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Copyright of Aydin Dental Journal is the property of Aydin Dental Journal and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Qubits, as we know, have great benefits as compared to classical bits in computing, research and technology; if these qubits are replaced by qudits, the technological constraints can be further diluted, and more advantages can be gained. In this article, we motivate the reader as to what happens when we go from a quantum world of qubits to a world of qudits. Elementary mathematical analysis of the transformation between the computational basis of qudits and the generalized qudit Bell state basis are derived. In reverence to the overwhelming properties of qudits, we give a detailed discussion of the most generalized quantum teleportation protocol using qudits. From the pedagogical angle, we provide rigorous, indepth calculations for the special case of qutrits. Last but not least, an epigrammatic representation of quantum teleportation is provided to sharpen the reader's understanding. [ABSTRACT FROM AUTHOR]

Let Tn be the semigroup of all full transformations on the finite set Xn={1,2,...,n}. For 1≤r≤n, set T(n,r)={α∈Tn:rank(α)≤r}. In this paper we describe the locally maximal regular subsemibands of the finite transformation semigroups T(n,r) and completely obtain their classification. [ABSTRACT FROM AUTHOR]

A nontrivial example of an eigenfunction in the sense of the theory of distributions for the planar Fourier transform was described by the authors in their previous work. In this paper, a method for obtaining other eigenfunctions is proposed. Positive homogeneous distributions in ℝn of order −n/2 are considered, and it is shown that F(ω)|x|−n/2, |ω| = 1, is an eigenfunction in the sense of the theory of distributions of the Fourier transform if and only if F(ω) is an eigenfunction of a certain singular integral operator on the unit sphere of ℝn. Since Ym,nkωx−n/2, where Ym,nk denote the spherical functions of order m in ℝn, are eigenfunctions of the Fourier transform, it follows that Ym,nk are eigenfunctions of the above-mentioned singular integral operator. In the planar case, all eigenfunctions of the Fourier transform of the form F(ω)|x|−1 are described by means of the Fourier coefficients of F(ω). [ABSTRACT FROM AUTHOR]

In this paper, a new class of operators called quasi n-class Q and quasi n-class Q* operators are introduced and studied some properties. Quasi n-class Q and quasi n-class Q* composition and weighted composition operators on L²(λ) and H²(β) are characterized. Also we discuss quasi n-class Q and quasi n-class Q* composite multiplication operator on L² space and Aluthge transformation of these class of operators are obtained. [ABSTRACT FROM AUTHOR]

We discuss and study several kinds of capacity transformations based on a given event B and a fixed implication function I. In particular, local, global and total invariantness of these transformations are examined and described. [ABSTRACT FROM AUTHOR]

Let T(X) be the full transformation semigroup on a set X. For two equivalence relations E and F on X with F ⊆, let T(X;E; F) = {α∊T(X): 8x,y ∊ X,(x,y) ∊E ⇒(x&#945, yα)∊F} Then T(X,E, F) is a subsemigroup of T(X). In this paper, we describe Green's relations and the regularity of elements for T(X.E,F) . Also, the relations F and E for which T(X,E, F) is a regular semigroup are described. [ABSTRACT FROM AUTHOR]

Elizalde (2011) characterized which permutations can be obtained by ordering consecutive elements in the trajectories of (positive) beta-transformations and beta-shifts. We prove similar results for negative bases beta. [ABSTRACT FROM AUTHOR]

We give identifications of the q-deformed Segal-Bargmann transform and define the Segal-Bargmann transform on mixed q-Gaussian variables. We prove that, when defined on the random matrix model of Śniady for the q-Gaussian variable, the classical Segal-Bargmann transform converges to the q-deformed Segal-Bargmann transform in the large N limit. We also show that the q-deformed Segal-Bargmann transform can be recovered as a limit of a mixture of classical and free Segal-Bargmann transform. [ABSTRACT FROM AUTHOR]

This paper investigates the Bogoyavlenskii–Kadomtsev– Petviashvili equation by using the binary Bell polynomials method and differential constraint technique. Several kinds of more general bilinear representations and Bäklund transformations are presented. At the same time, multiple wave solutions including the kink periodic solitary wave and bright–dark lump wave solutions are constructed. The resonant interactions between two kink solitary waves are investigated and exhibited mathematically and graphically. Lump wave solutions, a kind of rational function localized in all directions of the space, are obtained by the Taylor expansion of the kink periodic solitary wave. Also, we discuss the dynamical behavior of the lump wave solutions and their structures. [ABSTRACT FROM AUTHOR]

