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We establish that Grunsky norm of any normalized univalent function on a quasidisk is completely determined by the squares of holomorphic abelian differentials (in contrast to Teichmüller norm, which relates to all integrable holomorphic quadratic differentials). The result has important interesting applications in several fields of geometric function theory: it provides an explicit representation of Fredholm eigevalues of all quasiconformal curves, sheds a new light on the distortion theory for univalent functions with quasiconformal extension, etc. [ABSTRACT FROM AUTHOR]

This article addresses the problem of boundary correspondence for a sequence of homeomorphisms that change the capacity of a condenser in a controlled way. To study the overall boundary behavior of these mappings, we introduce some capacity metrics in a sequence of domains with nondegenerate core. Completions with respect to these metrics add to the domains new points called boundary elements. As one of the consequences, we obtain not only sufficient conditions for the global uniform convergence of a sequence of homeomorphisms, but some applications to elasticity theory as well. [ABSTRACT FROM AUTHOR]

In this note, we present the state-of-the-art theory of bi-Sobolev mappings. We recall that f is a Sobolev homeomorphism if f belongs to W loc 1 , 1 ∩ Hom (Ω ; Ω ′) , and f is a bi-Sobolev map if and only if f and f - 1 are Sobolev homeomorphisms. This concept, introduced in Hencl et al. (J. Math. Anal. Appl. 355, 22–32 2009), plays a central role in Geometric Function Theory. For instance, we just mention here that maps of bi-Sobolev type are strictly related to the notion of mappings of finite distortion; see, among others, the papers (Hencl and Koskela 2014) Pratelli (Nonlinear Anal. 154, 258–268 2017). [ABSTRACT FROM AUTHOR]

In light of the Alexander transformation, the class of spirallike functions is significant. The characteristics of special functions also appear very frequently in Geometric function theory. In this paper, we find the radii of γ -spirallike and convex γ -spirallike of order α of certain special functions. [ABSTRACT FROM AUTHOR]

In this paper, we prove a Schwarz lemma for the pentablock. The pentablock P is defined by P = { (a 21 , tr A , det A) : A = [ a ij ] i , j = 1 2 ∈ B 2 × 2 } where B 2 × 2 denotes the open unit ball in the space of 2 × 2 complex matrices. The pentablock is a bounded non-convex domain in C 3 which arises naturally in connection with a certain problem of μ -synthesis. We develop a concrete structure theory for the rational maps from the unit disc D to the closed pentablock P ¯ that map the unit circle T to the distinguished boundary b P ¯ of P ¯ . Such maps are called rational P ¯ -inner functions. We give relations between P ¯ -inner functions and inner functions from D to the symmetrized bidisc. We describe the construction of rational P ¯ -inner functions x = (a , s , p) : D → P ¯ of prescribed degree from the zeroes of a, s and s 2 - 4 p . The proof of this theorem is constructive: it gives an algorithm for the construction of a family of such functions x subject to the computation of Fejér–Riesz factorizations of certain non-negative trigonometric functions on the circle. We use properties and the construction of rational P ¯ -inner functions to prove a Schwarz lemma for the pentablock. [ABSTRACT FROM AUTHOR]

In this paper, we consider complete noncompact Kähler metrics with nonnegative holomorphic sectional curvature. In particular, we prove some results on existence, non-existence, and function theory on such manifolds. [ABSTRACT FROM AUTHOR]

We have previously shown that a -fold holomorphic covering of a domain in the complex plane by another domain is extremal in the majorization principle for -valent functions and quadratic forms associated with Green's functions of these domains. In this paper, dual majorization principles involving both Green's and Neumann functions are obtained, in which -fold coverings are also extremal. The results are exemplified by applications of these principles to geometric function theory. [ABSTRACT FROM AUTHOR]

