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Various operators of fractional calculus, as well as their quantum (or q -) extensions have been used widely and successfully in the study of the Taylor-Maclaurin coefficient estimation problems for many different families of normalized analytic, univalent and bi-univalent functions in Geometric Function Theory of Complex Analysis. On the other hand, Numerous writers have extensively employed orthogonal polynomials in the framework of Geometric Function Theory in Complex analysis. The recent and ongoing studies on this topic is primarily what drives us. In this paper, we solve the Fekete-Szegö problem for the symmetric function classes of analytical and bi-univalent functions involving the Euler polynomials. We also give estimates for the coefficients and an upper bound for the second Hankel determinant. [ABSTRACT FROM AUTHOR]

The principal goal of this paper is to extend the classical problem of finding the values of α ∈ ℂ for which either f ˆ α (z) = ∫ 0 z (f (ζ) ∕ ζ) α d ζ or f α (z) = ∫ 0 z (f ′ (ζ)) α d ζ are univalent, whenever f belongs to some subclasses of univalent mappings in D , to the case of harmonic mappings, by considering the shear construction introduced by Clunie and Sheil-Small in [4]. [ABSTRACT FROM AUTHOR]

Abstract Group encryption (GE) is the natural encryption analogue of group signatures in that it allows verifiably encrypting messages for some anonymous member of a group while providing evidence that the receiver is a properly certified group member. Should the need arise, an opening authority is capable of identifying the receiver of any ciphertext. As introduced by Kiayias, Tsiounis and Yung (Asiacrypt'07), GE is motivated by applications in the context of oblivious retriever storage systems, anonymous third parties and hierarchical group signatures. This paper provides the first realization of group encryption under lattice assumptions. Our construction is proved secure in the standard model (assuming interaction in the proving phase) under the Learning-With-Errors (LWE) and Short-Integer-Solution (SIS) assumptions. As a crucial component of our system, we describe a new zero-knowledge argument system allowing to demonstrate that a given ciphertext is a valid encryption under some hidden but certified public key, which incurs to prove quadratic statements about LWE relations. Specifically, our protocol allows arguing knowledge of witnesses consisting of X ∈ Z q m × n , s ∈ Z q n and a small-norm e ∈ Z m which underlie a public vector b = X ⋅ s + e ∈ Z q m while simultaneously proving that the matrix X ∈ Z q m × n has been correctly certified. We believe our proof system to be useful in other applications involving zero-knowledge proofs in the lattice setting. [ABSTRACT FROM AUTHOR]

Abstract In the present paper we study the class of all those copulas that are invariant under a special class of transformations, called reflections. In particular, we focus on the special role played by the independence copula within this class. For this purpose, we introduce a bijective transformation which turns every copula into a reflection invariant copula and enforces a strong geometric property: The n -fold composition of this transformation to a d -dimensional copula coincides with the independence copula on the mesh { 0 , 1 2 n ,... , 2 n − 1 2 n , 1 } d. It turns out that the independence copula is the unique fixed point of the introduced transformation. [ABSTRACT FROM AUTHOR]

Abstract Strong extrema of functions on some quasi-metric and compact spaces are studied. It is shown that the maximum cardinalities of the set of strong extrema of discontinuous functions can be larger than for continuous ones. We construct quasi-metric spaces with uncountable weight, on which any function has no more than a countable set of strong extrema. [ABSTRACT FROM AUTHOR]

Let G be a graph with adjacency matrix A ( G ) and let D ( G ) be the diagonal matrix of the degrees of G . For any real α ∈ [ 0 , 1 ] , Nikiforov (2017) [7] defined the matrix A α ( G ) as A α ( G ) = α D ( G ) + ( 1 − α ) A ( G ) . Let u and v be two vertices of a connected graph G . Suppose that u and v are connected by a path w 0 ( = v ) w 1 ⋯ w s − 1 w s ( = u ) where d ( w i ) = 2 for 1 ≤ i ≤ s − 1 . Let G p , s , q ( u , v ) be the graph obtained by attaching the paths P p to u and P q to v . Let s = 0 , 1 . Nikiforov and Rojo (2018) [9] conjectured that ρ α ( G p , s , q ( u , v ) ) < ρ α ( G p − 1 , s , q + 1 ( u , v ) ) if p ≥ q + 2 . In this paper, we confirm the conjecture. As applications, firstly, the extremal graph with maximal A α -spectral radius with fixed order and cut vertices is characterized. Secondly, we characterize the extremal tree which attains the maximal A α -spectral radius with fixed order and matching number. These results generalize some known results. [ABSTRACT FROM AUTHOR]

