Jorge Olivares Funes ^{1}
^{1}Universidad de Antofagasta , Departamento de Matemáticas , Chile
In this paper, we show how nonhomogeneous linear differential equations, especially those of the second order, are solved by means of GeoGebra applets by indeterminate coefficient methods and variation of parameters, for the course of differential equations of engineering students. and pedagogy in mathematics from the University of Antofagasta in Chile. The free software GeoGebra has caused that it is increasingly used in the teaching of mathematics, especially in nonhomogeneous linear differential equations, because it facilitates the teaching and learning process.
Jaykov Foukzon^{1}
^{1}Israel Institute of Technology, Department of mathematics, Israel
We introduce HausdorffColombeau measure in respect with negative fractal dimensions. Axiomatic quantum field theory in spacetime with negative fractal dimensions is proposed.Spacetime is modelled as a multifractal subset of $R^{4}$ with positive and negative fractal dimensions.The cosmological constant problem arises because the magnitude of vacuum energy density predicted by quantum field theory is about 120 orders of magnitude larger than the value implied by cosmological observations of accelerating cosmic expansion. We pointed out that the fractal nature of the quantum spacetime with negative HausdorffColombeau dimensions can resolve this tension. The classical Quantum Field Theory is widely believed to break down at some fundamental highenergy cutoff $E$ and therefore the quantum fluctuations in the vacuum can be treated classically seriously only up to this highenergy cutoff. In this paper we argue that Quantum Field Theory in fractal spacetime with negative Hausdorff Colombeau dimensions gives high energy cutoff on natural way. In order to obtain disered physical result we apply the canonical PauliVillars regularization up to $E$. It means that there exist the ghostdriven acceleration of the univers hidden in cosmological constant. http://arxiv.org/abs/1004.0451
Jorge Olivares Funes ^{1} , Luis Cortés Vega^{2} , Pablo Martin^{3} , Elvis Valero^{4}
^{1}Universidad de Antofagasta , Departamento de Matemáticas , Chile
^{2}University of Antofagasta, matemáticas, Chile
^{3}University of Antofagasta, Physics department, Chile
^{4}Universidad de Tarapacá, matemáticas, Chile
In this article we will show how to find approximate solutions, using the numerical analysis placement method with the GeoGebra software to the second order linear differential equations of the form d^2y/dx^2+A(x)dy/dx+B (x)y=Q (x), y (0) = y (a) = 0, where "a" is a positive number. The use of GeoGebra in the numerical analysis allows us to simultaneously, interactively and dynamically view the solutions and approximations of the differential equations.
Jorge Olivares Funes ^{1} , Pablo Martin^{2} , Fernando Maass^{3} , Elvis Valero^{4}
^{1}Universidad de Antofagasta , Departamento de Matemáticas , Chile
^{2}University of Antofagasta, Physics department, Chile
^{3}University of Antofagasta, Physics department, Chile
^{4}Universidad de Tarapacá, matemáticas, Chile
Fractional differential equations have a great importance and application. That is why the relationship between the fractional derivative and the erf (x) function will be shown below. The objective of this work is to solve the fractional differential equation D ^α y (x) =erf (x), and y(0) = 0, where 0<α<1. We will show the type of generalized hypergeometric solutions obtained by defining the fractional derivative of Caputo and the Laplace transform.
Pablo Martin^{1} , Jorge Olivares^{2} , Adrian Sotomayor^{3}
^{1}Universidad de Antofagasta, Física, Chile
^{2}Universidad de Antofagasta, Matemáticas, Chile
^{3}Universidad de Antofagasta, Matemáticas, Chile
New and more accurate approximation to the modified Bessel function I1 has been found by improving the multipoint quasi rational approximation method, MPQA. The approximation obtained in previous work (1) , has been improved by using the hyperbolic function sinh, instead of cosh. This change also the structure of the approximation , but there is not change in the structure of the approximation , and the number of parameters is also equal.Three terms of the power series and one term of the asymptotic expansion are also used to obtain the parameters of the approximation. In this way there is a decreasing of the relative error from 0.011 to 0.007 . A detail explication of the new procedure is carry on in this presentation. Ref. P. Martin, J. Olivares and A. Sotomayor, “ Precise Analytic Approximation for the Modified Bessel Function I1”, Rev. Mex. Física 63 (2017) 130 133 .
Jaykov Foukzon^{1}
^{1}Israel Institute of Technology, Department of mathematics, Israel
A new approach, which is proposed in this paper allows one to construct the Bellman function V(t,x) and optimal control u(t) directly,i.e.,without any reference to the Bellman equation, by way of using strong large deviations principle for the solutions ColombeauIto's SDE.
Franco Lindstron^{1}
^{1}Universidad Nacional de La Plata, Matemática, Argentina
This paper shows, for the first time, that the explicit and exact solution to the Troesch nonlinear twopoint boundary value problem may be computed in a direct and straightforward fashion from the general solution obtained by a generalized Sundman transformation for the related differential equation, which appeared to be a special case of a more general equation. As a result, various initial and boundary value problems may be solved explicitly and exactly.
yehuda roth^{1}
^{1}Oranim college, science, Israel
It is known that a dissipative environment is well described by the chaotic process while regular dynamics is associated with animate systems. In this paper, we explore the inverse map of some chaotic maps to find that they are always regular. The result that by reversing a chaotic map we obtain a regular process is associated with the birth of animate systems.
