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In this paper, we obtain a version of the John-Nirenberg inequality suitable for Campanato spaces Cp,β with 0 < p < 1 and show that the spaces Cp,β are independent of the scale p ∈ (0,∞) in sense of norm when 0 < β < 1. As an application, we characterize these spaces by the boundedness of the commutators [b,Bα]j (j = 1, 2) generated by bilinear fractional integral operators Bα and the symbol b acting from Lp1 × Lp2 to Lq for p1, p2 ∈ (1,∞), q ∈ (0,∞) and 1/q = 1/p1 + 1/p2 − (α + β)/n. [ABSTRACT FROM AUTHOR]

For positive integers c, s ≥ 1, r ≥ 3, let Wr(c, s) be the least integer such that if a set of at least Wr(c, s) points in the plane, no three of which are collinear, is colored with c colors, then this set contains a monochromatic r-gon with at most s interior points. As is known, if r = 3, then Wr(c, s)=Wr(c, s). In this paper, we extend these results to the case r = 4. We prove that W4(2, 1) = 11, W4(3, 2) ≤ 120, and the least integer μ4(c) such that W4(c, μ4(c)) < ∞ is bounded by ⌊c−12⌋⋅2≤μ4(c)≤2c−3,where c ≥ 2. [ABSTRACT FROM AUTHOR]

The canonical representation of the Klein group K4 = ℤ2⊕ℤ2 on the space ℂ* = ℂ {0} induces a representation of this group on the ring L = C[z, z−1], z ∈ ℂ*, of Laurent polynomials and, as a consequence, a representation of the group K4 on the automorphism group of the group G = GL(4,L) by means of the elementwise action. The semidirect product ĜG = GK4 is considered together with a realization of the group Ĝ as a group of semilinear automorphisms of the free 4-dimensional L-module M4. A three-parameter family of representations R of K4 in the group Ĝ and a three-parameter family of elements X ∈ M4 with polynomial coordinates of degrees 2(ℓ − 1), 2ℓ, 2(ℓ − 1), and 2ℓ, where ℓ is an arbitrary positive integer (one of the three parameters), are constructed. It is shown that, for any given family of parameters, the vector X is a fixed point of the corresponding representation R. An algorithm for calculating the polynomials that are the components of X was obtained in a previous paper of the authors, in which it was proved that these polynomials give explicit formulas for automorphisms of the solution space of the doubly confluent Heun equation. [ABSTRACT FROM AUTHOR]

In this paper, a comprehensive analysis is presented to investigate a codimension two bifurcation that exists in a nonlinear railway bogie dynamic system combining theoretical analysis with numerical investigation. By using the running velocity V and the primary longitudinal stiffness K1x as bifurcation parameters the first and second Lyapunov coefficients are calculated to determine which kind of Hopf bifurcation can happen and how the system states change with the variance of the bifurcation parameters. It is found that multiple solution branches both stable and unstable coexist in a range of the bifurcation parameters which can lead to jumps in the lateral oscillation amplitude of the railway bogie system. Furthermore, reduce the values of the bifurcation parameters gradually. Firstly, the supercritical Hopf bifurcation turns into a subcritical one with multiple limit cycles both stable and unstable near the Hopf bifurcation point. With a further reduction in the bifurcation parameters two saddle-node bifurcation points emerge, resulting in the loss of the stable limit cycle between these two bifurcation points. [ABSTRACT FROM AUTHOR]

The paper is concerned with the problem of generalized spline interpolation of functions having large-gradient regions. Splines of the class C2, represented on each interval of the grid by the sum of a second-degree polynomial and a boundary layer function, are considered. The existence and uniqueness of the interpolation L-spline are proven, and asymptotically exact two-sided error estimates for the class of functions with an exponential boundary layer are obtained. It is established that the cubic and parabolic interpolation splines are limiting for the solution of the given problem. The results of numerical experiments are presented. [ABSTRACT FROM AUTHOR]