Let C v ( k ; T ) be the number of closed walks of length k starting at vertex v in a tree T . We prove that for any tree T with a given degree sequence π , the vector C ( k ; T ) ≡ ( C v ( k ; T ), v  ∈  V ( T )) is weakly majorized by the vector C ( k ; T π * ) ≡ ( C v ( k ; T π * ) , v ∈ V ( T π * ) ) , where T π * is the greedy tree with the degree sequence π . In addition, for two trees degree sequences π and π ′, if π is majorized by π ′, then C ( k ; T π * ) is weakly majorized by C ( k ; T π ′ * ) . [ABSTRACT FROM AUTHOR]

Let A be the local ring at a point of a normal complex variety with completion R = A ˆ . Srinivas has asked about the possible images of the induced map Cl A → Cl R over all geometric local normal domains A with fixed completion R . We use Noether–Lefschetz theory to prove that all finitely generated subgroups are possible in some familiar cases. As a byproduct we show that every finitely generated abelian group appears as the class group of the local ring at the vertex of a cone over some smooth complex variety of each positive dimension. [ABSTRACT FROM AUTHOR]

A delayed predator–prey diffusion system with Beddington–DeAngelis functional response under Dirichlet boundary condition is investigated. The existence and stability of the positive spatially nonhomogeneous steady-state solution are obtained via the implicit function theorem. Moreover, taking feedback time delay τ as the bifurcation parameter, Hopf bifurcation near the positive steady-state solution is proved to occur at a sequence of critical values, we can show that feedback time delay can induce nonhomogeneous periodic oscillatory patterns. The direction of Hopf bifurcation is forward when parameter m in model (1.2) is sufficiently large. Numerical simulations and numerical solutions are presented to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this note we study restrictions on the recently introduced super-additive and sub-additive transformations, A ↦ A ⁎ and A ↦ A ⁎ , of an aggregation function A . We prove that if A ⁎ has a slightly stronger property of being strictly directionally convex, then A = A ⁎ and A ⁎ is linear; dually, if A ⁎ is strictly directionally concave, then A = A ⁎ and A ⁎ is linear. This implies, for example, the existence of pairs of functions f ≤ g sub-additive and super-additive on [ 0 , ∞ [ n , respectively, with zero value at the origin and satisfying relatively mild extra conditions, for which there exists no aggregation function A on [ 0 , ∞ [ n such that A ⁎ = f and A ⁎ = g . [ABSTRACT FROM AUTHOR]

Improper affine spheres have played an important role in the development of geometric methods for the study of the Hessian one equation. Here, we review most of the advances we have made in this direction during the last twenty years. [ABSTRACT FROM AUTHOR]

This paper proposes an original decision-support approach to address over-constrained geometric configurations in Computer-Aided Design. It focuses particularly on the detection and resolution of redundant and conflicting constraints when deforming free-form surfaces made of NURBS patches. Based on a series of structural decompositions coupled with numerical analyses, the proposed approach handles both linear and non-linear constraints. The structural decompositions are particularly efficient because of the local support property of NURBS. Since the result of this detection process is not unique, several criteria are introduced to drive the designer in identifying which constraints should be removed to minimize the impact on his/her original design intent. Thus, even if the kernel of the algorithm works on equations and variables, the decision is taken by considering the user-specified geometric constraints. The method is illustrated on academic and industrial examples realized with our prototype software. [ABSTRACT FROM AUTHOR]

