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Journal articles on the topic 'Functions of several real vari'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Evans, Michael J., and Paul D. Humke. "Baire one, Gibson and weakly Gibson real functions of several real variables." Rendiconti del Circolo Matematico di Palermo 59, no. 1 (April 2010): 47–51. http://dx.doi.org/10.1007/s12215-010-0002-6.

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2

Carpintero, C., N. Rajesh, and E. Rosas. "On real valued ω-continuous functions." Acta Universitatis Sapientiae, Mathematica 10, no. 2 (December 1, 2018): 242–48. http://dx.doi.org/10.2478/ausm-2018-0019.

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Abstract The aim of this paper is to introduce and study upper and lower ω-continuous functions. Some characterizations and several properties concerning upper (resp. lower) ω-continuous functions are obtained.

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3

ALMIRA, J. M., and KH F. ABU-HELAIEL. "On Montel’s theorem in several variables." Carpathian Journal of Mathematics 31, no. 1 (2015): 1–10. http://dx.doi.org/10.37193/cjm.2015.01.01.

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Recently, the first author of this paper, used the structure of finite dimensional translation invariant subspaces of C(R, C) to give a new proof of classical Montel’s theorem, about continuous solutions of Frechet’s functional equation ∆m h f = 0, for real functions (and complex functions) of one real variable. In this paper we use similar ideas to prove a Montel’s type theorem for the case of complex valued functions defined over the discrete group Z d. Furthermore, we also state and demonstrate an improved version of Montel’s Theorem for complex functions of several real variables and complex functions of several complex variables.

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4

Evans, Michael J., and Paul D. Humke. "Generalizations of Young’s Theorem to real functions of several variables." Rendiconti del Circolo Matematico di Palermo 58, no. 2 (July 18, 2009): 287–96. http://dx.doi.org/10.1007/s12215-009-0023-1.

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5

Burke, Maxim R. "Approximation and Interpolation by Entire Functions of Several Variables." Canadian Mathematical Bulletin 53, no. 1 (March 1, 2010): 11–22. http://dx.doi.org/10.4153/cmb-2010-006-4.

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AbstractLet f : ℝn → ℝ be C∞ and let h: ℝn → ℝ be positive and continuous. For any unbounded nondecreasing sequence ﹛ck﹜ of nonnegative real numbers and for any sequence without accumulation points ﹛xm﹜ in ℝn, there exists an entire function g : ℂn → ℂ taking real values on ℝn such thatThis is a version for functions of several variables of the case n = 1 due to L. Hoischen.

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6

Sprecher, David. "On computational algorithms for real-valued continuous functions of several variables." Neural Networks 59 (November 2014): 16–22. http://dx.doi.org/10.1016/j.neunet.2014.05.015.

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7

Chen, So-Chin, and Cin-Chang Lu. "ON DOMINATING PHENOMENON FOR BOUNDED REAL HARMONIC FUNCTIONS IN SEVERAL VARIABLES." Taiwanese Journal of Mathematics 14, no. 2 (April 2010): 501–15. http://dx.doi.org/10.11650/twjm/1500405804.

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8

Domański, Paweł, and Michael Langenbruch. "Multiplier projections on spaces of real analytic functions in several variables." Complex Variables and Elliptic Equations 62, no. 2 (August 16, 2016): 241–68. http://dx.doi.org/10.1080/17476933.2016.1218854.

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9

Kraus, Christiane. "Bernstein–Walsh Type Theorems for Real Analytic Functions in Several Variables." Constructive Approximation 33, no. 2 (May 15, 2010): 191–217. http://dx.doi.org/10.1007/s00365-010-9097-4.

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10

Ciesielski, Krzysztof. "Topologizing Different Classes of Real Functions." Canadian Journal of Mathematics 46, no. 06 (December 1994): 1188–207. http://dx.doi.org/10.4153/cjm-1994-067-x.

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AbstractThe purpose of this paper is to examine which classesof functions fromcan be topologized in a sense that there exist topologies τ1and τ2onandrespectively, such thatis equal to the class C(τ1, τ2) of all continuous functions. We will show that the Generalized Continuum Hypothesis GCH implies the positive answer for this question for a large number of classes of functionsfor which the sets {x : f(x) = g(x)} are small in some sense for all f, g ∈f ≠ g. The topologies will be Hausdorff and connected. It will be also shown that in some model of set theory ZFC with GCH these topologies could be completely regular and Baire. One of the corollaries of this theorem is that GCH implies the existence of a connected Hausdorff topology T onsuch that the class L of all linear functions g(x) = ax + b coincides with. This gives an affirmative answer to a question of Sam Nadler. The above corollary remains true for the classof all polynomials, the classof all analytic functions and the class of all harmonic functions.We will also prove that several other classes of real functions cannot be topologized. This includes the classes of C∞functions, differentiable functions, Darboux functions and derivatives.

