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In this paper, we introduce a ground-breaking approach to defining fractional calculus for a selected class of analytic functions. Our new definitions, based on a novel and intuitive understanding of fractional derivatives and integrals, offer improved mathematical tractability for a variety of applications, including physics, engineering and finance. Our approach significantly simplifies the complexity of mathematical functions compared to the traditional Riemann-Liouville approach, by using simple functions rather than special functions, while preserving the intrinsic sense of fractional calculus. This article not only presents our proposed definitions but also provides a thorough analysis of their properties and advantages. The conclusion of this paper discusses the potential for future research in the field of fractional calculus. [ABSTRACT FROM AUTHOR]

Let A be a complex unital Banach algebra and D be a non-empty open connected subset of C. Let f be a holomorphic A-valued function on D. We set: ∑(f) = {z ∈ D | f(z) ∉ ∈ Inv(A)}, where Inv(A) is the set of all invertible elements in A. In this paper, we give a description of ∑(f) using the classical spectrum of f(z) (z ∈ D). Moreover, within the framework of this paper, we give a partial positive answer to the following problem which was posed by B. Aupetit: If the usual spectrum σ(f(z)) is polar for all z ∈ D, is it true that ∑(f) is polar? [ABSTRACT FROM AUTHOR]

The research presented in this paper concerns the notion of geometric function theory called fuzzy differential subordination. Using the technique associated with fuzzy differential subordination, a new subclass of analytic functions related with the strongly Janowski-type functions is defined. The class is introduced by using a new operator defined by the convolution of the generalized Sălăgean differential operator and Choi integral linear operator. Certain inclusion relations are proved for this class by using the notion of fuzzy differential subordination. In addition, new fuzzy differential subordinations are obtained that characterize this class. [ABSTRACT FROM AUTHOR]

AbstractLet ⅅ be the unit disk in the complex plane ℂ. For α > −1, the weighted Sobolev disk algebra SA(ⅅ, dAα) consists of all analytic functions in the weighted Sobolev space W2,2(ⅅ, dAα). In this paper, we prove that the multiplication operator is similar to on SA(ⅅ, dAα) if and only if n = m, where n, m are positive integers. Then we characterize when a bounded operator P on SA(ⅅ, dAα) belongs to the commutant of by using the matrix representation of P. In addition, we compute the exact norm of Mz on SA(ⅅ, dAα). Finally, we prove that on the unweighted Sobolev disk algebra SA(ⅅ) the restrictions of to different invariant subspaces zkSA(ⅅ) (k ≥ 1) are not unitarily equivalent, and the restrictions of (n ≥ 2) to different invariant subspaces Sj (0 ≤ j < n) are also not unitarily equivalent. [ABSTRACT FROM AUTHOR]

This paper aims to introduce a measure of the non-univalency of a harmonic mapping. By using it, we find the best approximation of an analytic function by a univalent harmonic mapping. [ABSTRACT FROM AUTHOR]

AbstractThis paper is devoted to develop the concepts of semi-c-periodicity, c-uniform recurrence and almost automorphy for functions defined on vertical strips in the complex plane, where c is a non-zero complex number. As an extension of the study performed for functions defined on the real axis, this work aims to investigate the main properties of these classes of functions and establish their connections with the more known class of c-almost periodic functions defined on vertical strips. In fact, we resolve an open problem which was raised in 2020 for the real case. Additionally, we also use this approach to introduce an asymptotic version of these new classes of functions. [ABSTRACT FROM AUTHOR]

The object of the present paper is to derive some argument properties associated with meromorphic close-to-starlike and Bazilević functions in the punctured open unit disk. Furthermore, we investigate integral-preserving properties in a sector with some special cases of the main results presented here. [ABSTRACT FROM AUTHOR]

The usual process for solving a nonhomogeneous system of linear differential equations is to find the general complementary homogeneous solution first and then construct a particular solution from it. When can we flip the script on this process and compute a particular solution first? This paper argues this is possible when the nonhomogeneous forcing function is analytic. It presents two different series expansions for this particular particular solution using power series methods, and reveals a surprising connection to the more familiar variation of parameters formula. [ABSTRACT FROM AUTHOR]