Based on the density functional theory in conjunction with the non-equilibrium Green's function formalism, we explore the effect of transition metal (Mn, Fe, Co, Ni) ions on the magnetic transport properties of a new synthesized colorimetric chemosensor L . The calculated results show that only Mn- L can present high-efficiency spin filtering effect, even at room temperature. The underlying mechanism is explained by the spin-resolved electron occupation number, transmission spectra, molecular projected self-consistent Hamiltonian orbitals and their spatial distribution. [ABSTRACT FROM AUTHOR]

The Statistical Learning Theory (SLT) defines five assumptions to ensure learning for supervised algorithms. Data independency is one of those assumptions, once the SLT relies on the Law of Large Numbers to ensure learning bounds. As a consequence, this assumption imposes a strong limitation to guarantee learning on time-dependent scenarios. In order to tackle this issue, some researchers relax this assumption with the detriment of invalidating all theoretical results provided by the SLT. In this paper we apply a kernel function, more precisely the Takens’ immersion theorem, to reconstruct time-dependent open-ended sequences of observations, also referred to as data streams in the context of Machine Learning, into multidimensional spaces (a.k.a. phase spaces) in attempt to hold the data independency assumption. At first, we study the best immersion parameterization for our kernel function using the Distance-Weighted Nearest Neighbors (DWNN). Next, we use this best immersion to recursively forecast next observations based on the prediction horizon, estimated using the Lyapunov exponent. Afterwards, predicted observations are compared against the expected ones using the Mean Distance from the Diagonal Line (MDDL). Theoretical and experimental results based on a cross-validation strategy provide stronger evidences of generalization, what allows us to conclude that one can learn from time-dependent data after using our approach. This opens up a very important possibility for ensuring supervised learning when it comes to time-dependent data, being useful to tackle applications such as in the climate, animal tracking, biology and other domains. [ABSTRACT FROM AUTHOR]

We investigate the quadratic descent of totally decomposable algebras with involution of orthogonal type in characteristic two. Both separable and inseparable extensions are included. [ABSTRACT FROM AUTHOR]

In this paper the stable extended domain of a noncommutative rational function is introduced and it is shown that it can be completely described by a monic linear pencil from the minimal realization of the function. This result amends the singularities theorem of Kalyuzhnyi-Verbovetskyi and Vinnikov. Furthermore, for noncommutative rational functions which are regular at a scalar point it is proved that their domains and stable extended domains coincide. [ABSTRACT FROM AUTHOR]

The score function method used to compute first order probabilistic sensitivities is extended in this work to arbitrary-order derivatives included mixed partial derivatives through the use of multicomplex mathematics. Multicomplex mathematics provides an effective and convenient numerical means to compute the high-order kernel functions with respect to natural parameters or moments (mean and standard deviation) obviating the need to analytically determine the kernel functions. Using these numerical kernel functions, high-order derivatives of the response moments or the probability-of-failure with respect to the parameters of the input distributions can be obtained. Numerical results indicate that the high-order probabilistic sensitivities converge with respect to the number of samples at the same rate as standard Monte Carlo estimates. Implementation of multicomplex mathematics is facilitated through the use of the Cauchy–Riemann matrices; therefore, the extension of common engineering probability distributions to matrix form is presented. [ABSTRACT FROM AUTHOR]

Surface stress in solids can have profound effects in semi-infinite and nanoscale materials. The current work pertains to the simulation of surface stress, using the concept proposed by Shuttleworth [ Proceedings of Physical Society 63 (1949) 444–457]. A two-scale approach is used for the simulation of surface stress. Density functional theory is used to compute the lattice parameter of a free-standing layer (or two layers in the case of (1 1 0) surface) of atoms, which is further used as an input into a finite element model. Aluminium is used as a model material for the computation of surface tension of (1 0 0), (1 1 1) and (1 1 0) planes and the results of the simulations are validated by comparison with results from literature. The utility of the model developed is highlighted by demonstrating the effect of surface tension on the: (i) stress variation in a thin slab & (ii) lattice parameter of nanoscale free-standing crystals. [ABSTRACT FROM AUTHOR]

