scholarly journals Calculation of the Maximum Number of Cutting Finite Fields in the Multi-dimensions

2017 ◽  
Vol 9 (4) ◽  
pp. 49
Author(s):  
Erick C. Huang ◽  
Sharon S. Huang ◽  
Cheng-Hua Tsai
Keyword(s):  
General Formula ◽  
Finite Fields ◽  
Original Problem ◽  
Three Dimensional ◽  
Maximum Amount ◽  
Three Dimensions ◽  
Infinite Plane ◽  
Euler’S Formula ◽  
Relationship Of

The original problem that serves as a basis for this project comes from an American contest (PUMaC, 2014) regarding the maximum amount of enclosed spaces given a limited number of cuts on an infinite plane. In this study, we explore the same problem and extend it in the context of m dimensions given n (m-1) dimensional cuts using the recursive relationship of finite cuts and enclosed spaces in lower dimensions. Once the general formula of f(m,n) was proven for dimensions, an Euler’s inspired formula was used to check the accuracy of the formula in two and three dimensions. The Euler’s formula also allowed us to derive the formula for the maximum number of unenclosed spaces in three-dimensional F(3, n). The results are as follows:

Three-dimensional X-ray diffraction imaging of process-induced dislocation loops in silicon

2011 ◽  
Vol 44 (3) ◽  
pp. 526-531 ◽  
Author(s):  
David Allen ◽  
Jochen Wittge ◽  
Jennifer Stopford ◽  
Andreas Danilewsky ◽  
Patrick McNally
Keyword(s):  
Semiconductor Industry ◽  
Three Dimensional ◽  
Crystal Defects ◽  
Three Dimensions ◽  
Dimensional Structure ◽  
Dislocation Loops ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffraction Imaging ◽  
Relationship Of

In the semiconductor industry, wafer handling introduces micro-cracks at the wafer edge and the causal relationship of these cracks to wafer breakage is a difficult task. By way of understanding the wafer breakage process, a series of nano-indents were introduced both into 20 × 20 mm (100) wafer pieces and into whole wafers as a means of introducing controlled strain. Visualization of the three-dimensional structure of crystal defects has been demonstrated. The silicon samples were then treated by various thermal anneal processes to initiate the formation of dislocation loops around the indents. This article reports the three-dimensional X-ray diffraction imaging and visualization of the structure of these dislocations. A series of X-ray section topographs of both the indents and the dislocation loops were taken at the ANKA Synchrotron, Karlsruhe, Germany. The topographs were recorded on a CCD system combined with a high-resolution scintillator crystal and were measured by repeated cycles of exposure and sample translation along a direction perpendicular to the beam. The resulting images were then rendered into three dimensions utilizing open-source three-dimensional medical tomography algorithms that show the dislocation loops formed. Furthermore this technique allows for the production of a video (avi) file showing the rotation of the rendered topographs around any defined axis. The software also has the capability of splitting the image along a segmentation line and viewing the internal structure of the strain fields.

Optimization Analysis on Gyroscope’s Three Dimensions Complicated Motion and Lash-Force

2014 ◽  
Vol 945-949 ◽  
pp. 581-586
Author(s):  
Wen Li Yang ◽  
Xiang Hui Lu
Keyword(s):  
Nonlinear Differential Equations ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Optimization Analysis ◽  
Motion Equations ◽  
Sliding Motion ◽  
Motion State ◽  
Motion Characteristics ◽  
Force Time ◽  
Relationship Of

The complicated motion of the gyroscope includes the rotation, the precession, the nutation and the sliding motion which are coupled, and it is affected by the lash-force by the whip. Taking the gyroscope which is moving stably as the research subject, according to the motion characteristics of the gyro’s rotation and precession, the gyro is assumed to be the two-force bar, and the coupled relationship of the gyroscope is analyzed quantitatively. The three-dimensional complicated motion in the different categories is analyzed. The nonlinear differential equations in the different categories is derived and linearized by the minor variables method, and then the three-dimensional motion equations on the rotation, precession, nutation and slipping of the gyroscope in the different categories is established. Take the big gym gyroscope as the example, the influence of the force, time and position of the whip on the motion state of the gyroscope is analyzed in detail, and provides the basis for the design of the gyroscope.

A contribution to the application of photoelasticity to the micromechanics of composite materials

1969 ◽  
Vol 4 (2) ◽  
pp. 88-94 ◽  
Author(s):  
D E W Stone
Keyword(s):  
Composite Materials ◽  
Three Dimensional ◽  
Maximum Amount ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Casting Technique ◽  
Intensity Measurements ◽  
Photoelastic Model ◽  
Composite Models

Photoelastic-model methods can prove advantageous for the investigation of microstresses in composite materials. Some two-dimensional investigations of this type are discussed and the extension of this work into three dimensions is considered. It is suggested that more than one approach to the three-dimensional problem may be practicable, and special attention is paid to obtaining the maximum amount of information from a sandwiched polariscope by means of light-intensity measurements. A cold-casting technique for the fabrication of composite models is also described.