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11

MATSUMOTO, KEIJI, and MASAAKI YOSHIDA. "INVARIANTS FOR SOME REAL HYPERBOLIC GROUPS." International Journal of Mathematics 13, no. 04 (June 2002): 415–43. http://dx.doi.org/10.1142/s0129167x02001320.

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For several discontinuous groups acting on the hyperbolic 3-space, which are commensurable with the group arising from the Whitebread link complement, we construct systems of invariant functions, in terms of theta functions, which give explicit projective embeddings of the quotient spaces.

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12

HATORI, OSAMU. "SEPARATION PROPERTIES AND OPERATING FUNCTIONS ON A SPACE OF CONTINUOUS FUNCTIONS." International Journal of Mathematics 04, no. 04 (August 1993): 551–600. http://dx.doi.org/10.1142/s0129167x93000303.

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Characterizations of the space CR (X) of all real-valued continuous functions on a compact Hausdorff space X among its subspaces are investigated under the circumstances of operating functions. One of the main purpose in this paper is to disprove the following conjecture: if a non-affine function operates on an ultraseparating real Banach function space E on X, then E = CR (X). A positive answer is given in the case that E satisfies a stronger separation axiom than ultraseparation one, which the real part of an ultraseparating Banach function algebra satisfies. For the original conjecture a counterexample is given; there is an ultraseparating real Banach function space on a compact metric space Y on which the function |·| operates, but it does not coincide with CR (Y). A characterization is given for non-affine functions which operate only on CR (X) among ultraseparating real Banach function spaces on X. By using these results the symbolic calculus on real Banach function spaces is investigated without extra hypothesis of ultraseparation. Several non-local-Lipschitz functions are shown not to operate on a real Banach function space E on X unless E = CR (X). In particular, the function tp defined on [0,1) for a p with 0 < p < 1 or the standard Cantor function on [0, 1] never operates on a real Banach function space E on X unless E = CR (X). Functions which operate on the real part of a real function algebra are also investigated. A positive answer is given for the conjecture that only affine functions operate on the real part of a non-trivial real function algebra.

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13

KALONDA, LUHANDJULA MONGA, and RANGOAGA MOETI JOSEPH. "MATHEMATICAL PROGRAMMING PROBLEMS WITH SEVERAL FUZZY OBJECTIVE FUNCTIONS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 21, supp01 (July 2013): 51–62. http://dx.doi.org/10.1142/s0218488513400047.

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In this paper we propose an approach for multiobjective programming problems with fuzzy number coefficients. The main idea behind our approach is to approximate involved fuzzy numbers by their respective nearest interval approximation counterparts. An algorithm that returns a nearest interval approximation to a given fuzzy number, plays a pivotal role in the proposed method. Our approach contrasts markedly with those based on deffuzification operators which replace a fuzzy set by a single real number leading to a loss of many important information. A numerical example is also provided for the sake of illustration.

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14

Domański, Paweł, Michael Langenbruch, and Dietmar Vogt. "Hadamard type operators on spaces of real analytic functions in several variables." Journal of Functional Analysis 269, no. 12 (December 2015): 3868–913. http://dx.doi.org/10.1016/j.jfa.2015.09.011.

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15

Estaji, A. A., Darghadam Mahmoudi, and H. Yousefpour. "Maximal ideals in rings of real measurable functions." Filomat 32, no. 15 (2018): 5191–203. http://dx.doi.org/10.2298/fil1815191e.

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Let M(X) be the ring of all real measurable functions on a measurable space (X,A). In this article, we show that every ideal of M(X) is a Z?-ideal. Also, we give several characterizations of maximal ideals of M(X), mostly in terms of certain lattice-theoretic properties of A. The notion of T-measurable space is introduced. Next, we show that for every measurable space (X,A) there exists a T-measurable space (Y,A') such that M(X) ? M(Y) as rings. The notion of compact measurable space is introduced. Next, we prove that if (X,A) and (Y,A') are two compact T-measurable spaces, then X ? Y as measurable spaces if and only if M(X) ? M(Y) as rings.