In this paper we set up a bivariate representation of partial theta functions which not only unifies some famous identities for partial theta functions due to Andrews and Warnaar but also unveils a new characteristic of such identities. As further applications, we establish a general form of Warnaar's identity and a general q -series transformation associated with Bailey pairs via the use of the power series expansion of partial theta functions. [ABSTRACT FROM AUTHOR]

The presence of high spectral correlation in hyperspectral images has demanded dimensionality reduction. Selection of bands based on supervised techniques has been already developed for dimensionality reduction. In this manuscript, the selection of an optimal set of bands is formulated as an unsupervised problem. The images are initially compressed using discrete wavelet transform (DWT). Then, the details of the image are extracted in the transform domain using entropy which accounts for spatial information content and first spectral derivative (FSD) that exploits the temporal redundancy. These details are optimized using meta-heuristic algorithms to obtain the final set of bands. A new Binary Social Spider Optimization algorithm (BSSO) is proposed which maintains the exploration–exploitation balance and avoids premature convergence of solutions. The performance of BSSO is compared with other benchmark algorithms: Clonal algorithm (BCLONAL), Time-varying transfer function Binary Particle Swarm Optimization (TV-BPSO), Binary Genetic Algorithm (BGA), Improved Gravitational Search Algorithm (IBGSA) and New Binary Bat Algorithm (NBBA). A simulation study is carried on four standard hyperspectral images. The proposed BSSO have provided with 83% of overall accuracy for 24% bands in Salinas image set, 75% for 33% in Pavia University, 75% against 26% for Pavia Center and finally 91% in KSC with 32% bands retention. The achievement of higher accuracy at less than 50% bands is appreciable. [ABSTRACT FROM AUTHOR]

For a connected graph G , the multiplicative eccentricity resistance-distance is defined as ξ R * ( G ) = ∑ { x , y } ⊂ V ( G ) ɛ G ( x ) · ɛ G ( y ) R G ( x , y ) , where ε G ( · ) is the eccentricity of the corresponding vertex and R G ( x, y ) is the effective resistance between vertices x and y in G . A connected graph G is called a cactus if any two of its cycles have at most one common vertex. Let Cat ( n ; t ) be the set of cacti possessing n vertices and t cycles, where 0 ≤ t ≤ n − 1 2 . In this paper, we introduce some edge-grafting transformations which decrease ξ R * ( G ) . As their applications, the extremal graphs with minimum and second minimum ξ R * ( G ) -value in Cat ( n ; t ) are characterized. [ABSTRACT FROM AUTHOR]

In this paper we obtain isomorphism classes of spaces of 2 π -periodic holomorphic functions on the upper half-plane endowed with L p norm with respect to a bounded positive non-atomic measure. [ABSTRACT FROM AUTHOR]

In this paper, we characterize some natural transformations between the bundle functors TA o T* and T* o TA on Mfm. In the particular case where A = Jr0 (R, R), we determine all natural transformations between the bundle functors Tr o T* and T* o Tr on Mfm. These lifts of 1-forms are studied with application to the theory of presymplectic structures. [ABSTRACT FROM AUTHOR]

The problem of consistency of a solution over time remains an important issue in cooperative dynamic games. Payoffs to players prescribed by an inconsistent solution may not be achievable since such a solution is extremely sensitive to its revision in the course of a game developing along an agreed upon cooperative behavior. The paper proposes a strong time-consistent payment scheme which is stable to a revision of cooperative set solutions, e.g., the core. Using a linear transformation of the solution, it becomes possible to obtain non-negative payments to players. In the paper, we also deal with a limit linear transformation of the solution whose convergence is proved. Developing a non-negative strong time-consistent payment scheme in a closed form, we guarantee that the solution supported by the scheme will not be revised over time. [ABSTRACT FROM AUTHOR]

We establish new properties of the solutions of functional-differential equations with constant delay and linearly transformed arguments. [ABSTRACT FROM AUTHOR]

Fullerene graphs are cubic, 3-connected planar graphs with only pentagonal and hexagonal faces. A fullerene is called a leapfrog fullerene, Le( F ), if it can be constructed by a leapfrog transformation from other fullerene graph F . Here we determine the relation between the Wiener index of Le( F ) and the Wiener index of the original graph F . We obtain lower and upper bounds of the Wiener index of Le i ( F ) in terms of the Wiener index of the original graph. As a consequence, starting with any fullerene F , and iterating the leapfrog transformation we obtain fullerenes, Le i ( F ), with Wiener index of order O ( n 2.64 ) and Ω ( n 2.36 ), where n is the number of vertices of Le i ( F ). These results disprove Hua et al. (2014) conjecture that the Wiener index of fullerene graphs on n vertices is of order Θ ( n 3 ). [ABSTRACT FROM AUTHOR]

