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In this paper, we introduce the R package gendist that computes the probability density function, the cumulative distribution function, the quantile function and generates random values for several generated probability distribution models including the mixture model, the composite model, the folded model, the skewed symmetric model and the arc tan model. These models are extensively used in the literature and the R functions provided here are flexible enough to accommodate various univariate distributions found in other R packages. We also show its applications in graphing, estimation, simulation and risk measurements. [ABSTRACT FROM AUTHOR]

A computational procedure to search for selective ligands for structurally related protein targets was developed and verified for serotonergic 5-HT7/5-HT1A receptor ligands. Starting from a set of compounds with annotated activity at both targets (grouped into four classes according to their activity: selective toward each target, not-selective and not-selective but active) and with an additional set of decoys (prepared using DUD methodology), the SVM (Support Vector Machines) models were constructed using a selective subset as positive examples and four remaining classes as negative training examples. Based on these four component models, the consensus classifier was then constructed using a data fusion approach. The combination of two approaches of data representation (molecular fingerprints vs. structural interaction fingerprints), different training set sizes and selection of the best SVM component models for consensus model generation, were evaluated to determine the optimal settings for the developed algorithm. The results showed that consensus models with molecular fingerprints, a larger training set and the selection of component models based on MCC maximization provided the best predictive performance. [ABSTRACT FROM AUTHOR]

The study of processes evolving on networks has recently become a very popular research field, not only because of the rich mathematical theory that underpins it, but also because of its many possible applications, a number of them in the field of biology. Indeed, molecular signaling pathways, gene regulation, predator-prey interactions and the communication between neurons in the brain can be seen as examples of networks with complex dynamics. The properties of such dynamics depend largely on the topology of the underlying network graph. In this work, we want to answer the following question: Knowing network connectivity, what can be said about the level of third-order correlations that will characterize the network dynamics? We consider a linear point process as a model for pulse-coded, or spiking activity in a neuronal network. Using recent results from theory of such processes, we study third-order correlations between spike trains in such a system and explain which features of the network graph (i.e. which topological motifs) are responsible for their emergence. Comparing two different models of network topology—random networks of Erdős-Rényi type and networks with highly interconnected hubs—we find that, in random networks, the average measure of third-order correlations does not depend on the local connectivity properties, but rather on global parameters, such as the connection probability. This, however, ceases to be the case in networks with a geometric out-degree distribution, where topological specificities have a strong impact on average correlations. [ABSTRACT FROM AUTHOR]

Let E (respectively; T , S ) denote the set of all lines which are external (respectively; tangent, secant) to an irreducible conic in P G ( 2 , q ) . We give a brief survey of the known results regarding the minimum size L -blocking sets of P G ( 2 , q ) for L ∈ { E , S , T ∪ E , T ∪ S } and study the other two cases when L = T , E ∪ S . [ABSTRACT FROM AUTHOR]

We investigate the well-posedness of the Kelvin–Voigt equations in spaces based on L q ( Ω ) , 1 < q < ∞ , where Ω is a bounded domain of R d , d ≥ 2 . [ABSTRACT FROM AUTHOR]

We study parametric estimation in the Cox-Ingersoll-Ross model and establish the stochastic differential equations for the parameters involved in it. [ABSTRACT FROM AUTHOR]

Given a one-parameter path of equations for which there is a trivial branch of solutions, to determine the points on the branch from which there bifurcate nontrivial solutions, there is the heuristic principle of linearization. That is to say, at each point on the branch, linearize the equation, and justify the inference that points on the branch that are bifurcation points for the path of linearized equations are also bifurcation points for the original path of equations. In quite general circumstances, for the bifurcation of critical points, we show that, at isolated singular points of the path of linearizations, a property of the path that is known to be sufficient to force bifurcation of nontrivial critical points is also necessary. To be more precise, let I be an open interval of real numbers that contains the point λ0 and B an open ball about the origin of a real, separable Hilbert space H. Let Ψ: I × B → R be a family of C2 functions. For λ ∊ I, assume ▿ xΨ(λ, 0) = 0, and set Hessianx Ψ(λ, 0) ≡ Lλ. Assume Lλ is invertible if λ ≠ λλ0 and Lλ0 is Fredholm. It is known that if the spectral flow of L: I → L(H) across λ0 is nonzero, then in each neighborhood of (λ0, 0) there are pairs (λ, x), x ≠ 0, for which ▿ xΨ(λ, x) = 0. We prove that if L: I → L(H) is a continuous path of symmetric operators for which Lλ is invertible for λ ≠ λ0, Lλ0 is Fredholm, and the spectral flow of L: I → L(H) across λ0 is zero, then there is an open interval J that contains the point λ0, an open ball B about the origin, and a family Ψ: J × B → R of C2 functions such that, for each λ ∊ J, ▿ xΨ(λ, 0) = 0 and Hessianx Ψ(λ, 0) = Lλ, but ▿ xΨ(λ, x) ≠ 0 if x ≠ 0. Therefore, at an isolated singular point of the path of linearizations of the gradient, under the sole further assumption that the linearization at the singular point is Fredholm, spectral flow is a complete invariant for the detection of bifurcation of nontrivial critical points. [ABSTRACT FROM AUTHOR]

