simulated takeoff flight. We conducted experiments to comprehend the correlation between work and facial temperature within the flight simulator. The experiment involved a group of 10 participants who played the role of pilots in a simulated A-320 flight. Six different flying scenarios were designed to simulate normal and emergency situations on airplane takeoff that would occur in different levels of mental workload for the participants. The measurements were workload assessment, face temperatures, and heart rate monitoring. Throughout the experiments, we collected a total of 120 instances of takeoffs, together with over 10 hours of time-series data including heart rate, workload, and face thermal images and temperatures. Comparative analysis of EEG data and thermal image types, revealed intriguing findings. The results indicate a notable inverse relationship between workload and facial muscle temperatures, as well as facial landmark points. The results of this study contribute to a deeper understanding of the physiological effects of workload, as well as practical implications for aviation safety and performance.

Fuzzy Henstock-Kurzweil Triple Integral on a Type 1 Quasi-Fuzzy Parallelepipedal Domain

In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, thin δ-fine partitions are introduced. The integration domain is a quasi-fuzzy parallelipiped. A numerical example is presented in order to show the application and the significance of the method.

New Fusion Approach of Spatial and Channel Attention for Semantic Segmentation of Very High Spatial Resolution Remote Sensing Images

The semantic segmentation of very high spatial resolution remote sensing images is difficult due to the complexity of interpreting the interactions between the objects in the scene. Indeed, effective segmentation requires considering spatial local context and long-term dependencies. To address this problem, the proposed approach is inspired by the MAC-UNet network which is an extension of U-Net, densely connected combined with channel attention. The advantages of this solution are as follows: 4) The new model introduces a new attention called propagate attention to build an attention-based encoder. 2) The fusion of multi-scale information is achieved by a weighted linear combination of the attentions whose coefficients are learned during the training phase. 3) Introducing in the decoder, the Spatial-Channel-Global-Local block which is an attention layer that uniquely combines channel attention and spatial attention locally and globally. The performances of the model are evaluated on 2 datasets WHDLD and DLRSD and show results of mean intersection over union (mIoU) index in progress between 1.54% and 10.47% for DLRSD and between 1.04% and 4.37% for WHDLD compared with the most efficient algorithms with attention mechanisms like MAU-Net and transformers like TMNet.

The Dual of the Two-Variable Exponent Amalgam Spaces (Lq(),lp())(Ω)

Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (Lq(),lp())(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.

无界域上1-集弱压缩算子的新不动点结果(英文)

本文证明Banach空间中无界域上一类弱序列连续和1-集弱压缩算子的若干新不动点定理.我们引入原点处弱半闭算子,得到该算子的若干不动点定理.进而将著名的Leray-Schauder不动点定理、Altman定理、Roth定理和Petryshyn定理推广到弱序列连续算子和1-集弱压缩算子以及原点处弱半闭算子的情形.本文的主要结果依赖于非紧性弱原子测度的有关条件.

中国五加科植物的分类学研究:罗伞属和鹅掌柴属的新种和新异名(英文)

在编写《FloraofChina》五加科Araliaceae时,发现两个新种,即拟榕叶罗伞BrassaiopsispseudoficifoliaLowry&C.B.Shang和光华鹅掌柴SchefflerazhuanaLowry&C.B.Shang。前者与榕叶罗伞B.ficifoliaDunn很相似,其区别在于,叶裂片数目较多,花序上具较多的伞形花序,花序轴具刺,主要分布于云南,广西偶见。后者与白花鹅掌柴S.leucanthaR.Vig.相似,其区别在于,子房心皮数目较多,果时具明显的萼缘,花盘扁平,叶质地较薄,局限分布于西藏墨脱县。同时发现越南产的BrassaiopsisgausseniiBui和中国产的细序鹅掌柴ScheffleratenuisH.L.Li、球序鹅掌柴S.glomerulataH.L.Li均不能成立,处理为异名。

Blow-Up Phenomena for a Class of Parabolic Systems with Time Dependent Coefficients

Blow-up phenomena for solutions of some nonlinear parabolic systems with time dependent coefficients are investigated. Both lower and upper bounds for the blow-up time are derived when blow-up occurs.