The paper explores the impact of Palmer's spontaneous gesture of a red stripe that completed his abstract painting—emotionally and aesthetically—in response to a difficult analytic relationship. The red stripe arises from his search for greater openness, emotional freedom, and creative responses to the flow of communication with his patient. The analyst's ethical intentions are inward to be open and available to the influx of the patient's emotional world, and outward, found in actions and gestures with the patient striving for honesty, transparency, a willingness to take risks and accept accidents in a search for emotion truth and authentically being present. The analyst inhabits, gathers, and concentrates feeling that provides a medium for feelings to live, take shape, and be recognized by an analytic function called "the aesthetic" that then fosters "aesthetic experiences"—intense passages of shared living that are transformative. [ABSTRACT FROM AUTHOR]

This paper consists of two parts. The first part is devoted to the study of the Beltrami equation with a polar singularity in a circle centred at the origin, with a cut along the positive semiaxis. The coefficients of the equation have a first-order pole at the origin and do not belong to the class $ L_2(G). $ L 2 (G). Therefore, despite having a unique form, this equation is not covered in the analysis of I.N.Vekua [Generalized analytic functions. Nauka: Moscow; 1988. Russian] and needs to be independently studied. In the second part of the article, the coefficients of the equation are chosen so that the resulting solutions are continuous in a circle without a cut. These results can be used in the theory of infinitesimal bendings of surfaces of positive curvature with a flat point and in constructing a conjugate isometric coordinate system on a surface of positive curvature with a planar point. [ABSTRACT FROM AUTHOR]

In the paper, we prove a general universality theorem for the Riemann zeta-function ζ (s) on approximation of a class of analytic functions by generalized shifts ζ (s + ia(τ)). Here a(τ) is a real-valued continuous increasing to +∞ function, uniformly distributed modulo 1 and such that |ζ(σ + ia(τ) + it)|2, for σ > 1/2, has a traditional mean estimate for every t ∈ ℝ. For example, the function tv(τ), v > 0, where t(τ) is the Gram function, satisfies the hypotheses of the proved theorem. For the proof, the method of weak convergence of probabilistic measures in the space of analytic functions is developed. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the Riemann boundary value problems for the analytic functions with period a π (a > 0) in the situation where the solution can be unbounded at z = ± ∞ i. When the jump curve is a closed contour, by using the tangent transformation ζ = tan ⁡ (z / a) , we transform the singularities ± ∞ i on the z plane to the singularities ± i on the ζ plane. When the jump curve is the real axis, by using the transformation ω = e i z , we transform the singularities ± ∞ i on the z plane to the singularities 0 and ∞ on the ω plane. Thus, the original periodic Riemann boundary value problems are reduced to the classical Riemann boundary value problems whose solutions and the corresponding solvability conditions are well known. [ABSTRACT FROM AUTHOR]

This paper investigates multiplicative doubly quasi-periodic Riemann boundary value problems for null-solutions to a class of polynomially Cauchy-Riemann equations, i.e. meta-analytic functions. To begin with, the decomposition theorem for multiplicative doubly quasi-periodic meta-analytic functions is constructed. Then the growth order of multiplicative doubly quasi-periodic meta-analytic functions at origin is discussed. Finally, Riemann boundary value problems for multiplicative doubly quasi-periodic analytic functions and for multiplicative doubly quasi-periodic meta-analytic functions are investigated, respectively. The explicit integral expressions of their solutions and conditions of solvability are attained. [ABSTRACT FROM AUTHOR]

Let Π = { z ∈ C / ℑ z > 0 } , the upper half-plane in the complex plane C . Let H (Π) be the set of all analytic functions on Π and S (Π) be the set of all analytic self-maps on Π. For φ ∈ S (Π) , N ∈ N 0 = N ∪ { 0 } and ψ (N) = (ψ 0 , ψ 1 , ... , ψ N) , where ψ j ∈ H (Π) , j = 0 , 1 , ... , N , define an operator T ψ (N) , φ (f) := ∑ j = 0 N ψ j ⋅ (f (j) ∘ φ) , f ∈ H (Π). In this paper, we characterize the boundedness and compactness of the operator T ψ (N) , φ on the Hardy, weighted-Bergman spaces on Π to weighted-type spaces on Π. [ABSTRACT FROM AUTHOR]

