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.

Crystallography in the Spaces E², E³, E⁴, E⁵...N⁰II Isomorphism Classes and Study of Five Crystal Families of Space E⁵

In the paper N0II, we describe some isomorphism classes and we apply their properties to the study of five crystal families of space E5. The names of these families are the following ones (monoclinic di iso squares)-al, decadic-al, (monoclinic di iso hexagons)-al, (rhombotopic cosa=-1/4)-al and rhombotopic cosa=-1/5. The meaning of these names will be given in Paragraphs 5 and 6 with some geometric properties of their cell.

Asymptotic Formulas for Thermography Based Recovery of Anomalies

We start from a realistic half space then use to develop a mathematical asymptotic model for thermal imaging, which we analysis well suited for the design of reconstruction algorithms. We seek to reconstruct thermal anomalies only through their rough features. With this way our proposed algorithms are stable against measurement noise and geometry perturbations. Based on rigorous asymptotic estimates, we first obtain an approximation for the temperature profile which we then use to design noniterative detection algorithms. We show on numerical simulations evidence that they are accurate and robust. Moreover, we provide a mathematical model for ultrasonic temperature imaging, which is an important technique in cancerous tissue ablation therapy.

Feynman Perturbation Series for the Morse Potential

In this paper we give an alternative treatment of the Schrodinger equation with the Morse potential, which based on the exact summation of the Feynman perturbation series in its original form. Using Fourier transform we establish a recurrence equation between terms of the perturbation series. Finally, by the inverse Fourier transform and some technical tools of the ordinary differential equations of the second order, we can compute the exact sum of the perturbation series which is the Green’s function of the problem.

Pythagorician Divisors and Applications to Some Diophantine Equations

We consider the Pythagoras equation X2 +Y2 = Z2, and for any solution of the type (a,b = 2sb1 ≠0,c) ∈ N*3, s ≥ 2, b1odd, (a,b,c) ≡ (±1,0,1)(mod 4), c > a , c > b, and gcd(a,b,c) = 1, we then prove the Pythagorician divisors Theorem, which results in the following: , where (d,d′′) (resp. (e,en)) are unique particular divisors of a and b, such that a = dd′′ (resp. b = ee′′ ), these divisors are called: Pythagorician divisors from a, (resp. from b). Let’s put λ ∈{0,1}, defined by: and S = s -λ (s -1). Then such that . Moreover the map is a bijection. We apply this new tool to obtain a new classification of the primitive, positive and non-trivial solutions of the Pythagoras equations: a2 + b2 = c2 via the Pythagorician parameters (d,e,S ). We obtain for (d, e) fixed, the equivalence class of any Pythagorician solution (a,b,c), checking , namely: . We also update the solutions of some Diophantine equations of degree 2, already known, but very important for the resolution of other equations. With this tool of Pythagorean divisors, we have obtained (in another paper) new recurrent methods to solve Fermat’s equation: a4 + b4 = c4, other than usual infinite descent method;and to solve congruent numbers problem. We believe that this tool can bring new arguments, for Diophantine resolution, of the general equations of Fermat: a2p + b2p = c2p and ap + bp = cp. MSC2020-Mathematical Sciences Classification System: 11A05-11A51-11D25-11D41-11D72.

A New Approach for Solving Fuzzy Linear Multi-Criterion Problems: An Approach Based on Minimization of the Errors Functions

The main purpose of this paper is to build a new approach for solving a fuzzy linear multi-criterion problem by defining a function called “error function”. For this end, the concept of level set is used to construct the error function. In addition, we introduce the concept of deviation variable in the definition of the error function. The algorithm of the new approach is summarized in three main steps: first, we transform the original fuzzy problem into a deterministic one by choosing a specific level . second, we solve separately each uni-criteria problem and we compute the error function for each criteria. Finally, we minimize the sum of error functions in order to obtain the desired compromise solution. A numerical example is done for a comparative study with some existing approaches to show the effectiveness of the new approach.

Novel criteria for exponential synchronization of inner time-varying complex networks with coupling delay

This paper mainly investigates the exponential synchronization of an inner time-varying complex network with coupling delay. Firstly, the synchronization of complex networks is decoupled into the stability of the corresponding dynamical systems. Based on the Lyapunov function theory, some sufficient conditions to guarantee its stability with any given convergence rate are derived, thus the synchronization of the networks is achieved. Finally, the results are illustrated by a simple time-varying network model with a coupling delay. All involved numerical simulations verify the correctness of the theoretical analysis.

