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1.
A class of bent functions which contains bent functions with various properties like regular, weakly regular and not weakly regular bent functions in even and in odd dimension, is analyzed. It is shown that this class includes the Maiorana–McFarland class as a special case. Known classes and examples of bent functions in odd characteristic are examined for their relation to this class. In the second part, normality for bent functions in odd characteristic is analyzed. It turns out that differently to Boolean bent functions, many – also quadratic – bent functions in odd characteristic and even dimension are not normal. It is shown that regular Coulter–Matthews bent functions are normal. 相似文献
2.
D. V. Prokhorov 《Mathematical Notes》1972,11(5):311-315
We consider a class of functions, including the Bazilevich functions, which are regular in the unit disk. The theorems of Levandovskii identifying the class of close-to-convex functions with the class of linearly accessible functions are generalized, and the geometric structure of this class is established. A method constructing a subordinating homotopy chain is used.Translated from Matematicheskie Zametki, Vol. 11, No. 5, pp. 509–516, May, 1972. 相似文献
3.
Summary We introduce a new class of functions called strongly precontinuous functions in topological spaces. Some properties and several characterizations of this type of functions are obtained. We investigate the relationships between this class of functions and other classes of non-continuous functions. 相似文献
4.
A popular approach to solving the complementarity problem is to reformulate it as an equivalent equation system via a complementarity
function. In this paper, we propose a new class of functions, which contains the penalized natural residual function and the
penalized Fischer–Burmeister function for symmetric cone complementarity problems. We show that this class of functions is
indeed a class of complementarity functions. We finally prove that the merit function of this new class of complementarity
functions is coercive. 相似文献
5.
Pantelimon Stănică Thor Martinsen Sugata Gangopadhyay Brajesh Kumar Singh 《Designs, Codes and Cryptography》2013,69(1):77-94
In this paper, we investigate the properties of generalized bent functions defined on ${\mathbb{Z}_2^n}$ with values in ${\mathbb{Z}_q}$ , where q ≥ 2 is any positive integer. We characterize the class of generalized bent functions symmetric with respect to two variables, provide analogues of Maiorana–McFarland type bent functions and Dillon’s functions in the generalized set up. A class of bent functions called generalized spreads is introduced and we show that it contains all Dillon type generalized bent functions and Maiorana–McFarland type generalized bent functions. Thus, unification of two different types of generalized bent functions is achieved. The crosscorrelation spectrum of generalized Dillon type bent functions is also characterized. We further characterize generalized bent Boolean functions defined on ${\mathbb{Z}_2^n}$ with values in ${\mathbb{Z}_4}$ and ${\mathbb{Z}_8}$ . Moreover, we propose several constructions of such generalized bent functions for both n even and n odd. 相似文献
6.
Applying minimum-type functions and plus-cogauges, we construct a closed, convex cone in order to separate a boundary point of a radiant set from its interior. Abstract convexity of positively homogeneous functions is studied as well. Since a locally Lipschitz function is degree-one calm, the class of degree-one calm functions is large. We study degree-one calm functions and investigate how these functions can be generated by a class of min-type functions. Then, we derive a method to find an element of the subdifferential of a non-negative, lower semicontinuous and degree-one calm function with respect to the class of min-type functions. 相似文献
7.
In this paper, we first give some characterizations for P-class functions. Then giving a Hermite–Hadamard type inequality for P-class functions, we prove equivalency of some significant metrics in normed linear spaces. We also obtain an operator version of the Jensen inequality for P-class functions. Introducing operator (mid) P-class functions, we present some characterizations for such functions. 相似文献
8.
F. Pukelsheim 《Journal of Optimization Theory and Applications》1983,41(4):533-546
LetP be a closed convex cone. Information functions, i.e., nonnegative functions onP which are positively homogeneous and concave, are shown to be in a one-to-one correspondence with certain convex subsets ofP. Information functions are always isotone with respect to the vector ordering induced byP, and this order-preserving property distinguishes them from their convex analogues, gauge functions. A polarity concept for information functions is proposed which slightly deviates from the well-known polarity correspondence for gauge functions. Finally, those functions are characterized which differ from information functions only by some nondecreasing concave transformation. 相似文献
9.
10.
在仿射等价类中找具有好的密码学性质的布尔函数 总被引:1,自引:0,他引:1
CHEN Wei-hong LI Na 《数学季刊》2005,20(4):395-400
The Boolean functions in an affine equivalence class are of the same algebraic degree and nonlinearity, but may satisfy different order of correlation immunity and propagation criterion. A method is presented in this paper to find Boolean functions with higher order correlation immunity or satisfying higher order propagation criterion in an affine equivalence class. 8 AES s-box functions are not better Boolean functions in their affine equivalence class. 相似文献
11.