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16

Kocinac, Ljubisa. "On spaces of group-valued functions." Filomat 25, no. 2 (2011): 163–72. http://dx.doi.org/10.2298/fil1102163k.

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17

Du, Wei-Shih, Marko Kostić, and Manuel Pinto. "Almost Periodic Functions and Their Applications: A Survey of Results and Perspectives." Journal of Mathematics 2021 (April 14, 2021): 1–21. http://dx.doi.org/10.1155/2021/5536018.

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The main aim of this survey article is to present several known results about vector-valued almost periodic functions and their applications. We separately consider almost periodic functions depending on one real variable and almost periodic functions depending on two or more real variables. We address several open problems and possibilities for further investigations of almost periodic functions, quoting more than two hundred references about the subject under our consideration.

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18

Fenoy-Muñoz, Mar, José Luis Gámez-Merino, Gustavo A. Muñoz-Fernández, and Eva Sáez-Maestro. "A hierarchy in the family of real surjective functions." Open Mathematics 15, no. 1 (April 26, 2017): 486–501. http://dx.doi.org/10.1515/math-2017-0042.

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Abstract This expository paper focuses on the study of extreme surjective functions in ℝℝ. We present several different types of extreme surjectivity by providing examples and crucial properties. These examples help us to establish a hierarchy within the different classes of surjectivity we deal with. The classes presented here are: everywhere surjective functions, strongly everywhere surjective functions, κ-everywhere surjective functions, perfectly everywhere surjective functions and Jones functions. The algebraic structure of the sets of surjective functions we show here is studied using the concept of lineability. In the final sections of this work we also reveal unexpected connections between the different degrees of extreme surjectivity given above and other interesting sets of functions such as the space of additive mappings, the class of mappings with a dense graph, the class of Darboux functions and the class of Sierpiński-Zygmund functions in ℝℝ.

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19

Długosz, Renata, and Piotr Liczberski. "Some Results of Fekete-Szegö Type. Results for Some Holomorphic Functions of Several Complex Variables." Symmetry 12, no. 10 (October 16, 2020): 1707. http://dx.doi.org/10.3390/sym12101707.

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This paper is devoted to a generalization of the well-known Fekete-Szegö type coefficients problem for holomorphic functions of a complex variable onto holomorphic functions of several variables. The considerations concern three families of such functions f, which are bounded, having positive real part and which Temljakov transform Lf has positive real part, respectively. The main result arise some sharp estimates of the Minkowski balance of a combination of 2-homogeneous and the square of 1-homogeneous polynomials occurred in power series expansion of functions from aforementioned families.

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20

Rashid, Saima, Muhammad Amer Latif, Zakia Hammouch, and Yu-Ming Chu. "Fractional Integral Inequalities for Strongly h -Preinvex Functions for a kth Order Differentiable Functions." Symmetry 11, no. 12 (November 25, 2019): 1448. http://dx.doi.org/10.3390/sym11121448.

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The objective of this paper is to derive Hermite-Hadamard type inequalities for several higher order strongly h -preinvex functions via Riemann-Liouville fractional integrals. These results are the generalizations of the several known classes of preinvex functions. An identity associated with k-times differentiable function has been established involving Riemann-Liouville fractional integral operator. A number of new results can be deduced as consequences for the suitable choices of the parameters h and σ . Our outcomes with these new generalizations have the abilities to be implemented for the evaluation of many mathematical problems related to real world applications.

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21

ÓCONNOR, RUSSELL. "A monadic, functional implementation of real numbers." Mathematical Structures in Computer Science 17, no. 1 (February 2007): 129–59. http://dx.doi.org/10.1017/s0960129506005871.

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Large scale real number computation is an essential ingredient in several modern mathematical proofs. Because such lengthy computations cannot be verified by hand, some mathematicians want to use software proof assistants to verify the correctness of these proofs. This paper develops a new implementation of the constructive real numbers and elementary functions for such proofs by using the monad properties of the completion operation on metric spaces. Bishop and Bridges's notion (Bishop and Bridges 1985) of regular sequences is generalised to what I call regular functions, which form the completion of any metric space. Using the monad operations, continuous functions on length spaces (which are a common subclass of metric spaces) are created by lifting continuous functions on the original space. A prototype Haskell implementation has been created. I believe that this approach yields a real number library that is reasonably efficient for computation, and still simple enough to verify its correctness easily.

