Binary Archimedes Optimization Algorithm for Computing Dominant Metric Dimension Problem

In this paper,we consider the NP-hard problem of finding the minimum dominant resolving set of graphs.A vertex set B of a connected graph G resolves G if every vertex of G is uniquely identified by its vector of distances to the vertices in B.A resolving set is dominating if every vertex of G that does not belong to B is a neighbor to some vertices in B.The dominant metric dimension of G is the cardinality number of the minimum dominant resolving set.The dominant metric dimension is computed by a binary version of the Archimedes optimization algorithm(BAOA).The objects of BAOA are binary encoded and used to represent which one of the vertices of the graph belongs to the dominant resolving set.The feasibility is enforced by repairing objects such that an additional vertex generated from vertices of G is added to B and this repairing process is iterated until B becomes the dominant resolving set.This is the first attempt to determine the dominant metric dimension problem heuristically.The proposed BAOA is compared to binary whale optimization(BWOA)and binary particle optimization(BPSO)algorithms.Computational results confirm the superiority of the BAOA for computing the dominant metric dimension.

结构参数对二维Archimedes A7晶格光子晶体禁带的影响

利用平面波展开法对空气背景中介质圆柱和方柱构造的二维Archimedes A7晶格光子晶体的禁带结构随介质折射率、填充比的变化关系进行了研究,并进一步计算了介质方柱的旋转角度对完全光子禁带宽度的影响.研究发现,介质圆柱构造的Archimedes A7晶格结构在介质柱折射率最低为n=2.40时出现完全光子禁带,当n=2.60时禁带宽度达到最大值.介质方柱构造的Archimedes A7晶格结构在介质柱折射率n=3.80时完全禁带宽度达到最大值,且随着折射率的增加禁带宽度变化很小;在介质方柱折射率恒定情况下,其最大禁带宽度与旋转角度无关,但旋转后出现完全禁带的填充比范围明显扩大.

试论Archimedes的数学思想

依据 Archimedes的数学贡献 ,尤其是 Archimedes在求抛物线弓形面积时所创立的方法 ,分析了Archim edes的数学思想 ,认为 Archimedes既善于进行巧妙的物理论证 ,又善于进行严格的数学论证。由Archim edes的数学思想得到的启示是 :巧妙的物理论证是科学发现的重要方法 ;严格的数学论证是确立结论的必需步骤 ;要精选若干基本原理 ,作为论证的基础 ;要献身科学真理 ,不为俗世需求所动摇。

一类特殊的非Archimedes序域其构造

本文讨论了一类特殊的非Archimedes序列，这种序域可用来以简单而自然的方法定义实数，这种序域的构造方式也是自然的，自由然数集N的一种特殊保真扩张模型N出发，使用通常的分数程序来构造，本文在讨论N的保真扩张的一般方法基础上着重讨论相论容方程组方法与超滤方法。

Archimedes螺线盘转动问题的差分处理

所计算的匀质可燃Archimedes螺线盘 ,是一个在水平支撑面上发生燃喷并做定轴转动的变质量力学系统 .采用差分方法对其进行了有关计算 。

二维介质柱型Archimedes(4，8^2)复式晶格光子晶体禁带特性研究

采用平面波展开法分别模拟了空气背景下由介质圆柱和方柱构造的二维Archimedes(4,82)复式晶格光子晶体的能带结构,讨论了介质柱形状、折射率、填充比和旋转对称性等因素对完全光子禁带的影响.研究发现,当折射率在2.60到5.40之间时,介质圆柱和方柱构造的二维Archimedes(4,82)复式晶格光子晶体都出现了完全光子禁带.随着折射率的增大,最大完全禁带宽度并非随之增大而是存在峰值,介质圆柱型晶格在折射率为2.80时出现峰值;介质方柱型晶格在折射率为2.80和4.40两处出现峰值,且旋转介质方柱能够明显增大禁带宽度,同时存在最佳旋转角度.分析结果表明,在最大完全禁带处,折射率、填充比以及旋转角度等因素的变化对禁带特性的影响很小.

