scholarly journals Multifeatured Image Retrieval Techniques Based on Partial Differential Equations for Online Shopping

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Jiaohui Yu

In today’s rapid development of network and multimedia technology, the booming of electronic commerce, users in the network shopping species of images and other multimedia information showing geometric growth, in the face of this situation, how to find the images they need in the vast amount of online shopping images has become an urgent problem to solve. This paper is based on the partial differential equation to do the following research: Based on the partial differential equation is a kind of equation that simulates the human visual perception system to analyze images; based on the summary of the advantages and disadvantages of multifeature image retrieval technology, we propose a multifeature image retrieval technology method based on the partial differential equation to alleviate the indexing imbalance caused by the mismatch of multifeature image retrieval technology distribution. To improve the search speed of the data-dependent locally sensitive hashing algorithm, we propose a query pruning algorithm compatible with the proposed partial differential equation-based multifeature image retrieval technology method, which greatly improves the retrieval speed while ensuring the retrieval accuracy; to implement the data-dependent partial differential equation algorithm, we need to distribute the data set among different operation nodes, and to better achieve better parallelization of operations, we need to measure the similarity between categories, and we achieve the problem of distributing data among various categories in each operation node by introducing a clustering method with constraints. The purpose of this article for image recognition is for better shopping platforms for merchants. This algorithm has trained multiple samples and has data support. The experimental results show that our proposed data set allocation method shows significant advantages over the data set allocation method that does not consider category correlation. However, the image features used in image retrieval systems are often hundreds or even thousands of dimensions, and these features are not only high in dimensionality but also huge in number, which makes image retrieval systems encounter an inevitable problem—“dimensionality disaster.” To overcome this problem, scholars have proposed a series of approximate nearest neighbor methods, but multifeature image retrieval techniques based on partial differential equations are more widely used in people’s daily life.

Author(s):  
Michael Doebeli

This chapter discusses partial differential equation models. Partial differential equations can describe the dynamics of phenotype distributions of polymorphic populations, and they allow for a mathematically concise formulation from which some analytical insights can be obtained. It has been argued that because partial differential equations can describe polymorphic populations, results from such models are fundamentally different from those obtained using adaptive dynamics. In partial differential equation models, diversification manifests itself as pattern formation in phenotype distribution. More precisely, diversification occurs when phenotype distributions become multimodal, with the different modes corresponding to phenotypic clusters, or to species in sexual models. Such pattern formation occurs in partial differential equation models for competitive as well as for predator–prey interactions.


1927 ◽  
Vol 46 ◽  
pp. 126-135 ◽  
Author(s):  
E. T. Copson

A partial differential equation of physics may be defined as a linear second-order equation which is derivable from a Hamiltonian Principle by means of the methods of the Calculus of Variations. This principle states that the actual course of events in a physical problem is such that it gives to a certain integral a stationary value.


1863 ◽  
Vol 12 ◽  
pp. 420-424

Jacobi in a posthumous memoir, which has only this year appeared, has developed two remarkable methods (agreeing in their general character, but differing in details) of solving non-linear partial differential equations of the first order, and has applied them in connexion with that theory of the differential equations of dynamics which was established by Sir W. R. Hamilton in the 'Philosophical Transactions’ for 1834-35. The knowledge, indeed, that the solution of the equation of a dynamical problem is involved in the discovery of a single central function, defined by a single partial differential equation of the first order, does not appear to have been hitherto (perhaps it will never be) very fruitful in practical results.


2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Falei Wang

We introduce a type of fully nonlinear path-dependent (parabolic) partial differential equation (PDE) in which the pathωton an interval [0,t] becomes the basic variable in the place of classical variablest,x∈[0,T]×ℝd. Then we study the comparison theorem of fully nonlinear PPDE and give some of its applications.


1985 ◽  
Vol 5 (3) ◽  
pp. 437-443 ◽  
Author(s):  
R. Rudnicki

AbstractWe prove that the dynamical systems generated by first order partial differential equations are K-flows and chaotic in the sense of Auslander & Yorke.


2018 ◽  
Vol 6 (4) ◽  
Author(s):  
Ziad Salem Rached

Constructing exact solutions of nonlinear ordinary and partial differential equations is an important topic in various disciplines such as Mathematics, Physics, Engineering, Biology, Astronomy, Chemistry,… since many problems and experiments can be modeled using these equations. Various methods are available in the literature to obtain explicit exact solutions. In this correspondence, the enhanced modified simple equation method (EMSEM) is applied to the Phi-4 partial differential equation. New exact solutions are obtained.


1898 ◽  
Vol 62 (379-387) ◽  
pp. 283-285

The general feature of most of the methods of integration of any partial differential equation is the construction of an appropriate subsidiary system and the establishment of the proper relations between integrals of this system and the solution of the original equation. Methods, which in this sense may be called complete, are possessed for partial differential equations of the first order in one dependent variable and any number of independent variables; for certain classes of equations of the first order in two independent variables and a number of dependent variables; and for equations of the second (and higher) orders in one dependent and two independent variables.


Author(s):  
Amit Kumar, Et. al.

In this paper we will discuss Euler’s theorem for homogenous functions to solve different order partial differential equations. We will see that how we can predict the solution of partial differential Equation using different approaches of this theorem. In fact we also consider the case when more than two independent variables will be involved in the partial differential equation whenever dependent functions will be homogenous functions. We will throw a light on one method called Ajayous rules to predict the solution of homogenous partial differential equation.


Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2980
Author(s):  
Daniela Marian

In this paper, we study the semi-Hyers–Ulam–Rassias stability and the generalized semi-Hyers–Ulam–Rassias stability of some partial differential equations using Laplace transform. One of them is the convection partial differential equation.


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