In this paper, first we prove two refined Bohr-type inequalities associated with area for bounded analytic functions f (z) = ∑ n = 0 ∞ a n z n in the unit disk. Later, we establish the Bohr-type operator on analytic functions and sections. [ABSTRACT FROM AUTHOR]

Let H be the class of complex-valued harmonic mappings f = h + g ¯ defined in the unit disk D := { z ∈ C : | z | < 1 } , where h and g are analytic functions in D with the normalization h (0) = 0 = h ′ (0) − 1 and g (0) = 0. Let H 0 = { f = h + g ¯ ∈ H : g ′ (0) = 0 }. Let P H 0 (M) := { f = h + g ¯ ∈ H 0 : Re (z h ′ ′ (z)) > − M + | z g ′ ′ (z) | , z ∈ D and M > 0 }. be the class of harmonic univalent mappings in the unit disk D [Ghosh N, Allu V. On some subclasses of harmonic mappings. Bull Aust Math Soc. 2020;101:130–140.]. In this paper, we obtain the sharp Bohr–Rogosinski inequality, improved Bohr inequality, refined Bohr inequality and Bohr-type inequality for the class P H 0 (M). [ABSTRACT FROM AUTHOR]

In this paper, we study the corona theorem and Wolff theorem for the multiplier algebra of the Besov–Morrey space $ \mathcal {B}_p^{\lambda }(s) $ B p λ (s) when $ 0 0 < λ , s < 1 < p < ∞. Here the Besov–Morrey space $ \mathcal {B}_p^{\lambda }(s) $ B p λ (s) is the space consisting of those analytic functions on the unit disc $ {\mathbb D} $ D such that $ |f'(z)|^p(1-|z|^2)^{p+s-2}{\rm d}A(z) $ | f ′ (z) | p (1 − | z | 2) p + s − 2 d A (z) is a $ \lambda s $ λs -Carleson measure. [ABSTRACT FROM AUTHOR]

A class $ \mathcal {F} $ F consisting of analytic functions $ f(z)=\sum _{n=0}^{\infty }a_nz^n $ f (z) = ∑ n = 0 ∞ a n z n in the unit disc $ \mathbb {D}=\{z\in \mathbb {C}:|z| D = { z ∈ C : | z | < 1 } satisfies a Bohr phenomenon if there exists an $ r_f>0 $ r f > 0 such that \[ \sum_{n=1}^{\infty}|a_n|r^n\leq{d}\left(f(0),\partial f(\mathbb{D})\right) \] ∑ n = 1 ∞ | a n | r n ≤ d (f (0) , ∂f (D)) for every function $ f\in \mathcal {F} $ f ∈ F , and $ |z|=r\leq r_f $ | z | = r ≤ r f . The largest radius $ r_f $ r f is the Bohr radius and the inequality $ \sum _{n=1}^{\infty }|a_n|r^n\leq {d}\left (f(0),\partial f(\mathbb {D})\right) $ ∑ n = 1 ∞ | a n | r n ≤ d (f (0) , ∂f (D)) is Bohr inequality for the class $ \mathcal {F} $ F , where 'd' is the Euclidean distance. In this paper, we prove sharp refinement of the Bohr–Rogosinski inequality for certain classes of harmonic mappings. [ABSTRACT FROM AUTHOR]

A Banach space X of analytic function in , the unit disc in , is said to be admissible if it contains the polynomials and convergence in X implies uniform convergence in compact subsets of. If X and Y are two admissible Banach spaces of analytic functions in and g is a holomorphic function in , g is said to be a multiplier from X to Y if g ·f ∈ Y for every f ∈ X. The space of all multipliers from X to Y is denoted M (X, Y), and M (X) will stand for M (X, X). The closed graph theorem shows that if g ∈ M (X, Y) then the multiplication operator Mg, defined by Mg (f) = g · f, is a bounded operator from X into Y. It is known that M (X) ⊂ H∞ and that if g ∈ M (X), then ∥g∥H∞ ≤ ||Mg||. Clearly, this implies that M (X, Y) ⊂ H∞ if Y ⊂ X. If Y ⊄ X, the inclusion M (X, Y) ⊂ H∞ may not be true. In this paper we start presenting a number of conditions on the spaces X and Y which imply that the inclusion M (X, Y) ⊂ H∞ holds. Next, we concentrate our attention on multipliers acting an BMOA and some related spaces, namely, the Qs-spaces (0