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22

Khemaratchatakumthorn, Tammatada, and Prapanpong Pongsriiam. "Remarks on uniformly symmetrically continuous functions." Asian-European Journal of Mathematics 09, no. 03 (August 2, 2016): 1650069. http://dx.doi.org/10.1142/s1793557116500698.

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We give the definition of uniform symmetric continuity for functions defined on a nonempty subset of the real line. Then we investigate the properties of uniformly symmetrically continuous functions and compare them with those of symmetrically continuous functions and uniformly continuous functions. We obtain some characterizations of uniformly symmetrically continuous functions. Several examples are also given.

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23

LIAW, SY-SANG, and FENG-YUAN CHIU. "CONSTRUCTING CROSSOVER-FRACTALS USING INTRINSIC MODE FUNCTIONS." Advances in Adaptive Data Analysis 02, no. 04 (October 2010): 509–20. http://dx.doi.org/10.1142/s1793536910000598.

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Real nonstationary time sequences are in general not monofractals. That is, they cannot be characterized by a single value of fractal dimension. It has been shown that many real-time sequences are crossover-fractals: sequences with two fractal dimensions — one for the short and the other for long ranges. Here, we use the empirical mode decomposition (EMD) to decompose monofractals into several intrinsic mode functions (IMFs) and then use partial sums of the IMFs decomposed from two monofractals to construct crossover-fractals. The scale-dependent fractal dimensions of these crossover-fractals are checked by the inverse random midpoint displacement method (IRMD).

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24

Cho, Nak, Sushil Kumar, Virendra Kumar, V. Ravichandran, and H. Srivastava. "Starlike Functions Related to the Bell Numbers." Symmetry 11, no. 2 (February 13, 2019): 219. http://dx.doi.org/10.3390/sym11020219.

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The present paper aims to establish the first order differential subordination relations between functions with a positive real part and starlike functions related to the Bell numbers. In addition, several sharp radii estimates for functions in the class of starlike functions associated with the Bell numbers are determined.

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25

PETERZIL, YA'ACOV, and SERGEI STARCHENKO. "EXPANSIONS OF ALGEBRAICALLY CLOSED FIELDS II: FUNCTIONS OF SEVERAL VARIABLES." Journal of Mathematical Logic 03, no. 01 (May 2003): 1–35. http://dx.doi.org/10.1142/s0219061303000224.

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Let ℛ be an o-minimal expansion of a real closed field R. We continue here the investigation we began in [11] of differentiability with respect to the algebraically closed field [Formula: see text]. We develop the basic theory of such K-differentiability for definable functions of several variables, proving theorems on removable singularities as well as analogues of the Weierstrass preparation and division theorems for definable functions. We consider also definably meromorphic functions and prove that every definable function which is meromorphic on Kn is necessarily a rational function. We finally discuss definable analogues of complex analytic manifolds, with possible connections to the model theoretic work on compact complex manifolds, and present two examples of "nonstandard manifolds" in our setting.

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26

Nakasho, Kazuhisa, Yuichi Futa, and Yasunari Shidama. "Topological Properties of Real Normed Space." Formalized Mathematics 22, no. 3 (September 1, 2014): 209–23. http://dx.doi.org/10.2478/forma-2014-0024.

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Summary In this article, we formalize topological properties of real normed spaces. In the first part, open and closed, density, separability and sequence and its convergence are discussed. Then we argue properties of real normed subspace. Then we discuss linear functions between real normed speces. Several kinds of subspaces induced by linear functions such as kernel, image and inverse image are considered here. The fact that Lipschitz continuity operators preserve convergence of sequences is also refered here. Then we argue the condition when real normed subspaces become Banach’s spaces. We also formalize quotient vector space. In the last session, we argue the properties of the closure of real normed space. These formalizations are based on [19](p.3-41), [2] and [34](p.3-67).

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27

Saikia, Nipen. "A Product of Theta-Functions Analogous to Ramanujan's Remarkable Product of Theta-Functions and Applications." Journal of Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/620756.

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We define a productlk,nfor any positive real numberskandninvolving Ramanujan's theta-functionsϕ(q)andψ(q)which is analogous to Ramanujan's remarkable product of theta-functions recorded by Ramanujan (1957) and study its several properties. We prove general theorems for the explicit evaluations oflk,nand find some explicit values. As application of the productlk,n, we also offer explicit formulas for explicit values of Ramanujan's continued fractionV(q)in terms oflk,nand give examples.