Recently, metal oxides are attracting increasing interests as hydrogenation catalyst. Herein we studied the hydrogenation of ethylene on perfect and oxygen defective Co 3 O 4 (1 1 1) using periodic density functional theory. The energetics and pathways of ethylene hydrogenation to ethane were determined. We have demonstrated that (i) H 2 dissociation on Co 3 O 4 is a complicated two-step process through a heterolytic cleavage, followed by the migration of H atom and finally yields the homolytic product on both perfect and oxygen defective Co 3 O 4 (1 1 1) surfaces easily. (ii) After introducing the surface oxygen vacancy, the stepwise hydrogenation of ethylene by atomic hydrogen is much easier than that on perfect surface due to the weaker bond strength of OH group. The strength of O H bond is a crucial factor for the hydrogenation reaction which involves the breakage of O H bond. The formation of oxygen vacancy increases the electronic charges at the adjacent surface O, which reduces its capability of further gaining electrons from adsorbed atomic hydrogen and then weakens the strength of O H bond. These results emphasize the importance of the oxygen vacancies for hydrogenation on metal oxides. [ABSTRACT FROM AUTHOR]

Penny Pincher is a recently introduced template matching $-family gesture recognizer that exhibits competitive accuracy with even just one template. However, our recognizer is also able to rapidly compare a candidate gesture against numerous templates in a short amount of time, as compared to other recognizers, in order to achieve higher accuracy within a given time budget. Penny Pincher achieves this goal by reducing the template matching process to merely addition and multiplication; by avoiding translation, scaling, and rotation; and by avoiding calls to expensive geometric functions. In an evaluation compared against four other $-family recognizers, in three of our six datasets, Penny Pincher achieves the highest accuracy of all recognizers reaching 97.5%, 99.8%, and 99.9% user independent recognition accuracy, while remaining competitive with the three remaining datasets. Further, when a time constraint is imposed, our recognizer always exhibits the highest accuracy, realizing a reduction in recognition error of between 83% and 99% in most cases as Penny Pincher is able to process five times as many templates in the same amount of time as its closest competitor. Further, in this extended work, we also evaluate the effectiveness of Penny Pincher in a stressful setting using a video game prototype that makes heavy use of gestures, so that rushed and malformed gesture articulation is more likely. Our evaluation was conducted with a 24 participant between-subject user study of Protractor and Penny Pincher. Training data and in-game data collected during the user study was further used to evaluate several $-family recognizers. Again we find that our recognizer is on par with or better than the others, reducing the recognition error by as much as 5.8% to 10.4% with just a small number of templates per gesture. [ABSTRACT FROM AUTHOR]

When using the dynamic mesh method to deal with moving boundary problems, the Geometric Conservation Law (GCL) must be considered carefully. This paper reviews the study on GCL problem of dynamic grid in finite volume framework based on Arbitrary Lagrangian-Eulerian (ALE) methods. Several common approaches to satisfy discretized geometric conservation law (DGCL) are studied and simplified to a uniform form. The uniform flow and the isentropic vortex are tested to validate the geometric conservation property and the temporal-accuracy. Numerical results illustrate that although the violating of GCL does not pollute the original time-accuracy of numerical schemes for the governing equations, it may introduce extra artificial errors. When the “Adding Source Term” methods are adopted, the temporal accuracy order of face velocity scheme must match the temporal accuracy order of numerical schemes for the governing equations, otherwise it will pollute the original temporal accuracy. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove the existence of multiple solutions for a family of nonlinear elliptic systems in divergence form coupled with a pointwise gradient constraint: div { A (| x | , | u | 2 , | ∇ u | 2) ∇ u } + B (| x | , | u | 2 , | ∇ u | 2) u = div { P (x) [ cof ∇ u ] } in Ω , det ∇ u = 1 in Ω , u = φ on ∂ Ω , where Ω ⊂ R n (n ≥ 2) is a bounded domain, u = (u 1 , ... , u n) is a vector-map and φ is a prescribed boundary condition. Moreover P is a hydrostatic pressure associated with the constraint det ∇ u ≡ 1 and A = A (| x | , | u | 2 , | ∇ u | 2) , B = B (| x | , | u | 2 , | ∇ u | 2) are sufficiently regular scalar-valued functions satisfying suitable growths at infinity. The system arises in diverse areas, e.g., in continuum mechanics and nonlinear elasticity, as well as geometric function theory to name a few and a clear understanding of the form and structure of the solutions set is of great significance. The geometric type of solutions constructed here draw upon intimate links with the Lie group SO (n) , its Lie exponential and the multi-dimensional curl operator acting on certain vector fields. Most notably, a discriminant type quantity Δ = Δ (A , B) prompting from the system, will be shown to have a decisive role on the structure and multiplicity of these solutions. [ABSTRACT FROM AUTHOR]