Improved Archimedes Optimization Algorithm with Deep Learning Empowered Fall Detection System

Human fall detection(FD)acts as an important part in creating sensor based alarm system,enabling physical therapists to minimize the effect of fall events and save human lives.Generally,elderly people suffer from several diseases,and fall action is a common situation which can occur at any time.In this view,this paper presents an Improved Archimedes Optimization Algorithm with Deep Learning Empowered Fall Detection(IAOA-DLFD)model to identify the fall/non-fall events.The proposed IAOA-DLFD technique comprises different levels of pre-processing to improve the input image quality.Besides,the IAOA with Capsule Network based feature extractor is derived to produce an optimal set of feature vectors.In addition,the IAOA uses to significantly boost the overall FD performance by optimal choice of CapsNet hyperparameters.Lastly,radial basis function(RBF)network is applied for determining the proper class labels of the test images.To showcase the enhanced performance of the IAOA-DLFD technique,a wide range of experiments are executed and the outcomes stated the enhanced detection outcome of the IAOA-DLFD approach over the recent methods with the accuracy of 0.997.

Archimedes’ Principle Revisited

Based on Newton’s third law of motion, we present a different but quite general analysis of Archimedes’ principle. This analysis explains the reduction in apparent weight of a submerged object in all cases, regardless of its position in the fluid. We also study the case in which the object rests on the bottom of the container where the net hydrostatic force on it is downward, and explain where in this case the reduction in the apparent weight comes from.

A New Physical Interpretation of Archimedes’ Principle

The interpretation of the equilibrium of a solid body floating on the surface of a liquid body is well known as the “Archimedes’ Principle”. Presently, the equilibrium of the solid body is interpreted as the result of the concurrence of two mechanical actions which are equivalent and opposite: the “weight” of the body, directed downwards, and the “Archimedes’ force” having a magnitude equivalent to the weight of the volume of liquid displaced by the volume of the body immersed in the liquid, directed upwards. We show arguments proving that this interpretation is not a correct physical interpretation. The same arguments show that a new different interpretation is a correct one. The new interpretation is based on the hypothesis that the “weight” of a body immersed in a body-medium is proportional to the volume of the body immersed in the body-medium and to the difference in density between the matter of the body and the matter of the body-medium. Accordingly, if a body is completely immersed in a body-medium, there is only one mechanical action on the body. This action may be downwards or upwards, or its magnitude may be zero. In this last case, the body is in equilibrium within the body-medium.

Investigation of Physical and Numerical Model of Archimedes Screw Turbine

Archimedes screw turbines have been developed as they work with a low head with high efficiency, where flow energy can be exploited in small rivers, streams, regulators and others. The power can be produced using Archimedes turbines and depends on some parameters including the number of blades, flow, and angle of the shaft inclination and the length of the pitch. A physical and numerical model has been developed to determine the performance of the Archimedes turbine on the Ramadi Dam in Iraq. The physical model was made of stainless steel with the following parameters (length 1000 mm, pitch 70 mm, diameter ratio 0.536, inclination angles 30°, 35°, 40°, 45°). Work was carried out on different flow rates and inclination angles. The experimental results showed that the highest efficiency was 81.4% at 35° inclination angle and a flow rate of 1.12 l/s; the maximum power of 9.03 watts was at a 45° inclination angle and a flow rate of 2.065 l/s and 72% efficiency. Also, the impact of the pitch and the number of blades were studied. The results show that torque is increase with an increase in the pitch length, and torque is decreased with increase in several blades. The numerical results showed that the using of two blades led to a greater power produced. The comparison of the numerical and experimental results showed a good agreement, also the comparison with the published data showed a good agreement. As a final result the Archimedes screw has many positive points making it a good potential candidate. The results that emerged show the possibility of using this type of turbine in the Euphrates River in Anbar Governorate—Iraq, as the province is characterized by the presence of many regulators on the river in which turbines can be employed.

Archimedes螺线式Fresnel透镜的设计及加工方法

为解决传统同心环式Fresnel透镜及其模具金刚石刀具加工存在对加工系统要求过高及效率较低的问题,给出了Archimedes螺线式Fresnel透镜的设计方法。从几何聚光比和能流透射率方面对比了2种透镜的性能,发现两者性能基本一致。分析了大型Fresnel透镜及其模具金刚石车削机床的运动。计算了Archimedes螺线式Fresnel透镜车削加工的刀具轨迹。对比机床各轴精度对透镜光学性能的影响,发现刀具摆角、透镜法线方向进给轴的精度影响最大,采用附加沿刀具轴线方向微进给装置的机床结构能有效提高加工精度。