ESSENTIAL APPROXIMATE POINT SPECTRA FOR UPPER TRIANGULAR MATRIX OF LINEAR RELATIONS

When A E ∈LR（H） and B E ∈LR（K） are given, for C E∈LR（K, H） we denoteby Mc the linear relation acting on the infinite dimensional separable Hilbert space H Kof the formIn this paper, we give the necessary and sufficient conditionson A and B for wh{ch Mc is upper semi-Fredholm with negative index or Weyl for some C C ∈LR（K, H）.

MADCR:Mobility Aware Dynamic Clustering-Based Routing Protocol in Internet of Vehicles

Internet of Vehicles(IoV)is an evolution of the Internet of Things(IoT)to improve the capabilities of vehicular ad-hoc networks(VANETs)in intelligence transport systems.The network topology in IoV paradigm is highly dynamic.Clustering is one of the promising solutions to maintain the route stability in the dynamic network.However,existing algorithms consume a considerable amount of time in the cluster head(CH)selection process.Thus,this study proposes a mobility aware dynamic clustering-based routing(MADCR)protocol in IoV to maximize the lifespan of networks and reduce the end-to-end delay of vehicles.The MADCR protocol consists of cluster formation and CH selection processes.A cluster is formed on the basis of Euclidean distance.The CH is then chosen using the mayfly optimization algorithm(MOA).The CH subsequently receives vehicle data and forwards such data to the Road Side Unit(RSU).The performance of the MADCR protocol is compared with that ofAnt Colony Optimization(ACO),Comprehensive Learning Particle Swarm Optimization(CLPSO),and Clustering Algorithm for Internet of Vehicles based on Dragonfly Optimizer(CAVDO).The proposed MADCR protocol decreases the end-toend delay by 5–80 ms and increases the packet delivery ratio by 5%–15%.

Assessing Safety of Ferry Routes by Ship Handling Model through AHP and Fuzzy Approach

Ferry accidents often occur the result of ship handling difficulty which interfacing human, machine and environment. Therefore, a decision tool model as a comprehensive information system, based on the ship handling difficulty, needs to be developed through the combination of Analytic Hierarchy Process (AHP) and Fuzzy Logic System. The Fuzzy Logic System part consists of ship condition, ship handling facility condition, navigation condition and weather condition. The output of decision tool is the ship handling difficulty level in linguistic form. The simulation of model is conducted at several straits in Indonesia water. The decision tool model could be used as management information system by port authority to monitor the ferry/ship movement in real time regarding the ship handling difficulty. Further, it would be used to take some useful safety operation strategies and safety policies to improve ferry transportation safety at port water and strait water.

ANALYTICAL SMOOTHING EFFECT OF SOLUTION FOR THE BOUSSINESQ EQUATIONS

In this article, we study the analytical smoothing effect of Cauchy problem for the incompressible Boussinesq equations. Precisely, we use the Fourier method to prove that the Sobolev H^1 -solution to the incompressible Boussinesq equations in periodic domain is analytic for any positive time. So the incompressible Boussinesq equations admit exactly same smoothing effect properties of incompressible Navier-Stokes equations.

High egg rejection rate in a Chinese population of grey-backed thrush(Turdus hortulorum)