This paper studies the recovery of the height field function of an object from its surface normal vectors in terms of uniform bi-quadratic B-spline surfaces. The study is motivated by two modern technological needs namely, the recovery of the height field function of an object from its surface normal vectors obtained by photometric stereo techniques, and the introduction of new design methodology of streamlined aesthetic surfaces through the direct editing of normal vectors. Our mathematical formulation for explicit surface reconstruction is based on differential geometry and geometric modeling techniques. Complex examples are provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper we present a new way to construct the pro-category of a category. This new model is very convenient to work with in certain situations. We present a few applications of this new model, the most important of which solves an open problem of Isaksen [7] concerning the existence of functorial factorizations in what is known as the strict model structure on a pro-category. Additionally we explain and correct an error in one of the standard references on pro-categories. [ABSTRACT FROM AUTHOR]

In 2007, Harmer, Hyland and Melliès gave a formal mathematical foundation for game semantics using a notion they called a ⊸-schedule, and the similar notion of ⊗-schedule, both structures describing interleavings of plays in games. Their definition was combinatorial in nature, but researchers often draw pictures when describing schedules in practice. Moreover, several proofs of key properties, such as that the composition of ⊸-schedules is associative, involve cumbersome combinatorial detail, whereas in terms of pictures the proof is straightforward, reflecting the geometry of the plane. Here, we give a geometric formulation of ⊸-schedules and ⊗-schedules, prove that they are isomorphic to Harmer et al.'s definitions, and illustrate their value by giving such geometric proofs. Harmer et al.'s notions may be combined to describe plays in multi-component games, and researchers have similarly developed intuitive graphical representations of plays in these games. We give a characterisation of these diagrams and explicitly describe how they relate to the underlying schedules, finally using this relation to provide new, intuitive proofs of key categorical properties. [ABSTRACT FROM AUTHOR]

A new computational method is proposed for solving fractional differential equations with nonlocal boundary conditions based on the reproducing kernel method (RKM). The present method can avoid finding a reproducing kernel satisfying nonlocal boundary conditions. Four numerical examples are provided to demonstrate the accuracy and efficiency of the method. [ABSTRACT FROM AUTHOR]

Peak-details are often smoothed when deconvolution methods are used for spectral restoration. In order to preserve spectral details, detail-preserving regularization is devised and a semi-blind deconvolution method with the detail-preserving regularization (SBD-DP) is proposed. The cost function of SBD-DP is formulated and the numerical solution processes are deduced for restoring spectra and estimating parameter of blur kernel. The deconvolution results of simulated spectra demonstrate that the proposed SBD-DP can restore the spectrum effectively and has a merit on preserving peak details, as well as can estimate the parameter of blur kernel accurately. Then the deconvolution result of experimental Raman spectrum indicates the effectiveness of the proposed SBD-DP method on improving spectral resolution. [ABSTRACT FROM AUTHOR]

In Information Security, intrusion detection is the act of detecting actions that attempt to compromise the security goals. One of the primary challenges to intrusion detection is the problem of misjudgment, misdetection and lack of real time response to the attack. Various data mining techniques as clustering, classification and association rule discovery are being used for intrusion detection. The proposed hybrid technique combines data mining approaches like K Means clustering algorithm and RBF kernel function of Support Vector Machine as a classification module. The main purpose of proposed technique is to decrease the number of attributes associated with each data point. So, the proposed technique can perform better in terms of Detection Rate and Accuracy when applied to KDDCUP’99 Data Set. [ABSTRACT FROM AUTHOR]