In this paper, we study the computation of the moments associated to rational weight functions given as a power spectrum with known or unknown poles of any order in the interior of the unit disc. A recursive algebraic procedure is derived that computes the moments in a finite number of steps. We also study the associated interpolatory quadrature formulas with equidistant nodes on the unit circle. Explicit expressions are given for the positive quadrature weights in the case of a polynomial weight function. For rational weight functions with simple poles, mostly real or uniformly distributed on a circle in the open unit disc, we also obtain expressions for the quadrature weights and sufficient conditions that guarantee that they are positive. The Poisson kernel is a simple example of a rational weight function, and in the last section, we derive an asymptotic expansion of the quadrature error. [ABSTRACT FROM AUTHOR]

In this paper, we apply the Galerkin method with sinc bases for solving the boundary-value problems involving nonhomogeneous heat, convection diffusion, wave, and telegraph equations. The accuracy of the method for equation is $ \mathrm {O} (({\Delta } t)+e^{-k\sqrt {N} })$ . Error analysis is included. Several examples are given to illustrate the efficiency and implementation of the sinc-Galerkin method. Comparisons are made to confirm the reliability of the method. [ABSTRACT FROM AUTHOR]

Similar to the reverse-time migration, full waveform inversion in the time domain is a memory-intensive processing method. The computational storage size for waveform inversion mainly depends on the model size and time recording length. In general, 3D and 4D data volumes need to be saved for 2D and 3D waveform inversion gradient calculations, respectively. Even the boundary region wavefield-saving strategy creates a huge storage demand. Using the last two slices of the wavefield to reconstruct wavefields at other moments through the random boundary, avoids the need to store a large number of wavefields; however, traditional random boundary method is less effective at low frequencies. In this study, we follow a new random boundary designed to regenerate random velocity anomalies in the boundary region for each shot of each iteration. The results obtained using the random boundary condition in less illuminated areas are more seriously affected by random scattering than other areas due to the lack of coverage. In this paper, we have replaced direct correlation for computing the waveform inversion gradient by modified interferometric imaging, which enhances the continuity of the imaging path and reduces noise interference. The new imaging condition is a weighted average of extended imaging gathers can be directly used in the gradient computation. In this process, we have not changed the objective function, and the role of the imaging condition is similar to regularization. The window size for the modified interferometric imaging condition-based waveform inversion plays an important role in this process. The numerical examples show that the proposed method significantly enhances waveform inversion performance. [ABSTRACT FROM AUTHOR]

In this paper, we consider a time-dependent diffusion problem with two-sided Riemann-Liouville fractional derivatives. By introducing a fractional-order flux as auxiliary variable, we establish the saddle-point variational formulation, based on which we employ a locally conservative mixed finite element method to approximate the unknown function, its derivative and the fractional flux in space and use the backward Euler scheme to discrete the time derivative, and thus propose a fully discrete expanded mixed finite element procedure. We prove the well-posedness and the optimal order error estimates of the proposed procedure for a sufficiently smooth solution. Numerical experiments are presented to confirm our theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two variables norm functionals of τ-measurable operators and establish their joint log-convexity. Applications of this log-convexity will include interpolated Young, Heinz and Trace inequalities related to τ-measurable operators. Additionally, interpolated versions and their monotonicity will be presented as well. [ABSTRACT FROM AUTHOR]

Two-by-two block matrices of special form with square matrix blocks arise in important applications, such as in optimal control of partial differential equations and in high order time integration methods. Two solution methods involving very efficient preconditioned matrices, one based on a Schur complement reduction of the given system and one based on a transformation matrix with a perturbation of one of the given matrix blocks are presented. The first method involves an additional inner solution with the pivot matrix block but gives a very tight condition number bound when applied for a time integration method. The second method does not involve this matrix block but only inner solutions with a linear combination of the pivot block and the off-diagonal matrix blocks. Both the methods give small condition number bounds that hold uniformly in all parameters involved in the problem, i.e. are fully robust. The paper presents shorter proofs, extended and new results compared to earlier publications. [ABSTRACT FROM AUTHOR]