The compensated quotient-difference ( Compqd ) algorithm is proposed along with some applications. The main motivation is based on the fact that the standard quotient-difference ( qd ) algorithm can be numerically unstable. The Compqd algorithm is obtained by applying error-free transformations to improve the traditional qd algorithm. We study in detail the error analysis of the qd and Compqd algorithms and we introduce new condition numbers so that the relative forward rounding error bounds can be derived directly. Our numerical experiments illustrate that the Compqd algorithm is much more accurate than the qd algorithm, relegating the influence of the condition numbers up to second order in the rounding unit of the computer. Three applications of the new algorithm in the obtention of continued fractions and in pole and zero detection are shown. [ABSTRACT FROM AUTHOR]

Lane departure warning is the key issues of automobile active safety problems. In this paper, an improved lane departure warning method is proposed based on Hough transformation and Kalman filter, noted as HK-LDWS. At first, the captured colour lane videos are decomposed into frames which are transformed and truncated into binary images subsequently. Secondly, Hough transformation is explored to detect lane lines in the truncated binary images, and Kalman filter is used to predict and track the detected lines. Finally, lane departure warnings are delivered out regarding as the predetermined safe distance based on the lateral distances. The actual road test results show that HK-LDWS can track lanes and make all departure warning correctly besides that it costs less than 35 milliseconds for per frame processing. HK-LDWS is an efficient solution for the lane departure warning problem. [ABSTRACT FROM AUTHOR]

We point out that recently published analyses of null and timelike infinity and long-range structures in electrodynamics to large extent rediscover results present in the literature. At the same time, some of the conclusions these recent works put forward may prove controversial. In view of these facts, we find it desirable to revisit the analysis taken up more than two decades ago, starting from earlier works on null infinity by other authors. [ABSTRACT FROM AUTHOR]

Let and be the partial transformation and the strictly partial transformation semigroups on the finite set . It is well known that the ranks of the semigroups and are , for , and , for , respectively. The idempotent rank, defined as the smallest number of idempotents generating set, of the semigroup has the same value as the rank. Idempotent can be seen as a special case (with ) of -potent. In this paper, we determine the -potent ranks, defined as the smallest number of -potents generating set, of the semigroups , for , and , for . [ABSTRACT FROM AUTHOR]

The article presents an analogous procedure in subdividing an equilateral triangle into four congruent triangles to form Sierpinski gasket. It mentions that the subdivision consists of two pairs of inscribed circles, with each circle tangential to the ones adjacent to it. It outlines some factors to consider in determining the k-th subdivision, locating the circles and the case r=s.

A category of spaces with fuzzy partitions is introduced, which could serve as a ground category for F-transform constructions. Axioms of fuzzy transformations systems are defined, and it is proved that the upper F-transform is the only fuzzy transformation satisfying these axioms. Relationships among the category of fuzzy partitions, categories of Kuratowski closure and interior operators and the category of fuzzy preorder relations are investigated. [ABSTRACT FROM AUTHOR]

We continue the study of rational envelope (RE) surfaces. Although these surfaces are parametrized with the help of square roots, when considering an RE patch as the medial surface transform in 4D of a spatial domain it yields a rational parametrization of the domain’s boundary, i.e., the envelope of the corresponding 2 -parameter family of spheres. We formulate efficient algorithms for G 1 data interpolation using RE surfaces and apply the developed methods to rational skinning and blending of sets of spheres and cones/cylinders, respectively. Our results are demonstrated on several computed examples of skins and blends with rational parametrizations. [ABSTRACT FROM AUTHOR]

We construct a sequence of balanced finite presentations of the trivial group with two generators and two relators with the following property: The minimal number of relations required to demonstrate that a generator represents the trivial element grows faster than the tower of exponentials of any fixed height of the length of the finite presentation. [ABSTRACT FROM AUTHOR]

We consider the class of approximation spaces in the present paper. In this class we define the concept of lower natural transformations, upper natural transformations and natural transformations. We prove that the class of approximation spaces with the lower natural transformations, upper natural transformations and natural transformations form categories which are denoted by $$\underline{\mathbf{Apr }}{} \mathbf S $$ , $$\overline{\mathbf{Apr }}{} \mathbf S $$ and $$\mathbf Apr {} \mathbf S $$ , respectively. We characterize a lower (upper) natural transformation through equivalence classes in an approximation space. We prove that two categories $$\mathbf Apr {} \mathbf S $$ and $$\underline{\mathbf{Apr }}{} \mathbf S $$ are the same. We characterize several kinds of epimorphisms and monomorphisms. In addition, we show that $$\underline{\mathbf{Apr }}{} \mathbf S $$ is a ( ExtrEpi, ExtrMono)-structured. [ABSTRACT FROM AUTHOR]

