Partial Enclosure Range Searching

2019 ◽  
Vol 29 (01) ◽  
pp. 73-93
Author(s):  
Gregory Bint ◽  
Anil Maheshwari ◽  
Michiel Smid ◽  
Subhas C. Nandy
Keyword(s):  
Parallel Line ◽  
Range Searching ◽  
Axis Parallel ◽  
Fixed Proportion ◽  
Query Region ◽  
New Type ◽  
The First Variation ◽  
Original Size ◽  
The Second Variation ◽  
Rectangle Formula

A new type of range searching problem, called the partial enclosure range searching problem, is introduced in this paper. Given a set of geometric objects [Formula: see text] and a query region [Formula: see text], our goal is to identify those objects in [Formula: see text] which intersect the query region [Formula: see text] by at least a fixed proportion of their original size. Two variations of this problem are studied. In the first variation, the objects in [Formula: see text] are axis-parallel line segments and the goal is to count the total number of members of [Formula: see text] so that their intersection with [Formula: see text] is at least a given proportion of their size. Here, [Formula: see text] can be an axis-parallel rectangle or a parallelogram of arbitrary orientation. In the second variation, [Formula: see text] is a polygon and [Formula: see text] is an axis-parallel rectangle. The problem is to report the area of the intersection between the polygon [Formula: see text] and a query rectangle [Formula: see text].

Optimal Trajectories and the Accessory Minimum Problem

1965 ◽  
Vol 16 (3) ◽  
pp. 205-220 ◽  
Author(s):  
D. J. Bell
Keyword(s):  
Necessary Conditions ◽  
Sounding Rocket ◽  
Necessary Condition ◽  
Minimum Problem ◽  
Multiplier Rule ◽  
Variation Of A Function ◽  
Accessory Minimum Problem ◽  
The First Variation ◽  
The Second Variation

SummaryThe necessary conditions of Clebsch and Weierstrass and of the multiplier rule in the calculus of variations, which arise from the study of the first variation of a function, are summarised. A further necessary condition associated with the second variation is stated. The latter condition is applied to two problems: (i) the determination of the thrust-time programme which maximises the altitude of a sounding rocket, (ii) the determination of the thrust direction programme for a rocket with a known propellant expenditure programme which yields a maximum range. In both problems it is found that the additional necessary condition is satisfied.

scholarly journals THE FIRST AND SECOND VARIATION OF THE TOTAL ENERGY OF CLOSED DUPLEX DNA IN PLANAR CASE

2010 ◽  
Vol 24 (05) ◽  
pp. 587-597 ◽  
Author(s):  
XIAO-HUA ZHOU
Keyword(s):  
Total Energy ◽  
Equilibrium Shape ◽  
Variation Method ◽  
Second Variation ◽  
General Shape ◽  
Planar Case ◽  
The First Variation ◽  
The Second Variation ◽  
First And Second Variation ◽  
Classical Variation

DNA's shape mostly lies on its total energy F. Its corresponding equilibrium shape equations can be obtained by classical variation method: letting the first energy variation δ(1)F = 0. Here, we not only provide the first variation δ(1)F but also give the second variation δ(2)F in planar case. Moreover, the general shape equations of DNA are abstained and a mistake in Zhang et al., [Phys. Rev. E70, 051902 (2004)] is pointed out.

scholarly journals A Quasi-constant Envelope Multiplexing Technique for GNSS Signals

2015 ◽  
Vol 68 (4) ◽  
pp. 791-808 ◽  
Author(s):  
Tao Yan ◽  
Zuping Tang ◽  
Jiaolong Wei ◽  
Bo Qu ◽  
Zhihui Zhou
Keyword(s):  
Satellite System ◽  
Significant Feature ◽  
Constant Envelope ◽  
Modulation Techniques ◽  
Combining Efficiency ◽  
The First Variation ◽  
Global Navigation Satellite ◽  
The Second Variation ◽  
Numerical Optimisation ◽  
Composite Signal

A significant feature of the modernised Global Navigation Satellite System (GNSS) signals is that there are multiple signal components needing to be transmitted on a carrier frequency. How to combine these signal components into a constant envelope composite signal is a challenge. Existing constant envelope modulation techniques have some limitations, and are not effective enough. To solve this problem, we propose a quasi-constant-envelope multiplexing technique in this paper. The proposed method is based on numerical optimisation, and can work in two ways. The corresponding objective functions are provided. To verify the performance of the proposed method, we present three application examples. Results show that the first variation of our method can reach the same combining performance as Phase-Optimised Constant-Envelope Transmission (POCET). In the second variation, the combining efficiency can be pre-set. We can reach higher combining efficiency than POCET, and the envelope of the composite signal becomes quasi-constant. Furthermore, the inter-modulation signals in the final composite signal are adjustable. With the help of the proposed method, we can learn more details of the combining scheme than with POCET.