In this paper a concept of amenability for an arbitrary subset A of discrete semigroup S called A-amenable is introduced and studied. This concept is characterized by several equivalent statements which are analogues of properties characterizing left amenable semigroups. We also obtain the relationship between this version of amenability and Følner's condition. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of exponential stability and stabilization for a class of delayed distributed parameter systems, which is modeled by partial integro-differential equations (PIDEs). By employing the vector-valued Wirtinger's inequality, the sufficient condition of exponential stability of the PIDE system with a given decay rate is investigated. The condition is presented by linear matrix inequality (LMIs). After that, we develop a spatial proportional-integral-derivative state-feedback controller that ensures the exponential stabilization of the PIDE system in terms of LMIs. Finally, numerical examples are presented to verify the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the impacts of state-dependent impulses on the stability of switching Cohen-Grossberg neural networks (CGNN) by means of B-equivalence method. Under certain conditions, the state-dependent impulsive switching systems can be reduced to the fixed-time ones. Furthermore, a stability criterion for the considered CGNN using the proposed comparison system is established. Finally, two numerical examples are provided to illustrate the efficiency of the theoretical results. [ABSTRACT FROM AUTHOR]

Delays, arising in nonoscillatory and stable ordinary differential equations, can induce oscillation and instability of their solutions. That is why the traditional direction in the study of nonoscillation and stability of delay equations is to establish a smallness of delay, allowing delay differential equations to preserve these convenient properties of ordinary differential equations with the same coefficients. In this paper, we find cases in which delays, arising in oscillatory and asymptotically unstable ordinary differential equations, induce nonoscillation and stability of delay equations. We demonstrate that, although the ordinary differential equation x''(t) + c(t)x(t) = 0 can be oscillating and asymptotically unstable, the delay equation x''(t) + a(t)x(t - h(t)) - b(t)x(t - g(t)) = 0, where c(t) = a(t) - b(t), can be nonoscillating and exponentially stable. Results on nonoscillation and exponential stability of delay differential equations are obtained. On the basis of these results on nonoscillation and stability, the new possibilities of non-invasive (non-evasive) control, which allow us to stabilize a motion of single mass point, are proposed. Stabilization of this sort, according to common belief, requires a damping term in the second order differential equation. Results obtained in this paper refute this delusion. [ABSTRACT FROM AUTHOR]

Control problems in dynamic systems allowing pulse forces due to the presence of unilateral active constraints are considered. This paper gives an analysis of controls used during impact interactions. A new kind of pulse controls arising at the time of impact is introduced. These problems are typical for the so-called vibroimpact systems with numerous applications, whose number is constantly increasing in recent years. The goal of the paper is to describe the phase of a controllable impact and to determine the constraint reactions. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of Abelian afi-groups. A subgroup A of an Abelian group G is called its absolute ideal if A is an ideal of any ring on G. We will call an Abelian group an afi-group if all of its absolute ideals are fully invariant subgroups. In this paper, we will describe afi-groups in the class of fully transitive torsion groups (in particular, separable torsion groups) and divisible torsion groups. [ABSTRACT FROM AUTHOR]

In this paper we show that the degrees of interpretability of finitely axiomatized extensions-in-the-same-language of a finitely axiomatized sequential theory-like Elementary Arithmetic EA, IΣ, or the Gödel-Bernays theory of sets and classes GB-have suprema. This partially answers a question posed by Švejdar in his paper (Commentationes Mathematicae Universitatis Carolinae 19:789-813, ). The partial solution of Švejdar's problem follows from a stronger fact: the convexity of the degree structure of finitely axiomatized extensions-in-the-same-language of a finitely axiomatized sequential theory in the degree structure of the degrees of all finitely axiomatized sequential theories. In the paper we also study a related question: the comparison of structures for interpretability and derivability. In how far can derivability mimic interpretability? We provide two positive results and one negative result. [ABSTRACT FROM AUTHOR]

This paper deals with the inversion problem for linear time-invariant dynamical systems. Earlier in this formulation the discussed issue has been addressed and solved for invertible systems that meet the definition of Isidori relative degree. But in fact, this problem is well-posed for a wider range of linear dynamical systems. In this paper we examine a particular case based on a definition that is similar to the definition of relative degree by Isidori. Presented here columnwise relative degree and its properties allow to consider and effectively solve the inversion problem for invertible systems that meet this definition. [ABSTRACT FROM AUTHOR]