According to the theory of regular geometric functions, the relevance of geometry to analysis is a critical feature. One of the significant tools to study operators is to utilize the convolution product. The dynamic techniques of convolution have attracted numerous complex analyses in current research. In this effort, an attempt is made by utilizing the said techniques to study a new linear complex operator connecting an incomplete beta function and a Hurwitz–Lerch zeta function of certain meromorphic functions. Furthermore, we employ a method based on the first-order differential subordination to derive new and better differential complex inequalities, namely differential subordinations. [ABSTRACT FROM AUTHOR]

We consider the problem of extreme partition of the complex plane well known in the geometric theory of functions. We obtain estimates for the maximum value of the product of some powers of inner radii of n disjoint domains in the complex plane with respect to n arbitrary points of the plane one of which can be located at infinity. The estimates established in the paper can be applied to various problems of the geometric theory of functions. [ABSTRACT FROM AUTHOR]

We explore the correspondence between geometric function theory (GFT) and quantum field theory (QFT). The crossing symmetric dispersion relation provides the necessary tool to examine the connection between GFT, QFT, and effective field theories (EFTs), enabling us to connect with the crossing-symmetric EFT-hedron. Several existing mathematical bounds on the Taylor coefficients of Typically Real functions are summarized and shown to be of enormous use in bounding Wilson coefficients in the context of 2-2 scattering. We prove that two-sided bounds on Wilson coefficients are guaranteed to exist quite generally for the fully crossing symmetric situation. Numerical implementation of the GFT constraints (Bieberbach-Rogosinski inequalities) is straightforward and allows a systematic exploration. A comparison of our findings obtained using GFT techniques and other results in the literature is made. We study both the three-channel as well as the two-channel crossing-symmetric cases, the latter having some crucial differences. We also consider bound state poles as well as massless poles in EFTs. Finally, we consider nonlinear constraints arising from the positivity of certain Toeplitz determinants, which occur in the trigonometric moment problem. [ABSTRACT FROM AUTHOR]

The study of the Dirichlet problem with arbitrary measurable data for harmonic functions in the unit disk 𝔻 is due to the dissertation of Luzin. Later on, the known monograph of Vekua was devoted to boundary-value problems only with Hölder continuous data for generalized analytic functions, i.e., continuous complex-valued functions f(z) of the complex variable z = x + iy with generalized first partial derivatives by Sobolev satisfying equations of the form ∂ z ¯ f + af + b f ¯ = c , where the complexvalued functions a; b, and c are assumed to belong to the class Lp with some p > 2 in smooth enough domains D in ℂ. Our last paper [12] contained theorems on the existence of nonclassical solutions of the Hilbert boundaryvalue problem with arbitrary measurable data (with respect to logarithmic capacity) for generalized analytic functions f : D → ℂ such that ∂ z ¯ f = g with the real-valued sources. On this basis, the corresponding existence theorems were established for the Poincaré problem on directional derivatives and, in particular, for the Neumann problem to the Poisson equations △U = G ∈ Lp; p > 2, with arbitrary measurable boundary data over logarithmic capacity. The present paper is a natural continuation of the article [12] and includes, in particular, theorems on the existence of solutions for the Hilbert boundary-value problem with arbitrary measurable data for the corresponding nonlinear equations of the Vekua type ∂ z ¯ f z = h z q f z . On this basis, existence theorems were also established for the Poincar´e boundary-value problem and, in particular, for the Neumann problem for the nonlinear Poisson equations of the form △U(z) = H(z)Q(U(z)) with arbitrary measurable boundary data over logarithmic capacity. The Dirichlet problem was investigated by us for the given equations, too. Our approach is based on the interpretation of boundary values in the sense of angular (along nontangential paths) limits that are a conventional tool of the geometric function theory. As consequences, we give applications to some concrete semi-linear equations of mathematical physics arising from modelling various physical processes. Those results can also be applied to semi-linear equations of mathematical physics in anisotropic and inhomogeneous media. [ABSTRACT FROM AUTHOR]

The central purpose of this effort is to investigate analytic and geometric properties of a class of normalized analytic functions in the open unit disk involving Bernoulli's formula. As a consequence, some solutions are indicated by the well-known hypergeometric function. The class of starlike functions is investigated containing the suggested class. [ABSTRACT FROM AUTHOR]