A Procedure for Trisecting an Acute Angle (Method 2)

This paper presents an alternate graphical procedure (Method 2), to that presented in earlier publications entitled, “A Procedure for Trisecting an Acute Angle” and “A Key to Solving the Angle Trisection Problem”. The procedure, when applied to the 30˚ and 60˚ angles that have been “proven” to be nottrisectable and the 45˚ benchmark angle that is known to be trisectable, in each case produced a construction having an identical angular relationship with Archimedes’ Construction, as in Section 2 on THEORY of this paper, where the required trisection angle was found to be one-third of its respective angle (i.e. DE’MA = 1/3 DE’CG). For example, the trisection angle for the 30˚, 45˚ and 60˚ angles were 10.00000˚, 15.00000˚, and 20.00000˚, respectively, and Section 5 on PROOF in this paper. Therefore, based on this identical angular relationship and the numerical results (i.e. to five decimal places), which represent the highest degree of accuracy and precision attainable by The Geometer’s Sketch Pad software, one can only conclude that not only the geometric requirements for arriving at an exact trisection of the 30˚ and 60˚ angle (which have been “proven” to be not-trisectable) have been met, but also, the construction is valid for any arbitrary acute angle, despite theoretical proofs to the contrary by Wantzel, Dudley, and others.

Archimedes 3~2,4,3,4结构光子晶体中与偏振无关的自准直分束器

通过等频图分析并结合时域有限差分法法模拟,在Archimedes32,4,3,4结构排列的二维光子晶体中同一频率下同时实现了电磁波两种偏振态的自准直.研究发现,在该结构光子晶体中引入缺陷,当线缺陷宽度改变时,TE和TM两种偏振态光束的分束效果将会随之变化.由此通过控制缺陷宽度,分别实现了两种偏振态光束的50%:50%分束以及90°大角度光折弯,分束和折弯的效率都较为理想,为未来设计基于光子晶体的新型光子学器件提供了一种新的思路。

How did Archimedes discover the law of buoyancy by experiment？

After Archimedes and Vitruvius era, for more than 2000 years, it has been believed that the displaced water measurement of golden crown is impossible, and at his Eureka moment, Archimedes discovered the law of buoyancy （Proposition 7 of his principles） and proved the theft of a goldsmith by weighing the golden crown in water. A previous study showed that a small amount of displaced water was able to be measured with enough accuracy by the introduced method. Archimedes measured the weight of displaced water. He did not find the law of buoyancy but rather specific gravity of things at the moment. After which, Archimedes continued to measure the specific gravity of various solids and fluids. Through these measurements, he reached the discovery of the law of buoyancy directly by experiment. In this paper, the process to the discovery of Archimedes＇ principle （Proposition 5） is presented.

Optimal allocation of solar photovoltaic distributed generation in electrical distribution networks using Archimedes optimization algorithm

This paper proposes to resolve optimal solar photovoltaic(SPV)system locations and sizes in electrical distribution networks using a novel Archimedes optimization algorithm(AOA)inspired by physical principles in order to minimize network dependence and greenhouse gas(GHG)emissions to the greatest extent possible.Loss sensitivity factors are used to predefine the search space for sites,and AOA is used to identify the optimal locations and sizes of SPV systems for reducing grid dependence and GHG emissions from conventional power plants.Experiments with composite agriculture loads on a practical Indian 22-bus agricultural feeder,a 28-bus rural feeder and an IEEE 85-bus feeder demonstrated the critical nature of optimally distributed SPV systems for minimizing grid reliance and reducing GHG emissions from conventional energy sources.Additionally,the voltage profile of the network has been enhanced,resulting in significant reductions in distribution losses.The results of AOA were compared to those of several other nature-inspired heuristic algorithms previously published in the literature,and it was observed that AOA outperformed them in terms of convergence and redundancy when solving complex,non-linear and multivariable optimization problems.