We define the invariant sequentially planned decision procedure under a group of measurable transformations. By means of a previous reduction of the problem, we obtain the optimal invariant sequentially planned decision procedure that minimizes the risk function. First we find the solution for the horizon with a maximal number of stages, based on the present information; later, the general case is solved but the solution is based on the past information. Finally, we study the possibility of approximating the general case by a sequence of truncated problems with a maximal number of stages, obtaining a solution based on the present information. [ABSTRACT FROM AUTHOR]

In this article, we study the oscillatory behavior of the third-order neutral type difference equation ∆(an(∆² (xn + pnxn-k))α) + qnƒ(xn-l) = 0 where α > 0, an > 0, qn ≥ 0 and 0 ≤ pn ≤ p < ∞. By using generalized Ricatti type transformation we present some new criteria which ensure that every solution is oscillatory. Also we provide examples that illustrate the importance of our results. [ABSTRACT FROM AUTHOR]

J. -L. Loday introduced the notion of a dimonoid and constructed the free dimonoid. Cayley's theorem for dimonoids states that every dimonoid is isomorphic to some transformation dimonoid. In this paper we propose another approach to constructing dimonoids which is based on using a semigroup operation. Several dimonoid-theoretical constructions are suggested, and it is shown that any dimonoid is isomorphically embedded into some dimonoid constructed from a semigroup. A similar result is obtained for dirings. [ABSTRACT FROM AUTHOR]

We introduce the depth parameters of a finite semigroup, which measure how hard it is to produce an element in the minimum ideal when we consider generating sets satisfying some minimality conditions. We estimate such parameters for some families of finite semigroups, and we obtain an upper bound for wreath products and direct products of two finite (transformation) monoids. [ABSTRACT FROM AUTHOR]

Let be the set of trees with vertices. The first six trees with the maximal Estrada indices in with were previously reported. A new transformation for studying the Estrada index is introduced. Then, with the aid of the new transformation, we completely deduce the 7th to the 13th trees with the maximal Estrada indices in with . Furthermore, for the trees in with , we obtain the relationship among three decreasing orders, namely, by their largest Estrada indices, by their largest eigenvalues, and by their largest resolvent Estrada indices, respectively. [ABSTRACT FROM AUTHOR]

In this paper we show that various continued fractions for the quotient of general Ramanujan functions G ( a q , b , λ q ) / G ( a , b , λ ) may be derived from each other via Bauer–Muir transformations. The separate convergence of numerators and denominators play a key part in showing that the continued fractions and their Bauer–Muir transformations converge to the same limit. We also show that these continued fractions may be derived from either Heine's continued fraction for a ratio of ϕ 1 2 functions, or other similar continued fraction expansions of ratios of ϕ 1 2 functions. Further, by employing essentially the same methods, a new continued fraction for G ( a q , b , λ q ) / G ( a , b , λ ) is derived. Finally we derive a number of new versions of some beautiful continued fraction expansions of Ramanujan for certain combinations of infinite products, with the following being an example: ( − a , b ; q ) ∞ − ( a , − b ; q ) ∞ ( − a , b ; q ) ∞ + ( a , − b ; q ) ∞ = ( a − b ) 1 − a b − ( 1 − a 2 ) ( 1 − b 2 ) q 1 − a b q 2 − ( a − b q 2 ) ( b − a q 2 ) q 1 − a b q 4 − ( 1 − a 2 q 2 ) ( 1 − b 2 q 2 ) q 3 1 − a b q 6 − ( a − b q 4 ) ( b − a q 4 ) q 3 1 − a b q 8 − ⋯ . [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of Lelong numbers of negative plurisubharmonic currents. We prove first that ifTis a negative plurisubharmonic current of bidimension (p, p) on a neighbourhood of the origin inwhere, then the projective massofTsatisfiesforrsmall enough. Then we study the case of the Lelong–Skoda potential associated with a positive closed current to prove that the setis not analytic in general for a positive pluriharmonic currentR.Nombres de Lelong des potentiels associés à des courants positifs fermés et applicationsRésumé Dans cet article, on s’intéresse à l’étude des nombres de Lelong des courants négatifs plurisousharmoniques. On montre tout d’abord que siTest un courant négatif plurisousharmonique de bidimension (p, p) sur un voisinage de l’origine de, alors la masse projectivedeTsatisfaitpourrassez petit. En suite on étudie le cas du potentiel de Lelong-Skoda associé à un courant positif fermé pour conclure que, pour un courant positif pluriharmoniqueR, l’ensemblen’est pas analytique en générale. [ABSTRACT FROM AUTHOR]