Manuel Fiolhais^{1}
^{1}University of Coimbra, Department of Physics, Portugal
The use of coherent states to describe boson systems goes back to the 1960's in the context of the radiation field. Since the 1970's, they have also been applied to meson clouds, mainly pions, in the context of the description of baryons by means of effective models involving a quark core surrounded by scalar and pseudoscalar mesons. The use of coherent states allows for an {\em abinitio} quantum mechanical description of the mesons, therefore going beyond semiclassical approximations. The coherent state e.g. for pwave pions (with angular momentum and isospin quantum numbers both equal to 1) is given by $\psi > = {\cal N}(\xi) \exp (\sum_{tm} \xi_{tm} a^\dagger _{tm} ) B> $ where ${\cal N}$ is a normalization factor, $  B > $ is a bare baryon state and $\xi_{tm}$ are amplitudes to be determined variationally. The $a^\dagger _{tm}$ is the creation operator for a pion state with angular momentum third component, $m$, and isospin third component, $t$. The radial profile of the pion amplitude results from a variational calculation and it is frozen. Hence, only angular momentum and isospin matters to construct the coherent state above. As already mentioned, the idea of mathematically modelling the meson clouds by means of coherent states, having in mind a full quantum mechanical description of baryon systems in the framework of chiral effective models, is not new. Actually, the author, among others, published several papers on the topic, in order to obtain various properties of the nucleon, the delta resonance and other excited states. However, the goal here is to bring together many aspects that are scattered in the literature, focusing on the versatility of the coherent states and stressing their capabilities. In this study, instead of the more realistic chiral effective models of quarks and mesons, we use a toy model whose Hamiltonian is written as $ H= \sum_{tm} a^\dagger_{tm} a_{tm} + G \sum _{tm} B_{tm} \left[ a_{tm} + (1)^{t+m} a_{tm}^\dagger \right]\!, $ where $B_{tm}$ is a baryon spinisospin operator. The model describes a system of non selfinteracting pions linearly coupled to a bare baryon core, $G$ being the coupling constant. This model is simple enough for its exact solutions to be worked out in the strong and weak regimes. These accurate solutions are then compared with the variational approximate solutions. Because the multiparticle coherent state, $\psi>$, cannot directly describe a nucleon, with definite angular momentum and isospin quantum numbers $\left( J={1\over 2}, I={1\over 2} \right)$, the PeiersYoccoz angular momentum (and isospin) projection method is used to construct a state, $\psi_N>$, with the proper nucleon quantum numbers. The variational method consists in minimizing the energy with respect to the amplitudes, i.e. $ d< H > / d \xi_{tm}=0 $, with the normalization condition $<\psi_N\psi_N>=1$ dully implemented in the process. We show that the socalled hedgehog configuration for the quark core and for the pion amplitudes minimizes the meanfield energy. On the other hand, we show that the (PeierlsYoccoz) projected coherent state is an extremely powerful ansatz since it reproduces the accurate solutions of the model both in the strong coupling regime (which is not surprising) but also in the weak coupling regime. We emphasise the use of the variationafterprojection method, for which the variational Hilbert space is larger, therefore with the trial function spanning a larger space than in the simpler variationbeforeprojection method. The toy model turns out to be a valuable tool to test different approaches which might be used in more realistic models with, for instance, selfinteracting mesons.
Yajuvindra Kumar ^{1}
^{1}Government Girls Degree College, Behat, Mathematics, India
In this paper, author studied free vibrations of a functionally graded (FG) annular plate having porosity. The plate is elastically restrained along the boundary. The material properties of the plate are Porosity dependent. An even porosity distribution is taken in the analysis. The mathematical model of the problem is developed using the concept of physical neutral surface of the plate. The physical neutral surface is taken as the reference plane. Out of many, only first three natural frequencies of the plate are reported using differential quadrature method (DQM). A parametric study is conducted to show the effects of porosity and material distribution parameters on the vibration behavior of the plate.
Yuriy Dimitrienko^{1} , Igor Krasnov^{2} , Kirill Zubarev^{3}
^{1}Bauman Moscow State Techical University, Fundamental sciences, Russian Federation
^{2}Bauman Moscow State Techical University, Fundamental sciences, Russian Federation
^{3}Bauman Moscow State Techical University, Fundamental sciences, Russian Federation
In this work the integration of two methods of electroinvestigation is considered. One method represents intubation by a direct current, the second intubation by alternating current. The integration is carried out for the purpose of increase in accuracy of results of the solution of the inverse task, the problem is solved in a twodimensional approximation. The direct task for the first and second method is solved numerically. The received values were compared with the experimental datas. The inverse task is formulated as a problem of minimization with the functional considering the experimental values received by both the first and second method of electroinvestigation. The problem of optimization is solved on a compact (for each parameter are set top and bottom border).
Julio S EspinozaOrtiz^{1} , Roberto E Lagos^{2}
^{1}Federal University of Goias, Physics, Brazil
^{2}UNESP, Rio Claro, SP, Departamento de Fı́sica, IGCE, Brazil
Billiards are physical models employed to probe experiments that measure the conductivity of quantum dots. In this context, the stadium billiard have been adopted as an standard model for realizations. We study the effect of softening this system in the classical mechanics, pursuing for a more realistic model. This classical approach is a first step towards the truly quantum or semiclassical case. We define the soft stadium as a monomial potential with an exponent {$\alpha\in\Re$} as a parameter, such that for {$\alpha=1$} the system is integrable and the {$\alpha\rightarrow\infty$} limit it converges to the hard billiard. Then, and for computational simplicity, we set up the construction of the classical Poincare map in such a way that it only depends on the partial separability of the system which holds for all {$\alpha$}'s. We present numerical results describing the classical transition from the integrable regime towards the chaotic regime.
The authors would like to thank the support of the Goi\'as Research Foundation  FAPEG.
Yannick Joel Wadop Ngouongo^{1}
^{1}University of Yaounde 1, Department of Physics, Cameroon
In connection with stochastic resonance (SR), we study the dynamics of a particle in the deformable travellingwave potentials in the presence of the external excitation force and the thermal fluctuations force. We model the deformation of the systems by the i) asymmetric deformable onsite potential (ASDP) and ii) double well deformable onsite potential (DWDP). The phenomenon of SR is known to take place in sinusoidal and nonsinusoidal systems. However, the question of the appeareance of SR in the ASDP as well as DWDP systems has not been resolved. The cooperative effect of noise and external force does show up in these systems. This numerical work presents the characterization of SR through an investigation of the input energy lost by the system to the environment per period of the external force which is also equivalent to the hysteresis loop area or average input energy. SR is characterized by the presence of a peak when the temperature increases. A double SR is observed in the ASDP case, first peak occurring at weak temperature has nothing to do with usual mechanical resonance. But it just associated to intrawell dynamics. However, second peak arising at higher temperature, relates to a classical SR phenomenon. In the DWDP case, only one resonance peak is observed. In both the systems the average input energy of occurrence of SR nonmonotonically depends of the shape parameter. We show that at low temperature the input energy depends very strongly on the initial positions of the particle. For each of the two models, this input energy is confined to two narrow bands in some range of the shape parameter. The input energy distribution of these is also explored. As function of the shape parameter, it can be unimodal or bimodal. Using the DWDP system, we investigated the presence of Chaos in the system in the goal to show that the disappearance of SR in the system can be due to Chaos.
Hafedh Zghidi^{1}
^{1}Silesian University of Technology , Institute of Informatics, Poland
The article presents a complete solution for filtering and diffusive fractal characterization of 2dimensional images. This includes preparing the sample by subtracting background, application of random walk procedure and its parallelization using two different approaches. For each technique the processing time is measured to compare speedups with regard to a sequential implementation. To prove the correctness of the results, a black square is used as the reference sample, for which diffusive fractal dimension is known and equls 2. Finally the results for a complex image are elaborated.