scholarly journals Fabrication of dye Rhoeospathacea with concentration variation in dye-sensitized solar cells (DSSC)

2017 ◽  
Vol 1 (1) ◽  
pp. 83
Author(s):  
Sri Sumardiasih ◽  
Agus Supriyanto ◽  
C Cari
Keyword(s):  
Titanium Dioxide ◽  
Dye Sensitized Solar Cells ◽  
Electrical Energy ◽  
Second Variation ◽  
First Variation ◽  
Dye Sensitized ◽  
The First Variation ◽  
The Second Variation ◽  
Sensitized Solar Cells ◽  
Absorbance Spectra

<p class="Abstract">Dye-sensitized solar cell (DSSC) is a device that directly converts visible light into electrical energy. In this work we used dye was extracted from Rhoeo spathacea. A natural dye was directly mixed with TiO<sub>2 </sub>anatase to obtain <em>dyed titanium dioxide</em> which can be used as photoanode for DSSC by varying the volume of dye. The first variation is 2 ml dye mixed with 1 ml of TiO<sub>2</sub>, and the second variation is 3 ml dye mixed with 1 ml of TiO<sub>2</sub>. The absorbance spectra of the dye and dye titanium dioxide have been investigated by spectroscopy UV-<em>Visible Lambda </em>25 and the conversion efficiency of dye titanium dioxide used Keithley 2602A meter. The DSSC based on dye titanium dioxide with varying volume of dye showed that the efficiency of the the second variation is 0,033% which is higher than the first variation (0,023%) as obtained from I-V characterization.</p><p class="Abstract"> </p>

scholarly journals Efficiency of Multi Soil Layering (MSL) System in A Household Scale of Wastewater Treatment Using Environmental Friendly Materials

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Badrus Zaman ◽  
Wiharyanto Oktiawan
Keyword(s):  
Wastewater Treatment ◽  
Treatment Plant ◽  
Domestic Wastewater ◽  
Quality Standards ◽  
Environmental Damage ◽  
Effluent Quality ◽  
Soil Layering ◽  
The First Variation ◽  
The Second Variation ◽  
Required Quality

Most community settlements in Indonesia do not have a household scale of a wastewater treatment plant. Fatal impacts on the environment and human health can occur at any time, including (a) causing environmental damage (disaster), (b) damaging beauty/aesthetics for the scenery will be unpleasant and foul-smelling, (c) polluting water bodies, and (d ) endangering health. The purpose of this study is to optimize the Multi Soil Layering (MSL) System to treat domestic wastewater (greywater) using environmentally friendly materials that are available in Indonesia. The research method used the MSL system with the first variation using a batch system with Hydraulic retention time (HRT) for 24 hours and the second variation using an intermittent system with 3, 6, 9 hours HRT. The results showed that the MSL system was able to eliminate COD well. The highest COD removal efficiency was 93.44% at 9 hours HRT, but the effluent quality did not meet the required quality standards. The development of MSL systems that produces an effluent quality that meets the quality standards needs to be studied further.

Second-Order Conditions

2018 ◽  
Author(s):  
John E. Prussing
Keyword(s):  
Optimal Control ◽  
Optimization Problems ◽  
Conjugate Point ◽  
Test Procedure ◽  
Second Order ◽  
Order Conditions ◽  
Second Order Conditions ◽  
The First Variation ◽  
The Cost ◽  
The Second Variation

Second-order conditions for both parameter optimization problems and optimal control problems are analysed. A new conjugate point test procedure is discussed and illustrated. For an optimal control problem we will examine the second variation of the cost. The first variation subject to constraints provides first-order NC for a minimum of J. Second-order conditions provide SC a minimum.

Weigh-in-Motion Data Quality Assurance Based on 3-S2 Steering Axle Load Analysis

1996 ◽  
Vol 1536 (1) ◽  
pp. 12-18 ◽  
Author(s):  
W. C. Ott ◽  
A. T. Papagiannakis
Keyword(s):  
Quality Assurance ◽  
Confidence Interval ◽  
Vehicle Model ◽  
Static Loads ◽  
Motion Data ◽  
Innovative Method ◽  
Weigh In Motion ◽  
Air Resistance ◽  
The First Variation ◽  
The Second Variation

An innovative method is offered for conducting the quality assurance of weigh-in-motion (WIM) data by analyzing the variation in the measurements of five-axle semitrailer (3-S2) truck steering-axle loads. Confidence-interval limits for those measurements are established on the basis of their historic mean static loads adjusted for the effect of air resistance and their combined variation from two sources, the variation within a fleet of 3-S2 trucks and the variation due to axle dynamics at a WIM site. The first variation was determined by analyzing historic 3-S2 load data obtained by FHWA using static scales. The second variation was established through dynamic vehicle simulations of a “typical” 3-S2 truck using vehicle model VESYM and the roughness profile at a particular WIM site. The method was tested with data from four WIM systems in the state of Washington, two bending-plate systems and two piezoelectric systems. The proposed method resulted in clear indications of the performance of the scale versus time by the number of confidence interval violations observed.