The Shannon entropy and the cumulative residual entropy (CRE) of a random variable are useful tools in probability theory. Recently, a new concept called generalized cumulative residual entropy (GCRE) of ordernwas introduced and studied. It is related with the record values of a sequence of i.i.d. random variables and with the relevation transform. In this paper, we show that, under some assumptions, the GCRE function of a fixed ordernuniquely determines the distribution function. Some characterizations of particular probability models are obtained from this general result. [ABSTRACT FROM PUBLISHER]

The following equation is considered in this paper: x ″ + ( − α + β cos ⁡ ( γ t ) ) x = 0 , where α , β and γ are real parameters and γ > 0 . This equation is referred to as Mathieu's equation when γ = 2 . The parameters determine whether all solutions of this equation are oscillatory or nonoscillatory. Our results provide parametric conditions for oscillation and nonoscillation; there is a feature in which it is very easy to check whether these conditions are satisfied or not. Parametric oscillation and nonoscillation regions are drawn to help understand the obtained results. [ABSTRACT FROM AUTHOR]

Let s∈R and 2≤p≤∞. We prove that the Segal-Bargmann transform B is a bounded operator from fractional Hermite-Sobolev spaces WHs,pRn to fractional Fock-Sobolev spaces FRs,p. [ABSTRACT FROM AUTHOR]

In this work, we implement the natural decomposition method (NDM) to solve nonlinear partial differential equations. We apply the NDM to obtain exact solutions for three applications of nonlinear partial differential equations. The new method is a combination of the natural transform method and the Adomian decomposition method. We prove some of the properties that are related to the natural transform method. The results are compared with existing solutions obtained by other methods, and one can conclude that the NDM is easy to use and efficient. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We produce in an explicit form free generators of the affine $$\mathcal {W}$$ -algebra of type A associated with a nilpotent matrix whose Jordan blocks are of the same size. This includes the principal nilpotent case and we thus recover the quantum Miura transformation of Fateev and Lukyanov. [ABSTRACT FROM AUTHOR]

N -dimensional Bäcklund transformation (BT), Cole–Hopf transformation and Auto-Bäcklund transformation (Auto-BT) of n -dimensional Burgers system are derived by using simplified homogeneous balance (SHB). By the Auto-BT, another solution of the n -dimensional Burgers system can be obtained provided that a particular solution of the Burgers system is given. Since the particular solution of n -dimensional Burgers system can be given easily by the Cole–Hopf transformation, then using the Auto-BT repeatedly, more solutions of n -dimensional Burgers system can be obtained successively. [ABSTRACT FROM AUTHOR]

The chaotic systems with hidden attractors, such as chaotic systems with a stable equilibrium, chaotic systems with infinite equilibria or chaotic systems with no equilibrium have been investigated recently. However, the relationships between them still need to be discovered. This work explains how to transform a system with one stable equilibrium into a new system with an infinite number of equilibrium points by using a memristive device. Furthermore, some other new systems with infinite equilibria are also constructed to illustrate the introduced methodology. [ABSTRACT FROM AUTHOR]

We give a construction of a Poisson transform mapping density valued differential forms on generalized flag manifolds to differential forms on the corresponding Riemannian symmetric spaces, which can be described entirely in terms of finite dimensional representations of reductive Lie groups. Moreover, we will explicitly generate a family of degree-preserving Poisson transforms whose restriction to real valued differential forms has coclosed images. In addition, as a transform on sections of density bundles it can be related to the classical Poisson transform, proving that we produced a natural generalization of the classical theory. [ABSTRACT FROM AUTHOR]

The author investigates the relationships of some potential objects for a right Markov process and the same objects for the Girsanov transformed process induced by α-excessive function including Revuz measures, energy functionals, capacities and Lévy systems in this paper. [ABSTRACT FROM AUTHOR]

In this paper we discuss Bäcklund transformations with two pseudo-potentials. We obtain two such transformations, one of which is from the modified KdV equation to itself, and the other from the modified KdV equation to another known nonlinear equation. As applications, from the trivial solutions of the modified KdV equation, we construct some novel solutions. [ABSTRACT FROM AUTHOR]