Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Fischer Projections

Fischer Projections

Learning to draw Fischer projections of molecules and understanding their relevance plays a crucial role in the visual depiction of organic molecules. A Fischer projection is a two-dimensional projection on a planar surface to simplify the three-dimensional wedge–dash representation of molecules. This is especially helpful in the case of molecules with multiple chiral centers that can be difficult to draw. Here, all the bonds of interest are represented as horizontal or vertical lines.

Newman Projections

Newman Projections

Different notations are used to represent the three-dimensional structure of molecules on two-dimensional surfaces. One of the most commonly used representations is the dash-wedge formula. The dashed wedges, solid wedges, and the plane lines indicate the groups situated behind the plane, coming out of the plane, and in the plane, respectively.
The organic molecules rotate across the single bonds leading to numerous temporary three-dimensional structures of varying energy known as...

Spherical and Cylindrical Capacitor

Spherical and Cylindrical Capacitor

A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
Conventionally, considering the symmetry, the electric field between the concentric shells of a spherical capacitor is directed radially outward. The magnitude of the field,...

Convolution Properties II

Convolution Properties II

The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...

Parallel-Axis Theorem for an Area

Parallel-Axis Theorem for an Area

The moment of inertia is a fundamental concept in mechanical engineering that plays a significant role in designing rotationally symmetric objects such as flywheels, gears, and other mechanical systems. In this context, we will discuss the moment of inertia of a flywheel rotating about its centroidal axis and how it relates to the moment of inertia about an axis parallel to it.
For a flywheel approximated as a solid disc, consider an infinitesimal differential element with an arbitrary distance...

Enlargement of the Plasma Membrane

Enlargement of the Plasma Membrane

Cell division and enlargement are processes that require precise control. The control ensures that cell division cannot proceed unless the cell has grown to a specific size. A spherical, dividing cell requires an approximately 1.6X increase in its surface area to double its volume. The secretory pathway also has a significant role in cell membrane enlargement. Secretory vesicles that bud off from the Golgi apparatus and later fuse with the plasma membrane during exocytosis are a major source of...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

A central limit theorem for integer partitions into small powers.

Monatshefte fur Mathematik·2024

Same author

Large subsets of <math></math> without arithmetic progressions.

Designs, codes, and cryptography·2023

Same author

Asymptotic Analysis of <i>q</i>-Recursive Sequences.

Algorithmica·2022

Same author

Sums of four and more unit fractions and approximate parametrizations.

The bulletin of the London Mathematical Society·2021

Same author

Caps and progression-free sets in <math></math>.

Designs, codes, and cryptography·2020

Same author

Romanov type problems.

The Ramanujan journal·2019

Same journal

Extreme values of derivatives of the Riemann zeta function.

Mathematika·2023

Same journal

Filling space with hypercubes of two sizes - The pythagorean tiling in higher dimensions.

Mathematika·2022

See all related articles

Search research articles

Related Experiment Video

Updated: Aug 2, 2025

Size Matters: Measurement of Capsule Diameter in Cryptococcus neoformans

Size Matters: Measurement of Capsule Diameter in Cryptococcus neoformans

Published on: February 27, 2018

Exponentially larger affine and projective caps.

Christian Elsholtz¹, Gabriel F Lipnik¹

¹Institute of Analysis and Number Theory Graz University of Technology Graz Austria.

|April 21, 2023

Summary

This summary is machine-generated.

Researchers developed a novel method for constructing larger cap sets in affine spaces. This new technique significantly improves the known lower bounds for cap set sizes, offering exponential growth.

More Related Videos

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Published on: April 16, 2017

Automated Charting of the Visual Space of Housefly Compound Eyes

Automated Charting of the Visual Space of Housefly Compound Eyes

Published on: March 31, 2022

Related Experiment Videos

Last Updated: Aug 2, 2025

Size Matters: Measurement of Capsule Diameter in Cryptococcus neoformans

Size Matters: Measurement of Capsule Diameter in Cryptococcus neoformans

Published on: February 27, 2018

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Published on: April 16, 2017

Automated Charting of the Visual Space of Housefly Compound Eyes

Automated Charting of the Visual Space of Housefly Compound Eyes

Published on: March 31, 2022

Area of Science:

Combinatorics
Finite Geometry
Number Theory

Background:

Classical cap set constructions remained unaffected by recent breakthroughs in upper bound calculations.
Existing constructions did not achieve the theoretical upper bounds for cap set sizes.

Purpose of the Study:

To introduce a novel method for constructing caps in affine spaces over finite fields.
To demonstrate that this new construction yields exponentially larger cap sets compared to previous methods.

Main Methods:

Development of a new construction technique for caps in affine spaces with an odd prime modulus.
Analysis of the growth rate of affine and projective caps resulting from the new construction.

Main Results:

The new construction provides an exponentially larger growth for affine and projective caps for primes p > 3.
Improved the lower bound for cap sets in F_3^n from 2^(n/6) to 2^(n/4).

Conclusions:

The novel cap set construction offers a significant advancement in understanding the size of these combinatorial objects.
This work provides a new lower bound for cap set sizes, surpassing previous improvements.