Recently the author has presented a new approach to solving the coefficient problems for holomorphic functions based on the deep features of Teichmüller spaces. It involves the Bers isomorphism theorem for Teichmüller spaces of punctured Riemann surfaces. The aim of the present paper is to provide new applications of this approach and extend the indicated results to more general classes of functions [ABSTRACT FROM AUTHOR]

In this note, we formulate a new linear operator given by Airy functions of the first type in a complex domain. We aim to study the operator in view of geometric function theory based on the subordination and superordination concepts. The new operator is suggested to define a class of normalized functions (the class of univalent functions) calling the Airy difference formula. As a result, the suggested difference formula joining the linear operator is modified to different classes of analytic functions in the open unit disk. [ABSTRACT FROM AUTHOR]

Given a nonempty compact set in a proper subdomain of the complex plane, we denote the diameter of and the distance from to the boundary of by and , respectively. The quantity is invariant under similarities and plays an important role in geometric function theory. In case has the hyperbolic distance , we consider the infimum of the quantity over compact subsets of with at least two points, where stands for the hyperbolic diameter of . Let the upper half-plane be . We show that is positive if and only if the boundary of is uniformly perfect and for all , with equality holding precisely when is convex. [ABSTRACT FROM AUTHOR]

We consider a well-known problem of the geometric theory of functions on the extreme partition of the complex plane. For this problem, we establish estimates for the maximum value of the product of inner radii of n nonoverlapping domains with respect to n arbitrary points in the complex plane one of which may be infinitely remote. At present, the exact solutions of this problem are known only for n = 2, 3, 4. We establish estimates that can be used in various extreme problems of the geometric theory of functions. [ABSTRACT FROM AUTHOR]

We consider a quite general problem from the geometric theory of functions, namely, the problem of finding the maximal value of the product of inner radii of n nonoverlapping domains that contain points of the unit circle and are symmetric with respect to this circle and the γ power of the inner radius of a domain containing the origin. The posed problem is solved for n ≥ 20 and 1 < γ ≤ n 2 3 − q n . [ABSTRACT FROM AUTHOR]

We provide an analytical solution for the elastic fields in a two-dimensional unbounded isotropic body with a rigid inclusion. Our analysis is based on the boundary integral formulation of the elastostatic problem and geometric function theory. Specifically, we use the coordinate system provided by the exterior conformal mapping of the inclusion to define a density basis functions on the boundary of the inclusion, and we use the Faber polynomials associated with the inclusion for a basis inside the inclusion. The latter, which constitutes the main novelty of our approach, allows us to obtain an explicit series solution for the plane elastostatic problem for an inclusion of arbitrary shape in terms of the given arbitrary far-field loading. [ABSTRACT FROM AUTHOR]

Bieberbach's conjecture was very important in the development of geometric function theory, not only because of the result itself, but also due to the large amount of methods that have been developed in search of its proof. It is in this context that the integral transformations of the type f α (z) = ∫ 0 z (f (ζ) / ζ) α d ζ or F α (z) = ∫ 0 z (f ′ (ζ)) α d ζ appear. In this note we extend the classical problem of finding the values of α ∈ C for which either f α or F α are univalent, whenever f belongs to some subclasses of univalent mappings in D , to the case of logharmonic mappings by considering the extension of the shear construction introduced by Clunie and Sheil-Small in (Clunie and Sheil-Small in Ann. Acad. Sci. Fenn., Ser. A I 9:3–25, 1984) to this new scenario. [ABSTRACT FROM AUTHOR]

In the geometric theory of functions of a complex variable, the well-known direction is related to the estimates of the products of the inner radii of pairwise nonoverlapping domains. This direction is called extreme problems in classes of pairwise nonoverlapping domains. One of the problems of this type is considered in the present work. [ABSTRACT FROM AUTHOR]

