The sequences with good correlation properties are widely used in engineering applications, especially in the area of communications. In this paper, the relationships among crosscorrelation functions of arbitrary four...The sequences with good correlation properties are widely used in engineering applications, especially in the area of communications. In this paper, the relationships among crosscorrelation functions of arbitrary four binary sequences of period N are presented. Based on them, for a sequences set, the relationships between cross-correlation functions and autocorrelation functions are studied, by which we prove that they cannot keep optimal at the same time.展开更多
Functions with difference uniformity have important applications in cryptography. Some planar functions and almost perfect nonlinear（APN） functions are presented in the note. In addition, an upper bound of the unifo...Functions with difference uniformity have important applications in cryptography. Some planar functions and almost perfect nonlinear（APN） functions are presented in the note. In addition, an upper bound of the uniformity of some power mappings is provided by using an interesting identity on Dickson polynomials. When the character of the finite field is less than 11, the upper bound is proved to be the best possibility.展开更多
We study the functions with low differential uniformity,and concentrates mainly on the properties of perfect nonlinear（PN） functions,including the properties of the derivative of the components of those functions.So...We study the functions with low differential uniformity,and concentrates mainly on the properties of perfect nonlinear（PN） functions,including the properties of the derivative of the components of those functions.Some sufficient and necessary conditions have been explored to judge when a function is a PN function.These conditions may be useful in constructing new PN functions.We also construct some functions with differential 4-uniformity that have rarely been studied in the literature.Some of the constructed functions with differential 4-uniformity have high nonlinearity as well.Finally,a class of functions with differential 4-uniformity which are not extended affine equivalent to any power functions are constructed.展开更多
In this note, we experimentally demonstrate, on a variety of analytic and nonanalytic functions, the novel observation that if the least squares polynomial approximation is repeated as weight in a second, now weighted...In this note, we experimentally demonstrate, on a variety of analytic and nonanalytic functions, the novel observation that if the least squares polynomial approximation is repeated as weight in a second, now weighted, least squares approximation, then this new, second, approximation is nearly perfect in the uniform sense, barely needing any further, say, Remez correction.展开更多
It is widely accepted that the Marginal Value Theorem (MVT) describes optimal foraging strategies of animals and the mechanism proposed by the MVT has been supported by a number of field observations. However, finding...It is widely accepted that the Marginal Value Theorem (MVT) describes optimal foraging strategies of animals and the mechanism proposed by the MVT has been supported by a number of field observations. However, findings of many researchers indicate that in natural conditions foragers do not always behave according to the MVT. To address this inconsistency, in a series of computer simulation experiments, we examined the behaviour of four types of foragers having specific foraging efficiencies and using the MVT strategies in 15 different landscapes in an ideal environment (no intra-and inter-specific interactions). We used data on elk (Cervus elaphus) to construct our virtual forager. Contrary to the widely accepted understanding of the MVT (residence time in a patch should be longer in environments where travel time between patches is longer) we found that in environments with the same average patch quality and varying average travel times between patches, patch residence times of some foragers are not affected by travel times. Based on our analysis we propose a mechanism responsible for this observation and formulate the perfect forager theorem (PFT). We also introduce the concepts of a foraging coefficient (F) and foragers’ hub (α), and propose a model to describe the relationship between the perfect forager and all other forager types.展开更多
A naïve discussion of Fermat’s last theorem conundrum is described. The present theorem’s proof is grounded on the well-known properties of sums of powers of the sine and cosine functions, the Minkowski norm de...A naïve discussion of Fermat’s last theorem conundrum is described. The present theorem’s proof is grounded on the well-known properties of sums of powers of the sine and cosine functions, the Minkowski norm definition, and some vector-specific structures.展开更多
基金Supported by the Natural Science Foundation of Anhui(1608085MF143)the National Natural Science Foundation of China(60573026,10101008)the Natural Science Foundation of Anhui Higher Education Institutions of China(KJ2018A0678)
文摘The sequences with good correlation properties are widely used in engineering applications, especially in the area of communications. In this paper, the relationships among crosscorrelation functions of arbitrary four binary sequences of period N are presented. Based on them, for a sequences set, the relationships between cross-correlation functions and autocorrelation functions are studied, by which we prove that they cannot keep optimal at the same time.
文摘Functions with difference uniformity have important applications in cryptography. Some planar functions and almost perfect nonlinear（APN） functions are presented in the note. In addition, an upper bound of the uniformity of some power mappings is provided by using an interesting identity on Dickson polynomials. When the character of the finite field is less than 11, the upper bound is proved to be the best possibility.
基金Supported by the National Natural Science Foundation of China (60673068)the Fundamental Research Funds for the Central Universities (2009B27414)the Natural Science Foundation of Hohai University (2084/409270)
文摘We study the functions with low differential uniformity,and concentrates mainly on the properties of perfect nonlinear（PN） functions,including the properties of the derivative of the components of those functions.Some sufficient and necessary conditions have been explored to judge when a function is a PN function.These conditions may be useful in constructing new PN functions.We also construct some functions with differential 4-uniformity that have rarely been studied in the literature.Some of the constructed functions with differential 4-uniformity have high nonlinearity as well.Finally,a class of functions with differential 4-uniformity which are not extended affine equivalent to any power functions are constructed.
文摘In this note, we experimentally demonstrate, on a variety of analytic and nonanalytic functions, the novel observation that if the least squares polynomial approximation is repeated as weight in a second, now weighted, least squares approximation, then this new, second, approximation is nearly perfect in the uniform sense, barely needing any further, say, Remez correction.
文摘It is widely accepted that the Marginal Value Theorem (MVT) describes optimal foraging strategies of animals and the mechanism proposed by the MVT has been supported by a number of field observations. However, findings of many researchers indicate that in natural conditions foragers do not always behave according to the MVT. To address this inconsistency, in a series of computer simulation experiments, we examined the behaviour of four types of foragers having specific foraging efficiencies and using the MVT strategies in 15 different landscapes in an ideal environment (no intra-and inter-specific interactions). We used data on elk (Cervus elaphus) to construct our virtual forager. Contrary to the widely accepted understanding of the MVT (residence time in a patch should be longer in environments where travel time between patches is longer) we found that in environments with the same average patch quality and varying average travel times between patches, patch residence times of some foragers are not affected by travel times. Based on our analysis we propose a mechanism responsible for this observation and formulate the perfect forager theorem (PFT). We also introduce the concepts of a foraging coefficient (F) and foragers’ hub (α), and propose a model to describe the relationship between the perfect forager and all other forager types.
文摘A naïve discussion of Fermat’s last theorem conundrum is described. The present theorem’s proof is grounded on the well-known properties of sums of powers of the sine and cosine functions, the Minkowski norm definition, and some vector-specific structures.