Pantea Davoudifar^{1} , Keihanak Rowshan Tabari^{2}
^{1}Research Institute for Astronomy and Astrophysics of Maragha, Astroparticle Physics, Iran (Islamic Republic of)
^{2}Research Institute for Astronomy and Astrophysics of Maragha, , Iran, Islamic Republic Of
In space physics the use of living organisms is not always possible. To study the environment condition, here a method were developed to create a network of given neurons. Different geometrical structures of the neurons were built using biological constraint. The fluence dose due to cosmic radiation were studied for the resulted structures. A factor of survival were defined and the structures were studied under short and long term radiation dosimetry. The effect of solar cycles and solar events were studied on radiation environment.
Andry Sedelnikov^{1} , Ekaterina Khnyryova^{2}
^{1}Samara National Research University, , Russian Federation
^{2}Samara national research university , Further Mathematics , Russian Federation
To know and understand the conditions of carrying out technological processes it is necessary to estimate the rotational motion parameters of the spacecraft. The parameters of the AIST small spacecraft rotational motion around its center of mass were estimated using measurement data of current from solar panels. At the same time, there is a problem in interpretation the telemetry data from small spacecraft: sometimes the significant current was recorded on two opposite solar panels. The paper shows a way to solve this problem using the fuzzy sets. As a membership function it is offered to use the normality condition of the direction cosines. The processing of telemetry data is given for AIST small spacecraft prototype. The offered approach can significantly increase the accuracy of angular velocity estimating using measurements of current from solar battery.
Avi Messica^{1} , Asnat GreensteinMessica ^{2}
^{1}COMAS, Finance and Quantitative Methods, Israel
^{2}BenGurion University of the Negev, Data Science and Information Systems, Israel
A new emerging technology, viewed as disruptive, occasionally generates a surge of public expectations over its potential application. This collective excitation (and decay) is generated and diffuses in a complex array of large random networks (e.g. social, media) that are difficult to model via small world models. Former studies of this phenomenon – termed as hype cycle  have focused mainly on descriptive, few casestudies, analysis using a corpus of newspaper articles and explained specific dynamics in a specific context. Motivated by the lack of a mathematical model, we studied a simple twophase mean field model that is able to explain the dynamics, as well as various patterns, of correlated expectations. Our contribution is as follows, we used an online query data (via Google Trends) as a proxy for public expectations to study more than one hundred technologies. We extended the classification of the diffusion pattern with three new categories to better reflect different observed dynamics. Lastly, we present a datadriven mathematical model that enables to draw useful insights on the rich dynamics of hype cycles.
Serena Doria^{1}
^{1}University G.d'Annunzio ChietiPescara, Department of Engineering and Geology, Italy
A new mathematical model of coherent upper conditional expectations based on Hausdorff outer measures is proposed in a metric space $(\Omega,d)$ to make prevision when the conditioning events are fractal sets, i.e. sets with noninteger Hausdorff dimension. The necessity to propose a new tool to define coherent upper conditional expectations arises because they cannot be obtained as extensions of linear conditional expectations defined, by the RadonNikodym derivative, in the axiomatic approach (Billingsley, 1986); it occurs because one of the defining properties of the RadonNikodym derivative, that is to be measurable with respect to the $\sigma$field of the conditioning events, contradicts a necessary condition for the coherence. Given a partition $\textbf{B}$ of $\Omega$ for every $B \in \textbf{B}$ denote by $s$ the Hausdorff dimension of $B$ and let $h^{s}$ be the Hausdorff $s$dimensional Hausdorff outer measure associated to the coherent upper conditional expectation $. For every bounded random variable $X$ a coherent upper conditional expectation $\overline{P}(XB)$ is defined by the Choquet integral with respect to its associated Hausdorff outer measure if the conditioning event has positive and finite Hausdorff outer measure in its Hausdorff dimension. Otherwise if the conditioning event has Hausdorff outer measure in its Hausdorff dimension equal to zero or infinity it is defined by a 01 valued finitely, but not countably, additive probability.
ZhongCheng Liang^{1}
^{1}Nanjing University of Posts and telecommunications, College of Electronic and Optical Engineering , China
Pointlike and wavelike particles are foundations of classical and modern physics. They are so idealized models that lose the physical authenticity. Real particles are threedimensional body with mass and volume. The spatial intersection of real particles is empty set, thus ensuring limited density of particles. In the centreofmass frame of reference, a real particle has three independent modes of motion: vibration, rotation and translation. Three mode energies $(H,L,K)$ constitute a Cartesian space. The energy space is quantized by vibrating quantum $(H_s=Y_s V_s=hv)$, rotating quantum $(L_s=I_s ω_s^2=lz)$ and translating quantum $(K_s=M_s u_s^2=kT)$. The energy space is divided into six phases and three zones. Three zones represent gas, solid and liquid state of object. There are three equilibrium surfaces, each of which has two stable areas and two excited areas. Two types of phase transition are distinguished by two types of phase interface. Complete energy relations and differential equations can be derived through the statistics of particle ensemble. The results show that the order parameters of liquid, solid and gas are the correlative functions of the particle mass $(M)$, the rotary inertia $(I)$ and the elastic modulus $(Y)$, respectively. Thermodynamic laws are the natural inferences of the theoretical results. A physical theory based on the real particle model has simplicity, consistency and universality.
Mayken EspinozaAndaluz^{1}
^{1}ESPOL, Centro de Energías Renovables y Alternativas, Ecuador
The energy demand to supply micro devices has been increasing during the last years. Considering the power output of the laminar flow microfluidic fuel (LFFC), it appears as a suitable solution to provide the required electrical energy in small devices. Absence of electrolyte and not requirement of platinum as catalytic material are two of the most important advantages of this type of fuel cells. The current study aims to provide a detailed information about the design and characteristics of a LFFC. A complete analysis of the different shape channels has been considered in this study being selected the best option as the Yshaped channels. The impact of the inclination degree for the inlet channels has been considered to evaluate the average velocity that the flow can acquire into the channel. In addition, the voltagecurrent behaviour considering the materials, fuel/oxidant and design characteristics has been obtained from a modelling point of view.
The authors kindly acknowledge the financial support from FIMCPCERA052017. In addition, Åforsk project No 17331 is gratefully acknowledged.
Vania Rangelova^{1}
^{1}Technical University Sofia  branch Plovdiv, Electrical Engineering, Bulgaria
The biosensor amperometric transducers can work in the case of three basic types of reversible inhibitor enzyme systems – with competitive inhibition, with noncompetitive inhibition and mixed inhibition. Tipicaly they work in static mode. Now they are investigated in dynamic mode. The kinetic in those type biosensors is generally discussed in terms of a simple extension to the MichaelisMenten reaction scheme. The investigated biosensors are amperometric product sensitive. The parameters for simulations are chosen from some real experiments with biosensors. The models are described in non stationary diffusion conditions. Solving system of nonlinear partial differential equations is reseived in three dimensional size and the concentration profiles in active membrane of substrate S(x,t), inhibitor I(x,t) and product P(x,t) are reseived. The systems of nonlinear differential partial equations have been solved numerically in MATLAB medium. The influence of starting concentration of substrate, inhibitor and kinetic parameters  reaction constants of biosensors for substrate and for inhibitor over output current have been investigated.
