Mathematical Representation of Spatially Multiplexed Channels Using Azimuthal Index and Modified Laguerre Gaussian Beams

AbstractWe dispersed electrochemically etched Si into ultrabright ultrasmall nanoparticles, with brightness higher than fluorescein or rhodamine. The emission from single particles is readily detectable. Aggregates or films of the particles exhibit emission with highly nonlinear characteristics. We observe directed blue beams at ∼ 410 nm between faces of aggregates excited by femtosecond radiation at 780 nm; and at ∼ 610 nm from aggregates of red luminescent Si nanoparticles excited by radiation at 550-570 nm from a mercury lamp. Intense directed Gaussian beams, a pumping threshold, spectral line narrowing, and speckle patterns manifest the emission. The results are analyzed in terms of population inversion and stimulated emission in quantum confinement-induced Si-Si dimer phase, found only on ultrasmall Si nanoparticles. This microlasing constitutes an important step towards the realization of a laser on a chip.

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ANALYSIS OF NARRATIVE MATHEMATICAL QUESTIONS ON TEXTBOOKS BASED ON SOLO TAXONOMY AND MATHEMATICAL POWER

Jurnal Daya Matematis ◽

10.26858/jds.v5i3.4839 ◽

2017 ◽

Vol 5 (3) ◽

pp. 299

Author(s):

Imam Kusmaryono

Keyword(s):

Problem Solving ◽

Grade Level ◽

Mathematical Representation ◽

Structural Level ◽

Mathematics Textbooks ◽

Solo Taxonomy ◽

Research Procedure ◽

Quantitative Descriptive ◽

The Ideal

This study aimed to identify the proportion of diversity and suitability of narrative mathematical questions with SOLO taxonomy level and mathematical power ability. The research was conducted through quantitative descriptive. Sources of data in the forms of narrations contained in mathematics textbooks. The research procedure was conducted by making the classification and determining the percentage of the narrations based on the compatibility of SOLO taxonomy and the mathematical power ability. The results showed that, the narrative mathematical questions with uni-structural level are of 7.5%, multi-structural of 33.8%, relational of 46.6% and extended abstract of 12.1 %. In terms of compatibility of the narrative questions were able to measure 23% reasoning aspect, 18% problem solving, 8.3% connection, 28% communication and 22.6% mathematical representation. In general, mathematics textbooks as the object of research should be revised, since they have not yet achieved the ideal alignment between SOLO taxonomy based on grade level and the objective of learning develop mathematical power

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Entanglement

10.1093/oso/9780198714057.003.0003 ◽

2017 ◽

Author(s):

Richard Healey

Keyword(s):

Quantum Theory ◽

Quantum State ◽

Physical Condition ◽

Physical System ◽

Polarization State ◽

Quantum Systems ◽

Ghz State ◽

Mathematical Representation ◽

Entangled State ◽

Physical Relation

Often a pair of quantum systems may be represented mathematically (by a vector) in a way each system alone cannot: the mathematical representation of the pair is said to be non-separable: Schrödinger called this feature of quantum theory entanglement. It would reflect a physical relation between a pair of systems only if a system’s mathematical representation were to describe its physical condition. Einstein and colleagues used an entangled state to argue that its quantum state does not completely describe the physical condition of a system to which it is assigned. A single physical system may be assigned a non-separable quantum state, as may a large number of systems, including electrons, photons, and ions. The GHZ state is an example of an entangled polarization state that may be assigned to three photons.

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Design, Construction, and Control for an Underwater Vehicle Type Sepiida

Robotica ◽

10.1017/s0263574720000739 ◽

2020 ◽

pp. 1-18

Author(s):

M. Garcia ◽

P. Castillo ◽

E. Campos ◽

R. Lozano

Keyword(s):

Embedded System ◽

Closed Loop ◽

Underwater Vehicle ◽

Mathematical Representation ◽

Closed Loop System ◽

Vehicle Type ◽

Mathematical Equations ◽

And Control ◽

Design Construction

SUMMARY A novel underwater vehicle configuration with an operating principle as the Sepiida animal is presented and developed in this paper. The mathematical equations describing the movements of the vehicle are obtained using the Newton–Euler approach. An analysis of the dynamic model is done for control purposes. A prototype and its embedded system are developed for validating analytically and experimentally the proposed mathematical representation. A real-time characterization of one mass is done to relate the pitch angle with the radio of displacement of the mass. In addition, first validation of the closed-loop system is done using a linear controller.

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