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28

Deb Ray, A., and Atanu Mondal. "On rings of Baire one functions." Applied General Topology 20, no. 1 (April 1, 2019): 237. http://dx.doi.org/10.4995/agt.2019.10776.

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<p>This paper introduces the ring of all real valued Baire one functions, denoted by B<sub>1</sub>(X) and also the ring of all real valued bounded Baire one functions, denoted by B<sup>∗</sup><sub>1</sub>(X). Though the resemblance between C(X) and B<sub>1</sub>(X) is the focal theme of this paper, it is observed that unlike C(X) and C<sup>∗</sup>(X) (real valued bounded continuous functions), B<sup>∗</sup><sub>1</sub> (X) is a proper subclass of B<sub>1</sub>(X) in almost every non-trivial situation. Introducing B<sub>1</sub>-embedding and B<sup>∗</sup><sub>1</sub>-embedding, several analogous results, especially, an analogue of Urysohn’s extension theorem is established.</p>

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29

SUKHOV, ALEXANDRE. "PLURIPOLAR SETS, REAL SUBMANIFOLDS AND PSEUDOHOLOMORPHIC DISCS." Journal of the Australian Mathematical Society 109, no. 2 (April 8, 2019): 270–88. http://dx.doi.org/10.1017/s1446788719000119.

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We prove that a compact subset of full measure on a generic submanifold of an almost complex manifold is not a pluripolar set. Several related results on boundary behavior of plurisubharmonic functions are established. Our approach is based on gluing a family of complex discs to a generic manifold along a boundary arc and could admit further applications.

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30

Mesiar, Radko, and Andrea Stupňanová. "Directional Shift-Stable Functions." Mathematics 9, no. 10 (May 11, 2021): 1077. http://dx.doi.org/10.3390/math9101077.

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Recently, some new types of monotonicity—in particular, weak monotonicity and directional monotonicity of an n-ary real function—were introduced and successfully applied. Inspired by these generalizations of monotonicity, we introduce a new notion for n-ary functions acting on [0,1]n, namely, the directional shift stability. This new property extends the standard shift invariantness (difference scale invariantness), which can be seen as a particular directional shift stability. The newly proposed property can also be seen as a particular kind of local linearity. Several examples and a complete characterization for the case of n=2 of directionally shift-stable aggregation and pre-aggregation functions are also given.

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31

Zhao, Chuan, Han Jiang, Qiuliang Xu, Xiaochao Wei, and Hao Wang. "Several Oblivious Transfer Variants in Cut-and-Choose Scenario." International Journal of Information Security and Privacy 9, no. 2 (April 2015): 1–12. http://dx.doi.org/10.4018/ijisp.2015040101.

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Oblivious transfer is a fundamental tool in modern cryptography. In the past few years, many studies concentrate on oblivious transfer variants with more powerful functions. In this paper, the authors propose several variants of oblivious transfer in cut-and-choose scenario, providing multiple ways of transferring data in an oblivious manner. In addition, based on homomorphic encryption, the authors construct instantiations of these primitives, which can be proven secure in malicious model under ideal/real simulation paradigm and achieve the highest security level in the real world.

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32

Erakoviќ, Vesna, Stevan Pilipovic, and Vasko Reckovski. "Analytic representations of sequences in Lp spaces, 1 ≤ p < ∞." Filomat 31, no. 7 (2017): 1959–66. http://dx.doi.org/10.2298/fil1707959e.

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In this paper we consider a sequence of functions in Lp(R), 1 ? p < ? and, in the second part, we include a sequence of real analytic functions without real roots. We obtain several results regarding their convergence or the convergence of the sequence of their analytic representations. We, also, give results about the analytic representation of the product of the boundary functions and other additional results.

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33

Ma, Rong, Yana Niu, and Yulong Zhang. "On asymptotic properties of the generalized Dirichlet L-functions." International Journal of Number Theory 15, no. 06 (July 2019): 1305–21. http://dx.doi.org/10.1142/s1793042119500738.

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Let [Formula: see text] be an integer, [Formula: see text] denote a Dirichlet character modulo [Formula: see text], for any real number [Formula: see text], we define the generalized Dirichlet [Formula: see text]-functions [Formula: see text] where [Formula: see text] with [Formula: see text] and [Formula: see text] both real. It can be extended to all [Formula: see text] by analytic continuation. In this paper, we study the mean value properties of the generalized Dirichlet [Formula: see text]-functions, and obtain several sharp asymptotic formulae by using analytic method.