Yuriy Dimitrienko^{1} , Kirill Zubarev^{2} , Igor Krasnov^{3}
^{1}Bauman Moscow State Techical University, Fundamental sciences, Russian Federation
^{2}Bauman Moscow State Techical University, Fundamental sciences, Russian Federation
^{3}Bauman Moscow State Techical University, Fundamental sciences, Russian Federation
This article discusses the results of solving the problem of electrical exploration using direct current. The developed methods and algorithms for solving the direct and inverse exploration tasks are tested on several inhomogeneous models of the environment. The task is considered in threedimensional approximation. To solve using the finite element method. On the basis of the direct problem algorithm, a method for solving the inverse problem was implemented, which consists in finding the minimum of the deviation functional, which in turn leads to the multiple solution of the direct problem. The obtained results were analyzed, the advantages and shortcomings of the developed methods were revealed, the evaluation of the search time for the optimal solution for the inverse problem was carried out, and the dependence of the solution accuracy on the thickening of the grid when solving the problem by the finite element method was discussed.
Sabine Upnere^{1}
^{1}Riga Technical University, Institute of Mechanics, Latvia
The numerical modelling of crossflow through the rods bundle with triangular arrangement has been done to analyse flowinduced forces on the rod located in the middle of the bundle. Significant problems of rods in the bundle during the operational time of the system can be caused by the crossflow. At the same time, it is known that the behaviour of the system is strongly related to many parameters such as bundle geometry, flow, rods support and others. Therefore, there is needed to investigate the characteristics of each type of typical bundles. In this paper is analysed flowinduced hydrodynamic forces in closelypacked rods bundle using Computational Fluid Dynamics. Unsteady Reynolds Averaged NavierStokes equations are solved using Finite Volume discretization. The impact of the size of the computational domain and the number of rows in it was investigated to find the optimal case for numerical modelling. Obtained results are compared with references from literature and experimental data.
Ashraf Zaher^{1}
^{1}American University of Kuwait, Electrical and Computer Engineering, Kuwait
This paper proposes an efficient technique for detecting mechanical faults in threephase induction motors, without using mechanical sensors. Only measurements of the currents of every phase are used to identify the fault. The proposed system can diagnose two types of faults corresponding to shaft misalignment or imbalance, along with normal operation. The power spectrum of the experimental data is generated, followed by applying a softcomputing mathematical algorithm that will extract the peaks of the fundamental frequencies and their harmonics, while filtering out noise. These peaks will be compiled in a vector form such that it can be used as inputs to train an artificial neural network (ANN) to produce a decision regarding the operating condition of the motor, via applying intelligent pattern recognition techniques. Mathematical details regarding the structure of the ANN, its training, tuning of its synaptic weights, and the testing/validation phase will be investigated. Detailed analysis of the obtained results is provided to highlight the advantages and limitations of the proposed algorithm. In addition, a comparison is made with similar techniques that use mechanical sensors to contrast their differences and highlight the superiority of the proposed system. The obtained results prove the intelligence and robustness of the proposed system and allows for versatile extensions that promote its application in realtime scenarios for many industrial applications.
This work was supported by a grant from the American University of Kuwait, during the academic year 201819.
Santanu Chatterjee^{1} , Sanjoy Mukherjee^{2}
^{1}RGM International (India) Pvt. Ltd., Civil, India
^{2}KEC International Limited, Engineering Services, India
For decades, scientists have worked relentlessly to move forward to see what lies beyond the third dimension and to find out if there is any existence of a unified theory to explain all the workings of the universe from subatomic to gigantic inhabitants of cosmos. This insurmountable task has been taken on by many over the last century or so until the emergence of “super string theory” or “string theory” happened showcasing the fact that an answer seemed possible. From the concepts of a “string”, our ideation on this theory started. In this paper we strived to put forward that the concept of a vibrating onedimensional microscopic object named “string” can be taken as a fundamental ingredient (in place of point particle) for developing nonrelativistic quantum mechanics. Unlike point particle, we take a vibrating string as the quantum object & build a perfectly reasonable quantum mechanical description of the microscopic world. Our main objective in this paper to show that complete development of quantum mechanics is possible based on one dimensional open string.
Santanu Chatterjee^{1} , Sanjoy Mukherjee^{2}
^{1}RGM International (India) Pvt. Ltd., Civil, India
^{2}KEC International Limited, Engineering Services, India
String theory provides an encouraging way to unify all force fields in our universe into a single framework. Different vibrational patterns of a single string resemble different particles. Bosonic strings require 26 spatial dimensions in order to produce particles in a similar fashion as 10 spatial dimensions are required to produce Fermions states. These extra dimensions (beyond 3 spatial & 1 time dimension) are compactified into very small scale and thus in today’s scale of probing energy it is not possible to detect them experimentally. This idea of extra dimensions, hidden from our perception is tempting & worth indepth theoretical work. Certain topological features and its application on String theory will also be discussed in this paper. We will try to fathom these small plank scale compactified dimensions & will try to throw some light on the various topological aspects of quantum geometry offered by this remarkable theory.
Nadir MAGHLAOUI^{1}
^{1}Higher School of Applied Sciences, Physics, Algeria
Phasedarray transducer are becoming of common use in ultrasound imaging either in medical applications or in the field of non destructive technique. The modelling of the acoustic field emitted by phasedarrays transducers can be realized by different methods developed in the frequency domain or in the time domain. The method proposed here consists in using the Rayleigh integral method where the reflection at the plane interface is taken into account by using the reflection coefficients for harmonic plane waves. The transient field is obtained by an inverse Fourier transform of the harmonic results. The results obtained put in evidence the fact that the ultrasonic waveforms reflected by a liquidsolid interface and detected by the phasedarrays transducer depend strongly on the geometrical and physical parameters of these kind of transducers. The transient representation of these waves have been analysed and discussed by the rays model. . A potential application of this work would be the study of the acoustic signature of materials by using phasedarrays transducer working in pulsed mode. The obtained results have been compared to those obtained by using a finite element method package.