This paper presents new variants of the Hodges-Lehmann estimates, which belong to the class of $$R$$ -estimates. The new approach to this method arises from the need of taking into account differences in accuracy of geodetic measurements, which is not possible while applying traditional $$R$$ -estimates. The theoretical assumptions of the conventional Hodges-Lehmann estimates are supplemented with the information about the accuracy of observations and two new variants of the estimates in question are derived by applying the principles proposed by Hodges and Lehmann, hence they are called the Hodges-Lehmann weighted estimate. The main properties of the new estimates follow from such approach, and from the practical point of view, the most important seems to be their robustness against outliers. Since the first estimate proposed is a natural estimator of the shift between two samples, it can be applied in deformation analysis to estimate point displacements. The paper presents two numerical examples that show the properties as well as possible applications of the new estimates. [ABSTRACT FROM AUTHOR]

The Deficiency-One Theorem states that there exists a unique positive steady state in each positive stoichiometric class for weakly reversible deficiency-one mass action systems with one linkage class (regardless of the values of the rate coefficients). The non-emptiness of the set of positive steady states does not remain valid if we omit the weak reversibility. A recently published paper provided an equivalent condition to the existence of a positive steady state for deficiency-one mass action systems that are not weakly reversible, but still has only one linkage class. Based on that result, we characterise in this paper those of these mass action systems for which the non-emptiness of the set of positive steady states holds regardless of the values of the rate coefficients. Also, we provide an equivalent condition to the existence of rate coefficients such that the set of positive steady states is nonempty for the resulting mass action system. [ABSTRACT FROM AUTHOR]

This paper studies the risk-sensitive optimal control problem for a backward stochastic system. More precisely, we set up a necessary stochastic maximum principle for a risk-sensitive optimal control of this kind of equations. The control domain is assumed to be convex and the generator coefficient of such system is allowed to be depend on the control variable. As a preliminary step, we study the risk-neutral problem for which an optimal solution exists. This is an extension of initial control system to this type of problem, where the set of admissible controls is convex. An example to carried out to illustrate our main result of risk-sensitive control problem under linear stochastic dynamics with exponential quadratic cost function. [ABSTRACT FROM AUTHOR]

The paper reports the results of theoretical and experimental tests of a forming process for producing ball studs which are widely used in the automotive industry. It is proposed that semi-finished ball studs are produced by cross wedge rolling in a double configuration. The theoretical analysis was performed by numerical techniques based on the finite element method. Numerical computations were made using the simulation software DEFORM v 11.0. During the simulations, the accuracy of the adopted tool design was verified, and optimal parameters of the process along with the effect of selected parameters of the process and the quality of produced parts were determined. The proposed rolling process was verified under laboratory conditions using a flat-wedge forging machine available at the Lublin University of Technology. The experimental findings show a high agreement with the numerical results, in terms of both quality and quantity. The results confirm that ball studs can be produced by the proposed cross wedge rolling technique. [ABSTRACT FROM AUTHOR]

The paper describes the congruent centralizer of the matrix $$ {\Delta}_n=\left(\begin{array}{llll}\hfill & \hfill & \hfill & 1\hfill \\ {}\hfill & \hfill & \dots \hfill & i\hfill \\ {}\hfill & 1\hfill & \dots \hfill & \hfill \\ {}1\hfill & i\hfill & \hfill & \hfill \end{array}\right) $$ , representing one of three blocks in the Horn-Sergeichuk canonical form, i.e., the set of matrices X such that X Δ X = Δ. [ABSTRACT FROM AUTHOR]

In the current paper, a powerful approximate analytical approach namely the global residue harmonic balance method (GRHBM) is proposed for obtaining higher-order approximate frequency and periodic solution of nonlinear conservative oscillatory systems arising in engineering problems. The proposed method has a main difference with other traditional harmonic balance methods such that the residual errors obtained in pervious order approximation are used in the present one. Comparison of the obtained results with the exact and numerical solution as well as well-known analytical methods such as Hamiltonian approach, Max-Min approach, variational approach, and He's amplitude-frequency formulation reveals the correctness and usefulness of the GRHBM. It is shown that the results are valid for different values of system parameters and both small and large amplitudes. Hence, the method can be easily applied to other strongly nonlinear conservative oscillatory systems. Furthermore, using the obtained analytical expressions, the effect of amplitude and system parameters on nonlinear frequency is studied. [ABSTRACT FROM AUTHOR]