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34

Roth, Walter. "A Korovkin type theorem for weighted spaces of continuous functions." Bulletin of the Australian Mathematical Society 55, no. 2 (April 1997): 239–48. http://dx.doi.org/10.1017/s0004972700033906.

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We prove a Korovkin type approximation theorem for positive linear operators on weighted spaces of continuous real-valued functions on a compact Hausdorff space X. These spaces comprise a variety of subspaces of C (X) with suitable locally convex topologies and were introduced by Nachbin 1967 and Prolla 1977. Some early Korovkin type results on the weighted approximation of real-valued functions in one and several variables with a single weight function are due to Gadzhiev 1976 and 1980.

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35

Bugeaud, Yann, Lingmin Liao, and Michał Rams. "Metrical Results on the Distribution of Fractional Parts of Powers of Real Numbers." Proceedings of the Edinburgh Mathematical Society 62, no. 2 (November 29, 2018): 505–21. http://dx.doi.org/10.1017/s0013091518000585.

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AbstractWe establish several new metrical results on the distribution properties of the sequence ({xn})n≥1, where {·} denotes the fractional part. Many of them are presented in a more general framework, in which the sequence of functions (x ↦ xn)n≥1 is replaced by a sequence (fn)n≥1, under some growth and regularity conditions on the functions fn.

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36

Arnold, Dirk V., and Alexander MacLeod. "Step Length Adaptation on Ridge Functions." Evolutionary Computation 16, no. 2 (June 2008): 151–84. http://dx.doi.org/10.1162/evco.2008.16.2.151.

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Step length adaptation is central to evolutionary algorithms in real-valued search spaces. This paper contrasts several step length adaptation algorithms for evolution strategies on a family of ridge functions. The algorithms considered are cumulative step length adaptation, a variant of mutative self-adaptation, two-point adaptation, and hierarchically organized strategies. In all cases, analytical results are derived that yield insights into scaling properties of the algorithms. The influence of noise on adaptation behavior is investigated. Similarities and differences between the adaptation strategies are discussed.

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37

DRAGOMIR, S. S. "A CONCEPT OF SYNCHRONICITY ASSOCIATED WITH CONVEX FUNCTIONS IN LINEAR SPACES AND APPLICATIONS." Bulletin of the Australian Mathematical Society 82, no. 2 (June 18, 2010): 328–39. http://dx.doi.org/10.1017/s0004972710000341.

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AbstractA concept of synchronicity associated with convex functions in linear spaces and a Chebyshev type inequality are given. Applications for norms, semi-inner products and convex functions of several real variables are also given.

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38

Xiao, Jie. "Some properties and characterizations ofA-normal functions." International Journal of Mathematics and Mathematical Sciences 20, no. 3 (1997): 503–10. http://dx.doi.org/10.1155/s0161171297000689.

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LetMbe the set of all functions meromorphic onD={z∈ℂ:|z|<1}. Fora∈(0,1], a functionf∈Mis calleda-normal function of bounded (vanishing) type orf∈Na(N0a), ifsupz∈D(1−|z|)af#(z)<∞(lim|z|→1(1−|z|)af#(z)=0). In this paper we not only show the discontinuity ofNaandN0arelative to containment asavaries, which shows∪0<a<1Na⊂UBC0, but also give several characterizations ofNaandN0awhich are real extensions for characterizations ofNandN0.

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39

Rehman, Hameed Ur, Maslina Darus, and Jamal Salah. "Generalizing Certain Analytic Functions Correlative to the n-th Coefficient of Certain Class of Bi-Univalent Functions." Journal of Mathematics 2021 (April 26, 2021): 1–14. http://dx.doi.org/10.1155/2021/6621315.

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In the present paper, the authors implement the two analytic functions with its positive real part in the open unit disk. New types of polynomials are introduced, and by using these polynomials with the Faber polynomial expansion, a formula is structured to solve certain coefficient problems. This formula is applied to a certain class of bi-univalent functions and solve the n -th term of its coefficient problems. In the last section of the article, several well-known classes are also extended to its n -th term.

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40

Rehberg, Martin. "Log-Like Functions and Uniform Distribution Modulo One." Uniform distribution theory 13, no. 2 (December 1, 2018): 93–101. http://dx.doi.org/10.2478/udt-2018-0013.

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Abstract For a function f satisfying f (x) = o((log x) K), K > 0, and a sequence of numbers (qn) n, we prove by assuming several conditions on f that the sequence (αf (qn)) n≥n0 is uniformly distributed modulo one for any nonzero real number α. This generalises some former results due to Too, Goto and Kano where instead of (qn) n the sequence of primes was considered.