The paper considers certain problems of plates and shells analysis allowing to seek solutions obtained in terms of special functions. Orthotropic and isotropic plates and shells are under study. The solutions are received in terms of hyper-geometric and confluent hyper-geometric functions, Legendre and Bessel functions, orthogonal polynomials. [ABSTRACT FROM AUTHOR]

Let A denote the family of all analytic functions f in the unit disk D with the normalization f ( 0 ) = 0 = f ′ ( 0 ) - 1 . In this note, we mainly consider the radius of univalence of F defined by F ( z ) = z 2 / f ( z ) , where f belongs to some subclasses of A or S , the class of univalent functions from A . The results of the present article sharpen the earlier known results. [ABSTRACT FROM AUTHOR]

We are interested in the "almost" global-in-time existence of classical solutions in the general theory for nonlinear wave equations. All the three such cases are known to be sharp due to blow-up results in the critical case for model equations. However, it is known that we have a possibility to get the global-in-time existence for two of them in low space dimensions if the nonlinear term is of derivatives of the unknown function and satisfies the so-called null condition, or non-positive condition. But another one for the quadratic term in four space dimensions is out of the case as the nonlinear term should include a square of the unknown function itself. In this paper, we get one more example guaranteeing the sharpness of the almost global-in-time existence in four space dimensions. It is also the first example of the blow-up of classical solutions for non-single and indefinitely signed term in high dimensions. Such a term arises from the neglect of derivative-loss factors in Duhamel's formula for positive and single nonlinear term. This fact may help us to describe a criterion to get the global-in-time existence in this critical situation. [ABSTRACT FROM AUTHOR]

Abstract: We provide a general procedure for characterizing radical-like functions of skew polynomial and skew Laurent polynomial rings under grading hypotheses. In particular, we are able to completely characterize the Wedderburn and Levitzki radicals of skew polynomial and skew Laurent polynomial rings in terms of ideals in the coefficient ring. We also introduce the T-nilpotent radideals, and perform similar characterizations. [Copyright &y& Elsevier]

We analyze the role of the implicit function theorem and some of its substitutes in the work of Henri Poincaré. Special emphasis is given upon his PhD thesis, his first work on the periodic solutions of the three body problem, his memoir crowned by King Oscar II Prize and its development in Les méthodes nouvelles de la mécanique céleste , and finally his contributions on the figures of equilibrium of rotating fluid masses. Résumé Nous analysons le rôle du théorème des fonctions implicites et de certains substituts dans l׳oeuvre de Henri Poincaré. L׳accent est mis en particulier sur sa thèse de doctorat, son premier travail sur les solutions périodiques du problème des trois corps, son mémoire couronné par le Prix du Roi Oscar II et son développement dans Les méthodes nouvelles de la mécanique céleste , et finalement ses contributions aux figures d’équilibre d׳une masse fluide en rotation. [ABSTRACT FROM AUTHOR]

Henri Poincaré acquired a reputation in his lifetime for being difficult to read. It was said that he missed out important steps in his arguments, assumed the truth of claims that would be difficult if not impossible to prove, and in short that he lacked rigour. In the years after his death this view coalesced into an exaggerated claim that his work was simply too vague, and has become a cliché. This paper argues that Poincaré was far from indifferent to rigour, and that what characterises his work is an attempt to convey a particular sense of what it is to understand a topic. Throughout his working life Poincaré was concerned to promote the understanding of many domains of mathematics and physics. This is as apparent in his views about geometry, his conventionalism, and his theory of knowledge, as it is in his work on electricity and optics, on number theory, and function theory. It is one of the ways Poincaré discharged his responsibilities as a scientist, and that it accounts not only for a surprising degree of unity in his work but also gives it its distinctive character—at once profound and elusive. [ABSTRACT FROM AUTHOR]

Highlights: [•] A general method for developing friction factor formulas was proposed. [•] The method was based on the two-layer wall function theory and the Van Direst transformation. [•] It can be applied to different flow channels and supercritical water. [•] Comparisons with experimental data showed good agreement between the developed method and data. [ABSTRACT FROM AUTHOR]