Ginzburg-Landau方程的齐次化

本文研究了Ginzburg-Landau边值问题加罚齐次化方程解的存在唯一性,文中通过引入两个参数ε和δ,分别研究ε→0和δ→0时,上述方程解的渐近性态得到的。

Global Transmission Dynamics of a Schistosomiasis Model and Its Optimal Control

Drug treatment, snail control, cercariae control, improved sanitation and health education are the effective strategies which are used to control the schistosomiasis. In this paper, we consider a deterministic model for schistosomiasis transmission dynamics in order to explore the role of the several control strategies. The global stability of a schistosomiasis infection model that involves mating structure including male schistosomes, female schistosomes, paired schistosomes and snails is studied by constructing appropriate Lyapunov functions. We derive the basic reproduction number R0 for the deterministic model, and establish that the global dynamics are completely determined by the values of R0. We show that the disease can be eradicated when R0?≤1;otherwise, the system is persistent. In the case where ?R0?>1, we prove the existence, uniqueness and global asymptotic stability of an endemic steady state. Sensitivity analysis and simulations are carried out in order to determine the relative importance of different control strategies for disease transmission and prevalence. Next, optimal control theory is applied to investigate the control strategies for eliminating schistosomiasis using time dependent controls. The characterization of the optimal control is carried out via the Pontryagins Maximum Principle. The simulation results demonstrate that the insecticide is important in the control of schistosomiasis.

Complementarity of Sentinel-1 and Sentinel-2 Data for Mapping Agricultural Areas in Senegal

The small size of agricultural plots is the main difficulty for crops mapping with remote sensing data in the Sahelian region of Africa. The study aims to combine Sentinel-1 (radar) and Sentinel-2 (Optic) data to discriminate millet, maize and peanut crops. Training plots were used in order to analyse temporal variation of the three crops’ signals. The NDVI (Normalized Difference Vegetation Index) was able to differentiate crops only at the end of the rainy season (October). The optical data as well as the radar ones could not easily discriminate the three crops during the growing season, because in that period vegetation cover is low, and soil contribution to the signals (due to roughness and moisture) was more important than that of real vegetation. However, the ratio of VH/VV (VH: incident signal in vertical polarization and reflected signal in horizontal polarization;VV: incident signal in vertical polarization and reflected signal in horizontal polarization) gave a difference between millet and the two other crops at the beginning cultural season (July 11). Difference appears from the second third of September when the harvest of cereals crops (millet and maize) began. From middle of October, the peanut signal dropped sharply thus facilitating the differentiation of peanut from the two other crops. This analysis led to the identification of data that have could be used to discriminate these crops (useful data). Classification of the combined useful data gave an overall high accuracy of 82%, with 96%, 61% and 65% for peanut, maize and millet, respectively. The non-agricultural areas (water, natural vegetation, habit, bare soil) were well classified with an accuracy greater than 90%.

Crystallography in Spaces E², E³, E⁴, E⁵...N⁰I Isomorphism Classes: Properties and Applications to the Study of Incommensurate Phase Structures, Molecular Symmetry Groups and Crystal Families of Space E<sup>5</sup

This paper mainly consists of the classification of all crystallographic point groups of n-dimensional space with n ≤ 6 into different isomorphism classes. An isomorphism class is defined by a type of finite mathematic group;for instance, the different types of mathematic groups have been well defined and studied by Coxeter. This classification may be used in the investigation of several domains of crystallography such as the study of the incommensurate phases, the quasi crystals … Indeed, each mathematic substitution group characterizes an isomorphism class of crystallographic point groups (spaces E2 or E3), of point groups of super crystals (spaces E4 or E5), and of molecular symmetry groups (spaces E2 or E3). This mathematic group gives interesting information about: 1) the incommensurate phase structures and their phase transitions according to the Landau’s theory in their super spaces E4, E5, E6, ···;2) the molecular symmetry group of chemisorbed molecules in space E2 (paragraph 2) or of the molecular crystal or solution in view of studying the molecule structure or its rotations or vibrationsin space E3;3) the geometric polyhedron symmetry groups as the regular rhombohedron in space E3, the rhombotope in space E4 or the rhombotope in space E5. Then, thanks to the isomorphism classes, we shall give properties of some crystal families that we have not published up to now. This formalism may be used to study crystal families in n-dimensional space with n > 6.

基于D-InSAR对流层效应的多时相改正方法及其在科林斯海湾地震中的应用

在缓慢变形监测中,造成差分干涉测量(D-InSAR)技术误差的一个主要原因是对流层的不均一性所致。因为在两次雷达获取影像过程中气候条件有很大的差异性,并在差分干涉图中形成干扰的条纹。这些对干涉图产生很大的影响,需要在变形测量中给予剔除。本文提出一种在干涉测量中能够同时减少全局和局部对流效应的方法。首先,它要求利用稳定散射体来形成大量的、连续的多时相干涉图,全局大气校正是基于相位和地形,局部校正则基于干涉图之间的相关性。结合GPS技术测量科林斯海湾地表形变的结果验证该技术是有效的,实验数据包括81幅差分干涉图。

Bayesian autoregressive adaptive refined descriptive sampling algorithm in the Monte Carlo

This paper deals with the Monte Carlo Simulation in a Bayesian framework.It shows the impor-tance of the use of Monte Carlo experiments through refined descriptive sampling within the autoregressive model Xt=ρXt-1+Yt,where 0<ρ<1 and the errors Yt are independent ran-dom variables following an exponential distribution of parameterθ.To achieve this,a Bayesian Autoregressive Adaptive Refined Descriptive Sampling(B2ARDS)algorithm is proposed to esti-mate the parametersρandθof such a model by a Bayesian method.We have used the same prior as the one already used by some authors,and computed their properties when the Nor-mality error assumption is released to an exponential distribution.The results show that B2ARDS algorithm provides accurate and efficient point estimates.