In this paper, we give the nth derivertive criterion for functions belonging to function spaces H K 2 . Furthermore, some sufficient conditions for coefficients of the linear differential equation f (k) + A k − 1 (z) f (k − 1) + ⋯ + A 1 (z) f ′ + A 0 (z) f = A k (z) are found such that all solutions belong to the H K 2 spaces, where A j (z) are analytic functions in D , j = 0 , ... , k. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to study the structure of Green's function for heat equation in several spatial dimensions and with rough heat conductivity coefficient. We take the heat conductivity coefficient to be of bounded variation in the x direction and study the dispersion in the (y, z) direction. The goal is to understand the coupling of dissipation across rough heat conductivity and the multi-dimensional dispersion in the Green's function H (x → , t ; x → *) , x → = (x , y , z). A series of exponential functions of path integral with coefficients over a field of complex analytic functions around imaginary axis are formulated in the Laplace and Fourier transforms variables. The Green's function in the transformed variables is written as the sum of these integrals over random paths. The integral over a random path is rearranged through the reflection property over a variation of heat conductivity coefficient and become a simple form in terms of path phase and amplitude. The complex analytic and combinatorics method is then used to yield a precise pointwise structure of the Green's function in the physical domain (x → , t). [ABSTRACT FROM AUTHOR]

In this paper we prove among others that f y z − z f x ≤ 1 2 π y z − z x ∫ γ f ξ R y ξ R x ξ d ξ ≤ 1 2 π y z − z x ∫ γ f ξ d ξ ξ − y ξ − x , where f : D ⊂ C → C is an analytic function on the domain D, x, y, z ∈ B with σ x , σ y ⊂ D , R y ⋅ , R x ⋅ are the resolvent functions for the elements y and x, and γ is a closed rectifiable path in D and such that σ x , σ y ⊂ i n s γ. Applications for the exponential function on the Banach algebra B are also given. [ABSTRACT FROM AUTHOR]

A hypersurface X (resp., a pair of hypersurfaces { Y , Z }) is called a hypersurface (resp., a pair of hypersurfaces) of uniqueness for holomorphic mappings from C to P N (C) if for two non-degenerate holomorphic mappings f , g from C to P N (C) , the condition ν f (X) = ν g (X) (resp., ν f (Y) = ν g (Y) , ν f (Z) = ν g (Z)) implies f ≡ g , where for a mapping φ, ν φ (V) denotes the pull-back of a divisor V in P N (C) by φ. In this paper, we give some classes of hypersurfaces and of pairs of hypersurfaces of uniqueness for holomorphic mappings from C to P N (C). [ABSTRACT FROM AUTHOR]

This paper is dealing with the problem of finding the "best" multipoint Padé approximant of an analytic function when data in some neighborhoods of sampling points are more important than others. More exactly, we obtain a multipoint Padé approximants as limits of best rational Lp-approximations on union of disks, when the measure of them tends to zero with different speeds. As such, this technique provides useful qualitative and analytic information concerning the approximants, which is difficult to obtain from a strictly numerical treatment. [ABSTRACT FROM AUTHOR]

Each function which is analytic and univalent in the open unit disk in the complex plane has a tangential boundary limit almost everywhere with an approach having exponential contact. In this paper, we obtain corresponding results for the fractional derivatives of univalent functions, for . [ABSTRACT FROM AUTHOR]

The present paper gives a formal solution of a certain Abel-type integral equation involving the Appell hypergeometric function in the kernel. The integral equation and its solution give rise to new forms of generalized fractional calculus operators (viz. the generalized fractional integrals and generalized fractional derivatives). These and their various consequences are also mentioned. The concluding remarks briefly point out possibilities of further work concerning the operators studied in this paper. [ABSTRACT FROM AUTHOR]

This paper studies limiting behaviour of infeasible weighted central paths in semidefinite programming under strict complementarity assumption. It is known that weighted central paths associated with the 'Cholesky factor' symmetrization of the μ-parameterized centring condition are well defined for some classes of weight matrices, and they are analytic functions of μ for μ>0, sufficiently small. In this paper, we show that these paths, considered as functions of √μ, can be analytically extended to μ=0. Moreover, we show that the paths are analytic functions of μ at μ=0 if and only if the weight matrix is block diagonal in terms of the optimal block partition of variables. [ABSTRACT FROM AUTHOR]