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41

PARVATE, ABHAY, and A. D. GANGAL. "CALCULUS ON FRACTAL SUBSETS OF REAL LINE — I: FORMULATION." Fractals 17, no. 01 (March 2009): 53–81. http://dx.doi.org/10.1142/s0218348x09004181.

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A new calculus based on fractal subsets of the real line is formulated. In this calculus, an integral of order α, 0 < α ≤ 1, called Fα-integral, is defined, which is suitable to integrate functions with fractal support F of dimension α. Further, a derivative of order α, 0 < α ≤ 1, called Fα-derivative, is defined, which enables us to differentiate functions, like the Cantor staircase, "changing" only on a fractal set. The Fα-derivative is local unlike the classical fractional derivative. The Fα-calculus retains much of the simplicity of ordinary calculus. Several results including analogues of fundamental theorems of calculus are proved. The integral staircase function, which is a generalization of the functions like the Cantor staircase function, plays a key role in this formulation. Further, it gives rise to a new definition of dimension, the γ-dimension. Spaces of Fα-differentiable and Fα-integrable functions are analyzed. Analogues of Sobolev Spaces are constructed on F and Fα-differentiability is generalized using Sobolev-like construction. Fα-differential equations are equations involving Fα-derivatives. They can be used to model sublinear dynamical systems and fractal time processes, since sublinear behaviors are associated with staircase-like functions which occur naturally as their solutions. As examples, we discuss a fractal-time diffusion equation, and one-dimensional motion of a particle undergoing friction in a fractal medium.

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Thakur, Ramkrishna, and S. K. Samanta. "A Study on Some Fundamental Properties of Continuity and Differentiability of Functions of Soft Real Numbers." Advances in Fuzzy Systems 2018 (2018): 1–8. http://dx.doi.org/10.1155/2018/6429572.

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We introduce a new type of functions from a soft set to a soft set and study their properties under soft real number setting. Firstly, we investigate some properties of soft real sets. Considering the partial order relation of soft real numbers, we introduce concept of soft intervals. Boundedness of soft real sets is defined, and the celebrated theorems like nested intervals theorem and Bolzano-Weierstrass theorem are extended in this setting. Next, we introduce the concepts of limit, continuity, and differentiability of functions of soft sets. It has been possible for us to study some fundamental results of continuity of functions of soft sets such as Bolzano’s theorem, intermediate value property, and fixed point theorem. Because the soft real numbers are not linearly ordered, several twists in the arguments are required for proving those results. In the context of differentiability of functions, some basic theorems like Rolle’s theorem and Lagrange’s mean value theorem are also extended in soft setting.

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Zaprawa, Paweł, and Katarzyna Tra̧bka-Wiȩcław. "Estimates of Coefficient Functionals for Functions Convex in the Imaginary-Axis Direction." Symmetry 12, no. 10 (October 20, 2020): 1736. http://dx.doi.org/10.3390/sym12101736.

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Let C0(h) be a subclass of analytic and close-to-convex functions defined in the open unit disk by the formula Re{(1−z2)f′(z)}>0. In this paper, some coefficient problems for C0(h) are considered. Some properties and bounds of several coefficient functionals for functions belonging to this class are provided. The main aim of this paper is to find estimates of the difference and of sum of successive coefficients, bounds of the sum of the first n coefficients and bounds of the n-th coefficient. The obtained results are used to determine coefficient estimates for both functions convex in the imaginary-axis direction with real coefficients and typically real functions. Moreover, the sum of the first initial coefficients for functions with a positive real part and with a fixed second coefficient is estimated.

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Belitskii, Genrich, and Vadim Tkachenko. "On solvability of linear difference equations in smooth and real analytic vector functions of several variables." Integral Equations and Operator Theory 18, no. 2 (June 1994): 123–29. http://dx.doi.org/10.1007/bf01192455.

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SONO, KEIJU. "PAIR CORRELATION OF LOW-LYING ZEROS OF QUADRATIC -FUNCTIONS." Nagoya Mathematical Journal 223, no. 1 (August 18, 2016): 87–135. http://dx.doi.org/10.1017/nmj.2016.26.

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In this paper, we investigate the nontrivial zeros of quadratic $L$-functions near the real axis. Assuming the generalized Riemann hypothesis, we give an asymptotic formula for the weighted pair correlation function of quadratic $L$-functions associated to the Kronecker symbols. From this formula, we obtain several results on the rate of simple zeros of quadratic $L$-functions and on the average distance of such nontrivial zeros.