In this paper, we provided conditions for an entire constant mean curvature Killing graph lying inside a possible unbounded region to be necessarily a slice. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new family of codes, called projective nested cartesian codes. They are obtained by the evaluation of homogeneous polynomials of a fixed degree on a certain subset of $$\mathbb {P}^n(\mathbb {F}_q)$$ , and they may be seen as a generalization of the so-called projective Reed-Muller codes. We calculate the length and the dimension of such codes, an upper bound for the minimum distance and the exact minimum distance in a special case (which includes the projective Reed-Muller codes). At the end we show some relations between the parameters of these codes and those of the affine cartesian codes. [ABSTRACT FROM AUTHOR]

This paper is concerned with the dissipativity of Runge-Kutta methods for a class of nonlinear functional-integro-differential equations (FIDEs). The dissipativity results of Runge-Kutta methods for the FIDEs are given. It is shown under a suitable condition that an algebraically stable Runge-Kutta method is dissipative when applied to the FIDEs. Numerical examples are given to illustrate the correctness of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate how the initial value belonging to spaces $W_{\sigma}(\mathbb{R}^{N})$ ( $0<\sigma

This paper presents an integral formulation for Helmholtz problems with mixed boundary conditions. Unlike most integral equation techniques for mixed boundary value problems, the proposed method uses a global boundary charge density. As a result, Calderón identities can be utilized to avoid the use of hypersingular integral operators. Numerical results illustrate the performance of the proposed solution technique. [ABSTRACT FROM AUTHOR]

We introduce a new structure for a set of points in the plane and an angle $$\alpha $$ , which is similar in flavor to a bounded-degree MST. We name this structure $$\alpha $$ -MST. Let P be a set of points in the plane and let $$0 < \alpha \le 2\pi $$ be an angle. An $$\alpha $$ -ST of P is a spanning tree of the complete Euclidean graph induced by P, with the additional property that for each point $$p \in P$$ , the smallest angle around p containing all the edges adjacent to p is at most $$\alpha $$ . An $$\alpha $$ -MST of P is then an $$\alpha $$ -ST of P of minimum weight, where the weight of an $$\alpha $$ -ST is the sum of the lengths of its edges. For $$\alpha < \pi /3$$ , an $$\alpha $$ -ST does not always exist, and, for $$\alpha \ge \pi /3$$ , it always exists (Ackerman et al. in Comput Geom Theory Appl 46(3):213-218, 2013; Aichholzer et al. in Comput Geom Theory Appl 46(1):17-28, 2013; Carmi et al. in Comput Geom Theory Appl 44(9):477-485, 2011). In this paper, we study the problem of computing an $$\alpha $$ -MST for several common values of $$\alpha $$ . Motivated by wireless networks, we formulate the problem in terms of directional antennas. With each point $$p \in P$$ , we associate a wedge $${\textsc {w}_{p}}$$ of angle $$\alpha $$ and apex p. The goal is to assign an orientation and a radius $$r_p$$ to each wedge $${\textsc {w}_{p}}$$ , such that the resulting graph is connected and its MST is an $$\alpha $$ -MST (we draw an edge between p and q if $$p \in {\textsc {w}_{q}}$$ , $$q \in {\textsc {w}_{p}}$$ , and $$|pq| \le r_p, r_q$$ ). We prove that the problem of computing an $$\alpha $$ -MST is NP-hard, at least for $$\alpha =\pi $$ and $$\alpha =2\pi /3$$ , and present constant-factor approximation algorithms for $$\alpha = \pi /2, 2\pi /3, \pi $$ . One of our major results is a surprising theorem for $$\alpha = 2\pi /3$$ , which, besides being interesting from a geometric point of view, has important applications. For example, the theorem guarantees that given any set P of 3 n points in the plane and any partitioning of the points into n triplets, one can orient the wedges of each triplet independently, such that the graph induced by P is connected. We apply the theorem to the antenna conversion problem and to the orientation and power assignment problem. [ABSTRACT FROM AUTHOR]