Esha Kashyap^{1} , Kannan Sr^{2}
^{1}Pondicherry University(A Central University of India), Mathematics, India
^{2}Pondicherry University(A Central University of India), Mathematics, India
This paper reviews the influence of kernel function in unsupervised way of clustering in data analysis. Unsupervised clustering analysis is considered as an explorative data analysis tool that assists in discovering hidden patterns or natural grouping in data, and has been effectively applied in various applications. The implementation of kernel function with the objective functions of unsupervised clustering techniques contribute an effective works for recognizing nonlinear structures of high dimensional databases and the objective functions are robust in clustering the high dimensional databases which contains outliers with heavy noise. This paper mainly discusses the kernels with the objective functions of fuzzy cmeans, possiblistic cmeans, and intutionistic fuzzy cmeans for clustering the nonliner structured databases. Experimental section of the paper supports to understand the effective of kernel in various clustering methods.
This work was financially supported by DST India and MOST Israel
Uri BenYa'acov^{1}
^{1}Kinneret Academic College on the Sea of Galilee, School of Engineering, Israel
Is it possible to encompass the full extent of the Universe with a finite number of first principles and inference rules ? The belief that it is possible to arrive at a complete theory that fully describes the whole of the physical world – a theory that accounts, via few and simple first principles, for all the phenomena already observed and that will ever be observed – has been, for manymany years and for most researches, a fundamental tenet of the scientific research. However, Gödel's incompleteness theorem implies that any formal structure, based on a finite number of first principles and inference rules, which is rich enough, cannot be at the same time both consistent and complete. Completeness, in terms of physical theories, implies that if the necessary initial data are given then the state of a physical system can be predicted for any time in the future. Does Gödel's theorem apply to physics ? A common argument in favour of applying Gödel's theorem to physics, is, more or less, that "Gödel's theorem applies to arithmetics which is the basis of mathematics, physics uses mathematics, therefore Gödel's theorem applies to physics". However, the counterargument says that there are mathematical theories to which Gödel's theorem does not apply, e.g. geometry, and that this is the type of mathematics that physics uses, therefore we should not expect that Gödel's theorem applies to physics. The purpose of the talk is to present and put forward another argument, which I believe is the decisive one. Gödel's theorem (whenever it applies) points to incompleteness in the sense that there will always be claims that may be formulated within this formal system but are undecidable – propositions that cannot be either proved or refuted. A close inspection of Gödel's theorem demonstrates that this impossibility arises when the claims are selfreferential, or, more precisely, when the system asks to define itself in its own terms. Selfreferencing occurs in physics whenever the observer is also part of the observed system. In most physical system this is not the case, therefore the counter argument should apply. However, when it is the whole Universe that is dealt with, then we, the observers, are also part of it, and Gödel's theorem should apply. The talk will discuss selfreferencing in Gödel's theorem, its relation with our involvement in the Universe, and consequences thereof.
Alena Astrakhantseva^{1} , Alexander Chebotarev^{2} , Andrey Kovtanyuk^{3}
^{1}Far Eastern Federal University, Department of computer science, mathematical and computer modelling, Russian Federation
^{2}Far Eastern Federal University, Institute for Applied Mathematics FEB RAS, , Russian Federation
^{3}Far Eastern Federal University, Institute for Applied Mathematics FEB RAS , , Russian Federation
Endovenous laser ablation is a very effective minimally invasive therapy to manage leg varicosities. The corresponding mathematical model is based on conversion of absorbed laser energy into heat. To describe the process of endovenous laser ablation, the radiativeconductive heat transfer model with moving source is chosen. The conventional nonstationary normalized $P_1$ approximation of the radiativeconductive heat transfer model is considered in a bounded domain $\Omega \subset \mathbf{R}^3$ which consists of a finite number of disjoint subdomains $\Omega_j$, $j=1,..., p$\,: \begin{equation}\label{1} a \partial\theta/\partial t  \mathrm{div}\,(k\nabla\theta)  b \varphi = u_1,\;  \mathrm{div}\,(\alpha \nabla \varphi) + \beta \varphi = u_2,\; x\in\Omega,\ t\in (0,T). \end{equation} Here, $\theta$ is the normalized temperature; $\varphi$ is the normalized radiation intensity averaged over all directions; $k$ is the thermal conductivity; $a$, $b$, $\alpha$, and $\beta$ are piecewise constant functions describing the thermal and radiation properties of the medium (see, e.g., \cite{1}), $a(x)=a_i$, $b(x)=b_i$, $\alpha(x)=\alpha_i$, $\beta(x)=\beta_i$ if $x \in \Omega_i$, $j=1,..., p$. The functions $u_{1,2}=u_{1,2}(x,t)$ describe the intensities of heat and radiation sources. Let $k(x) = k_j$ if $x \in \Omega_j$, $j=2,...,p$\,;\, $k(x) = c(\theta) k_1$ if $x \in \Omega_1$, where $c(\theta) = 1$ if $\theta < \theta_*$, and $c(\theta) = m > 1$ if $\theta \geq \theta_*$\,;\, $k_1, ... k_p, m = Const$. The subdomain $\Omega_1$ corresponds to blood fraction, and the factor $c(\theta)$ simulates the rise of thermal conductivity due to boiling effect. We consider the righthand sides of equations (1) having the structure $u_{1,2} = P_{1,2}(t)f_\varepsilon(x,r(t))$, $x\in \Omega,\,t\in (0,T)$. The functions $P_{1,2}$ describe the powers of heat and radiation sources, $f_\varepsilon(x,r(t))=1$ if $xr(t)<\varepsilon$, and $f_\varepsilon(x,r(t))=0$ otherwise; $r(t)$ is a given trajectory of a moving source. The following boundary conditions on $\Gamma := \partial \Omega$ and the initial condition at $t=0$ are assumed: \begin{equation}\label{2} a\partial_n \theta + h(\theta  \theta_b)_\Gamma = 0,\;\; \alpha\partial_n \varphi + 0.5\varphi_\Gamma = 0, \quad \theta_{t=0} = \theta_0. \end{equation} Here, $\partial_n$ denotes the derivative in direction of the outward normal $n$; the boundary functions, $\theta_{b}$, $h$, and the initial function, $\theta_0$, are given. Let $\theta_i(x) = \theta(x)$ and $\varphi_i(x) = \varphi(x)$ if $x \in \Omega_i$, $j=1,..., p$. At the internal boundaries between adjoint subdomains $\Omega_i$ and $\Omega_j$, \, $1 \leq i,j \leq p$,\, $i \neq j$, we set the following conjugation conditions: \begin{equation}\label{3} \theta_i = \theta_j, \;\; a_i\partial_n \theta_i = a_j\partial_n \theta_j, \;\;\; \varphi_i = \varphi_j, \;\; \alpha_i\partial_n \varphi_i = \alpha_j\partial_n \varphi_j,\;\;\; x \in \overline{\Omega}_i \cap \overline{\Omega}_j. \end{equation} In the current work, a priori estimates of temperature and radiation intensity in the space $L^{\infty}$ ensuring the unique solvability of the problem (1)(3) are presented. The theoretical analysis is illustrated by numerical examples simulated the process of endovenous laser ablation. \begin{thebibliography}{9} \bibitem{1} G.V.~Grenkin, A.Yu.~Chebotarev, A.E.~Kovtanyuk, N.D.~Botkin, K.H.~Hoffmann, \textit{J. Math. Anal. Appl.}, \textbf{433}, 12431260 (2016). %\bibitem{2} A.E.~Kovtanyuk, A.Yu.~Chebotarev, N.D.~Botkin, K.H.~Hoffmann, \textit{Commun. Nonlinear Sci. Numer. Simulat.}, \textbf{20}, 776784 (2015). \end{thebibliography}