Abstract: Following constructions of McMullen [11] and Vasilyev [15] we list strict quadratic differentials on (marked) tori defined by twists of one-forms on hyperelliptic surfaces. We count the total number of twists in each genus and show that the quadratic differentials on (marked) tori are strict. Taking universal covers we obtain a variety of (non-arithmetic) lattice Panov planes [14] from genus two lattice surfaces. [Copyright &y& Elsevier]

Abstract: We first investigate the linear Dirac structure from the viewpoint of a mixed Hodge structure. Then we discuss a Hodge-decomposition-type theorem for the generalized Kähler manifold and study the moduli space of a generalized weak Calabi–Yau manifold. We present a holomorphic anomaly equation and a one-loop partition function in a topological B-model under the generalized geometric context. [Copyright &y& Elsevier]

We derive analytical solutions of the Schrödinger wave equation for some q-deformed potentials. Most of these solutions are obtained in terms of Heun functions. However, for some particular cases the solutions are obtained in terms of geometric and hypergeometric functions. Different observations are realized for each potential. However, for all the cases which we study the oscillations are the usual ones. It is also noted that all of these functions are sensitive to variation in the parameters involved. Our discussion for some particular potential has shown us that for a large value of the parameter q the system tends to exhibit the energy for an infinite potential well between two points zero and a in addition to a free particle. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, an algorithm to construct -point (for any integer ) binary approximating subdivision schemes has been developed using the Cox–de Boor recursion formula. Some properties like symmetry of basis functions and polynomial reproduction are also discussed. It can be observed that most of the existing binary approximating schemes (corner cutting scheme developed by Chaikin, and 3-point, 4-point, 5-point and 6-point schemes introduced by Siddiqi and Ahmad) are either special cases or can be reproduced by the proposed algorithm. [Copyright &y& Elsevier]

Abstract: The aim of this investigation is to reveal some relationships between certain multivalently analytic functions and multivalently meromorphic functions, and then to focus on certain consequences of these which will be important or interesting for analytic or geometric function theory. [Copyright &y& Elsevier]

Abstract: In this paper, a characteristic condition of Einstein–Kropina metrics is given. By the characteristic condition, we prove that a non-Riemannian Kropina metric with constant Killing form β on an n-dimensional manifold M, , is an Einstein metric if and only if α is also an Einstein metric. By using the navigation data , it is proved that an n-dimensional () Kropina metric is Einstein if and only if the Riemannian metric h is Einstein and W is a unit Killing vector field with respect to h. Moreover, we show that every Einstein–Kropina metric must have vanishing S-curvature, and any conformal map between Einstein–Kropina metrics must be homothetic. [Copyright &y& Elsevier]

Abstract: In the framework of effective-mass envelope function theory, we present a theoretical investigation of the electronic and optical properties for a system of nano layer consisting of spherical nano layer of GaAs (core) with capping layer of GaAlAs (shell). An exact analytical solution of the corresponding Schrödinger equation is obtained; in addition to that a transcendent equation for determination of electron energetic spectrum is derived as well. Dependences of the electron energy, threshold frequency and absorption coefficient versus the external radius, and the thickness of the capping layer are presented. The results showed that the electronic and the optical properties strongly depended on the thickness of the capping layer. We expect that such systems may be significant for practical application. [Copyright &y& Elsevier]

Abstract: We have investigated the evolution of the magnetization reversal mechanism in asymmetric Ni nanowires as a function of their geometry. Circular nanowires are found to reverse their magnetization by the propagation of a vortex domain wall, while in very asymmetric nanowires the reversal is driven by the propagation of a transverse domain wall. The effect of shape asymmetry of the wire on coercivity and remanence is also studied. Angular dependence of the remanence and coercivity is also addressed. Tailoring the magnetization reversal mechanism in asymmetric nanowires can be useful for magnetic logic and race-track memory, both of which are based on the displacement of magnetic domain walls. Finally, an alternative method to detect the presence of magnetic drops is proposed. [Copyright &y& Elsevier]