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De Angelis, Valerio. "Positivity conditions for polynomials." Ergodic Theory and Dynamical Systems 14, no. 1 (March 1994): 23–51. http://dx.doi.org/10.1017/s0143385700007719.

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AbstractWe study several notions of positivity for a class of real-valued functions of several variables that includes the Laurent polynomials. We show that Handelman's positivity condition is characterized by boundedness of the associated Legendre transformation, or boundedness of the entropy function, while another notion of positivity here introduced characterizes the mapping property of the Legendre transformation derived by Marcus and Tuncel for beta functions. Several examples are given to distinguish the various notions of positivity.

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Grozev, Georgi R., and Qazi I. Rahman. "Reconstruction of Entire Functions From Irregularly Spaced Sample Points." Canadian Journal of Mathematics 48, no. 4 (August 1, 1996): 777–93. http://dx.doi.org/10.4153/cjm-1996-040-7.

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AbstractLet where {λn}n ∈ Ζ is a sequence of real numbers such that |λn — n| ≤ Δ for some Δ > 0 and all n ∈ ℤ . Extending an obvious property of sin πz to which the function G reduces when Δ = 0 we show that is bounded by a constant independent of n. The result is then applied to a problem concerning derivative sampling in one and several variables.

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Riza, Ion, and Marius Constantin Popescu. "Modeling of Diffusion with Bessel Functions." Applied Mechanics and Materials 760 (May 2015): 269–74. http://dx.doi.org/10.4028/www.scientific.net/amm.760.269.

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The equation with partial derivatives studied in this paper models the diffusion of oxygen through a passive layer made up of two oxides at low temperature or three oxides of iron at high temperature, estimating the fact that the corrosion phenomenon takes place into the oxides interface only after the oxygen penetrates the oxides layer. We model and analyze the diffusion phenomenon to which, until now, only the Bessel functions were recommended. In order to solve the differential equations with partial derivatives which model the diffusion, some analytic solutions with Bessel functions were obtained. These functions can be used in several technical domains due to the fact that they admit both real and imaginary input values.

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Yamasaki, Nobuyuki. "Responsive Multithreaded Processor for Distributed Real-Time Systems." Journal of Robotics and Mechatronics 17, no. 2 (April 20, 2005): 130–41. http://dx.doi.org/10.20965/jrm.2005.p0130.

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The Responsive MultiThreaded (RMT) Processor is a system LSI that integrates almost all functions for parallel/distributed real-time systems including robots, intelligent rooms/buildings, ubiquitous computing systems, and amusement systems. Concretely, the RMT Processor integrates real-time processing (RMT Processing Unit), real-time communication (Responsive Link II), computer I/O peripherals (DDR SDRAM I/Fs, DMAC, PCI-X, USB2.0, IEEE1394, etc.), and control I/O peripherals (PWM generators, pulse counters, etc.). The RMT Processor, with a design rule of 0.13<I>μ</I>m CMOS Cu 1P8M and a die size 10.0mm square, was fabricated by TSMC. The RMT Processing Unit (RMT PU) executes eight prioritized threads simultaneously using fine-grained multithreading based on priority, called the RMT architecture. Priority of real-time systems is introduced into all functional units, including cache, fetch, and execution, so the RMT PU guarantees real-time execution of prioritized threads. If resource conflicts occur at functional units, higher priority threads overtake lower priority threads. Flexible powerful vector operation units for multimedia processing are also designed. System designers use on-chip functions easily by connecting required I/Os to this chip and the designers realize distributed control by connecting several RMT Processors with their own functions via Responsive Link II.

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Krieger, Henry A. "Stochastic orderings induced by star-shaped functions." International Journal of Mathematics and Mathematical Sciences 14, no. 4 (1991): 639–64. http://dx.doi.org/10.1155/s016117129100087x.

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The non-decreasing functions whicl are star-shaped and supported above at each point of a non-empty closed proper subset of the real line induce an ordering, on the class of distribution functions with finite first moments, that is strictly weaker than first degree stochastic dominance and strictly stronger than second degree stochastic dominance. Several characterizations of this ordering are developed, both joint distribution criteria and those involving only marginals. Tle latter are deduced from a decomposition theorem, which reduces the problem to consideration of certain functions which are star-shaped on the complement of an open interval.

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