Learning models for colorectal cancer signature reconstruction and classification in patients with chronic inflammatory bowel disease

BACKGROUND In their everyday life,clinicians face an overabundance of biological indicators potentially helpful during a disease therapy.In this context,to be able to reliably identify a reduced number of those markers showing the ability of optimising the classification of treatment outcomes becomes a factor of vital importance to medical prognosis.In this work,we focus our interest in inflammatory bowel disease(IBD),a long-life threaten with a continuous increasing prevalence worldwide.In particular,IBD can be described as a set of autoimmune conditions affecting the gastrointestinal tract whose two main types are Crohn’s disease and ulcerative colitis.AIM To identify the minimal signature of microRNA(miRNA)associated with colorectal cancer(CRC)in patients with one chronic IBD.METHODS We provide a framework of well-established statistical and computational learning methods wisely adapted to reconstructing a CRC network leveraged to stratify these patients.RESULTS Our strategy resulted in an adjusted signature of 5 miRNAs out of approximately 2600 in Crohn’s Disease(resp.8 in Ulcerative Colitis)with a percentage of success in patient classification of 82%(resp.81%).CONCLUSION Importantly,these two signatures optimally balance the proportion between the number of significant miRNAs and their percentage of success in patients’stratification.

Talagrand's T_2-Transportation Inequality and Log-Sobolev Inequality for Dissipative SPDEs and Applications to Reaction-Diffusion Equations

We establish Talagrand＇s T2-transportation inequalities for infinite dimensional dissipative diffusions with sharp constants, through Galerkin type＇s approximations and the known results in the finite dimensional case. Furthermore in the additive noise case we prove also logarithmic Sobolev inequalities with sharp constants. Applications to Reaction- Diffusion equations are provided.

COUPLING OF FINITE ELEMENT AND BOUNDARY ELEMENT METHODS FOR THE SCATTERING BY PERIODIC CHIRAL STRUCTURES

Consider a time-harmonic electromagnetic plane wave incident on a biperiodic structure in R^3. The periodic structure separates two homogeneous regions. The medium inside the structure is chiral and nonhomogeneous. In this paper, variational formulations coupling finite element methods in the chiral medium with a method of integral equations on the periodic interfaces are studied. The well-posedness of the continuous and discretized problems is established. Uniform convergence for the coupling variational approximations of the model problem is obtained.

Pattern dynamics of a reaction-diffusion predator-prey system with both refuge and harvesting

We are concerned with a reaction-diffusion predator–prey model under homogeneous Neumann boundary condition incorporating prey refuge(proportion of both the species)and harvesting of prey species in this contribution.Criteria for asymptotic stability(local and global)and bifurcation of the subsequent temporal model system are thoroughly analyzed around the unique positive interior equilibrium point.For partial differential equation(PDE),the conditions of diffusion-driven instability and the Turing bifurcation region in two-parameter space are investigated.The results around the unique interior feasible equilibrium point specify that the effect of refuge and harvesting cooperation is an important part of the control of spatial pattern formation of the species.A series of computer simulations reveal that the typical dynamics of population density variation are the formation of isolated groups within the Turing space,that is,spots,stripe-spot mixtures,labyrinthine,holes,stripe-hole mixtures and stripes replication.Finally,we discuss spatiotemporal dynamics of the system for a number of different momentous parameters via numerical simulations.

Rational map ax+1/x on the projective line over Q2 Dedicated to the Memory of Professor Lei Tan

The dynamical structure of the rational map ax+1/x on the projective line P^1(Q_2) over the field Q_2 of 2-adic numbers, is fully described.

A BOUNDARY INTEGRAL METHOD FOR COMPUTING ELASTIC MOMENT TENSORS FOR ELLIPSES AND ELLIPSOIDS

The concept of elastic moment tensor occurs in several interesting contexts, in particular in imaging small elastic inclusions and in asymptotic models of dilute elastic composites. In this paper, we compute the elastic moment tensors for ellipses and ellipsoids by using a systematic method based on layer potentials. Our computations reveal an underlying elegant relation between the elastic moment tensors and the single layer potential.

Semi-classical analysis on H-type groups Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday

In this paper, we develop semi-classical analysis on H-type groups. We define semi-classical pseudodifferential operators, prove the boundedness of their action on square integrable functions and develop a symbolic calculus. Then, we define the semi-classical measures of bounded families of square integrable functions which consist of a pair formed by a measure defined on the product of the group and its unitary dual, and by a field of trace class positive operators acting on the Hilbert spaces of the representations. We illustrate the theory by analyzing examples, which show in particular that this semi-classical analysis takes into account the finite-dimensional representations of the group, even though they are negligible with respect to the Plancherel measure.