In this paper, we describe the inhomogeneous Hilbert boundary-value problem of the theory of analytic functions with an infinite index and a boundary condition for a half-plane. The coefficients of the boundary condition are Hölder-continuous everywhere except for a finite number of singular points at which the argument of the coefficient function has second-type discontinuities (of a power order with exponent <1). We obtain formulas for the general solution of the inhomogeneous problem and discuss the existence and uniqueness of the solution. The study is based on the theory of entire functions and the geometric theory of functions of a complex variable. [ABSTRACT FROM AUTHOR]

A new approach to modeling the geometric structure of real materials based on a new type of functions – porous functions – is introduced. The general concept, basic operations, operations of calculus, visualization and interpretations, and potential applications of porous functions are outlined. [ABSTRACT FROM AUTHOR]

We consider the well-known problem of the geometric theory of functions of a complex variable on non-overlapping domains with free poles on radial systems. The main results of the present work strengthen and generalize several known results for this problem. [ABSTRACT FROM AUTHOR]

Quantum calculus (the calculus without limit) appeared for the first time in fluid mechanics, noncommutative geometry and combinatorics studies. Recently, it has been included into the field of geometric function theory to extend differential operators, integral operators, and classes of analytic functions, especially the classes that are generated by convolution product (Hadamard product). In this effort, we aim to introduce a quantum symmetric conformable differential operator (Q-SCDO). This operator generalized some well-know differential operators such as Sàlàgean differential operator. By employing the Q-SCDO, we present subclasses of analytic functions to study some of its geometric solutions of q-Painlevé differential equation (type III). [ABSTRACT FROM AUTHOR]

Grunsky operators play an important role in classical geometric function theory and in the study of Teichmüller spaces. The Grunsky map is known to be holomorphic on the universal Teichmüller space. In this paper the authors deal with the compactness of a Grunsky differential operator. They will give upper and lower estimates of the essential norm of a Grunsky differential operator and discuss when a Grunsky differential operator is a p-Schatten class operator. [ABSTRACT FROM AUTHOR]

The concept of hyperelastic deformations of bi-conformal energy is developed as an extension of quasiconformality. These deformations are homeomorphisms h : X → onto Y between domains X , Y ⊂ R n of the Sobolev class W loc 1 , n (X , Y) whose inverse f = = def h - 1 : Y → onto X also belongs to W loc 1 , n (Y , X) . Thus the paper opens new topics in Geometric Function Theory (GFT) with connections to mathematical models of Nonlinear Elasticity (NE). In seeking differences and similarities with quasiconformal mappings we examine closely the modulus of continuity of deformations of bi-conformal energy. This leads us to a new characterization of quasiconformality. Specifically, it is observed that quasiconformal mappings behave locally at every point like radial stretchings; if a quasiconformal map h admits a function ϕ as its optimal modulus of continuity at a point x ∘ , then f = h - 1 admits the inverse function ψ = ϕ - 1 as its modulus of continuity at y ∘ = h (x ∘) . That is to say, a poor (possibly harmful) continuity of h at a given point x ∘ is always compensated by a better continuity of f at y ∘ , and vice versa. Such a gain/loss property, seemingly overlooked by many authors, is actually characteristic of quasiconformal mappings. It turns out that the elastic deformations of bi-conformal energy are very different in this respect. Unexpectedly, such a map may have the same optimal modulus of continuity as its inverse deformation. In line with Hooke's Law, when trying to restore the original shape of the body (by the inverse transformation), the modulus of continuity may neither be improved nor become worse. However, examples to confirm this phenomenon are far from being obvious; indeed, elaborate computations are on the way. We eventually hope that our examples will gain an interest in the materials science, particularly in mathematical models of hyperelasticity. [ABSTRACT FROM AUTHOR]

We consider an open extremal problem in geometric function theory of complex variables on the maximum of the functional [ABSTRACT FROM AUTHOR]

A new approach to modeling the geometric structure of real materials based on a new type of functions – porous functions – is introduced. The general concept, basic operations, operations of calculus, visualization and interpretations, and potential applications of porous functions are outlined. [ABSTRACT FROM AUTHOR]