Stabilometry is a technique that aims to study the body sway of human subjects, employing a force platform. The signal obtained from this technique refers to the position of the foot base ground-reaction vector, known as the center of pressure (CoP). The parameters calculated from the signal are used to quantify the displacement of the CoP over time; there is a large variability, both between and within subjects, which prevents the definition of normative values. The intersubject variability is related to differences between subjects in terms of their anthropometry, in conjunction with their muscle activation patterns (biomechanics); and the intrasubject variability can be caused by a learning effect or fatigue. Age and foot placement on the platform are also known to influence variability. Normalization is the main method used to decrease this variability and to bring distributions of adjusted values into alignment. In 1996, O'Malley proposed three normalization techniques to eliminate the effect of age and anthropometric factors from temporal-distance parameters of gait. These techniques were adopted to normalize the stabilometric signal by some authors. This paper proposes a new method of normalization of stabilometric signals to be applied in balance studies. The method was applied to a data set collected in a previous study, and the results of normalized and nonnormalized signals were compared. The results showed that the new method, if used in a well-designed experiment, can eliminate undesirable correlations between the analyzed parameters and the subjects' characteristics and show only the experimental conditions' effects. [ABSTRACT FROM AUTHOR]

For an arbitrary set X (finite or infinite), denote by T( X) the semigroup of full transformations on X. For α∈ T( X), let C( α)={ β∈ T( X): αβ= βα} be the centralizer of α in T( X). The aim of this paper is to characterize the elements of C( α). The characterization is obtained by decomposing α as a join of connected partial transformations on X and analyzing the homomorphisms of the directed graphs representing the connected transformations. The paper closes with a number of open problems and suggestions of future investigations. [ABSTRACT FROM AUTHOR]

For an algebra A, denote by V ( n) the dimension of the vector space spanned by the monomials whose length does not exceed n. Let T ( n) = V ( n) − V ( n − 1). An algebra is said to be boundary if T ( n) − n < const. In the paper, the normal bases are described for algebras of slow growth or for boundary algebras. Let L be a factor language over a finite alphabet A. The growth function T ( n) is the number of subwords of length n in L. We also describe the factor languages such that T ( n) ≤ n + const. [ABSTRACT FROM AUTHOR]

The paper presents the proof of the uniqueness theorem formultiple series in the Franklin systemthat converge inmeasure and whosemajorant of cubic partial sums with numbers 2 satisfies a certain necessary condition. This result is new in the one-dimensional case as well. [ABSTRACT FROM AUTHOR]

This paper studies the impact of service outsourcing under three supply chain power structures: manufacturer-Stackelberg, vertical-Nash and retailer-Stackelberg supply chains. We first investigate price and service decisions by comparing the integrated channel and the decentralized channel with service outsourcing. It is found that a lower retail price or a higher service level could occur in the decentralized channel with service outsourcing compared to those in the integrated channel, but they never occur simultaneously. Next, we examine the manufacturer's channel strategies, and demonstrate that service outsourcing can always help the manufacturer earn more profit from the decentralized channel than from the integrated channel in the manufacturer-Stackelberg and retailer-Stackelberg markets, as long as the retailer's service investment is sufficiently efficient. However, in the vertical-Nash supply chain, this occurs only when the manufacturer is inefficient and the retailer is efficient enough in service provision. Finally, comparisons of channel efficiency and numerical analysis are provided. [ABSTRACT FROM AUTHOR]

A code with words in a finite alphabet is said to be an ( s, l) separating code if for any two disjoint collections of its words of size at most s and l, respectively, there exists a coordinate in which the set of symbols of the first collection do not intersect the set of symbols of the second. The main goal of the paper is obtaining new bounds on the rate of ( s, l) separating codes. Bounds on the rate of binary ( s, l) separating codes, the most important for applications, are studied in more detail. We give tables of numerical values of the best presently known bounds on the rate. [ABSTRACT FROM AUTHOR]