M.O.U.S.E.

1956 ◽  
Vol 9 (3) ◽  
pp. 335-337
Author(s):  
J. G. Porter
Keyword(s):  
Lower Atmosphere ◽  
Artificial Satellites ◽  
Second Stage ◽  
Successful Experiment ◽  
Solar Battery ◽  
Third Stage ◽  
Axis Parallel ◽  
New Type ◽  
The Moment ◽  
Turn Over

Although no details of the proposed artificial satellites are yet available, the idea is by no means new, and it seems likely that any successful experiment of this kind must follow the plans already outlined by Professor S. F. Singer of Maryland University. At the Astronautical Conference at Zürich in 1953 he gave details of a small spherical satellite, weighing only 100 lb., which would revolve about the Earth in a period of 90 minutes at a height of 190 miles above the surface. In collaboration with Arthur C. Clarke and A. V. Cleaver of the British Interplanetary Society, Singer called this instrument MOUSE (Minimum Orbital Unmanned Satellite Earth) and proposed that it should be launched as a three-stage rocket with an initial all-up weight of about 35,000 lb., and a thrust of 65,000 lb., which is very little different from the performance of the V2 rocket. The first step would take the rocket vertically through the lower atmosphere and then turn over to begin the inclined part of its flight; the second stage would come into action when the first had burned out, and complete the climb to give the correct altitude and direction of motion. The third stage would merely give sufficient boost to attain the required speed, which is about 17,400 m.p.h. At the moment of cut-out (controlled from the ground) the nose tip would open and release the satellite. This would take the form of a sphere, about three feet in diameter, spinning so as to maintain a constant orientation, and packed with instruments. The spin axis, parallel to the Earth's surface and perpendicular to the direction of motion, would point to the Sun, so that one half of the sphere would be strongly heated by the Sun's rays, and the other hemisphere would be extremely cold. Power would be obtained from a new type of solar battery, and the readings of the instruments would be radioed continuously to Earth.

scholarly journals Symplectic connections and the linearisation of Hamiltonian systems

1991 ◽  
Vol 117 (3-4) ◽  
pp. 329-380 ◽  
Author(s):  
J. E. Marsden ◽  
T. Ratiu ◽  
G. Raugel
Keyword(s):  
Hamiltonian System ◽  
Symplectic Structure ◽  
Equilibrium Solution ◽  
Hamiltonian Structure ◽  
Second Variation ◽  
First Variation ◽  
Space Construction ◽  
Symplectic Connections ◽  
The First Variation ◽  
The Second Variation

SynopsisThis paper uses symplectic connections to give a Hamiltonian structure to the first variation equation for a Hamiltonian system along a given dynamic solution. This structure generalises that at an equilibrium solution obtained by restricting the symplectic structure to that point and using the quadratic form associated with the second variation of the Hamiltonian (plus Casimir) as energy. This structure is different from the well-known and elementary tangent space construction. Our results are applied to systems with symmetry and to Lie–Poisson systems in particular.

THE MINIMUM GUARDING TREE PROBLEM

2014 ◽  
Vol 06 (01) ◽  
pp. 1450011 ◽  
Author(s):  
ADRIAN DUMITRESCU ◽  
JOSEPH S. B. MITCHELL ◽  
PAWEL ŻYLIŃSKI
Keyword(s):  
Approximation Algorithms ◽  
Nonempty Subset ◽  
Parallel Line ◽  
Minimum Length ◽  
Np Hard ◽  
Orthogonal Axis ◽  
Line Segments ◽  
Parallel Lines ◽  
Simple Alternative ◽  
Axis Parallel

Given a set ℒ of non-parallel lines in the plane and a nonempty subset ℒ′ ⊆ ℒ, a guarding tree for ℒ′ is a tree contained in the union of the lines in ℒ such that if a mobile guard (agent) runs on the edges of the tree, all lines in ℒ′ are visited by the guard. Similarly, given a connected arrangement 𝒮 of line segments in the plane and a nonempty subset 𝒮′ ⊆ 𝒮, we define a guarding tree for 𝒮′. The minimum guarding tree problem for a given set of lines or line segments is to find a minimum-length guarding tree for the input set. We provide a simple alternative (to [N. Xu, Complexity of minimum corridor guarding problems, Inf. Process. Lett.112(17–18) (2012) 691–696.]) proof of the problem of finding a guarding tree of minimum length for a set of orthogonal (axis-parallel) line segments in the plane. Then, we present two approximation algorithms with factors 2 and 3.98, respectively, for computing a minimum guarding tree for a subset of a set of n arbitrary non-parallel lines in the plane; their running times are O(n8) and O(n6 log n), respectively. Finally, we show that this problem is NP-hard for lines in 3-space.

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