Marco Zoli^{1}
^{1}University of Camerino, School of Science & Technology, Italy
The stability properties of dsDNA are important in a number of molecular biology techniques (e.g., polymerase chain reaction) and nanotechnological devices (e.g., DNAbased sensors) in which short fragments of synthetic DNA are used as a recognition element by virtue of the peculiar WatsonCrick base pairing, allowing for selective hybridization with a target sequence. The helix stability properties are also key to single molecule denaturation mapping experiments, recently used combined with nanochannel arrays, which confine and stretch the DNA molecule to be analyzed. These techniques are based on the fact that AT rich regions melt at lower temperatures than GC rich regions; staining the molecule with a fluorescent dye that binds only to ds regions one obtains an optical barcode unique to the sequence of the specific molecule. The DNA properties are also strongly affected in confined conditions as those which occur in vivo in the crowded environments of cells where macromolecules \textit{i)} reduce the free volume for base pair fluctuations thus suppressing the melting entropy, \textit{ii)} interfere with the dynamics of DNA looping thus affecting the speed of gene activation or repression. While considerable amount of experimental work has been carried out over the last decades to investigate the relation among macromolecular crowding, DNA dynamics and its biological functioning, much less theoretical studies have been produced so far on DNA in crowded conditions. Here I focus on the interplay between DNA structure and confining environment analyzing how a crowders distribution around a single DNA chain may concur to shape the helical conformation and the overall size of the molecule itself. The study assumes a coarse grained Hamiltonian model which describes the helical molecule at the level of the base pair. The equilibrium statistics of the system is obtained by a computational method based on a finite temperature path integral method which I have developed over the last years. The method has been widely discussed in conjunction with calculations of some fundamental indicators of DNA flexibility at short length scale such as the cyclization probabilities, the persistence lengths and the single molecule response to stretching perturbations induced by external loads. After reviewing the method and previous researches, I present some recent results regarding the stretching and twisting of short DNA fragments simulating the presence of specific crowders profiles.
Manuel De la Sen^{1}
^{1}University of the Basque Country, Elwctricity and Electronics, Spain
This paper is concerned with the investigation of the global stability and global asymptotic stability of the error with respect to its nominal version of a nonlinear timevarying perturbed functional differential system which is influenced by point, finitedistributed and Volterratype distributed delayed dynamics. The boundedness of the error and its asymptotic convergence to the zero equilibrium are investigated and some formal “ ad hoc” results are proved.
Andrei Melekhin^{1}
^{1}National Research Moscow State University of Civil Engineering, Heat and gas supply and ventilation, Russian Federation
The modeling of the process of cleaning polluted washing water in circulating water use systems and solutions to the problems of optimizing the process parameters.
Irina Mazilu^{1} , Anthony Lorson^{2} , Sho Gibbs^{3} , Will Hanstedt^{4} , Dan Mazilu^{5}
^{1}Washington and Lee University, Department of Physics and Engineering, United States
^{2}Washington and Lee University, Physics and Engineering, United States
^{3}Washington and Lee University, Physics and Engineering, United States
^{4}Washington and Lee University, Physics and Engineering Department, United States
^{5}Washington and Lee University, Department of Physics and Engineering, United States
As the political landscape becomes increasingly complex, the classic paradigms used in political science have failed to remain relevant and other methods of study are needed. We use a multitemperature kinetic Ising model to analyze the partisanship dynamics of the US Senate. We use Monte Carlo simulations, mean field theory and numerical analysis of the master equation of a system of 100 senators (agents) separated into various categories based on their political leanings and interactions with each other. Results show an interesting development of partisanship between the agents after a short time. The model can be extended to other cooperative stochastic systems in physics and social sciences.
Matthew Withers^{1} , Elise Baker^{2} , Dan Mazilu^{3} , Irina Mazilu^{4}
^{1}Washington and Lee University, Department of Physics and Engineering, United States
^{2}Washington and Lee University, Department of Physics and Engineering, United States
^{3}Washington and Lee University, Department of Physics and Engineering, United States
^{4}Washington and Lee University, Department of Physics and Engineering, United States
We design and model an experiment to study the effect of electric bias on particlecoverage densities produced during ionic nanoparticle selfassembly. The experiment involves the application of a uniform external electric field parallel to a glass substrate during the selfassembly of silica nanoparticles. We refer to this procedure as directed selfassembly of monolayers (DSAM). In our theoretical analysis, we modify existing cooperative sequential adsorption models to account for diffusion under an applied electric field. We use the mean field approximation to solve for particlecoverage densities. To ascertain the validity of this method, we compare our solutions to Monte Carlo simulations of the system.
Elise Baker^{1} , Matthew Withers^{2} , Emma Aldrich^{3} , Isabel Shaffrey^{4} , Justin Pusztay^{5} , Dan Mazilu^{6} , Irina Mazilu^{7}
^{1}Washington and Lee University, Department of Physics and Engineering, United States
^{2}Washington and Lee University, Department of Physics and Engineering, United States
^{3}Washington and Lee University, Department of Physics and Engineering, United States
^{4}Washington and Lee University, Department of Physics and Engineering, United States
^{5}Washington and Lee University, Department of Physics and Engineering, United States
^{6}Washington and Lee University, Department of Physics and Engineering, United States
^{7}Washington and Lee University, Department of Physics and Engineering, United States
We present a class of cooperative stochastic models for adsorption and evaporation of monomers on two and threedimensional lattices subjected to perpendicular external electric fields. These models are motivated by the fabrication of optical coatings using layerbylayer selfassembly. We report computational and analytical results for the timedependent particle density and discuss a particular experimental implementation of an ionic selfassembled monolayer under the influence of a constant electric field.