In this paper we study the two-dimensional profiles of the superfluid component velocity and the quantized vortex-points density in a counterflow channel where the influence of the walls cannot be neglected. The numerical results obtained show the presence of vortex density waves in the channel, as shown in a recent paper by means of the one-fluid model. [ABSTRACT FROM AUTHOR]

In this paper, we present an optimization technique to find the optimal parameters of the AOR iteration, which just needs to minimize the 2-norm of the residual vector and avoids solving the spectral radius of the iteration matrix of the SOR method. Meanwhile, numerical results are provided to indicate that the new method is more robust than the AOR method for larger intervals of the parameters ω and γ. [ABSTRACT FROM AUTHOR]

In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified under the name of tangential extremal principles, combine primal and dual approaches to the study of variational systems being in fact first extremal principles applied to infinite systems of sets. The first part of the paper concerns the basic theory of tangential extremal principles while the second part presents applications to problems of semi-infinite programming and multiobjective optimization. [ABSTRACT FROM AUTHOR]

In literature, there is no exact analytical solution available for determining the radius of Roche equipotential surfaces of distorted close binary systems in synchronous rotation. However, Kopal (Roche Model and Its Application to Close Binary Systems, Advances in Astronomy and Astrophysics, Academic Press, New York ) and Morris (Publ. Astron. Soc. Pac. 106:154, ) have provided the approximate analytical solutions in the form of infinite mathematical series. These series expressions have been commonly used by various authors to determine the radius of the Roche equipotential surfaces, and hence the equilibrium structures of rotating stars and stars in the binary systems. However, numerical results obtained from these approximating series expressions are not very accurate. In the present paper, we have expanded these series expressions to higher orders so as to improve their accuracy. The objective of this paper is to check, whether, there is any effect on the accuracy of these series expressions when the terms of higher orders are considered. Our results show that in most of the cases these expanded series give better results than the earlier series. We have further used these expanded series to find numerically the volume radius of the Roche equipotential surfaces. The obtained results are in good agreement with the results available in literature. We have also presented simple and accurate approximating formulas to calculate the radius of the primary component in a close binary system. These formulas give very accurate results in a specified range of mass ratio. [ABSTRACT FROM AUTHOR]

The paper deals with optimal control of heterogeneous systems, that is, families of controlled ODEs parameterized by a parameter running over a domain called domain of heterogeneity. The main novelty in the paper is that the domain of heterogeneity is endogenous: it may depend on the control and on the state of the system. This extension is crucial for several economic applications and turns out to rise interesting mathematical problems. A necessary optimality condition is derived, where one of the adjoint variables satisfies a differential inclusion (instead of equation) and the maximization of the Hamiltonian takes the form of 'min-max'. As a consequence, a Pontryagin-type maximum principle is obtained under certain regularity conditions for the optimal control. A formula for the derivative of the objective function with respect to the control from L is presented together with a sufficient condition for its existence. A stylized economic example is investigated analytically and numerically. [ABSTRACT FROM AUTHOR]

A right-chain semigroup is a semigroup whose right ideals are totally ordered by set inclusion. The main result of this paper says that if S is a right-chain semigroup admitting a ring structure, then either S is a null semigroup with two elements or sS= S for some s∈ S. Using this we give an elementary proof of Oman's characterization of semigroups admitting a ring structure whose subsemigroups (containing zero) form a chain. We also apply this result, along with two other results proved in this paper, to show that no nontrivial multiplicative bounded interval semigroup on the real line ℝ admits a ring structure, obtaining the main results of Kemprasit et al. (ScienceAsia 36: 85-88, 2010). [ABSTRACT FROM AUTHOR]