Some extremal problems of the geometric theory of functions of a complex variable related to the estimates of functionals defined on systems of non-overlapping domains are considered. Till now, many such problems have not been solved, though some partial solutions are available. In the paper, the improved method is proposed for solving the problems on extremal decomposition of the complex plane. The main results generalize and strengthen some known results in the theory of non-overlapping domains with free poles to the case of an arbitrary arrangement of systems of points on the complex plane. [ABSTRACT FROM AUTHOR]

We review the main results of the geometric theory of ordinary differential equations obtained by the prominent Russian geometer N. V. Stepanov (1926–1991). Some results obtained by Stepanov are illustrated by examples of third- and five-order equations. [ABSTRACT FROM AUTHOR]

The paper is devoted to one open extremal problem in the geometric function theory of complex variables associated with estimates of a functional defined on the systems of non-overlapping domains. We consider the problem of the maximum of a product of inner radii of n non-overlapping domains containing points of a unit circle and the power γ of the inner radius of a domain containing the origin. The problem was formulated in 1994 in Dubinin's paper in the journal "Russian Mathematical Surveys" in the list of unsolved problems and then repeated in his monograph in 2014. Currently, it is not solved in general. In this paper, we obtained a solution of the problem for five simply connected domains and power γ ∈ (1; 2:57] and generalized this result to the case of multidimensional complex space. [ABSTRACT FROM AUTHOR]

In this paper we study the convergence of the continuous Newton method for solving nonlinear equations with holomorphic mappings in complex Banach spaces. Our contribution is based on recent progress in the geometric theory of spiral-like functions. We prove convergence theorems and illustrate them by numerical simulations. [ABSTRACT FROM AUTHOR]

We compute the asymptotic growth rate of the number N(C,R) of closed geodesics of length ≤R in a connected component C of a stratum of quadratic differentials. We prove that, for any 0≤θ≤1, the number of closed geodesics γ of length at most R such that γ spends at least θ-fraction of its time outside of a compact subset of C is exponentially smaller than N(C,R). The theorem follows from a lattice counting statement. For points x, y in the moduli space M(S) of Riemann surfaces, and for 0≤θ≤1 we find an upper-bound for the number of geodesic paths of length ≤R in C which connect a point near x to a point near y and spend at least a θ-fraction of the time outside of a compact subset of C. [ABSTRACT FROM AUTHOR]

Recent research on shape retrieval render highly acute feature descriptors that are computationally intensive. Hence, a simple approach through a novel tessellated version of the Tetrakis Square tiling scheme for acute feature descriptor aiding supervised shape retrieval is contributed in this paper. The proposed descriptor labeled as Triangulated Second-Order Shape Derivative (TSOSD) performs feature characterization and abstraction by fusing hybrid geometrical concepts with image derivative operators. First, the mechanism tessellates the image into square tiles that are later organized as right-angled triangles. Secondly, the derivatives from the right-angled triangular neighbors interact locally using the trigonometric identities to produce an angle-based feature map. Finally, the feature descriptor is then formulated by local segmentation of the attained feature maps to produce the shape histogram. Experimental results on three standard benchmark databases demonstrate the effectiveness of the proposed approach, particularly rendering a consistent retrieval rate greater than 95% in comparison with the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Dimensionality reduction methods have commonly been used as principled ways to understand high-dimensional data. In this paper, a novel non-linear method named supervised data-dependent kernel sparsity preserving projection (SDKSPP) is proposed for dimensionality reduction. SDKSPP is a non-linear extension of sparsity preserving projection, it adopts a data-dependent kernel (DK) instead of standard kernels to achieve performance improvements. Different from previous dimensionality reduction methods based on DK, SDKSPP can simultaneously optimize the coefficients in DK and explore the manifold structure, i.e., the sparse reconstructive relationship of data. The manifold structure in the feature space is shared in the label space so that the information of labels can be utilized to help optimizing the coefficients in DK and improving the discriminative ability. After the optimal sparse reconstructive relationship is obtained, a transform matrix that can preserve this relationship is calculated to project the mapped data into a low-dimensional space. The effectiveness of the proposed method is tested and compared on nine popular databases. [ABSTRACT FROM AUTHOR]