Dan Mazilu^{1} , Matthew Withers^{2} , Will Hanstedt^{3} , Sho Gibbs^{4} , Anthony Lorson^{5} , Irina Mazilu^{6}
^{1}Washington and Lee University, Department of Physics and Engineering, United States
^{2}Washington and Lee University, Department of Physics and Engineering, United States
^{3}Washington and Lee University, Physics and Engineering Department, United States
^{4}Washington and Lee University, Department of Physics and Engineering, United States
^{5}Washington and Lee University, Physics and Engineering, United States
^{6}Washington and Lee University, Department of Physics and Engineering, United States
We present a versatile cooperative threestate model with adsorption and evaporation defined on different topologies: two and threedimensional lattices and Cayley trees. We discuss this model in the context of two main applications: silica and titania selfassembled optical coatings on glass substrates and drug encapsulation of two different types of nanoparticles on treelike synthetic polymers called dendrimers and described mathematically as Cayley trees. We present analytical and Monte Carlo simulation results for these different topologies and discuss other possible extensions of the model to social sciences.
Rustem Sakhapov^{1}
^{1}Kazan State University of Architecture and Engineering, ROAD CONSTRUCTION MACHINERY, Russian Federation
This article investigates the increase of tractioncoupling properties of propellers, patency of machinetractor units and decrease of soil compaction. For a propulsor equipped with antiskid devices, the slippage process is formed due to factors of soil compression by the soiltread and shear of the soil by tire hooks. With the decrease in the number of detachable hooks, the period when the first hook disengaged and the second has not yet entered in interaction with the ground, increases. At the moment, traction and coupling properties of the wheel are formed only due to the tire hooks. When the detachable hook engages with the soil, the traction capacity of the wheel is made up of the forces of shear of soil "bricks" sandwiched between tire hooks and the forces of soil deformation by detachable hooks. As a result of integrating the dependence of the shear stress and deformation of the soil, a formula was obtained to determine the tangential traction force of the tractor. If the skidding of the wheel assembly depends on the pulling force, then the drag force from the antiskid device. Using the known dependencies of the slippage of wheeled propellers, dependences are obtained to determine the slippage of the propulsion unit with the antiskid device. With the increase in the number of antiskid devices on the wheel, slippage is reduced, however, according to the research, the time required for the assembly and disassembly of the device reduces the interchangeability of the wheel assembly. We calculated he number of antiskid devices at which the maximum exchange capacity will be reached. The penetration depths at which the maximum efficiency of the wheel assembly running system will be reached are obtained and the results are tabulated.
Daniel Clark^{1}
^{1}Washington and Lee University, Department of Physics and Engineering , United States
The polarization and intractability of American politics has received increased scrutiny throughout the 21st century. We attempt to model the complex mechanisms of political cooperation in a finite democratic system. Due to the shorter termlimits and subsequently limited external influences, we select the House of Representatives as an ideal setting to examine the interactions between United States politicians, and therefore we utilize the structure and political topology of the 115th House of Representatives for recent, realistic data. Within this model, legislation is first voted on in a small committee before moving to the entire House. Throughout these voting steps certain agents are assigned a maverick state, which holds their initial vote as fixed, while others’ votes vary based on political values and social influences. At each step the votes and transitions of each agent are studied using Monte Carlo Simulations on networks and network theory. We study the dynamics of both committees and the House as a whole, specifically the impact of inflexible voters, political alignments, and party affiliations.
Dmitrii Kiselyov^{1} , Igor Inovenkov^{2} , Vladimir Nefedov^{3}
^{1}Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Russian Federation
^{2}Lomonosov Moscow State University, Department of Computational Math & Cybernatics, Russian Federation
^{3}Lomonosov Moscow State University, Department of Computational Math & Cybernatics, Russian Federation
The problem of the interaction of various population groups in the framework of urban environment is of current interest this time. The population is divided into different strata according to their economic and social characteristics. For example, a population could be classified according to genetic and phenotypic characteristics, belonging to a particular ethnic group and, first of all, according to income level. In a number of countries, the coexistence of population groups belonging to different social strata gives rise to serious problems and therefore has been studied from different points of view, mainly from a sociological. Due to the qualitative analysis of various situations, it becomes possible to predict and prevent possible conflicts and problems. The significance of this problem is obvious, but reasonable proposals for its solution have not been put forward. In this regard, the construction of a qualitative, but fairly general mathematical model of the dynamics of various groups of the population is of particular interest. Such a mathematical model should be built within the framework of the concept of spatial economics. This paper discusses the first version of the model for a situation where there are only two groups of people. The corresponding system of equations includes two nonlinear diffusion equations with terms describing the interaction of the population groups in model. Of course, the basic difficulty is the selection of coefficients, which will provide the picture as close as possible to reality, so it makes sense to add to the model and stochastic terms that will be responsible for random environmental factors. Thus, a twodimensional stochastic model of the temporal dynamics of the distribution of two population groups in an urban environment was presented and numerically investigated. As a result of the mathematical modeling certain estimates were obtained regarding the feasibility of taking into account stochastic factors in the proposed mathematical model.
Igor Emel'yanov^{1} , Alexey Polyakov^{2} , Anastasia Hodak^{3}
^{1}Ural Federal University, Institute of Engineering Science, Russian Academy of Sciences (Ural Branch), Laboratory of Materials Engineering, Russian Federation
^{2}Ural Federal University, Structural mechanics, Russian Federation
^{3}Ural Federal University, Institute of Fundamental Education, Russian Federation
An approach is proposed to solve the problem of estimating the stress state of a shell structure loaded with a thermomechanical load and in contact with a hydrogencontaining medium. The stress state of the steel housing of the diffusion apparatus for the production of highly pure hydrogen was determined. The object of study is presented in the form of a composite shell of rotation, loaded by internal pressure and operating at elevated temperatures. The purpose of the work is to determine the stress state of the shell at normal and elevated pressure, taking into account changes in the mechanical properties of the combined effect of temperature and hydrogen. In the general case, the task of calculating such a structure under given operating conditions is related. But for processes with different physical times, it can be represented by a sequence of individual problems of heat propagation, hydrogen diffusion, and the calculation of the stress state. In the phenomenological approach, the relationship between thermal diffusion and mechanical problems is manifested in a change in the parameters of the sample deformation diagram with increasing temperature and hydrogen concentration. The integration of differential equations of a boundary value problem for a shell under pressure is performed by the discrete orthogonalization method S.К. Godunov. The solution obtained made it possible to determine the location of the maximum stresses, in which the greatest changes in the mechanical properties of the material should be expected. According to the results of the calculations, a conclusion was given on the bearing capacity of the structure in the working mode and with increasing hydrogen concentration and internal pressure.