In this paper, we give Schwarz-Pick Lemma for functions in the Schur class on the polydisc of ? n , and generalize some early work of Schwarz-Pick Lemma for functions in the Schur class on the unit disk of C and functions in the Schur-Agler class on the polydisc of ? n . 相似文献
12.
V. V. Zhukov 《Moscow University Computational Mathematics and Cybernetics》2017,41(3):134-141
A model of limited-depth recursive schemes for the functions of Boolean algebra (Boolean functions), constructed from multi-output functional elements, is considered. A lower estimate of the Shannon function for the complexity of schemes of this class is derived. Upper estimates for the complexity of some specific functions and systems of functions in this class of schemes are obtained. A method is proposed for synthesizing schemes of this class for arbitrary functions that allow us (using the derived lower estimate) to determine the asymptotics of the Shannon function for their complexity. 相似文献
13.
Oleg Khamisov 《Journal of Global Optimization》1999,14(1):79-101
We give a definition of the class of functions with a concave minorant and compare these functions with other classes of functions often used in global optimization, e.g. weakly convex functions, d.c. functions, Lipschitzian functions, continuous and lower semicontinuous functions. It is shown that the class of functions with a concave minorant is closed under operations mainly used in optimization and how a concave minorant can be constructed for a given function. 相似文献
14.
Seppo Hassi Manfred Mö ller Henk de Snoo 《Proceedings of the American Mathematical Society》2006,134(10):2885-2893
The class of Nevanlinna functions consists of functions which are holomorphic off the real axis, which are symmetric with respect to the real axis, and whose imaginary part is nonnegative in the upper halfplane. The Kac subclass of Nevanlinna functions is defined by an integrability condition on the imaginary part. In this note a further subclass of these Kac functions is introduced. It involves an integrability condition on the modulus of the Nevanlinna functions (instead of the imaginary part). The characteristic properties of this class are investigated. The definition of the new class is motivated by the fact that the Titchmarsh-Weyl coefficients of various classes of Sturm-Liouville problems (under mild conditions on the coefficients) actually belong to this class.
15.
It is known that there are feasible algorithms for minimizing convex functions, and that for general functions, global minimization
is a difficult (NP-hard) problem. It is reasonable to ask whether there exists a class of functions that is larger than the
class of all convex functions for which we can still solve the corresponding minimization problems feasibly. In this paper,
we prove, in essence, that no such more general class exists. In other words, we prove that global optimization is always
feasible only for convex objective functions. 相似文献
16.
A new class of generalized convex set-valued functions, termed nearly-subconvexlike functions, is introduced. This class is a generalization of cone-subconvexlike maps, nearly-convexlike set-valued functions, and preinvex set-valued functions. Properties for the nearly-subconvexlike functions are derived and a theorem of the alternative is proved. A Lagrangian multiplier theorem is established and two scalarization theorems are obtained for vector optimization. 相似文献
17.
A class of penalty functions for solving convex programming problems with general constraint sets is considered. Convergence theorems for penalty methods are established by utilizing the concept of infimal convergence of a sequence of functions. It is shown that most existing penalty functions are included in our class of penalty functions. 相似文献
18.
Wolter Groenevelt 《The Ramanujan Journal》2018,47(2):317-337
The 6j-symbols for representations of the q-deformed algebra of polynomials on \(\mathrm {SU}(2)\) are given by Jackson’s third q-Bessel functions. This interpretation leads to several summation identities for the q-Bessel functions. Multivariate q-Bessel functions are defined, which are shown to be limit cases of multivariate Askey–Wilson polynomials. The multivariate q-Bessel functions occur as 3nj-symbols. 相似文献
19.
Emanuele Bottazzi 《P-Adic Numbers, Ultrametric Analysis, and Applications》2018,10(3):179-191
We discuss the properties of the continuations of real functions to the Levi-Civita field. In particular, we show that, whenever a function f is analytic on a compact interval [a, b] ? ?, f and its analytic continuation f?∞ satisfy the same properties that can be expressed in the language of real closed ordered fields. If f is not analytic, then this equivalence does not hold. These results suggest an analogy with the internal and external functions of nonstandard analysis: while the canonical continuations of analytic functions resemble internal functions, the continuations of non-analytic functions behave like external functions. Inspired by this analogy, we suggest some directions for further research. 相似文献
20.
Grigor A. Barsegian 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2007,42(2):61-68
The paper announces some new inequalities that refer to broken lines, curves and real and complex functions. Their derivation is based on a new principle of angles and lengths for curves. The inequality in the complex analysis, called the principle of derivatives, is valid for analytic functions in arbitrary domains and extends to a broad class of sufficiently smooth complex functions. A new inequality follows for real functions of two variables concerning their level sets. For all cases mentioned above, both for curves and functions, we obtain some analogues of the second fundamental theorem in Nevanlinna theory of meromorphic functions. At the end we discuss a new point-domain inequality dealing with finite point sets in an arbitrary domain. 相似文献