In this paper, the authors prove a general Schwarz lemma at the boundary for the holomorphic mapping f between unit balls B and B′ in separable complex Hilbert spaces H and H′, respectively. It is found that if the mapping f ∈ C1+α at z0∈∂B with f(z0)=w0∈∂B′, then the Fréchet derivative operator Df(z0) maps the tangent space Tz0(∂Bn) to Tw0(∂B′), the holomorphic tangent space Tz0(1,0)(∂Bn) to Tw0(1,0)(∂B′), respectively. [ABSTRACT FROM AUTHOR]

The authors obtain the estimates of all homogeneous expansions for a subclass of ε quasi-convex mappings on the unit ball in complex Banach spaces. Moreover, the estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in ℂn are also obtained. Especially, the above estimates are only sharp for a subclass of starlike mappings, quasi-convex mappings and quasi-convex mappings of type A. The results are the generalization of many known results. [ABSTRACT FROM AUTHOR]

Consider the vanishing locus of a real analytic function on Rn restricted to [0, 1]n. We bound the number of rational points of bounded height that approximate this set very well. Our result is formulated and proved in the context of o-minimal structures which give a general framework to work with sets mentioned above. It complements the theorem of Pila-Wilkie that yields a bound of the same quality for the number of rational points of bounded height that lie on a definable set. We focus our attention on polynomially bounded o-minimal structures, allow algebraic points of bounded degree, and provide an estimate that is uniform over some families of definable sets. We apply these results to study fixed length sums of roots of unity that are small in modulus. [ABSTRACT FROM AUTHOR]

We consider a fully inhomogeneous stochastic higher spin six vertex model in a quadrant. For this model we derive concise integral representations formulti-point q-moments of the height function and for the q-correlation functions. At least in the case of the step initial condition, our formulas degenerate in appropriate limits to many known formulas of such type for integrable probabilistic systems in the (1+1)d KPZ universality class, including the stochastic six vertex model, ASEP, various q-TASEPs, and associated zero range processes. Our arguments are largely based on properties of a family of symmetric rational functions that can be defined as partition functions of the inhomogeneous higher spin six vertex model for suitable domains. In the homogeneous case, such functions were previously studied in Borodin (On a family of symmetric rational functions, 2014); they also generalize classical Hall-Littlewood and Schur polynomials. A key role is played by Cauchy-like summation identities for these functions, which are obtained as a direct corollary of the Yang-Baxter equation for the higher spin six vertex model. [ABSTRACT FROM AUTHOR]

Traditional control charts assume a baseline parametric model, against which new observations are compared in order to identify significant departures from the baseline model. To monitor a process without a baseline model, real-time contrasts (RTC) control charts were recently proposed to monitor classification errors when seperarting new observations from limited phase I data using a binary classifier. In contrast to the RTC framework, the distance between an in-control dataset and a dataset of new observations can also be used to measure the shift of the process. In this paper, we propose a distance-based multivariate process control chart using support vector machines (SVM), referred to as D-SVM chart. The SVM classifier provides a continuous score or distance from the boundary for each observation and allows smaller sample sizes than the previously random forest based RTC charts. An extensive experimental study shows that the RTC charts with the SVM scores are more efficient than those with the random forest for detecting changes in high-dimensional processes and/or non-normal processes. A real-life example from a mobile phone assembly process is also considered. [ABSTRACT FROM AUTHOR]

We consider the conditions under which a continuous function φ:Rn→R is the imaginary part If of the characteristic function f of a probability measure on Rn. A similar problem about such an φ that it is the argument of the characteristic function was solved by Ilinskii [Theory Probab. Appl. 20 (1975), 410-415]. In this paper, a characterization of what φ might serve as the imaginary part of the characteristic function f is given. As a consequence, we provide an answer to the following question posed by N. G. Ushakov [7]: Is it true that f is never determined by its imaginary part If? In other words, is it true that for any characteristic function f there exists a characteristic function g such that If≡Ig but f≢g? We prove that the answer to this question is negative. In addition, several examples of characteristic functions which are uniquely determined by their imaginary parts are given. [ABSTRACT FROM AUTHOR]

