scholarly journals On the Universal Encoding Optimality of Primes

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3155
Author(s):  
Ioannis N. M. Papadakis
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Optimization Problem ◽  
Prime Numbers ◽  
Prime Factors ◽  
Universal Quantum ◽  
Optimality Properties ◽  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture

The factorial-additive optimality of primes, i.e., that the sum of prime factors is always minimum, implies that prime numbers are a solution to an integer linear programming (ILP) encoding optimization problem. The summative optimality of primes follows from Goldbach’s conjecture, and is viewed as an upper efficiency limit for encoding any integer with the fewest possible additions. A consequence of the above is that primes optimally encode—multiplicatively and additively—all integers. Thus, the set P of primes is the unique, irreducible subset of ℤ—in cardinality and values—that optimally encodes all numbers in ℤ, in a factorial and summative sense. Based on these dual irreducibility/optimality properties of P, we conclude that primes are characterized by a universal “quantum type” encoding optimality that also extends to non-integers.

scholarly journals A Study of Authenticated Communication Based on Magic Square and Goldbach’s Conjecture

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Group Learning ◽  
Prime Numbers ◽  
Learning Problems ◽  
Student Group ◽  
Magic Square ◽  
Innovative Method ◽  
Encryption Decryption ◽  
Novel Applications ◽  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture

Although the magic square is a historical and universal study, its progress has been limited, to numeric games, which is closer to digital games or word games, and lacks the connection with mainstream mathematics. Recently, its study has extended from exciting mathematical games to various novel applications, such as image encryption, decryption processing, watermarking solutions, and student group learning problems, or different engineering applications. In terms of employment in information security, it is the blue ocean that requires more innovative research to enrich its content. In this study, we engage the magic square and Goldbach’s Conjecture to develop an innovative method to search prime numbers

scholarly journals Exploring Goldbach’s conjecture, the Pebonacci sequence and its five-dimensional vortex structure based on the logarithm of the circle

2020 ◽  
Vol 7 (8) ◽  
pp. 398-408
Author(s):  
Yiping Wang
Keyword(s):  
Mathematical Model ◽  
Closed Interval ◽  
Three Dimensional ◽  
Prime Numbers ◽  
Quadratic Equation ◽  
Space Structure ◽  
Number Sequence ◽  
Number Series ◽  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture

A method based on circle logarithm to prove Goldbach’s conjecture and Pebonacci sequence is proposed. Its essence is to deal with the real infinite series, each of the finite three elements (prime numbers, number series) has asymmetry problems, forming a basic even function one-variable quadratic equation and odd function one-variable three-dimensional number sequence; it is converted to "The irrelevant mathematical model expands latently in a closed interval of 0 to 1," forming a five-dimensional vortex space structure.

scholarly journals Global Inference for Sentence Compression: An Integer Linear Programming Approach

2008 ◽  
Vol 31 ◽  
pp. 399-429 ◽  
Author(s):  
J. Clarke ◽  
M. Lapata
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Optimization Problem ◽  
State Of The Art ◽  
Experimental Results ◽  
Global Constraints ◽  
Programming Approach ◽  
Linear Programming Approach ◽  
Sentence Compression ◽  
Global Inference

Sentence compression holds promise for many applications ranging from summarization to subtitle generation. Our work views sentence compression as an optimization problem and uses integer linear programming (ILP) to infer globally optimal compressions in the presence of linguistically motivated constraints. We show how previous formulations of sentence compression can be recast as ILPs and extend these models with novel global constraints. Experimental results on written and spoken texts demonstrate improvements over state-of-the-art models.

scholarly journals Exact and heuristic approaches to solve the Internet shopping optimization problem with delivery costs

2016 ◽  
Vol 26 (2) ◽  
pp. 391-406 ◽  
Author(s):  
Mario C. Lopez-Loces ◽  
Jedrzej Musial ◽  
Johnatan E. Pecero ◽  
Hector J. Fraire-Huacuja ◽  
Jacek Blazewicz ◽  
...  
Keyword(s):  
Linear Programming ◽  
Exact Solutions ◽  
Integer Linear Programming ◽  
Optimization Problem ◽  
State Of The Art ◽  
Processing Algorithm ◽  
The Internet ◽  
Internet Shopping ◽  
Delivery Costs ◽  
Cellular Processing

AbstractInternet shopping has been one of the most common online activities, carried out by millions of users every day. As the number of available offers grows, the difficulty in getting the best one among all the shops increases as well. In this paper we propose an integer linear programming (ILP) model and two heuristic solutions, the MinMin algorithm and the cellular processing algorithm, to tackle the Internet shopping optimization problem with delivery costs. The obtained results improve those achieved by the state-of-the-art heuristics, and for small real case scenarios ILP delivers exact solutions in a reasonable amount of time.

scholarly journals Proof of the Goldbach's Conjecture

2021 ◽  
Author(s):  
K.H.K. Geerasee Wijesuriya
Keyword(s):  
Prime Numbers ◽  
Goldbach’S Conjecture ◽  
Mathematics Problem ◽  
Goldbach's Conjecture

Goldbach’s Conjecture states that every even number greater than 3, can be written as a summation of two prime numbers. This conjecture is roughly 300 years old and a very famous unsolved mathematics problem. To prove the Goldbach’s Conjecture, I use the contradiction method in mathematics as below.

A NEW APPROACH TO SELECT THE BEST SUBSET OF PREDICTORS IN LINEAR REGRESSION MODELLING: BI-OBJECTIVE MIXED INTEGER LINEAR PROGRAMMING

2019 ◽  
Vol 61 (1) ◽  
pp. 64-75 ◽  
Author(s):  
HADI CHARKHGARD ◽  
ALI ESHRAGH
Keyword(s):  
Linear Programming ◽  
Linear Regression ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Optimization Problem ◽  
Computational Study ◽  
Mixed Integer ◽  
Programming Approach ◽  
Objective Functions ◽  
New Approach

We study the problem of choosing the best subset of $p$ features in linear regression, given $n$ observations. This problem naturally contains two objective functions including minimizing the amount of bias and minimizing the number of predictors. The existing approaches transform the problem into a single-objective optimization problem. We explain the main weaknesses of existing approaches and, to overcome their drawbacks, we propose a bi-objective mixed integer linear programming approach. A computational study shows the efficacy of the proposed approach.

OPTIMAL SOFTWARE PIPELINING UNDER RESOURCE CONSTRAINTS

2001 ◽  
Vol 12 (06) ◽  
pp. 697-718 ◽  
Author(s):  
DIRK FIMMEL ◽  
JAN MÜLLER
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Rational Number ◽  
Optimization Problem ◽  
Resource Constraints ◽  
Software Pipelining ◽  
Limited Resources ◽  
Pipeline Architecture ◽  
Novel Approach ◽  
Functional Units

In this paper we present a novel approach to find an optimum loop schedule under consideration of limited resources. The initiation interval λ is assumed to be a rational number. Our approach is formulated as a single optimization problem that can be solved using integer linear programming. The objective is to minimize the initiation interval, while both numerator and denominator of λ can be incorporated as variables of the optimization problem. the resources (functional units) may have a pipeline architecture; the approach also supports heterogeneous functional units.

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