This paper presents an argument against the wider adoption of complex forms of data analysis, using multi-level modeling (MLM) as an extended case study. MLM was devised to overcome some deficiencies in existing datasets, such as the bias caused by clustering. The paper suggests that MLM has an unclear theoretical and empirical basis, has not led to important practical research results, is largely unnecessary due to the availability of a range of alternatives, and is therefore overly complex, making research reports harder to read and understand for a general audience for no apparent analytic gain. Above all, the paper shows via examples that MLM has made so little difference in practice that it is worth us also considering its analytic costs. These costs include the promotion of an educational form of 'asterix economics', the creation of unworkable premises such as denying the existence of population data, and the tension between the contradictory need for both a large and small number of cases at each sub-level. The paper concludes by outlining a substantial number of alternative methods of analysis which can have the same effect as MLM in examining structures in the data or overcoming the problems caused by clustering. Many of these alternatives are easier to use and understand, do not require specialist software, and avoid the problems - such as having to ignore cases with missing variables - created by the use of MLM. [ABSTRACT FROM AUTHOR]

The document is an introduction to Issue 34:1 of Psychoanalytic Dialogues, written in November 2023. The authors acknowledge the recent conflict between Hamas and Israel and the impact it has had on communities worldwide, including within the field of psychoanalysis. They emphasize the importance of dialogue and recognition of the Other in the face of intergenerational trauma. The issue includes papers that explore topics such as enactment in therapy, the analyst's mortality, and working with traumatized Afghan students. The authors hope that these papers will facilitate a transformative dialogue for readers. [Extracted from the article]

This paper concerns univalent analytic functions f for which log ⁡ f ′ belong to Dirichlet-Morrey spaces. We establish some characterizations of Dirichlet-Morrey domains. Our results involve Schwarzian derivatives, quasiconformal extensions and Grunsky kernels of univalent functions. [ABSTRACT FROM AUTHOR]

In this paper we prove that the restricted Ahlfors-Beurling transform of a Lebesgue integrable function is A-integrable and derive an analogue of Riesz's equality holds. [ABSTRACT FROM AUTHOR]

In this paper, we consider logharmonic mappings which are stable univalent, stable starlike, stable with positive real part, stable close to starlike and stable typically real. We prove that the mappings are starlike logharmonic (resp. logharmonic univalent, close to starlike logharmonic, typically real logharmonic) for all if and only if the mappings are starlike analytic (resp. analytic univalent, close to starlike analytic, typically real analytic) for all . We also prove growth distortion theorems for these family of functions. [ABSTRACT FROM AUTHOR]

This paper considers controllability of multi-agent systems with periodically switching topologies and switching leaders. The concept of m-periodic controllability is proposed, and a criterion for m-periodic controllability is established. The effect of the duration of subsystems on controllability is analysed by utilising a property of analytic functions. In addition, the influence of switching periods on controllability is investigated, and an algorithm is proposed to search for the fewest periods to ensure controllability. A necessary condition for m-periodic controllability is obtained from the perspective of eigenvectors of the subsystems’ Laplacian matrices. For a system with switching leaders, it is proved that switching-leader controllability is equivalent to multiple-leader controllability. Furthermore, both the switching order and the tenure of agents being leaders have no effect on the controllability. Some examples are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Letbe the open unit disk in the complex planeandthe class of all analytic functions on. Letbe an analytic self-map ofand. In this paper, the boundedness and compactness for product-type operators from Zygmund spaces to Bloch–Orlicz spaces are characterized by constructing some new test functions in Zygmund spaces. [ABSTRACT FROM AUTHOR]