Deep Learning-Based FOPID Controller for Cascaded DC-DC Converters

Smart grids and their technologies transform the traditional electric grids to assure safe,secure,cost-effective,and reliable power transmission.Non-linear phenomena in power systems,such as voltage collapse and oscillatory phenomena,can be investigated by chaos theory.Recently,renewable energy resources,such as wind turbines,and solar photovoltaic(PV)arrays,have been widely used for electric power generation.The design of the controller for the direct Current(DC)converter in a PV system is performed based on the linearized model at an appropriate operating point.However,these operating points are everchanging in a PV system,and the design of the controller is usually accomplished based on a low irradiance level.This study designs a fractional-order proportional-integrated-derivative(FOPID)controller using deep learning(DL)with quasi-oppositional Archimedes Optimization algorithm(FOPID-QOAOA)for cascaded DC-DC converters in micro-grid applications.The presented FOPIDQOAOA model is designed to enhance the overall efficiency of the cascaded DC-DC boost converter.In addition,the proposed model develops a FOPID controller using a stacked sparse autoencoder(SSAE)model to regulate the converter output voltage.To tune the hyper-parameters related to the SSAE model,the QOAOA is derived by the including of the quasi-oppositional based learning(QOBL)with traditional AOA.Moreover,an objective function with the including of the integral of time multiplied by squared error(ITSE)is considered in this study.For validating the efficiency of the FOPID-QOAOA method,a sequence of simulations was performed under distinct aspects.A comparative study on cascaded buck and boost converters is carried out to authenticate the effectiveness and performance of the designed techniques.

3D Path Optimisation of Unmanned Aerial Vehicles Using Q Learning-Controlled GWO-AOA

Unmanned Aerial Vehicles(UAVs)or drones introduced for military applications are gaining popularity in several other fields as well such as security and surveillance,due to their ability to perform repetitive and tedious tasks in hazardous environments.Their increased demand created the requirement for enabling the UAVs to traverse independently through the Three Dimensional(3D)flight environment consisting of various obstacles which have been efficiently addressed by metaheuristics in past literature.However,not a single optimization algorithms can solve all kind of optimization problem effectively.Therefore,there is dire need to integrate metaheuristic for general acceptability.To address this issue,in this paper,a novel reinforcement learning controlled Grey Wolf Optimisation-Archimedes Optimisation Algorithm(QGA)has been exhaustively introduced and exhaustively validated firstly on 22 benchmark functions and then,utilized to obtain the optimum flyable path without collision for UAVs in three dimensional environment.The performance of the developed QGA has been compared against the various metaheuristics.The simulation experimental results reveal that the QGA algorithm acquire a feasible and effective flyable path more efficiently in complicated environment.

A Procedure for the Squaring of a Circle (of Any Radius)

This paper presents a graphical procedure for the squaring of a circle of any radius. This procedure, which is based on a novel application of the involute profile, when applied to a circle of arbitrary radius (using only an unmarked ruler and a compass), produced a square equal in area to the given circle, which is 50 cm2. This result was a clear demonstration that not only is the construction valid for the squaring of a circle of any radius, but it is also capable of achieving absolute results (independent of the number pi (π), in a finite number of steps), when carried out with precision.

A Key to Solving the Angle Trisection Problem

This paper describes the methodology (or approach) that was key to the solution of the angle trisection problem published earlier in article entitled, “A Procedure For Trisecting An Acute Angle.” It was an approach that required first, designing a working model of a trisector mechanism, second, studying the motion of key elements of the mechanism and third, applying the fundamental principles of kinematics to arrive at the desired results. In presenting these results, since there was no requirement to provide a detailed analysis of the final construction, this information was not included. However, now that the publication is out, it is considered appropriate as well as instructive to explain more fully the mechanism analysis of the trisector in graphical detail, as covered in Section 3 of this paper, that formed the basis of the long sought solution to the age-old Angle Trisection Problem.

How Gravitational Effects on the Quantum Vacuum Might Explain Dark Energy and Dark Matter Observations

Following a brief review of the “black hole dark energy radiation” and “gravitized vacuum” references, a novel theory of how gravity might affect the quantum vacuum is proposed. This overarching theory proposes that the gravitational field of a sufficiently concentrated collection of matter and/or energy upregulates the virtual particle activity of the adjacent quantum vacuum, thus its energy density and lensing capacity. In contrast to general relativity, the particle and wave duality of quantum physics is necessary for understanding quantum vacuum gravitational effects. Very recent supporting and pending observational studies are discussed, including the ingenious and extremely sensitive vacuum scale to be deployed for the Archimedes Experiment. Support or falsification of this proposal may be imminent.