Nikolay Evstigneev^{1} , Oleg Ryabkov^{2}
^{1}Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow, Russia, 81 Macrodynamical systems, Russian Federation
^{2}Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow, Russia, , Russian Federation
We are considering the problem of divergence  free projection in rectangular domains for the Oseen (stationary NavierStokes) operator ($F(\mathbf{u}, p)$): $$F(\mathbf{u}, p) := (\mathbf{u}, \nabla) \mathbf{u}+\nabla p  \nu \Delta \mathbf{u}\mathbf{h} = \mathbf{0},$$ $$\nabla \cdot \mathbf{u}=0,$$ with zero wall boundary conditions. It uses nodal Finite Element method (space $\mathcal{P}$) to reconstruct pressure and Finite Difference method (space $\mathcal{V}$ for scalar functions and $\mathcal{V}^d$ for vector functions with $d=2,3$) for other parts of the equations. This allows us to use simple finite difference schemes for linear part (compact difference schemes) and WENOtype schemes for the the nonlinear part in the space of discrete velocities. The boundary conditions in $\mathcal{V}$ are formulated in Finite Volume conservative approach. Besides, such approach compies with the LBB condition automatically. We form the projection operator matrix $\mathtt{P}$ as follows: $$\mathtt{P}:=\mathtt{E}_d+\mathtt{G} \mathtt{A}^{1} \mathtt{I} \mathtt{D},$$ where matrices are identity ($\mathtt{E}_d:\mathcal{V}^d \to \mathcal{V}^d$), gradient ($\mathtt{G}:\mathcal{P} \to \mathcal{V}^d$), regularized inverse Laplace ($\mathtt{A}^{1}:\mathcal{P} \to \mathcal{P}$), interpolation ($\mathtt{I}:\mathcal{V} \to \mathcal{P}$) and divergence ($\mathtt{D}:\mathcal{V}^d \to \mathcal{V}$), respectively, from left to right. We wish to use the suggested method in the framework of continuation process in bifurcation analysis problem of stationary solutions. In this case we need so solve the problem using Newton's method: $$\mathcal{P} F_{\mathbf{u}^n} \delta \mathbf{u} =  \mathcal{P}F(\mathbf{u}^n),$$ $$\mathbf{u}^{n+1} = \mathbf{u}^{n} + \delta \mathbf{u}, \mathbf{u}^{n} \leftarrow \mathbf{u}^{n+1},$$ where the application of the projector nulls the pressure gradient. The method is applied incrementally, i.e. $\mathbf{f} = F(\mathbf{u}^n)$, $\mathbf{g} = \mathcal{P}\mathbf{f}$, and use $\mathbf{g}$ in the right hand side of the linear system. We numerically analize the operator $\mathtt{R}$ that acts in the $\mathcal{V}$ space of divergence operator image: $$\mathtt{R}:=\mathtt{E}_1+\mathtt{D} \mathtt{G} \mathtt{A}^{1} \mathtt{I},$$ where $\mathtt{E}_1: \mathcal{V} \to \mathcal{V}$. It is shown that all eigenvalues of the operator are less than unity for Oseledetstype wall (marked $w$) boundary conditions for velocity, namely: $(\mathbf{n}_w, \mathbf{u}_w) = 0, (\mathbf{\tau}_w, \mathbf{u}_w) = \nabla_{\tau} p$ and zero Neumann conditions for the Poisson equation. We illustrate that the convergence rate depends on the smoothness of the projected function and that the projection method allows one to obtain divergencefree solutions with desired tolerance. We show that for smooth functions we obtain 4th order convergence in divergence. Finally we demonstrate the method by solving some problems for the 2D Oseen operator. The test 2D MATLAB code in square domain for the projection problem is available at the author's GitHub.
This work is supported by RFBR grant no. 182910008 mk.
Asher Yahalom^{1}
^{1}Ariel University, Electrical & Electronic Engineering, Israel
Galaxies are huge physical systems having dimensions of many tens of thousands of light years. Thus any change at the galactic center will be noticed at the rim only tens of thousands of years later. Those retardation effects seems to be neglected in present day galactic modelling used to calculate rotational velocities of matter in the rims of the galaxy and surrounding gas. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this presentation we will show that taking general relativity seriously without neglecting retardation effects one can explain the radial velocities of galactic matter without postulating dark matter.
Jaykov Foukzon^{1}
^{1}Israel Institute of Technology, Department of mathematics, Israel
One of the Bell's assumptions in the original derivation of his inequalities was the hypothesis of locality, i.e., the absence of the influence of two remote measuring instruments on one another. That is why violations of these inequalities observed in experiments are often interpreted as a manifestation of the nonlocal nature of quantum mechanics, or a refutation of a local realism. It is well known that the Bell's inequality was derived in its traditional form, without resorting to the hypothesis of locality and without the introduction of hidden variables, the only assumption being that the probability distributions are nonnegative. This can therefore be regarded as a rigorous proof that the hypothesis of locality and the hypothesis of existence of the hidden variables not relevant to violations of Bell's inequalities. The physical meaning of the obtained results is examined. Physical nature of the violation of the Bell inequalities is explained under new EPRB nonlocality postulate.We show that the correlations of the observables involved in the BohmBell type experiments can be expressed as correlations of classical random variables. The revisited Bell type inequality reads

Zuleima Carrasco^{1}
^{1}Escuela Superior Politecnica de Chimborazo, Physics Research Group  ESPOCH, Ecuador
Quantum tunneling theory is widely used for many applications in different areas from the fundamental research to technological applications. In particular, the quantum tunneling appears in scanning tunneling microscope, nuclear physics, quantum computing, tunnel diode, among other. Here, we show a simple mathematical derivation of the onedimensional quantum transmission considering two particular cases: (i) for comparison purposes, the conventional quantum tunneling with one potential barrier and (ii) the quantum tunneling with two potential barriers considering a small distance between barriers, in which a pseudopotential is created and the particle is nonfree. As known, the quantum transmission in the first case, depends only on the incident particle energy (kinetic energy), the mass of particle, the energy barrier (potential energy) and the barrier length that the particle passes through. However, on the second case, an extra dependency is observed, i.e., the separation distance between barriers (the Harmant effect is cancel). We have corrobarated that the first case evidence the major quantum transmition probability respect to second one. Aditionally, we evidence that transmition probability can be modulate and controlled by changing the separation distance between barriers, which produces a region where the particles can be free or trapped. If this discovery is confirmed by future experiments, such as waveguide experiments, it could enhance the particle manipulation at nanometer scale improving the image resolution.
I would thanks Physics Research Group  ESPOCH and Dr. Cristian Vacacela Gomez, Ms. Noemi Moreta, Dennys Colcha and Dr. Richard Pachacama for the opportunity to present this work at the event, which help me to increase my expertise and aptitudes taken from my undergraduate career.