This paper deals with 2-player coordination games with vanishing actions, which are repeated games where all diagonal payoffs are strictly positive and all non-diagonal payoffs are zero with the following additional property: At any stage beyond r, if a player has not played a certain action for the last r stages, then he unlearns this action and it disappears from his action set. Such a game is called an r-restricted game. To evaluate the stream of payoffs we use the average reward. For r = 1 the game strategically reduces to a one-shot game and for r ≥ 3 in Schoenmakers (Int Game Theory Rev 4:119-126, ) it is shown that all payoffs in the convex hull of the diagonal payoffs are equilibrium rewards. In this paper for the case r = 2 we provide a characterization of the set of equilibrium rewards for 2 × 2 games of this type and a technique to find the equilibrium rewards in m × m games. We also discuss subgame perfection. [ABSTRACT FROM AUTHOR]

family of tenth algebraic order eight-step methods is constructed in this paper. For this family of methods, we require the phase-lag and its first, second and third derivatives to be vanished. Three alternative methods are proposed which satisfy the above requirements. An error analysis and a stability analysis is also investigated in this paper and a comparison with other methods is also studied. The new proposed methods are applied for the numerical solution of the one dimensional Schrödinger equation. The efficiency of the new methodology is proved via theoretical analysis and numerical applications. [ABSTRACT FROM AUTHOR]

We consider a class of branching-selection particle systems on $${\mathbb{R}}$$ similar to the one considered by E. Brunet and B. Derrida in their 1997 paper “Shift in the velocity of a front due to a cutoff”. Based on numerical simulations and heuristic arguments, Brunet and Derrida showed that, as the population size N of the particle system goes to infinity, the asymptotic velocity of the system converges to a limiting value at the unexpectedly slow rate (log N)−2. In this paper, we give a rigorous mathematical proof of this fact, for the class of particle systems we consider. The proof makes use of ideas and results by R. Pemantle, and by N. Gantert, Y. Hu and Z. Shi, and relies on a comparison of the particle system with a family of N independent branching random walks killed below a linear space-time barrier. [ABSTRACT FROM AUTHOR]

We seek the optimal boundary control of vibrations of a spherical layer in the spherically symmetric case. This paper continues the series of papers by V.A. Il’in and his students and, unlike the previous papers, uses a more general control optimality criterion. We obtain closed formulas for the controls; these formulas are consistent with Il’in’s earlier results. [ABSTRACT FROM AUTHOR]

We point out that the main results—the analytic expressions for the Groverian measure of entanglement, in the above mentioned paper are erroneous. The technical mistake of the paper is discussed. It is shown by an explicit example that the formula for calculating the Groverian measure yields $${G(|\psi\rangle)=0}$$ for some entangled states. [ABSTRACT FROM AUTHOR]

In this paper, structure-preserving time-integrators for rigid body-type mechanical systems are derived from a discrete Hamilton–Pontryagin variational principle. From this principle, one can derive a novel class of variational partitioned Runge–Kutta methods on Lie groups. Included among these integrators are generalizations of symplectic Euler and Störmer–Verlet integrators from flat spaces to Lie groups. Because of their variational design, these integrators preserve a discrete momentum map (in the presence of symmetry) and a symplectic form. In a companion paper, we perform a numerical analysis of these methods and report on numerical experiments on the rigid body and chaotic dynamics of an underwater vehicle. The numerics reveal that these variational integrators possess structure-preserving properties that methods designed to preserve momentum (using the coadjoint action of the Lie group) and energy (for example, by projection) lack. [ABSTRACT FROM AUTHOR]

Abstract  This paper presents the splitting cubes, a fast and robust technique for performing interactive virtual cutting on deformable objects. The technique relies on two ideas. The first one is to embed the deformable object in a regular grid, to apply the deformation function to the grid nodes and to interpolate the deformation inside each cell from its 8 nodes. The second idea is to produce a tessellation for the boundary of the object on the base of the intersections of such boundary with the edges of the grid. Please note that the boundary can be expressed in any way; for example it can be a triangle mesh, an implicit or a parametric surface. The only requirement is that the intersection between the boundary and the grid edges can be computed. This paper shows how the interpolation of the deformation inside the cells can be used to produce discontinuities in the deformation function, and the intersections of the cut surface can be used to visually show the cuts on the object. The splitting cubes is essentially a tessellation algorithm for growing, deformable surface, and it can be applied to any method for animating deformable objects. In this paper the case of the mesh-free methods (MMs) is considered: in this context, we described a practical GPU friendly method, that we named the extended visibility criterion, to introduce discontinuities of the deformation. [ABSTRACT FROM AUTHOR]