Community structure is considered one of the most interesting features in complex networks. Many real-world complex systems exhibit community structure, where individuals with similar properties form a community. The identification of communities in a network is important for understanding the structure of said network, in a specific perspective. Thus, community detection in complex networks gained immense interest over the last decade. A lot of community detection methods were proposed, and one of them is the label propagation algorithm (LPA). The simplicity and time efficiency of the LPA make it a popular community detection method. However, the LPA suffers from instability detection due to randomness that is induced in the algorithm. The focus of this paper is to improve the stability and accuracy of the LPA, while retaining its simplicity. Our proposed algorithm will first detect the main communities in a network by using the number of mutual neighbouring nodes. Subsequently, nodes are added into communities by using a constrained LPA. Those constraints are then gradually relaxed until all nodes are assigned into groups. In order to refine the quality of the detected communities, nodes in communities can be switched to another community or removed from their current communities at various stages of the algorithm. We evaluated our algorithm on three types of benchmark networks, namely the Lancichinetti-Fortunato-Radicchi (LFR), Relaxed Caveman (RC) and Girvan-Newman (GN) benchmarks. We also apply the present algorithm to some real-world networks of various sizes. The current results show some promising potential, of the proposed algorithm, in terms of detecting communities accurately. Furthermore, our constrained LPA has a robustness and stability that are significantly better than the simple LPA as it is able to yield deterministic results. [ABSTRACT FROM AUTHOR]

The paper shows that under some mild conditions n -dimensional spherical wavelets derived from approximate identities build semi-continuous frames. Moreover, for sufficiently dense grids Poisson wavelets on n -dimensional spheres constitute a discrete frame. In the proof we only use the localization properties of the reproducing kernel and its gradient. [ABSTRACT FROM AUTHOR]

We extend the recent sparse Fourier transform algorithm of [1] to the noisy setting, in which a signal of bandwidth N is given as a superposition of k ≪ N frequencies and additive random noise. We present two such extensions, the second of which exhibits a form of error-correction in its frequency estimation not unlike that of the β -encoders in analog-to-digital conversion [2] . On k -sparse signals corrupted with additive complex Gaussian noise, the algorithm runs in time O ( k log ⁡ ( k ) log ⁡ ( N / k ) ) on average, provided the noise is not overwhelming. The error-correction property allows the algorithm to outperform FFTW [3] , a highly optimized software package for computing the full discrete Fourier transform, over a wide range of sparsity and noise values. [ABSTRACT FROM AUTHOR]

This paper considers the problem of minimizing a nonlinear objective function subject to a system of bipolar fuzzy relational equations with max- $T_{L}$ composition, where $T_{L}$ is the Łukasiewicz triangular norm. It shows that the feasible domain, i.e., the solution set of a system of bipolar fuzzy relational equations, can be reformulated as a system of 0-1 mixed integer inequalities. Consequently, such a type of optimization problems can be handled within the framework of 0-1 mixed integer optimization requiring no particular solving techniques. [ABSTRACT FROM AUTHOR]

Mesh matching is an effective way to convert the non-conforming interfaces between two hexahedral meshes into conforming ones, which is very important for achieving high-quality finite element analysis. However, the existing mesh matching algorithm is neither efficient nor effective enough to handle complex interfaces and self-intersecting sheets. In this paper, the algorithm is improved in three aspects: (1) by introducing a more precise criteria for chord matching and the concept of partition chord set, complex interfaces with internal loops can be handled more effectively; (2) by proposing a new solution, self-intersecting sheet can be inflated and extracted locally; and (3) by putting forward a mesh quality evaluation method, the sheet extraction operation during mesh matching can be done more efficiently. Our improved mesh matching algorithm is fully automatic, and its effectiveness is demonstrated by several examples in different matching situations. [ABSTRACT FROM AUTHOR]