Relationship of Challenge and Hindrance Stressors With Burnout and Its Three Dimensions

2015 ◽  
Vol 14 (4) ◽  
pp. 203-212 ◽  
Author(s):  
Angus Yongheng Yao ◽  
Muhammad Jamal ◽  
Evangelia Demerouti
Keyword(s):  
Emotional Exhaustion ◽  
Positive Relationship ◽  
Life Stage ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Cross Sectional ◽  
Cross Sectional Studies ◽  
Relationship Of

Abstract. The two-dimensional-work-stressor framework suggests that both challenge stressors and hindrance stressors have an undesirable (positive) relationship with burnout for all employees. However, the existing studies testing this framework either treated burnout as a global construct or used one burnout dimension and have not used age as a possible moderator. This paper reports two cross-sectional studies that examined the stressor-burnout relationship while burnout is conceptualized as three-dimensional (i.e., emotional exhaustion, cynicism, and inefficacy). Results indicate that although challenge and hindrance stressors show a similar (positive) relationship with exhaustion, they have differing relationships with cynicism and inefficacy. This study also explored how life stage influences the relationships between the two stressors and emotional exhaustion, cynicism, and inefficacy.

Experiments on Supersonic Boundary-Layer Separation in Three Dimensions

1975 ◽  
Vol 42 (2) ◽  
pp. 289-294 ◽  
Author(s):  
W. D. Bachalo
Keyword(s):  
Three Dimensional ◽  
Cross Flow ◽  
Separated Flow ◽  
Flow Region ◽  
Boundary Layer Separation ◽  
Supersonic Boundary Layer ◽  
Three Dimensions ◽  
Pressure Gradients ◽  
Flat Plates ◽  
Relationship Of

A detailed experimental study of three-dimensional separation in supersonic flow is described. Three-dimensional wedges affixed to flat plates were used to generate the flow fields that were used to examine the relationship of cross flow to the extent of separation. Models with strong transverse pressure gradients resulted in a diminished extent of separation about the model plane of symmetry but demonstrated expansive growth of separation to a limit with distance from the plane of symmetry. A secondary flow region was found embedded in the separated flow.

convergent-beam diffraction from surfaces

1987 ◽  
Vol 45 ◽  
pp. 30-33
Author(s):  
J. A. Eades ◽  
A. E. Smith ◽  
D. F. Lynch
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Plane Figure ◽  
Transmission Electron ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

It is quite simple (in the transmission electron microscope) to obtain convergent-beam patterns from the surface of a bulk crystal. The beam is focussed onto the surface at near grazing incidence (figure 1) and if the surface is flat the appropriate pattern is obtained in the diffraction plane (figure 2). Such patterns are potentially valuable for the characterization of surfaces just as normal convergent-beam patterns are valuable for the characterization of crystals.There are, however, several important ways in which reflection diffraction from surfaces differs from the more familiar electron diffraction in transmission.GeometryIn reflection diffraction, because of the surface, it is not possible to describe the specimen as periodic in three dimensions, nor is it possible to associate diffraction with a conventional three-dimensional reciprocal lattice.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

scholarly journals An investigation of polyhedral deformation in two mixed-metal diarsenates: SrZnAs2O7and BaCuAs2O7

2015 ◽  
Vol 71 (4) ◽  
pp. 330-337 ◽  
Author(s):  
Sabina Kovač ◽  
Ljiljana Karanović ◽  
Tamara Đorđević
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
General Formula ◽  
Three Dimensional ◽  
X Ray Diffraction ◽  
Hydrothermal Conditions ◽  
X Ray ◽  
Open Framework ◽  
Geometrical Characteristics ◽  
Barium Copper

Two isostructural diarsenates, SrZnAs2O7(strontium zinc diarsenate), (I), and BaCuAs2O7[barium copper(II) diarsenate], (II), have been synthesized under hydrothermal conditions and characterized by single-crystal X-ray diffraction. The three-dimensional open-framework crystal structure consists of corner-sharingM2O5(M2 = Zn or Cu) square pyramids and diarsenate (As2O7) groups. Each As2O7group shares its five corners with five differentM2O5square pyramids. The resulting framework delimits two types of tunnels aligned parallel to the [010] and [100] directions where the large divalent nine-coordinatedM1 (M1 = Sr or Ba) cations are located. The geometrical characteristics of theM1O9,M2O5and As2O7groups of known isostructural diarsenates, adopting the general formulaM1IIM2IIAs2O7(M1II= Sr, Ba, Pb;M2II= Mg, Co, Cu, Zn) and crystallizing in the space groupP21/n, are presented and discussed.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

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