Given a prime number p we consider C p the topological completion of the algebraic closure of the field of p-adic numbers with respect to the usual p-adic absolute value. In this paper, we point out new connections between zeros and singularities of the trace functions associated with arbitrary elements of C p. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish properties of solutions to the α-harmonic equations: Δ α (f (z)) = ∂ z [ (1 − | z | 2 ) − α ∂ ¯ z f ] (z) = g (z) , where g : D ¯ → C is a continuous function and D ¯ denotes the closure of the unit disc D in the complex plane C . We obtain Schwarz type and Schwarz-Pick type inequalities for solutions to the α-harmonic equation. In particular, for g ≡ 0 , solutions to the above equation are called α-harmonic functions. We determine the necessary and sufficient conditions for an analytic function ψ to have the property that f ∘ ψ is α-harmonic function for any α-harmonic function f. Furthermore, we discuss the Bergman-type spaces on α-harmonic functions. [ABSTRACT FROM AUTHOR]

Structure and distribution of cells in histological images cause considerable variability among the tissue patterns and make the retrieving and classification as challenging tasks for this type of medical images. In this paper, we propose to extract four local features, namely local energetic information, local structural information, local geometric information, and local patterns to represent the huge texture variability of the histological images in a feature space. For extracting these features, the Riesz transform and Monogenic local binary patterns are used. Riesz transform is an extension of the Hilbert transform for 2-D signals. It provides a monogenic representation for an image where we can capture some local structure information. We used these local features for classification and retrieving purposes. We validated our proposed method on two multiclass archives of histological images, namely Kimiapath24 and Kather datasets. We achieved performance of more than 90% for classification and retrieval in two datasets. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of numerical analytic continuation of an analytic functionon a strip domain, where the data are given approximately only on the line. This is a unilaterally ill-posed problem, and due to the idea of modified ‘kernel’, a novel unilateral regularization method is constructed. The convergence rate is also obtained. Numerical experiments show that the method works effectively. The comparisons of numerical results between the Fourier method and our modified method are also provided. [ABSTRACT FROM AUTHOR]

Here we consider the following functional equation, Ψ (X (t , x , Ψ (x))) = Y (t , x , Ψ (x)) , where X (t , x , y) and Y (t , x , y) are holomorphic functions in t < θ , | x | < θ , | y | < θ , and x is a function of t such that x = x (t). If we have a solution of nonlinear second order difference equations, then we can write general solutions by making use of a solution Ψ. In this present paper, we will prove the existence of a solution of the above functional equation, after we will show a relationship between the above functional equation and nonlinear second order q-difference equations which has only one characteristic value. [ABSTRACT FROM AUTHOR]

This paper studies the performance of pairs trading strategy under a specific spread model. Based on the empirical evidence of mean reversion and jumps in the spread between pairs of stocks, we assume that the spread follows a Lévy-driven Ornstein–Uhlenbeck process with two-sided jumps. To evaluate the performance of a pairs trading strategy, we propose the expected return per unit time as the value function of the strategy. Significantly different from the current related works, we incorporate an excess jump component into the calculation of return and time cost. Further, we obtain the analytic expression of strategy value function, where we solve out the probabilities of crossing thresholds via the Laplace transform of first passage time of the Lévy-driven Ornstein–Uhlenbeck process in one-sided and two-sided exit problems. Through numerical illustrations, we calculate the value function and optimal thresholds for a spread model with symmetric jumps, reveal the non-negligible contribution of incorporating the excess jumps into the value function, and analyze the impact of model parameters on the strategy performance. [ABSTRACT FROM AUTHOR]

Of concern on this paper are complex-valued functions defined on the integer lattice (i.e. the set [image omitted] ) which are discrete analytic according to the definition given by Ferrand. In particular, we will study a Hilbert space consisting of the boundary values of discrete analytic functions defined on a finite simply connected union of unit squares of the integer lattice (a simple region), which is a discrete version of the Szëgo space. We will prove that this space admits a reproducing kernel, the discrete Szëgo kernel and will develop a general method to construct it. To sum up, the main merit of this paper is to present by means of an orthogonal projection operator a way to select among boundary values, those that can be extended to an analytic continuation. [ABSTRACT FROM AUTHOR]