In this paper we study the powers under umbral composition and degeneration for Sheffer sequences, where we presented several applications related to Bernoulli polynomials, Frobenius-Euler polynomials, falling factorial polynomials and Bell polynomials and their degeneration cases. [ABSTRACT FROM AUTHOR]

Time delay due to maturation time, capturing time or other reasons widely exists in biological systems. In this paper, a predator-prey system of Leslie type with diffusion and time delay is studied based on mathematical analysis and numerical simulations. Conditions for both delay induced and diffusion induced Turing instability are obtained by using bifurcation theory. Furthermore, a series of numerical simulations are performed to illustrate the spatial patterns, which reveal the information of density changes of both prey and predator populations. The obtained results show that the interaction between diffusion and time delay may give rise to rich dynamics in ecosystems. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the properties of curves of constant breadth in a 3-dimensional Lie group. Also, we find the condition of general helix as constant breadth curves and construct constant breadth curves which the tangent component of the curve vanishes. [ABSTRACT FROM AUTHOR]

The importance of mathematics in the context of the scientific and technological development of humanity is determined by the possibility of creating mathematical models of the objects studied under the different branches of Science and Technology. The arithmetisation process that took place during the nineteenth century consisted of the quest to discover a new mathematical reality in which the validity of logic would stand as something essential and central. Nevertheless, in contrast to this process, the development of mathematical analysis within a framework that largely involves intuition and geometry is a fact that cannot go unnoticed amongst the mathematics community, as we shall show in this paper through the research made by Bernhard Riemann on complex variables. [ABSTRACT FROM AUTHOR]

With the arrival of the nineteenth century, a process of change guided the treatment of three basic elements in the development of mathematics: rigour, the arithmetization and the clarification of the concept of function, categorised as the most important tool in the development of the mathematical analysis. In this paper we will show how several prominent mathematicians contributed greatly to the development of these basic elements that allowed the solid underpinning of mathematics and the consideration of mathematics as an axiomatic way of thinking in which anyone can deduce valid conclusions from certain types of premises. This nineteenth century stage shares, possibly with the Heroic Age of Ancient Greece, the most revolutionary period in all history of mathematics. [ABSTRACT FROM AUTHOR]

We prove the irreducibility of the universal non-degenerate Whittaker modules for the affine Lie algebra sl 2 ˆ of type A 1 ( 1 ) with noncritical level. These modules can become simple Whittaker modules over sl 2 ˜ = sl 2 ˆ + C d with the same Whittaker function and central charge. We have to modulo a central character for sl 2 to obtain simple degenerate Whittaker sl 2 ˆ -modules with noncritical level. In the case of critical level the universal Whittaker module is reducible. We prove that the quotient of universal Whittaker sl 2 ˆ -module by a submodule generated by a scalar action of central elements of the vertex algebra V − 2 ( sl 2 ) is simple as sl 2 ˆ -module. We also explicitly describe the simple quotients of universal Whittaker modules at the critical level for sl 2 ˜ . Quite surprisingly, with the same Whittaker function some simple degenerate sl 2 ˜ Whittaker modules at the critical level have semisimple action of d and others have free action of d . At last, by using vertex algebraic techniques we present a Wakimoto type construction of a family of simple generalized Whittaker modules for sl 2 ˆ at the critical level. This family includes all classical Whittaker modules at critical level. We also have Wakimoto type realization for degenerate Whittaker modules for sl 2 ˆ at noncritical level. [ABSTRACT FROM AUTHOR]

We classify all compact simply connected biquotients of the form G ⫽ SU ( 2 ) 2 for G = SU ( 4 ) , SO ( 7 ) , Spin ( 7 ) , or G = G 2 × SU ( 2 ) . In particular, we show there are precisely 2 inhomogeneous reduced biquotients in the first and last case, and 10 in the middle cases. [ABSTRACT FROM AUTHOR]

We show that for every 2-bridge knot K , there is an infinite family of Montesinos knots { K q } such that each K q is 2-adjacent to K . We also give a new example of 2-adjacency relation between 2-bridge knots. [ABSTRACT FROM AUTHOR]