Yang-Baxter (YB) deformations of type IIB string theory have been well studied from the viewpoint of classical integrability. Most of the works, however, are focused upon the local structure of the deformed geometries and the global structure still remains unclear. In this work, we reveal a non-geometric aspect of YB-deformed backgrounds as T -fold by explicitly showing the associated O( D, D; ℤ) T -duality monodromy. In particular, the appearance of an extra vector field in the generalized supergravity equations (GSE) leads to the non-geometric Q-flux. In addition, we study a particular solution of GSE that is obtained by a non-Abelian T-duality but cannot be expressed as a homogeneous YB deformation, and show that it can also be regarded as a T -fold. This result indicates that solutions of GSE should be non-geometric quite in general beyond the YB deformation. [ABSTRACT FROM AUTHOR]

We continue our investigation of the Nikol'skii and Bernstein-Walsh-type estimations for complex algebraic polynomials in the bounded and unbounded quasidisks on the weighted Bergman spaces. [ABSTRACT FROM AUTHOR]

Cam mechanism is the most difficult part in the design and manufacture of stamping dies of automobile panels. The same series of cam products need to meet the needs of different working angles. Each specification needs to design and prepare a three-dimensional model, which brings great challenges to the design, editing, and management of the models. Therefore, a new design system of full parametric association modeling based on geometric features for standard cam was proposed, which is seamlessly integrated in NX software platform. The models of different work angles of the same series of cam are integrated into a fully parametric model. The specification and assembly location of standard parts, activation and suppression of detail features will automatically change with work angle based on parametric feature and association constraint technique. By modifying the work angle, the system can automatically instantiate different specification models of cam. Furthermore, the optimized design of cam structural is easier to achieve by motion simulation and finite element analysis based on the parametric model and geometric features. The system can also output the BOM table, when the model is instantiated. The cam of KMACG 600 demonstrates that the newly developed system shows an excellent performance on the model simplification, data management, and optimization design of cam, which can generate high quality design and reduce cost and designing time significantly. [ABSTRACT FROM AUTHOR]

In this paper we study the hyperbolic and Euclidean area distortion of measurable sets under some classes of K-quasiconformal mappings from the upper half-plane and the unit disk onto themselves, respectively. [ABSTRACT FROM AUTHOR]

A new type of displacement pile, the X-section cast-in-place concrete (XCC) pile, has recently been developed in China. Extensive field tests and laboratory experiments are undertaken to evaluate its performance and quantify the non-uniform deformation effect (NUDE) of the X-shaped cross section during installation. This paper develops a simplified theoretical model that attempts to capture the NUDE. Based on the theory of complex variable plane elasticity, closed-form solutions of the stress and displacement for the X-shaped cavity boundary value problem are given. Subsequently, the analytical solution is used to evaluate the NUDE, the concrete filling index (CFI), and the perimeter reduction coefficient of the XCC pile cross section. The computed results are compared with field test results, showing reasonable agreement. The present simplified theoretical model reveals the deformation mechanism of the X-shaped cavity and facilitates application of the newly developed XCC pile technique in geotechnical engineering. [ABSTRACT FROM AUTHOR]

We study the relationship between knotoids and knots in the direct product of the two-dimensional torus and an interval. Each knotoid on the sphere can be lifted to a knot of geometric degree 1 in the thickened torus. We prove that lifting is a bijection on the set of prime knotoids of complexity greater than 1. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a new class of generalized functions, called generalized geometrically convex functions. We establish several basic inequalities related to generalized geometrically convex functions. We also derive several new inequalities of the Hermite-Hadamard type for generalized geometrically convex functions. Several special cases are discussed, which can be deduced from our main results. [ABSTRACT FROM AUTHOR]