In this paper, we develop the concept of polar analyticity introduced in Bardaro C, et al. [A fresh approach to the Paley-Wiener theorem for Mellin transforms and the Mellin-Hardy spaces. Math Nachr. 2017;290:2759–2774] and successfully applied in Mellin analysis and in quadrature of functions defined on the positive real axis (see Bardaro C, et al. [Quadrature formulae for the positive real axis in the setting of Mellin analysis: sharp error estimates in terms of the Mellin distance]. Calcolo. 2018;55(3):26. Available from: ]). This appears as a simple way to describe functions which are analytic on a part of the Riemann surface of the logarithm. We study analogues of Cauchy's integral theorems for polar-analytic functions and obtain two series expansions in terms of polar-derivatives and Mellin polar-derivatives, respectively. We also describe some geometric properties of polar-analytic functions related to conformality. By these studies, we launch the proposal to develop a complete complex function theory, independent of the classical function theory, which is built upon the new notion of polar analyticity. [ABSTRACT FROM AUTHOR]

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Integral representation formulas play an essential role in the modern function theory. They serve to solve boundary value problems for differential equations. As an example of such integral representations is the Cauchy formula for analytic functions but it, thus, is just a special case of the Cauchy–Pompieu formula. Higher Cauchy–Pompieu formulas in the complex, hypercomplex and Clifford analysis have been presented by iteration in [Begehr, H., 2000, Integral representations for differentiable functions. Ricci, P. E. (Ed.), Current Problems in Analysis and Mathematical Physics. Papers of the 2nd international symposium dedicated to the memory of Prof. Gaetano Fichera (1922–1996). (Roma: Dipartimento di Matematica, Universita di Roma), 111–130, Begehr, H., 2002, Integral representations in complex, hypercomplex and Clifford analysis. Integral Transforms and Special Functions , 13(3), 223–241]. In this paper, certain special cases of higher order Cauchy–Pompeiu integral representations are given. [ABSTRACT FROM AUTHOR]

Tyre behavior plays an important role in vehicle dynamics research. Knowledge of tyre properties is necessary to properly design vehicle components and advance control system. For that purpose mathematical models of the tyre are being used in vehicle simulation models. The Magic Formula Tyre Model is a semi-empirical tyre model which describes tyre behavior quite accurately. The Magic Formula Tyre Model needs a set of parameters to describe the tyre properties; the determination of these parameters is dealt with in this paper. A new method based on genetic techniques is used to determine these parameters. The main advantages of the method are its simplicity of implementation and its fast convergence to optimal solution, with no need of deep knowledge of the searching space. So to start the search, it is not necessary to know a set of starting values of the Magic Formula parameters. The comparison between analytical optimization methods and the method proposed is discussed din this paper. [ABSTRACT FROM AUTHOR]

The analytic hierarchy process (AHP) is a powerful multiple-criteria decision analysis technique for dealing with complex problems. Traditional AHP forces decision-makers to converge vague judgements to single numeric preferences in order to estimate the pairwise comparisons of all pairs of objectives and decision alternatives required in the AHP. The resultant rankings of alternatives cannot be tested for statistical significance and it lacks a systematic approach that addresses managerial/soft aspects. To overcome the above limitations, the present paper presents a modified analytic hierarchy process, which incorporates probabilistic distributions to include uncertainty in the judgements. The vector of priorities is calculated using Monte Carlo simulation. The final rankings are analysed for rank reversal using analysis of variance, and managerial aspects (stake holder analysis, soft system methods, etc.) are introduced systematically. The focus is on the actual methodology of the modified analytic hierarchy process, which is illustrated by a brief account of a case study. [ABSTRACT FROM AUTHOR]

In the paper, a theorem on the approximation of collections of a wide class of analytic functions by collections of shifts of zeta-functions with periodic co-efficients involving imaginary parts of non-trivial zeros of the Riemann zeta-function is obtained. For this, a version of the Montgomery pair correlation conjecture is required. [ABSTRACT FROM AUTHOR]

In this paper, we introduce generalizations of the classical growth order and the growth type of analytic functions in the context of polymonogenic functions. Polymonogenic functions are null-solutions of higher integer order iterates of a generalized higher dimensional Cauchy–Riemann operator. One of the main goals is to prove generalizations of the famous Lindelöf–Pringsheim theorem linking explicitly these growth orders and growth types with the Taylor series coefficients in the context of this function class. [ABSTRACT FROM PUBLISHER]

The Hardy space of vector valued analytic functions in tube domains in and with values in Banach space are defined. Analytic functions in tube domains in with values in Hilbert space which have functions with values in Hilbert space as distributional boundary value are proved to be in. A Poisson integral representation for such vector valued analytic functions is obtained. [ABSTRACT FROM AUTHOR]