In the last decades, heuristic algorithms are widely used in solving problems in different fields of science and engineering. Most of these methods are inspired by natural phenomena, such as biological behaviours or physical principles. In this paper, a new optimization method based on the dynamic of sliding motion along a frictionless inclined plane is introduced. In the proposed algorithm, a collection of agents cooperate with each other and move toward better positions in the search space by employing Newton's second law and equations of motion. Our method is compared with other popular optimization algorithms and the results on 23 standard benchmark functions show its effectiveness in most cases. [ABSTRACT FROM AUTHOR]

Based on our site investigation conducted in 2013, we found that the pedestrian red light crossing at the midblock connecting the campus of Southwest University and living area was low, where most of pedestrians are university students and staff. This paper reports a supplementary work applying the Theory of Planned Behaviour (TPB) to identify any psychological differences toward pedestrian red light crossing between university students and their peers. Three social groups participated in the investigation. The first group is the university students in Grade one (Group 1), the other two groups are their previous senior middle school classmates who are now working full time (Group 2) or who are now out of work and school (Group 3). The statistical results indicated The TPB components accounted for 42.9%, 55.3% and 55.4% of the variance of red signal crossing intention for Group 1, Group 2 and Group 3 in the depicted road crossing scenario. The data also showed that there are obvious differences among the participants’ responses to “refrain from crossing” between university students and others, and the subsequent regression analysis revealed the ability to “refrain from crossing” played the most important role in the intention of red light crossing in the depicted scenario. [ABSTRACT FROM AUTHOR]

We introduce the notion of an ordered quasi-ideal of an ordered semiring and show that ordered quasi-ideals and ordered bi-ideals coincide in regular ordered semirings. Then we give characterizations of regular ordered semirings, regular ordered duo-semirings, and left (right) regular ordered semirings by their ordered quasi-ideals. [ABSTRACT FROM AUTHOR]

We construct from a finitary exact category with duality A a module over its Hall algebra, called the Hall module, encoding the first order self-dual extension structure of A . We study in detail Hall modules arising from the representation theory of a quiver with involution. In this case we show that the Hall module is naturally a module over the specialized reduced σ -analogue of the quantum Kac–Moody algebra attached to the quiver. For finite type quivers, we explicitly determine the decomposition of the Hall module into irreducible highest weight modules. [ABSTRACT FROM AUTHOR]

We obtain a new class of compact Hausdorff spaces K for which c 0 can be nontrivially twisted with C ( K ) . [ABSTRACT FROM AUTHOR]

In this paper we prove that spectral synthesis holds for a variety on an Abelian group if spectral analysis holds on it and the residue ring of the annihilator of the variety is a Noether ring. This extends the fundamental result of M. Lefranc about spectral synthesis on finitely generated Abelian groups. [ABSTRACT FROM AUTHOR]

This paper addresses the properties of the C 0 -semigroup generated by the reparable system with finite repair time. In particular, it can be shown that the C 0 -semigroup is eventually differentiable and eventually compact, which is not true for the case when the repair time is infinite, as discussed in [9] and [11] . [ABSTRACT FROM AUTHOR]

We consider a class X of continuous functions on [ 0 , 1 ] that is of interest from two different perspectives. First, it is closely related to sets of functions that have been studied as generalizations of the Takagi function. Second, each function in X admits a linear pathwise quadratic variation and can thus serve as an integrator in Föllmer's pathwise Itō calculus. We derive several uniform properties of the class X . For instance, we compute the overall pointwise maximum, the uniform maximal oscillation, and the exact uniform modulus of continuity for all functions in X . Furthermore, we give an example of a pair x , y ∈ X for which the quadratic variation of the sum x + y does not exist. [ABSTRACT FROM AUTHOR]

We find smoothly slice (in fact doubly slice) knots in the 3-sphere with trivial Alexander polynomial that are not superslice, answering a question posed by Livingston and Meier. [ABSTRACT FROM AUTHOR]

In this note, we follow the strategy of Haller, Rybicki and Teichmann to give a short, self contained, and elementary proof that Diff0(M) is a perfect group, given a theorem of Herman on diffeomor-phisms of the circle. [ABSTRACT FROM AUTHOR]

In this paper, we present several necessary conditions for the reversed Dickson polynomial E n ( 1 , x ) of the second kind to be a permutation of F q . In particular, we give explicit evaluation of the sum ∑ a ∈ F q E n ( 1 , a ) . [ABSTRACT FROM AUTHOR]