Several previous studies have indicated that nest sanitation behavior is a general adaptation in altricial birds,with egg recog nition capacity evolvi ng as a specific response to in terspecific brood parasitism(IBP).However,a rece nt study suggested an alternative hypothesis,con cludi ng that con specific brood parasitism(CBP)selects for egg rejection in thrushes,with IBP as a by-product.In the present study,we used a spectrophotometer to quantify egg coloration and egg mimicry and performed artificial parasitism experiments in the grey?backed thrush(Turdus hortulorum).We showed that individuals of this species rejected 100%of 12 foreign eggs,without IBP or CBP detected.In a review of previous studies,we also discuss possible explanations for the high egg rejection rate in the grey-backed thrush and suggest areas for future study.Altricial birds have evolved advaneed reproductive behavior to in crease the fitn ess of their offspring by buildi ng elaborate structures(i.e.,nests),in which they lay eggs and rear their nestlings(Hansell,2000).Bird nests not only provide a suitable place for nestling development,but also act as a concealed location for safety from predators.Furthermore,bird parents have evolved nest sanitation behavior to clean foreig n objects from their n ests,in eluding feces,eggshells,branches,and leaves,because they induce predation,facilitate microorganism growth,damage eggs,or hurt nestlings during brooding(Guigueno&Sealy,2012).Therefore,nest sanitation has evolved as a general behavior in altricial birds for distinguishing between egg-shaped and non-egg-shaped objects.

Annual spatio-temporal migration patterns of Hooded Cranes wintering in Izumi based on satellite tracking and their implications for conservation

Background: The Hooded Crane(Grus monacha) is listed as a vulnerable species by IUCN. Knowledge about the migration of the Hooded Crane is still limited. Here we reported the spatio-temporal migration patterns of Hooded Cranes wintering in Izumi, Japan, as well as important stopover areas for their conservation.Methods: Four adult and five subadult cranes, all wintering in Izumi, Japan, were fitted with satellite transmitters(GPS–GSM system) at their stopover sites in northeastern China in 2014 and 2015. We analyzed the time and duration of adults and subadults in spring and autumn migration, as well as the time and duration they stayed in breeding and wintering ground. In addition, we analyzed the land use of the cranes in stopover areas.Results: Adult cranes took much longer time to migrate both north in spring(mean days) compared with subadult cranes(15.3 and 5.2 days, respectively). H= 44.3 days) and south in fall(mean = 54.0 owever, the subadults had longer wintering(mean = 149.8 days) and nomadic(breeding season for adults) seasons(mean d with adults(133.8 and 122.3 days, respectively). Three important stopover areas have been= 196.8 days) compare identified: the region around Muraviovka Park in Russia, the Songnen Plain in China, and the west coast of South Korea, where cranes spent most of their migration time(62.2 and 85.7% in spring and autumn, respectively). During migration, nomadic period and winter, Hooded Cranes usually stay in croplands for resting and feeding. In non-wintering season, less than 6% of stopover sites were located within protected areas.Conclusion: Overall, our results contribute to understanding the annual spatio-temporal migration patterns of Hooded Cranes in the eastern flyway, and planning conservation measures for this species.

BEST APPROXIMATION FOR WEIERSTRASS TRANSFORM CONNECTED WITH SPHERICAL MEAN OPERATOR

Using reproducing kernels for Hilbert spaces, we give best approximation for Weierstrass transform associated with spherical mean operator. Also, estimates of extremal functions are checked.

Exponential Dichotomy and Eberlein-Weak Almost Periodic Solutions

We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equation dx/dt(t) = A(t)x(t) + f(t) in a Banach space X, where (A(t)) t ∈□ is a family of infinitesimal generators such that for all t ∈□, A(t + T) = A(t) for some T > 0, for which the homogeneuous linear equation dx/dt(t) = A(t)x(t) is well posed, stable and has an exponential dichotomy, and f:□ →X is Eberlein-weakly amost periodic.

Network Access Control Technology—Proposition to Contain New Security Challenges

Traditional products working independently are no longer sufficient, since threats are continually gaining in complexity, diversity and performance;In order to proactively block such threats we need more integrated information security solution. To achieve this objective, we will analyze a real-world security platform, and focus on some key components Like, NAC, Firewall, and IPS/IDS then study their interaction in the perspective to propose a new security posture that coordinate and share security information between different network security components, using a central policy server that will be the NAC server or the PDP (the Policy Decision Point), playing an orchestration role as a central point of control. Finally we will conclude with potential research paths that will impact NAC technology evolution.