scholarly journals A refinement of the Ozsváth-Szabó large integer surgery formula and knot concordance

2020 ◽  
pp. 1
Author(s):  
Linh Truong
Keyword(s):  
Large Integer ◽  
Knot Concordance ◽  
Surgery Formula

Text Encryption based on Huffman Coding and ElGamal Cryptosystem

2020 ◽  
Vol 14 ◽  
Author(s):  
Khoirom Motilal Singh ◽  
Laiphrakpam Dolendro Singh ◽  
Themrichon Tuithung
Keyword(s):  
Data Transfer ◽  
Huffman Coding ◽  
Large Integer ◽  
Text Data ◽  
Storage Devices ◽  
Scientific World ◽  
Elgamal Cryptosystem ◽  
Encryption Schemes ◽  
Transfer Operation ◽  
And Performance

Background: Data which are in the form of text, audio, image and video are used everywhere in our modern scientific world. These data are stored in physical storage, cloud storage and other storage devices. Some of it are very sensitive and requires efficient security while storing as well as in transmitting from the sender to the receiver. Objective: With the increase in data transfer operation, enough space is also required to store these data. Many researchers have been working to develop different encryption schemes, yet there exist many limitations in their works. There is always a need for encryption schemes with smaller cipher data, faster execution time and low computation cost. Methods: A text encryption based on Huffman coding and ElGamal cryptosystem is proposed. Initially, the text data is converted to its corresponding binary bits using Huffman coding. Next, the binary bits are grouped and again converted into large integer values which will be used as the input for the ElGamal cryptosystem. Results: Encryption and Decryption are successfully performed where the data size is reduced using Huffman coding and advance security with the smaller key size is provided by the ElGamal cryptosystem. Conclusion: Simulation results and performance analysis specifies that our encryption algorithm is better than the existing algorithms under consideration.

Periodic Solutions of Non-autonomous Allen–Cahn Equations Involving Fractional Laplacian

2020 ◽  
Vol 20 (3) ◽  
pp. 725-737 ◽  
Author(s):  
Zhenping Feng ◽  
Zhuoran Du
Keyword(s):  
Variational Methods ◽  
Periodic Solutions ◽  
Smooth Function ◽  
Fractional Laplacian ◽  
Type Inequality ◽  
Energy Functional ◽  
Large Integer ◽  
Existence Of Periodic Solutions ◽  
Double Well Potential

AbstractWe consider periodic solutions of the following problem associated with the fractional Laplacian: {(-\partial_{xx})^{s}u(x)+\partial_{u}F(x,u(x))=0} in {\mathbb{R}}. The smooth function {F(x,u)} is periodic about x and is a double-well potential with respect to u with wells at {+1} and -1 for any {x\in\mathbb{R}}. We prove the existence of periodic solutions whose periods are large integer multiples of the period of F about the variable x by using variational methods. An estimate of the energy functional, Hamiltonian identity and Modica-type inequality for periodic solutions are also established.

scholarly journals On Waring’s problem: Three cubes and a sixth power

2001 ◽  
Vol 163 ◽  
pp. 13-53 ◽  
Author(s):  
Jörg Brüdern ◽  
Trevor D. Wooley
Keyword(s):  
Exponential Sums ◽  
Large Integer ◽  
Natural Numbers ◽  
Waring’S Problem ◽  
Smooth Numbers ◽  
Waring's Problem ◽  
Order Of Magnitude ◽  
Almost All ◽  
Hardy Littlewood Method

We establish that almost all natural numbers not congruent to 5 modulo 9 are the sum of three cubes and a sixth power of natural numbers, and show, moreover, that the number of such representations is almost always of the expected order of magnitude. As a corollary, the number of representations of a large integer as the sum of six cubes and two sixth powers has the expected order of magnitude. Our results depend on a certain seventh moment of cubic Weyl sums restricted to minor arcs, the latest developments in the theory of exponential sums over smooth numbers, and recent technology for controlling the major arcs in the Hardy-Littlewood method, together with the use of a novel quasi-smooth set of integers.

scholarly journals On independence of iterated Whitehead doubles in the knot concordance group

2018 ◽  
Vol 27 (01) ◽  
pp. 1850003
Author(s):  
Kyungbae Park
Keyword(s):  
Correction Term ◽  
Khovanov Homology ◽  
Floer Theory ◽  
Knot Concordance ◽  
Torus Knot ◽  
Linearly Independent ◽  
Heegaard Floer

Let [Formula: see text] be the positively clasped untwisted Whitehead double of a knot [Formula: see text], and [Formula: see text] be the [Formula: see text] torus knot. We show that [Formula: see text] and [Formula: see text] are linearly independent in the smooth knot concordance group [Formula: see text] for each [Formula: see text]. Further, [Formula: see text] and [Formula: see text] generate a [Formula: see text] summand in the subgroup of [Formula: see text] generated by topologically slice knots. We use the concordance invariant [Formula: see text] of Manolescu and Owens, using Heegaard Floer correction term. Interestingly, these results are not easily shown using other concordance invariants such as the [Formula: see text]-invariant of knot Floer theory and the [Formula: see text]-invariant of Khovanov homology. We also determine the infinity version of the knot Floer complex of [Formula: see text] for any [Formula: see text] generalizing a result for [Formula: see text] of Hedden, Kim and Livingston.

scholarly journals A light-weight version of Waring's problem

2004 ◽  
Vol 76 (3) ◽  
pp. 303-316 ◽  
Author(s):  
Trevor D. Wooley
Keyword(s):  
Asymptotic Formula ◽  
Large Integer ◽  
Light Weight ◽  
Natural Numbers ◽  
Waring’S Problem ◽  
Waring's Problem ◽  
Large Solutions ◽  
Homogeneous Weight

AbstractAn asymptotic formula is established for the number of representations of a large integer as the sum of kth powers of natural numbers, in which each representation is counted with a homogeneous weight that de-emphasises the large solutions. Such an asymptotic formula necessarily fails when this weight is excessively light.

scholarly journals Applications of Donaldson's theorems to classical knot concordance, homology 3-spheres and Property P

Topology ◽  
1988 ◽  
Vol 27 (4) ◽  
pp. 495-512 ◽  
Author(s):  
Tim D. Cochran ◽  
Robert E. Gompf
Keyword(s):  
Knot Concordance

On the construction of very large integer multipliers

Euro ASIC '91 ◽  
1991 ◽  
Author(s):  
G. Hotz ◽  
P. Molitor ◽  
W. Zimmer
Keyword(s):  
Large Integer

Parametric Throughput Oriented Large Integer Multipliers for High Level Synthesis

2021 ◽  
Author(s):  
Emanuele Vitali ◽  
Davide Gadioli ◽  
Fabrizio Ferrandi ◽  
Gianluca Palermo
Keyword(s):  
High Level Synthesis ◽  
Large Integer ◽  
High Level

scholarly journals Borromean surgery formula for the Casson invariant

2008 ◽  
Vol 8 (2) ◽  
pp. 787-801
Author(s):  
Jean-Baptiste Meilhan
Keyword(s):  
Surgery Formula
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