Waveform design is a pivotal component of the fully adaptive radar construct. In this paper, we consider waveform design for radar space time adaptive processing (STAP), accounting for the waveform dependence of the clutter correlation matrix. Due to this dependence, in general, the joint problem of receiver filter optimization and radar waveform design becomes an intractable, nonconvex optimization problem, Nevertheless, it is, however, shown to be individually convex either in the filter or in the waveform variables. We derive constrained versions of a) the alternating minimization algorithm, b) proximal alternating minimization, and c) the constant modulus alternating minimization, which, at each step, iteratively optimizes either the STAP filter or the waveform independently. A fast and slow time model permits waveform design in radar STAP, but the primary bottleneck is the computational complexity of the algorithms. [ABSTRACT FROM PUBLISHER]

A well-known theorem, due to C. J. Smyth, asserts that two conjugates of a Pisot number, having the same modulus are necessary complex conjugates. We show that this result remains true for K-Pisot numbers, where K is a real algebraic number field. Also, we prove that a j-Pisot number, where j is a natural number, can not have more than 2j conjugates with the same modulus. [ABSTRACT FROM AUTHOR]

An investigation of the codominance maximum computing time of the continued fractions method (CF) for isolation of the real roots of a squarefree integral polynomial when applied to the two-parameter family of polynomials A a , n ( x ) = x n − 2 ( a x 2 − ( a + 2 ) x + 1 ) 2 , with n ≥ 5 and a ≥ 1 . These polynomials have two roots, r 1 and r 2 , in the interval ( 0 , 1 ) , with | r 1 − r 2 | < a − n . It is proved that for these polynomials the maximum time required by CF to isolate those two close roots would be codominant with n 5 ( ln ⁡ a ) 2 even if an “ideal” root bound were available and either the Horner method or the Budan method is used for translations. It is proved that if a power-of-two Hong root bound is used by CF to determine translation amounts then the time required to isolate the two close roots is dominated by n 6 ( ln ⁡ a ) if a multiplication-free Budan translation method is used. Computations reveal that the Hong root bound is surprisingly effective when applied to the transformed polynomials that arise, engendering a minimum efficiency conjecture. It is proved that if the conjecture is true then the time to isolate the two close roots is dominated by n 5 ( ln ⁡ a ) 2 . There is also evidence for a maximum efficiency conjecture. The two conjectures together, if true, make it likely that this time is codominant with n 5 ( ln ⁡ a ) 2 . [ABSTRACT FROM AUTHOR]

Copyright of Turkish Journal of Education is the property of Mehmet Tekerek 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.)

Because of size and covariance matrix problems, computing much of anything along the nondominated frontier of a large-scale (1000-3000 securities) portfolio selection problem with semi-continuous variables is a task that has not previously been achieved. But given (a) the speed at which the nondominated frontier of a classical portfolio problem can now be computed and (b) the possibility that there might be overlaps between the nondominated frontier of the classical problem and that of the same problem but with semi-continuous variables, the paper shows how considerable amounts of the nondominated frontier of a large-scale mean-variance portfolio selection problem with semi-continuous variables can be computed in very little time. [ABSTRACT FROM AUTHOR]

Spatial visualization is a crucial ability to understand and solve real world problems. Typically, important features of visual-spatial abilities in mathematics learning have been the skills required to construct mental models of mathematical objects from teacher drawings or oral descriptions. However, spatial ability is not a static trait but instead a dynamic process which could be fostered through interaction of real and virtual objects. This ability could be enriched with the development of new technologies such as augmented reality. We are part of a team of innovative and educational research aiming to foster mathematical cognitive skills, crucial but generally taken for granted. The purpose of this paper is to present an augmented reality application in order to promote spatial visualization in Calculus courses for engineering students. [ABSTRACT FROM AUTHOR]

Optimal reactive power planning is one of the major and important problems in electrical power systems operation and control. This is nothing but multi-objective, nonlinear, minimization problem of power system optimization. This paper presents the relevance of New Improved Differential Evolution (NIDE) algorithm to solve the Reactive Power Planning (RPP) problem based on Multi-objective optimization. Minimization of total cost of energy loss and cost of F A C T controlers installments are taken as the objectives incorporating (RPP) problem. With help of New Voltage Stability Index (NVSI), the critical lines and buses are identified to install the FACTS controllers. The optimal settings of the control variables of the generator voltages, transformer tap settings and provision and parameter settings of the FACT controllers SVC, TCSC, and UPFC are considered for reactive power planning. The approach applied to IEEE 30 and 72-bus Indian system for minimization of active power loss. Simulation results are compared with other optimization algorithm. [ABSTRACT FROM AUTHOR]

Assuming AD + + V = L ( P ( R ) ) , and assuming there is no proper class inner model containing all the reals that satisfies AD R + “ θ is regular” , we prove that in some forcing extension, either V is a derived model of a premouse or V embeds into a derived model of a premouse. [ABSTRACT FROM AUTHOR]

We prove global existence of solutions to space–time monopole equations in one space dimension. Observing the null structure of the system, we first prove local existence in L p by applying a bilinear estimate. From a priori L p estimates, we can extend the local solution to the global one. For the critical case L 1 , the concentration of the solution is denied to show the time global solvability. [ABSTRACT FROM AUTHOR]

Under the simple conditions on f and g , we show that entire positive k -convex radial solutions exist for the Hessian equation σ k ( λ ( D 2 u ) ) = p ( | x | ) f ( u ) , x ∈ R N and system σ k ( λ ( D 2 u ) ) = p ( | x | ) f ( v ) , σ k ( λ ( D 2 v ) ) = q ( | x | ) g ( u ) , x ∈ R N , where p , q : [ 0 , ∞ ) → ( 0 , ∞ ) are continuous. [ABSTRACT FROM AUTHOR]

These remarks are based on a talk the writer gave at the 11th International Conference in Fixed Point Theory and Applications, held at Galatasaray University in Istanbul, Turkey, July 20-24, 2015. They represent selected thoughts on a career in research, largely devoted to metric fixed point theory, that has spanned over 50 years. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study the motion of two associated ruled surfaces in Euclidean 3-space E3. In particular, the motion of Bishop Frenet offsets of ruled surfaces is investigated. Additionally, the characteristic properties for such ruled surfaces are given. Finally, an application is presented and plotted using computer aided geometric design. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study the motion of two associated ruled surfaces in Euclidean 3-space E3. In particular, the motion of Bishop Frenet offsets of ruled surfaces is investigated. Additionally, the characteristic properties for such ruled surfaces are given. Finally, an application is presented and plotted using computer aided geometric design. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the Cauchy problem for a higher order shallow water type equation u t − u t x x + ∂ x 2 j + 1 u − ∂ x 2 j + 3 u + 3 u u x − 2 u x u x x − u u x x x = 0 , where x ∈ T = R / 2 π and j ∈ N + . Firstly, we prove that the Cauchy problem for the shallow water type equation is locally well-posed in H s ( T ) with s ≥ − j − 2 2 for arbitrary initial data. By using the I -method, we prove that the Cauchy problem for the shallow water type equation is globally well-posed in H s ( T ) with 2 j + 1 − j 2 2 j + 1 < s ≤ 1 . Our results improve the results of A.A. Himonas, G. Misiolek (Himonas and Misiolek, 1998 [11] , 2000 [12] ). [ABSTRACT FROM AUTHOR]

We study the well-posedness of the Dirac–Klein–Gordon system in one space dimension with initial data that have an analytic extension to a strip around the real axis. It is proved that the radius of analyticity σ ( t ) of the solutions at time t cannot decay faster than 1 / t 4 as | t | → ∞ . [ABSTRACT FROM AUTHOR]

The paper is devoted to the study of metallic Riemannian structures. An integrability condition and curvature properties for these structures by means of a Φ-operator applied to pure tensor fields are presented. Examples of these structures are also given. [ABSTRACT FROM AUTHOR]

In this paper we prove that spacelike and timelike magnetic trajectories corresponding to the para-Kähler 2-form on a para-Kähler manifold (M, p, g) are circles on M. We then classify all para-Kähler magnetic curves in pseudo-Euclidean spaces E2nn. [ABSTRACT FROM AUTHOR]

This paper deals with the global attractivity of positive solutions of the second-order nonlinear difference equationxn+1 = axkn + bk-1Σj=1xjnxk-jn-1 + cxkn-1/Axkn + Bk-1Σj=1xjnxk-jn-1 + Cxkn-1, k = 3, 4; ..., n = 0, 1, ..., where the parameters a, b, c, A, B, C and the initial values x0, x-1 are arbitrary positive real numbers. [ABSTRACT FROM AUTHOR]

An almost null ring is a ring R in which for all a, b ∊ R, a³ = 0, Ma² = 0 for some square-free integer M that depends on a and ab = ka² = lb² for some integers k, l. This paper is devoted to the classification of the almost null rings. [ABSTRACT FROM AUTHOR]